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MIT HAN Lab 73

--- abstract: 'We consider a mechanism to generate controllable qudit-qudit interactions in a charge-position paradigm for a quantum computer, through the use of auxiliary states. By controlling the tunneling rates onto these auxiliaries from the qudits proper, we can controllably switch the entangling operations. We consider a practical architecture in which to realize such a computer and examine the associated Hilbert space dimension.' author: - 'S. G. Schirmer' - 'Andrew D. Greentree' - 'D. K. L. Oi' title: 'Implementation of controlled multi-qudit operations for a solid-state quantum computer based on charge qudits' --- Quantum computing [@bib:NielsenBook] has been identified as an important field recently, and significant work is being undertaken to find suitable systems in which to observe scalable, coherent interactions. Recent advances in semi-conductor technology have opened up new possibilities for silicon-based solid-state realizations of quantum computers, which are highly attractive due to their compatibility with conventional Silicon metal-oxide-semiconductor technology [@bib:ClarkReview2003]. All scalable quantum computing proposals require some particle that can be placed into a superposition of several distinguishable quantum states, and for which particle-particle entanglement can be achieved. The Hilbert space dimension of an $N$ particle quantum register obtained by entangling all the particles simultaneously has been shown to be a good measure for the power of a quantum computer [@bib:Blume-Kohout2002]. One model for a scalable quantum computer is based on localization of an electronic charge in potential wells, the so-called charge-qubit approach. This has been discussed by Ekert [@bib:Ekert1995] and appears in various flavors in the literature, see for example Refs [@bib:EkertRMP1996; @bib:BarencoPRL1995]. A generic problem with charge-based quantum computing schemes is that, although it is relatively easy to generate single particle operations, i.e., to realize the Hadamard transform gate, it is usually quite difficult to obtain *controllable* particle-particle interactions. The mechanism normally suggested is the Coulomb interaction, which has the problem of being difficult to turn off. It may be possible to perform universal operations with an “always on” interaction, and schemes for realizing global operations in this setting have been considered by Benjamin [@bib:BenjaminPRL2003] and Pachos and Vedral [@bib:PachosPreprint2003]. However, for practical purposes it seems highly desirable to have controllable multi-particle interactions. Here we suggest ways to achieve this by making use of local tunneling to auxiliary states, which has the effect of switching the Coulomb action by changing the effective distance between components of the electronic wavefunction. The basic schemes we propose are in principle not limited to a particular charge-based implementation, and may in fact be useful for a variety of charge-based proposals including, for instance, Cooper-pair box schemes [@bib:MakhlinNature1999]. However, for concreteness we consider a generalization of a specific recent proposal by Hollenberg *et al.* [@bib:Hollenberg2003] where the confining potentials are obtained from individual Phosphorus implants in a Silicon matrix. We envisage this being fabricated via a “bottom up” approach to nanofabrication such as has been recently realized [@bib:OBrienPRB2001]. Hollenberg’s charge proposal deserves particular consideration in our opinion since it takes advantage of existing fabrication technologies and medium-scale realizations of such an architecture appear to be within experimental reach in the near future. Although the original proposal involved charge qubits, we shall consider a generalization to qudits (i.e., systems whose single particle Hilbert space has dimension $D\ge 2$), and concentrate on qutrit structures ($D=3$) as they have been shown to optimize the total Hilbert space dimension of the composite system [@bib:GreentreePrePrint2003]. We propose concrete scalable architectures that permit efficient, controlled multi-particle gates in this setting, which is essential for the operation of quantum error-correction algorithms. The donor impurities in the Hollenberg *et al.* scheme can be regarded as quantum dots that create an electric potential with $D$ local minima located at the sites of the donor impurities, which confines the shared electron as shown in Fig. \[figure1\]. The $D$ ground states $\ket{d}$ for $d=1,\ldots,D$, corresponding to the various localizations of the electron at the donor impurities, form a basis for the Hilbert space $\H$ of a single charge qudit. The height of the potential barrier between a pair of adjacent quantum dots belonging to the same qudit can be manipulated by applying an external electric potential via surface electrodes located between the two sites. By adjusting the voltages applied we can manipulate the height of the potential barrier and therefore the rate of tunneling between adjacent sites. We follow the notation of Ref [@bib:Hollenberg2003] and refer to these surface electrodes as barrier or $B$-gates. Quantum tunneling through the potential barriers leads to the creation of coherent superposition states of the localized charge qudit states $\ket{d}$. Furthermore, by applying electric potentials to surface electrodes located directly above the donor impurities we can create asymmetries in the potential, and thus change the ground state energy $E_d$ of state $\ket{d}$, introducing local energy shifts. We shall call these electrodes (energy) shift gates, or $S$-gates. It can be shown that by combining $S$-gates and $B$-gates, arbitrary single qudit operations (local unitary operations) can be performed. One of the main advantages of the proposed charge qudit architecture compared to the original Kane proposal [@bib:Kane1998] using the nuclear spins of the donor atoms as qubits is the possibility of *easy readout* of quantum information via single electron transistors [@bib:GrabertNATO1992], the suitability of which has already been shown for quantum computing applications when run in RF mode [@bib:RFSET]. Moreover, charge qudit quantum logic operations can be implemented using voltage gates only, without the need for additional radio frequency control pulses. Besides reducing the operational complexity, this should largely avoid problems of non-selective excitation of multiple sites, which may complicate the implementation of selective single and multi-qubit quantum logic operations in the original Kane proposal. One of the main disadvantages of charge qudits compared to nuclear spin qubits is their much shorter coherence lifetime. However, local operations can be performed much faster for charge qudits than for nuclear spin qubits, on the order of $10^{-11}$ seconds, and estimates suggest that the decoherence lifetime of a charge qudit should be much longer than that, at least on the order of $10$ ns [@bib:Hollenberg2003; @bib:Barrett2003]. It also seems likely that advances in technology and control will lead to further reductions of the gate operation time, and that the coherence lifetime might be increased though decoherence control measures. For instance, continuous quantum error correction by means of quantum feedback control has recently been shown to be able to reduce spontaneous emission errors [@bib:Ahn2003], and similar control techniques might be able to reduce decoherence. We present our proposal for a scalable charge-qudit quantum computer in Fig. \[figure3a\]. As mentioned above, we differentiate it from previous models by the use of (a) qutrits to optimise the Hilbert-space dimensionality, and (b) auxillary dots to effectively switch the Coulomb interaction to mediate particle-particle interactions. The qudits are arranged vertically, alternatingly above and below a center row of auxiliary quantum dots which mediate interactions between multiple adjacent qudits. The alternating arrangement of the qudits above and below the row of auxiliary quantum dots reduces unwanted Coulomb interactions between quantum dots belonging to different qudits. The efficiency of this shielding effect can be further enhanced by adding “trenches” filled with a conducting material between adjacent qudits as shown in the figure. Since the donor impurities are buried, realizing such shielding trenches would require a 3D structure. One way to realize such a structure would be to metalize a sheet of delta-doped Silicon, which could be achieved with a bottom-up strategy [@bib:OBrienPRB2001]. The staggering of the qudits further reduces unwanted interactions between diagonally facing qudits. The efficiency of multi-qudit operations might be enhanced by embedding the auxiliary quantum dots into a high-permittivity material to facilitate the Coulomb interaction. This would require that the silicon substrate be replaced by another material in the region occupied by the auxiliary quantum dots. This would be difficult to realize given current technology, however it may well become feasible with further advances in fabrication technology. The high permittivity material would reduce the time needed to implement multi-qudit gates, increasing the number of such operations that can be performed within the coherence lifetime of the qudit register, potentially improving the performance of a working quantum device. To activate the Coulomb interaction between two or more adjacent qudits, we coherently transfer the populations of state $\ket{1}$ of the corresponding qudits to the auxiliary state $\ket{0}$ by *simultaneously* lowering the height of the potential barriers between the corresponding quantum dots by applying suitable gate voltages to the auxiliary tunneling gates. Then we restore the potential barriers and let the Coulomb interaction between the auxiliary quantum dots create the necessary controlled phase gate. After a certain predetermined time, the populations of the auxiliary quantum dots are coherently transferred back to the original qudit states by simultaneously lowering the corresponding auxiliary potential barriers, thus switching off the Coulomb interaction. The details of how to implement a sufficient set of elementary gates required for universal quantum computation and efficient qudit error correction will be discussed in a forthcoming, more detailed paper. Note that this arrangement of the qudits is scalable and permits not only the implementation of arbitrary two-qudit gates between any pair of adjacent qudits by combining controlled phase gates with single qudit operations, but, in principle, the implementation of arbitrary gates involving a set of $k\le N$ adjacent qudits. Furthermore, since the effects of the control fields (voltage gates) are strictly spatially confined, unlike for radio-frequency control fields for instance, it should be easily possible to implement multi-qudit interactions on disjoint subsets of qudits simultaneously. One drawback of the proposed architecture is that it requires a comparatively large number of auxiliary sites to mediate the interactions. In principle, it is possible to reduce the number of auxiliary quantum dots required by modifying the architecture as shown in Fig. \[figure3b\], for instance. In this modified arrangement the auxiliary sites are horizontally offset such that each auxiliary site is shared by four qudits. This reduces the number of auxiliary sites required by half. However, a potential drawback of this architecture is that, while it should be easy to implement four-qudit gates, it would appear to be difficult to implement controlled *two*-qudit interactions since the Coulomb interaction will always affect all four qudits surrounding an auxiliary quantum dot. Finally, we consider the effect of the auxiliary quantum dots on the Hilbert space dimension of the register. As mentioned earlier, in absence of auxiliary quantum dots, partitioning into qutrits will always optimize the Hilbert space dimension of the quantum register. Clearly, given any fixed number of quantum dots, the need for auxiliary quantum dots reduces the dimension of the Hilbert space of the quantum register. If one auxiliary site is needed for each qudit, as in the architecture shown in Fig. \[figure3a\] for instance, then the dimension of the Hilbert space of a register of $K$ quantum dots partitioned into $D$-qudits will be $D^{K/(D+1)}$ instead of $D^{K/D}$. If only a single auxiliary site for every two qudits is needed as in Fig. \[figure3b\] then the Hilbert space dimension of the register will be $D^{K/(D+0.5)}$ instead. Fig. \[figure4\] shows the Hilbert space dimension of a qudit register comprised of a fixed number of quantum dots as a function of qudit size for the three architectures discussed. The graph clearly shows that partitioning into qutrits maximizes the Hilbert space dimension of the quantum register if either no auxiliary quantum dots or only a single dot per pair of qudits is required. If one auxiliary dot for each qudit is used then partitioning into four-qudits increases the Hilbert space dimension slightly. However, this increase is rather small compared to the increase from qubits to qutrits and may be offset by other considerations such as the increased complexity of single qudit gates or the number of measurements required to extract a comparable amount of quantum information for $D>3$. In summary, we have proposed concrete scalable architectures for a charge qudit quantum computer that allow the efficient implementation of controlled multi-qudit gates by making use of auxiliary sites to mediate multi-qudit interactions. Our emphasis has been on the implementation of such schemes for a practical realization of a charge qudit quantum computer based on donor impurities embedded in a Silicon matrix, but they are not fundamentally limited to this specific case. SGS and DKLO are supported by the Cambridge-MIT Institute project on quantum information. ADG is supported by the Australian Research Council.\ [99]{} M. A. Nielsen and I. L. Chuang, [*Quantum Computation and Quantum Information*]{} (Cambridge University Press, Cambridge, England, 2000). R. G. Clark *et al.* *Progress in silicon-based quantum computing*, submitted to Phil. Trans. R. Soc. Lond. A. R. Blume-Kohout, C. M. Caves, and I. H. Deutsch, Found. Phys. [**32**]{}, 1641 (2002). A. K. Ekert, *Quantum Cryptography and Computation* in Advances in Quantum Phenomena (Plenum Press, New York, 1995), pp243-262. A. Barenco, D. Deutsch, A. Ekert and R. Jozsa, Phys. Rev. Lett. [**74**]{}, 4083 (1995) A. Ekert and R. Jozsa, Rev. Mod. Phys. [68]{}, 733 (1996). S. C. Benjamin, Phys. Rev. Lett. [**88**]{}, 017904 (2002). J. K. Pachos and V. Vedral, *Topological Quantum Gates with Quantum Dots*, eprint arXiv:quant-ph/0302077. L. C. L. Hollenberg, C. Wellard, A. R. Hamilton, D. J. Reilly, G. J. Milburn, and R. G. Clark, *Charge-based quantum computing using single donors in semiconductors*, to be submitted. Yu. Makhlin, G. Schön, A. Shnirman, Nature [**398**]{}, 305 (1999). B. E. Kane, *A Silicon-based Nuclear Spin Quantum Computer*, Nature [**393**]{}, 133 (1998). J. L. O’Brien, *et al.*, Phys. Rev. B [**64**]{}, 161401 (2001). A. D. Greentree, S. G. Schirmer, F. Green, L. C. L. Hollenberg, A. R. Hamilton, and R. G. Clark, submitted and eprint arXiv:quant-ph/0304050. H. Grabert, and M. H. Devoret, NATO Adv. Study Inst. Ser., Ser. B 294 (1992). M. H. Devoret and R. J. Schoelkopf, Nature (London) [**406**]{}, 1039 (2000); A. A. Clerk, S. M. Girvin, A. Nguyen, and A. D. Stone, Phys. Rev. Lett. [**89**]{}, 176804 (2002); T. M. Buehler *et al.*, eprint arXiv:cond-mat/0304384. S. D. Barrett and G. J. Milburn, eprint arXiv:cond-mat/0302238. C. Ahn, H. M. Wiseman and G. J. Milburn, eprint arXiv:quant-ph/0302006.

[Clinical and molecular genetic study of cystic fibrosis in the 5th Region of Chile]. Cystic fibrosis (CF) is the most common autosomal recessive disease in Caucasian population. More than 900 mutations have been detected in the Cystic Fibrosis Transmembrane Regulator (CFTR) gene. The most common worldwide, is a deletion of phenylalanine 508 (delta F508). To analyze the presence of mutations delta F508, G542X, N1303K, G551D, R553X and S549N in patients from the 5th Region of Chile, with a clinical diagnosis of CF. We studied 17 non-related patients, presenting frequent respiratory tract infections, malabsorption and positive sweat tests, or meconial ileum. Serum immunoglobulins (IgG, IgA, IgM), and total, CD3+ and B-lymphocytes, were determined to discard the presence of an immune deficiency. The molecular study of the gene was performed by Polymerase Chain Reaction amplification and restriction analysis. Immunological parameters were normal in all patients. The delta F508 mutation was detected in 11 chromosomes and the mutation G542X in 3 chromosomes. The mutation G542X was the second most frequent mutation found in this sample of Chilean CF patients. Since this mutation has a high frequency in Spanish CF patients, we suggest that this mutation might have had its origin in Spain.

An electrostatic deceleration lens for highly charged ions. The design and implementation of a purely electrostatic deceleration lens used to obtain beams of highly charged ions at very low energies is presented. The design of the lens is such that it can be used with parallel as well as diverging incoming beams and delivers a well focused low energy beam at the target. In addition, tuning of the final energy of the beam over a wide range (1 eV/q to several hundred eV/q, where q is the beam charge state) is possible without any change in hardware configuration. The deceleration lens was tested with Ar(8+), extracted from an electron cyclotron resonance ion source, having an initial energy of 30 keV/q and final energies as low as 70 eV/q have been achieved.

Management of CMV retinal detachments in the new era of antiretroviral therapy. In the past, retinal detachment occurred at a rate of 38% after one year of cytomegalovirus retinitis (CMVR). The current rate of detachment may be reduced by improved therapies for CMVR. In addition, the number of new patients acquiring CMVR has fallen, resulting in a lower incidence of these detachments. Another important effect of the new era of antiviral therapy on CMVR-related detachments includes longer patient survival with a need to select surgical strategies that will provide the best long-term visual outcome while still recognizing the unique difficulties posed by detachments in necrotic retinas. Vitrectomy with planned removal of silicone oil, scleral buckle, vitrectomy with gas tamponade, and laser demarcation are strategies that may provide excellent visual and anatomic results for retinal detachments with various characteristics. The final selection of the surgical approach depends on the mechanical factors of the detachment and patient factors such as immune status, expected survival, control of retinitis, and visual needs.

Women's beachwear fashion Women's beachwear fashion is a modern phenomenon that has been developing in the last two centuries, especially as the railway arrived in Europe and mass tourism became widespread. The beach in particular became a tourist venue for people to relieve stress. This began from the desire to contrast the effects from the rise of large cities and Industrialization. It spread around the world, becoming a cultural phenomenon, and as a result, along with this new outdoor pastime, came the need for a stylish garment for the privileged lady. This "fashion" is a form of imitation and social equalization, displaying a set of styles and trends in women's clothing and accessories that have been developed together from the mind-set of society. The role of women is a subject of particular attention because of the change of their position in a male-dominated society in which they had to maintain modesty and seriousness in the behaviors of clothing. This begins the steps that led to fill the gap between the roles of men and women in society and its customs in new contexts, such as for leisure and entertainment. Seaside tourism Seaside tourism was born in the middle of the 18th century. Before that period, the coastal landscape was synonymous with danger, where natural disasters occurred. Philosophers thought the sea was a sort of social power that separated people. Also, a lot of Shakespeare's stories about the sea is an emblem of chaotic travels and shipwrecks. In the 16th and 17th centuries, France was the cradle of a revolution. In those years, there was a change in the perspectives concerning the seaside. Starting from poetry, the ocean and the beach did not symbolize something frightful any longer. English doctors suggested to the nobles that going to the sea was therapy against melancholia and was helpful for the spleen. In the middle of the 19th century, Thomas Cook started to organize collective travel for the English nobles in the Mediterranean areas, especially in the French Riviera and Liguria. Between 1860 and 1914, Nice was one of the most famous places for holidays. The beach became a place of human consumption as a way to escape from the city, where the air was polluted and loud. The development of trains facilitated this cultural and commercial process. At the beach, people's bodies were the most potent cultural symbol because bodies represent cultural identities and styles. History The early 1800s was the beginning of a revolution in swimwear when women flocked to the beaches for seaside recreation—typically using knee-length, puffed-sleeved, wool dresses, often black in color, and featuring a sailor collar. This outfit had the goal of covering all of the woman's skin to avoid suntans, since being tan was a sign of belonging to the social class of common laborers. In that period, there were bathing machines, which were little wood houses on wheels hauled by horses, and were usually located along recreational beaches where the water was shallow. Inside these bathing machines, people undressed and were drawn out into deep water in order to let them swim. freely Afterwards, they would come back when their bath was finished, and get dressed again. By the end of the 19th century, there was a need to have swimsuits that were less burdensome. This allowed exposure of the sun and better comfort for the new popular seaside activities. However, at the time, the only game for women at the beach involved jumping through the waves while holding on a rope attached to a buoy, so the development of the bikini became essential to women. The bikini was introduced in 1946, when two French designers, Louis Reard and Jacob Heim, reinvented the female swimsuit by dividing it into two pieces. At the beginning of its invention, it was given the name of 'atome'. Although the bottom of the stomach was still covered, as it is not always today, this was an important transformation because this new form of beachwear was quickly accepted and gave women more physical and metaphorical freedom. In the 1950s, women's curves were emphasized together with vivid colors until the 1970s, when sexual revolution was in full force and was letting people show off their bodies. The cultural parameters were increasingly influenced by the media and being inspired by multiple TV series, such as the famous "Baywatch" show in 1989, where the high-cut leg become popular, modeling a look of sports. Nowadays, fashion continues on this track. The swimwear industry is driven by the influences of ever-changing fashion styles, and the media, such as TV, advertising, and the web. Business Thanks to the birth of beachwear fashion, business developed in relation to swimwear. Occasions of use and materials The principal occasion of using beachwear was the maritime holiday, where the most used material in the making of swimwear was the Lycra that was created in 1958. It had the ability to stretch up to 7 times its original size, and then it could return to the original size. In 1974, the Lycra enters into the market of beachwear. This transformation allowed the replacement of swimwear from wet and misshapen clothes to lighter garments. Another occasion refers to the use of beachwear in sport. In 2008, swimwear provided inserts of plastic material with the aim of reducing friction with the water and improving sport performance. An example is "Speedo LZR Racer," a suit with an ultra-light fabric. Fashion shows are another occasion of use where many brands choose to show their swimwear lines. In this case, the beachwear is created to attract attention. An example is the brand Victoria's Secret, who devotes entire shows to its swimwear line. Main competitors There are different companies and brands (online and offline) that produce beachwear in order to satisfy the market demand. Some examples are: Arena (swimwear), Bikinicolors, Bikinilovers, Calzedonia, Golden Point, Just Cavalli Beachwear, La Perla, Lovable, Parah, Pin-Up Stars, Speedo, Triumph, and Yamamay. Industry innovations Thanks to the development of science, society, and new technologies, there are innovations. The first concerns the birth of burkinis, created for Muslim women. This is similar to a diving suit made more feminine, so that these women can swim in comfortable clothes that respect their religious faith. Another innovation concerns ecological beach bags that are created using recycled sails. Even thongs present innovations: from Indonesia comes the Paperflop, the first thong made of recyclable and Eco-sustainable materials. Their bottom is made from recycled newspapers and other Eco-friendly materials, such as palm roots and husks of coconuts. As for the bikini, the Canadian Franky Shaw has developed a hydrophobic material that repels water. Something different is the Sponge Suit, which is designed in California, and is a bikini made with a material that absorbs pollutants: people will use it up to twenty-five times, and then it can be recycled. The cost is low and safe for those who use it—plus, it is Eco-friendly. Beachwear and social network Nowadays, it is important for companies or people with private businesses to sell their products on social platforms. In the past, the means of communication were magazines or TV, but now users prefer to use social network because it is faster and easier with the invention of smartphones and tablets. In fact, those who have at least one profile on one of these platforms are always increasing day by day. That is why it is essential for them to use social networks as selling platforms—to not only sell their products, but also to create a relationship with the users with active participation. This happens in all the market sectors. Now there are not only pages or profiles of beachwear companies, in which the buyer can compare the price, quality, material, and feedback, but also private sellers can focus directly on social platforms. In this case, users can purchase with a single click or comment. In brief, social networks simplify the sale and purchase markets in all sectors. See also Bikini in popular culture Swimsuit competition Underwear as outerwear Victoria's Secret Fashion Show References Bibliography Alain Corbin, The Lure of the Sea: The Discovery of the Seaside in the Western World, 1750-1840, Berkley, University of California Press, Douglas Booth, Australian Beach Cultures: The History of Sun, Sand and Surf, Psychology Press, 2001, Emma Salizzoni, Turismo lungo le aree costiere euro mediterranee: dalla scoperta, al consumo, al progetto del paesaggio, Firenze University Press, January - June 2012 Category:Swimsuits

This review may contain spoilers for DC continuity. Skip To The Verdict? » Many of you will have heard of the Secret Six but until a couple of years ago no such super-team existed. In fact, several members of it didn’t exist either, or at least not in their current guises. Catman, Rag Doll, Parademon and Scandal Savage are the more unknown characters who, along with Deadshot and Cheshire, make up the Secret Six. The miniseries itself was a direct tie-in with the 2005 DC Universe-changing title Infinite Crisis, one of 6 or so major tie-in/precursor titles for the event. Out of all these tie-ins, Villains United is one of the few tie-ins that can be enjoyed separately from the main story. This trade has more links to the previous mini-crisis, Identity Crisis, than most of the other tie-ins, which for me is pretty nice as I like books that don’t just forget what has happened. Following the fallout of Identity Crisis and the shock revelation of what the Justice League did to Dr. Light, the super-villain community is allying up to make themselves stronger against the so called heroes; they are forming “The Society“. We join them in the full swing of their recruitment drive which features some fan favourite villains starting off with Mr. Freeze and ending with Sabbac and Catman. They all swiftly say yes, in a similar fashion to LOTR’s “You have my sword” followed by “And my …” (replace … with axe/bow/freeze-ray). All except Catman that is. “No,” he sternly responds to Talia al Ghul and Dr. Psycho, which goes down like a lead balloon. Being turned down by Catman of all people does even more to infuriate the society’s “recruitment officers.” He isn’t even a B-list villain. With the Society wanting to become a major force to be reckoned with, this isn’t the kind of underground press they wanted. The majority of the Society want to kill Catman to make an example of him, but Luthor steps in, as devious as ever, suggesting that there is a better way to make an example out of him. The plot then skips to the other 5 members of the Secret Six, who are joined by the Fiddler out on a mission in the Amazon. It becomes apparent that they are acting as a force against the Society on behalf of some faceless employer, Mockingbird. During the course of this mission Fiddler [Spoiler: is tragically killed], meaning they are currently one member shy of being the Secret Six. Obviously they have to replace him. It would be bad juju to not have the right number of members for a phonetically pleasing team name. This is where Catman comes in. The plot then flows forward in a mostly linear fashion. It is not really a spoiler to find out that part of Luthor’s plans involved humiliating Blake by killing not just him but the entire Secret Six. So now we get to enjoy a full-on super-villain-on-super-villain (ultra-hyphenated) war. The writer for this series is Gail Simone, best known before this series for her work on the popular Birds of Prey ongoing. I am happy to report that her writing in this volume is of the same high standard I had come to expect from her previous work. In fact, this team shows off her ability to write characters from scratch that manage to hold my attention better than she ever did before. The Secret Six also allow her to show of the darker side of her humour more than ever, which is the central force behind my affection for this team. The interaction involving Rag Doll and Parademon is prime example of this, as is almost anything Rag Doll says. That Rag Doll is one sick character but you cannot help loving him. After all, he is so well spoken and so polite, even when someone has kneed him in the groin. One of the most fun things about this volume is how it spans the whole range of super-villains in the DCU. There are a ton of different characters popping up everywhere! So many, in fact, that there is a guide in the back that acts a visual role call of who was in the book (by my count, over 70 different villains!). The downside of the title being a tie-in is that some of the plot is aimed at having some affect on the Crisis, meaning sometimes the plot seems slightly unnatural. The artwork is primarily drawn by Dale Eaglesham (Green Lantern Volume 3) which is up to a decent standard. It isn’t artwork that you will wow you, but neither would you find it insulting to your retinas. As mentioned earlier, there is a whole array of different characters in this volume and I can imagine Dale had a great time getting to draw so many. As I am sure Val Semeiks (Lobo) did when he covered for Dale in issue 3. His pencils are a little bit better than the main artist’s. I would also like to point out another neat feature of this collected edition. The first few pages of the book compromise of a summary of events leading up to this trade, taken from all over the DCU. It acts as a very good introduction to the book and a check-in to make sure you know anything needed to enjoy the story. This is a feature I would like to see more in books featuring new teams. For example, something in the beginning of the new Batgirl could have had a brief run-down of Stephanie Brown’s life, Cassandra Cain’s career in the cowl, and the other main events in the Batverse that come up in the trade. Without it, the story might be a little hard to follow for new comic readers. I have attempted to keep this review relatively vague so as not to spoil anything from Identity Crisis or Infinite Crisis. These are two titles that I would 100% suggest reading before you stumble across a spoiler somewhere, if you haven’t already. So what of Countdown To Infinite Crisis: Villains United? Do the new characters hold their own? Does the team fit together and work? Is there enough here that it deserves its own ongoing? Should that title be successful? Yes, yes, yes and hell yes. On the whole this is a very good book with only the average art and slightly forced links to Infinite Crisis letting it down. This is the start of one of the best additions to the DC Universe in a long time. Or let me put it this put it this way: out of 3 direct titles that came out of Infinite Crisis, Secret Six is the only one still going with no signs of stopping. And it all started here. Verdict: 4 out of 5. A solid start to a new team that only grows stronger with each trade. The trade itself is what an example of how modern collections should be put together and adds thoroughly to the enjoyment factor. Essential Continuity: Not overly essential for Infinite Crisis. Small ties to Identity Crisis. Entirely essential for the Secret Six. Read first: Surprisingly, nothing is essential to read before hand. The collected edition has a rare and really useful 8 page segment at the beginning of the trade detailing everything you need to know. You would be missing out if you haven’t read the main Identity Crisis trade, however. I would say it would be wise to also read Countdown to Infinite Crisis: The OMAC Project if you intend to read this and the main Infinite Crisis collection. Read next: I would suggest reading the back up story featured in Infinite Crisis: Companion, and from there move onto the limited series collected in Secret Six: Six Degrees of Separation. Chris just posted a review of that book. After that, just follow along the Secret Six Trade Reading Order. And despite having utterly nothing to do with the DCU, I would heartily recommend Enid Blyton’s similarly named classic Secret Seven books. « Back to the top?

Nora NLK-2600 - 6 in. - MR16 Low Voltage Retrofit Transformer Nora NLK-2600 - 6 in. - MR16 Low Voltage Retrofit Transformer Nora Lighting's Low Voltage Retrofit Kits provide an easy and affordable solution to convert existing standard 6 in. incandescent housings to high performance low voltage halogen fixtures. Kits require the use of a low voltage trim. Ideal for instantly changing general lighting to halogen spot and accent effects. This is for non-IC components only and includes a low voltage socket for MR16's. It includes a class H electronic transformer.

<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> <html xmlns="http://www.w3.org/1999/xhtml"> <head> <meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/> <title>CMSIS DSP Software Library: High Precision Q31 Biquad Cascade Filter</title> <link href="tabs.css" rel="stylesheet" type="text/css"/> <link href="search/search.css" rel="stylesheet" type="text/css"/> <script type="text/javaScript" src="search/search.js"></script> <link href="doxygen.css" rel="stylesheet" type="text/css"/> </head> <body onload='searchBox.OnSelectItem(0);'> <!-- Generated by Doxygen 1.7.2 --> <script type="text/javascript"><!-- var searchBox = new SearchBox("searchBox", "search",false,'Search'); --></script> <div class="navigation" id="top"> <div class="tabs"> <ul class="tablist"> <li><a href="index.html"><span>Main&#160;Page</span></a></li> <li><a href="modules.html"><span>Modules</span></a></li> <li><a href="annotated.html"><span>Data&#160;Structures</span></a></li> <li><a href="files.html"><span>Files</span></a></li> <li><a href="examples.html"><span>Examples</span></a></li> <li id="searchli"> <div id="MSearchBox" class="MSearchBoxInactive"> <span class="left"> <img id="MSearchSelect" src="search/mag_sel.png" onmouseover="return searchBox.OnSearchSelectShow()" onmouseout="return searchBox.OnSearchSelectHide()" alt=""/> <input type="text" id="MSearchField" value="Search" accesskey="S" onfocus="searchBox.OnSearchFieldFocus(true)" onblur="searchBox.OnSearchFieldFocus(false)" onkeyup="searchBox.OnSearchFieldChange(event)"/> </span><span class="right"> <a id="MSearchClose" href="javascript:searchBox.CloseResultsWindow()"><img id="MSearchCloseImg" border="0" src="search/close.png" alt=""/></a> </span> </div> </li> </ul> </div> </div> <div class="header"> <div class="summary"> <a href="#func-members">Functions</a> </div> <div class="headertitle"> <h1>High Precision Q31 Biquad Cascade Filter<br/> <small> [<a class="el" href="group__group_filters.html">Filtering Functions</a>]</small> </h1> </div> </div> <div class="contents"> <table class="memberdecls"> <tr><td colspan="2"><h2><a name="func-members"></a> Functions</h2></td></tr> <tr><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="group___biquad_cascade_d_f1__32x64.html#ga44900cecb8083afcaabf905ffcd656bb">arm_biquad_cas_df1_32x64_init_q31</a> (<a class="el" href="structarm__biquad__cas__df1__32x64__ins__q31.html">arm_biquad_cas_df1_32x64_ins_q31</a> *S, uint8_t numStages, <a class="el" href="arm__math_8h.html#adc89a3547f5324b7b3b95adec3806bc0">q31_t</a> *pCoeffs, <a class="el" href="arm__math_8h.html#a5aea1cb12fc02d9d44c8abf217eaa5c6">q63_t</a> *pState, uint8_t postShift)</td></tr> <tr><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="group___biquad_cascade_d_f1__32x64.html#ga953a83e69685de6575cff37feb358a93">arm_biquad_cas_df1_32x64_q31</a> (const <a class="el" href="structarm__biquad__cas__df1__32x64__ins__q31.html">arm_biquad_cas_df1_32x64_ins_q31</a> *S, <a class="el" href="arm__math_8h.html#adc89a3547f5324b7b3b95adec3806bc0">q31_t</a> *pSrc, <a class="el" href="arm__math_8h.html#adc89a3547f5324b7b3b95adec3806bc0">q31_t</a> *pDst, uint32_t <a class="el" href="arm__variance__example__f32_8c.html#ab6558f40a619c2502fbc24c880fd4fb0">blockSize</a>)</td></tr> </table> <hr/><a name="_details"></a><h2>Detailed Description</h2> <p>This function implements a high precision Biquad cascade filter which operates on Q31 data values. The filter coefficients are in 1.31 format and the state variables are in 1.63 format. The double precision state variables reduce quantization noise in the filter and provide a cleaner output. These filters are particularly useful when implementing filters in which the singularities are close to the unit circle. This is common for low pass or high pass filters with very low cutoff frequencies.</p> <p>The function operates on blocks of input and output data and each call to the function processes <code>blockSize</code> samples through the filter. <code>pSrc</code> and <code>pDst</code> points to input and output arrays containing <code>blockSize</code> Q31 values.</p> <dl class="user"><dt><b>Algorithm </b></dt><dd>Each Biquad stage implements a second order filter using the difference equation: <pre> y[n] = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] </pre> A Direct Form I algorithm is used with 5 coefficients and 4 state variables per stage. <div align="center"> <img src="Biquad.gif" alt="Biquad.gif"/> <p><strong>Single Biquad filter stage</strong></p></div> Coefficients <code>b0, b1, and b2 </code> multiply the input signal <code>x[n]</code> and are referred to as the feedforward coefficients. Coefficients <code>a1</code> and <code>a2</code> multiply the output signal <code>y[n]</code> and are referred to as the feedback coefficients. Pay careful attention to the sign of the feedback coefficients. Some design tools use the difference equation <pre> y[n] = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] - a1 * y[n-1] - a2 * y[n-2] </pre> In this case the feedback coefficients <code>a1</code> and <code>a2</code> must be negated when used with the CMSIS DSP Library.</dd></dl> <dl class="user"><dt><b></b></dt><dd>Higher order filters are realized as a cascade of second order sections. <code>numStages</code> refers to the number of second order stages used. For example, an 8th order filter would be realized with <code>numStages=4</code> second order stages. <div align="center"> <img src="BiquadCascade.gif" alt="BiquadCascade.gif"/> <p><strong>8th order filter using a cascade of Biquad stages</strong></p></div> A 9th order filter would be realized with <code>numStages=5</code> second order stages with the coefficients for one of the stages configured as a first order filter (<code>b2=0</code> and <code>a2=0</code>).</dd></dl> <dl class="user"><dt><b></b></dt><dd>The <code>pState</code> points to state variables array . Each Biquad stage has 4 state variables <code>x[n-1], x[n-2], y[n-1],</code> and <code>y[n-2]</code> and each state variable in 1.63 format to improve precision. The state variables are arranged in the array as: <pre> {x[n-1], x[n-2], y[n-1], y[n-2]} </pre></dd></dl> <dl class="user"><dt><b></b></dt><dd>The 4 state variables for stage 1 are first, then the 4 state variables for stage 2, and so on. The state array has a total length of <code>4*numStages</code> values of data in 1.63 format. The state variables are updated after each block of data is processed; the coefficients are untouched.</dd></dl> <dl class="user"><dt><b>Instance Structure </b></dt><dd>The coefficients and state variables for a filter are stored together in an instance data structure. A separate instance structure must be defined for each filter. Coefficient arrays may be shared among several instances while state variable arrays cannot be shared.</dd></dl> <dl class="user"><dt><b>Init Function </b></dt><dd>There is also an associated initialization function which performs the following operations:<ul> <li>Sets the values of the internal structure fields.</li> <li>Zeros out the values in the state buffer. </li> </ul> </dd></dl> <dl class="user"><dt><b></b></dt><dd>Use of the initialization function is optional. However, if the initialization function is used, then the instance structure cannot be placed into a const data section. To place an instance structure into a const data section, the instance structure must be manually initialized. Set the values in the state buffer to zeros before static initialization. For example, to statically initialize the filter instance structure use <pre> <a class="el" href="structarm__biquad__cas__df1__32x64__ins__q31.html" title="Instance structure for the high precision Q31 Biquad cascade filter.">arm_biquad_cas_df1_32x64_ins_q31</a> S1 = {numStages, pState, pCoeffs, postShift}; </pre> where <code>numStages</code> is the number of Biquad stages in the filter; <code>pState</code> is the address of the state buffer; <code>pCoeffs</code> is the address of the coefficient buffer; <code>postShift</code> shift to be applied which is described in detail below. </dd></dl> <dl class="user"><dt><b>Fixed-Point Behavior </b></dt><dd>Care must be taken while using Biquad Cascade 32x64 filter function. Following issues must be considered:<ul> <li>Scaling of coefficients</li> <li>Filter gain</li> <li>Overflow and saturation</li> </ul> </dd></dl> <dl class="user"><dt><b></b></dt><dd>Filter coefficients are represented as fractional values and restricted to lie in the range <code>[-1 +1)</code>. The processing function has an additional scaling parameter <code>postShift</code> which allows the filter coefficients to exceed the range <code>[+1 -1)</code>. At the output of the filter's accumulator is a shift register which shifts the result by <code>postShift</code> bits. <div align="center"> <img src="BiquadPostshift.gif" alt="BiquadPostshift.gif"/> <p><strong>Fixed-point Biquad with shift by postShift bits after accumulator</strong></p></div> This essentially scales the filter coefficients by <code>2^postShift</code>. For example, to realize the coefficients <pre> {1.5, -0.8, 1.2, 1.6, -0.9} </pre> set the Coefficient array to: <pre> {0.75, -0.4, 0.6, 0.8, -0.45} </pre> and set <code>postShift=1</code></dd></dl> <dl class="user"><dt><b></b></dt><dd>The second thing to keep in mind is the gain through the filter. The frequency response of a Biquad filter is a function of its coefficients. It is possible for the gain through the filter to exceed 1.0 meaning that the filter increases the amplitude of certain frequencies. This means that an input signal with amplitude &lt; 1.0 may result in an output &gt; 1.0 and these are saturated or overflowed based on the implementation of the filter. To avoid this behavior the filter needs to be scaled down such that its peak gain &lt; 1.0 or the input signal must be scaled down so that the combination of input and filter are never overflowed.</dd></dl> <dl class="user"><dt><b></b></dt><dd>The third item to consider is the overflow and saturation behavior of the fixed-point Q31 version. This is described in the function specific documentation below. </dd></dl> <hr/><h2>Function Documentation</h2> <a class="anchor" id="ga44900cecb8083afcaabf905ffcd656bb"></a><!-- doxytag: member="arm_biquad_cascade_df1_32x64_init_q31.c::arm_biquad_cas_df1_32x64_init_q31" ref="ga44900cecb8083afcaabf905ffcd656bb" args="(arm_biquad_cas_df1_32x64_ins_q31 *S, uint8_t numStages, q31_t *pCoeffs, q63_t *pState, uint8_t postShift)" --> <div class="memitem"> <div class="memproto"> <table class="memname"> <tr> <td class="memname">void arm_biquad_cas_df1_32x64_init_q31 </td> <td>(</td> <td class="paramtype"><a class="el" href="structarm__biquad__cas__df1__32x64__ins__q31.html">arm_biquad_cas_df1_32x64_ins_q31</a> *&#160;</td> <td class="paramname"> <em>S</em>, </td> </tr> <tr> <td class="paramkey"></td> <td></td> <td class="paramtype">uint8_t&#160;</td> <td class="paramname"> <em>numStages</em>, </td> </tr> <tr> <td class="paramkey"></td> <td></td> <td class="paramtype"><a class="el" href="arm__math_8h.html#adc89a3547f5324b7b3b95adec3806bc0">q31_t</a> *&#160;</td> <td class="paramname"> <em>pCoeffs</em>, </td> </tr> <tr> <td class="paramkey"></td> <td></td> <td class="paramtype"><a class="el" href="arm__math_8h.html#a5aea1cb12fc02d9d44c8abf217eaa5c6">q63_t</a> *&#160;</td> <td class="paramname"> <em>pState</em>, </td> </tr> <tr> <td class="paramkey"></td> <td></td> <td class="paramtype">uint8_t&#160;</td> <td class="paramname"> <em>postShift</em>&#160;</td> </tr> <tr> <td></td> <td>)</td> <td></td><td></td> </tr> </table> </div> <div class="memdoc"> <dl><dt><b>Parameters:</b></dt><dd> <table class="params"> <tr><td class="paramdir">[in,out]</td><td class="paramname">*S</td><td>points to an instance of the high precision Q31 Biquad cascade filter structure. </td></tr> <tr><td class="paramdir">[in]</td><td class="paramname">numStages</td><td>number of 2nd order stages in the filter. </td></tr> <tr><td class="paramdir">[in]</td><td class="paramname">*pCoeffs</td><td>points to the filter coefficients. </td></tr> <tr><td class="paramdir">[in]</td><td class="paramname">*pState</td><td>points to the state buffer. </td></tr> <tr><td class="paramdir">[in]</td><td class="paramname">postShift</td><td>Shift to be applied after the accumulator. Varies according to the coefficients format. </td></tr> </table> </dd> </dl> <dl class="return"><dt><b>Returns:</b></dt><dd>none</dd></dl> <p><b>Coefficient and State Ordering:</b></p> <dl class="user"><dt><b></b></dt><dd>The coefficients are stored in the array <code>pCoeffs</code> in the following order: <pre> {b10, b11, b12, a11, a12, b20, b21, b22, a21, a22, ...} </pre> where <code>b1x</code> and <code>a1x</code> are the coefficients for the first stage, <code>b2x</code> and <code>a2x</code> are the coefficients for the second stage, and so on. The <code>pCoeffs</code> array contains a total of <code>5*numStages</code> values.</dd></dl> <dl class="user"><dt><b></b></dt><dd>The <code>pState</code> points to state variables array and size of each state variable is 1.63 format. Each Biquad stage has 4 state variables <code>x[n-1], x[n-2], y[n-1],</code> and <code>y[n-2]</code>. The state variables are arranged in the state array as: <pre> {x[n-1], x[n-2], y[n-1], y[n-2]} </pre> The 4 state variables for stage 1 are first, then the 4 state variables for stage 2, and so on. The state array has a total length of <code>4*numStages</code> values. The state variables are updated after each block of data is processed; the coefficients are untouched. </dd></dl> <dl><dt><b>Examples: </b></dt><dd><a class="el" href="arm_graphic_equalizer_example_q31_8c-example.html#a19">arm_graphic_equalizer_example_q31.c</a>.</dd> </dl> <p>Definition at line <a class="el" href="arm__biquad__cascade__df1__32x64__init__q31_8c_source.html#l00077">77</a> of file <a class="el" href="arm__biquad__cascade__df1__32x64__init__q31_8c_source.html">arm_biquad_cascade_df1_32x64_init_q31.c</a>.</p> </div> </div> <a class="anchor" id="ga953a83e69685de6575cff37feb358a93"></a><!-- doxytag: member="arm_biquad_cascade_df1_32x64_q31.c::arm_biquad_cas_df1_32x64_q31" ref="ga953a83e69685de6575cff37feb358a93" args="(const arm_biquad_cas_df1_32x64_ins_q31 *S, q31_t *pSrc, q31_t *pDst, uint32_t blockSize)" --> <div class="memitem"> <div class="memproto"> <table class="memname"> <tr> <td class="memname">void arm_biquad_cas_df1_32x64_q31 </td> <td>(</td> <td class="paramtype">const <a class="el" href="structarm__biquad__cas__df1__32x64__ins__q31.html">arm_biquad_cas_df1_32x64_ins_q31</a> *&#160;</td> <td class="paramname"> <em>S</em>, </td> </tr> <tr> <td class="paramkey"></td> <td></td> <td class="paramtype"><a class="el" href="arm__math_8h.html#adc89a3547f5324b7b3b95adec3806bc0">q31_t</a> *&#160;</td> <td class="paramname"> <em>pSrc</em>, </td> </tr> <tr> <td class="paramkey"></td> <td></td> <td class="paramtype"><a class="el" href="arm__math_8h.html#adc89a3547f5324b7b3b95adec3806bc0">q31_t</a> *&#160;</td> <td class="paramname"> <em>pDst</em>, </td> </tr> <tr> <td class="paramkey"></td> <td></td> <td class="paramtype">uint32_t&#160;</td> <td class="paramname"> <em>blockSize</em>&#160;</td> </tr> <tr> <td></td> <td>)</td> <td></td><td></td> </tr> </table> </div> <div class="memdoc"> <dl><dt><b>Parameters:</b></dt><dd> <table class="params"> <tr><td class="paramdir">[in]</td><td class="paramname">*S</td><td>points to an instance of the high precision Q31 Biquad cascade filter. </td></tr> <tr><td class="paramdir">[in]</td><td class="paramname">*pSrc</td><td>points to the block of input data. </td></tr> <tr><td class="paramdir">[out]</td><td class="paramname">*pDst</td><td>points to the block of output data. </td></tr> <tr><td class="paramdir">[in]</td><td class="paramname">blockSize</td><td>number of samples to process. </td></tr> </table> </dd> </dl> <dl class="return"><dt><b>Returns:</b></dt><dd>none.</dd></dl> <dl class="user"><dt><b></b></dt><dd>The function is implemented using an internal 64-bit accumulator. The accumulator has a 2.62 format and maintains full precision of the intermediate multiplication results but provides only a single guard bit. Thus, if the accumulator result overflows it wraps around rather than clip. In order to avoid overflows completely the input signal must be scaled down by 2 bits and lie in the range [-0.25 +0.25). After all 5 multiply-accumulates are performed, the 2.62 accumulator is shifted by <code>postShift</code> bits and the result truncated to 1.31 format by discarding the low 32 bits.</dd></dl> <dl class="user"><dt><b></b></dt><dd>Two related functions are provided in the CMSIS DSP library. <code><a class="el" href="group___biquad_cascade_d_f1.html#ga27b0c54da702713976e5202d20b4473f" title="Processing function for the Q31 Biquad cascade filter.">arm_biquad_cascade_df1_q31()</a></code> implements a Biquad cascade with 32-bit coefficients and state variables with a Q63 accumulator. <code><a class="el" href="group___biquad_cascade_d_f1.html#ga456390f5e448afad3a38bed7d6e380e3" title="Fast but less precise processing function for the Q31 Biquad cascade filter for Cortex-M3 and Cortex-...">arm_biquad_cascade_df1_fast_q31()</a></code> implements a Biquad cascade with 32-bit coefficients and state variables with a Q31 accumulator. </dd></dl> <dl><dt><b>Examples: </b></dt><dd><a class="el" href="arm_graphic_equalizer_example_q31_8c-example.html#a25">arm_graphic_equalizer_example_q31.c</a>.</dd> </dl> <p>Definition at line <a class="el" href="arm__biquad__cascade__df1__32x64__q31_8c_source.html#l00176">176</a> of file <a class="el" href="arm__biquad__cascade__df1__32x64__q31_8c_source.html">arm_biquad_cascade_df1_32x64_q31.c</a>.</p> </div> </div> </div> <!--- window showing the filter options --> <div id="MSearchSelectWindow" onmouseover="return searchBox.OnSearchSelectShow()" onmouseout="return searchBox.OnSearchSelectHide()" onkeydown="return searchBox.OnSearchSelectKey(event)"> <a class="SelectItem" href="javascript:void(0)" onclick="searchBox.OnSelectItem(0)"><span class="SelectionMark">&#160;</span>All</a><a class="SelectItem" href="javascript:void(0)" onclick="searchBox.OnSelectItem(1)"><span class="SelectionMark">&#160;</span>Data Structures</a><a class="SelectItem" href="javascript:void(0)" onclick="searchBox.OnSelectItem(2)"><span class="SelectionMark">&#160;</span>Files</a><a class="SelectItem" href="javascript:void(0)" onclick="searchBox.OnSelectItem(3)"><span class="SelectionMark">&#160;</span>Functions</a><a class="SelectItem" href="javascript:void(0)" onclick="searchBox.OnSelectItem(4)"><span class="SelectionMark">&#160;</span>Variables</a><a class="SelectItem" href="javascript:void(0)" onclick="searchBox.OnSelectItem(5)"><span class="SelectionMark">&#160;</span>Typedefs</a><a class="SelectItem" href="javascript:void(0)" onclick="searchBox.OnSelectItem(6)"><span class="SelectionMark">&#160;</span>Enumerations</a><a class="SelectItem" href="javascript:void(0)" onclick="searchBox.OnSelectItem(7)"><span class="SelectionMark">&#160;</span>Enumerator</a><a class="SelectItem" href="javascript:void(0)" onclick="searchBox.OnSelectItem(8)"><span class="SelectionMark">&#160;</span>Defines</a></div> <!-- iframe showing the search results (closed by default) --> <div id="MSearchResultsWindow"> <iframe src="" frameborder="0" name="MSearchResults" id="MSearchResults"> </iframe> </div> <hr class="footer"/><address class="footer"><small>Generated on Fri Jul 15 2011 13:16:20 for CMSIS DSP Software Library by&#160; <a href="http://www.doxygen.org/index.html"> <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.7.2 </small></address> </body> </html>

I’m thrilled to report that I’m a co-author of the article “An ultra-stable gold-coordinated protein cage displaying reversible assembly“, which was recently published in Nature. This work is the result of an exciting collaboration between biochemists, physicists, structural biologists, mathematicians, and others (including yours truly, a computer scientist!), spread over at least five countries on three continents. The project is overseen by Jonathan Heddle from the Małopolska Centre of Biotechnology at Jagiellonian University in Poland. Now, I do not have sufficient expertise in most of the science behind this work to unpack the whole article here; you might instead read the summary that appeared in Nature‘s “News and Views” section. My contribution relates to a few words that the journal chopped off of the end of the title due to space constraints. The original title read “…reversible assembly and paradoxical geometry“. The phrase “paradoxical geometry” refers to near-miss Johnson solids, a topic that I’ve studied for a long time; the “protein cage” referred to in the title is, from my point of view, a near miss realized at molecular scale (a fact that is mentioned only in passing in the News and Views summary). I helped to explain the geometry of the cage, and to some extent measure just how paradoxical it is. Here I will give a bit of background on this topic, leading up to a geometric view of the cage’s structure. Near misses The five Platonic solids, the thirteen Archimedean solids, and the prisms and antiprisms are convex polyhedra with regular polygons as faces. But they’re not the only polyhedra with this property. For example, you can imagine a square-based pyramid that’s just tall enough that its triangular sides are equilateral. In 1966, Norman Johnson identified 92 additional convex polyhedra with regular faces, starting with the square-based pyramid; today these are known as the Johnson solids. They’re a motley crew of geometric oddities, which look as if they were assembled out of leftover parts from the Archimedeans. In 2001, George Hart and I published a paper about polyhedra in which we included a brief mention of “near misses”: convex polyhedra with faces that are almost—but not quite—regular. We did not attempt to define near misses rigorously, merely saying that the angles were close enough that you could assemble a model from cut-out regular polygons “without noticing the discrepancy”. The paper offered these three examples: The second and third polyhedra are easily exposed as Johnson solid impostors, by identifying vertices that could not exist in a Johnson solid. For example, the second polyhedron has a vertex surrounded by two hexagons and two triangles. A regular hexagon has an interior angle of 120°, and an equilateral triangle has an interior angle of 60°. So, if those faces were all regular, the angles around the vertex would be 60° + 60° + 120° + 120° = 360°. But that’s impossible! When you pack that much angle around a vertex, you force the faces there to lie flat, contradicting our assumption that this polyhedron is convex. The polyhedron on the left is not so easily dismissed. You need to grind through some trigonometry to prove that if the enneagons (9-sided polygons) and squares are regular, then the triangular faces are slightly isosceles and not really equilateral (I get an angle of about 63.1° at the triangle vertex nestled between two enneagons). I’ve written about near misses elsewhere, including a 2016 post about a new one I had constructed. In 2017, Evelyn Lamb wrote a wonderful article about the more general phenomenon of near misses in mathematics, leading off with near-miss Johnson solids. She also had the good fortune to interview Norman Johnson, who noted that he stumbled on near misses while enumerating his solids, but cared about them only to the extent that he had to eliminate them from his list. Sadly, Johnson passed away shortly after the article was published. A hendecagonal near miss Around the time that we wrote that 2001 paper, I found another interesting near miss, one that didn’t fit with the techniques in the paper. To construct it, start with the pentagonal icositetrahedron (PI), the dual of the more familiar (and Archimedean) snub cube. This solid is made from 24 identical shield-shape pentagonal faces: Let’s focus on a single shield, as in the shape on the left below: We can imagine slicing through each of the four upper corners of the shield, as suggested by the four dashed lines. If we do this correctly, the corners are truncated to create new edges that have the same length as the leftover bits of the original shape. The pointy bottom of the shield still sticks out, but by coincidence we can just about fit two more short edges into the point, as shown in the middle. The right drawing shows that these lines define a shape that bears an uncanny resemblance to a regular hendecagon (i.e., a regular 11-sided polygon). Looked at another way, if we take a perfectly regular hendecagon and fit it by eye to the shield, we can achieve an amazingly good fit. In the diagram below, I’ve lined up the midpoints of the top edges of a shield and a regular hendecagon, and manually scaled the latter until it straddles the edges of the former. The close-up shows just how tight the fit is. You can just barely see the hendecagonal edge tilted relative to the shield edge. As a final demonstration of the closeness of the fit, let’s compare angles in the shield and the hendecagon: The angle α on the left is a property of the PI, and measures around 114.8°. The angle β on the right is exactly 180°⨉(7/11), or around… 114.5°. Again, an amazing coincidence, one that makes it possible to inscribe the hendecagon almost perfectly within the shield. To complete the construction of a near miss, we can simply glue together regular hendecagons in the same pattern as the shields in the PI. The holes around the tops of shields can easily be filled with equilateral triangles, and the holes around the pointy corners of shields can be filled with clusters of four triangles around a square. Here’s the result: The paper model on the right is actually easiest to construct, because you can let the laws of physics absorb and distribute the mathematical error inherent in the construction. To build a computer model, you must make explicit decisions about where that error should go. For example, the faces could be made slightly irregular, or slightly non-planar. Again, I have no rigorous test for near-miss-ness that I could apply to this solid. But intuitively, the miss is very near indeed, and the paper model can easily be constructed without noticing the error. As an aside, my goal at the time was to create interesting tilings of the sphere to serve as a scaffolding for drawing spherical Islamic geometric patterns. I eventually created a few 3D designs based on the techniques in the paper, and on the hendecagonal near miss. I then turned these models into 3D printed sculptures. However, I didn’t have much else to say on the mathematics of near misses, so I put the shape on a short web page and left it at that. The TRAP Cage Fast forward to late 2013. A team of biochemists had been working with a custom-engineered protein ring called TRAP, which they knew had 11-fold rotational symmetry. They observed that under suitable encouragement from gold nanoparticles, a set of TRAP rings would assemble into a round solid form, which they called a TRAP Cage. But the structure of this cage was something of a mystery, because they didn’t know of a simple geometric form made from pieces with 11-fold symmetry. I assume they searched the web for polyhedra with hendecagonal faces, because they eventually found me by chance. And sure enough, it looked like the TRAP rings in their cage were arranged like the hendecagons in my near miss! I joined the collaboration, with the aim of building a computational model of the TRAP Cage, from which we could measure the likelihood that the cage could hold itself together based on the distribution of error in the model. The TRAP Cage is a bit more flexible than the near miss. First, it is constructed purely from TRAP rings, so we don’t have to worry about fitting squares and triangles into the model. Second, the rings aren’t actually attached directly to each other as they would be in a polyhedron; instead, the ring has 11 tiny arms that stick out, and arms from neighbouring rings grab on to gold atoms to hold the structure together. This extra flexibility means that we can likely construct a model cage with even lower error than the original near miss. I tested this hypothesis using numerical optimization, searching for a symmetric arrangement of TRAP rings for which the gold bonds would have the correct lengths predicted by chemical considerations. The goal of the optimization was to minimize the worst error in bond length, while also trying to keep the arrangement of TRAP rings as round as possible. This optimization was easily able to find virtual cages where the bond lengths between neighbouring rings never deviated by more than one part in a billion from their ideal lengths. That’s an astonishing degree of nearness for a near miss. I’m not a physicist, so I can’t say exactly how near, but allow me to speculate. I’ve got to assume that this deviation is well within the chemical tolerances for atomic bonds, meaning that the TRAP Cage would hold together without ever running afoul of its own mathematical impossibility. Going further, I note that the ideal bond length was given to me with just two significant digits, suggesting that an error of one part in a billion is much smaller than our uncertainty in measuring the “true” bond length in the first place. In other words, we may as well round the error to zero in the messy real world. The TRAP Cage is, then, a real-world near miss at molecular scale: you could build it out of regular microscopic pieces without, as I said earlier, “noticing the discrepancy”. Conclusion The article appeared in the May 16th issue of Nature. Even if you’re not a subscriber, they have provided a link that will allow you to read the full article. I tried to use my meagre 3D modelling skills to create a flashy image for the issue’s cover, but it didn’t pass muster. Of course, my blog is the perfect place to display the image. I’m incredibly excited to see this curious corner of geometry find a real-world application. Perhaps this discovery will motivate me or others to establish a more rigorous theory of near misses. Indeed, Agnieszka Kowalczyk, a mathematics PhD student at Jagiellonian University, together with Bernard Piette from Durham University, are already researching other cage structures with “paradoxical geometry” and have found numerous examples (aided by the fact that these cages don’t need to be fully watertight like polyhedra). They force their polygons to join edge-to-edge but permit them to deform slightly away from regularity, and then work on measuring and minimizing that deformation. They’ll be presenting some of their initial findings at this year’s Bridges conference in Linz. I’m looking forward to seeing what else we can do with this work.

The next time you pull up at the traffic lights, look to your left and right at the cars heading in the same way. How many empty seats can you count? Chances are there’s only one or two people in a car that could hold four or five. Now imagine if we could fill extra seats in each of these cars. wouldn’t that lead to significantly less cars on the road? With uberPOOL, that’s now possible as we can match people traveling in the same direction at the same time, just at the tap of a button. It’s why we are so excited to introduce uberPOOL to three more Indian cities starting this World Environment Day, Sunday June 5 in Hyderabad, Mumbai and Kolkata. More people in fewer cars means more affordable rides for passengers and less traffic congestion over time. Amit Jain, President Uber India said: “Uber is committed to India and to meeting the transportation needs of the country, with the help of smartphones and technology. We are incredibly excited to bring carpooling to three more Indian cities at the push of a button. Introducing uberPOOL to Mumbai, Kolkata and Hyderabad means more affordable rides for passengers and less congestion on the roads over time. Getting more people in fewer cars – at no extra costs to the government – and at reduced costs to riders, is a simple yet powerful example of how technology can actually transform our cities.” uberPOOL is a proven model Globally: Over 1,00,000 people are taking pooled trips every week in over 11 cities globally, including New York, Los Angeles, Beijing, Chengdu, and Shanghai. In China, the number of uberPOOL trips has grown to over 30 million per month. In 2016, if Uber riders had driven alone instead of sharing their rides we estimate that over 90mn more miles would have been travelled — consuming 1.8mn gallons of gas, emitting 16,000 metric tons of CO2. uberPOOL benefits riders, drivers and the environment Cheaper rides for passengers: uberPOOL is cheaper because the cost of the trip is shared. The fare per trip is up to 50% cheaper than uberGO, which is typically our most affordable service – whether Uber pairs you up with another passenger or not. Less congestion: uberPOOL is a convenient solution to cut congestion and pollution across cities, by pairing people travelling in the same direction at the same time. And because uberPOOL is cheap and easy to use, over time it offers a credible alternative to car ownership. Less time between trips for drivers: uberPOOL means less idle time between paying trips for drivers. It also means more demand overall because as the cost of a trip falls more people use the service – which means more rides for drivers. HOW uberPOOL WORKS Choose the uberPOOL option, enter your destination and request a ride. uberPOOL will then match you with another rider heading in the same direction: – that passenger will either be in the car at the start of your trip, in which case you’ll see their name, or – your driver will pick them up along the way, in which case Uber will notify you via the app Whether you’re first or second into the car, Uber ensures that you’re never taken more than a few minutes out of your way At the end of your trip, you’ll pay just like a normal Uber trip and receive an electronic receipt LEARN MORE ABOUT uberPOOL IN MUMBAI | HYDERABAD | KOLKATA

Q: Switch flooding when bonding interfaces in Linux +--------+ | Host A | +----+---+ | eth0 (AA:AA:AA:AA:AA:AA) | | +----+-----+ | Switch 1 | (layer2/3) +----+-----+ | +----+-----+ | Switch 2 | +----+-----+ | +----------+----------+ +-------------------------+ Switch 3 +-------------------------+ | +----+-----------+----+ | | | | | | | | | | eth0 (B0:B0:B0:B0:B0:B0) | | eth4 (B4:B4:B4:B4:B4:B4) | | +----+-----------+----+ | | | Host B | | | +----+-----------+----+ | | eth1 (B1:B1:B1:B1:B1:B1) | | eth5 (B5:B5:B5:B5:B5:B5) | | | | | | | | | +------------------------------+ +------------------------------+ Topology overview Host A has a single NIC. Host B has four NICs which are bonded using the balance-alb mode. Both hosts run RHEL 6.0, and both are on the same IPv4 subnet. Traffic analysis Host A is sending data to Host B using some SQL database application. Traffic from Host A to Host B: The source int/MAC is eth0/AA:AA:AA:AA:AA:AA, the destination int/MAC is eth5/B5:B5:B5:B5:B5:B5. Traffic from Host B to Host A: The source int/MAC is eth0/B0:B0:B0:B0:B0:B0, the destination int/MAC is eth0/AA:AA:AA:AA:AA:AA. Once the TCP connection has been established, Host B sends no further frames out eth5. The MAC address of eth5 expires from the bridge tables of both Switch 1 & Switch 2. Switch 1 continues to receive frames from Host A which are destined for B5:B5:B5:B5:B5:B5. Because Switch 1 and Switch 2 no longer have bridge table entries for B5:B5:B5:B5:B5:B5, they flood the frames out all ports on the same VLAN (except for the one it came in on, of course). Reproduce If you ping Host B from a workstation which is connected to either Switch 1 or 2, B5:B5:B5:B5:B5:B5 re-enters the bridge tables and the flooding stops. After five minutes (the default bridge table timeout), flooding resumes. Question It is clear that on Host B, frames arrive on eth5 and exit out eth0. This seems ok as that's what the Linux bonding algorithm is designed to do - balance incoming and outgoing traffic. But since the switch stops receiving frames with the source MAC of eth5, it gets timed out of the bridge table, resulting in flooding. Is this normal? Why aren't any more frames originating from eth5? Is it because there is simply no other traffic going on (the only connection is a single large data transfer from Host A)? I've researched this for a long time and haven't found an answer. Documentation states that no switch changes are necessary when using mode 6 of the Linux interface bonding (balance-alb). Is this behavior occurring because Host B doesn't send any further packets out of eth5, whereas in normal circumstances it's expected that it would? One solution is to setup a cron job which pings Host B to keep the bridge table entries from timing out, but that seems like a dirty hack. A: Yes - this is expected. You've hit a fairly common issue with NIC bonding to hosts, unicast flooding. As you've noted, the timers on your switch for the hardware addresses in question as no frames sourced from these addresses are being observed. Here are the general options- 1.) Longer address table timeouts. On a mixed L2/L3 switch the ARP and CAM timers should be close to one another (with the CAM timer running a few seconds longer). This recommendation stands regardless of the rest of the configuration. On the L2 switch the timers can generally be set longer without too many problems. That said, unless you disable the timers altogether you'll be back in the same situation eventually if there isn't some kind of traffic sourcing from those other addresses. 2.) You could hard-code the MAC addresses on the switches in question (all of the switches in the diagram, unfortunately). This is obviously not optimal for a number of reasons. 3.) Change the bonding mode on the Linux side to one that uses a common source MAC (i.e. 802.3ad / LACP). This has a lot of operational advantages if your switch supports it. 4.) Generate gratuitous arps via a cron job from each interface. You may need some dummy IP's on the various interfaces to prevent an oscillation condition (i.e. the host's IP cycles through the various hardware addresses). 5.) If it's a traffic issue, just go to 10GE! (sorry - had to throw that in there) The LACP route is probably the most common and supportable and the switches can likely be configured to balance inbound traffic to the server fairly evenly across the various links. Failing that I think the gratuitous arp option is going to be the easiest to integrate.

Sometimes we don’t realize how important people are around us until they’re not there. Dale is one of those people to me and I want to make sure I do all I can to help him and his family through this very difficult time. Dale was involved in a car accident yesterday morning on his way to the gym. His car flipped several times breaking his back and ribs. It was very difficult to see him laying in the hospital bed not able to move with wires and tubes attached to him everywhere. As you can see, Dale was very dedicated to keeping in shape. His goal was to become a sponsored body builder. I watched him for years compete only to come up short. The most admiring trait he possesses is his will to succeed. I saw him achieve that success this year by working his tail off. He has a long road ahead to recovering and knowing that he has that desire to succeed I have no doubt he will get through this. Help me help Dale. Read more

Brodie's abscess. A study of 181 cases, with special reference to radiographic diagnostic criteria. A study of 181 cases of Brodie's abscess, in which the diagnosis was histologically confirmed, was made in order to demonstrate radiographic factors common to other conditions, and therefore likely to pose questions of differential diagnosis. Some of the pathological characteristics of Brodie's abscess are described and correlated with the differing radiographic appearances of this inflammatory bone lesion.

The association between quality of life, depressive symptoms and glycemic control in a group of type 2 diabetes patients: comment on Papelbaum et al. This comment on the article: "The association between quality of life, depressive symptoms and glycemic control in a group of type 2 diabetes patients" by Papelbaum et al. was aimed to provide some critical remarks concerning the focus of the results section which showed significant discrepancies compared to the introduction and the research question. In addition, we would like to exhort the authors for a more comprehensive approach and for a more complete and congruent description of their results, in order to avoid misunderstanding.

Q: Compile PHP on Linux or use apt-get / yum? I have been compiling PHP for years with the configuration options I want. I compile extensions I use from source. Is there an advantage to doing this versus installing it from a package manager like apt-get or yum. I assumed it would also give me a leaner binary. I noticed that their are PHP modules in the repos such as "php53-gd". What if there wasn't a package available for something I wanted such as cURL for PHP? I understand the disadvantages of compiling such as needing to download/install dependencies based on my configuration options. I'm not really concerned with that. So the question is: Compile PHP on Linux or just use apt-get / yum? Can I get all the things I need from the repos? Does anyone out there still compile it from source? Any insight is appreciated! Thanks. A: I compile from source every time. It's not hard to corral the mentioned issues with regards to compiling manually. For example, my ./configure settings are saved to a file which is version controlled, so when a new version of PHP is stable and I am ready to make the switch, I download and extract the file, then run this command: ./configure `sh /path/to/my/configure/php.sh` Not too difficult. And because it's in version control, I can add notes as to why a module was added or removed. Another benefit of manual compilation is it allows me to keep the PHP footprint as minimal as possible. I pass the --disable-all flag, then add the modules I need. However, there is a downside to this minimalist approach, recently I needed to install Magento, so I had to recompile with --enable-hash and --with-mcyrpt flags. Even though I needed to add new flags, it wasn't difficult to add to the configure file and recompile.

US +1 AF +93 AL +355 DZ +213 AS +1684 AD +376 AO +244 AI +1264 AG +1268 AR +54 AM +374 AW +297 SH +290 AU +61 AT +43 AZ +994 BS +1242 BH +973 BD +880 BB +1246 BY +375 BE +32 BZ +501 BJ +229 BM +1441 BT +975 BO +591 BL +590 BA +387 BW +267 BR +55 VG +1284 IO +246 BN +673 BG +359 BF +226 BI +257 KH +855 CM +237 CA +1 CV +238 KY +1345 CF +236 TD +235 CL +56 CN +86 CX +61 CC +672 CO +57 KM +269 CG +242 CK +682 CR +506 HR +385 CU +53 CW +599 CY +357 CZ +420 KP +850 DK +45 DJ +253 DM +1767 DO +1809 EC +593 EG +20 SV +503 GQ +240 ER +291 EE +372 ET +251 FO +298 FK +500 FJ +679 FI +358 FR +33 GF +594 PF +689 TF +0 GA +241 GM +220 GE +995 DE +49 GH +233 GI +350 GR +30 GL +299 GD +1473 GP +590 GU +1671 GT +502 GG +44 GN +224 GW +245 GY +592 HT +509 HN +504 HK +852 HU +36 IS +354 IN +91 ID +62 IR +98 IQ +964 IE +353 IL +972 IT +39 CI +225 JM +1876 JP +81 JE +0 JO +962 KZ +7 KE +254 KI +686 KW +965 KG +996 LA +856 LV +371 LB +961 LS +266 LR +231 LY +218 LI +423 LT +370 LU +352 MO +853 MK +389 MG +261 MW +265 MY +60 MV +960 ML +223 MT +356 MH +692 MQ +596 MR +222 MU +230 MX +52 FM +691 MD +373 MC +377 MN +976 ME +382 MS +1664 MA +212 MZ +258 MM +95 NA +264 NR +674 NP +977 NL +31 AN +599 NC +687 NZ +64 NI +505 NE +227 NG +234 NU +683 NF +672 MP +1670 NO +47 OM +968 PK +92 PW +680 PA +507 PG +675 PY +595 PE +51 PH +63 PN +64 PL +48 PT +351 PR +1787 QA +974 RE +262 RO +40 RU +7 RW +250 SS +0 SM +378 ST +239 SA +966 SN +221 RS +381 YU +0 SC +248 SL +232 SG +65 SK +421 SI +386 GS +0 SB +677 SO +252 ZA +27 KR +82 ES +34 LK +94 SX +0 KN +1869 LC +1758 MF +0 VL +0 VC +1784 SD +249 SR +597 SZ +268 SE +46 CH +41 SY +963 TW +886 TJ +992 TZ +255 PM +508 YT +269 TH +66 TG +228 TK +690 TO +676 TL +670 TT +1868 TN +216 TR +90 TM +7370 TC +1649 TV +688 VI +1340 UG +256 UA +380 AE +971 GB +44 US +1 UM +1 UY +598 UZ +998 VU +678 VA +39 VE +58 VN +84 WF +681 EH +212 WS +684 YE +967 ZR +0 ZM +260 ZW +263 Enter your mobile phone number Sign up

namespace LiveSplit.View { partial class EditHistoryDialog { /// <summary> /// Required designer variable. /// </summary> private System.ComponentModel.IContainer components = null; /// <summary> /// Clean up any resources being used. /// </summary> /// <param name="disposing">true if managed resources should be disposed; otherwise, false.</param> protected override void Dispose(bool disposing) { if (disposing && (components != null)) { components.Dispose(); } base.Dispose(disposing); } #region Windows Form Designer generated code /// <summary> /// Required method for Designer support - do not modify /// the contents of this method with the code editor. /// </summary> private void InitializeComponent() { System.ComponentModel.ComponentResourceManager resources = new System.ComponentModel.ComponentResourceManager(typeof(EditHistoryDialog)); this.btnOK = new System.Windows.Forms.Button(); this.btnCancel = new System.Windows.Forms.Button(); this.tableLayoutPanel3 = new System.Windows.Forms.TableLayoutPanel(); this.historyListBox = new System.Windows.Forms.ListBox(); this.btnRemove = new System.Windows.Forms.Button(); this.tableLayoutPanel3.SuspendLayout(); this.SuspendLayout(); // // btnOK // this.btnOK.Anchor = ((System.Windows.Forms.AnchorStyles)((System.Windows.Forms.AnchorStyles.Bottom | System.Windows.Forms.AnchorStyles.Right))); this.btnOK.DialogResult = System.Windows.Forms.DialogResult.Cancel; this.btnOK.Location = new System.Drawing.Point(200, 192); this.btnOK.Name = "btnOK"; this.btnOK.Size = new System.Drawing.Size(75, 23); this.btnOK.TabIndex = 16; this.btnOK.Text = "OK"; this.btnOK.UseVisualStyleBackColor = true; this.btnOK.Click += new System.EventHandler(this.btnOK_Click); // // btnCancel // this.btnCancel.Anchor = ((System.Windows.Forms.AnchorStyles)(((System.Windows.Forms.AnchorStyles.Bottom | System.Windows.Forms.AnchorStyles.Left) | System.Windows.Forms.AnchorStyles.Right))); this.btnCancel.DialogResult = System.Windows.Forms.DialogResult.Cancel; this.btnCancel.Location = new System.Drawing.Point(281, 192); this.btnCancel.Name = "btnCancel"; this.btnCancel.Size = new System.Drawing.Size(75, 23); this.btnCancel.TabIndex = 17; this.btnCancel.Text = "Cancel"; this.btnCancel.UseVisualStyleBackColor = true; this.btnCancel.Click += new System.EventHandler(this.btnCancel_Click); // // tableLayoutPanel3 // this.tableLayoutPanel3.ColumnCount = 2; this.tableLayoutPanel3.ColumnStyles.Add(new System.Windows.Forms.ColumnStyle(System.Windows.Forms.SizeType.Percent, 100F)); this.tableLayoutPanel3.ColumnStyles.Add(new System.Windows.Forms.ColumnStyle(System.Windows.Forms.SizeType.Absolute, 81F)); this.tableLayoutPanel3.Controls.Add(this.btnCancel, 1, 2); this.tableLayoutPanel3.Controls.Add(this.btnOK, 0, 2); this.tableLayoutPanel3.Controls.Add(this.historyListBox, 0, 0); this.tableLayoutPanel3.Controls.Add(this.btnRemove, 0, 1); this.tableLayoutPanel3.Dock = System.Windows.Forms.DockStyle.Fill; this.tableLayoutPanel3.Location = new System.Drawing.Point(7, 7); this.tableLayoutPanel3.Name = "tableLayoutPanel3"; this.tableLayoutPanel3.RowCount = 3; this.tableLayoutPanel3.RowStyles.Add(new System.Windows.Forms.RowStyle(System.Windows.Forms.SizeType.Percent, 100F)); this.tableLayoutPanel3.RowStyles.Add(new System.Windows.Forms.RowStyle(System.Windows.Forms.SizeType.Absolute, 29F)); this.tableLayoutPanel3.RowStyles.Add(new System.Windows.Forms.RowStyle(System.Windows.Forms.SizeType.Absolute, 29F)); this.tableLayoutPanel3.Size = new System.Drawing.Size(359, 218); this.tableLayoutPanel3.TabIndex = 41; // // historyListBox // this.tableLayoutPanel3.SetColumnSpan(this.historyListBox, 2); this.historyListBox.Dock = System.Windows.Forms.DockStyle.Fill; this.historyListBox.FormattingEnabled = true; this.historyListBox.Location = new System.Drawing.Point(3, 3); this.historyListBox.Name = "historyListBox"; this.historyListBox.SelectionMode = System.Windows.Forms.SelectionMode.MultiExtended; this.historyListBox.Size = new System.Drawing.Size(353, 150); this.historyListBox.TabIndex = 18; // // btnRemove // this.btnRemove.Anchor = ((System.Windows.Forms.AnchorStyles)((System.Windows.Forms.AnchorStyles.Top | System.Windows.Forms.AnchorStyles.Right))); this.tableLayoutPanel3.SetColumnSpan(this.btnRemove, 2); this.btnRemove.Location = new System.Drawing.Point(236, 159); this.btnRemove.Name = "btnRemove"; this.btnRemove.Size = new System.Drawing.Size(120, 23); this.btnRemove.TabIndex = 19; this.btnRemove.Text = "Remove Selected"; this.btnRemove.UseVisualStyleBackColor = true; this.btnRemove.Click += new System.EventHandler(this.btnRemove_Click); // // EditHistoryDialog // this.AcceptButton = this.btnOK; this.AutoScaleDimensions = new System.Drawing.SizeF(6F, 13F); this.AutoScaleMode = System.Windows.Forms.AutoScaleMode.Font; this.ClientSize = new System.Drawing.Size(373, 232); this.Controls.Add(this.tableLayoutPanel3); this.Icon = ((System.Drawing.Icon)(resources.GetObject("$this.Icon"))); this.MaximumSize = new System.Drawing.Size(600, 10000); this.MinimumSize = new System.Drawing.Size(300, 258); this.Name = "EditHistoryDialog"; this.Padding = new System.Windows.Forms.Padding(7); this.Text = "Edit History"; this.tableLayoutPanel3.ResumeLayout(false); this.ResumeLayout(false); } #endregion private System.Windows.Forms.Button btnOK; private System.Windows.Forms.Button btnCancel; private System.Windows.Forms.TableLayoutPanel tableLayoutPanel3; private System.Windows.Forms.ListBox historyListBox; private System.Windows.Forms.Button btnRemove; } }

Martin Kilcoyne Martin J. Kilcoyne (born March 17, 1968) is the sports director at KTVI-TV FOX 2 in St. Louis, Missouri. Kilcoyne anchors the 5, 6 and 9 p.m. sportscasts on Sunday through Thursday nights. From 2006-2010, Kilcoyne was FOX 2's play-by-play announcer for the St. Louis Rams' pre-season football games. Kilcoyne hosts The Martin Kilcoyne Show, a weekday (12:00 PM–3:00 PM CT) talk show on St. Louis-area radio station KTRS (AM) 550. St. Louis Magazine featured him on its 2007 "A-List." Kilcoyne was named "Best TV Sports Anchor" in St. Louis by The Riverfront Times. He won the 2008 Emmy for best Sports Anchor from the Mid-America Chapter of the National Academy of Television Arts & Sciences. Kilcoyne returned to his hometown of St. Louis when he joined FOX 2 in 1997. Before that, his broadcasting career took him to KNAZ-TV in Flagstaff, Arizona, WJFW-TV in Rhinelander, Wisconsin, and WISC-TV in Madison, Wisconsin. He is a 1990 graduate of Marquette University in Milwaukee, Wisconsin. References External links FOX 2 website Category:1968 births Category:Living people Category:American sports announcers Category:American television journalists Category:National Football League announcers Category:People from St. Louis Category:American sports radio personalities Category:American male journalists

Applications for Lasker Clinical Research Scholars Program due August 25 The program aims to grow the diminishing pool of talented clinician-scientists by providing the necessary financial support to establish their careers, protected research time and access to hospital facilities and patient enrollments. Researchers Discover BACH2-Related Genetic Disorder Dr. Behdad Afzali, a NIAMS visiting researcher from England, worked with an international team, including experts at the National Institute of Allergy and Infectious Diseases, to uncover a genetic disorder related to the BACH2 gene. Policy Limits the Appendices in Grant Applications NIH Policy strictly limits the appendix materials that can be included with applications. An application that is submitted with appendix materials other than those specifically covered by the policy will not be reviewed. Germ Cell Formation in Mice Relies on RNA Clearance Mechanism Investigators led by Markus Hafner, Ph.D., head of the RNA Molecular Biology Group at NIAMS and Thomas Tuschl, Ph.D., at The Rockefeller University have revealed clues about the mechanisms by which each cell type chooses the genes to express.

2nd Miyakibashevo 2nd Miyakibashevo (; , 2-se Miäkäbaş) is a rural locality (a village) in Miyakibashevsky Selsoviet of Miyakinsky District, Russia. The population was 56 as of 2010. Geography The village is located 12 km from Kirgiz-Miyaki, 12 km from Anyasevo and 56 km from the nearest railway station (Aksyonovo). Ethnicity The village is inhabited by Bashkirs and other. Streets Tsentralnaya References External links 2nd Miyakibashevo on komandirovka.ru Category:Rural localities in Bashkortostan

Tel Aviv’s assertion that it attacked Iranian forces stationed near Damascus is untrue, the former head of Iran's elite Revolutionary Guards has said, warning that the airstrikes would be answered by Syria’s “defenders.” Major General Mohsen Rezaei dismissed allegations that the cross-border strikes had targeted Iranian military personnel who were planning to launch drone attacks aimed at targets inside Israel. “This is a lie and not true. Israel and the United States do not have the power to attack Iran's various centers, and our (military) advisory centers have not been harmed,” Rezaei told the semi-official ILNA news agency. Earlier this week, Israeli airstrikes targeted an alleged Iranian weapons depot in Iraq – a move which was also strongly condemned by Rezaei. Also on rt.com ‘Kill first!’ Netanyahu claims Israel’s Syrian strikes thwarted imminent ‘Iranian aggression’ “The actions carried out jointly by Israel and the United States in Syria and Iraq are in breach of international law and will soon be answered by Syria and Iraq's defenders,” he said. Israel has carried out countless airstrikes inside Syria, claiming that the attacks target Iranian and Hezbollah forces. Damascus has accused Israel of using the alleged threat posed by Tehran to hit Syrian military targets. Although it often declines to comment on its involvement in such strikes, Tel Aviv acknowledged that it was behind the most recent attack, boasting that it was a message to Iran that it should “not feel safe anywhere.” Also on rt.com Lebanese PM accuses Israel of ‘open attack’ on sovereignty after 2 drones crash in Beirut Like this story? Share it with a friend!

// Copyright (c) AlphaSierraPapa for the SharpDevelop Team (for details please see \doc\copyright.txt) // This code is distributed under the GNU LGPL (for details please see \doc\license.txt) using System; using System.Diagnostics; namespace ICSharpCode.AvalonEdit.Document { /// <summary> /// Describes a change to a TextDocument. /// </summary> sealed class DocumentChangeOperation : IUndoableOperationWithContext { TextDocument document; DocumentChangeEventArgs change; public DocumentChangeOperation(TextDocument document, DocumentChangeEventArgs change) { this.document = document; this.change = change; } public void Undo(UndoStack stack) { Debug.Assert(stack.state == UndoStack.StatePlayback); stack.RegisterAffectedDocument(document); stack.state = UndoStack.StatePlaybackModifyDocument; this.Undo(); stack.state = UndoStack.StatePlayback; } public void Redo(UndoStack stack) { Debug.Assert(stack.state == UndoStack.StatePlayback); stack.RegisterAffectedDocument(document); stack.state = UndoStack.StatePlaybackModifyDocument; this.Redo(); stack.state = UndoStack.StatePlayback; } public void Undo() { OffsetChangeMap map = change.OffsetChangeMapOrNull; document.Replace(change.Offset, change.InsertionLength, change.RemovedText, map != null ? map.Invert() : null); } public void Redo() { document.Replace(change.Offset, change.RemovalLength, change.InsertedText, change.OffsetChangeMapOrNull); } } }

\name{Lcross} \alias{Lcross} \title{Multitype L-function (cross-type)} \description{ Calculates an estimate of the cross-type L-function for a multitype point pattern. } \usage{ Lcross(X, i, j, ..., from, to, correction) } \arguments{ \item{X}{The observed point pattern, from which an estimate of the cross-type \eqn{L} function \eqn{L_{ij}(r)}{Lij(r)} will be computed. It must be a multitype point pattern (a marked point pattern whose marks are a factor). See under Details. } \item{i}{The type (mark value) of the points in \code{X} from which distances are measured. A character string (or something that will be converted to a character string). Defaults to the first level of \code{marks(X)}. } \item{j}{The type (mark value) of the points in \code{X} to which distances are measured. A character string (or something that will be converted to a character string). Defaults to the second level of \code{marks(X)}. } \item{correction,\dots}{ Arguments passed to \code{\link{Kcross}}. } \item{from,to}{ An alternative way to specify \code{i} and \code{j} respectively. } } \details{ The cross-type L-function is a transformation of the cross-type K-function, \deqn{L_{ij}(r) = \sqrt{\frac{K_{ij}(r)}{\pi}}}{Lij(r) = sqrt(Kij(r)/pi)} where \eqn{K_{ij}(r)}{Kij(r)} is the cross-type K-function from type \code{i} to type \code{j}. See \code{\link{Kcross}} for information about the cross-type K-function. The command \code{Lcross} first calls \code{\link{Kcross}} to compute the estimate of the cross-type K-function, and then applies the square root transformation. For a marked point pattern in which the points of type \code{i} are independent of the points of type \code{j}, the theoretical value of the L-function is \eqn{L_{ij}(r) = r}{Lij(r) = r}. The square root also has the effect of stabilising the variance of the estimator, so that \eqn{L_{ij}}{Lij} is more appropriate for use in simulation envelopes and hypothesis tests. } \value{ An object of class \code{"fv"}, see \code{\link{fv.object}}, which can be plotted directly using \code{\link{plot.fv}}. Essentially a data frame containing columns \item{r}{the vector of values of the argument \eqn{r} at which the function \eqn{L_{ij}}{Lij} has been estimated } \item{theo}{the theoretical value \eqn{L_{ij}(r) = r}{Lij(r) = r} for a stationary Poisson process } together with columns named \code{"border"}, \code{"bord.modif"}, \code{"iso"} and/or \code{"trans"}, according to the selected edge corrections. These columns contain estimates of the function \eqn{L_{ij}}{Lij} obtained by the edge corrections named. } \seealso{ \code{\link{Kcross}}, \code{\link{Ldot}}, \code{\link{Lest}} } \examples{ data(amacrine) L <- Lcross(amacrine, "off", "on") plot(L) } \author{\adrian and \rolf } \keyword{spatial} \keyword{nonparametric}

In Donald Trump's Washington, there are many people vying for the President-elect's attention. The Washington Post's Robert Costa explains how Trump will seek advice during the transition. (Bastien Inzaurralde,Victoria Walker/The Washington Post) In Donald Trump's Washington, there are many people vying for the President-elect's attention. The Washington Post's Robert Costa explains how Trump will seek advice during the transition. (Bastien Inzaurralde,Victoria Walker/The Washington Post) President-elect Donald Trump plans to meet this weekend with former Massachusetts governor Mitt Romney, a fierce critic during the campaign, to discuss his transition operation and a potential role as secretary of state, people close to the transition said Thursday. Trump’s outreach to Romney, the 2012 Republican presidential nominee, could help bridge the divide between the president-elect’s advisers and the GOP establishment, and send a signal to foreign capitals that Trump is interested in a more conventional figure as the nation’s top diplomat. Late Thursday night, Trump offered the national security adviser post to retired Lt. Gen. Mike Flynn, according to a person close to the transition team. Also Thursday, Newt Gingrich, the former Republican House speaker, said in an interview with McClatchy News Service that he would not have an official role in Trump’s administration, despite having previously been identified as a potential secretary of state. Gingrich confirmed the report in an interview with The Washington Post. “I think it’s good that the president-elect is meeting with people like Mr. Romney,” Sen. Jeff Sessions (R-Ala.), who also is being considered for Trump’s Cabinet, told reporters outside Trump Tower in New York. “He’s meeting with a lot of talented people that he needs good relationships with. I think Mr. Romney would be quite capable of doing a number of things, but he’ll be one of those I’m sure that’s reviewed, and Mr. Trump will make that decision.” The disclosure of their meeting came as something of a surprise. Romney had been one of the earliest and most vocal critics of Trump among the GOP leadership, ripping the real estate mogul last March after squelching speculation that he would mount a late primary challenge to Trump. “If we Republicans choose Donald Trump as our nominee, the prospects for a safe and prosperous future are greatly diminished,” Romney said, adding that “dishonesty is Trump’s hallmark.” Romney also criticized Trump for racially charged campaign rhetoric, prompting Trump to write on Twitter that “Mitt Romney had his chance to beat a failed president but he choked like a dog. Now he calls me racist — but I am least racist person there is.” Romney took a more tempered tone after Trump’s general election triumph last week, and called him to offer his congratulations. The news came as Trump’s transition to power kicked into higher gear. Transition officials were expected to fan out across federal agencies, and Trump prepared for an important meeting with Japan’s prime minister. The 5 p.m. session with Japanese Prime Minister Shinzo Abe, Trump’s first with a foreign leader since the election, has raised questions among some in Washington’s foreign policy community because Trump has apparently not been briefed by the State Department. Officials said Wednesday that the transition team has not reached out to State. A former State Department official said such a meeting with a foreign leader would normally be preceded by numerous briefings from key diplomats, which is considered especially important here because the Japanese are concerned about comments Trump made on the campaign trail. The president-elect repeatedly said that Japan should pay more for its own defense and be less reliant on the United States. [Japan’s prime minister hopes to start building ‘trusting relationship’ with Trump] 1 of 74 Full Screen Autoplay Close Skip Ad × Here’s what president-elect Donald Trump has been doing after the election View Photos He has been holding interviews and meeting with Congress and the president as he prepares to transition into the White House. Caption He has been holding interviews and meetings as he prepares to enter the White House. Jan. 19, 2017 President-elect Donald Trump and his wife, Melania, visit the Lincoln Memorial before the “Make America Great Again” concert. Jabin Botsford/The Washington Post Buy Photo Wait 1 second to continue. “The world does not stop for the transition,’’ said the official, who spoke on condition of anonymity to speak freely. Trump “would want an intelligence briefing. You’d probably want to get briefed on what’s what happening in the region.’’ But Trump’s campaign manager, Kellyanne Conway, said Thursday that the session at Trump Tower, which Vice President-elect Mike Pence will attend, will be “much less formal” than in the future because Trump has yet to assume office. “We are very sensitive to the fact that President Obama is still in office for the next two months,’’ Conway said. As Trump remained ensconced with close aides in his Manhattan office tower, his transition team appeared to signal Thursday that Sessions is a leading candidate to be attorney general. “The President-elect has been unbelievably impressed with Senator Sessions and his phenomenal record as Alabama’s Attorney General and U.S. Attorney,’’ the team said in a statement about Trump’s meeting with Sesisons on Wednesday. While the statement cautioned that “nothing has been finalized,’’ Sessions’s 14-year stint in those two posts in the 1980s and 1990s would be his primary qualifications to lead the Justice Department. Sessions’s former staff director of the Senate Judiciary Committee, Brian Benczkowski, is also helping to manage the Justice Department transition for Trump’s team, lawyers familiar with the matter have said. Sessions, a top Trump adviser known for his hardline views on immigration, has been a rising force in the transition team and is also under consideration for defense secretary. His nomination for Justice would likely bring a re-examination of his failed nomination by President Ronald Reagan in 1986 to be a federal judge. A bipartisan panel of senators on the Judiciary Committee declined to send his nomination to the Senate floor that year amid allegations that he had made what some characterized as racist remarks. Sessions, who has been a senator for 20 years, has vehemently denied holding any racist views and has said he supported civil rights in Alabama, where he grew up outside of Selma. [In Trump’s Washington, rival powers and whispers in the president’s ear] Trump’s meeting with Abe arose from a phone conversation between the Japanese leader and Trump. When Abe called to congratulate Trump shortly after his victory, he mentioned that he would be passing through New York this week and suggested a meeting. “That would be awesome,” Trump immediately responded, according to people briefed on the conversation. The two leaders have much to discuss. Trump has vowed to scrap the Trans-Pacific Partnership trade deal that Abe recently pushed through his parliament. And the president-elect caused jitters in both Japan and South Korea during the campaign by saying both nations were not paying enough for their defense and that he would make them pay more — perhaps even all — of the costs of hosting U.S. military bases. Since Trump’s victory, the Japanese government has been taking a wait-and-see approach. “Trump said various things during his campaign, but I will not presuppose what he will do as president,” Tomomi Inada, Japan’s defense minister, said late last week. She added, however, that Japan is paying its fair share toward base costs. In a new development Thursday, Trump’s transition team announced that anyone serving in the new administration would be banned for life from lobbying for any foreign government. Trump had proposed such a ban in an ethics plan he unveiled last month, but it is unclear how the ban would be implemented. There is no current law that imposes a lifetime ban on post-government employment for administration officials, with one exception — there is a lifetime ban on certain members of the U.S. Trade Representative’s Office from representing foreign governments after leaving the agency. The reasoning is to prevent them from essentially “switching sides” and using the knowledge they gained while representing U.S. interests to weaken or amend the agreement to the benefit a foreign country. A lifetime ban like the one Trump proposed raises constitutional issues, and would have to be more narrowly tailored to pass muster in the courts — for example, if the ban was limited to certain State Department or Defense Department officials whose jobs involved working closely with foreign governments. But a blanket lifetime ban could be unconstitutional. “Lifetime bans are really problematic from a legal standpoint because it prevents people from making a living,” said Brett Kappel, a political law and government ethics attorney. “A lifetime ban on anybody in the administration ever becoming a representative of a foreign government? I don’t see how that would hold up in court.” It is also unclear whether the ban would be implemented by legislation or executive order. Meanwhile, the pace of the transition appeared to quicken. Offices prepared for Trump’s teams in departments and agencies across the government had remained empty Wednesday. But the White House said that it received paperwork, signed Tuesday evening by Vice President-elect Mike Pence, necessary for the teams to move into the department offices and begin to receive briefings from current officials. The names of people on the “landing teams” for the State Department, the Justice Department, the Pentagon and the National Security Council will be submitted to the White House on Thursday and announced Friday, the transition team said Thursday in a conference call with reporters. Economic policy landing teams will be announced Monday, followed by teams devoted to domestic policy and independent federal agencies. The transition released a list of 29 presidents and prime ministers with whom it said Trump and Pence have spoken since the election. And transition communications director Jason Miller said that reports of turmoil within the transition following the ouster of several senior team members in recent days came largely from “folks on the outside” and those who feared that Trump was preparing to “drain the swamp, as he’s promised.” Miller declined to speculate on the timing of appointment announcements, saying that “the president-elect is going to get this right” and that names would be put forward when Trump was ready. He also denied reports that Jared Kushner, Trump’s son-in-law, had been instrumental in purging members of the transition seen as close to New Jersey Gov. Chris Christie, whom Pence replaced as the head of the team last week. Miller said Trump met with several advisers and candidates for administration positions Wednesday, including Rep. Tom Price (R-Ga.), investor Steve Feinberg, Success Academy Charter Schools chief executive Eva Moskowitz and Rep. Mike Pompeo (R-Kan.). Miller did not elaborate on which people on the list are candidates to join the administration. Price is considered a candidate to lead the Department of Health and Human Services. Trump will meet Thursday with South Carolina Gov. Nikki Haley, Rep. Jeb Hensarling (R-Tex.), Florida Gov. Rick Scott, former secretary of state Henry Kissinger and retired Gen. Jack Keane, among others, Miller said. Attention continued to be mainly focused on potential national security picks. Trump campaign surrogates said former New York mayor Rudolph W. Giuliani remained at the top of the rumored list for secretary of state, along with former State Department official John Bolton. Sen. Tom Cotton (R-Ark.), who visited Trump on Tuesday in Manhattan, emerged as a defense secretary candidate. Farther down the defense list were George W. Bush national security adviser Stephen V. Hadley and former senator James M. Talent (R-Mo.). Frank Gaffney, a far-right conspiracy theorist who was described in some media reports as a Trump transition adviser and possible pick for a national security job, said Wednesday that he had “not been contacted by anyone from the team.” His statement followed one by Miller, the transition communication chief, that Gaffney is “a nice guy, but he’s not part of the transition team” and was not advising it. House Intelligence Committee Chairman Devin Nunes (R-Calif.), mentioned as a possible CIA director after the leading candidate, former chairman Mike Rogers of Michigan, was among those purged early this week, is a transition adviser but is “not interested in a post,” a congressional aide said. Former congressman Pete Hoekstra, also a Michigan Republican and a former committee chairman, said in an interview that he’d told the transition “if they have a role for me, I’d be more than happy to discuss it with them.” Hoekstra said the Trump team was “going to expand its outreach, absolutely. But they’re going to do it in a methodical way.” Despite intense media scrutiny and swirling rumors in Washington, Trump’s timetable was still well within the bounds of his immediate predecessors. Obama did not announce his first Cabinet pick until nearly a month after the 2008 election; he presented his national security team en masse Dec. 1 that year. Confirmation of George W. Bush’s 2000 victory did not come until a Supreme Court decision more than a month after the Nov. 7 election. Anna Fifield in Tokyo and Catherine Ho, Sari Horwitz, Dan Lamothe, Greg Miller, Ellen Nakashima, Philip Rucker, Missy Ryan, Julie Tate and Elise Viebeck in Washington contributed to this report.

Police arrested a suspect in connection with The Hague stabbing, according to a report. The alleged attacker, who is at least 35 years old and apparently homeless, reportedly stabbed three children in a shopping district in the Dutch city Friday, the BBC reported. The victims — a 13-year-old boy and two 15-year-old girls — have been released from the hospital. Authorities had not ruled out terrorism in the attack, they said earlier.

Periodontal conditions following surgical and orthodontic treatment of palatally impacted maxillary canines--a follow-up study. This follow-up study reports on the periodontal status 1 to 18 years after the completion of orthodontic treatment of unilateral palatally impacted maxillary canines and their adjacent incisors and premolars. Registrations were performed on 42 patients, 19 to 59 years old (mean 35 years) at investigation. An orthodontic pin with eyelet had been placed after exploration of the canine and, in some cases, bone removal. A flap had been raised and resutured after bone removal in 11 cases. The results showed greater mesial probing depth of the canines on the treated side, on the adjacent lateral incisors distolingually, and on the first premolars mesiolingually. Marginal bone level was found to be lower on the distal aspect of the treated canines and adjacent laterals. In general, the results showed a good gingival and periodontal status with slight differences between treated and untreated sides.

The primary purpose of the present study was to evaluate the effect of manipulating load and repetition duration (i.e. time under tension) during RE performed to task failure on muscle fibre activation, which we quantified via fibre type‐specific glycogen depletion (Bell & Jacobs, 1989 ; Robergs et al . 1991 ; Koopman et al . 2006 ). In addition, we measured surface EMG to determine how well EMG amplitude aligned with muscle fibre type‐specific glycogen depletion. Additionally, to obtain mechanistic insight into how muscle fibre activation would be translated, we examined the phosphorylation of select signalling proteins prominent in contraction‐related anabolism. We hypothesized that performing RE to task failure, independent of any specific RE variable, would result in the activation of type I and type II muscle fibres to an equivalent extent and show comparable increases in anabolic signalling. In addition, we hypothesized that surface EMG would be a poor indicator of muscle fibre type‐specific glycogen depletion (i.e. fibre activation) and that muscle fibre glycogen depletion and anabolic signalling would be related. According to the size principle of motor unit recruitment, performing submaximal contractions results predominantly in the recruitment of smaller (i.e. lower threshold) motor units that innervate type I fibres, although increasing fatigue necessitates the recruitment of larger (i.e. higher threshold) motor units that innervate type II muscle fibres (Mendell, 2005 ). Accordingly, several acute aerobic (Gollnick et al. 1973 , 1974b ; Vollestad et al . 1984 ; Vollestad & Blom, 1985 ; Prats et al . 2013 ; Kristensen et al . 2015 ) and resistance (Bell & Jacobs, 1989 ; Robergs et al . 1991 ; Koopman et al . 2006 ) exercise studies have shown that sustained submaximal contractions result in the substrate depletion (which is indicative of preceding depolarization or ‘activation’) of type II muscle fibres as fatigue ensues. Nonetheless, despite considerable debate on the ability of surface EMG to provide insight into motor unit recruitment during fatiguing contractions (Dideriksen et al. 2010 , 2011 ; Enoka & Duchateau, 2015 ; Vigotsky et al . 2016 ), the thesis that type II fibre activation is confined to or superior with the lifting of heavier loads has been asserted. It has been proposed that performing resistance exercise (RE) with heavier loads [greater than 60% one repetition maximum (1RM) strength] is required to elicit muscle hypertrophy and to recruit and result in hypertrophy of type II muscle fibres (Ratamess et al . 2009 ; Grgic & Schoenfeld, 2018 ). By contrast, studies show that performing RE training with relatively lighter loads to task failure (i.e. volitional fatigue) results in hypertrophy of both type I and type II muscle fibres (Mitchell et al . 2012 ; Morton et al . 2016 ; Schoenfeld et al . 2017 ). Indeed, type II muscle fibre hypertrophy, even when lighter loads are lifted to task failure, is indicative of recurrent type II fibre activation (Mitchell et al . 2012 ; Morton et al. 2015 , 2016 ). However, on the basis of greater surface electromyography (EMG) amplitude (Jenkins et al . 2015 ; Looney et al . 2016 ; Haun et al . 2017 ) or decomposition of the EMG signal (Muddle et al . 2018 ), other studies have reported that heavier loads are superior to lighter loads in terms of recruiting higher threshold motor units and thus the eventual hypertrophy of type II fibres (Grgic & Schoenfeld, 2018 ). Methods Ethical approval All participants were informed of the purpose, methodology, and potential risks of the study before giving verbal and written informed consent. The study conformed to the standards set by the latest revision of the Declaration of Helsinki and to the most recent Canadian Tri‐Council policy statement on the use of human participants in research (http://www.pre.ethics.gc.ca/eng/policy-politique/initiatives/tcps2-eptc2/Default). The study was approved by the Hamilton Integrated Research Ethics Board (Project Number 0802) and was registered at clinicaltrials.gov (NCT03991117). Study participants Ten recreationally‐trained young men (mean ± SD: 22 ± 3 years, 81.6 ± 8.9 kg, 178 ± 6 cm) volunteered to participate in the present study. We defined ‘recreationally‐trained’ as engaging in at least one to three RE sessions per week for at least 2 years. Resistance exercise training conditions Participants’ legs were assigned in randomized cross‐over fashion to perform one of four unilateral RE protocols. The four RE conditions varied in the repetition duration and load (percentage of single maximal voluntary isotonic strength: %1RM). The conditions were: 80 %1RM Regular [80R; 1s:1s:1s (eccentric:pause:concentric)], 80 %1RM Slow (80S; 3:1:3), 30 %1RM Regular (30R; 1:1:1) and 30 %1RM Slow (30S; 3:1:3). Three sets were performed for each condition and each set was separated by 180 s rest. Repetition cadence was maintained by an in‐ear metronome at 60 beats min–1; however, for greater accuracy, repetition duration was quantified with the rise and fall of vastus lateralis (VL) EMG activity. RE volume (kg) was calculated by multiplying the number of repetitions in all three sets by the load lifted per repetition. Total time under load (TUL; s) was calculated by multiplying repetition duration by the number of repetitions in all three sets determined from signal from the VL EMG. Finally, impulse (kg·s) was calculated by multiplying the load lifted per repetition by the repetition duration and by the number of repetitions in all three sets. Study design Each participant came in for a familiarization session before the RE trials began, which was used to obtain an independent assessment of 1RM for each leg during knee extension (Atlantis, Laval, QC, Canada) and to familiarize them with performing isometric maximum voluntary contractions (MVC; leg curl and knee extension; Biodex dynamometer, System 3; Biodex Medical Systems Inc., Shirley, NY, USA). Using a unilateral within‐subject cross‐over design, participants came in on two separate occasions (separated by at least 72 h) to perform two of the four RE conditions each day (one on each leg) in a randomized order (Fig. 1). Briefly, on each of the two trial days, participants arrived following an overnight fast and a muscle biopsy was taken from their VL under local anaesthesia (2% xylocaine) to serve as the baseline for both conditions performed that day. After the muscle biopsy, dry reusable electrodes (Biometrics SX230; Biometrics Ltd., Newport, UK) were placed on each participant's VL, vastus medialis (VM) and semi‐tendinosus (ST; in line with the direction of muscle action) along with a reference electrode and electronic joint goniometer (SG 150, Biometrics Ltd.) on the head of the fibula and about their knee joint, respectively. When the electrodes were in place, each participant performed three isometric knee extensions with their leg positioned at 60° and isometric leg curls at 45° to record peak torque and maximum voluntary excitation (MVE; i.e. the highest EMG signal: knee extension and leg curls, respectively) (Mathiassen et al. 1995) of the quadriceps and hamstrings, respectively. Afterwards, each participant performed two of the four conditions consecutively (one on each leg), which involved three sets to task failure (i.e. the participant was unable to complete another concentric muscle action) with three isometric knee extension MVCs between each condition's set (∼15 s delay between the knee extension machine and their first MVC). One h following the last MVC in each condition, a muscle biopsy was taken from the VL (one each leg). Figure 1. Study schematic representing one of the two trial days Open in figure viewer PowerPoint The two arrows represent each of the participant's legs. Reduction in peak torque and EMG analyses Muscle fatigue was quantified in the knee extensors as the reduction in isometric peak torque relative to the pre‐testing peak toque. Surface EMG was recorded on a Biometrics data logger (DataLOG MWX8, Biometrics Ltd.; band‐pass 20–450 Hz, input impedance ∼1015 Ω, common mode rejection ratio >96 dB) and analysed with LabVIEW, version 8.2 (National Instruments, Austin, TX, USA). The raw EMG signals were sampled at 2048 Hz, full‐wave rectified and smoothed with a 6 Hz low pass filter. The skin was shaved and marked (with a dot from a permanent marker) prior to bipolar integral dry reusable electrode (Biometrics SX230; Biometrics Ltd.) placement with a fixed inter‐electrode distance of 2 cm. Care was taken not to place electrodes directly over a biopsy site in the case that the biopsy‐induced oedema impaired motor unit recruitment or EMG signal. The average for each phase of each repetition was modelled with a second order polynomial regression equation, and a fast Fourier transformation was performed on each 250 ms window to calculate mean power frequency (MnPF). The peak EMG amplitude (EMG amp ) of the second repetition of each set is referred to as the ‘initial EMG amp ’. Similarly, the peak EMG amp of the last repetition of each set is referred to as ‘final EMG amp ’. The integrated (or total) EMG is the area under the curve throughout each set. The initial EMG amp , final EMG amp and integrated EMG were calculated as %MVE for each muscle (VL, VM and ST). MVE was measured each trial day during the initial isometric knee extension (VL and VM) and leg curl (ST) MVCs. MnPF and average EMG of the second repetition of each set (initial MnPF and initial average EMG) and the last repetition of each set (final MnPF and final average EMG) were also calculated. Muscle glycogen and fibre‐type histochemistry Muscle tissue from each biopsy was mounted in OCT media, frozen in liquid nitrogen‐cooled isopentane and stored in a −80 °C freezer until analysis. Cross‐sections were cut 5 µm thick using a Microm HM550 Cyrostat (Thermo Fisher Scientific, Waltham, MA, USA) with particular care taken not to expose samples to any freeze‐thaw cycles (Fairchild & Fournier, 2004). Fibre type‐specific glycogen depletion was quantified by combining a brightfield periodic acid‐Schiff stain (PAS), as described previously (McManus, 1948; Gollnick et al. 1973; Gollnick et al. 1974a, 1974b; Vollestad et al. 1984; Vollestad & Blom, 1985; Robergs et al. 1991; Koopman et al. 2006; Cumming et al. 2014), with a immunofluorescent myosin heavy chain (MHC) stain (Bloemberg & Quadrilatero, 2012; Morton et al. 2016; Jakubowski et al. 2019) on single cross‐sections similar to the methodology described elsewhere (Schaart et al. 2004). Briefly, cross‐sections were fixed using 3.7% formaldehyde in PBS for 60 min, treated with 1% periodic acid in distilled water for 5 min (#3951; Sigma‐Aldrich, Toronto, ON, Canada), rinsed in tap water, stained with Schiff's reagent for 15 min (#3952016; Sigma‐Aldrich), rinsed with distilled water and then rinsed in PBS prior to fluorescence staining. For fluorescence immunohistochemistry, antibodies raised against dystrophin [MANDYS1 (3B7)], MHC I (BA‐F8), MHC IIA/X (SC‐71) and MHC IIX (6H1) (Developmental Studies Hybridoma Bank, Iowa City, IA, USA) were combined with secondary isotype‐specific antibodies [488 (A‐21131), 594 (A‐21125) and 647 (A‐21238)] (Alexa Fluor, Thermo Fisher Scientific) before they were mounted with Prolong Diamond Antifade Reagant (Life Technologies, Toronto, ON, Canada) (Bloemberg & Quadrilatero, 2012). Each slide included muscle sections from a single participant within a single day (e.g. slide 1: pre, 80R and 30R; slide 2: pre, 30S and 80S) and all staining was performed within a period of 2 weeks in batches of three to five slides per day. One day after each stain cross‐sections were imaged (brightfield before fluorescence, similar to a previous study; Schaart et al. 2004) with a CoolSNAP HQ2 fluorescence camera (Nikon Instruments, Melville, NY, USA) at 20× magnification with the exposure times: 400 ms (FITC), 100 ms (TRITC) and 200 ms (Cy5). Muscle glycogen and fibre type analyses Fibre type, cross‐sectional area and glycogen content were determined by tracing the fibre dystrophin border in ImageJ, version 2 (NIH, Bethesda, MD, USA). Each trace was converted to a region of interest (ROI) and saved before being superimposed to another image of interest (i.e. brightfield or another fluorescence channel). Quantification of PAS intensity was determined by first converting the image to a greyscale image and then calibrating the stain to 0.68 µm pixel–1. In addition, by setting thresholds for background vs. stain intensity, we excluded the quantification of freezing‐induced artefact from each ROI on every channel. To quantify fibre type, the intensity of each colour within each ROI was exported alongside the brightfield data for objective quantification of type I and type II fibres. Only fibres with a circularity >0.85 were used for analyses and care was taken not to circle any fibres along the outside of the cross‐section. An average of 275 ± 167 and 191 ± 126 fibres per section (1322 ± 400 and 896 ± 350 fibres per participant) were used for the fibre type/PAS and cross‐sectional area analysis, respectively. The tracer was blinded to both the participant and conditions during the image analysis. Western blot analysis Muscle samples were homogenized using RIPA buffer (#R0278; Sigma‐Aldrich) and a bead homogenizer with protease and phosphatase inhibitors (#05892970001 and 04906837001; Sigma‐Aldrich). A bicinchoninic acid assay (#23227; Thermo Fisher Scientific) was performed on the whole muscle homogenate to quantify the protein content of each sample. Samples were prepared in Laemmli buffer (#1610747; Bio‐Rad, Hercules, CA, USA) with beta‐mercaptoethanol (M6250; Sigma‐Aldrich) and brought to equal concentrations of 20 µg µL–1. SDS‐PAGE was performed on 7.5 µL per sample along with two 7.5 µL prestained protein standards (#1610375; Bio‐Rad) and a calibration curve (2.5, 5, 7.5 and 10 µL of all post‐training samples pooled) on 26‐well gels (4‐15% Criterion TGX Stain‐Free, #5678085; Bio‐Rad). As a quality check for protein separation along the gel, the gel was imaged by ultraviolet activation with the Chemidoc MP StainFree Imager (Bio‐Rad) before it was transferred to a nitrocellulose membrane via a Trans‐Blot Turbo Transfer System (Bio‐Rad) at 100 V for 30 min in 4°C transfer buffer (25 mm Tris, 192 mm glycine, 0.1% SDS and 20% methanol, pH 8.3). Transfer success was visualized with ultraviolet activation of both the gel and membrane via a Chemidoc MP StainFree Imager (Bio‐Rad). Nitrocellulose membranes were blocked in BSA for 2 h, washed three times for five minutes with Tris‐buffered saline‐Tween 20 (TBST), cut into specific sections according to the molecular weights of our protein targets, and incubated in primary antibodies at 4°C with the 5% BSA block at concentrations between 1:500 and 1:1500 (depending on the affinity of the primary antibody). The primary antibodies we used were total mTOR (#2972), phosphorylated mTOR (Ser2448; #5536), total p70 S6k (#9202), phosphorylated p70 S6k (Thr389; #9205), total 4E‐BP1 (#9452), phosphorylated 4E‐BP1 (Thr37 and Thr46; #2855), total S6 ribosomal protein (#2217), phosphorylated S6 ribosomal protein (Ser240 and Ser244; #2211), total AkT (#4691), phosphorylated AkT (Ser473; #9271), total FAK (#13009), phosphorylated FAK (Tyr397; #8556), total p44/42 MAPK ERK1/2 (#9102) and phosphorylated p44/42 MAPK ERK1/2 (Thr202 and Tyr204; #9101), which were all obtained from Cell Signaling Technologies (Danvers, MA, USA). After an overnight incubation, membranes were washed again three times for 5 min in TBST, incubated in secondary antibody (dilution 1:20,000; anti‐rabbit, HRP‐linked; #7074; Cell Signaling Technologies) for 1 h at room temperature, washed another three times in TBST, rocked for 5 min in ECL substrate (Clarity Max; #1705062; Bio‐Rad) and then imaged on the ChemiDoc MP (Bio‐Rad). The ladder was imaged in colourmetric mode and the proteins of interest were measured in chemilumescence mode. All image analysis was performed in ImageLab, version 5.2.1 (Bio‐Rad). Each gel lane was calibrated to the gel lanes of our calibration curve and each protein band was calibrated to the protein bands of our calibration curve as described elsewhere (Murphy & Lamb, 2013; MacInnis et al. 2017). Afterwards, the calibrated protein band was divided by the calibrated gel lane to quantify absolute protein band intensity.

Deactivate Facebook Account on Mobile App – How To Disable Facebook Account Temporarily 2019 // Are you looking to take a break from social media? Maybe you just from some time away from Facebook and want to temporarily deactivate your facebook profile. In this step by step help guide I will help you disable your account.

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--- abstract: 'I show that a particle structure in conformal field theory is incompatible with interactions. As a substitute one has particle-like exitations whose interpolating fields have in addition to their canonical dimension an anomalous contribution. The spectra of anomalous dimension is given in terms of the Lorentz invariant quadratic invariant (compact mass operator) of a conformal generator $R_{\mu }$ with pure discrete spectrum. The perturbative reading of $R_{0\text{ }}$as a Hamiltonian in its own right i.e. associated with an action in a functional integral setting naturally leads to the AdS formulation. The formal service role of AdS in order to access CQFT by a standard perturbative formalism (without being forced to understand first massive theories and then taking their scale-invariant limit) vastly increases the realm of conventionally accessible 4-dim. CQFT beyond those for which one had to use Lagrangians with supersymmetry in order to have a vanishing Beta-function.' author: - | Bert Schroer\ presently CBPF, Rua Dr. Xavier Sigaud, 22290-180 Rio de Janeiro, Brazil\ email: schroer@cbpf.br\ Prof. emeritus of the Institut für Theoretische Physik\ FU-Berlin, Arnimallee 14, 14195 Berlin, Germany date: 'May 9, 2000' title: Particle versus Field Structure in Conformal Quantum Field Theories --- A few introductory remarks ========================== Ideas about the use of conformal quantum field theory entered particle physics for the first time at the height of the Kramers-Kronig dispersion relations [@Kastrup]. They were met with reactions ranging from doubts to outright rejection and the subject lay dormant for another 10 years when it reemerged on the statistical mechanics side in connection with second order phase transitions. In the next section we will show that these early doubts of the old-time particle physicists were partially justified, because the particle structure in CQFT is indeed incompatible with interactions. However far from supplying a coffin nail for its utility in high energy physics, this no-go theorem also contains the message that one must use finer concepts in order preserve the usefulness of conformal quantum field theory as a theoretical laboratory for particle physics. There are massive particle-like objects (“infraparticles” [@Bu]) which have a continuous mass distribution with an accumulation of spectral weight at $p^{2}=m^{2}$ whose generating local fields have an anomalous non-integer (non-semi-integer in the case of Fermion fields) contribution to their long distance behavior. In a CQFT long and short distance behavior coalesce and the accumulation of spectral weight at $p^{2}=0\,$ which becomes related to the anomalous dimension of operators is the vestige of the particle interaction in the massive parent theory from which the CQFT arose by taking the scale-invariant limit. This structure is the collective effect of a total collapse of all multiparticle thresholds on top of each other. The standard LSZ large time scattering limit does not commute with this scaling limit, in fact the LSZ limit of such fields vanishes. It is believed that in order to re-extract from such a situation anything which resembles particle physics one has to apply a more general form of scattering theory [@Bu] which is based on expectation values and probabilities for inclusive cross sections (where outcoming “stuff” below a prescribed energy-momentum resolution is not registered) rather than on amplitudes. But it is presently not clear how one can achieve this. In the case of infraparticles (the electron in QED which is inexorably linked to its photon-cloud) where one also meete a situation of coalescing thresholds, this generalized scattering theory is known to be very useful [@Bu]. Recently there has been a quite different and conceptually[^1] less ambitious but formally quite attractive idea which promises to strengthen the utility of CQFT for particle physics and which is presented in the third section. It basically consists in finding a theory which radically reprocesses the spacetime interpretation and degrees of freedom of CQFT in such a way that now the “energy momentum vector” $R_{\mu }$ of the Dirac-Weyl compactified world $\bar{M}$ becomes the bona fide energy momentum instead of $P_{\mu }$ which in standard canonical or functional terminology means that $R_{\mu }$ is the one related to an action and not $P_{\mu }$. If one insists that this total reshuffling of physical interpretation should leave the basic mathematical building blocks (a certain generating set of algebras and the symmetry group structure) untouched, then there is only one answer: an associated anti De Sitter (AdS) theory [@Wit]. The nontrivial reprocessing leads to a mathematical isomorphism as described in [@Reh1] i.e. it goes far beyond that picture about the AdS-CQFT correspondence which is limited to the (infinitely remote) boundary of AdS (see in particular the remarks at the end of [@Reh2]). The AdS appearance of the AdS structure as a kind of reprocessed CQFT is less surprizing if one recalls the 6-dimensional lightcone formalism which one uses in order to obtain an efficient description of the conformal compactification $\bar{M}$ of Minkowski space $M $ and the construction of its covering $\tilde{M}$ [@Schroer]. In this way one obtains a (perturbative) new constructive non-Lagrangian access to CQFT which opens a new window into the realm of CQFT beyond those few 4-dimensional Lagrangian candidates for which one had to use a combination of gauge theory with supersymmetry. This means that one has no guaranty that the conformal side at all permits a description in terms of an action. Particle Structure and Triviality ================================= We start with recalling an old theorem which clarifies the relation between the particle-versus-field content of conformal field theories. To be more precise the following statement is a result of the adaptation of a combination of several theorems [@BF][@Pohl] The existence of one-particle states in conformally invariant theories forces the associated interpolating fields to be canonical free fields. The only particle-like structures consistent with interactions are hidden in the structure of those interpolating fields which have anomalous dimensions and whose mass spectrum is continuous with an accumulation of weight at $p^{2}=0,\,\,p_{0}>0.$ The easiest way to get a first glimpse at this situation is to look at conformal two-point functions $$\left\langle \psi (x)\psi ^{\ast }(y)\right\rangle =\left\{ \begin{array}{c} c\frac{1}{-\left( x-y\right) ^{2}},\,\,dim\psi =1 \\ c(\frac{1}{-\left( x-y\right) ^{2}})^{d_{\psi }},\,\,dim\psi =d_{\psi }>1 \end{array} \right. \label{an}$$ In the first case the application of the LSZ large time scattering limit yields $$\left\langle \psi (x)\psi ^{\ast }(y)\right\rangle =\left\langle \psi _{in}(x)\psi _{in}^{\ast }(y)\right\rangle$$ which preempts the equality $\psi =\psi ^{in}=\psi ^{out},$ whereas in the anomalous case the large distance fall-off is too strong in order to be reconcilable with the mass shell structure of a zero mass particle which means $$\psi (x)\overset{LSZ}{\rightarrow }0$$ It is worthwhile to reconsider the argument which leads to the absence of interaction in the space created by the interpolating field $\psi .$ The crucial observation is that the presence of a zero mass scalar particle state vector $\left| p\right\rangle $ with $$\left\langle p\left| \psi \right| 0\right\rangle \neq 0$$ forces $\psi $ to have a two-point function with a canonical scale dimension dim$\psi =1.$ The special feature of conformal invariance is that this implies that the two-point function is free i.e. $$\left\langle 0\left| \psi ^{\ast }(x)\psi (y)\right| \right\rangle =c\frac{1}{\left[ -(x-y-i\varepsilon )\right] ^{2}}$$ Such a conclusion relating canonical short distance dimension with absence of interactions cannot be drawn in the massive case. However the following theorem which was proven in the late 50$^{ies}$ by Jost and the present authors, and can be found in [@St-Wi], holds for both cases: The freeness of the $\psi $ two-point function implies the field $\psi $ to be a free field in Fock space. The guiding idea is to show that a localized operator or pointlike field which vanishes on the vacuum, vanishes automatically on all states i.e. is the zero operator. This is a consequence of the Reeh-Schlieder theorem [@St-Wi] which in conformal field theory is also known under the name state-field relation). It says that the operators from a region with a nontrivial causal complement (or fields smeared with test functions with support in such a region) act cyclically on the vacuum (and on any other finite energy state). If we denote by $\mathcal{A}(\mathcal{O})$ either the polynomial $^{\ast }$-algebra of unbounded smeared fields with supports of testfunctions in $\mathcal{O}$ or the affiliated bounded operator algebra, this cyclicity property reads $$\overline{\mathcal{A}(\mathcal{O})\Omega }=\mathcal{H}$$ where the bar denotes the closure and $H$ is the Hilbert space generated by all fields (bosonic and fermionic). Since (for fermionic $\psi $ there will be a change of sign) $$\psi (x)\mathcal{A}(\mathcal{O})\Omega =\mathcal{A}(\mathcal{O})\psi (x)\Omega$$ if we choose $O$ spacelike with respect to $x,$ the vanishing of the “current” $j(x)=(\partial _{\mu }\partial ^{\mu }+m^{2})\psi (x)$ on the vacuum implies the vanishing on the dense set $\mathcal{A}(\mathcal{O})\Omega $ and hence (operators in physics are closable) on all $\mathcal{H}.\,$The next step consists in proving that the commutator of two $\psi s$ on the vacuum is a c-number $$\left( \left[ \psi (x),\psi (y)\right] -i\Delta (x-y)\right) \Omega =0$$ It then follows according to the previous argument that the bracket vanishes identically. We prove this last relation by using the frequency decomposition $\psi =\psi ^{(-)}+\psi ^{(+)}$ (which follows from $j\equiv 0) $ in the commutator $$\left[ \psi (x),\psi (y)\right] \Omega =(\left[ \psi ^{(+)}(x),\psi ^{(+)}(y)\right] +\psi ^{(-)}(x),\psi ^{(+)}(y)-\psi ^{(-)}(y),\psi ^{(+)}(x))\Omega$$ where we omitted all annihilation terms. The on-shell creation with subsequent on-shell annihilation as in the last two terms and the physical spectrum condition only admits the vacuum as its energy momentum content and therefore they yield a c-number which, by a finite renormalization of $\psi $ if necessary, yields $$(\psi ^{(-)}(x),\psi ^{(+)}(y)-\psi ^{(-)}(y),\psi ^{(+)}(x))\Omega =i\Delta (x-y)\mathbf{1}\Omega$$ Since this and the full commutator is causal, the first term on the right hand side has to vanish all by itself. But on the other hand it is the separate Fouriertransform of momenta which lie on the forward mass shell and hence it is the boundary value of an analytic function in two complex 4-vectors of the form $z=\xi -i\eta ,\eta $ from the forward light cone. However an analytic function which vanish on an open set on its boundary vanished identically (generalized Schwartz reflection principle). The resulting relation on the vacuum holds according to the previous arguments for the operators and therefore we obtained the characterizing relation for a free field. The generalization to any spin including half-integer values is now a routine matter. A closer look at the zero mass situation reveals that contrary to the massive case where the difference of two on-shell vectors is either spacelike or zero, the difference of two lightlike vectors may in addition be lightlike but this only happens for parallel vectors. Since this special configurations should not matter in the sense of L$^{2}$-integrability of zero mass particle wave functions one again expects at least for $d>1+1$ the above result. However a mathematical proof of this result turned out to be quite nontrivial [@Pohl]. It is very helpful to place the above theorem into the setting of a more general theorem relating interactions and particle properties in general local quantum physics which states that operators localized in sub-wedge regions in interacting theories which possess nontrivial matrix elements between vacuum and one-particle states necessarily show the phenomenon of vacuum polarization i.e. operators which create polarization-free one-particle states exist only in interaction free field theories. Polarization-free-generators (PFG) which create pure one-particle states from the vacuum do however exist in any QFT if their localization region is a semi-infinite wedge region or larger [@Essay][@BBS]. Since in conformal theories the wedge region is conformally equivalent to a compact double cone, a conformal one-particle structure according to this more general theorem is only possible in conformal free field theories. The above argument is typical for a real-time structure which cannot be unraveled in the euclidean formulation. Trying to make the best out of it ================================= The negative result on the compatibility of zero mass particle structure with nontriviality of conformal theories should not be misread as an incompatibility with an intuitive idea about what constitutes particle-like excitations. The point here is that conformal theories in particle physics should be considered as the zero mass (scaling) limits of massive theories with mass gaps for which the LSZ scattering theory can be derived. In the scaling limit all the multiparticle thresholds in momentum space coalesce on top of each other and build up the possibly anomalous dimension. In this limit the Wigner particle theory (irreducible representation of the Poincaré group) and with it the prerequisite of the LSZ scattering theory gets lost in the presence of interactions, a fact which we have demonstrated above where it was shown that the field is either free or the LSZ limits are zero. So the right question would be: can one think of a more general scattering theory which may recuperate some of the lost structure in the aforementioned collapse of multiparticle cuts on top of each other? There is indeed another particle concept (“infraparticle”) which goes together with a generalized scattering theory build on inclusive scattering probabilities instead of amplitudes [@Bu]. This concept is expected to distinguish those anomalous dimensional fields which are of relevance in particle physics (which originate from the previous collapse in the scaling limit) from mere mathematical constructs as e.g. generalized free fields with anomalous dimensions. But we think that for the problem at hand, namely the formulation of a theory of anomalous dimension, we do not need to enter this deep and difficult issue of particle-like interpretation since here we restrict our interests in conformal theories as a simplified theoretical laboratory for field- and algebra- aspects and not for the study of particles and their scattering theory. We believe that the setting of local observable algebras which fulfill in addition to Einstein causality also Huygens principle for timelike distances [@Sch] contains all scale limits of theories which are of interest for particle physics and that interaction in this setting is characterized by the appearance of charge-carrying fields with anomalous dimensions. In view of the above No-Go theorem we will consider the noncanonical (anomalous dimension) nature of those fields as our pragmatic definition of interaction in this conformal setting. But we defer this analysis to a following longer paper which contains the relevant mathematical machinery [@Sch]. As a consequence the observable algebra of an interacting conformal field theory (conserved currents etc.) should not have the structure of composites of free fields (e.g. free currents) since otherwise the fields carrying the superselected charges may not have anomalous dimensions. Apart from normalization constants the 2- and 3-point functions of conformal observable fields (currents) are indistinguishable from those formed with free composites with the same integer dimensions. If all correlations would be indistinguishable from those of free composites (total protection) then also the charge-carrying fields associated with such observables can be shown to be free. A weak form of what in the case of conformal SYM theories has been called (partial) “protection” would be one where the relative normalization between 2-and 3-point functions is that of free composites (partial protection). Apparently perturbative supersymmetry causes partial protections [@prot]. Although such models hardly represent realistic particle physics, they are the only *Lagrangian* candidates for d=1+3 nontrivial conformal field theories and may yet turn out to be the first 4-dimensional mathematically completely controllable models. The interest and fascination in conformal field theories originates to a large part from the well-founded belief that the simplest nontrivial 4-dimensional conformal field theories which will break the age old existence deadlock[^2] for nontrivial quantum field theories in physical spacetime. For this one wants to have as much protection as possible without ending with a free conformal theory. Instead of entering an ambitious program in order to extract the particle physics “honey” from CQFT which requires a heavy conceptual investment in the area of a generalized scattering theory, there is another way which is more faithful to the formal aspects with which QFT is often identified (erroneously in my opinion, if one uses them for a definition of QFT) namely canonical formalism and/or functional integrals. It starts from the observation that in addition to the translation generator $P_{\mu }$ there is another translation-analogue described by a Lorentz-vector $R_{\mu }.$ It has a timelike purely discrete spectrum and the L-invariant “mass” $m_{c}$ with $m_{c}^{2}=R_{\mu }R^{\mu }$ plays a similar role as the rigid rotation operator $L_{0}$ in chiral theories. In fact it describes a generalized rotation around the Dirac-Weyl compactified Minkowski space $\bar{M}\simeq S^{3}\times S^{1}.$ Therefore it is not surprising that the bottom of the spectrum of $m_{c}$ is the anomalous part of the scaling dimension common to a whole equivalence class of fields which carry the same superselected charge. But despite all analogies to $P_{\mu }$ this operator is not related to an imagined functional integral action of CQFT. Nevertheless one can ask the question: is there a theory whose Lagrangian can be associated with a Hamiltonian interpretation of $R_{0}?$ In order for this new theory to be useful for particle physics it should keep the same algebraic and group-theoretical building blocks as CQFT i.e. one seeks a mathematical isomorphism which goes hand in hand with that total physical reprocessing which is necessary to accomplish such an impossible looking task. The unique answer is the AdS-CQFT correspondence [@Wit] which was proven to be a such a “radical” isomorphism [@Reh1]. Although this step does not completely answer the question posed at the beginning of how to extract and analyze the particle content of CQFT, it goes a long way to open up conformal field theory as a genuine theoretical laboratory for particle physics. And last not least it facilitates the unsolved problem number one: find a nontrivial physically relevant (i.e. one which fits at least the conceptual framework of local quantum physics, even if it falls short in describing nature) and mathematically controllable model in 4-dimensional QFT. The presented arguments suggest strongly that there exists a whole world of non-Lagrangian non-supersymmetric CQFT (in the sense that they cannot be accessed in the standard perturbative way) besides the Lagrangian SYM family. In fact the perturbative calculations in the literature already give some support in this direction. This is most visible in [@Ruehl] although these authors, evidently under the strong spell of the string-theoretic origin of the AdS-CQFT, do not interprete their calculations from this viewpoint. The possible non-Lagrangian nature of most CQFT is in a certain way explained by Rehren’s deep observation [@Reh1][@Reh2] that due to the isomorphic nature of the AdS-CQFT relation there must be degrees of freedom on the conformal side which cannot be described in terms of local fields namely those which originate from the AdS bulk (and not from the boundary) and which are necessary in order to return $CQFT\rightarrow AdS$. This leaves the interesting question of what should one make of the original observation by which the protagonists of the AdS-CQFT correspondence found this relation which is the relation between two Lagrangian field theories namely the conformal SYM model with some form of AdS supergravity [@Wit]. Since this is based on consistency checks within string theory which owes its widespread acceptance to perturbative mathematical consistency and a kind of globalized social contract but certainly not to its harmonious coexistence with the principles underlying particle physics, there is reason for some scepticism; in particular because such degrees of freedom would be easily overlooked in perturbative calculations on the CQFT side. It cannot be overstressed that this correspondence is very different and much more radical then those which arise from a different choice of  “field coordinates”. It is impossible to understand its full content in terms of pointlike physical fields. Some concluding remarks ======================= If, as argued in this letter, the AdS theories are a useful new calculational tool which open up CQFT to particle physics studies within the standard Lagrangian quantization framework, than perhaps with an additional conceptual investment one could directly understand the structure underlying the anomalous dimension spectra within CQFT i.e. without the described reprocessing on the AdS side. This turns out to be true and will be the subject of a subsequent paper [@Sch] since the necessary conceptual investment does not fit the format of a letter like this. *Acknowledgements*: I am indebted to Detlev Buchholz and Karl-Henning Rehren for a helpful exchange of emails. Furthermore I would like to thank Francesco Toppan for interesting questions which helped in shaping the presentation. [99]{} H.A. Kastrup, Ann. Physik 7, (1962) 388 J. Maldacena, Adv. Theor. Math. Phys. **2 (**1998**)**, 231 S.S. Gubser, I. R. Klebanov and A.M. Polyakov, Phys. Lett. **B448**, (1998) 253 E. Witten, Adv. Theor. Math. Phys. **2** (1998) 253 D. Buchholz, “Mathematical Physics Towards the 21st Century”, Proceedings Beer-Sheva 1993, Ben Gurion University Press 1994 K-H Rehren, “Algebraic Holography”, hep-th/9905179 K-H Rehren, “Local Quantum Observables in the Anti-deSitter - Conformal QFT Correspondence”, hepth/0003120 D. Buchholz and K. Fredenhagen, JMP **18**, Vol.5 (1977) 1107 K. Pohlmeyer, Commun. Math. Phys. **12**, (1969) 201 R.F. Streater and A.S. Wightman, *PCT, Spin and Statistics and all That*, Benjamin 1964 B. Schroer, “Facts and Fictions about Anti de Sitter Spacetimes with Local Quantum Matter”, hep-th/9911100 B. Schroer, “Particle Physics and QFT at the Turn of the Century: Old principles with new concepts, (an essay on local quantum physics)”, Invited contribution to the Issue 2000 of JMP, in print, to appear in the June issue H-J Borchers, D. Buchholz and B. Schroer, “Polarization-Free Generators and the S-Matrix”, hep-th/0003243 B. Schroer, “A Theory of Anomalous Scale-Dimensions”, hep-th/0005134 for example: J. Erdmenger, M. Perez-Victoria, “Non-renormalization of next-to-extremal correlators in N=4 SYM and the AdS/CFT correspondence” and literature quoted therein L. Hoffmann, A.C. Petkou and W. Ruehl, “Aspects of Conformal Operator Product Expansion in AdS/CFT Correspondence”, hep-th/0002154 [^1]: The attribute “conceptually” here refers to the local quantum physical aspects and not to differential-geometric ones. [^2]: In any area of Theoretical Physics there always have been plenty of nontrivial mathematically controllable illustrations which demonstrate the nontrivial physical content of the conceptual basis of those areas, not so in 4-dim. QFT. This annoying totally singular situation has been sometimes overemphasized at the cost of practical calculations, but most of the time it went totally ignored.

/** * *************************************************************************** * Copyright (c) 2010 Qcadoo Limited * Project: Qcadoo MES * Version: 1.4 * * This file is part of Qcadoo. * * Qcadoo is free software; you can redistribute it and/or modify * it under the terms of the GNU Affero General Public License as published * by the Free Software Foundation; either version 3 of the License, * or (at your option) any later version. * * This program is distributed in the hope that it will be useful, * but WITHOUT ANY WARRANTY; without even the implied warranty * of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. * See the GNU Affero General Public License for more details. * * You should have received a copy of the GNU Affero General Public License * along with this program; if not, write to the Free Software * Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA * *************************************************************************** */ package com.qcadoo.mes.technologies.tree.builder.api; import com.qcadoo.mes.technologies.tree.builder.TechnologyTreeBuilder; /** * Abstraction for technology tree's operation node * * @author Marcin Kubala * @since 1.2.1 */ public interface TechnologyOperationComponent extends EntityWrapper { /** * Set custom field value. You should not set basic tree fields such as parent, children, in/out product components, operation * or entityType. The {@link TechnologyTreeBuilder} will deal with them for you. * * @param name * @param value */ void setField(final String name, final Object value); }

Per AppleInsider, Apple on Tuesday introduced AppleCare+ for iPhone, a new extended warranty service that combines traditional tech support, software support, and hardware support with the addition of the company’s first accidental damage plan. Like the traditional $US69 version of AppleCare for iPhone that it replaces, the new US$99 AppleCare+ for iPhone extends an iPhone’s repair coverage and technical support to two years from the original purchase date but also adds coverage for up to two incidents of accidental damage due to an owner’s poor handling of the device. Each accidental damage incident is subject to a US$49 service fee and is available only for the iPhone and its original included accessories. In turn, Apple promises that the replacement equipment it provides to customers taking advantage of the “may be new or equivalent to new in both performance and reliability” (meaning either a new iPhone or a certified refurbished one). AppleCare+ also bundles standard AppleCare features, such as software troubleshooting and telephone-based technical support, while also offering customers with repair needs the option for mail-in or carry-in repairs, and an express replacement service. iPhones that exhibit defects in materials, workmanship or see their battery charge fall by 50 percent or more from original specification, remain eligible for a replacement from Apple at no cost under the new plan. Apple also notes that customers must purchased AppleCare+ together with their new iPhone, with the safest bet being to have both items appear on the same receipt (fine print). For Apple, the new service marks the first time that company has offered accidental coverage for drops, spills, and other incidents caused by the owner. Previously, iPhone customers seeking full coverage of their device were left to seek out pricey third-party alternatives that sell for the same price or more. Replacement costs for an out-of-contract iPhone can cost hundreds to replace new or US$200 previously though Apple’s Out-of-Warranty Service. Yes. You can purchase a replacement iPhone from the Apple Online Store, an Apple Retail Store, or your carrier’s store. Your price will depend on whether you qualify for a carrier subsidy. You can also purchase an unlocked iPhone from the Apple Online Store or Apple Retail Store and obtain a micro-SIM card directly from your supported GSM carrier. When I buy from the Apple Online Store, does my iPhone come ready to use? Yes, if you have selected a mobile phone carrier. When your iPhone arrives, all you have to do is turn it on and follow the onscreen instructions to set it up. There’s no need to call the carrier or visit a store to complete the activation. If you have selected an unlocked GSM phone, you will need to acquire a micro-SIM from the supported GSM carrier of your choice and activate it in order to use your iPhone.” Information in a footnote on both that page and the iPhone 4S tech specs page further suggests the iPhone 4S will be available unlocked: For those who are not qualified customers, are not eligible for an early upgrade, are purchasing an unlocked iPhone (for supported GSM wireless service provider networks only), or wish to buy an iPhone as a gift, see your carrier, an Apple Retail Store Specialist, the Apple Online Store, or an Apple Authorized Reseller for pricing. No official pricing info for unlocked iPhone 4S models is available yet, though the 8 GB iPhone 4, available for US$99 with a 2-year contract, costs $549 without a contract. Extrapolating from the iPhone 4’s pricing suggests the following pricing scheme for unlocked models: – A “Siri” feature will allow you to give spoken commands (such as “What will the weather be like today?” to the device). – Siri will allow you to reply to texts while the device is in a pocket and will allow for a reply text with a Bluetooth headset. – Siri’s interface is both onscreen as well as audio, the feature being hardware-dependent and running on the iPhone 4S only. – Siri will apparently read a text message to you and ask you questions as to how you’d like to reply. – Siri can do dictations for emails too, the app placing a microphone next to the space bar in the keyboard. The app will start as a beta in the U.S., U.K., Australia, French and German with more languages and services coming. – The iPhone 4S apparently features an identical screen size to the current iPhone 4. – And now, your long-awaited pricing and capacities for the iPhone 4S: 16GB for US$199, 32GB for US$299 and 64 GB for US$399. – The iPhone 3G can now be purchased new for US$49. – Sprint has now been added to the list of iPhone wireless carriers along with AT&T and Verizon. – Pre-orders for the iPhone 4S begin Friday, October 7th. – The iPhone 4S will be released on Friday, October 14th. – The iPhone 4S will be available in 22 additional countries on October 28th and reach 70 countries by the end of 2011. Per iPhone-Ticker.de, Apple’s iPhone 4S has recently appeared in the inventory list for Vodafone’s German division. The device was spotted in listings for various iPhone accessories on the mobile carrier’s website. The listing includes both white and black models of the iPhone 4S in 16, 32, and 64 GB capacities. These sizes and colors match perfectly with one expectation for the next generation iPhone model. Fortunately, we only have to wait about 24 hours to find out whether Apple is releasing either the iPhone 4S, the iPhone 5 or both. With all of one day to go prior to its much-anticipated iPhone media announcement, an iTunes beta is telling more than it should about Apple’s forthcoming product line. Per AppleInsider, references to the much-used “iPhone 4S” moniker could be found in the Info.plist file of the MobileDevices bundle that was included with the ninth beta of iTune 10.5 released on Friday. The discovery can be seen as further evidence that Apple is gearing up to introduce iPhones next Tuesday, Oct. 4th that bundle an 8MP camera, 512MB of RAM, support for HSPA+ and the iPad 2’s A5 processor and dual graphics, but do so in a the current CMDA iPhone 4 design. However, the new iPhone 4S is expected to be a dual-mode phone, meaning the same iPhone 4S can be used on either CDMA or GSM networks. Currently, Apple markets separate iPhone 4 models for CDMA and GSM networks. Talk of Apple taking a dual-route strategy this year by releasing both an iPhone 4S and a more advanced iPhone 5 began to cool off this week, with leaked parts and casings all pointing to a product dubbed iPhone 4S. In addition, insider Ming-Chi Kuo reported that his industry checks turned up no sign of a redesigned iPhone 5 in the pipeline. Instead, he stated that Apple was manufacturing a model that looks largely the same as the current iPhone 4, only with an improved antenna design. Dubbed “N94,” the new iPhone model will reportedly also use the same Gorilla glass for its back panel. Kuo also said it will be available in both black and white models at launch, and 60 percent of units assembled so far have been of the black variety. Echoing a report from earlier this month, he also said that Foxconn will be responsible for manufacturing 85 percent of Apple’s fifth-generation iPhone units. The other 15 percent will reportedly be assembled by Pegatron. Each will run iOS 5, which is rumored to bundle new voice recognition technology in the form of a new application dubbed Assistant, which will allow users to speak to their iPhone and accomplish a number of tasks through natural language, like sending text messages, looking up information, or scheduling an appointment. The functionality is believed to stem from Siri, a “personal assistant” application for the iPhone that Apple purchased in April of 2010. Per MacRumors, a picture showing iPhone 5 cases entered into the carrier’s inventory system, more evidence has emerged that AT&T has begun stocking third-party iPhone 5 cases days before Apple is expected to unveil its next handset. An alleged store employee at an AT&T retail store sent to MacRumors photos of newly arrived silicone sleeves for the as-yet-unannounced “iPhone 5.” The product appears to be a low-end generic case, as it carries no distinguishable brand, is simply labeled “cell phone accessory” and comes in oversized packaging. The sleeve features a tapered design with the mute switch on the right side of the device, resembling purported iPhone 5 cases that have proliferated in China for months. However, the publication took care to note that the cases run against the “growing feeling that Apple may not be releasing such a device” because of recent evidence suggesting that Apple’s design for its next iPhone may be “nearly identical to the iPhone 4.” Earlier on Thursday, a leaked photo allegedly of AT&T’s inventory system surfaced, showing entries for iPhone 5 hard case, soft case and skin products from Case-Mate. The case maker had previously posted its case designs on its website, but took them down shortly after they went up. Anticipation for the next-generation iPhone reached a fever pitch after Apple sent out invitations to an event next Tuesday, Oct. 4, with the tagline “Let’s talk iPhone.” The tagline has prompted renewed speculation that Apple will include voice recognition features on its fifth-generation smartphone. The next iPhone is widely believed to feature the A5 processor found in the iPad 2 and an 8-megapixel camera. There has been some disagreement, however, about whether Apple will introduce a redesigned iPhone 4 in addition to a new model. It had been suggested that Apple was looking to release a cheaper iPhone 4S alongside the iPhone 5, but recent reports have poured cold water on the rumor. A series of purporting to be the structural case design for a revamped, cheaper new iPhone 4 indicate changes in its antenna design. The images, published by MacRumors and iPatchiPods, appear to show a unibody frame without case seams on the top or either side of the top of the phone. Existing GSM iPhone 4 models sold by AT&T and other global carriers have a single seam on the top, while the Verizon CDMA model has two seams on either side of the top end. The seams separate the external edge of the iPhone 4 into antenna segments; the GSM model has two antennas (one for mobile use and one for WiFi/Bluetooth/GPS, as shown below) while the CDMA model has three (dual mobile antennas required in the CDMA specification and a WiFi/Bluetooth/GPS segment). The modified case also incorporates a SIM card, something that only the existing GSM version of the current iPhone 4 has or needs. It’s not yet known whether the anticipated new cheaper iPhone 4 (sometimes referred to as the “iPhone 4S”) will be dual band, allowing it to work on both major mobile network types. It is expected that the separate iPhone 5 model, bearing an original new design, will support both networks. The primary feature of the new iPhone 4 phone design is expected to be its reduced cost, achieved through the use of streamlined components and a smaller 8GB of storage capacity. A similarly purported “iPhone 5” prototype case design appeared in January, similarly lacking seams on the top two sides, instead bearing a single seam on the top. The report also portrays a bottom frame segment that appears to lack a defined Home button, suggesting that Apple may change the appearance and design of the Home button on the phones it releases later this fall. Interestingly enough, it’s the upcoming cases that tend to provide the most interesting tidbits. Per UK web site MobileFun.co.uk, a leaked schematic claimed to be for a case for Apple’s anticipated fifth-generation iPhone shows a larger area for the home button, a slightly larger screen, and the return of curved sides like on the iPhone 3GS. The documents allegedly come from a Chinese case manufacturer and show a design with curved sides, similar to iPhone models released before the current iPhone 4. On the front, the case appears to have a larger, oval-shaped opening for where the device’s home button would go. That could lend support to rumors from earlier this year that Apple’s next-iPhone would feature a multi-touch “gesture area” in place of the current home button. That same report also predicted that Apple’s next iPhone would have a slightly larger 3.7-inch edge-to-edge screen. The images that claim to show a so-called “iPhone 5” case also suggest that the device may have a larger screen. The photos show the handset’s volume buttons and SIM card slot in the same place, but also show placement of the vibrate switch on the opposite side. The case also suggests the device will feature an unmoved LED camera flash, which would contradict purported fifth-generation iPhone parts (1, 2), which leaked in May and suggested the camera lens and flash would be moved further apart to improve picture quality. Separating the camera flash and lens can reduce the red-eye effect seen in photographs. The alleged schematic would contradict other rumors that the next iPhone will have a design largely similar to the current iPhone 4, with one of the biggest changes being a new, higher-resolution 8-megapixel camera and the addition of the A5 processor. Some reports have characterized the device as an “iPhone 4S,” in references to the alleged minor changes. Though the next iPhone will arrive later than usual this year, reports from Apple’s supply chain have been picking up, indicating that the company is preparing to begin mass production of the next-generation device. Last week, during the company’s quarterly earnings conference call, Apple executives revealed that an unnamed major product transition is in the cards to take place by the end of September. Stay tuned for additional details as they become available and let us know what’s on your mind in the comments. The time to the iPhone 5’s release is apparently now two months and counting. Per Digitimes, Apple is rumored to have ordered 15 million iPhone 5 units from Taiwanese notebook manufacturer Pegatron Technology has received orders for 15 million units from Apple. The company has declined to comment on the report. Pegatron produced somewhere in the region of four million iPhone 4s for Apple in the first quarter of 2011, though due to a slump in iPhone 4 sales this figure was well down on the 10 million it had prepared to manufacture. The shipping date won’t come as a surprise to industry-watchers: Apple traditionally holds a music-themed event in September and rumours that the next-generation iPhone would be announced then strengthened after no new iPhone was revealed during June’s Worldwide Developer Conference. However, the reports do seem to contradict earlier information from Morgan Stanley analyst Katy Huberty that suggested iPhone 5 production would not begin until mid- to late August. Digitimes reports that the iPhone 5 “does not seem to have any major update from iPhone 4” and refers to it as the iPhone 4S at one stage in the article. Meanwhile, the same outlet reports that production of touch sensors for the iPad 2 has reached five million a month.

Significance of unilateral ear extinction on the dichotic listening test. The association between unilateral ear extinction on the dichotic listening test and the lateralization of epileptogenic foci was examined in a sample of 49 seizure patients undergoing preoperative evaluation for epilepsy surgery. Results from patients who were left hemisphere dominant for speech indicated that right ear impairment was always predictive of a unilateral left hemisphere focus, but left ear extinction was associated with unilateral lesions of either hemisphere. In this patient sample, dichotic listening performance reflected an interaction of both lateralized foci and hemispheric preference of language processing. Implications concerning clinical use of the dichotic listening test are discussed.

As I entered my 15th year of teaching young children and supporting adult learners, I found myself searching for answers. Answers to why CLASS implementation was so difficult, why teacher buy-in was such a challenge, and why long-term improvement seemed impossible. In my role as the Director of Curriculum and Instruction, I’m constantly checking the data. Data drives instruction, instruction drives learning, learning drives comprehension, and comprehension equals success! It’s been a great year. You have just conducted some professional development trainings for the group of teachers you are coaching. You got the opportunity to visit their classrooms and see them in action, do formal and informal CLASS observations, and had countless coaching conversations. You see that it’s all beginning to click. You have the teachers’ buy-in, and the motivation is high. Empowering and equipping coaches with the information and resources they need to mentor also empowers the teachers they're coaching. Check out these coaching resources that discuss how to provide feedback based on CLASS data, how to prepare teachers for a CLASS observation, and much more. I lived in rural Japan for three years. While there, I became very accustomed to ordering the same types of entrees at restaurants due to my limited ability to read menus and my unwillingness to eat foods outside my comfort zone. So imagine how overwhelmed I felt when I returned to the States and had to decide on one entree amid pages and pages and pages of delicious options. It took a few weeks to learn how to navigate my way through these endless options without wanting to close my eyes and blindly point while ordering my meals. As a CLASS Group Coaching (MMCI) instructor, the sections of any given two-hour session may feel, at times, very goal driven. These sections titled "Know," "See," and "Do” are interconnected. In particular, it is possible to consider "Do" within "Know," and "See." When an instructor supports in-the-moment experiences that connect new knowledge to current practice, they make the CLASS dimensions more relevant to the educators' daily work. But how can we infuse more “Do” into “Know” and “See?” First, let's re-cap what happens in each section. "I’ve just begun my journey into the world of coaching. I am eager and excited about this opportunity to help pave the way for more effective teaching. I’ve recently been given my list of classrooms that I will be working with and I’m anxious to get started. I get ready to meet my first teacher, Ms. Linda, and I just know that she will be excited to meet me and we will form an instant bond and work together for the benefit of the children in that classroom. Being an instructional coach or mentor is difficult. Sometimes it may feel like you don't have any support—especially when it comes to providing effective feedback to the teachers you work with. Have you, as a coach, ever asked yourself any of the following questions? CLASS Specialists are always thinking about the complexity of the CLASS tool as we prepare for our trainings. As a trained CLASS observer, I am comfortable observing and recognizing quality interactions that fit in the tool. But I needed a strategy to convey this information to those who may not be as familiar with the tool. As it turns out, using an analogy is a perfect way to make the complex relatable, less overwhelming, and more familiar to our participants.

GP retention - a creative approach. Given that about 46% of general practitioners in Australia are aged over 55 years and a recent survey indicated that 35% of the GPs in one state were considering early retirement, strategies aimed at GP retention are of particular importance to the current Australian health system.

Q: How to stop sending $_FILES['name'] if nobody provides thefile? I Have a multipart/form-data form but I not require from users to send me the picture. I am changing the name of the file to random number and the put the path to MySQL. Whenever somebody doesn't put the file, in my database a new recor is beeing created without an extension(obviesly). How to stop this from happening? Sorry for my english. Here is a a part from the code: case 'Sleep Aid': { ?> <section class="summarySection"> <div class="summaryHeadingDIV"> <h1 class="summaryH1">Please check the details below</h1> </div> <article class="summaryPage"> <p class="boldSummaryDescr">Brand:</p><p class="paraSummary"><?php echo $brand; ?></p><br> <p class="boldSummaryDescr">Model:</p><p class="paraSummary"><?php echo $model; ?></p><br> <p class="boldSummaryDescr">Colour:</p><p class="paraSummary"><?php echo $colour; ?></p><br> <p class="boldSummaryDescr">Material:</p><p class="paraSummary"><?php echo $material; ?></p><br> <p class="boldSummaryDescr">Suitable Age:</p><p class="paraSummary"><?php echo $suitable; ?></p><br> <p class="boldSummaryDescr">Purchase date:</p><p class="paraSummary"><?php echo $month . '/' . $year; ?></p><br> <p class="boldSummaryDescr">Condition:</p><p class="paraSummary"><?php echo $condition; ?></p><br> <p class="boldSummaryDescr">Dimesions:</p><p class="paraSummary"><?php echo $width . ' cm <span class="smallcaps">x</span> ' . $height . ' cm <span class="smallcaps">x</span> ' . $depth . ' cm'; ?></p><br> <p class="boldSummaryDescr">Weight:</p><p class="paraSummary"><?php echo $weight . ' kg'; ?></p> </article> <div class="imageg_container"> <figure class="img_figure_show"> <?php if(empty($picture)) { ?> <img src="/_images/no-picture.png" alt="no picture added"> <?php } else { $random_id = rand_img_id(); add_file(db_user_connect(), $email, $random_id); $arry = show_picture(db_user_connect(), $email, $random_id); print "<img src=".$arry["sciezka"]." alt='product picture'>"; } ?> </figure> </div> <div class="clear-left"></div> <div class="summaryButtonContainer"> <a href="javascript:goBack();" class="summaryLinks" title="Go Back">Edit details</a> <a href="/_pages/transaction/quotation.php?location=sleepaid&brand=<?php echo urlencode($brand);?>&model=<?php echo urlencode($model)?>&month=<?php echo urlencode($month);?>&year=<?php echo urlencode($year);?>&condition=<?php echo urlencode($condition);?>" class="summaryLinks">Proced to Quote</a> </div> </section> <?php break; } A: You need to check the $_FILES['error'] value: if ($_FILES['name']['error'] === UPLOAD_ERR_OK) ... The manual lists all possible values, which you could use to display different messages/do different things: https://secure.php.net/manual/en/features.file-upload.errors.php

Q: Can I make my desktop background active? I want my desktop background to look like the Chrome extension, Currently. How would I accomplish this? A: I can give you similar conky script but no 100%. You need to change the font, alignment and icon set. Result Step 1. Install conky sudo apt-get install conky Step 2. Install conky forecast sudo add-apt-repository ppa:conky-companions/ppa sudo apt-get update && sudo apt-get install conkyforecast Step 3. Save at home folder .conky1 .conky2 .weather-ob .conkyForecast.config Step 4. Open .conky2 and locate --location=MYXX0006 Replace MYXX0006 with you location code. You can find your code here Step 5. Run your conky By terminal: conky -c ~/.conky1 conky -c ~/.conky2 Make startup application Open startup application Name : Conky1 Command : conky -p 20 -c ~/.conky1 Name : Conky2 Command : conky -p 20 -c ~/.conky2

Q: Woo Commerce - Offer to register at checkout (don't force) As the title says, is there anyway I can allow a customer to register at checkout. The ideal situation would be to get their shipping and billing address included in the registration at the same time they enter it for the actual purchase. However, I don't want to force the customer to register if they don't really want to. A: I don't know which version of woocommerce you have, but certainly the latest vesion let's you set if customer's can create an account at checkout, or if they can check out without account (guest checkout). These settings are all in: woocommerce/settings/accounts & privacy tab

Description of Metopiellus painensis sp. nov. (Coleoptera, Staphylinidae), first troglobitic Pselaphinae from Brazil. Metopiellus painensis new species, of the Neotropical pselaphine tribe Metopiasini, is described from Pains region, Brasil (Minas Gerais). Major diagnostic features are illustrated and a key to the known species is given.

Percutaneous mitral valve repair using the edge-to-edge technique: six-month results of the EVEREST Phase I Clinical Trial. This study sought to evaluate the clinical results of a percutaneous approach to mitral valve repair for mitral regurgitation (MR). A surgical technique approximating the middle scallops of the mitral leaflets to create a double orifice with improved leaflet coaptation was introduced in the early 1990s. Recently, a percutaneous method to create the same type of repair was developed. A trans-septal approach was used to deliver a clip device that grasps the mitral leaflet edges to create the double orifice. General anesthesia, fluoroscopy, and echocardiographic guidance are used. A 24-F guide is positioned in the left atrium. The clip is centered over the mitral orifice, passed into the left ventricle, and pulled back to grasp the mitral leaflets. After verification that MR is reduced, the clip is released. Twenty-seven patients had six-month follow-up. Clips were implanted in 24 patients. There were no procedural complications and four 30-day major adverse events: partial clip detachment in three patients, who underwent elective valve surgery, and one patient with post-procedure stroke that resolved at one month. Three additional patients had surgery for unresolved MR, leaving 18 patients free from surgery. In 13 of 14 patients with reduction of MR to < or =2+ after one month, the reduction was maintained at six months. Percutaneous edge-to-edge mitral valve repair can be performed safely and a reduction in MR can be achieved in a significant proportion of patients to six months. Patients who required subsequent surgery had elective mitral valve repair or intended replacement.

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SBWS Services Consumers are notoriously impatient and mobile browsers of content are no exception. In fact they expect instantaneous response from any website that they encounter. There are many factors that website ... Read more..

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--- abstract: 'We study the fine scale $L^{2}$-mass distribution of toral Laplace eigenfunctions with respect to random position, in $2$ and $3$ dimensions. In $2$d, under certain flatness assumptions on the Fourier coefficients and generic restrictions on energy levels, both the asymptotic shape of the variance is determined and the limiting Gaussian law is established, in the optimal Planck-scale regime. In $3$d the asymptotic behaviour of the variance is analysed in a more restrictive scenario (“Bourgain’s eigenfunctions"). Other than the said precise results, lower and upper bounds are proved for the variance, under more general flatness assumptions on the Fourier coefficients.' address: - | IW: Department of Mathematics\ King’s College London\ Strand\ London WC2R 2LS\ England, UK - | NY: Department of Mathematics\ King’s College London\ Strand\ London WC2R 2LS\ England, UK author: - Igor Wigman - Nadav Yesha title: CLT for Planck scale mass distribution of toral Laplace eigenfunctions --- Introduction ============ Given a smooth compact $d$-manifold ${\mathcal{M}}$ we are interested in the spectral properties of the Laplace-Beltrami operator $\Delta$ on ${\mathcal{M}}$. It is well-known that the eigenvalue spectrum of $\Delta$ is purely discrete, i.e., the set of numbers $E$ admitting a solution to the Helmholtz equation $$\Delta \phi + E\phi = 0$$ is a sequence $\{E_{j}\}_{j\ge 1}$ of numbers ordered with multiplicity in a non-decreasing order such that $ E_j \to \infty $. We denote the corresponding sequence $\{\phi_{j} \}_{j\ge 1}$ of (real-valued) eigenfunctions constituting an orthonormal basis of the square-integrable functions $L^{2}({\mathcal{M}})$ on ${\mathcal{M}}$; the sequence $\{\phi_{j} \}_{j\ge 1}$ is uniquely determined up to the spectral degeneracies (i.e., up to orthogonal transformations in each eigenspace of dimension $\ge 2$). Shnirelman’s Theorem and Small-Scale Equidistribution ----------------------------------------------------- Assuming w.l.o.g. that ${\mathcal{M}}$ is unit volume ${\operatorname{Vol}}({\mathcal{M}})=1$, the celebrated Shnirelman’s Theorem  [@Sn; @Ze; @CdV] asserts that if ${\mathcal{M}}$ is chaotic (i.e., the geodesic flow on $ \mathcal{M} $ is ergodic), then “most" of the $\{\phi_{j}\}$ are $L^{2}$-equidistributed. In particular, they are equidistributed in position space, i.e., there exists a density $1$ sequence $j_{k}$ such that for all “nice" domains ${\mathcal{A}}\subseteq{\mathcal{M}}$ we have $$\label{eq:L2 mass phi->A/M} \lim\limits_{k\rightarrow\infty}\int\limits_{{\mathcal{A}}}\phi_{j_{k}}(x)^{2}dx= {\operatorname{Vol}}({\mathcal{A}}).$$ Beyond Shnirelman’s Theorem, Berry’s universality conjecture  [@Berry1; @Berry2] implies that for a [*generic*]{} chaotic manifold holds for ${\mathcal{A}}$ shrinking with $k$, slower than the Planck’s scale $E_{j_{k}}^{-1/2}$. More precisely, it states that there exists a density $1$ sequence $\{j_{k}\}_{k}$ so that if $r_{0}(E):{\mathbb{R}}_{> 0}\rightarrow{\mathbb{R}}_{> 0}$ satisfies $r_{0}(E)\cdot E^{1/2}\rightarrow\infty$ diverging arbitrarily slowly, then, for $B_{x}(r)$ the radius $r$ geodesic ball in ${\mathcal{M}}$ centred at $x$, we have $$\label{eq:|mass-exp|=o(r^d)} \left|\int\limits_{B_{x}(r)}\phi_{j_{k}}(y)^{2}dy - {\operatorname{Vol}}(B_{x}(r)) \right| = o_{k\rightarrow\infty} (r^{d})$$ uniformly for all $x\in{\mathcal{M}}$ and $r>r_{0}(E_{j_{k}})$, i.e., $$\label{eq:L2mass shrinking uniform} \sup\limits_{\substack{x\in{\mathcal{M}}\\ r>r_{0}(E_{j_{k}})}} \left|\frac{\int\limits_{B_{x}(r)}\phi_{j_{k}}(y)^{2}dy}{{\operatorname{Vol}}(B_{x}(r))} - 1\right| \rightarrow 0.$$ The following recent results are rigorous manifestations of the small-scale (“shrinking balls") statement . Luo and Sarnak  [@Luo-Sarnak Theorem 1.2] established the small-scale equidistribution for Laplace eigenfunctions on the modular surface (assuming in addition that they are Hecke eigenfunctions) where $r>E^{-\alpha}$ with a small $ \alpha>0 $, and Young [@Young], conditionally on GRH, refined this estimate for $r>E^{-1/6+o(1)}$ holding for *all* such eigenfunctions. Hezari and Rivière  [@Hezari-Riviere1], and independently Han  [@Han1] established the equidistribution for Laplace eigenfunctions on manifolds of negative curvature on logarithmic scale (i.e., $r>(\log{E})^{-\alpha}$, for some $\alpha>0$), and Han  [@Han2] considered random Laplace eigenfunctions on “symmetric" manifolds, of high spectral degeneracy; here the higher the spectral degeneracy is the smaller the allowed scale is. More recently, Han and Tacy [@HanTacy] proved small-scale equidistribution for random Gaussian combinations of eigenfunctions on compact manifolds for $ r>E^{-1/2+o(1)} $, and de Courcy-Ireland [@DeCourcyIreland] showed that, with high probability, the $L^{2}$-mass of random Gaussian spherical harmonics is, up to a small error, equidistributed, slightly above Planck scale. Toral Laplace eigenfunctions ---------------------------- For the $d$-dimensional torus ${\mathbb{T}}^{d}={\mathbb{R}}^{d}/{\mathbb{Z}}^{d}$, $d\ge 2$, there are high spectral degeneracies; in this case Lester and Rudnick  [@LeRu Theorem 1.1] proved that the small-scale equidistribution is satisfied by a generic Laplace eigenfunction (also considered by Hezari and Rivière  [@Hezari-Riviere2]). More precisely, they showed that every o.n.b. $\{\phi_{j}\}$ admits a density one subsequence $\{\phi_{j_{k}}\}$ of Laplace eigenfunctions obeying , with $r_{0}(E)=E^{-\alpha(d)}$, where $\alpha(d)$ is any number smaller than $$\label{eq:alpha(d) LeRu} \alpha(d)<\frac{1}{2(d-1)},$$ an (almost) optimal Planck-scale result for $d=2$, yet somewhat weaker than Berry’s conjecture for $d> 2$. One can express the real toral Laplace eigenfunctions explicitly as a sum of exponentials $$\label{eq:fn sum exp} f_{n}\left(x\right)=\sum_{\lambda\in\mathcal{E}_{n}}c_{\lambda}e\left(\left\langle x,\lambda\right\rangle \right), \hspace{10pt} (c_{-\lambda}=\overline{c_\lambda})$$ for $$\label{eq:S_d} n\in S_{d}:=\{n=a_{1}^{2}+\ldots +a_{d}^{2}:\: a_{1},\ldots,a_{d}\in{\mathbb{Z}}\}$$ expressible as a sum of $d$ integer squares, and the corresponding frequencies $\lambda$ are the standard lattice points $$\label{eq:E_n} {\mathcal{E}}_{n} = {\mathcal{E}}_{d;n}=\{\lambda\in{\mathbb{Z}}^{d}:\: \|\lambda\|^{2}=n\}$$ lying on the $(d-1)$-dimensional sphere (a circle for $ d=2 $) of radius-$\sqrt{n}$; in this case the energy is $E=E_{n}=4\pi^{2}n$. We will assume w.l.o.g. that $f_{n}$ is $L^{2}$-normalised, equivalent to $$\label{eq:BasicNormalization} \|f_{n}\|_{L^{2}({\mathbb{T}}^{d})}^{2} = \sum_{\lambda\in\mathcal{E}_{n}}\left|c_{\lambda}\right|^{2}=1.$$ For every $ n\in S_d $, denote $$\label{eq:N} N=N_{d;n}=\#\mathcal{E}_n.$$ When $d=2$, by Landau’s theorem, $ \left\{ n\le x:\,n\in S_{2}\right\} \sim K\frac{x}{\sqrt{\log x}} $ where $ K>0 $ is the “Landau-Ramanujan constant". On average $N=N_{2;n}$ is of order of magnitude $\sqrt{\log n}$; however, for a density one sequence in $S_{2}$ we have $ N=\left(\log n\right)^{\log2/2+o\left(1\right)}. $ In general, for $n\in S_{2}$ we have $$N=n^{o\left(1\right)}.$$ For $d=3$, Siegel’s theorem asserts that for $n\not\equiv0,4,7\,\left(8\right)$, $$N=N_{3;n}=n^{1/2+o\left(1\right)};$$ since $x\mapsto2^{a}x$ is a bijection between the solutions to $x_{1}^{2}+x_{2}^{2}+x_{3}^{2}=n$ and $x_{1}^{2}+x_{2}^{2}+x_{3}^{2}=4^{a}n$, we can always assume that $n\not\equiv0,4,7\,\left(8\right)$ with no loss of generality. Granville and Wigman  [@GranvilleWigman Theorem 1.2] refined the aforementioned estimate by Lester-Rudnick for $d=2$. They proved that in this case, is valid slightly above Planck-scale $r_{0}(E)=E^{-1/2+o(1)}$, for [*all*]{} eigenfunctions $f_{n}$ as in , corresponding to numbers $n$ so that the lattice points ${\mathcal{E}}_{n}$ are well-separated (“Bourgain-Rudnick sequences"), a condition satisfied  [@Bourgain-Rudnick Lemma 5] by “generic" integers $n\in S_{2}$ in a strong quantitative sense, subsequently refined in  [@GranvilleWigman Theorem 1.4], see section \[sec:quasi corr\]. Averaging mass w.r.t. ball centre --------------------------------- For both the $2$-dimensional and the higher-dimensional tori it is possible to construct exceptional examples of sequences of toral eigenfunctions where the equidistribution condition is not satisfied: for $d\ge 2$ thin sequences  [@LeRu Theorem $3.1$] $\{\phi_{j_{k}}\}$ of eigenfunctions violating condition at Planck-scale $r \cdot E_{j_{k}}^{1/2} \rightarrow \infty$, around the origin $x=0$, and even stronger, for $d\ge 3$  [@LeRu Theorem $4.1$ (construction by J. Bourgain)] eigenfunctions violating with $r \gg E^{-\alpha(d)}$ where $\alpha(d)> \frac{1}{2(d-1)}$, again around the origin $x=0$. In these cases, rather than keeping the ball centre $x=0$ at the origin, one may vary $x$, and study whether the “typical" discrepancy on the l.h.s. of is [*small*]{}, even if the existence of $x$ so that the l.h.s. of is [*not small*]{} is known, so that, in particular, is not satisfied. A natural way to vary $x$ is to think of $x$ as [*random*]{}, drawn uniformly in ${\mathbb{T}}^{d}$. We define the random variable $$\label{eq:X_RV} X_{f_{n},r}=X_{f_{n},r;x}:= \int\limits_{B_{x}(r)}f_{n}(y)^{2}dy,$$ and are interested in the distribution of $X_{f_{n},r}$ where $x$ is drawn randomly uniformly in ${\mathbb{T}}^{d}$. The relevant moments are: expectation $$\label{eq:Expectation} {\mathbb{E}}[X_{f_{n},r}] = \int\limits_{{\mathbb{T}}^{d}}X_{f_{n},r;x}dx,$$ higher centred moments $$\label{eq:centred moments} {\mathbb{E}}[(X_{f_{n},r}-{\mathbb{E}}[X_{f_{n},r}])^{k}] = \int\limits_{{\mathbb{T}}^{d}}\left(X_{f_{n},r;x}-{\mathbb{E}}[X_{f_{n},r}]\right)^{k}dx, \hspace{1em}k\ge2,$$ and in particular the variance $$\label{eq:Variance} {\mathcal{V}}(X_{f_{n},r}) = {\mathbb{E}}[(X_{f_{n},r}-{\mathbb{E}}[X_{f_{n},r}])^{2}].$$ This approach of averaging the $L^{2}$-mass with respect to the ball centre (and keeping $f_{n}$ fixed) was pursued by Granville-Wigman  [@GranvilleWigman] in the $2$-dimensional case, again slightly above the Planck scale $r>E^{-1/2+o(1)}$. In this regime, by proving an upper bound for ${\mathcal{V}}(X_{f_{n},r})$ beyond $({\mathbb{E}}[X_{f_{n},r}])^{2} = O(r^4)$, valid for [*all*]{} $n\in S_{2}$, under some flatness assumption on $f_{n}$ (cf. Definition \[def:ultraflat\] below), they established for [*“typical"*]{}, if [*not all*]{} $x\in{\mathbb{T}}^{2}$. It would be desirable to find a regime where it is possible to analyse the precise asymptotic behaviour of the variance ${\mathcal{V}}(X_{f_{n},r})$ of $X_{f_{n},r}$, and, if possible, determine the limit distribution law for $X_{f_{n},r}$; our principal results below achieve both of these in the $2$-dimensional case, and the former in the $3$-dimensional one (see theorems \[thm:VarMain\] and \[thm:Var3D\]). Such an approach of bounding the discrepancy variance while averaging over ball centres was recently used by Sarnak  [@Sa] for mass distribution of forms on symmetric spaces, and P. Humphries  [@Humphries] for mass distribution of automorphic forms. Statement of the main results for $d=2,3$: asymptotics for the variance, CLT ---------------------------------------------------------------------------- Our principal results below are applicable to “flat" functions for $d=2,3$, understood in suitable, more and less restrictive, senses. For example, “Bourgain’s eigenfunction" [@Bourgain] $$\label{eq:BourgainEF} f_{n}\left(x\right)=\frac{1}{\sqrt{N}}\sum_{\lambda\in\mathcal{E}_{n}}\varepsilon_{\lambda}e\left(\left\langle x,\lambda\right\rangle \right)$$ with $\varepsilon_{\lambda}=\pm1$ for every $\lambda\in\mathcal{E}_{n}$, i.e. corresponding to $\left|c_{\lambda}\right|=N^{-1/2},$ satisfies any of the flatness conditions in the most restrictive sense. Denote ${\mathcal{B}}_{n}$ to be the class of Bourgain’s eigenfunctions. Our first principal result determines the precise asymptotic behaviour of the variance ${\mathcal{V}}(X_{f_n,r})$ for the $2$-dimensional case, and moreover asserts that the moments of the standardized random $L^{2}$-mass of $f_{n}$ are asymptotically Gaussian; we subsequently deduce a Central Limit Theorem (see Corollary \[cor:CLT\_result\]). For the sake of elegance of presentation, it is formulated for Bourgain’s eigenfunctions ; below we formulate a more general result which holds for a larger class of flat eigenfunctions (see Theorem \[thm:VarMainGeneralized\] in section \[sec:statement results strong\]), and later a result where the averaging over the ball centre $x$ is itself restricted to shrinking balls (Theorem \[thm:VarMainExplRestricted\] in section \[sec:RestrictedAverages\]). \[thm:VarMain\] There exists a density one sequence $S_{2}'\subseteq S_{2}$ so that the following holds. Let $r_{0}=r_{0}\left(n\right)=n^{-1/2}T_{0}\left(n\right)$ with $T_{0}\left(n\right)\to\infty $. 1. Fix a number $\epsilon>0$, and suppose that $ T_0(n) < \left(\log n\right)^{\frac{1}{2}\log\frac{\pi}{2}-\epsilon} $. Then as $n\to\infty$ along $S_{2}'$ we have $$\label{eq:var asympt d=2 Bourgain} {\mathcal{V}}\left(X_{f_{n},r}\right)\sim\frac{16}{3 \pi}r^{4}T^{-1}$$ uniformly for all $$\label{eq:r0<r<n^-1/2*discr} r_{0} < r <n^{-1/2}\left(\log n\right)^{\frac{1}{2}\log\frac{\pi}{2}-\epsilon}$$ and $ f_n \in {\mathcal{B}}_{n} $, where $T:=n^{1/2}r.$ 2. Under the above notation let $$\label{eq:standardizedX} \hat{X}_{f_{n},r}:=\frac{X_{f_{n},r}-{\mathbb{E}}[X_{f_{n},r}]}{\sqrt{{\mathcal{V}}\left(X_{f_{n},r}\right)}}$$ be the standardized random $L^{2}$-mass of $f_{n}$, $r_{1}=r_{1}(n)=n^{-1/2}T_{1}\left(n\right)$, and suppose further that the sequence of numbers $T_{1}(n)>T_{0}(n)$ satisfies $T_{1}(n)=O\left(N^{\xi}\right)$ for every $\xi>0$. Then for all $k\ge 3$ the $k$-th the moment of $\hat{X}_{f_{n},r}$ converges, for $n\rightarrow\infty$ along $S_{2}'$, to the standard Gaussian moment $$\label{eq:moments Gaussian lim} {\mathbb{E}}[\hat{X}_{f_{n},r}^{k}] \rightarrow {\mathbb{E}}[Z^{k}],$$ uniformly for $r_{0}<r<r_{1}$ and $ f_n \in {\mathcal{B}}_{n} $, where $Z\sim N(0,1)$ is the standard Gaussian variable. The claimed uniform asymptotics of the variance means explicitly that, as $n\rightarrow\infty$ along $S_{2}'$, one has $$\label{eq:var unif asymp d=2} \sup\limits_{\substack{r_0 < r < \left(\log n\right)^{\frac{1}{2}\log\frac{\pi}{2}-\epsilon} \\ f_n \in {\mathcal{B}}_{n}}} \left|\frac{{\mathcal{V}}\left(X_{f_{n},r}\right)}{\frac{16}{3 \pi}r^{4}T^{-1}} - 1\right| \rightarrow 0$$ and the uniform convergence of the moments means that for every $k\ge 3$, $$\sup\limits_{\substack{r_0 < r < r_1 \\ f_n \in {\mathcal{B}}_{n}}} \left|{\mathbb{E}}[\hat{X}_{f_{n},r}^{k}] - {\mathbb{E}}[Z^{k}]\right| \rightarrow 0.$$ Concerning the restricted range in Theorem \[thm:VarMain\] (and ) for the possible radii, it is directly related to a well-known result on the angular distribution of lattice points in ${\mathcal{E}}_{n}$, for generic $n\in S_{2}$. Namely, it was shown  [@ErdosHall] that ${\mathcal{E}}_{n}$, projected by homothety to the unit circle, is equidistributed, and moreover, a quantitative measure for the discrepancy is asserted (see section \[sec:ang distr\] below, and, in particular, ), satisfied by [*generic*]{} $n\in S_{2}$. Bourgain  [@Bourgain] observed that $f_{n}\in {\mathcal{B}}_{n}$, when averaged over $x\in {\mathbb{T}}^{d}$, exhibits Gaussianity in the following sense. Let $T>0$ be a fixed number, and define the scaled function $\varphi_{x}:[-1,1]^{2}\rightarrow{\mathbb{R}}$ around $x$ as $$\label{eq:varphi rand x def} \varphi_{x}(y):= f_{n}\left( x+ \frac{T}{\sqrt{n}}\cdot y\right),$$ i.e. the trace of $f_{n}$ on the side-$2\frac{T}{\sqrt{n}}$ square centred at $x$. It was found  [@Bourgain], that, upon thinking of $x\in{\mathbb{T}}^{2}$ as [*random*]{}, and $\varphi_{x}(\cdot)$ as a [*random field*]{} indexed by $[-1,1]^{2}$, it converges, in a suitable sense, to a particular [*Gaussian*]{} field (“monochromatic isotropic waves") on ${\mathbb{R}}^{2}$, restricted to $[-1,1]^{2}$. This allows one to infer some results on the (deterministic) functions $f_{n}\in {\mathcal{B}}_{n}$ from the analogous results on the limit Gaussian random field. We may then reinterpret the quantitative version of the angular equidistribution of lattice points as allowing the parameter $T$ in to grow as a (positive) logarithmic power of $n$, while still retaining the said asymptotic Gaussianity, also allowing for the comparison between the mass distribution of $f_{n}$ w.r.t. the position and mass distribution of monochromatic isotropic waves. Our intuition regarding the possibility of carrying on the explained “de-randomisation" argument for establishing results of similar nature to the presented results was recently validated by Sartori  [@Sartori]. An application of the standard theory [@Feller §XVI.3 Lemma 2] allows us to infer a uniform Central Limit Theorem for the random variables $\hat{X}_{f_{n},r}$ from the convergence of their respective moments to the Gaussian ones. \[cor:CLT\_result\] In the setting of Theorem \[thm:VarMain\] part (2), the distribution of the random variables $\{\hat{X}_{f_{n},r}\}$ converges uniformly to the standard Gaussian distribution: as $n\rightarrow\infty$ along $S_{2}'$ $${\operatorname{meas}}\{ x\in \mathbb{T}^2:\: \hat{X}_{f_{n},r;x} \le t\} \rightarrow \frac{1}{\sqrt{2\pi}}\int\limits_{-\infty}^{t}e^{-z^{2}/2}dz,$$ uniformly for $t\in{\mathbb{R}}$, $r_{0}<r<r_{1}$ and $ f_n \in {\mathcal{B}}_{n} $. For the $3$-dimensional case, for Bourgain’s eigenfunctions, we only claim precise asymptotic result on $\text{\ensuremath{\mathcal{V}}}\left(X_{f_{n},r}\right)$, the good news being that the claimed results are valid for [*all*]{} energies satisfying the natural congruence assumptions. \[thm:Var3D\] There exists a number $\eta>0$ such that if $r_{0}=r_{0}(n)=n^{-1/2}T_{0}(n)$ with $T_{0}(n)\rightarrow\infty$, then for all $n\not\equiv0,4,7\,\left(8\right)$ we have $$\text{\ensuremath{\mathcal{V}}}\left(X_{f_{n},r}\right)\sim r^{6}T^{-2},$$ uniformly for $r_{0} < r < n^{-1/2+\eta}$ and $ f_n \in {\mathcal{B}}_{n} $. The meaning of the uniform statement in Theorem \[thm:Var3D\] is that $$\sup_{\begin{subarray}{c} r_{0} < r < n^{-1/2+\eta} \\ f_n \in {\mathcal{B}}_{n} \end{subarray}}\left|\frac{\text{\ensuremath{\mathcal{V}}}\left(X_{f_{n},r}\right)}{r^{6}T^{-2}}-1\right|\to0\label{eq:AympVar3D}$$ as $n\to\infty$ along $n\not\equiv0,4,7\,\left(8\right)$, cf. in the $2$-dimensional case. Statement of the main results for $d=2,3$: more general upper and lower bounds {#sec:statement results weak} ------------------------------------------------------------------------------ Let $f_{n}$ be as in , and consider the vector $$\label{eq:v_def} \underline{v}:=(|c_{\lambda}|^{2})_{\lambda \in{\mathcal{E}}_{n}} \in {\mathbb{R}}^{\mathcal{E}_n} $$ of the squared absolute values of its coefficients; we denote its normalised $\ell_{\infty}$-norm $$\label{eq:vnorm inf} [\underline{v}]_{\infty} := N \cdot \max\limits_{\lambda\in{\mathcal{E}}_{n}}|c_{\lambda}|^{2}.$$ \[def:ultraflat\] We say that an eigenfunction $f_{n}$ in is $\epsilon$-ultraflat if its coefficients satisfy $$\label{eq:ultra_flat_cond} [\underline{v}]_{\infty} \le N^{\epsilon}.$$ Denote ${\mathcal{U}}_{n;\epsilon}$ to be the class of $\epsilon$-ultraflat functions. The following couple of theorems establish more general upper and lower bounds on ${\mathcal{V}}(X_{f_n,r})$ in the $2$ and $3$-dimensional cases respectively. \[thm:UpperBound2d\] There exists a density $1$ sequence $S_{2}'\subseteq S_{2}$ and an absolute constant $C>0$ such that for every $ \epsilon>0 $, $ \eta >0 $, $r_{0}=r_{0}(n)=n^{-1/2}T_{0}(n)$ with $T_{0}(n)\rightarrow\infty$ arbitrarily slowly, and $r=n^{-1/2}T>r_{0}$, as $n\to\infty$ along $S_{2}'$ we have $$\label{eq:bounds var ultraflat d=2} T^{-1}N^{-2\epsilon}\ll \frac{{\mathcal{V}}(X_{f_n,r})}{r^{4}} \ll N^{\epsilon}\cdot \left(T^{-1}+(\log{n})^{-\frac{1}{2}\log{\frac{\pi}{2}}+\eta} \right)$$ uniformly for $r_{0} < r< Cn^{-1/2}N^{1-\epsilon}$ and $f_{n}\in {\mathcal{U}}_{n;\epsilon}$, with the constant involved in the “$\ll$"-notation in is absolute for the lower bound, and depends only on $\eta$ for the upper bound. Moreover, the upper bound is valid for the extended range $r > r_{0}$ (with no upper bound on $r$ imposed), and the lower bound is valid for every $ n\in S_2 $. \[thm:UpperBound3d\] There exists a number $\eta>0$ and a constant $C>0$ such that for every $\epsilon>0$, $r_{0}=r_{0}(n)=n^{-1/2}T_{0}(n)$ with $T_{0}(n)\rightarrow\infty$ arbitrarily slowly, $r=n^{-1/2}T>r_{0}$, and $n\not\equiv 0,4,7\,\left(8\right)$ we have $$\label{eq:bounds var ultraflat d=3} T^{-2}N^{-2\epsilon} \ll \frac{{\mathcal{V}}(X_{f_{n},r})}{r^{6}} \ll N^{\epsilon} \left( T^{-2}+n^{-\eta}\right),$$ uniformly for $r_{0} < r < Cn^{-1/2}N^{1-\epsilon}$ and $f_{n}\in {\mathcal{U}}_{n;\epsilon}$, where the constants involved in the “$\ll$"-notation are absolute. Moreover, the upper bound in is valid for the extended range $r > r_{0}$. For Bourgain’s eigenfunctions, the proofs of Theorem \[thm:UpperBound2d\] and Theorem \[thm:UpperBound3d\] yield slightly stronger bounds compared to and , namely $$T^{-1}\ll \frac{{\mathcal{V}}(X_{f_n,r})}{r^{4}} \ll T^{-1}+(\log{n})^{-\frac{1}{2}\log{\frac{\pi}{2}}+\epsilon}$$ for $ d=2 $, and $$T^{-2} \ll \frac{{\mathcal{V}}(X_{f_{n},r})}{r^{6}} \ll T^{-2}+n^{-\eta}$$ for $ d=3 $. Outline of the paper -------------------- The rest of the paper is organised as follows. In section \[sec:statement results strong\] we formulate Theorem \[thm:VarMainGeneralized\], which, on one hand generalizes Theorem \[thm:VarMain\] for a larger class of flat eigenfunctions, and on the other hand, explicates a sufficient condition on $ n\in S_2 $ for its statements to hold; a few examples of application of Theorem \[thm:VarMainGeneralized\], corresponding to different asymptotic behaviour of the variance , are also discussed. Section \[sec:Proof\_Main\_thm\_part1\] is dedicated to giving a proof of the first part of Theorem \[thm:VarMain\] (resp. $1$st part of Theorem \[thm:VarMainGeneralized\]), whereas the second part of Theorem \[thm:VarMain\] (resp. $2$nd part of Theorem \[thm:VarMainGeneralized\]) is proved in section \[sec:Proof\_Main\_thm\_part2\]. Theorem \[thm:Var3D\], claiming the precise asymptotics for the $L^{2}$-mass variance for Bourgain’s eigenfunctions in $3$d, is proved in section \[sec:Proof\_3d\_theorem\]. In section \[sec:ProofOfBoundsThm\] we prove the various upper and lower bounds asserted by theorems \[thm:UpperBound2d\] and \[thm:UpperBound3d\]. A refinement of Theorem \[thm:VarMainGeneralized\], where rather than draw $x$ w.r.t. the uniform measure on the full torus, $x$ is drawn on balls slightly above Planck scale, is presented in section \[sec:RestrictedAverages\], and the additional subtleties of its proof as compared to the proof of Theorem \[thm:VarMainGeneralized\] are highlighted. Finally, section \[sec:AuxLemmasProof\] contains the proofs of all auxiliary lemmas, postponed in course of the proofs of the various results. Acknowledgements {#acknowledgements .unnumbered} ---------------- The authors of this manuscript wish to express their gratitude to J. Benatar, A. Granville, P. Kurlberg, Z. Rudnick, P. Sarnak and M. Sodin for numerous stimulating and fruitful discussions concerning various aspects of our work, and their interest in our research. It is a pleasure to thank the anonymous referee for his comments on an earlier version of this manuscript. The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013), ERC grant agreement n$^{\text{o}}$ 335141. On Theorem \[thm:VarMain\]: CLT for mass distribution, $d=2$ {#sec:statement results strong} ============================================================ In this section we focus on Theorem \[thm:VarMain\]. Our first goal is to formulate a result, that on one hand generalises the statement of Theorem \[thm:VarMain\] to a larger class of eigenfunctions, and, on the other hand, provides a more explicit control over the generic numbers $n\in S_{2}$. To this end we discuss the angular distribution of $\lambda\in{\mathcal{E}}_{n}$ (section \[sec:ang distr\]), and the spectral correlations (section \[sec:quasi corr\]), also used in the course of the proof of the $3$-dimensional Theorem \[thm:Var3D\]; we will be able to formulate Theorem \[thm:VarMainGeneralized\], as prescribed above, by appealing to these. In section \[eq:examples varying theta\] we consider a few scenarios when Theorem \[thm:VarMainGeneralized\] is applicable, prescribing different asymptotic behaviour for the variance . Angular equidistribution of lattice points {#sec:ang distr} ------------------------------------------ For every $\lambda=\left(\lambda_{1},\lambda_{2}\right)\in\mathcal{E}_{n}$, write $\lambda_{1}+i\lambda_{2}=\sqrt{n}e^{i\phi}$, and denote the various angles by $$0\le\phi_{1}<\phi_{2}<\dots<\phi_{N}<2\pi.$$ Recall that the discrepancy of the sequence $\phi_{j}$ is defined by $$\label{eq:Discrepancy_2d} \Delta\left(n\right)=\sup_{0\le a\le b\le2\pi}\left|\frac{1}{N}\cdot \#\left\{ 1\le j\le N:\,\phi_{j}\in\left[a,b\right]\,\text{mod\,}2\pi\right\} -\frac{\left(b-a\right)}{2\pi}\right|.$$ For every $ \epsilon>0 $, we say that $ n\in S_2 $ satisfies the hypothesis $ \mathcal{D}(n,\epsilon) $ if $$\label{eq:D_n_epsilon} \Delta\left(n\right)\le \left(\log n\right)^{-\frac{1}{2}\log\frac{\pi}{2}+\epsilon}.$$ By Erdős-Hall [@ErdosHall Theorem 1], there exists a density one sequence $S_2'(\epsilon)\subseteq S_2 $ such that $ \mathcal{D}(n,\epsilon) $ is satisfied for every $n\in S_2'(\epsilon) $. By a standard diagonalization argument, there exists a density one sequence $ S_2'\subseteq S_2 $ such that $\mathcal{D}(n,\epsilon) $ is satisfied for *every* $ \epsilon>0 $ and $n\in S_2' $ sufficiently large. In particular, the angles $\left\{ \phi_{j}\right\} $ are equidistributed mod $2\pi$ along this sequence, i.e., the lattice points are equidistributed on the corresponding circles. Spectral correlations in $2d$ (and $3d$) {#sec:quasi corr} ---------------------------------------- For $d=2$, while computing the moments of $X_{f_{n},r}$ (e.g. for Bourgain’s eigenfunction ), with $x$ drawn uniformly on the whole of ${\mathbb{T}}^{2}$, one exploits the orthogonality relations $$\int\limits_{{\mathbb{T}}^{2}}e(\langle \lambda , x \rangle)dx = \begin{cases} 0 &\lambda\ne 0 \\ 1 &\lambda=0 \end{cases}$$ for $\lambda\in{\mathbb{Z}}^{2}$ to naturally encounter the length-$l$ spectral correlation problem. That is, for $l\ge 2$ and $n\in S_{2} $ one is interested in the size of the length-$ l $ spectral correlation set $$\label{eq:Sc correlations def} {\mathcal{S}}_{n}(l) = \left\{ (\lambda^{1},\ldots,\lambda^{l})\in({\mathcal{E}}_{n})^{l}:\: \sum\limits_{i=1}^{l}\lambda^{i}=0 \right\},$$ which, by an elementary congruence obstruction argument modulo $ 2 $, is only non-empty for $l=2k$ even. In this case $l=2k$ we further define the [*diagonal*]{} correlations set to be all the permutations of tuples of the form $(\lambda^{1},-\lambda^{1},\ldots, \lambda^{k},-\lambda^{k})$: $$\label{eq:Dc diag def} {\mathcal{D}}_{n}(l) = \left\{ \pi(\lambda^{1},-\lambda^{1},\ldots,\lambda^{k},-\lambda^{k}): \lambda^{1},\ldots,\lambda^{k}\in ({\mathcal{E}}_{n})^{k},\,\pi\in S_{l}\right\}.$$ The set ${\mathcal{D}}_{n}$ is dominated by non-degenerate tuples (i.e. $\lambda^{i}\ne \pm\lambda^{j}$ for $ i\ne j $), hence its size is asymptotic to $$|{\mathcal{D}}_{n}(l)|= \frac{(2k)!}{2^{k}\cdot k!}N^{k}\cdot \left(1 + O_{N\rightarrow\infty}\left( \frac{1}{N} \right) \right).$$ Clearly, ${\mathcal{D}}_{n}(l)\subseteq {\mathcal{S}}_{n}(l)$ so that, in particular ${\mathcal{S}}_{n}(l) \gg N^{l/2}$. To the other end, we have ${\mathcal{S}}_{n}(2) = {\mathcal{D}}_{n}(2)$ by the definition, and both the precise statement $$\label{eq:Zygmund 4-corr} {\mathcal{S}}_{n}(4) = {\mathcal{D}}_{n}(4)$$ (used for the variance computation below) and the bound $$|{\mathcal{S}}_{n}(l)| = O_{N\rightarrow\infty}(N^{l-2})$$ follow from Zygmund’s elementary observation  [@Zygmund]. For $ l=6 $, Bourgain (published in  [@K-K-W]) improved Zygmund’s bound to $$|{\mathcal{S}}_{n}(6)| = o_{N\rightarrow\infty}(N^{4});$$ this was improved  [@BombieriBourgain] to $$|{\mathcal{S}}_{n}(6)| = O_{N\rightarrow\infty}(N^{7/2}),$$ valid for [*all*]{} $n\in S_{2}$. If one is willing to excise a thin sequence in $S_{2}$, then the more striking estimate [@BombieriBourgain] $$|{\mathcal{S}}_{n}(6)| = |{\mathcal{D}}_{n}(6)| + O(N^{3-\gamma}),$$ with some $\gamma >0$, is valid for a density $1$ sequence $S_{2}'\subseteq S_{2}$. More generally [@Bourgain], for every $l\ge 6$ even, there exists a density $1$ sequence $S_{2}'(l)\subseteq S_{2}$ and a number $\gamma_{l}>0$ such that $$\label{eq:corr diag dom l} |{\mathcal{S}}_{n}(l)| = |{\mathcal{D}}_{n}(l)| + O(N^{l/2-\gamma_l})$$ along $n\in S_{2}'(l)$. A standard diagonal argument then yields the existence of a density $1$ sequence $S_2'\subseteq S_{2}$ so that is valid for [*all*]{} even $l\ge 4$. Given an even number $l=2k\ge 2$ we say that a sequence $S_{2}'\subseteq S_{2}$ satisfies the length-$l$ [**diagonal domination**]{} assumption if there exists a number $\gamma=\gamma_l >0$ so that holds. For the $3$-dimensional case under the consideration of Theorem \[thm:Var3D\] the analogous estimates to are required to evaluate the relevant moments of $X_{f_{n},r}$. We define ${\mathcal{S}}_{3;n}$ and ${\mathcal{D}}_{3;n}$ analogously to and respectively, this time the $\lambda^{i}$ are lying on the $2$-sphere of radius $\sqrt{n}$. Unlike the lattice points lying on circles, Zygmund’s argument is not applicable for the $2$-sphere, so that an analogue of is not valid; luckily the asymptotic statement $$\label{eq:3d 4-corr} |{\mathcal{S}}_{3;n}(4)| = |{\mathcal{D}}_{3;n}(4)| + O\left( N^{7/4 +\epsilon} \right),$$ a key input to the variance computation in Theorem \[thm:Var3D\], was recently established  [@BenatarMaffucci]. It was also shown in [@BenatarMaffucci] that the asymptotic diagonal domination for the higher length correlations sets does not hold in the $ 3 $-dimensional case. A more general version of Theorem \[thm:VarMain\], with explicit control over $S_{2}'$ {#sec:VarMainExpl} -------------------------------------------------------------------------------------- We are interested in extending Theorem \[thm:VarMain\] to a larger class of eigenfunctions. To this end, we introduce the following notation: Let $f_{n}$ be an eigenfunction on the $2$-torus corresponding to coefficients $(c_{\lambda})_{\lambda\in{\mathcal{E}}_{n}}$ via , and $\underline{v}\in{\mathbb{R}}^{\mathcal{E}_n}\simeq {\mathbb{R}}^{N}$ as above. 1. Denote $$\label{eq:A4Def} A_{4} = A_{4}(\underline{v}) = N\sum\limits_{\lambda\in{\mathcal{E}}_{n}} |c_{\lambda}|^{4} = N\cdot \|\underline{v}\|^{2}.$$ 2. Given $\lambda\in{\mathcal{E}}_{n}$ let $\lambda_{+}$ be the clockwise nearest neighbour of $\lambda$ on $\sqrt{n}\mathcal{S}^{1}$, and $$\label{eq:BasicVariablesV} V\left(\underline{v} \right):= N\sum_{\lambda\in\mathcal{E}_{n}}\left|\left|c_{\lambda_{+}}\right|^{2}-\left|c_{\lambda}\right|^{2}\right|.$$ 3. Let $$\label{eq:alphaDef} \widetilde{V}(\underline{v}) = \frac{[\underline{v}]_{\infty} \cdot V(\underline{v})}{A_{4}(\underline{v})}.$$ The following Lemma, proved in section \[sec:AuxLemmasProof\], summarizes some basic properties of the quantities in (\[eq:vnorm inf\]), (\[eq:A4Def\]), (\[eq:BasicVariablesV\]) and (\[eq:alphaDef\]): \[lem:BasicVarProp\] We have 1. $1\le A_{4} \le[\underline{v}]_{\infty}.$ 2. $[\underline{v}]_{\infty} \le1+V\left(\underline{v} \right)$. 3. $V\left(\underline{v} \right) \le\widetilde{V}(\underline{v})\le V\left(\underline{v} \right)\left(1+V\left(\underline{v} \right)\right)$. By we have that $$\label{eq:A4<->theta} A_{4} = \cos(\theta)^{-2},$$ where $\theta = \theta_{f_n} = \theta(\underline{v},\underline{v_{0}})$ is the angle between $\underline{v}$ and the vector $\underline{v_{0}}= (\frac{1}{N})_{\lambda\in{\mathcal{E}}_{n}}$ corresponding to Bourgain’s eigenfunctions, hence $ \theta $ reflects the proximity of $f_{n}$ to Bourgain’s eigenfunction; by the first part of Lemma \[lem:BasicVarProp\], the angle $\theta$ is restricted to the interval $ \left[0,\arccos \left(1/\sqrt{N}\right)\right] \subseteq [0,\pi/2) $. Given a sequence $T(n)\rightarrow\infty$ and a sequence $\eta(n)>0$ we define: 1. A sequence $\{{\mathcal{F}}_{1}(n;T(n),\eta(n))\}_{n}$ of families of functions consisting for $n\in S_2$ of all functions $f_{n}$ as in satisfying $$\label{eq:F_1_def}{\mathcal{F}}_{1}(n;T(n),\eta(n)) = \left\{f_{n}:\: \widetilde{V}(\underline{v})< \eta(n) \cdot \frac{T(n)}{\log T(n)} \right\}.$$ 2. A sequence $\{{\mathcal{F}}_{2}(n;T(n),\eta(n))\}_{n}$ of families of functions consisting for $n\in S_2$ of all functions $f_{n}$ as in satisfying $$\label{eq:F_2_def}{\mathcal{F}}_{2}(n;T(n),\eta(n)) = \left\{f_{n}:\: [\underline{v}]_{\infty} < T(n)^{\eta(n)} \right\},$$ where we recall the notation for $[\underline{v}]_{\infty}$. We are now in a position to state the generalized version of Theorem \[thm:VarMain\]: \[thm:VarMainGeneralized\] Let $r_{0}=r_{0}\left(n\right)=n^{-1/2}T_{0}\left(n\right)$ with $T_{0}\left(n\right)\to\infty$, and $\eta(n)>0$ any vanishing sequence $\eta(n)\rightarrow 0$. 1. Fix a number $\epsilon>0$, and suppose that $ T_0(n) < \left(\log n\right)^{\frac{1}{2}\log\frac{\pi}{2}-\epsilon} $. Then, if $S_{2}'\subseteq S_{2}$ is a sequence satisfying $ \mathcal{D}(n,\epsilon/2)$ for all $n\in S_{2}'$, as $n\rightarrow\infty$ along $S_{2}'$, we have $$\label{eq:var asympt d=2 precise} {\mathcal{V}}\left(X_{f_{n},r}\right)\sim\frac{16}{3 \pi \cos^{2}\theta_{f_{n}}}r^{4}T^{-1}$$ with $\theta_{f_{n}}$ as in , uniformly for all $r_{0} < r <n^{-1/2}\left(\log n\right)^{\frac{1}{2}\log\frac{\pi}{2}-\epsilon}$ and $f_{n}\in{\mathcal{F}}_{1}(n;T(n),\eta(n))$, where $T:=T(n)=n^{1/2}r.$ 2. Let $k\ge 3$ be an integer, $r_{1}=r_{1}(n)=n^{-1/2}T_{1}\left(n\right)$, and suppose further that the sequence of numbers $T_{1}(n)>T_{0}(n)$ satisfies $T_{1}(n)=O\left(N^{\xi}\right)$ for every $\xi>0$. Suppose that $S_{2}'\subseteq S_{2}$ is a sequence satisfying the length-$2k$ diagonal domination assumption and the hypothesis $\mathcal{D}(n,\epsilon)$ for all $n\in S_{2}'$. Then the $k$-th the moment of $\hat{X}_{f_{n},r}$ converges, as $n\rightarrow\infty$ along $S_{2}'$, to the standard Gaussian moment $${\mathbb{E}}[\hat{X}_{f_{n},r}^{k}] \rightarrow {\mathbb{E}}[Z^{k}],$$ uniformly for $r_{0}<r<r_{1}$ and $f_{n}\in {\mathcal{F}}_{2}(n;T(n),\eta(n))$ where $Z\sim N(0,1)$ is the standard Gaussian variable. Section \[eq:examples varying theta\] exhibits a few scenarios when Theorem \[thm:VarMainGeneralized\] is applicable; as in these the true asymptotic behaviour of the variance genuinely varies together with $\theta_{f_{n}}$, this demonstrates that $\theta_{f_{n}}$ (and hence $A_{4}$) is the proper flatness measure of $f_{n}$, see also examples \[ex:Bourgain\] and \[ex:flat vs nonflat\]. In the setting of Theorem \[thm:VarMainGeneralized\] part (2), the distribution of the random variables $\{\hat{X}_{f_{n},r}\}$ converges uniformly to the standard Gaussian distribution: as $n\rightarrow\infty$ along $S_{2}'$ $${\operatorname{meas}}\{ x\in\mathbb{T}^2 :\: \hat{X}_{f_{n},r;x} \le t\} \rightarrow \frac{1}{\sqrt{2\pi}}\int\limits_{-\infty}^{t}e^{-z^{2}/2}dz,$$ uniformly for $t\in{\mathbb{R}}$, $r_{0}<r<r_{1}$, and $f_{n}\in {\mathcal{F}}_{2}(n;T(n),\eta(n))$. Some examples of application of Theorem \[thm:VarMainGeneralized\] {#eq:examples varying theta} ------------------------------------------------------------------ \[ex:Bourgain\] Let $ f_n $ be Bourgain’s eigenfunction, so that $ [\underline{v}]_{\infty} =A_4 =1 $ and $ V\left(\underline{v} \right) = \widetilde{V}(\underline{v}) =0 $. For every $ \eta(n)>0,T(n)>1 $ we have $${\mathcal{B}}_{n} \subseteq {\mathcal{F}}_{1}(n;T(n),\eta(n)) \cap {\mathcal{F}}_{2}(n;T(n),\eta(n)).$$ Hence Theorem \[thm:VarMainGeneralized\] implies Theorem \[thm:VarMain\]. The following example exhibits a scenario when an application of Theorem \[thm:VarMainGeneralized\] yields a Central Limit Theorem for $X_{f_{n},r}$, corresponding to asymptotic behaviour of the respective variance ${\mathcal{V}}(X_{f_{n},r})$ which is very different from the behaviour in Theorem \[thm:VarMain\]. \[ex:flat vs nonflat\] Let $\epsilon>0$, $r_{0}$, and $ T_0(n) $ as in Theorem \[thm:VarMainGeneralized\], and $r_{1}= r_1(n)=n^{-1/2} T_{1}(n) > r_{0}$ with $T_{1}(n) \le (\log{n})^{\frac{1}{2}\log{\frac{\pi}{2}}-\epsilon}$. There exists a density $1$ sequence $S_{2}'\subseteq S_{2}$ so that the following holds. Let $t=t(n)\in (0,1)$ be a number satisfying $t(n) \gg \frac{1}{T_{0}(n)^{\xi}}$ for every $\xi>0$, such that $N\cdot t$ is an integer. We choose an ordering $\lambda^{1},\lambda^{2},\ldots \lambda^{N}\in{\mathcal{E}}_{n}$ such that for every $1\le i \le N-1$ we have that $\lambda^{i+1}$ is the (clockwise) nearest neighbour $\lambda^{i+1}=\lambda^{i}_{+}$, and set $$\left(\left|c_{\lambda^{1}}\right|^{2},,\dots,\left|c_{\lambda^{N}}\right|^{2}\right)=(\underset{\begin{subarray}{c} Nt\end{subarray}\text{\,times}}{\underbrace{\left(Nt\right)^{-1},\dots\dots,\left(Nt\right)^{-1}}},0\dots,0).$$ Then $$\label{eq:var asympt nonflat} {\mathcal{V}}(X_{f_{n},r}) \sim \frac{16}{3 \pi}r^{4}t^{-1}T^{-1},$$ uniformly for $r_{0}<r=n^{-1/2}T<r_{1}$, and $f_{n}$ with coefficients $c_{\lambda}$ as above. If, in addition, we have $T_{1}(n)=O(N^{\xi})$ for every $\xi>0$, then the distribution of the standardised random variable $\hat{X}_{f_{n},r}$ converges to standard Gaussian uniformly. Comparing to we observe that the asymptotic behaviour of the variance for the flat and the non-flat functions respectively is genuinely different, provided that we choose $t(n)\rightarrow 0$; we infer that the proposed flatness measure is the natural choice for this problem. One can also generalise Theorem \[thm:VarMain\] as follows: \[cor:VarAsympGen\] Let $\epsilon$, $r_{0}$, $T_{0}(n)$, $r_{1}$ and $T_{1}(n)$ be as in Theorem \[thm:VarMainGeneralized\], and $g:{\mathcal{S}}^{1}\rightarrow{\mathbb{R}}$ a non-negative function of bounded variation such that $ \|g\|_{L^{1}({\mathcal{S}}^{1})}=1$. For $n\in S_{2}$ and $\lambda\in {\mathcal{E}}_{n}$ we set $|\widetilde{c_{\lambda}}|^{2} := g(\lambda/\sqrt{n})$, and normalise the vector $\widetilde{\underline{v}}:=(|\widetilde{c_{\lambda}}|^{2})_{\lambda\in{\mathcal{E}}_{n}}$ by setting $\underline{v} := \frac{\widetilde{\underline{v}}}{\|\widetilde{\underline{v}}\|_{1}}$, i.e. $$\label{eq:v BV norm} v:=(|{c_{\lambda}}|^{2})_{\lambda\in{\mathcal{E}}_{n}} = \left(\frac{|\widetilde{c_{\lambda}}|^{2}}{\sum\limits_{\mu\in{\mathcal{E}}_{n}}|\widetilde{c_{\mu}}|^{2}}\right)_{\lambda\in{\mathcal{E}}_{n}}.$$ Then along a generic sequence $S_{2}'\subseteq S_{2}$ we have $${\mathcal{V}}(X_{f_{n},r}) \sim \frac{16}{3 \pi}\|g\|_{L^{2}({\mathcal{S}}^{1})}^{2}r^{4}T^{-1},$$ uniformly for $r_{0}<r=n^{-1/2}T<r_{1}$, and $f_{n}$ with coefficients $c_{\lambda}$ as in . If, in addition, we have $T_{1}(n)=O(N^{\xi})$ for every $\xi>0$, then the distribution of the standardised random variable $\hat{X}_{f_{n},r}$ converges to standard Gaussian. By Koksma’s inequality (see e.g. [@KuipersNiederreiter]), $A_{4}\left(\underline{v} \right)\sim\left\Vert g\right\Vert _{2}^{2}$ along a density one sequence in $S_{2}$. Also note that $$V(\underline{v}) \ll V\left(g\right),$$ with the l.h.s. as in , and r.h.s. the variation of $g$ on ${\mathcal{S}}^{1}$. In light of Lemma \[lem:BasicVarProp\], both parts of Corollary \[cor:VarAsympGen\] follow from Theorem \[thm:VarMainGeneralized\]. Notation ======== For the convenience of the reader, we summarize here the notation used in our paper. $ S_d=\{n=a_{1}^{2}+\ldots +a_{d}^{2}:\: a_{1},\ldots,a_{d}\in{\mathbb{Z}}\} $: the set of integers expressible as a sum of $ d $ squares, see .\ ${\mathcal{E}}_{n} = {\mathcal{E}}_{d;n}=\{\lambda\in{\mathbb{Z}}^{d}:\: \|\lambda\|^{2}=n\}$: the standard lattice points lying on the $(d-1)$-dimensional sphere (a circle for $ d=2 $) of radius-$\sqrt{n}$, see .\ $f_{n}\left(x\right)=\sum\limits_{\lambda\in\mathcal{E}_{n}}c_{\lambda}e\left(\left\langle x,\lambda\right\rangle \right)$: the toral Laplace eigenfunctions, see .\ $ N=N_{d;n}=\#\mathcal{E}_n$: the number of lattice points on the $(d-1)$-dimensional sphere (a circle for $ d=2 $) of radius-$\sqrt{n}$, see .\ $B_{x}(r)$: the radius $r$ geodesic ball in $\mathbb{T}^d$ centred at $x$.\ $X_{f_{n},r}=X_{f_{n},r;x}= \int\limits_{B_{x}(r)}f_{n}(y)^{2}dy$: the $L^{2}$-mass of $ f_n $ restricted to $ B_{x}(r) $, where $ x $ is drawn randomly uniformly in $ \mathbb{T}^d $, see .\ ${\mathbb{E}}[X_{f_{n},r}] = \int\limits_{{\mathbb{T}}^{d}}X_{f_{n},r;x}dx$: the expected value of $X_{f_{n},r} $, see .\ ${\mathcal{V}}(X_{f_{n},r}) = {\mathbb{E}}[(X_{f_{n},r}-{\mathbb{E}}[X_{f_{n},r}])^{2}]$: the variance of $X_{f_{n},r} $, see .\ $\hat{X}_{f_{n},r}:=\frac{X_{f_{n},r}-{\mathbb{E}}[X_{f_{n},r}]}{\sqrt{{\mathcal{V}}\left(X_{f_{n},r}\right)}}$: the standardized random $L^{2}$-mass of $ f_n $, see .\ $ T = n^{1/2}r $.\ $\underline{v}=(|c_{\lambda}|^{2})_{\lambda \in{\mathcal{E}}_{n}} \in {\mathbb{R}}^{\mathcal{E}_n} $: the vector of the squared absolute values of the coefficients of $f_n $, see .\ $[\underline{v}]_{\infty} = N \cdot \max\limits_{\lambda\in{\mathcal{E}}_{n}}|c_{\lambda}|^{2}$: the normalised $\ell_{\infty}$-norm of $ \underline{v} $, see .\ $\mathcal{B}_n$: the class of Bourgain’s eigenfunctions $f_{n}\left(x\right)=\frac{1}{\sqrt{N}}\sum\limits_{\lambda\in\mathcal{E}_{n}}\varepsilon_{\lambda}e\left(\left\langle x,\lambda\right\rangle \right)$, where $\varepsilon_{\lambda}=\pm1$ for every $\lambda\in\mathcal{E}_{n}$, see .\ ${\mathcal{U}}_{n;\epsilon}$: the class of $ \epsilon $-ultraflat functions, where $ [\underline{v}]_{\infty} \le N^{\epsilon} $, see .\ $A_{4} = A_{4}(\underline{v}) = N\sum\limits_{\lambda\in{\mathcal{E}}_{n}} |c_{\lambda}|^{4} = N\cdot \|\underline{v}\|^{2}$, see .\ $\theta = \theta_{f_n} = \theta(\underline{v},\underline{v_{0}})$: the angle between $\underline{v}$ and the vector $\underline{v_{0}}= (\frac{1}{N})_{\lambda\in{\mathcal{E}}_{n}}$ corresponding to Bourgain’s eigenfunctions, see .\ $V\left(\underline{v} \right)= N\sum\limits_{\lambda\in\mathcal{E}_{n}}\left|\left|c_{\lambda_{+}}\right|^{2}-\left|c_{\lambda}\right|^{2}\right|$, where $\lambda_{+}$ is the clockwise nearest neighbour of $\lambda$ on $\sqrt{n}\mathcal{S}^{1}$, see .\ $\widetilde{V}(\underline{v}) = \frac{[\underline{v}]_{\infty} \cdot V(\underline{v})}{A_{4}(\underline{v})}$, see .\ ${\mathcal{F}}_{1}(n;T(n),\eta(n)) = \left\{f_{n}:\: \widetilde{V}(\underline{v})< \eta(n) \cdot \frac{T(n)}{\log T(n)} \right\}$, see .\ ${\mathcal{F}}_{2}(n;T(n),\eta(n)) = \left\{f_{n}:\: [\underline{v}]_{\infty} < T(n)^{\eta(n)} \right\}$, see .\ $\widehat{\lambda}=\lambda/\sqrt{n}$: the projection of $\lambda \in \mathcal{E}_n$ onto $\mathcal{S}^{d-1}.$\ $\Delta\left(n\right)=\sup\limits_{0\le a\le b\le2\pi}\left|\frac{1}{N}\cdot \#\left\{ 1\le j\le N:\,\phi_{j}\in\left[a,b\right]\,\text{mod\,}2\pi\right\} -\frac{\left(b-a\right)}{2\pi}\right|$: the discrepancy of the angles $ \phi_j $ corresponding to the lattice points $ {\mathcal{E}}_{2;n} $, see .\ Hypothesis $ \mathcal{D}(n,\epsilon) $ holds if $\Delta\left(n\right)\le \left(\log n\right)^{-\frac{1}{2}\log\frac{\pi}{2}+\epsilon}$, see .\ $\Delta_{3}\left(n\right)=\sup\limits_{\begin{subarray}{c} x\in\mathcal{S}^{2}\\ 0<r\le2 \end{subarray}}\left|\frac{1}{N} \cdot \#\left\{ \lambda\in\mathcal{E}_{3;n}:\,\left|\widehat{\lambda}-x\right|\le r\right\} -\frac{r^{2}}{4}\right|$: the spherical cap discrepancy of the points $ \mathcal{E}_{3;n} $, see .\ ${\mathcal{S}}_{n}(l) = \left\{ (\lambda^{1},\ldots,\lambda^{l})\in({\mathcal{E}}_{n})^{l}:\: \sum\limits_{i=1}^{l}\lambda^{i}=0 \right\}$: the length-$ l $ spectral correlation set, see .\ ${\mathcal{D}}_{n}(l) = \left\{ \pi(\lambda^{1},-\lambda^{1},\ldots,\lambda^{k},-\lambda^{k}): \lambda^{1},\ldots,\lambda^{k}\in ({\mathcal{E}}_{n})^{k},\,\pi\in S_{l}\right\}$: the diagonal correlations set, see .\ $\mathcal{A}_n (2k) = \left\{\left(\lambda_{1},\dots,\lambda_{2k}\right)\in{\mathcal{D}}_{n}(2k): \; \forall 1\le i\le k \; \lambda_{2i-1}\ne-\lambda_{2i} \right\}$: the set of “admissible” $ 2k $-tuples of lattice points, see .\ $S\left(\lambda_{1},\dots,\lambda_{2k}\right)$: the structure set of an admissible $ 2k $-tuple $\left(\lambda_{1},\dots,\lambda_{2k}\right)$, see .\ $J_{\alpha}\left(x\right)$: the Bessel function of the first kind of order $\alpha$.\ $g_{d}\left(x\right)=\frac{J_{d/2}\left(2 \pi x\right)}{(2 \pi x)^{d/2}}$: the Fourier transform of the characteristic function of the unit ball in $\mathbb{R}^{d}$, see .\ $ h_{2}\left(x\right)=\frac{J_{1}\left(2 \pi x\right)^{2}}{(2\pi x)^{2}}$, see .\ $h_{3}\left(x\right)=2\pi^{-1}(2 \pi x)^{-4}\left(\frac{\sin 2 \pi x}{2\pi x}-\cos 2 \pi x\right)^{2}$, see .\ $F_{\lambda_{0}}\left(s\right)=\frac{1}{N}\cdot \#\left\{ \lambda\in\mathcal{E}_{2;n}:\,\left\Vert \widehat{\lambda}-\widehat{\lambda_{0}}\right\Vert \le s\right\}$, see .\ $F\left(s\right)=F_{f_{n}}\left(s\right)=\sum\limits_{\begin{subarray}{c} \lambda,\lambda'\in\mathcal{E}_{2;n}\\ 0<\left\Vert \widehat{\lambda}-\widehat{\lambda'}\right\Vert \le s \end{subarray}}\left|c_{\lambda}\right|^{2}\left|c_{\lambda'}\right|^{2}$, see .\ $F_{3}\left(s\right)=\frac{1}{N^{2}} \cdot \#\left\{ \lambda\ne\lambda'\in\mathcal{E}_{3;n}:\left\Vert \widehat{\lambda}-\widehat{\lambda'}\right\Vert \le s\right\}$, see .\ ${\mathbb{E}}_{x_{0},\rho}[X_{f_{n},r}] = \frac{1}{{\operatorname{Vol}}(B_{x_0}(\rho))}\int\limits_{B_{x_{0}}(\rho)}X_{f_{n},r;x}dx$: the “restricted” expected value of $X_{f_{n},r} $, see .\ ${\mathcal{V}}_{x_{0},\rho}(X_{f_{n},r}) = {\mathbb{E}}_{x_{0},\rho}[(X_{f_{n},r}-{\mathbb{E}}_{x_{0},\rho}[X_{f_{n},r}])^{2}]$: the restricted variance of $X_{f_{n},r} $, see .\ $\mathcal{C}_{n}(l;K) = \left\{(\lambda^{1},\ldots,\lambda^{l})\in\mathcal{E}_{n}^{l}:\: 0 < \left\| \sum\limits_{j=1}^{l}\lambda^{j} \right\| \le K \right\}$: the set of length-$l$ spectral quasi-correlations, see .\ Hypothesis $\mathcal{A}(n;l,\delta)$ holds if $\mathcal{C}_{n}(l;n^{1/2-\delta}) = \varnothing$, see . Proof of Theorem \[thm:VarMainGeneralized\], part 1: asymptotics for the variance, $d=2$. {#sec:Proof_Main_thm_part1} ========================================================================================= Expressing the variance ----------------------- We begin with some preliminary expressions for the variance. Note that if $x$ is drawn randomly, uniformly on $\mathbb{T}^{d}$, then $$\mathbb{E}\left[X_{f_{n},r}\right]=\frac{\pi^{d/2}}{\Gamma\left(d/2+1\right)}r^{d},\label{eq:ExpectationEquality}$$ and therefore in this case, we have $$\label{eq:variance_integral_form} {\mathcal{V}}(X_{f_{n},r}) = \int\limits_{{\mathbb{T}}^{d}}\left(\int_{B_{x}\left(r\right)}f_{n}\left(y\right)^{2}\,\text{d}y- \frac{\pi^{d/2}}{\Gamma\left(d/2+1\right)}r^{d} \right)^{2}dx.$$ Let $J_{\alpha}\left(x\right)$ be the Bessel function of the first kind of order $\alpha$. The following lemma, proved in section \[sec:AuxLemmasProof\], explicates the inner integral in : \[lem:InnerIntegral\]We have $$\begin{aligned} & \int_{B_{x}\left(r\right)}f_{n}\left(y\right)^{2}\,\text{d}y-\frac{\pi^{d/2}}{\Gamma\left(d/2+1\right)}r^{d} =\left(2\pi\right)^{d/2}r^{d}\sum_{\begin{subarray}{c} \lambda,\lambda'\in\mathcal{E}_{n}\\ \lambda\ne\lambda' \end{subarray}}c_{\lambda}\overline{c_{\lambda'}}e\left(\left\langle x,\lambda-\lambda'\right\rangle \right)g_{d}\left(r\left\Vert \lambda-\lambda'\right\Vert \right),\label{eq:IntegrandVar} \end{aligned}$$ where $$\label{eq:g_d} g_{d}\left(x\right):=\frac{J_{d/2}\left(2 \pi x\right)}{(2 \pi x)^{d/2}}$$ is the Fourier transform of the characteristic function of the unit ball in $\mathbb{R}^{d}$. The following formula for the variance follows from Lemma \[lem:InnerIntegral\], and : \[lem:VarExpd2\]  1. (Granville-Wigman [@GranvilleWigman Lemma 2.1]) For $d=2$ we have $$\label{eq:VarFormula2d} \text{\ensuremath{\mathcal{V}}}\left(X_{f_{n},r}\right)=8\pi^{2}r^{4}\sum_{\begin{subarray}{c} \lambda,\lambda'\in\mathcal{E}_{n}\\ \lambda\ne\lambda' \end{subarray}}\left|c_{\lambda}\right|^{2}\left|c_{\lambda'}\right|^{2}h_{2}\left(r\left\Vert \lambda-\lambda'\right\Vert \right)$$ where $$\label{eq:h_2} h_{2}\left(x\right):=\frac{J_{1}\left(2 \pi x\right)^{2}}{(2\pi x)^{2}}.$$ 2. For $d=3$ and for every $\epsilon>0$, we have $$\begin{aligned} \text{\ensuremath{\mathcal{V}}}\left(X_{f_{n},r}\right) & =16\pi^{3}r^{6}\sum_{\begin{subarray}{c} \lambda,\lambda'\in\mathcal{E}_{n}\\ \lambda\ne\lambda' \end{subarray}}\left|c_{\lambda}\right|^{2}\left|c_{\lambda'}\right|^{2}h_{3}\left(r\left\Vert \lambda-\lambda'\right\Vert \right)\label{eq:VarFormula3d}\\ & +O\left([\underline{v}]_{\infty}^2 r^{6}N^{-1/4+\epsilon}\right),\nonumber \end{aligned}$$ where $$\label{eq:h_3} h_{3}\left(x\right):=2\pi^{-1}(2 \pi x)^{-4}\left(\frac{\sin 2 \pi x}{2\pi x}-\cos 2 \pi x\right)^{2}.$$ Note that functions $g_{2}$ and $h_{2}$ satisfy the following properties: \[lem:H2Formulas\]We have 1. $\int_{0}^{\infty}h_{2}\left(s\right)\,\text{d}s=\frac{2}{3\pi^2}$. 2. $g_{2}\left(s\right)\sim\frac{1}{2}\hspace{1em}\left(s\to0\right)$. 3. $g_{2}\left(s\right)\ll s^{-3/2}\hspace{1em}\left(s\to\infty\right)$. 4. $g_{2}'\left(s\right)=-\frac{J_{2}\left(2\pi s\right)}{s}\ll\left(1+s\right)^{-3/2}.$ Proof of Theorem \[thm:VarMainGeneralized\], part 1: ---------------------------------------------------- For $\lambda\in\mathcal{E}_{n}$ let $\widehat{\lambda}=\lambda/\sqrt{n}$ be the projection of $\lambda$ onto the unit circle $\mathcal{S}^{1}.$ 1. For $ \lambda_0 \in \mathcal{E}_n $ and $0\le s\le2$, denote $$\label{eq:F_Lambda_Def} F_{\lambda_{0}}\left(s\right)=\frac{1}{N}\cdot \#\left\{ \lambda\in\mathcal{E}_{n}:\,\left\Vert \widehat{\lambda}-\widehat{\lambda_{0}}\right\Vert \le s\right\} .$$ 2. For $0\le s\le2$ denote $$F\left(s\right)=F_{f_{n}}\left(s\right)=\sum_{\begin{subarray}{c} \lambda,\lambda'\in\mathcal{E}_{n}\\ 0<\left\Vert \widehat{\lambda}-\widehat{\lambda'}\right\Vert \le s \end{subarray}}\left|c_{\lambda}\right|^{2}\left|c_{\lambda'}\right|^{2}.\label{eq:F_Function}$$ Recall that $\widetilde{V}(\underline{v})=\cos^{2}\theta \cdot [\underline{v}]_{\infty} V(\underline{v})$ by and . \[prop:DiscreteProp\]We have $$\begin{aligned} F\left(s\right) & =\frac{s}{\pi\cos^{2}\theta}\left(1+O\left(s^{2}+s^{-1}\Delta\left(n\right)+\widetilde{V}(\underline{v}) s+\widetilde{V}(\underline{v}) s^{-1}\Delta\left(n\right)^{2}\right)\right). \end{aligned}$$ We postpone the proof of Proposition \[prop:DiscreteProp\] until section \[sec:ProofOfLemmaDiscrete\] to present the proof of the first part of Theorem \[thm:VarMainGeneralized\] (that yields the first part of Theorem \[thm:VarMain\]): Assume that $ n\in S_2 $ satisfies the hypothesis $ \mathcal{D}(n,\epsilon/2) $. We may rewrite (\[eq:VarFormula2d\]) as $$\mathcal{V}\left(X_{f_{n},r}\right)=8\pi^{2}r^{4}\int_{0}^{2}h_{2}\left(Ts\right)\,\text{d}F\left(s\right).\label{eq:VarianceintegralForm}$$ We apply integration by parts to (\[eq:VarianceintegralForm\]) twice, in opposite directions: first, by integration by parts and Proposition \[prop:DiscreteProp\], we get $$\begin{aligned} 8\pi^{2}r^{4}\int_{0}^{2}h_{2}\left(Ts\right)\,\text{d}F\left(s\right) & =8\pi^{2}r^{4}h_{2}\left(2T\right)F\left(2\right)-8\pi^{2}r^{4}\int_{0}^{2}F\left(s\right)\,\text{d}h_{2}\left(Ts\right)\label{eq:VarEqAfterIntByParts}\\ & =8\pi^{2}r^{4}h_{2}\left(2T\right)F\left(2\right)-8\pi r^{4}\cos^{-2}\theta\int_{0}^{2}s\,\text{d}h_{2}\left(Ts\right)\nonumber \\ & +Err\left(X_{f_n,r}\right)\nonumber \end{aligned}$$ where $$\begin{aligned} & Err\left(X_{f_n,r}\right)\ll r^{4}\cos^{-2}\theta\int_{0}^{2}\left(s^{3}+\Delta\left(n\right)+\widetilde{V}(\underline{v}) s^{2}+\widetilde{V}(\underline{v})\Delta\left(n\right)^{2}\right)T\left|h_{2}'\left(Ts\right)\right|\,\text{d}s. \end{aligned}$$ Integrating by parts again, the first two terms on the r.h.s of (\[eq:VarEqAfterIntByParts\]) satisfy $$\begin{aligned} & 8\pi^{2}r^{4}h_{2}\left(2T\right)F\left(2\right)-8\pi r^{4}\cos^{-2}\theta\int_{0}^{2}s\,\text{d}h_{2}\left(Ts\right)=8\pi^{2}r^{4}h_{2}\left(2T\right)F\left(2\right)\label{eq:MainTermsVar}\\ & -16\pi r^{4}h_{2}\left(2T\right)\cos^{-2}\theta+8\pi r^{4}\cos^{-2}\theta\int_{0}^{2}h_{2}\left(Ts\right)\,\text{d}s.\nonumber \end{aligned}$$ By the first and the third parts of Lemma \[lem:H2Formulas\], $$\int_{0}^{2}h_{2}\left(Ts\right)\,\text{d}s=\frac{1}{T}\int_{0}^{2T}h_{2}\left(s\right)\,\text{d}s=\frac{2}{3\pi^2}T^{-1}+O\left(T^{-3}\right),\label{eq:h2Integral}$$ and therefore, substituting (\[eq:h2Integral\]) into (\[eq:MainTermsVar\]), we obtain $$\begin{aligned} \label{eq:VarianceMainTerms} 8\pi^{2}r^{4}h_{2}\left(2T\right)F\left(2\right)-8\pi r^{4}\cos^{-2}\theta\int_{0}^{2}s\,\text{d}h_{2}\left(Ts\right) & =\frac{16}{3\pi}\cos^{-2}\theta r^{4}T^{-1} +O\left(\cos^{-2}\theta r^{4}T^{-3}\right). \end{aligned}$$ By the fourth part of Lemma \[lem:H2Formulas\], $$\begin{aligned} \int_{0}^{2}T\left|h_{2}'\left(Ts\right)\right|\,\text{d}s & =\int_{0}^{2T}\left|h_{2}'\left(s\right)\right|\,\text{d}s\le\int_{0}^{\infty}\left|h_{2}'\left(s\right)\right|\,\text{d}s<\infty, \end{aligned}$$ $$\int_{0}^{2}s^{2}T\left|h_{2}'\left(Ts\right)\right|\,\text{d}s=T^{-2}\int_{0}^{2T}s^{2}\left|h_{2}'\left(s\right)\right|\,\text{d}s\ll T^{-2}\log T$$ and $$\int_{0}^{2}s^{3}T\left|h_{2}'\left(Ts\right)\right|\,\text{d}s=T^{-3}\int_{0}^{2T}s^{3}\left|h_{2}'\left(s\right)\right|\,\text{d}s\ll T^{-2},$$ and therefore for $ n $ satisfying $ \mathcal{D}(n,\epsilon/2), $ $$\begin{aligned} Err\left(X_{f_n,r}\right) & \ll\cos^{-2}\theta r^{4}\left(T^{-2}+\Delta\left(n\right)+\widetilde{V}(\underline{v}) T^{-2}\log T+\widetilde{V}(\underline{v})\Delta\left(n\right)^{2}\right)\nonumber \\ & \ll\cos^{-2}\theta r^{4}\left(T^{-2}+\left(\log n\right)^{-\frac{1}{2}\log\frac{\pi}{2}+\frac{\epsilon}{2}}+\widetilde{V}(\underline{v}) T^{-2}\log T+\widetilde{V}(\underline{v})\left(\log n\right)^{-\log\frac{\pi}{2}+\epsilon}\right),\label{eq:ErrorTerm} \end{aligned}$$ and follows from , and . Note that by (\[eq:ErrorTerm\]), for Bourgain’s eigenfunctions, for almost all $n\in S_{2}$ we have $$\sup_{\begin{subarray}{c} r > r_{0} \\ f_n\in {\mathcal{B}}{n} \end{subarray}}\left|\frac{\text{\ensuremath{\mathcal{V}}}\left(X_{f_{n},r}\right)}{r^{4}}-\frac{16}{3\pi}T^{-1}\right|=O\left(T_{0}^{-2}+\left(\log n\right)^{-\frac{1}{2}\log\frac{\pi}{2}+\epsilon}\right)$$ for every $\epsilon>0$, and in particular $$\label{eq:o_r4_2d} \text{\ensuremath{\mathcal{V}}}\left(X_{f_{n},r}\right)=o\left(r^{4}\right)$$ uniformly for $r > r_{0}$ for a density one sequence in $S_{2}$. Therefore, serves as a refinement of [@GranvilleWigman Corollary 1.10] for this specific case (for a density one sequence in $S_{2}$), since [@GranvilleWigman Corollary 1.10] yields $\mathcal{V}\left(X_{f_n,r}\right)=o\left(r^{4}\right)$ under the additional assumption $T_{0}\gg n^{4\epsilon}$. Proof of Proposition \[prop:DiscreteProp\] {#sec:ProofOfLemmaDiscrete} ------------------------------------------ In this section we prove Proposition \[prop:DiscreteProp\]. First, we define a binary relation on $\mathcal{E}_n$: for $\lambda\ne-\lambda'\in\mathcal{E}_{n}$, we say that $\lambda\prec\lambda'$ if the arc on the circle $\sqrt{n}\mathcal{S}^{1}$ that connects $\lambda$ to $\lambda'$ counter-clockwise to $\lambda'$ is shorter than the arc that connects them clockwise to $\lambda'$. Recall that $\lambda_{+}$ is the clockwise nearest neighbour of $\lambda$ on $\sqrt{n}\mathcal{S}^{1}$. The proof of Proposition \[prop:DiscreteProp\] employs the following auxiliary lemma to be proved at section \[sec:AuxLemmasProof\], establishing (\[eq:F\_Function\]) in the particular case $\left|c_{\lambda}\right|^{2}=1$ for every $\lambda\in\mathcal{E}_{n}$: \[lem:CosToDist\] Fix $\lambda'\in\mathcal{E}_{n}.$ For $0\le s<2$, we have $$\frac{1}{N}\cdot \#\left\{ \lambda\in\mathcal{E}_{n}:\,\lambda\succeq\lambda',\left\Vert \widehat{\lambda}-\widehat{\lambda'}\right\Vert \le s\right\} =\frac{s}{2\pi}+O\left(s^{3}+\Delta\left(n\right)\right)\label{eq:CosToDistEq}$$ where the constant involved in the ’O’-notation in (\[eq:CosToDistEq\]) is absolute. The estimate (\[eq:CosToDistEq\]) is also valid with either ‘$\succ$’, ‘$\preceq$’ or ‘$\prec$’ in place of ‘$\succeq$’. We are now in a position to prove Proposition \[prop:DiscreteProp\]: First, we write $$\begin{aligned} F\left(s\right) & =\sum_{\lambda'\in\mathcal{E}_{n}}\left|c_{\lambda'}\right|^{2}\sum_{\begin{subarray}{c} \lambda\in\mathcal{E}_{n}\\ \left\Vert \widehat{\lambda}-\widehat{\lambda'}\right\Vert \le s\\ \lambda\preceq\lambda' \end{subarray}}\left|c_{\lambda}\right|^{2}+\sum_{\lambda'\in\mathcal{E}_{n}}\left|c_{\lambda'}\right|^{2}\sum_{\begin{subarray}{c} \lambda\in\mathcal{E}_{n}\\ \left\Vert \widehat{\lambda}-\widehat{\lambda'}\right\Vert \le s\\ \lambda\succeq\lambda' \end{subarray}}\left|c_{\lambda}\right|^{2}\label{eq:PartialSummation} +O\left(\frac{A_{4}}{N}\right). \end{aligned}$$ Using summation by parts, we get that for every $\lambda'\in\mathcal{E}_{n}$ $$\begin{aligned} \sum_{\begin{subarray}{c} \lambda\in\mathcal{E}_{n}\\ \left\Vert \widehat{\lambda}-\widehat{\lambda'}\right\Vert \le s\\ \lambda\preceq\lambda' \end{subarray}}\left|c_{\lambda}\right|^{2} & =\left|c_{\lambda'}\right|^{2} \cdot \#\left\{ \lambda\in\mathcal{E}_{n}:\,\lambda\preceq\lambda',\left\Vert \widehat{\lambda}-\widehat{\lambda'}\right\Vert \le s\right\} \label{eq:PartialSumEq}\\ & -\sum_{\begin{subarray}{c} \lambda\in\mathcal{E}_{n}\\ \left\Vert \widehat{\lambda}-\widehat{\lambda'}\right\Vert \le s\\ \lambda\prec\lambda' \end{subarray}}\left(\left|c_{\lambda_{+}}\right|^{2}-\left|c_{\lambda}\right|^{2}\right) \cdot \#\left\{ \mu\in\mathcal{E}_{n}:\,\mu\preceq\lambda,\,\left\Vert \widehat{\mu}-\widehat{\lambda'}\right\Vert \le s\right\} .\nonumber \end{aligned}$$ By Lemma \[lem:CosToDist\], the contribution of the first term on the r.h.s of (\[eq:PartialSumEq\]) to $F\left(s\right)$ is $$\begin{aligned} \label{eq:first_term_discrete} \sum_{\lambda'\in\mathcal{E}_{n}}\left|c_{\lambda'}\right|^{4} \cdot \#\left\{ \lambda\in\mathcal{E}_{n}:\,\lambda\preceq\lambda',\left\Vert \widehat{\lambda}-\widehat{\lambda'}\right\Vert \le s\right\} =A_{4} \cdot \left(s/2\pi+O\left(s^{3}+\Delta\left(n\right)\right)\right). \end{aligned}$$ The contribution of the sum on the r.h.s of (\[eq:PartialSumEq\]) to $F\left(s\right)$ is $$\begin{aligned} \label{eq:second_term_discrete} & \sum_{\lambda'\in\mathcal{E}_{n}}\left|c_{\lambda'}\right|^{2}\sum_{\begin{subarray}{c} \lambda\in\mathcal{E}_{n}\\ \left\Vert \widehat{\lambda}-\widehat{\lambda'}\right\Vert \le s\\ \lambda\prec\lambda' \end{subarray}}\left(\left|c_{\lambda_{+}}\right|^{2}-\left|c_{\lambda}\right|^{2}\right) \cdot \#\left\{ \mu\in\mathcal{E}_{n}:\,\mu\preceq\lambda,\,\left\Vert \widehat{\mu}-\widehat{\lambda'}\right\Vert \le s\right\} \\ & \ll N\left(s+\Delta\left(n\right)\right)\sum_{\begin{subarray}{c} \lambda\in\mathcal{E}_{n}\end{subarray}}\left|\left|c_{\lambda_{+}}\right|^{2}-\left|c_{\lambda}\right|^{2}\right|\sum_{\begin{subarray}{c} \lambda'\in\mathcal{E}_{n} \nonumber \\ \left\Vert \widehat{\lambda}-\widehat{\lambda'}\right\Vert \le s\\ \lambda\prec\lambda' \end{subarray}}\left|c_{\lambda'}\right|^{2}\ll\left(s+\Delta\left(n\right)\right)^{2}[\underline{v}]_{\infty} V(\underline{v}) . \end{aligned}$$ By and , we have $$\label{eq:first_summation_discrete} \sum_{\begin{subarray}{c} \lambda\in\mathcal{E}_{n}\\ \left\Vert \widehat{\lambda}-\widehat{\lambda'}\right\Vert \le s\\ \lambda\preceq\lambda' \end{subarray}}\left|c_{\lambda}\right|^{2} = A_{4} \cdot \left(s/2\pi+O\left(s^{3}+\Delta\left(n\right)\right)\right) + O\left(\left(s+\Delta\left(n\right)\right)^{2}[\underline{v}]_{\infty}V(\underline{v}) \right).$$ By symmetry, the second summation in (\[eq:PartialSummation\]) obeys with ‘$ \succ $’, ‘$ \succeq $’ and $ |c_{\lambda_-}|^2 $ in place of ‘$ \prec $’, ‘$ \preceq $’ and $ |c_{\lambda_+}|^2 $, where $ \lambda_- $ is the counter-clockwise nearest neighbour to $ \lambda $. The statement of Proposition \[prop:DiscreteProp\] follows from the analogues of the estimates , and . Proof of Theorem \[thm:VarMainGeneralized\], part 2: Gaussian moments, $d=2$. {#sec:Proof_Main_thm_part2} ============================================================================= In this section we study the higher moments of $\hat{X}_{f_{n},r}$ defined in , and prove the second part of Theorem \[thm:VarMainGeneralized\], also implying the second part of Theorem \[thm:VarMain\]. The proof of the following lower bound for $ {\mathcal{V}}\left(X_{f_{n},r}\right) $ with $f_{n}\in {\mathcal{F}}_{2}(n;T(n),\eta(n))$ goes along the same lines as the proof of the lower bound in Theorem \[thm:UpperBound2d\] below: \[lem:Lower\_Bound\_F2\] In the setting of Theorem \[thm:VarMainGeneralized\] part (2), we have $$\frac{{\mathcal{V}}(X_{f_n,r})}{r^{4}} \gg T(n)^{-1-2\eta(n)}$$ uniformly for $r_{0} < r < r_1$ and $f_{n}\in {\mathcal{F}}_{2}(n;T(n),\eta(n))$. Before proceeding to the proof of Theorem \[thm:VarMainGeneralized\], we introduce some notation: 1. Define the set of “admissible” $2k$-tuples of lattice points by $$\label{eq:admissible_tuples} \mathcal{A}_n (2k) = \left\{\left(\lambda_{1},\dots,\lambda_{2k}\right)\in{\mathcal{D}}_{n}(2k): \; \forall 1\le i\le k \; \lambda_{2i-1}\ne-\lambda_{2i} \right\}.$$ 2. Given an admissible $2k$-tuple of lattice points $\left(\lambda_{1},\dots,\lambda_{2k}\right)\in \mathcal{A}_n (2k)$, let $\sim$ be the equivalence relation on the set $\left\{ 1,\dots,2k\right\} $, generated by: 1. $2i-1\sim2i$ for every $1\le i\le k$. 2. $j\sim j'$ if $\lambda_{j}+\lambda_{j}'=0.$ Let $\left\{ \Lambda_{1},\dots,\Lambda_{m}\right\} $ be the partition of $\left\{ 1,\dots,2k\right\} $ into equivalence classes of $\sim$, and denote $l_{j}=\#\Lambda_{m}/2$ for $1\le j\le m$, so that $\sum_{j=1}^{m}l_{j}=k$; clearly, $2\le l_{j}\in\mathbb{Z}$ for every $1\le j\le m$. We call the multiset $$\label{eq:structure_set} S\left(\lambda_{1},\dots,\lambda_{2k}\right):=\left\{ l_{1},\dots,l_{m}\right\}$$ the structure set of the $2k$-tuple $\left(\lambda_{1},\dots,\lambda_{2k}\right).$ Recall that the moments of a standard Gaussian random variable $Z\sim N(0,1)$ are $${\mathbb{E}}[Z^{k}]=\begin{cases} \left(k-1\right)!! & k\,\text{even}\\ 0 & k\,\text{odd}. \end{cases}$$ We are now in a position to prove the second part of Theorem \[thm:VarMainGeneralized\]. By the length-$2k$ diagonal domination assumption, we have $$\begin{aligned} {\mathbb{E}}[\hat{X}_{f_{n},r}^{k}] & =(2\pi)^k r^{2k}{\mathcal{V}}\left(X_{f_{n},r}\right)^{-k/2}\sum_{\begin{subarray}{c} \left(\lambda_{1},\dots,\lambda_{2k}\right)\in \mathcal{A}_n (2k)\end{subarray}}\label{eq:kthMoment}\prod_{j=1}^{k}c_{\lambda_{2j-1}}c_{\lambda_{2j}}g_{2}\left(r\left\Vert \lambda_{2j-1}+\lambda_{2j}\right\Vert \right) \\ &+O\left({\mathcal{V}}\left(X_{f_{n},r}\right)^{-k/2} [\underline{v}]_{\infty}^k r^{2k}N^{-\gamma}\right)\nonumber \end{aligned}$$ for some $ \gamma>0. $ We can rearrange the summation in (\[eq:kthMoment\]), first summing over all possible structure sets $\mathcal{L}=\left\{ l_{1},\dots,l_{m}\right\} $ and then summing over the admissible $2k$-tuples $\left(\lambda_{1},\dots,\lambda_{2k}\right)\in\mathcal{E}_{n}^{2k}$ with the given structure set $S\left(\lambda_{1},\dots,\lambda_{2k}\right)=\mathcal{L} $: let $$\begin{aligned} S_{\mathcal{L}} & :=\sum_{\begin{subarray}{c} \begin{subarray}{c} \left(\lambda_{1},\dots,\lambda_{2k}\right)\in \mathcal{A}_n (2k)\\ S\left(\lambda_{1},\dots,\lambda_{2k}\right)=\mathcal{L} \end{subarray}\end{subarray}}\prod_{j=1}^{k}c_{\lambda_{2j-1}}c_{\lambda_{2j}}g_{2}\left(r\left\Vert \lambda_{2j-1}+\lambda_{2j}\right\Vert \right), \end{aligned}$$ so that we may rewrite the summation on the r.h.s. of as $$\begin{aligned} \label{eq:Inner_Sum_with_SL} & \sum_{\begin{subarray}{c} \left(\lambda_{1},\dots,\lambda_{2k}\right)\in \mathcal{A}_n (2k)\end{subarray}}\prod_{j=1}^{k}c_{\lambda_{2j-1}}c_{\lambda_{2j}}g_{2}\left(r\left\Vert \lambda_{2j-1}+\lambda_{2j}\right\Vert \right)=\sum_{\begin{subarray}{c} l_{1}+\dots+l_{m}=k\\ l_{1},\dots,l_{m}\ge2 \end{subarray}}\sum_{\begin{subarray}{c} \begin{subarray}{c} \left(\lambda_{1},\dots,\lambda_{2k}\right)\in \mathcal{A}_n (2k)\\ S\left(\lambda_{1},\dots,\lambda_{2k}\right)=\mathcal{L} \end{subarray}\end{subarray}}S_{\mathcal{L}}. \end{aligned}$$ For a fixed structure set $\mathcal{L}=\left\{ l_{1},\dots,l_{m}\right\} $, we have $$\begin{aligned} S_{\mathcal{L}} =a\left(\mathcal{L}\right)\prod_{j=1}^{m}\sum_{\lambda_{1},\dots,\lambda_{l_{j}}\in\mathcal{E}_{n}}\left|c_{\lambda_{1}}\right|^{2}g_{2}\left(r\left\Vert \lambda_{l_{j}}-\lambda_{1}\right\Vert \right)\label{eq:RearrangeInPartition}\prod_{i=1}^{l_{j}-1}\left|c_{\lambda_{i+1}}\right|^{2}g_{2}\left(r\left\Vert \lambda_{i}-\lambda_{i+1}\right\Vert \right)+O\left([\underline{v}]_{\infty}^k N^{-1}\right) \end{aligned}$$ where $a\left(\mathcal{L}\right)$ is a constant depending on $\mathcal{L}$; omitting the condition that the lattice points are distinct on the r.h.s of (\[eq:RearrangeInPartition\]) is absorbed within the error term in (\[eq:RearrangeInPartition\]). Thus, $$\begin{aligned} \label{eq:SL_upper_bound} S_{\mathcal{L}} & \ll [\underline{v}]_{\infty}^k N^{-k}\prod_{j=1}^{m}\sum_{\lambda_{1}\in\mathcal{E}_{n}}\sum_{\lambda_{2}\in\mathcal{E}_{n}}\left|g_{2}\left(r\left\Vert \lambda_{2}-\lambda_{1}\right\Vert \right)\right|\cdots\sum_{\lambda_{l_{j}}\in\mathcal{E}_{n}}\left|g_{2}\left(r\left\Vert \lambda_{l_{j}-1}-\lambda_{l_{j}}\right\Vert \right)\right|+[\underline{v}]_{\infty}^k N^{-1}. \end{aligned}$$ Recall the definition of $ F_{\lambda_0} $ in . By Lemma \[lem:CosToDist\], we have $$\label{eq:f_lambda_zero} F_{\lambda_{0}}\left(s\right)=\frac{s}{\pi}+O\left(s^{3}+\Delta\left(n\right)\right)=O\left(s+\Delta\left(n\right)\right).$$ Thus, by Lemma \[lem:H2Formulas\] and , we have that $$\begin{aligned} \label{eq:abs_g2_bound} \frac{1}{N}\sum_{\lambda\in\mathcal{E}_{n}}\left|g_{2}\left(r\left\Vert \lambda-\lambda_{0}\right\Vert \right)\right| & =\int_{0}^{2}\left|g_{2}\left(Ts\right)\right|\,\text{d}F_{\lambda_{0}}\left(s\right)\\ & =\left|g_{2}\left(2T\right)\right|-\frac{1}{2N}+O\left(\int_{0}^{2}\left(s+\Delta\left(n\right)\right)T\left|g_{2}'\left(Ts\right)\right|\,\text{d}s\right) \nonumber \\ & =O\left(T^{-3/2}+\left(\Delta\left(n\right)+T^{-1}\right)\int_{0}^{2T}\left|g_{2}'\left(s\right)\right|\,\text{d}s\right) \nonumber \\ & =O\left(T^{-1}\right) \nonumber \end{aligned}$$ for $ n $ satisfying the hypothesis $ \mathcal{D}(n,\epsilon) $. Applying to each of the $l_{j}-1$ inner summations in , we obtain $$\begin{aligned} S_{\mathcal{L}} & \ll [\underline{v}]_{\infty}^k N^{-k+m}\prod_{j=1}^{m}\left(NT^{-1}\right)^{l_{j}-1} + [\underline{v}]_{\infty}^k N^{-1} \ll [\underline{v}]_{\infty}^k T^{-k+m}. \end{aligned}$$ Let $ \mathcal{L}_0 = \left\{ 2,2,\dots2,\right\} $. Note that if $\mathcal{L}\ne \mathcal{L}_0 $ then $m\le\frac{k-1}{2}$ and therefore $$\label{eq:SL_Estimate} S_{\mathcal{L}}=O\left([\underline{v}]_{\infty}^k T^{-\frac{k+1}{2}}\right).$$ If $\mathcal{\mathcal{L}}=\mathcal{L}_0 $ (this is a viable option for $k$ even), then $$\label{eq:SL_formula} S_{\mathcal{L}_0}=2^{k/2}\left(k-1\right)!!\left[\sum_{\lambda_{1}\ne\lambda_{2}\in\mathcal{E}_{n}}\left|c_{\lambda_{1}}\right|^{2}\left|c_{\lambda_{2}}\right|^{2}h_{2}\left(r\left\Vert \lambda_{1}-\lambda_{2}\right\Vert \right)\right]^{k/2}+O\left([\underline{v}]_{\infty}^k N^{-1}\right).$$ By (\[eq:VarFormula2d\]), $$\label{eq:SL_Variance_asympt} \sum_{\lambda_{1}\ne\lambda_{2}\in\mathcal{E}_{n}}\left|c_{\lambda_{1}}\right|^{2}\left|c_{\lambda_{2}}\right|^{2}h_{2}\left(r\left\Vert \lambda_{1}-\lambda_{2}\right\Vert \right)=\frac{{\mathcal{V}}\left(X_{f_{n},r}\right)}{8\pi^2 r^4}.$$ Hence, and yield $$\label{eq:SL_final_form} S_{\mathcal{L}_0}=\left(k-1\right)!!\left(\frac{{\mathcal{V}}\left(X_{f_{n},r}\right)}{4\pi^2r^4}\right)^{k/2}+O\left([\underline{v}]_{\infty}^k N^{-1}\right).$$ Substituting and into and applying Lemma \[lem:Lower\_Bound\_F2\], we finally obtain that for $k$ even $$\begin{aligned} \left|{\mathbb{E}}[\hat{X}_{f_{n},r}^{k}]-\left(k-1\right)!!\right| & \ll T^{k\eta(n)} [\underline{v}]_{\infty}^k\left(T^{-1/2}+T^{k/2}N^{-\min\{1,\gamma \}}\right) \ll T^{-1/2+2k\eta(n)} \end{aligned}$$ and since for $k$ odd $ \mathcal{L}=\mathcal{L}_0 $ is not a viable option, we obtain $$\begin{aligned} {\mathbb{E}}[\hat{X}_{f_{n},r}^{k}] & \ll T^{k\eta(n)} [\underline{v}]_{\infty}^k\left(T^{-1/2}+T^{k/2}N^{-\min\{1,\gamma \}}\right) \ll T^{-1/2+2k\eta(n) }, \end{aligned}$$ and the second part of Theorem \[thm:VarMainGeneralized\] follows. Proof of Theorem \[thm:Var3D\]: asymptotics for the variance, $d=3$ {#sec:Proof_3d_theorem} =================================================================== Proof of Theorem \[thm:Var3D\] ------------------------------ Denote $$\label{eq:F_3} F_{3}\left(s\right)=\frac{1}{N^{2}} \cdot \#\left\{ \lambda\ne\lambda'\in\mathcal{E}_{n}:\left\Vert \widehat{\lambda}-\widehat{\lambda'}\right\Vert \le s\right\}$$(cf. ), and recall that the spherical cap discrepancy for the points in $\mathcal{E}_{n}$ is defined by $$\label{eq:Discrepancy_3d} \Delta_{3}\left(n\right)=\sup_{\begin{subarray}{c} x\in\mathcal{S}^{2}\\ 0<r\le2 \end{subarray}}\left|\frac{1}{N} \cdot \#\left\{ \lambda\in\mathcal{E}_{n}:\,\left|\widehat{\lambda}-x\right|\le r\right\} -\frac{r^{2}}{4}\right|.$$ \[cor:DistMeasure3d\]We have $$\label{eq:3d_Discrepancy} F_{3}\left(s\right)=\frac{s^{2}}{4}+O\left(\Delta_{3}\left(n\right)\right).$$ The estimate follows immediately from the definition of spherical cap discrepancy, since $$\begin{aligned} F_{3}\left(s\right) & =\frac{1}{N}\sum_{\lambda'\in\mathcal{E}_{n}}\#\left\{ \lambda\in\mathcal{E}_{n}:\,0<\left\Vert \widehat{\lambda}-\widehat{\lambda'}\right\Vert \le s\right\} =\frac{s^{2}}{4}+O\left(\Delta_{3}\left(n\right)\right). \end{aligned}$$ The discrepancy $\Delta_{3}\left(n\right)$ satisfies $ \Delta_3(n) \le n^{-\eta} $ for some small $\eta>0$, see [@BourgainRudnickSarnak]. We are now in a position to prove Theorem \[thm:Var3D\]: By we have $$\begin{aligned} \label{eq:var_3d_asymp_formula} \text{\ensuremath{\mathcal{V}}}\left(X_{f_n,r}\right) & =16\pi^{3}r^{6}\frac{1}{N^{2}}\sum_{\begin{subarray}{c} \lambda,\lambda'\in\mathcal{E}_{n}\\ \lambda\ne\lambda' \end{subarray}}h_{3}\left(T\left\Vert \widehat{\lambda}-\widehat{\lambda'}\right\Vert \right)+O\left(r^{6}N^{-1/4+\epsilon}\right). \end{aligned}$$ For the summation in we have, $$\frac{1}{N^{2}}\sum_{\begin{subarray}{c} \lambda,\lambda'\in\mathcal{E}_{n}\\ \lambda\ne\lambda' \end{subarray}}h_{3}\left(T\left\Vert \widehat{\lambda}-\widehat{\lambda'}\right\Vert \right)=\int_{0}^{2}h_{3}\left(Ts\right)\,\text{d}F_{3}\left(s\right).$$ Thus, integrating by parts and using Lemma \[cor:DistMeasure3d\], $$\begin{aligned} \frac{1}{N^{2}}\sum_{\begin{subarray}{c} \lambda,\lambda'\in\mathcal{E}_{n}\\ \lambda\ne\lambda' \end{subarray}}h_{3}\left(T\left\Vert \widehat{\lambda}-\widehat{\lambda'}\right\Vert \right) & =h_{3}\left(2T\right)F_{3}\left(2\right)-\int_{0}^{2}F_{3}\left(s\right)\,\text{d}h_{3}\left(Ts\right)\label{eq:VarAftIntParts3D}\\ & =h_{3}\left(2T\right)F_{3}\left(2\right)-\frac{1}{4}\int_{0}^{2}s^{2}\,\text{d}h_{3}\left(Ts\right)+Err\left(X_{f_n,r}\right)\nonumber \end{aligned}$$ where $$\label{eq:error_term_3d} Err\left(X_{f_n,r}\right)\ll\Delta_{3}\left(n\right)\int_{0}^{2}T\left|h_{3}'\left(Ts\right)\right|\,\text{d}s.$$ Note that $h_{3}\left(s\right)\ll s^{-4}$ as $s\to\infty.$ Thus, integrating by parts, the main term on the r.h.s of (\[eq:VarAftIntParts3D\]) satisfies $$\label{eq:main_terms_after_intbyparts_3d} h_{3}\left(2T\right)F_{3}\left(2\right)-\frac{1}{4}\int_{0}^{2}s^{2}\,\text{d}h_{3}\left(Ts\right)=\frac{1}{2}\int_{0}^{2}s \cdot h_{3}\left(Ts\right)\,\text{d}s+O\left(T^{-4}\right),$$ so that $$\label{eq:main_int_after_intbyparts} \int_{0}^{2}s \cdot h_{3}\left(Ts\right)\,\text{d}s=\frac{1}{T^{2}}\int_{0}^{2T}s \cdot h_{3}\left(s\right)\,\text{d}s=\frac{1}{T^{2}}\int_{0}^{\infty}s \cdot h_{3}\left(s\right)\,\text{d}s+O\left(T^{-4}\right).$$ A direct computation shows that $$\label{eq:final_calc_main_term_3d} \int_{0}^{\infty}s \cdot h_{3}\left(s\right)\,\text{d}s=\frac{1}{2\pi^3}\int_{0}^{\infty}\frac{1}{s^{3}}\left(\frac{\sin s}{s}-\cos s\right)^{2}\,\text{d}s=\left(2\pi\right)^{-3},$$ and therefore, substituting into and then into we get $$\label{eq:main_term_final_form_3d} h_{3}\left(2T\right)F_{3}\left(2\right)-\frac{1}{4}\int_{0}^{2}s^{2}\,\text{d}h_{3}\left(Ts\right)=\frac{1}{16\pi^3}T^{-2}+O\left(T^{-4}\right).$$ Note that $h_{3}'\left(s\right)\ll\left(1+s^{4}\right)^{-1}$. Thus, $$\label{eq:err_upper_bound_3d} \int_{0}^{2}T\left|h_{3}'\left(Ts\right)\right|\,\text{d}s=\int_{0}^{2T}\left|h_{3}'\left(s\right)\right|\,\text{d}s\le\int_{0}^{\infty}\left|h_{3}'\left(s\right)\right|\,\text{d}s<\infty$$ and therefore, substituting into we obtain $$Err\left(X_{f_n,r}\right)=O\left(\Delta_{3}\left(n\right)\right).\label{eq:3DErrorVar}$$ Substituting into and finally into we obtain (\[eq:AympVar3D\]). Note that by (\[eq:3DErrorVar\]), $$\sup_{\begin{subarray}{c} r > r_{0} \\ f_n\in {\mathcal{B}}{n} \end{subarray}}\left|\frac{\text{\ensuremath{\mathcal{V}}}\left(X_{f_{n},r}\right)}{r^{6}}-T^{-2}\right|=O\left(T_{0}^{-4}+n^{-\eta}\right)$$ for every $n\not\equiv0,4,7\,\left(8\right)$, and in particular $$\text{\ensuremath{\mathcal{V}}}\left(X_{f_{n},r}\right)=o\left(r^{6}\right)$$ uniformly for $r > r_{0}$ for every $n\not\equiv0,4,7\,\left(8\right)$. Proofs of Theorem \[thm:UpperBound2d\] and Theorem \[thm:UpperBound3d\] {#sec:ProofOfBoundsThm} ======================================================================= By substituting the bound $\left|c_{\lambda}\right|^{2}\le N^{-1+\epsilon}$ into (\[eq:VarFormula2d\]), we have $$\begin{aligned} \label{eq:var_ultraflat_bound} \text{\ensuremath{\mathcal{V}}}\left(X_{f_{n},r}\right) & \ll r^{4} N^{-1+\epsilon}\sum_{\lambda_0 \in \mathcal{E}_n}\left|c_{\lambda_0}\right|^{2}\sum_{\lambda \in \mathcal{E}_n} h_{2}\left(r\left\Vert \lambda-\lambda_0\right\Vert \right).\end{aligned}$$ By Lemma \[lem:H2Formulas\] and by , we have $$\begin{aligned} \label{eq:H2_sum} \frac{1}{N}\sum_{\lambda\in\mathcal{E}_{n}}h_{2}\left(r\left\Vert \lambda-\lambda_{0}\right\Vert \right) & =\int_{0}^{2}h_{2}\left(Ts\right)\,\text{d}F_{\lambda_{0}}\left(s\right)\\ & =h_{2}\left(2T\right)-\frac{1}{4N}+O\left(\int_{0}^{2}\left(s+\Delta\left(n\right)\right)T\left|h_{2}'\left(Ts\right)\right|\,\text{d}s\right) \nonumber \\ & =O\left(T^{-1}+\left(\log n\right)^{-\frac{1}{2}\log\frac{\pi}{2}+\epsilon}\right) \nonumber\end{aligned}$$ for $ n $ satisfying the hypothesis $ \mathcal{D}(n,\epsilon) $. Substituting in , we get the upper bound in Theorem \[thm:UpperBound2d\]. The upper bound in Theorem \[thm:UpperBound3d\] follows along similar lines. We now turn to proving the claimed lower bounds for the variance of $X_{f_n,r}$. First, we need the following lemma, proved at the end of section \[sec:ProofOfBoundsThm\]: \[lem:LowerBoundPairs\] 1. Let $\left\{ x_{m}\right\} _{m=1}^{M}$ be $M$ points on the unit circle $\mathcal{S}^{1}.$ For every $1<T<M/2$ we have $$\#\left\{ x_{i}\ne x_{j}:\,\left|x_{i}-x_{j}\right|\le1/T\right\} \gg M^{2}/T.$$ 2. Let $\left\{ x_{m}\right\} _{m=1}^{M}$ be $M$ points on the unit sphere $S^{2}.$ For every $1<T<\sqrt{M}/2$ we have $$\#\left\{ x_{i}\ne x_{j}:\,\left|x_{i}-x_{j}\right|\le1/T\right\} \gg M^{2}/T^{2}.$$ We are now in a position to prove the lower bounds , of Theorem \[thm:UpperBound2d\] and Theorem \[thm:UpperBound3d\]: For $d=2$, we let $$R=\#\left\{ \lambda\in\mathcal{E}_{n}:\,\left|c_{\lambda}\right|^{2}\ge \frac{1}{2N}\right\},$$ so that $$1=\sum_{\lambda\in\mathcal{E}_{n}}\left|c_{\lambda}\right|^{2}=\sum_{\lambda\in R}\left|c_{\lambda}\right|^{2}+\sum_{\lambda\notin R}\left|c_{\lambda}\right|^{2}\le N^{-1+\epsilon} \cdot \#R+1/2,$$ and hence $\#R\ge 2N^{1-\epsilon}.$ By the second part of Lemma \[lem:H2Formulas\], for $c>0$ sufficiently small we have $$\begin{aligned} {\mathcal{V}}(X_{f_n,r}) & =8\pi^{2}r^{4}\sum_{\begin{subarray}{c} \lambda,\lambda'\in\mathcal{E}_{n}\\ \lambda\ne\lambda' \end{subarray}}\left|c_{\lambda}\right|^{2}\left|c_{\lambda'}\right|^{2}h_{2}\left(T\left\Vert \widehat{\lambda}-\widehat{\lambda'}\right\Vert \right) \gg r^{4}N^{-2}\sum_{\lambda\ne\lambda'\in R}h_{2}\left(T\left\Vert \widehat{\lambda}-\widehat{\lambda'}\right\Vert \right)\\ & \gg r^{4}N^{-2}\cdot \#\left\{ \lambda\ne\lambda'\in R:\,\left\Vert \widehat{\lambda}-\widehat{\lambda'}\right\Vert \le c/T\right\} . \end{aligned}$$ By the first part of Lemma \[lem:LowerBoundPairs\], $${\mathcal{V}}(X_{f_n,r})\gg r^{4}N^{-2}\left(\#R\right)^{2}T^{-1}\gg r^{4}N^{-2\epsilon}T^{-1}.$$ The lower bound of Theorem \[thm:UpperBound3d\] follows along the same lines as the above, this time using the second part of Lemma \[lem:LowerBoundPairs\] in place of the first one. Note that in the proof of of the lower bound in Theorem \[thm:UpperBound2d\] we have used the abundance of close-by pairs of lattice points with **$\left|c_{\lambda}\right|^{2}\ge \frac{1}{2N}$**; in the absence of such close-by lattice points, the bound does not hold. For example, for $d=2$, fix $\lambda_{0}\in\mathcal{E}_{n}$ and let $\left|c_{\pm\lambda_{0}}\right|^{2}=1/2$ and $c_{\lambda}=0$ for every $\lambda\ne\pm\lambda_{0}.$ Then $${\mathcal{V}}(X_{f_{n},r})=4\pi^{2}r^{4}h_{2}\left(2T\right)\ll r^{4}T^{-3}.$$ For the first part of Lemma \[lem:LowerBoundPairs\], divide $S^{1}$ into $k=O\left(T\right)$ arcs $I_{1},I_{2},\dots,I_{k}$ of length $<1/T$. For every $1\le j\le k,$ let $n_{j}=\#\left\{ m:\,x_{m}\in I_{j}\right\} ,$ so $\sum_{j=1}^{k}n_{j}=M$. By the Cauchy-Schwarz inequality, $$M^{2}=\left(\sum_{j=1}^{k}n_{j}\right)^{2}\le k\sum_{j=1}^{k}n_{j}^{2}\ll T\sum_{j=1}^{k}n_{j}^{2}.$$ Thus, $$\begin{aligned} \#\left\{ x_{i}\ne x_{j}:\,\left|x_{i}-x_{j}\right|\le1/T\right\} & =\#\left\{ x_{i},x_{j}:\,\left|x_{i}-x_{j}\right|\le1/T\right\} -M\\ & \gg\sum_{j=1}^{k}n_{j}^{2}-M\gg M^{2}/T-M\gg M^{2}/T. \end{aligned}$$ The second part of Lemma \[lem:LowerBoundPairs\] is proved similarly. Restricted averages {#sec:RestrictedAverages} =================== Restricted moments ------------------ For $ d=2 $, most of our principal results above are also valid in the more difficult scenario where $x$ is drawn in $B_{x_{0}}(\rho)$ for some $x_{0}\in{\mathbb{T}}^{2}$ and $\rho\gg n^{-1/2+o(1)}$. In this case, the restricted moments are: expectation $$\label{eq:restricted_expectation} {\mathbb{E}}_{x_{0},\rho}[X_{f_{n},r}] = \frac{1}{{\operatorname{Vol}}(B_{x_0}(\rho))}\int\limits_{B_{x_{0}}(\rho)}X_{f_{n},r;x}dx,$$ higher centred moments $$\label{eq:centred moments rest} {\mathbb{E}}_{x_{0},\rho}[(X_{f_{n},r}-{\mathbb{E}}_{x_{0},\rho}[X_{f_{n},r}])^{k}] = \frac{1}{{\operatorname{Vol}}(B_{x_0}(\rho))}\int\limits_{B_{x_{0}}(\rho)}\left(X_{f_{n},r;x}-{\mathbb{E}}_{x_{0},\rho}[X_{f_{n},r}]\right)^{k}dx, \hspace{1em}k\ge2,$$ and in particular the variance $$\label{eq:restricted_variance} {\mathcal{V}}_{x_{0},\rho}(X_{f_{n},r}) = {\mathbb{E}}_{x_{0},\rho}[(X_{f_{n},r}-{\mathbb{E}}_{x_{0},\rho}[X_{f_{n},r}])^{2}].$$ We reinterpret the statement of Granville-Wigman’s  [@GranvilleWigman Theorem 1.2] as evaluating the expected mass $${\mathbb{E}}_{x_{0},\rho}[X_{f_{n},r}] \sim \pi r^{2},$$ valid for almost all $n\in S_{2}$, uniformly for $\rho\gg n^{-1/2+o(1)}$, $x_{0}\in{\mathbb{T}}^{2}$, and $ r>0 $ (see the first part of Lemma \[lem:ExpVarShrinking\]). Quasi-correlations ------------------ For the restricted moments of $X_{f_{n},r}$ one also needs to cope with [*quasi-correlations*]{}, i.e. tuples $(\lambda^{1},\ldots,\lambda^{l}) \in {\mathcal{E}}_{n}^{l}$ with the sum $\sum\limits_{i=1}^{l}\lambda^{i}$ unexpectedly small, e.g. given a (small) fixed number $\delta >0$, $$\label{eq:sum tuple small l,delta} \left\|\sum\limits_{i=1}^{l}\lambda^{i}\right\| < n^{1/2-\delta};$$ unlike the correlations , here there are no congruence obstructions, so that makes sense with $l$ odd or even. \[def:separatedness Ac\] 1. For $n\in S_2$, $l\in\mathbb{Z}_{\ge 2}$, and $0 < K=K(n) < l\cdot n^{1/2}$ define the set of length-$l$ spectral quasi-correlations $$\label{eq:quasi_correlations} \mathcal{C}_{n}(l;K) = \left\{(\lambda^{1},\ldots,\lambda^{l})\in\mathcal{E}_{n}^{l}:\: 0 < \left\| \sum\limits_{j=1}^{l}\lambda^{j} \right\| \le K \right\}.$$ 2. Given $\delta>0$ we say that $n \in S_{2}$ satisfies the $(l,\delta)$-separateness hypothesis $\mathcal{A}(n;l,\delta)$ if $$\label{eq:sep_hypothesis} \mathcal{C}_{n}(l;n^{1/2-\delta}) = \varnothing.$$ For example, ${\mathcal{A}}(n;2,\delta)$ is equivalent to the aforementioned Bourgain-Rudnick separateness, satisfied  [@Bourgain-Rudnick Lemma 5] by a density $1$ sequence $S_{2}'\subseteq S_{2}$. More generally, it was shown in the forthcoming paper  [@BenatarBuckleyWigman], that for every $\delta>0$ and $l\ge 2$, the assumption ${\mathcal{A}}(n;l,\delta)$ is satisfied by generic $n\in S_{2}'(l,\delta)$, and hence a standard diagonal argument yields a density $1$ sequence $S_{2}'\subseteq S_{2}$ so that ${\mathcal{A}}(n;l,\delta)$ is satisfied for [*all*]{} $l\ge 2$ and $ \delta>0 $ for $ n\in S_2' $ sufficiently large. \[thm:quasi-corr small\] For every fixed $l\ge 2$ and $\delta>0$ there exist a set $S_2'(l,\delta)\subseteq S_2$ such that: 1. The set $S_2'(l,\delta)$ has density $1$ in $S_2$. 2. For every $n\in S_2'(l,\delta)$ the length-$l$ spectral quasi-correlation set $$\mathcal{C}_{n}(l;n^{1/2-\delta})=\varnothing$$ is empty, i.e., the $(l,\delta)$-separateness hypothesis $\mathcal{A}(n;l,\delta)$ is satisfied. A version of Theorem \[thm:VarMainGeneralized\] with restricted averages ------------------------------------------------------------------------ We have the following analogue of Theorem \[thm:VarMainGeneralized\]: \[thm:VarMainExplRestricted\] 1. If $S_{2}'\subseteq S_{2}$ is a sequence satisfying the hypotheses $ \mathcal{D}(n,\epsilon/2),$ $ {\mathcal{A}}(n;2,\epsilon)$, and ${\mathcal{A}}(n;4,\epsilon)$ for all $n\in S_{2}'$, then in the setting of Theorem \[thm:VarMainGeneralized\] part (1), $${\mathcal{V}}_{x_{0},\rho}\left(X_{f_{n},r}\right)\sim\frac{16}{3\pi \cos^{2}\theta_{f_{n}}}r^{4}T^{-1}$$ uniformly for all $x_{0}\in\mathbb{T}^{2}$, $n^{-1/2+\delta}\le\rho\le 1$ and $r_{0}< r< r_{1}$, and $f_{n}\in{\mathcal{F}}_{1}(n;T(n),\eta(n))$. 2. Let $k\ge 3$ be an integer. If $S_{2}'\subseteq S_{2}$ is a sequence satisfying the length-$2k$ diagonal domination assumption and the hypotheses $ \mathcal{D}(n,\epsilon),$ $ {\mathcal{A}}(n;2,\epsilon)$, $ {\mathcal{A}}(n;4,\epsilon)$, and ${\mathcal{A}}(n;2k,\epsilon)$ for all $n\in S_{2}'$, then in the setting of Theorem \[thm:VarMainGeneralized\] part (2), $$\mathbb{E}_{x_{0},\rho}\left[\hat{X}_{f_{n},r}^{k}\right] \to {\mathbb{E}}[Z^{k}]$$ uniformly for $x_{0}\in{\mathbb{T}}^{2}$, $r_{0} < r <r_{1}$, $n^{-1/2+\delta} \le \rho \le 1$, and $f_{n}\in {\mathcal{F}}_{2}(n;T(n),\eta(n))$, where $Z\sim N(0,1)$ is the standard Gaussian variable. Theorem \[thm:VarMainExplRestricted\] follows along similar lines as the proof of Theorem \[thm:VarMainGeneralized\], where we use the expressions for the restricted moments below (cf. equation , Lemma \[lem:VarExpd2\] and equation ). We remark that Theorem \[thm:UpperBound2d\] can also be extended to $ {\mathcal{V}}_{x_{0},\rho}(X_{f_{n},r}) $, however the lower bound will only hold for a generic $ n\in S_2 $. \[lem:ExpVarShrinking\] For $d=2$ let $0<\delta<1/2$, $0<\epsilon<\delta/5$, and $S_{2}'\subseteq S_{2}$. 1. If $n\in S_{2}'$ satisfy the hypothesis ${\mathcal{A}}(n;2,\epsilon) $, then $$\mathbb{E}_{x_{0},\rho}\left[X_{f_{n},r}\right]=\pi r^{2}+O\left(r^{2}n^{-\frac{3}{5}\delta+3\epsilon}\right)$$ uniformly for $x_{0}\in\mathbb{T}^{2},$ $n^{-1/2+\delta}\le\rho\le1$ and $r>0$. 2. \[lem:VarFormulaShrinking\] If $n\in S_{2}'$ satisfy the hypotheses $ {\mathcal{A}}(n;2,\epsilon) $ and ${\mathcal{A}}(n;4,\epsilon)$, then $$\begin{aligned} \text{\ensuremath{\mathcal{V}}}_{x_{0},\rho}\left(X_{f_{n},r}\right) & =8\pi^{2}r^{4}\sum_{\begin{subarray}{c} \lambda,\lambda'\in\mathcal{E}_{n}\\ \lambda\ne\lambda' \end{subarray}}\left|c_{\lambda}\right|^{2}\left|c_{\lambda'}\right|^{2}h_{2}\left(r\left\Vert \lambda-\lambda'\right\Vert \right) +O\left(r^{4} n^{-\frac{3}{5}\delta+4\epsilon}\right) \end{aligned}$$ uniformly for $x_{0}\in\mathbb{T}^{2},$ $n^{-1/2+\delta}\le\rho\le1$ and $r>0$. \[lem:KthMoment\]For $d=2$ let $ k\ge3 $, $0<\delta<1/2$, $0<\epsilon< \delta/5$, and $ S_2' \subseteq S_2 $ satisfying $ {\mathcal{A}}(2;n,\epsilon), $ $ {\mathcal{A}}(4;n,\epsilon), $ and ${\mathcal{A}}(n;2k,\epsilon) $ for every $ n\in S_2' $ . We have $$\begin{aligned} {\mathbb{E}}_{x_{0},\rho}[\hat{X}_{f_{n},r}^{k}] & =(2\pi)^k r^{2k}{\mathcal{V}}_{x_{0},\rho}\left(X_{f_{n},r}\right)^{-k/2}\sum_{\begin{subarray}{c} \forall1\le i\le k,\,\lambda_{i}\ne\lambda_{i}'\in\mathcal{E}_{n}\\ \sum_{i=1}^{k}\left(\lambda_{i}-\lambda_{i}'\right)=0 \end{subarray}}\prod_{j=1}^{k}c_{\lambda_{j}}\overline{c_{\lambda_{j}'}}g_{2}\left(r\left\Vert \lambda_{j}-\lambda_{j}'\right\Vert \right)\\ & +O\left({\mathcal{V}}_{x_{0},\rho}\left(X_{f_{n},r}\right)^{-k/2} r^{2k} n^{-\frac{3}{5}\delta+4\epsilon}\right)\nonumber \end{aligned}$$ uniformly for $x_{0}\in\mathbb{T}^{2},$ $n^{-1/2+\delta}\le\rho\le1$ and $r>0$. Proofs of Lemma \[lem:ExpVarShrinking\] and Lemma \[lem:KthMoment\] ------------------------------------------------------------------- We have $$\label{eq:exp_basic_formula} {\mathbb{E}}_{x_{0},\rho}\left[X_{f_{n},r}\right]=\frac{1}{\pi\rho^{2}}\int_{B_{x_{0}}\left(\rho\right)}\int_{B_{x}\left(r\right)}f_{n}\left(y\right)^{2}\,\text{d}y\,\text{d}x.$$ Granville-Wigman’s [@GranvilleWigman Theorem 1.2] asserts that for $ \epsilon_1 > \epsilon_2 > 0$, $ 0 < \epsilon_3 < \epsilon_1 - \epsilon_2 $ and $ n\in S_2 $ satisfying ${\mathcal{A}}(n;2,\epsilon_2) $, we have $$\label{eq:Granville_Wigman_theorem} \int_{B_{x}\left(r\right)}f_{n}\left(y\right)^{2}\,\text{d}y = \pi r^2 \left(1+ O\left(n^{-3\epsilon_3 /2}\right)\right)$$ uniformly in $ x\in \mathbb{T}^2 $ and $ r>n^{-1/2 + \epsilon_1} $. If $r>n^{-1/2+\frac{2}{5}\delta}$, then by substituting with $ \epsilon_1 = \frac{2}{5}\delta $, $ \epsilon_2 = \epsilon $ and $ \epsilon_3 = \frac{2}{5}\delta - 2\epsilon $ into , we have $${\mathbb{E}}_{x_{0},\rho}\left[X_{f_{n},r}\right]=\pi r^{2}\left(1+O\left(n^{-\frac{3}{2}\left( \frac{2}{5}\delta - 2\epsilon\right)}\right)\right)$$ for every $\rho$. Otherwise, note that $${\mathbb{E}}_{x_{0},\rho}\left[X_{f_{n},r}\right]=\frac{1}{\pi\rho^{2}}\int_{B_{x_{0}}\left(\rho+r\right)}f_{n}\left(y\right)^{2}\int_{B_{x_{0}}\left(\rho\right)\cap B_{y}\left(r\right)}\,\text{d}x\,\text{d}y,$$ so $$\label{eq:Exp_upper_lower_bnds} \frac{r^{2}}{\rho^{2}}\int_{B_{x_{0}}\left(\rho-r\right)}f_{n}\left(y\right)^{2}\,\text{d}y\le{\mathbb{E}}_{x_{0},\rho}\left[X_{f_{n},r}\right]\le\frac{r^{2}}{\rho^{2}}\int_{B_{x_{0}}\left(\rho+r\right)}f_{n}\left(y\right)^{2}\,\text{d}y.$$ Since $r/\rho \le n^{-\frac{3}{5}\delta}$, we can use with $ \epsilon_1 = \delta $, $ \epsilon_2 = \epsilon $ and $ \epsilon_3 = \delta - 2\epsilon $ to deduce that $$\label{eq:Exp_Inner_integral} \int_{B_{x_{0}}\left(\rho\pm r\right)}f_{n}\left(y\right)^{2}\,\text{d}y=\pi\rho^{2}\left(1+O\left(n^{-\frac{3}{5}\delta}\right)\right),$$ and the statement of the first part of Lemma \[lem:ExpVarShrinking\] follows upon substituting into . We have $${\mathcal{V}}_{x_{0},\rho}(X_{f_{n},r}) = \frac{1}{\pi\rho^{2}}\int_{B_{x_{0}}\left(\rho\right)}\left(\int_{B_{x}\left(r\right)}f_{n}\left(y\right)^{2}\,\text{d}y- {\mathbb{E}}_{x_{0},\rho}\left[X_{f_{n},r}\right]\right)^{2}\,\text{d}x.$$ By (\[eq:IntegrandVar\]), $$\begin{aligned} & \frac{1}{\pi\rho^{2}}\int_{B_{x_{0}}\left(\rho\right)}\left(\int_{B_{x}\left(r\right)}f_{n}\left(y\right)^{2}\,\text{d}y-\pi r^{2}\right)^{2}\,\text{d}x\\ & =4\pi^{2}r^{4}\sum_{\begin{subarray}{c} \lambda,\lambda',\lambda'',\lambda'''\in\mathcal{E}_{n}\\ \lambda\ne\lambda'\\ \lambda''\ne\lambda''' \end{subarray}}c_{\lambda}\overline{c_{\lambda'}}c_{\lambda''}\overline{c_{\lambda'''}}g_{2}\left(r\left\Vert \lambda-\lambda'\right\Vert \right)g_{2}\left(r\left\Vert \lambda''-\lambda'''\right\Vert \right)\\ & \times\frac{1}{\pi\rho^{2}}\int_{B_{x_{0}}\left(\rho\right)}e\left(\left\langle x,\lambda-\lambda'+\lambda''-\lambda'''\right\rangle \right)\,\text{d}x\\ & =8\pi^{2}r^{4}\sum_{\begin{subarray}{c} \lambda,\lambda'\in\mathcal{E}_{n}\\ \lambda\ne\lambda' \end{subarray}}\left|c_{\lambda}\right|^{2}\left|c_{\lambda'}\right|^{2}g_{2}\left(r\left\Vert \lambda-\lambda'\right\Vert \right)^{2}\\ & +8\pi^{2}r^{4}\sum_{\begin{subarray}{c} \lambda,\lambda',\lambda'',\lambda'''\in\mathcal{E}_{n}\\ \lambda\ne\lambda'\\ \lambda''\ne\lambda'''\\ \lambda-\lambda'+\lambda''-\lambda'''\ne0 \end{subarray}}c_{\lambda}\overline{c_{\lambda'}}c_{\lambda''}\overline{c_{\lambda'''}}g_{2}\left(r\left\Vert \lambda-\lambda'\right\Vert \right)g_{2}\left(r\left\Vert \lambda''-\lambda'''\right\Vert \right)\\ & \times e\left(\left\langle x_{0},\lambda-\lambda'+\lambda''-\lambda'''\right\rangle \right)g_{2}\left(\rho\left\Vert \lambda-\lambda'+\lambda''-\lambda'''\right\Vert \right). \end{aligned}$$ By the hypothesis ${\mathcal{A}}(n;4,\epsilon)$ and Lemma \[lem:H2Formulas\], we have $$\begin{aligned} & \sum_{\begin{subarray}{c} \lambda,\lambda',\lambda'',\lambda'''\in\mathcal{E}_{n}\\ \lambda\ne\lambda'\\ \lambda''\ne\lambda'''\\ \lambda-\lambda'+\lambda''-\lambda'''\ne0 \end{subarray}}c_{\lambda}\overline{c_{\lambda'}}c_{\lambda''}\overline{c_{\lambda'''}}g_{2}\left(r\left\Vert \lambda-\lambda'\right\Vert \right)g_{2}\left(r\left\Vert \lambda''-\lambda'''\right\Vert \right)\\ & \times e\left(\left\langle x_{0},\lambda-\lambda'+\lambda''-\lambda'''\right\rangle \right)g_{2}\left(\rho\left\Vert \lambda-\lambda'+\lambda''-\lambda'''\right\Vert \right)\\ & \ll\left(\sum_{\lambda\in\mathcal{E}_{n}}\left|c_{\lambda}\right|\right)^{4}\frac{1}{\left(n^{\delta-\epsilon}\right)^{3/2}}\ll N^{2}n^{-\frac{3}{2}(\delta-\epsilon)} \ll n^{-\frac{3}{2}\delta + 2\epsilon}. \end{aligned}$$ Next, note that $$\begin{aligned} \label{eq:inner_int_estimate} \int_{B_{x}\left(r\right)}f_{n}\left(y\right)^{2}\,\text{d}y-\pi r^{2} &= 2\pi r^{2}\sum_{\lambda\ne\lambda'\in\mathcal{E}_{n}} c_{\lambda}\overline{c_{\lambda'}}g_{2}\left(r\left\Vert \lambda-\lambda'\right\Vert \right) \ll r^2 \left(\sum_{\lambda\in\mathcal{E}_{n}}\left|c_{\lambda}\right|\right)^{2} \ll N r^2. \end{aligned}$$ By and the first part of Lemma \[lem:ExpVarShrinking\], $${\mathcal{V}}_{x_{0},\rho}(X_{f_{n},r}) = \frac{1}{\pi\rho^{2}}\int_{B_{x_{0}}\left(\rho\right)}\left(\int_{B_{x}\left(r\right)}f_{n}\left(y\right)^{2}\,\text{d}y-\pi r^{2}\right)^{2}\,\text{d}x + O\left(r^4 n^{-\frac{3}{5}\delta+4\epsilon}\right)$$ and the statement of Lemma \[lem:VarExpd2\] follows. We have $${\mathbb{E}}_{x_{0},\rho}[\hat{X}_{f_{n},r}^{k}] = {\mathcal{V}}_{x_{0},\rho}\left(X_{f_{n},r}\right)^{-k/2} \cdot \frac{1}{\pi\rho^{2}}\int_{B_{x_{0}}\left(\rho\right)}\left(\int_{B_{x}\left(r\right)}f_{n}\left(y\right)^{2}\,\text{d}y- {\mathbb{E}}_{x_{0},\rho}\left[X_{f_{n},r}\right]\right)^{k}\,\text{d}x.$$ By (\[eq:IntegrandVar\]), we have $$\begin{aligned} \frac{1}{\pi\rho^{2}}&\int_{B_{x_{0}}\left(\rho\right)} \left(\int_{B_{x}\left(r\right)}f_{n}\left(y\right)^{2}\,\text{d}y-\pi r^{2}\right)^{k}\,\text{d}x = \left(2\pi\right)^{k}r^{2k} \sum_{\begin{subarray}{c} \forall1\le i\le k,\,\lambda_{i}\ne\lambda_{i}'\in\mathcal{E}_{n}\\ \sum_{i=1}^{k}\left(\lambda_{i}-\lambda_{i}'\right)=0 \end{subarray}}\prod_{j=1}^{k}c_{\lambda_{j}}\overline{c_{\lambda_{j}'}}g_{2}\left(r\left\Vert \lambda_{j}-\lambda_{j}'\right\Vert \right)\\ & +\left(2\pi\right)^{k}r^{2k}\sum_{\begin{subarray}{c} \forall1\le i\le k,\,\lambda_{i}\ne\lambda_{i}'\in\mathcal{E}_{n}\\ \sum_{i=1}^{k}\left(\lambda_{i}-\lambda_{i}'\right)\ne0 \end{subarray}}\prod_{j=1}^{k}c_{\lambda_{j}}\overline{c_{\lambda_{j}'}}g_{2}\left(r\left\Vert \lambda_{j}-\lambda_{j}'\right\Vert \right)\\ & \times2e\left(\left\langle x_{0},\sum_{j=1}^{k}\left(\lambda_{j}-\lambda_{j}'\right)\right\rangle \right)g_{2}\left(\rho\left\Vert \sum_{j=1}^{k}\left(\lambda_{j}-\lambda_{j}'\right)\right\Vert \right). \end{aligned}$$ By the hypothesis ${\mathcal{A}}(n;2k,\epsilon)$, $$\begin{aligned} \sum_{\begin{subarray}{c} \forall1\le i\le k,\,\lambda_{i}\ne\lambda_{i}'\in\mathcal{E}_{n}\\ \sum_{i=1}^{k}\left(\lambda_{i}-\lambda_{i}'\right)\neq0 \end{subarray}}& \prod_{j=1}^{k}c_{\lambda_{j}}\overline{c_{\lambda_{j}'}}g_{2}\left(r\left\Vert \lambda_{j}-\lambda_{j}'\right\Vert \right) e\left(\left\langle x_{0},\sum_{j=1}^{k}\left(\lambda_{j}-\lambda_{j}'\right)\right\rangle \right)g_{2}\left(\rho\left\Vert \sum_{j=1}^{k}\left(\lambda_{j}-\lambda_{j}'\right)\right\Vert \right)\\ & \ll\left(\sum_{\lambda\in\mathcal{E}_{n}}\left|c_{\lambda}\right|\right)^{2k}\frac{1}{\left(n^{\delta - \epsilon}\right)^{3/2}}\ll N^k n^{-\frac{3}{2}(\delta-\epsilon)} \ll n^{-\frac{3}{2}+2\epsilon}. \end{aligned}$$ By and the first part of Lemma \[lem:ExpVarShrinking\], $$\begin{aligned} \mathbb{E}_{x_{0},\rho}[\hat{X}_{f_{n},r}^{k}] & = {\mathcal{V}}_{x_{0},\rho}\left(X_{f_{n},r}\right)^{-k/2} \cdot \frac{1}{\pi\rho^{2}}\int_{B_{x_{0}}\left(\rho\right)}\left(\int_{B_{x}\left(r\right)}f_{n}\left(y\right)^{2}\,\text{d}y-\pi r^2 \right)^{k}\,\text{d}x \\ &+ O\left({\mathcal{V}}_{x_{0},\rho}\left(X_{f_{n},r}\right)^{-k/2} r^{2k} n^{-\frac{3}{5}\delta+4\epsilon}\right), \end{aligned}$$ and the statement of Lemma \[lem:KthMoment\] follows. \[sec:AuxLemmasProof\]Proofs of auxiliary lemmas ================================================ In this section we provide the proofs for lemmas \[lem:BasicVarProp\], \[lem:InnerIntegral\], and \[lem:CosToDist\]:   1. The upper bound is straightforward, and the lower bound follows from (\[eq:BasicNormalization\]) by invoking the Cauchy-Schwarz inequality on . 2. By partial summation, for every $\lambda_{0}\in\mathcal{E}_{n}$ we have $$1=\sum_{\lambda\in\mathcal{E}_{n}}\left|c_{\lambda}\right|^{2}=N\left|c_{\lambda_{0}}\right|^{2}+E,$$ where $\left|E\right|\le V\left(\underline{v} \right)$. Since $\lambda_{0}$ is arbitrary, we deduce that $$[\underline{v}]_{\infty} \le1+V\left(\underline{v} \right).$$ 3. Follows directly from parts $1$ and $2$ of this lemma. We have $$\begin{aligned} \label{eq:inner_int_expansion} \int_{B_{x}\left(r\right)}f_{n}\left(y\right)^{2}\,\text{d}y&=\int_{B_{x}\left(r\right)}\sum_{\lambda,\lambda'\in\mathcal{E}_{n}}c_{\lambda}\overline{c_{\lambda'}}e\left(\left\langle y,\lambda-\lambda'\right\rangle \right)\,\text{d}y\\ & =\frac{\pi^{d/2}}{\Gamma\left(d/2+1\right)}r^{d}+\sum_{\begin{subarray}{c} \lambda,\lambda'\in\mathcal{E}_{n}\\ \lambda\ne\lambda' \end{subarray}}c_{\lambda}\overline{c_{\lambda'}}\int_{B_{x}\left(r\right)}e\left(\left\langle y,\lambda-\lambda'\right\rangle \right)\,\text{d}y.\nonumber \end{aligned}$$ Transforming the variables $y=rz+x$, we obtain $$\label{eq:var_transformation} \int_{B_{x}\left(r\right)}e\left(\left\langle y,\lambda-\lambda'\right\rangle \right)\,\text{d}y=r^{d}e\left(\left\langle x,\lambda-\lambda'\right\rangle \right)\int_{B_{0}\left(1\right)}e\left(\left\langle z,r\left(\lambda-\lambda'\right)\right\rangle \right)\,\text{d}z.$$ Note that $$\begin{aligned} \label{eq:Fourier_ball} \int_{B_{0}\left(1\right)}e\left(\left\langle z,r\left(\lambda-\lambda'\right)\right\rangle \right)\,\text{d}z & =\frac{\left(2\pi\right)^{d/2}J_{d/2}\left(2 \pi r\left\Vert \lambda-\lambda'\right\Vert \right)}{\left(2 \pi r\left\Vert \lambda-\lambda'\right\Vert \right)^{d/2}}, \end{aligned}$$ and (\[eq:IntegrandVar\]) follows upon substituting into and finally into . Let $\theta_{\lambda}$ be the angle between $\lambda$ and $\lambda'$. Then $$\begin{aligned} \frac{1}{N} \cdot \#\left\{ \lambda\in\mathcal{E}_{n}:\,\lambda\succeq\lambda',\left\Vert \widehat{\lambda}-\widehat{\lambda'}\right\Vert \le s\right\} & =\frac{1}{N}\cdot \#\left\{ \lambda\in\mathcal{E}_{n}:\,\theta_{\lambda}\ge0,\,\sqrt{2\left(1-\cos\theta_{\lambda}\right)}\le s\right\} \\ & =\frac{1}{N}\cdot \#\left\{ \lambda\in\mathcal{E}_{n}:\,\theta_{\lambda}\in\left[0,\arccos\left(1-s^{2}/2\right)\right]\right\} \\ & =\frac{1}{2\pi}\arccos\left(1-s^{2}/2\right)+O\left(\Delta\left(n\right)\right)\\ & =\frac{s}{2\pi}+O\left(s^{3}+\Delta\left(n\right)\right) \end{aligned}$$ which is the statement (\[eq:CosToDistEq\]) of Lemma \[lem:CosToDist\]. [10]{} Benatar, J., Buckley, J., Wigman, I., *Two applications of Bourgain’s de-randomization method on toral eigenfunctions and spectral quasi-correlations*, in preparation. Benatar, J., Marinucci, D., Wigman, I. *Planck-scale distribution of nodal length of arithmetic random waves*. Benatar, J., Maffucci R. W., *Random waves on $\mathbb{T}^{3}$: nodal area variance and lattice point correlations.* Int. Math. Res. Not., to appear. Berry, Michael. [*Regular and irregular semiclassical wavefunctions.*]{} J. Phys. A 10 (1977), no. 12, 2083–2091. Berry, Michael. [*Semiclassical mechanics of regular and irregular motion.*]{} Chaotic behavior of deterministic systems (Les Houches, 1981), 171–271, North-Holland, Amsterdam, 1983. Bombieri, E., Bourgain, J., *A problem on sums of two squares*. Int. Math. Res. Not. IMRN (2015), no. 11, 33433407. Bourgain, J. *On toral eigenfunctions and the random wave model*. Israel J. Math. **201** (2014), no. 2, 611630. Bourgain J., Rudnick Z., Sarnak P., *Spatial statistics for lattice points on the sphere I: Individual results*. The Bulletin of the Iranian Mathematical Society (BIMS), special issue in honor of Freydoon Shahidi’s 70’th birthday, to appear. Bourgain, Jean; Rudnick, Zeév. [*On the geometry of the nodal lines of eigenfunctions of the two-dimensional torus.*]{} Ann. Henri Poincaré 12 (2011), no. 6, 1027–1053. Y. Colin de Verdière, *Ergodicité et fonctions propres du Laplacien*, Comm. Math. Phys. [**102**]{} (1985), 497-502. de Courcy-Ireland, Matthew. [*Small-scale equidistribution for random spherical harmonics.*]{} Preprint. available online, <https://arxiv.org/abs/1711.01317> Erdős, P., Hall, R. R., *On the angular distribution of Gaussian integers with fixed norm*. Discrete Math. **200** (1999), no. 1-3, 8794. Feller W., *An introduction to probability theory and its applications, Vol. 2.* Second edition. Wiley, New York (1971). Gradhsteyn I. S., Rizhik I.M., *Table of integrals, series and products,* 6th Edition, Academic Press (2000). Granville, A., Wigman, I., *Planck-scale mass equidistribution of toral Laplace eigenfunctions,* Communications in Mathematical Physics, 355(2), 2017, pp.767-802. Han, Xiaolong. [*Small scale quantum ergodicity in negatively curved manifolds.*]{} Nonlinearity 28 (2015), no. 9, 3263–3288. Han, Xiaolong. [*Small Scale Equidistribution of Random Eigenbases.*]{} Comm. Math. Phys., to appear, available online <https://arxiv.org/abs/1511.01195> Han, Xiaolong, Tacy, Melissa. [*Equidistribution of random waves on small balls.*]{} Preprint. available online, <https://arxiv.org/abs/1611.05983> Hezari, Hamid; Rivière, Gabriel. [*$L^{p}$ norms, nodal sets, and quantum ergodicity.*]{} Adv. Math. 290 (2016), 938–966. Hezari, Hamid; Rivière, Gabriel. [Quantitative equidistribution properties of toral eigenfunctions.]{} J. Spec. Thr., to appear, available online <https://arxiv.org/abs/1503.02794> Humphries, P., 2017. Equidistribution in Shrinking Sets and $L^4$-Norm Bounds for Automorphic Forms. arXiv preprint arXiv:1705.05488. Kuipers L., Niederreiter H., *Uniform distribution of sequences.* Wiley, New York (1974). Krishnapur, M., Kurlberg, P., Wigman, I. *Nodal length fluctuations for arithmetic random waves*, Annals of Mathematics (2) 177, no. 2, 699–737 (2013). Lester, Stephen; Rudnick, Zeév. [*Small scale equidistribution of eigenfunctions on the torus.*]{} Comm. Math. Phys. 350 (2017), no. 1, 279–-300. Luo, Wen Zhi; Sarnak, Peter. [*Quantum ergodicity of eigenfunctions on $PSL_{2}({\mathbb{Z}})\setminus \mathbb{H}^{2}$.*]{} Inst. Hautes Études Sci. Publ. Math. No. 81 (1995), 207–237. Sarnak, P. [*Variance sums on symmetric spaces.*]{} Private communication. Sartori, A. [*Mass distribution for toral eigenfunctions via Bourgain’s de-randomisation.*]{} available online <https://arxiv.org/abs/1812.00962> A. Snirel’man, *Ergodic properties of eigenfunctions*, Uspekhi Mat. Nauk [**180**]{} (1974), 181-182. Young, M. *The quantum unique ergodicity conjecture for thin sets*. Adv. Math. **286** (2016), 958-1016. S. Zelditch, *Uniform distribution of eigenfunctions on compact hyperbolic surfaces*, Duke Math. J. [**55**]{} (1987), 919-941. Zygmund, A. *On Fourier coefficients and transforms of functions of two variables*. Studia Math. 50 (1974), 189201.

#ifndef CAFFE_SOFTMAX_LAYER_HPP_ #define CAFFE_SOFTMAX_LAYER_HPP_ #include <vector> #include "caffe/blob.hpp" #include "caffe/layer.hpp" #include "caffe/proto/caffe.pb.h" namespace caffe { /** * @brief Computes the softmax function. * * TODO(dox): thorough documentation for Forward, Backward, and proto params. */ template <typename Dtype> class SoftmaxLayer : public Layer<Dtype> { public: explicit SoftmaxLayer(const LayerParameter& param) : Layer<Dtype>(param) {} virtual void Reshape(const vector<Blob<Dtype>*>& bottom, const vector<Blob<Dtype>*>& top); virtual inline const char* type() const { return "Softmax"; } virtual inline int ExactNumBottomBlobs() const { return 1; } virtual inline int ExactNumTopBlobs() const { return 1; } protected: virtual void Forward_cpu(const vector<Blob<Dtype>*>& bottom, const vector<Blob<Dtype>*>& top); virtual void Forward_gpu(const vector<Blob<Dtype>*>& bottom, const vector<Blob<Dtype>*>& top); virtual void Backward_cpu(const vector<Blob<Dtype>*>& top, const vector<bool>& propagate_down, const vector<Blob<Dtype>*>& bottom); virtual void Backward_gpu(const vector<Blob<Dtype>*>& top, const vector<bool>& propagate_down, const vector<Blob<Dtype>*>& bottom); int outer_num_; int inner_num_; int softmax_axis_; /// sum_multiplier is used to carry out sum using BLAS Blob<Dtype> sum_multiplier_; /// scale is an intermediate Blob to hold temporary results. Blob<Dtype> scale_; }; } // namespace caffe #endif // CAFFE_SOFTMAX_LAYER_HPP_

8/22/2008 @ 1:30PM Palm Oil Pal Stockbroker Peter Lim knows that most investment tips are suspect–unless they come from a man whose last name is Kuok. In 1991 stockbroker Peter Lim invested $10 million in a palm oil startup. At the time he didn’t know much about the commodity. “If you gave me a coconut and a palm oil nut, I wouldn’t have been able to differentiate between the two,” he recalls. But he knew a lot about the guy who was starting the company. Kuok Khoon Hong used to be a stockbroking client and had since become his friend. “From the moment I first spoke to him, I thought: ‘This man is really very clever. I’d better follow him because he can make a lot of money for me,’” Lim says. Kuok is also the nephew of Malaysian businessman Robert Kuok, who by then was already one of Asia’s most highly regarded billionaires, nicknamed Sugar King for a series of coups in the commodities markets in the 1960s. Before striking out on his own, the younger Kuok had worked for his uncle. Thanks to his bet on Kuok, Lim, 55, is a billionaire, worth $1.1 billion and ranked No. 7 among Singapore’s 40 Richest. Plus he is still an investor in one of Singapore’s hottest stocks: the tiny palm oil outfit has become $18 billion (market cap) Wilmar International, one of Asia’s largest agribusinesses. It has been on fire lately thanks to rising palm oil prices and its high-profile merger with Robert Kuok’s palm plantation, edible oils and grain groups. The stock has more than tripled since its debut on the Singapore exchange in August 2006. Lim isn’t the only one to get rich off Wilmar. The younger Kuok (Wilmar’s CEO) is worth $1.3 billion, ranked 5 in Singapore’s top 40. His cofounder, Indonesian Martua Sitorus, is worth $1.9 billion. Kuok’s uncle added $2.4 billion to his net worth in the past year, thanks largely to Wilmar. But Lim is the luckiest. “Throughout [its] initial stage I never knew what was happening. Everyday I would ask Mr. Kuok what was happening,” recalls Lim, “and he would say, ‘Don’t worry.’” Now he’s happy–and living the high life. He has “many cars,” including Ferraris, Porsches and Lamborghinis, which he parks in the basement of an 11-story condominium block he owns not far from Orchard Road. He lives there with his second wife–an actress–his mother and two teenage children. Other luxuries include a yacht and private jet. Lim believes that his fortune is due to destiny. “It’s not possible for someone to go make a billion dollars–it’s when things just fall into place,” he says. “So I think it’s fate.” The son of a fishmonger, Lim has come a long way from the small flat he shared with his parents, seven siblings and an uncle. His hard childhood motivated him. He went to the top schools in Singapore and studied accounting and finance at the University of Western Australia in Perth, where he held several part-time jobs as a waiter and taxi driver to pay for his tuition. After graduating, Lim worked briefly as an accountant before starting out as a stockbroker. He eventually became known as the Remisier (Singapore term for stockbroker) King, servicing wealthy Indonesians and Singaporeans in the late 1980s and early 1990s. But it was Kuok who returned the service and by 1996 Lim stopped handling other people’s money to become a full-time investor and to take care of personal matters. (He was going through a divorce that dragged on until 2001.) Today he has 20 people, including former bankers and a nuclear physicist, tracking his investments and giving him daily stock updates. While his nearly 5% stake in Wilmar is his most valuable, worth almost $900 million, he also has stakes in fashion retailer FJ Benjamin, investment firm Rowsley Ltd. and brewery restaurant Brewerkz. It will be difficult to match his Wilmar success. He’s hunting for new investments, hoping to take advantage of the current downturn. He likes health care, mining and renewable energy, but what he really wants is another Kuok. “At the end of the day the key component is the person,” he says. “You may target the right company, but if you’ve chosen the wrong person, you’ll get a headache.”

Eula Hall Eula Hall (born October 29, 1927) is a prominent Appalachian activist and healthcare pioneer who founded the Mud Creek Clinic in Grethel in Floyd County, Kentucky. Biography A self-described "hillbilly activist", Eula was born the second of seven surviving children of Lee D. and Nanny Elizabeth Riley, tenant farmers living in Joe Boner Hollow near Greasy Creek, Kentucky. At the age of nine she attended Greasy Creek Elementary School in Pike County and graduated from the eighth grade in five years. The local high school, over 20 miles away, was too far away for her to continue her education. She briefly worked in a World War II canning factory in Ontario, New York, at the age of fifteen, but was sent back to Kentucky on charges of 'inciting a labor riot' concerned with poor working conditions. Upon returning to the mountains, she moved to Floyd County where she worked as a domestic servant for wealthy families who were boarding mine, oil and drilling workers. It was there she met her first husband, McKinley, a coal miner. They married when she was seventeen and together had five children. All were born at home: one was born premature and deaf, and another died in infancy. She rose to prominence as an activist as a member of the local 979 community group and the East Kentucky Worker's Rights Organization. She created the Mud Creek Water District and served as president of the Kentucky Black Lung Association. During President Johnson's War on Poverty she joined the VISTA (Volunteers in Service to America) program and later became one of two local Appalachian Volunteers working in the area. In response to the failed War on Poverty health program in Floyd County, in 1973, she established the Mud Creek Clinic in Grethel, Kentucky. In 1977, she divorced her first husband and the next year married Oliver Hall, a retired miner. A biography of Eula Hall, entitled Mud Creek Medicine: The Life of Eula Hall and the Fight for Appalachia, was written by Kiran Bhatraju and published by Butler Books on November 15, 2013. Mud Creek Clinic In 1973, Hall opened the doors to The Mud Creek Clinic in Mud Creek, Kentucky, for the uninsured and the under-insured. She began with a $1,400 donation and the commitment of two local doctors who volunteered from Our Lady of the Way hospital in Martin, Kentucky. The clinic began in a rented trailer on Tinker Fork, but it soon outgrew the facility and Hall decided to move her own family into a two-bedroom mobile home and use her own house as the new location for the clinic. She converted the three bedrooms into six exam rooms and the rest of the house into waiting rooms and offices. At the time, the clinic didn't have its own pharmacy and medications had to be delivered from the local hospital after the clinic had closed. Hall would spend half the night delivering medication to patients who had been at the clinic that day. By 1977, the patient population was so great that Mud Creek Clinic was struggling to meet the needs of the community. Patients often came from as far as Tennessee, West Virginia, and Ohio to get medical care. Mud Creek Clinic then joined forces with Big Sandy Health Care, Inc. (BSHC) a local nonprofit health care organization that operated another community clinic in neighboring Magoffin County. This merger allowed Mud Creek to receive some federal funding and widen its patient care. After the merger, Hall stayed on as a patient advocate for the Mud Creek Clinic and continues to work in that capacity today. Clinic rebuilt following arson In 1982, Hall and the Mud Creek community suffered a great loss when the clinic burned down at the hand of a mysterious arsonist. The next morning Hall and the clinic doctor pulled a picnic table under a willow tree and treated patients who had scheduled appointments. She had the telephone company place a telephone on the tree so that patients could call the clinic. Hall then had two used trailers joined together to use as a temporary clinic. A few months after the fire, Hall received a letter from the Appalachian Regional Commission (ARC) stating that they would donate funds for a new facility for Mud Creek Clinic. One of the conditions of the funding was that the community would be required to provide $80,000 in matching funds. She called a public meeting and more than 400 people showed up and pledged their support. People gave money and items to be raffled off at auction, Hall organized a two-day radiothon that raised $17,000 and multiple chicken-and-dumpling dinners that earned $1,300 apiece. With Eula's leadership, the community raised $120,000 - $40,000 more than the necessary $80,000 required by the ARC. The extra money paid for new X-ray equipment for the clinic. The new clinic opened its doors in 1984 as a modern brick building. It is still the home of the clinic today. The clinic houses its own laboratory, X-ray machines, and pharmacy. The clinic has expanded to include an adjacent building that houses a dental clinic, clothing room, and a food pantry that serves more than 100 families per month. Current operations The Mud Creek Clinic had more than 213,000 patient encounters last year and no one is ever turned away. As social director, Hall counsels patients on disability claims and Social Security benefits, arranges financial aid for food and drugs, answers questions about food stamps and housing opportunities, and attends civic board meetings and hearings. When patients can't afford lawyers, she often represents them in court. She wins approximately four percent of her cases. Awards and recognition Hall has received numerous awards for her advocacy work, including honorary doctorates from Berea College - Berea, Kentucky; Midway College - Midway, Kentucky; Pikeville College - Pikeville, Kentucky and Trinity College - Hartford, Connecticut. She was honored at Berea College alongside the Nobel Peace Prize winner Archbishop Desmond Tutu. In 2004, the Appalachian Ministries Educational Resource Center presented Hall with the Annual David S. Shuller Spirit of AMERC Award. She has received personal letters from President George Bush, Senator Mitch McConnell, and Representative Hal Rogers, among other notables who have recognized the amazing work and the ongoing effort Hall has devoted to the health and well-being of eastern Kentucky. Highway 979, which runs through the Mud Creek area, was named the Eula Hall Highway in her honor during October 2006. Big Sandy Healthcare also has started two funds in tribute to Hall. The Eula Hall Patient Assistance Fund will cover healthcare costs for uninsured and indigent patients and the Eula Hall Scholarship Fund will provide financial assistance for area students pursuing careers in healthcare or social services. The clinic has been visited by former President Bill Clinton, Senator Edward Kennedy, Reverend Jesse Jackson, and John Edwards. References Resources . Eula Hall, director of Mud Creek Clinic, is one of the five people from eastern Kentucky interviewed by Appalshop to give their ideas about the causes of violence and offer possible solutions. Category:Living people Category:American health activists Category:VISTA volunteers Category:1927 births Category:People from Pike County, Kentucky Category:Berea College alumni Category:People from Floyd County, Kentucky Category:Kentucky women in health

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Michael Owens/Getty Images The XFL concluded its opening weekend Sunday following an encouraging return with Saturday's two games. The New York Guardians hosted the Tampa Bay Vipers in the first of two matchups, and the Dallas Renegades brought the day to a close against the St. Louis BattleHawks. Here are some of the highlights from the action. New York Guardians def. Tampa Bay Vipers 23-3 The Guardians coasted to a 23-3 win over the Vipers thanks in large part to their defense, which forced three turnovers. Jamar Summers dealt the final blow to Tampa Bay in the fourth quarter. He recovered a fumble and returned for a touchdown, effectively sealing the victory. Matt McGloin only threw for 182 yards but had one touchdown pass and avoided making any big mistakes. He also scored on a one-yard touchdown run in the first quarter. The Guardians gave up 394 yards yet held the Vipers scoreless on four trips inside the red zone, which largely told the story. Tampa Bay's offense was out of sorts for most of the afternoon. The Vipers opened the second half with Quinton Flowers at quarterback following a shaky first half from Aaron Murray. The former Georgia star went 11-of-25 for 156 yards and two interceptions. The second interception was particularly costly as Tampa Bay was poised to get on the board to end the second quarter. Although Murray re-entered the game, Flowers made a positive impact by bringing a different dimension to the Vipers offense with his mobility. He ran for 34 yards on five carries. Drawing any firm conclusions after only one game is rarely a good idea, but the Vipers might be better off by leaning on Flowers more when they face off with the BattleHawks in Week 2. Marc Trestman and his staff have some things to iron out in the coming days. St. Louis BattleHawks def. Dallas Renegades 15-9 If Week 1 is any indication, the BattleHawks defense will be a factor all season. St. Louis set the tone on that side of the ball, keeping Bob Stoops' Renegades out of the end zone and spearheading a 15-9 victory Sunday. While Dallas quarterback Philip Nelson was a solid 33-of-42 passing for 209 yards, St. Louis sacked him four times and forced him into shorter underneath routes that ultimately didn't do much damage. It was only fitting Will Hill notched an interception to clinch the win. BattleHawks quarterback Jordan Ta'amu was 20-of-27 passing for 209 yards, one touchdown and zero interceptions with 77 rushing yards, but it was running back Keith Ford who put the winning side on the board first with a touchdown on a pitch play that saw him break through multiple arm tackles. That, along with a touchdown pass from Ta'amu to Alonzo Russell in the fourth quarter, was enough to outlast three field goals from Dallas kicker Austin MacGinnis. Field position also proved important in the defensive slugfest, and former Oakland Raiders and Denver Broncos punter Marquette King impressed for the BattleHawks: St. Louis will face the Houston Roughnecks in Week 2, while the Renegades will play the Los Angeles Wildcats.

Q: ms-access: query (concat multiple records into one) here's a glimpse of the original table: Occurrence Number Occurrence Date 1 0 Preanalytical (Before Testing) Cup Type 2 0 Analytical (Testing Phase) 2 0 Area 3 0 Postanalytical ( After Testing) 4 0 Other Practice Code Comments 1477 2/5/2010 1.1 Specimen Mislabeled PURSLEY 1476 2/5/2010 1.1 Specimen Mislabeled HPMR 1475 2/5/2010 1.1 Specimen Mislabeled ACCIM N008710 1474 2/5/2010 1.1 Specimen Mislabeled ACCIM N008636 1473 2/5/2010 1.3 QNS-Quantity Not Sufficient SAPMC 1472 2/5/2010 1.3 QNS-Quantity Not Sufficient RMG 1471 2/5/2010 1.1 Specimen Mislabeled NMED 1470 2/5/2010 1.9 QNS- Specimen Spilled in transit MRPS 1469 2/5/2010 1.9 QNS- Specimen Spilled in transit ANESPC 1468 2/5/2010 2.22 Instrument Problem-reinject LAB 1525 2/8/2010 2.5 Other - False (+) Blanks Tecan 2 LAB 1524 2/8/2010 2.5 Other - False (+) Blanks Tecan #1 LAB Blank 019 1523 2/8/2010 2.22 Instrument Problem, 2.5 Other Tecan LAB 1519 2/8/2010 3.3A Reporting Error 4.1 LIS Problem? (see LOM 1418,1520) LAB/SJC F356028 1518 2/8/2010 1.4 Tests Missed/Wrong Test Ordered SDPTC F316628 1516 2/8/2010 1.6 Test Requisition Missing TPMCF 2 specimens both unlabeled 1515 2/8/2010 1.1 Specimen Mislabeled PALMETTO 1514 2/8/2010 1.1 Specimen Mislabeled THWR 1513 2/8/2010 1.1 Specimen Mislabeled THWR i am getting information from this table using the following statement: select mid(Lom1,1,4) as LOM, sum([Count1]) as [Count] from ( SELECT [Lab Occurrence Form].[1 0 Preanalytical (Before Testing)] as Lom1,Count([Lab Occurrence Form].[1 0 Preanalytical (Before Testing)]) AS [Count1] FROM [Lab Occurrence Form] WHERE ((([Lab Occurrence Form].[Occurrence Date]) Between [Forms]![Meeting_Reasons_Frequency]![Text4] And [Forms]![Meeting_Reasons_Frequency]![Text2])) GROUP BY [Lab Occurrence Form].[1 0 Preanalytical (Before Testing)] HAVING Count([Lab Occurrence Form].[1 0 Preanalytical (Before Testing)])<>0 UNION SELECT [Lab Occurrence Form].[2 0 Analytical (Testing Phase)], Count([Lab Occurrence Form].[2 0 Analytical (Testing Phase)]) AS [CountOf2 0 Analytical (Testing Phase)] FROM [Lab Occurrence Form] WHERE ((([Lab Occurrence Form].[Occurrence Date]) Between [Forms]![Meeting_Reasons_Frequency]![Text4] And [Forms]![Meeting_Reasons_Frequency]![Text2])) GROUP BY [Lab Occurrence Form].[2 0 Analytical (Testing Phase)] HAVING Count([Lab Occurrence Form].[2 0 Analytical (Testing Phase)])<>0 union SELECT [Lab Occurrence Form].[3 0 Postanalytical ( After Testing)], Count([Lab Occurrence Form].[3 0 Postanalytical ( After Testing)]) AS [CountOf3 0 Postanalytical ( After Testing)] FROM [Lab Occurrence Form] WHERE ((([Lab Occurrence Form].[Occurrence Date]) Between [Forms]![Meeting_Reasons_Frequency]![Text4] And [Forms]![Meeting_Reasons_Frequency]![Text2])) GROUP BY [Lab Occurrence Form].[3 0 Postanalytical ( After Testing)] HAVING Count([Lab Occurrence Form].[3 0 Postanalytical ( After Testing)])<>0 UNION SELECT [Lab Occurrence Form].[4 0 Other], Count([Lab Occurrence Form].[4 0 Other]) AS [CountOf4 0 Other] FROM [Lab Occurrence Form] WHERE ((([Lab Occurrence Form].[Occurrence Date]) Between [Forms]![Meeting_Reasons_Frequency]![Text4] And [Forms]![Meeting_Reasons_Frequency]![Text2])) GROUP BY [Lab Occurrence Form].[4 0 Other] HAVING Count([Lab Occurrence Form].[4 0 Other])<>0 ORDER BY 1, 2) group by mid(Lom1,1,4); this is what the query returns: LOM Count 1.1 231 1.11 21 1.3 103 1.4 6 1.5 1 1.6 25 1.8 2 1.9 88 2.1 8 2.22 5 2.24 1 2.3 1 2.4 1 2.5 29 3.2 13 3.3 8 3.3A 4 4.1 2 4.6 1 4.8 7 i need to add another column here. let's say it is column3 this is the output that need: LOM Count column3 1.1 231 everything from original table where LOM LIKE *1.1* separated by "," 1.11 21 everything from original table where LOM=1.11 separated by "," 1.3 103 everything from original table where LOM=1.3 separated by "," 1.4 6 everything from original table where LOM=1.4 separated by "," 1.5 1 everything from original table where LOM=1.5 separated by "," 1.6 25 1.8 2 1.9 88 2.1 8 2.22 5 2.24 1 2.3 1 2.4 1 2.5 29 3.2 13 3.3 8 3.3A 4 4.1 2 4.6 1 4.8 7 prac 1 that would mean the first element in column 3 would be "something1, something2, etc...somethingelse231" i apologize if this explanation is horrible, please let me know if i can clarify anything A: Here's one solution I found: http://www.access-programmers.co.uk/forums/showpost.php?p=272455&postcount=2 It requires writing a VBA function. I don't know of a way to do it with straight SQL in Access. Public Function Conc(Fieldx, Identity, Value, Source) As Variant Dim cnn As ADODB.Connection Dim rs As ADODB.Recordset Dim SQL As String Dim vFld As Variant Set cnn = CurrentProject.Connection Set rs = New ADODB.Recordset vFld = Null SQL = "SELECT [" & Fieldx & "] as Fld" & _ " FROM [" & Source & "]" & _ " WHERE [" & Identity & "]=" & Value ' open recordset. rs.Open SQL, cnn, adOpenForwardOnly, adLockReadOnly ' concatenate the field. Do While Not rs.EOF If Not IsNull(rs!Fld) Then vFld = vFld & ", " & rs!Fld End If rs.MoveNext Loop ' remove leading comma and space. vFld = Mid(vFld, 3) Set cnn = Nothing Set rs = Nothing ' return concatenated string. Conc = vFld End Function You can then use it in a query like this: SELECT [tblData].[ID], Conc("Field1","ID",[ID],"tblData") AS Field1, Conc("Field2","ID",[ID],"tblData") AS Field2 FROM tblData GROUP BY [tblData].[ID]; Edit So your first query would look something like this: SELECT [Lab Occurrence Form].[1 0 Preanalytical (Before Testing)] as Lom1, Conc("NameOfTheFieldToConcatenate", "[Lab Occurrence Form].[1 0 Preanalytical (Before Testing)]", [Lab Occurrence Form].[1 0 Preanalytical (Before Testing)], "[Lab Occurrence Form]"), Count([Lab Occurrence Form].[1 0 Preanalytical (Before Testing)]) AS [Count1] FROM [Lab Occurrence Form] WHERE ((([Lab Occurrence Form].[Occurrence Date]) Between [Forms]![Meeting_Reasons_Frequency]![Text4] And [Forms]![Meeting_Reasons_Frequency]![Text2])) GROUP BY [Lab Occurrence Form].[1 0 Preanalytical (Before Testing)] HAVING Count([Lab Occurrence Form].[1 0 Preanalytical (Before Testing)])<>0 Note that you may have to tweak the Conc() function a little to get the wildard compare you want instead of an exact match on the LOM field.

［チューリヒ／ニューヨーク ２４日 ロイター］ - 米食品医薬品局（ＦＤＡ）は２４日、スイス製薬大手ノバルティスNOVN.Sの遺伝性疾患の脊髄性筋萎縮症（ＳＭＡ）に対処する遺伝子療法「ゾルゲンスマ」を承認した。２歳以下の小児に対する治療として認められる。 価格は２１２万５０００ドル（約２億３０００万円）と過去最高額。ただ、ゾルゲンスマは１回限りの治療であるため、年間数十万ドルのコストがかかる長期療法と比べ、患者が負担する最終的なコストは低減されるとノバルティス幹部は説明している。 日本と欧州でも年内の承認を見込む。 ＳＭＡは、新生児１万人当たり１人の割合で発症。乳幼児の遺伝性疾患の死因の第１位とされている。 ＳＭＡ治療では、これまでにバイオジェンBIIB.Oの「スピンラザ」が承認されている。 リフィニティブのまとめたアナリスト調査によると、ゾルゲンスマの売上高は２０２２年までに２０億ドルに達する見通し。スピンラザの昨年の売上高は１７億ドルで、２２年までに２２億ドルに拡大すると予想されている。

In a study conducted last year, women with breast cancer exposed to beta blocker drugs were apparently less likely to die after many years of treatment. With the same objective, scientists from the Cancer Research UK are gauging if beta-blockers could help in prohibiting breast cancer metastasis and increasing the survival rate. The investigators wished to gauge the efficacy of beta blocker drugs that are usually consumed for high blood pressure and anxiety prior to and during breast cancer treatment. The findings show a biological mechanism through which beta blockers can stop the mobility of cancer cells and thus prevent its spread.

Q: Infinite word size abstraction I was reading the java doc of BigInteger, they mentioned "infinite word size abstraction" more than one places. what are they referring to? https://docs.oracle.com/javase/7/docs/api/java/math/BigInteger.html A: They are referring to word as processing unit for a computer processor. https://en.wikipedia.org/wiki/Word_(computer_architecture) The word size is normally a small number like 32 or 64 bits for a given processor, but BigInteger provides an abstraction for infinite word size.

Weather Forecast Somerset School District approves levy for 2016-17 school year A sparse audience composed primarily of Somerset School District administrators, staff and school board members, unanimously approved a proposed tax levy of $4,993,942 for the 2016-17 school year at the district’s annual meeting held Monday night. The proposed levy translates into a projected mill rate of $9.88 per $1,000 of property value. Board Vice President Marie Colbeth and District Director of Business Services & Operations Dave Gerberding led a briskly paced budget hearing immediately preceding the annual meeting. The total school levy comprised of the General Fund, Referendum Debt Service Fund, Non-Referendum Debt Service Fund, Capital Expansion Fund, and Community Service Fund totaling $7,199,688 represents a 3.14 percent increase over the same levy for the 2015-16 school year. Total projected budget revenues for 2016-17 of 16,903,365 less total projected expenditures of $16,948,763 will result in a deficit for the 2016-17 school year of $45,398. In addition to the budget, audience members got a brief look at district enrollment numbers, the 2016-21 Strategic Plan, an update on state testing results (indefinitely embargoed), money saving projects proposed for 2016-17 and the new school year calendar. For questions regarding the proposed budget, contact your local school board member or District Director of Business Services & Operations, Dave Gerberding, at 715-247-4848.

Design, Images, and Artwork Cannot Be Reproduced Under Any Circumstances. Website Design and Development This web design and all associated website development and SEO was completed by Brett Henry d.b.a B-Interactive! Any inquiries about the design of this website design should be directed to: brett@honest.coffee.

I have a few theories of how I’m going to die: slowly, painfully, of cancer. Struck down in a traffic accident [as anyone who has ever seen me cross a road will agree with 100%]. A mugging gone wrong. [Trigger happy people abound]. But this is the year 2019, Syria and Iraq are still smouldering, the horrors of war are still emerging, and here, in Pakistan, one is now apparently waiting for war. To be struck down. For trigger-happy men to make decisions about the lives of millions of people. We do not have the right to choose our own deaths, to even plan for a future. Even that right has been stripped away. Every 2, 5, 10 years, I am reminded that choosing a future is a luxury. It is not a right. That the future is reduced to merely waiting, waiting for the big flash in the sky, for death.

Q: sed command to be used to modify the file name I am able to use the sed command for a simple things but I have a question which for me is complex to find the solution by my own, so if some one can help me it would be a great favour. example: how shall I modify the following file as following? orig_file_name = OBIEE_S99_TT_PLV_BI0026.rpd target_file_name = OBIEE_S99_TT_PLV.rpd so in my bash script, I will be doing following. 1. check the latest file in a directory. 2. pickup that file and modify its name, similar as above. situations: I do not know always what would be the file name is, but i know the part of pattern, file names always ends as "something_is_name_xxxx.rpd" so then I would want to modify the file name as "something_is_name.rpd" A: I would do something like this, but i don't doubt there are better solutions. for f in $(ls -1t OBIEE_S99_TT_PLV* | head -1) do mv $f $(echo $f | sed 's/_BI[0-9]*//g') done

/** * Copyright (C) 2010-2018 Gordon Fraser, Andrea Arcuri and EvoSuite * contributors * * This file is part of EvoSuite. * * EvoSuite is free software: you can redistribute it and/or modify it * under the terms of the GNU Lesser General Public License as published * by the Free Software Foundation, either version 3.0 of the License, or * (at your option) any later version. * * EvoSuite is distributed in the hope that it will be useful, but * WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU * Lesser Public License for more details. * * You should have received a copy of the GNU Lesser General Public * License along with EvoSuite. If not, see <http://www.gnu.org/licenses/>. */ package org.evosuite.javaagent; import org.evosuite.Properties; import org.evosuite.TestUtil; import org.evosuite.classpath.ClassPathHandler; import org.evosuite.instrumentation.InstrumentingClassLoader; import org.evosuite.instrumentation.testability.TestabilityTransformationClassLoader; import org.evosuite.testcase.execution.ExecutionTrace; import org.evosuite.testcase.execution.ExecutionTracer; import org.junit.Assert; import org.junit.BeforeClass; import org.junit.Ignore; import org.junit.Test; public class InstrumentingClassLoaderTest { @BeforeClass public static void initClass() { ClassPathHandler.getInstance().changeTargetCPtoTheSameAsEvoSuite(); } @Test public void testClassWithStaticInitializationCallingGetPackage() throws ClassNotFoundException { InstrumentingClassLoader instrumentingClassLoader = new InstrumentingClassLoader(); Class<?> stat = Class.forName("com.examples.with.different.packagename.StatInitIssue", true, instrumentingClassLoader); } /* * Tests the child-first/parent-last property of the classloader. */ @Ignore @Test public void testDependingInstrumentation() throws Exception { Class<?> originalClass = DependentClassLoaderTestSubject.class; Properties.TARGET_CLASS = originalClass.getName(); Properties.PROJECT_PREFIX = originalClass.getPackage().getName(); Properties.TARGET_CLASS_PREFIX = Properties.PROJECT_PREFIX; TestabilityTransformationClassLoader instrumentingClassLoader = new TestabilityTransformationClassLoader(); Class<?> changedClass = instrumentingClassLoader.loadClass(ClassLoaderTestSubject.class.getName()); Assert.assertEquals(instrumentingClassLoader, changedClass.getClassLoader()); Object changed = changedClass.getConstructor().newInstance(); ExecutionTracer.enable(); ExecutionTracer.getExecutionTracer().clear(); TestUtil.invokeMethod(changed, "trySomethingElse"); ExecutionTrace execTrace = ExecutionTracer.getExecutionTracer().getTrace(); execTrace = ExecutionTracer.getExecutionTracer().getTrace(); Assert.assertFalse(execTrace.getTrueDistances().isEmpty()); Assert.assertFalse(execTrace.getFalseDistances().isEmpty()); ExecutionTracer.getExecutionTracer().clear(); } @Ignore @Test public void testDirectInstrumentation() throws Exception { Class<?> originalClass = ClassLoaderTestSubject.class; Properties.TARGET_CLASS = originalClass.getName(); Properties.PROJECT_PREFIX = originalClass.getPackage().getName(); ClassLoaderTestSubject original = new ClassLoaderTestSubject(); ExecutionTracer.enable(); ExecutionTracer.getExecutionTracer().clear(); original.assess(6); ExecutionTrace execTrace = ExecutionTracer.getExecutionTracer().getTrace(); Assert.assertTrue(execTrace.getTrueDistances().isEmpty()); Assert.assertTrue(execTrace.getFalseDistances().isEmpty()); TestabilityTransformationClassLoader instrumentingClassLoader = new TestabilityTransformationClassLoader(); Class<?> changedClass = instrumentingClassLoader.loadClass(ClassLoaderTestSubject.class.getName()); Assert.assertEquals(instrumentingClassLoader, changedClass.getClassLoader()); Assert.assertTrue(changedClass.hashCode() != originalClass.hashCode()); Assert.assertFalse(changedClass.equals(originalClass)); Object changed = changedClass.getConstructor().newInstance(); try { @SuppressWarnings("unused") ClassLoaderTestSubject casted = (ClassLoaderTestSubject) changed; Assert.fail(); } catch (ClassCastException exc) { // expected } ExecutionTracer.getExecutionTracer().clear(); TestUtil.invokeMethod(changed, "assess", Integer.valueOf(6)); execTrace = ExecutionTracer.getExecutionTracer().getTrace(); Assert.assertFalse(execTrace.getTrueDistances().isEmpty()); Assert.assertFalse(execTrace.getFalseDistances().isEmpty()); ExecutionTracer.getExecutionTracer().clear(); } @Ignore @Test public void testInnerClasses() throws Exception { Class<? extends InnerClassesTestSubject> originalClass = InnerClassesTestSubject.class; Properties.TARGET_CLASS = originalClass.getName(); Properties.PROJECT_PREFIX = originalClass.getPackage().getName(); TestabilityTransformationClassLoader instrumentingClassLoader = new TestabilityTransformationClassLoader(); Class<?> changedClass = instrumentingClassLoader.loadClass(InnerClassesTestSubject.class.getName()); Assert.assertEquals(instrumentingClassLoader, changedClass.getClassLoader()); Assert.assertTrue(changedClass.hashCode() != originalClass.hashCode()); InnerClassesTestSubject original = originalClass.newInstance(); Assert.assertEquals("abcd", original.toString()); Object modified = changedClass.newInstance(); Assert.assertEquals("abcd", modified.toString()); } }

Psychologist Ty Tashiro, author of Awkward: The Science of Why We're Socially awkward and Why That's Awesome, explains why awkward people are more likely to demonstrate “striking talent.” Following is a transcript of the video. There is a stereotype in our culture that some people are too smart for their own good. There's a finding in psychology that people who are socially awkward are also more likely to demonstrate what psychologists call “striking talent,” which means that they have tremendous ability in a specific area. So it's not the case that people are usually smart across the board, it's usually the case that people are really smart in one or two areas and then they might be average or even below average in other areas. One of the splits that you see is that if someone's really smart in a certain area, they're less likely to be socially skilled or be a good communicator but they also have this obsessive interest. They have this tendency to focus really intensely and really narrowly sometimes on a specific topic. Now, that can work against them sometimes. Sometimes they're overly rigid or sometimes they don't like it when their routines are broken. But that can be a real strength as well because someone with great focus and great energy is more likely to persist through hard times, more likely to persist when task could get boring to other people. And this manifests in what psychologists call “deliberate practice,” which is the idea that you practice the same thing over and over until you reach a point of mastery and key to deliberate practice is the idea that you are willing to work the hardest on the parts that you are the worst at. And awkward people seem to enjoy the kind of persistence and long hours that go on to mastering a certain area or certain topic. So we often like to say that people are “nerding out” about something. That's actually a very awkward kind of characteristic. You are super enthusiastic about it, you are super focused on it. But all of this focus and energy can sometimes result in expertise and can even result in times when they reach groundbreaking innovation or redefine the way that a field operates or thinks.

1. Technical Field This invention relates to the field of data transmission, and in particular to systems and methods for reliably determining the voltage level of data signals transmitted at high speeds. 2. Background Art Computers and other data processing devices operate at ever increasing frequencies. In order to avoid bottlenecks, data must be provided to these devices at high speeds and without distortion. However, as transmission frequencies exceed 150 MHz, it becomes more difficult to ensure that transmitted data signals have sufficient time to settle before they are sampled and the next data transition begins. This problem is compounded by the need to operate computers at lower system voltages, to limit the power dissipated by high frequency processors. High frequency operation of buses, which transfer data signals to different parts of the computer system, poses especially difficult problems. At frequencies of 100 MHz or more, bus traces behave like transmission lines. In particular, the inductive and capacitive properties of bus traces distort data signals, increasing the time it takes for signal voltages to settle sufficiently to be sampled reliably. For example, at high frequencies, the capacitance of bus traces requires signal transitions to be driven with higher currents, and for 32-bit and wider buses, the number of signal transitions being driven results in substantial current pulses on the supply voltage lines. These current pulses couple with the inductance of the bus traces to generate voltage glitches. In addition, impedance mismatches between the bus and the circuits driving the data signal creates reflections on the bus. Data signals are distorted by reflected signals generated by voltage glitches and signal voltages. One result of these distortions is that a data signal in a given clock cycle may appear to be in either a high or low voltage state, depending on when in the clock cycle it is sampled by a receiver. Conventional strategies for handling high speed data signals employ circuitry to guarantee a window of relatively clean signal transitions, and a single reference voltage is selected within this voltage window. There are a number of drawbacks to this approach. Noise is generated differently for high-going and low-going transitions, and the resulting asymmetry in the signal distortion must be accounted for by the circuitry. In addition, the circuitry used to provide a clean voltage window becomes more complex and less effective as signal frequencies increase.

Lew Hoad Lewis Alan Hoad (23 November 1934 – 3 July 1994) was an Australian world No. 1 tennis player whose career lasted from the early 1950s until the early 1970s. Hoad won four Grand Slam tournaments as an amateur (Australian, French and twice Wimbledon). He was a member of the Australian team that won the Davis Cup four times between 1952 and 1956. Hoad turned professional in July 1957 and won the Forest Hills Tournament of Champions event in 1959. He also won the Ampol Tournament of Champions at Kooyong in 1958, one of the richest tournaments of the era. He won the Ampol World Tournament Championship Tour in 1959–1960. During his career his main competitors were his longtime amateur tennis teammate Ken Rosewall and, throughout his professional career, Pancho Gonzales. Hoad was ranked in the world top ten for amateurs from 1952 until 1957, reaching the world No. 1 spot in 1956. He was ranked the world No. 1 professional in Kramer's official 1959–1960 Ampol ranking of all the contract professionals. He was ranked the world No. 1 tennis player, professional or amateur, for 1962 in a poll of 85 U.S. sports editors. Serious back problems plagued Hoad throughout his career, probably caused by a weight-lifting exercise he devised in 1954, particularly after he turned professional, and led to his effective retirement from tennis in 1967 although he made sporadic comebacks, enticed by the advent of the open era in 1968. In his autobiography, Jack Kramer, the professional tennis promoter and former player, rated Hoad as one of the 21 best players of all time. Rod Laver in 2012 rated Hoad as the greatest player of the "past champions" era of tennis and stated that power, volleying and explosiveness were his strengths. Following his retirement in 1972, Hoad and his wife Jenny operated a tennis resort, Lew Hoad's Campo de Tenis in Fuengirola, Spain, near Málaga. Hoad died of leukemia on 3 July 1994. Early life and career Lewis Hoad was born on 23 November 1934, in the working-class Sydney inner suburb of Glebe, the eldest of three sons of tramway electrician Alan Hoad and his wife Ailsa Lyle Burbury. Hoad started playing tennis at age five with a racket gifted by a local social club. As a young child, he would wake up at 5 a.m. and hit tennis balls against a wall and garage door until the neighbours complained, and he was allowed to practice on the courts of the Hereford Tennis Club behind the house. At age 10 he competed in the seaside tournament at Manly in the under 16 category. In his youth, he often played with Ken Rosewall, and they became known as the Sydney "twins", although they had very different physiques, personalities and playing styles. Their first match was in their early teens and was played as an opener of an exhibition match between Australia and America. Rosewall won 6–0, 6–0. Hoad built up great physical strength, especially in his hands and arms, by training at a police boys' club, where he made a name as a boxer. Hoad was about 12 when he was introduced to Adrian Quist, a former Australian tennis champion and then general manager of the Dunlop sports goods company. Quist played a couple of sets with Hoad and was impressed by his natural ability. When Hoad was 14 he left school and joined the Dunlop payroll, following the pattern of that 'shamateur' era when most of Australia's brightest tennis prospects were employed by sporting goods companies. Hoad had just turned 15 when he and Rosewall were selected to play for New South Wales in an interstate contest against Victoria. In November 1949, Hoad won the junior title at the New South Wales Championships, and the same weekend, he also competed in the final of the junior table tennis championship in Sydney. Tennis career Amateur career: 1951–1957 1951 Hoad's first Grand Slam tournament appearance was at the 1951 Australian Championships held in January at the White City Tennis Club in Sydney. He won his first match against Ronald McKenzie in straight sets but lost in the following round to defending champion Frank Sedgman. It was the only Grand Slam tournament he played that year. 1952 In 1952, he reached the third round of the Australian Championships, played in Adelaide, and in April, he was selected by the Australasian Lawn Tennis Association as member of the team to play in overseas tournaments. In May, before departing to Europe, he won the singles title at the Australian Hardcourt Championships after a five-set win in the final against Rosewall. Hoad, who had never played a tournament on clay courts, received a walkover in the first round of the French Championships and lost in straight sets to sixth-seeded and 1947 and 1951 finalist Eric Sturgess. In only their second appearance as a doubles team at a Grand Slam event, Hoad and Rosewall reached the French semifinal. Hoad subsequently played the Belgian tennis championships in Brussels in early June and reached the quarterfinal in which he was outclassed by Budge Patty. Hoad's first entry at the grass court Queen's Club Championship in June 1952 ended in the quarterfinal against countryman and eventual champion Frank Sedgman. A week later, he played his first match at the Wimbledon Championships defeating Beppe Merlo in a nervous and unimpressive five-set encounter. Wins against Rolando del Bello and Freddie Huber were followed by a fourth round loss against second-seeded and eventual finalist Jaroslav Drobný. Hoad and Rosewall caused an upset when they defeated second-seeded Gardnar Mulloy and Dick Savitt in the third round of the doubles event in a run that ended in the semifinal against Vic Seixas and Eric Sturgess. After a semifinal result at the Swedish championships in July, and an exhibition between Australia and West Germany, Hoad and the Australian team traveled to the United States under the guidance of coach Harry Hopman. As a preparation for his first U.S. Championships he played the Meadow Club Invitational (Southampton), Eastern Grass Court Championships (South Orange), and Newport Invitational before teaming up with Rosewall to reach the semifinal of the U.S. National Doubles Championships in Brookline. Hoad was the eighth seeded foreign player at the U.S. Championships. He won four matches to reach his first Grand Slam quarterfinal but due in part to making 64 errors could not overcome his countryman Sedgman who would win the tournament without losing a set. With Thelma Coyne Long he reached the final of the mixed doubles event, the first Grand Slam final of his career, but they lost in straight sets to Doris Hart and Frank Sedgman. An early loss at the Pacific Southwest Championships in September concluded his first overseas tour. In September, he was jointly ranked No. 10 in the world for 1952 with Rosewall by Lance Tingay of The Daily Telegraph. 1953 Hoad started 1953 poorly in the singles with a second-round exit against Clive Wilderspin at the Australian Championships in Melbourne after playing an uncharacteristic baseline game. He was more successful in doubles where he and Rosewall became the youngest team to win the Australian doubles title after a victory in the final against Mervyn Rose and Don Candy. In March, Hoad successfully defended his singles title at the Australian Hardcourt Championships, defeating Rosewall in a five set semifinal, and 34-year-old John Bromwich in the final. In the semifinal, he survived six matchpoints against Rosewall. Two weeks later, Hoad lost the final of the N.S.W. Hardcourt Championships against Mervyn Rose. Hoad's second overseas tour started in late April, and after an exhibition in Cairo at the Gezira Sporting Club, he entered the Italian Championships in Rome. He reached the final, losing to Drobný in straight sets but won the doubles title with Rosewall. At the French Championships in May, Hoad was seeded fourth and made it to the quarterfinals in which he lost to Vic Seixas due to overhitting and an unreliable serve. Hoad and Rosewall followed up their Australian title with a win at the French Championships after a three-set win in the final against countrymen Rose and Wilderspin. In June Hoad's attacking serve-and-volley game proved too good for Wimbledon favorite Rosewall in the final of the Queen's Club Championship and he won the tournament without losing a set. At Wimbledon, Hoad was seeded sixth, and as at the French, Vic Seixas defeated him in the quarterfinal, this time in a close five-set match that ended on a Hoad double fault. In an all-Australian doubles final Hoad and Rosewall defeated Hartwig and Rose to win their third Grand Slam doubles title of the year. Hoad lost to Enrique Morea in the final of the Dutch Championships in mid July. He won his first title on U.S. soil in South Orange at the Eastern Grass Court Championships in mid August, defeating compatriot Rex Hartwig in the final. In the semifinal against Rosewall, he pulled a back muscle. Hoad and Rosewall's hopes of winning the doubles Grand Slam, two years after fellow Australians Ken McGregor and Frank Sedgman had first achieved that feat, were dashed when they lost surprisingly in the third round of the U.S. Doubles Championships. As the second-seeded foreign player, Hoad was one of the favorites for the singles title at the U.S. Championships. He won four matches to reach the semifinal where for the third time in 1953 he lost in a Grand Slam event to Vic Seixas. Following his defeat, and that of Rosewall in the other semifinal, there was criticism in the press that both 18-year-old players were physically and mentally worn out due to the intensive schedule imposed by coach Harry Hopman. In September, Seixas again beat Hoad, this time in the semifinal of the Pacific Southwest Championships in Los Angeles. Hoad was rested a few weeks upon his return to Australia and then entered the Queensland Championships in early November where he won the singles title in a 41-minute final against Hartwig. Two weeks later, Hoad won the N.S.W. Championships after a four-set victory in the final over Rosewall in front of a 10,000 Sydney crowd but had trouble with a sore right elbow. His good form continued in early December at the Victorian Championships when he again defeated Rosewall in the final. The much anticipated Davis Cup challenge round match against defendants United States took place at the Melbourne Kooyong Stadium in late December. Surprisingly Hartwig was selected to partner Hoad in the doubles instead of Rosewall, a decision widely criticized in the press. In the opening singles matches, Hoad defeated Seixas, his nemesis that season, in straight sets, while Trabert defeated Rosewall, also in straight sets. Hoad and Hartwig lost the doubles match against Seixas and Trabert and Australia trailed 1–2 at the start of the final day. Hoad is remembered for his match as a 19-year-old amateur against the United States champion Tony Trabert. In a hard-fought match in front of a 17,000 crowd, Hoad defeated Trabert in five sets to help his country retain the Cup. It was seen as one of the best Davis Cup matches in history. Directly following the final, Hoad received his call-up papers for National Service. Hoad was ranked No. 5 in the world for the year according to Lance Tingay. Hoad won 10 tournaments in 1953 and was 6 wins and 0 losses against Rosewall that year. 1954 In January, Hoad played just one tournament before entering his National Service training. At the South Australian Championships in Adelaide he reached the final but sub-par play led to a straight-sets defeat to Trabert. On 13 January, Hoad joined the 13th National Service Training battalion in Ingleburn for a period of 98 days and commented that "It will be a welcome break from tennis". As a consequence, Hoad was unable to participate in the Australian Championships. At the end of February, Hoad received a leave from service to play for the Australian team in the third test match against South Africa in front of the Queen and Duke of Edinburgh. He played a singles match, a doubles match with Rosewall and a mixed-doubles match with his girlfriend Jenny Staley. When Hoad returned to service, he was bitten by a spider while on maneuvers which caused him to become ill and hospitalized him for ten days. He spent two days in coma which was not made public. While he was in service, Hoad devised a weight-lifting exercise, doing push-ups with round 50 lb. weights placed on his back, which Hoad later believed probably initiated his back trouble. Hoad left the National Service at the end of April and his third overseas tour with an Australian team started on 5 May. For the first time in his career, Hoad was the top-seeded player at a Grand Slam tournament when he entered the French Championships but he failed to live up to it when he lost in the fourth round to 41-year-old Gardnar Mulloy. Hoad reached the doubles final with Rosewall but the pair were soundly beaten by Seixas and Trabert in a 56-minute final. Partnering Maureen Connolly, who had won the women's singles title, Hoad won the mixed-doubles event after a win in the final against Jacqueline Patorni and Rex Hartwig. In June, Hoad overcame countryman Rose in the final of the Queen's Club Championship to successfully defend his 1953 singles title. Hoad was one of the favorites for the Wimbledon Championships and was seeded second behind Trabert. In the fourth round, Hoad avenged his loss to Mulloy at the French Championships, defeating him in four sets. In the quarterfinal the powerful service and excellent returns of 33-year-old Jaroslav Drobný proved too much for Hoad and he was beaten in straight sets within the hour. Hoad and Rosewall were unable to defend their Wimbledon doubles title after losing in fives sets in the semifinal to Seixas and Trabert. A surprise loss against Roger Becker in the semifinal at the Midlands Counties Championships in Birmingham was followed in mid-July by winning the singles title at the Swiss Championships in Gstaad. As in the previous year, Hoad met Rosewall in the Eastern Grass Court Championships in August, this time in the final, and again the titleholder was victorious, overpowering Rosewall to win the singles title in three straight sets. At Newport in mid August, Hoad was beaten by 17-year-old compatriot Roy Emerson who won the deciding set 8–6. For the third time in 1954, Seixas and Trabert defeated Hoad and Rosewall at a Grand Slam doubles event, winning the U.S. Doubles Championships in Brookline. Hoad, seeded first among the foreign players at the U.S. Championships, failed to live up to his seeding when he lost to Ham Richardson in a five-set quarterfinal. His lackluster form continued when he was defeated by unseeded Luis Ayala in the quarterfinal of the Pacific Southwest Championships in mid-September. After returning to Australia at the end of September, Hoad scheduled extra practice to work on his serve and volley but subsequently lost to Don Candy in the semifinal of the Sydney Metropolitan Championships. In early November, matters briefly improved as he consolidated the Queensland title in Brisbane. In the final, he overcame a sunstroke and the loss of sets three and four by 0–6 to defeat Hartwig in five sets. In mid-November, he was upset by veteran John Bromwich who better exploited the windy conditions in the quarterfinal of the N.S.W. Championships. At the Victorian Championships, the last significant tournament before the Davis Cup Challenge Round, Hoad was defeated in straight sets in the semifinal by Seixas. As in the previous match against Sven Davidson he showed such poor form and at times an apparent lack of interest that he was jeered by the crowd and several left after he smashed a ball into the stands. The 1954 Davis Cup Challenge Round was played on 27–29 December on the grass courts at the White City Stadium in Sydney between title holders Australia and the United States. Hoad played the first rubber, in front of a record crowd of 25,000, which he lost to world No. 1, Trabert, in a high-quality four-set match. Rosewall also lost his singles match and the United States won back the cup after Seixas and Trabert defeated Hoad and Rosewall in four sets in the doubles rubber. At the end of an erratic and ultimately disappointing season Hoad's world ranking slipped to No. 7. In a 1956 interview, Hoad admitted that especially in 1954 he often got fed-up with tennis and didn't care whether he played or not. 1955 Hoad started the 1955 season on a low note when he was unable to play the South Australian tennis championship in early January due to a torn ligament. To some surprise he entered the mixed doubles event at the 1955 Australian Championships with his girlfriend Jenny Staley and the pair finished as runner-ups to Thelma Coyne Long and George Worthington. In the singles event, Hoad reached his first Grand Slam tournament final after solid wins over Seixas (quarterfinal) and Hartwig (semifinal). In the final Rosewall's accuracy and control, however, were too strong for him and he lost in three straight sets. Hoad did not participate in the French Championships as the Davis Cup team that he was part of only left for Europe at the end of May during the Championships. In the singles final of the Queen's Club Championship in mid-June Hoad, who had gotten married earlier that day, lost his service seven times and lost to Rosewall in two straight sets but won the doubles event with Hartwig. Hoad was the fourth-seeded player at the Wimbledon Championships at the end of June. In his quarterfinal match against seventh-seeded Budge Patty, his game lacked accuracy and he conceded a break in each set resulting in a loss in straight sets. Hoad was the second-seeded foreign player at the U.S. Championships in September held on the muddy courts of Forest Hills. In the quarterfinal, he lost his service three times in succession in the third set and suffered a straight-sets defeat in 50 minutes against Trabert, the first-seeded U.S. player, and eventual champion. Having lost the Davis Cup in 1954, Australia had to play through the 1955 Davis Cup preliminary rounds to challenge holders United States. In July, Australia defeated Mexico, Brazil and Canada to win the Americas Zone and subsequently beat Japan and Italy in the Inter-zone matches in August. In the Challenge Round, played at the West Side Tennis Club, Forest Hills from 26–28 August, Hoad defeated the French and Wimbledon champion Trabert in four sets in his first singles rubber and with Hartwig won the doubles match to reclaim the cup for Australia. In his first significant tournament after the Davis Cup, Hoad won the New South Wales Championships in November after a win in the final against Rosewall. In December, he added the singles title at the Victorian Championships after a tough five-sets final win over 19-year old Ashley Cooper. At the end of the year he was ranked No. 3 in the world according to Tingay. 1956 Hoad started the year with a five-set defeat in the final of the South Australian Championships against countryman Neale Fraser. At the following Manly tournament, the crowd overflowed the stands during the final hindering Rosewall's baseline game more than Hoad's, resulting in a straight-sets win for Hoad in 35 minutes. At the Australian Championships, played in Brisbane, Hoad overcame a two sets to one deficit against Mervyn Rose in the quarterfinal and beat Neale Fraser in the semifinal to reach his second consecutive Australian final. His opponent was again Ken Rosewall, and this time Hoad overcame his rival and titleholder in four sets to win his first Grand Slam singles title. His success was completed by winning the doubles title with Rosewall against Don Candy and Mervyn Rose. At the beginning of March, Hoad and his wife left for an overseas private tour, i.e. a tour sanctioned but not organized by the Australian tennis federation. First stop of the tour was Cairo where Hoad won the singles title at the Egyptian Championships against Sven Davidson followed by a tournament win in Alexandria over Fred Kovaleski. At Monte Carlo in late March, he was surprisingly beaten by Tony Vincent in the quarterfinal. In the Australian ranking published in April, reflecting the season until the end of March, Hoad overtook Rosewall as No. 1. Singles titles at the Lebanese Championships and at the Connaught Club in Essex followed in April but the month ended with a semifinal loss to Ham Richardson at the British Hard Court Championships in Bournemouth. Hoad won his first Italian Championships on the clay courts of the Foro Italico in Rome in early May when he outplayed Sven Davidson in straight sets. At the French Championships, Hoad survived a five-set scare against Robert Abdesselam in the third round before winning the final against Sven Davidson in straight sets to claim his second consecutive Grad Slam singles title. Unknown to the public, Hoad had stayed up the night previous to the final, invited by a Russian diplomat, and was drunk when he came home. An intensive workout by Rod Laver got him into a state that allowed him to play the final. In May, Hoad won the International Golden Ball tournament in Wiesbaden, West Germany after a straight-sets victory in the final over Art Larsen but at the Trofeo Conde de Godó in Barcelona, he lost in the quarterfinal to Bob Howe. As a preparation for Wimbledon, Hoad elected to play the singles event at the Northern Championships in Manchester instead of the Queen's Club Championships. He reached the final but had to bow for 34-year old Jaroslav Drobný who won the deciding set 7–5. Hoad was seeded first for the Wimbledon Championships and was the pre-tournament favorite. He lost two sets along the way to reach the final, in which he faced Rosewall. In the first all-Australian final since 1922, Hoad was victorious in four sets to gain his first Wimbledon and third successive Grand Slam championship title. Hoad also won the doubles title with Rosewall, their third Wimbledon title, outclassing Orlando Sirola and Nicola Pietrangeli in the final in straight sets. Following his Wimbledon title he entered the Midlands tournament and was beaten in the semifinal by Mike Davies. In August, Hoad won the singles title at the German Championships, held on the clay courts at Hamburg, with a four-set defeat of Orlando Sirola in the final. Shortly after Wimbledon, Hoad experienced severe pain and stiffness in his lower back, at a level higher than before the tournament. He arranged to travel to the U.S. by boat on the RMS Queen Mary rather than suffer a long plane trip. However, the pain continued and reduced the level of his play for the remainder of the year and into 1957. After his transatlantic voyage in August, Hoad played directly in the U.S. Championships, having missed the preparatory tournament at Newport. Having won the first three stages of the Grand Slam, Hoad was favoured to win the fourth and then turn professional for a lucrative contract offered by Jack Kramer. In an upset, however, he lost the final in four sets to Rosewall in the U.S. Championships at Forest Hills. Hoad and Rosewall won the doubles title against Seixas and Richardson. After this, Hoad played in the O'Keefe Invitational at the Toronto Lawn Tennis Club in Rosedale, Toronto on a red clay surface. He defeated Luis Ayala in the semifinal and Sven Davidson in a four set final. At the Pacific Southwest Championships in September, the last leg of his overseas tour before returning to Australia, Hoad was beaten by Alex Olmedo in the third round. In early November he lost the final of the Queensland Championships to Ashley Cooper in five sets and was hindered by numbness in the serving arm between the elbow and the wrist. The following week Hoad had to retire from the New South Wales Championships during his first round match against Ross Sherriff due to a sore arm. In mid December Hoad and Rosewall competed in the final of the Victorian Championships which was their last final as amateurs as Rosewall turned professional at the end of the month. The final started late due to rain and was stopped due to darkness at two sets to one for Hoad but the following day Rosewall won the last two sets and the title. In late December, Hoad was part of the Australian Davis Cup team which successfully defended the cup in the Challenge Round against the United States who were weakened by the absence of Tony Trabert who had turned professional in the fall of 1955. In his last Davis Cup appearance, Hoad won both his singles rubbers, against Herbie Flam and Seixas, as well as his doubles match with Rosewall to help Australia to a 5–0 victory. Hoad was confined to bed with back pain for the two days prior to the Davis Cup matches, and was relieved to find that he could play well. At the end of the year, Hoad was ranked No. 1 in the world for the first time in his career. 1957 Hoad played poorly in early 1957, due to back trouble, and was placed in an upper body cast for six weeks, following which he slowly returned to tennis competition in April 1957. He then experienced a period of pain-free playing for 11 months. Hoad won his second successive Wimbledon singles title, defeating Ashley Cooper in a straight-sets final that lasted 57 minutes. After the tournament, he turned professional by signing a two-year contract with Kramer for a record guarantee of $125,000 which included a $25,000 bonus for winning the 1957 Wimbledon singles title. In addition, Hoad would receive 20% of the gate receipts for each match, along with a 5% bonus if he won the match (against Gonzales). This "percentage of gate" clause of the contract would result in Hoad earning over £50,000 sterling ($140,000) in the first 11 months of his pro career (through May, 1958) and £71,400 sterling ($200,000) by late 1959. Hoad's biographers state that Hoad earned "nearly $200,000" by the end of the 1958 tour. By turning professional, Hoad was no longer eligible to compete in the amateur Grand Slam tournaments. Professional career: 1957–1966 Jack Kramer's first attempt to sign Hoad and Rosewall for his professional tour came in September 1954 when both players were in Los Angeles for the Pacific Coast Championships. Both signed a contract but later changed their minds and elected to remain amateurs. A renewed offer in October 1955 was also turned down. Fresh from his victory over Hoad at the 1956 U.S. Championships, it was Ken Rosewall who first signed the professional contract and went on to spend the new year as the regular victim of Pancho Gonzales on the pro tour. 1957 In July 1957, Hoad won his debut match as a professional against Frank Sedgman at the Forest Hills Tournament of Champions. He won his next match, against Pancho Segura, but then lost nine straight matches to various opponents as he adjusted to the pro tour. After Forest Hills, Hoad commented on the difference between amateur and professional tennis: "It's an entirely different league. These pros make mistakes but they don't make them on vital points. That's the difference." In September during a four-man tour of Europe by Hoad with Kramer, Rosewall, and Segura, Kramer and Hoad were interviewed by BBC television. Kramer stated in that interview his estimation of Hoad's game: "I feel that he's potentially the best player that tennis might ever have." 1958 In 1958 a series of 100 head-to-head matches was planned between Hoad and the reigning champion of professional tennis, Pancho Gonzales. The series started in January in a number of Australian cities in major stadiums on grass courts with a best-of-five set format, and at the end of the Australian subtour, Hoad was leading 8–5. The key match of the Australian series was the second Kooyong encounter, which Hoad won in four sets, a marathon 80 games, 4–6, 9–7, 11–9, 18–16 which leveled the series at five wins each. Hoad followed-up with a 15 to 3 winning streak against Gonzales (including the non-tour Kooyong Tournament of Champions deciding match). In February, the series continued in the United States, mostly in indoor venues and local gyms with a best-of-three set format. Hoad won 18 of the first 27 matches, and on 28 February, Gonzales met with Kramer and indicated that he had lost confidence of winning the series. However, after they played an outdoor match on 1 March on a chilly night in Palm Springs, Hoad's back stiffened which affected him significantly for the rest of the series. Twice Hoad was forced to take time off to rest his back and was substituted for in his absence by Rosewall and Trabert. From 9–18 Gonzales surged to a 26–23 lead, and at the end of the series on 8 June, he had defeated Hoad by 51 matches to 36. Gross receipts for the American portion of that series were reported in a Daily Mail interview with Hoad in 1959 to be $240,000. For the 1958/1959 seasons, Kramer had a powerful troupe of professional champions, including 11 Hall of Fame players, under contract, and he designed a series of major tournaments to provide a format in which all of them could participate. Kramer designated four tournaments as professional majors, Forest Hills, Kooyong, L.A. Masters, and Sydney White City. Hoad won three of these eight tournaments in 1958/59. In January 1958, Hoad won the Kooyong Tournament of Champions in Melbourne, with prize money of AUS£10,000 ($22,400). The tournament was funded by the Australian oil company Ampol. Hoad defeated Gonzales in the deciding match, and won all five of his matches in the round-robin event. He received AUS£2,500 ($5,600) for his win, a record payday in pro tennis. In the final of the Cleveland World Pro on 5 May, Hoad lost a two-set lead against Gonzales while struggling with a leg-muscle injury. Hoad dropped out of the tour in late May to rest his thigh injury. At the Forest Hills Tournament of Champions in June 1958, Hoad's thigh injury healed in time for his final match which he won against Gonzales on the final day in a weekend match televised nationally on CBS. The reporter for the L.A. Times called this Hoad/Gonzales broadcast "one of the most sensational displays of tennis that I can remember." However, Gonzales won the event with a better overall round-robin record. At Roland Garros in September, Hoad won his quarterfinal against Trabert, and his semifinal against Gonzales. While leading in the final against Rosewall, Hoad wrenched his back reaching for a ball, and could not play well in the remainder of the match. He had to default the Wembley Pro tournament in September due to an "arthritic" back.Hoad rested for the next three months and did not play again until 1959. Hoad had earned $140,000 through May of 1958, and nearly $200,000 by the end of the 1958 season. 1959 In early 1959, he began the Ampol world championship tournament series slowly, hampered by an elbow injury. However, at the end of January, Hoad defeated Rosewall and Cooper to win at Perth and in February 1959, he defeated Rosewall in three sets to win the South Australian Pro Championships in Adelaide. This gave Hoad the lead in Ampol points after the first group of five tournaments, a lead he would never relinquish until the series ended in January 1960. The Ampol World Series resumed in North America in June with the L.A. Masters at the L.A. Tennis Club on cement, followed by the O'Keefe Professional Championships at the Toronto Lawn Tennis Club in Rosedale, Toronto on red clay, and the Forest Hills Tournament of Champions in New York City at the Forest Hills stadium on grass. In the four-man 1959 Kramer Pro Tour, which ran from mid-February through May in the United States, Hoad built a lead of 12 to 5 in his series of matches against Gonzales, after a win in Newcastle, Pennsylvania in late April. Gonzales stated that "I had blisters under my blisters from the punishment" on that tour. However, the daily grind of the tour began to cause a renewal of Hoad's back trouble, and he finally won against Gonzales by 15 matches to 13. He also won his head-to-head's with newly turned pro Ashley Cooper (18–2) and Mal Anderson (9–5). With a win-loss record of 42–20 he finished second in the four-man tour ranking behind Gonzales (47–15) and earned $28,250. Gross receipts for that four-month American series were reported in a Daily Mail interview with Hoad as $160,000. At the Cleveland World Pro Championships in late April, not part of the Ampol world tour, Hoad lost the final to Gonzales in three straight sets. At the Forest Hills Tournament of Champions in June 1959, broadcast nationally on the CBS television network, Hoad defeated Rosewall in the semifinal and Gonzales in the final, both in four sets, to claim the title. According to tennis journalist and author Joe McCauley this was the zenith of Hoad's career. In the August 1959 issue of World Tennis, Riggs wrote of the Forest Hills final, "the match signified the end of an era. The great Gonzales who had dominated professional tennis for four years had been decisively beaten..." In that same issue of World Tennis, it was noted that Hoad had been seeded No. 1 at Forest Hills and Gonzales seeded No. 2 on the basis of Ampol points. In August 1959, Hoad finished runner-up to Cooper at the Slazenger Professional Tournament in Eastbourne, not part of the Ampol tour. In September, Hoad lost to Sedgman in the semifinal of the French Pro at Roland Garros but defeated Rosewall in a playoff for third place. In the Grand Prix de Europe regional tour of European locations from August to October, which excluded Roland Garros and Wembley (components of the Ampol tour), Hoad finished in third place behind Sedgman and Rosewall (Gonzales defaulted the Grand Prix de Europe tour), and at the end of 1959, Kramer placed Hoad in fourth place in his personal world professional rating, while the French sportspaper L'Équipe ranked Hoad fifth. However, Kramer's Australian tennis agent Bob Barnes placed Hoad in first spot, corresponding to Hoad's standing on the official Ampol ranking. The Ampol World Series moved back from Europe to Australia where it was completed with five tournaments in November and December/January. Hoad won the Perth and Adelaide events to begin the final series. The final event of the Ampol world tennis championship, the Qantas Kooyong Championships, began on 26 December 1959 with prize money of AUS£6,000 ($13,440). On 2 January 1960, Hoad defeated Rosewall in a three-hour, four-set match to win the Qantas Kooyong round-robin tournament, a match which Kramer acclaimed as one of the best ever played. With this win also came the Ampol world tournament tour championship trophy and bonus prize of AUS£2,500 ($5,600). The Ampol World Series tour had consisted of 15 tournaments around the world played between 10 January 1959 and 2 January 1960. Hoad finished first on the tour with 51 bonus points, ahead of Gonzales (43 points) and Rosewall (41 points). Hoad won six of the 15 tournaments and 71% (36/51) of his matches on the tour, while Gonzales won four tournaments and 72% (26/36) of his matches. Gonzales defaulted three Ampol tournaments, and played 15 fewer matches than Hoad. Hoad was three wins and five losses in matches against Gonzales in the Ampol World Series, although Hoad and Gonzales were two wins and two losses against each other in tournament deciding matches. Hoad won six of his eight matches against Rosewall on the Ampol world tour. The Melbourne newspaper "The Age" for 4 January 1960 declared, Hoad "was crowned the new world professional tournament champion at Kooyong" by winning the Ampol world series. French language "L'Impartial" for 6 January 1960 declared "Lewis Hoad world champion", the win at Kooyong "allows him at the same time to claim the world title for 1959". The order of finish of the 12 professionals on the Ampol tour was designated by Kramer to be the official ranking for 1959, and determined the seeding list for all tournaments.. The field of professional players for the Ampol World Series included 11 present-day members of the International Tennis Hall of Fame. This would turn out to be Hoad's only professional world championship tour victory in three full attempts, and the only world championship tournament series reported between 1946 and 1964. Kramer's office reported that for the 1959 year as a whole, Hoad had won his personal series of matches against Gonzales 24 to 23. He withdrew from the 1960 world championship tour, citing a need for family time. By then Hoad had made approximately $200,000 since turning pro, while another report had his career earnings at $224,000 including $70,000 in 1959 alone. Hoad's biographers stated that he made "almost $200,000" by the end of the 1958 season. He also estimated his endorsement income at about $22,400 per year, plus investment returns on a hotel ownership with other players. The total would be well over $250,000 through 1959. It was reported that Hoad would likely earn more in 1959 than top baseball player Mickey Mantle and the best-paid American football players. 1960 Hoad had been the number-one money winner in pro tennis for both 1958 and 1959, and his initial contract with Kramer was renegotiated in early February 1960, as well as Rosewall's, for a seven year term to run through the 1966 season. Hoad took a three-month layoff at the beginning of 1960 to rest his back and spend time with his family. When he returned to play, he was rusty, slow, and carried some extra weight, but he gradually recovered his form. He won a New Zealand tour in April, over Anderson, Sedgman, and Cooper. In May, he lost a five-set final to Rosewall at the Melbourne Olympic Pool where a court was set up on the drained pool floor. Hoad won tournament finals in June at Santa Barbara, California and in September at Geneva, Switzerland, both over Rosewall, but appeared out of condition in the Roland Garros final against Rosewall. In 1960, Hoad won the first Japanese Professional Championships in Tokyo, beating Rosewall, Cooper, and Gimeno to win the $10,000 tournament. In the final, Hoad prevailed at 13–11 in the fifth set over Rosewall. 1961 Hoad played a few matches on the 1961 pro championship tour in January, but soon withdrew because of a broken left foot and was substituted for by first Trabert and then Sedgman. He finished fourth in a tour of five Soviet cities in July. In September, Hoad lost in the first round of the French Pro to Luis Ayala, and at the Wembley Pro, he defeated Gonzales in a four-set semifinal but lost in a four-set final to Rosewall, appearing stiff and sluggish. Also that month, Hoad and Gonzales had already played a ten-match tour of Britain and Ireland, with Buchholz and Davies playing the undercard matches. Hoad won his series against Gonzales by a score of six matches to four. (The Sun-Herald, 8 October 1961, relying on the "Australian pros", reported Hoad winning seven of ten matches on that tour.) Hoad won four of the five matches in the series which were played on grass. The four players shared AUS£9,000 ($20,160). In November, Hoad won the fifth and deciding rubber for Australia against the United States in the inaugural Kramer Cup (the pro equivalent of the Davis Cup) by beating Trabert in four sets. Trabert said afterwards: "Trying to stop Lew in that final set was like fighting a machine gun with a rubber knife". L'Équipe ranked Hoad as the third-best player of the year. Gardnar Mulloy rated Hoad as world No. 1 for 1961 ahead of Gonzales, and the favourite to win a prospective open Wimbledon. 1962 There was no official pro championship tour in 1962, as Laver had declined to accept pro offers made by Kramer at the 1961 Wimbledon. Kramer resigned as tour promoter and director. Kramer's continuing player contracts, Hoad's contract among them, were assumed by the players in their own association, the International Professional Tennis Players Association. From 14 to 17 March 1962, Hoad won the Adelaide Professional Championships, beating Rosewall, Gimeno, and Sedgman, the final against Rosewall very close. On 12 August 1962, Hoad was awarded the Facis Trophy for winning the Italian tour. Hoad won the professional tournament in Zürich in September 1962 by a win in the final against Pancho Segura. In the 1962 Kramer Cup tournament, in best-of-five set formats, Hoad defeated Gimeno in the semifinal tie in Turin, Italy on clay, and Hoad won the opening match of the final at Adelaide in December against Olmedo on grass. Hoad was voted the top tennis player of 1962 in a poll by 85 U.S. sports editors. 1963 In January 1963, Hoad and Rosewall guaranteed the contract of new pro Rod Laver, and Hoad and Rosewall, longtime teammates, became the proprietors of the professional tour. Hoad agreed to reduce his own share of money taken in at the gate for the upcoming 1963 tour of Australia (his share dropped to 15%) in order for Laver to be able to take 25% of the gate, which arrangement would help Laver earn his guarantee more quickly. In January, Hoad went 8–0 over Laver in a series of matches in Australia, some of which were best-of-five and televised from sold-out stadiums. (Laver and Buchholz, who was also present on the undercard of the tour, both later claimed that there were 13 matches and a 13 to zero score for Hoad over Laver.) Hoad was then inactive for five months due to a shoulder injury. On his return in June, he lost to Laver in the semifinal of the Adler Pro, and at the Forest Hills U.S. Pro tournament he lost to Buchholz in the first round. The Forest Hills event did not have a television contract, was a financial failure, and the players, with the exception of Gonzales, were not paid. At the French Pro indoor event at Stade Coubertin in September, Hoad was defeated in straight sets by Rosewall in the semifinal and lost the third place play-off against Sedgman. At the Wembley Pro, he reached the final after surviving a marathon semifinal against Buchholz in which he strained his leg muscle and was limping throughout most of the match. Hoad was tired and sluggish in the final, which again he lost to Rosewall, this time in four sets. McCauley acclaimed the semi-final with Buchholz "one of the best contests ever staged at Wembley". At the end of the year, Laver had become the No. 2 professional player behind Rosewall, although Hoad held a head-to-head advantage over Laver on the year. Hoad's gross earnings from tennis play for the year were about $20,000, or fifth among the pro players. However, in addition to this prize money, Hoad's contract and the guarantees associated with it were reportedly met by a distribution of tournament profits above the purse prize money to meet his contract rights, inherited from the Kramer era by the IPTPA.. Gonzales expressed disapproval of the distribution of profits to those players with guaranteed contract levels. 1964–66 In February and March 1964, Hoad played a 16-day tour of New Zealand with Laver, Rosewall, and Anderson. Hoad and Laver both finished on top with seven wins and five losses, but Hoad won first place with a 3 to 1 head-to-head score against Laver. In late September 1964, Hoad and Gonzales played a four match best-of-three sets head-to-head series in Britain, at Brighton, Carlyon Bay (Cornwall), Cardiff (Wales), and Glasgow (Scotland). Hoad won the first three matches at Brighton, Carlyon Bay, and Cardiff, while Gonzales won the final match at Glasgow. Hoad experienced foot trouble in 1964 and finished in sixth place in the tournament series points system. In early 1965, much of his large right toe was removed, and he was only able to play a limited schedule thereafter. Hoad won his final victory against Laver on 24 January 1966 at White City in Sydney, his home town, defeating him in straight sets. Back problems plagued Hoad throughout his career and forced his retirement from the tennis tour in 1967 but the advent of the Open Era enticed him to make sporadic comebacks. According to research done for a 1970 British Pathé documentary film on Hoad's tennis ranch, Hoad had earned GBP 350,000 ($840,000 in 1970 exchange rates) during the course of his playing career. In a 1977 newspaper interview, Hoad's career earnings were stated to be GBP 250,000 ($436,000 per 1977 exchange rate). Open era Hoad participated in the 1967 Wimbledon Pro, a three-day BBC televised tournament organized by the All-England Club as a trial for "open" tennis and as such the first Wimbledon tournament open to male professional tennis players. Hoad was one of the eight players invited for the singles event and despite being in semi-retirement and without competitive play for ten months, he won his first match against 39-year-old Gonzales in three sets. The BBC television commentator called it "the finest match ever seen on these hallowed grounds." This would be the last match on grass between Hoad and Gonzales, with Hoad holding a lifetime edge on grass over Gonzales of 20 matches to 14. With little energy left he lost the semifinal to Rosewall in two straight sets. Hoad reached the final of the Irish Championships at Dublin in July 1968 but lost to Tom Okker in straight sets, hampered by a thigh injury. In November 1969, Hoad won the Dewar Cup Aberavon singles title, part of the Dewar Cup indoor circuit, after defeating Bob Hewitt in the final in two sets. At the 1970 Italian Open, he reached the third round which he lost in four sets to Alex Metreveli. At the 1970 French Open, he defeated Pasarell in four close sets, and reached the fourth round before succumbing to eventual finalist Željko Franulović. At Wimbledon that year he lost in the second round to Ismail El Shafei. In the spring of 1972, Hoad teamed up with Frew McMillan to play the doubles event at the Italian Open and reached the final against Ilie Năstase and Ion Ţiriac. They led 2–0 in sets but retired at 3–5 down in the fifth set in protest of the poor light conditions and the antics of the Rumanian pair. At the end of June, at the age of 37, he made his final Wimbledon appearance losing in the first round to Jürgen Fassbender in four sets. From 1970 to 1974, Hoad was the coach of the Spanish Davis Cup team. Playing style Strength of arm and wrist played an important part in Hoad's game, as he often drove for winners rather than rallying and waiting for the right opportunity. Although he assaulted his opponents, he also had the skill to win the French Championships on the slower clay court. Hoad played right-handed and had a powerful serve and groundstrokes but his game lacked consistency. At times Hoad had difficulty maintaining concentration. According to Kramer, "Hoad had the loosest game of any good kid I ever saw. There was absolutely no pattern to his game.... He was the only player I ever saw who could stand six or seven feet behind the baseline and snap the ball back hard, crosscourt. He'd try for winners off everything, off great serves, off tricky short balls, off low volleys. He hit hard overspin drives, and there was no way you could ever get him to temporise on important points." Kramer compares Hoad to Ellsworth Vines. "Both were very strong guys. Both succeeded at a very young age.... Also, both were very lazy guys. Vines lost interest in tennis (for golf) before he was thirty, and Hoad never appeared to be very interested. Despite their great natural ability, neither put up the outstanding records that they were capable of. Unfortunately, the latter was largely true because both had physical problems." Hoad was runner-up for the Australian junior table tennis championship in 1951, and developed strong wrists and arms through heavy weight-lifting regimes. Hoad would use wrist strength in his strokes to make last split-second changes in racquet direction. He would saw off about a half inch from the ends of his racquet handles, which were short to begin with, and move the grip higher to wield his racquets as if they were ping-pong bats. Assessment In 1956, his win/loss ratio in all matches was 114/129 or 88%. His win ratio in an injury-plagued 1958 was 41% (winning 64 of 155 matches). Hoad's win rates on the world championship tour that year (36/87 or 41%) and in the 1959 four-man tour (68%) compare favourably to Rosewall's percentages on the 1957 world championship tour (34%) and on the 1960 four man tour (56%). In the 1959 Ampol world tournament series, Hoad's winning percentage was 71% (36/51) compared to Gonzales' 72% (26/36). Gonzales defaulted three Ampol tournaments and played 15 fewer matches than Hoad on the tour. For the 1959 season as a whole, Hoad was credited with a 24 to 23 edge in wins against Gonzales, a series consistency which surpasses any other opponent of Gonzales during his world champion years. Hoad's consistency on grass surfaces is highlighted by his lifetime edge in play against Gonzales on grass of 20 to 14 (59%). Hoad trails Rosewall lifetime in grasscourt meetings, 18 to 26, Hoad's results declining after 1961. Hoad was 14 wins and 18 losses against Rosewall lifetime in grass court tournament play, Hoad was 8 wins and 10 losses lifetime on clay against Rosewall, and 11 wins and 11 losses lifetime on clay against Trabert. Lifetime on all surfaces, primarily indoor, Hoad trails Gonzales 77–104 and trails Rosewall 51–84. On outdoor surfaces, (grass, clay, and cement) Gonzales held a 36 to 31 lifetime edge over Hoad, or 53%. On the head-to-head world pro tours of the era, Hoad was 51 wins and 64 losses against Gonzales, the best head-to-head showing of any pro against the reigning champion Gonzales, and in spite of an extended period of substandard play during the 1958 season due to injury. On the 1959 Ampol world championship series of tournaments, Hoad's record was 3 wins and 5 losses against Gonzales, and 2 wins and 2 losses in tournament deciding matches Hoad was 6 wins and 2 losses against Rosewall on the 1959 Ampol tour. Hoad had a 15–13 edge over Gonzales in their meetings on the 4-man championship tour of 1959, but as Joe McCauley noted, Hoad was deprived of overall victory on this tour because he was less consistent than Gonzales when facing the rookie pros, Mal Anderson and Ashley Cooper. Hoad's combined record against the rookies was 27–7, admittedly a consistent edge, compared to Gonzales’ 34–0. Gonzales always maintained that Hoad was the toughest, most skillful adversary that he had ever faced. "He was the only guy who, if I was playing my best tennis, could still beat me." said Gonzales in a 1995 New York Times interview. "I think his game was the best game ever. Better than mine. He was capable of making more shots than anybody. His two volleys were great. His overhead was enormous. He had the most natural tennis mind with the most natural tennis physique." In a 1970 interview he stated that "Hoad was probably the best and toughest player when he wanted to be. After the first two years on the tour, his back injury plagued him so much that he lost the desire to practice. He was the only man to beat me in a head-to-head tour, 15 to 13." Kramer, however, had mixed feelings about Hoad's ability. In spite of calling him one of the 21 best players of all time, albeit in the second echelon, he also writes that "when you sum Hoad up, you have to say that he was overrated. He might have been the best, but day-to-day, week-to-week, he was the most inconsistent of all the top players." In a 1963 article in World Tennis Rosewall judges Gonzales to be a notch above Hoad but stated that "...the latter is the greatest of all time when he is 'on'.", an opinion echoed by Frew McMillan. In 2010, Rosewall rated Hoad at the top of his personal list of the top four greatest tennis players of all time. In 2007, Butch Buchholz rated Hoad as the greatest player of his era, but said he was "injury prone and not exactly a model of fitness". Buchholz stated that "If you had an Earth vs. Mars match, and had to send one man to represent the planet, I would send Hoad." Buchholz had played the undercard matches on Hoad's 1961 British tour against Gonzales, and Hoad's 1963 Australian tour against Laver. In July, 1961, Gardnar Mulloy rated Hoad as the greatest player of the time, based on his results against Gonzales, and named Hoad as the favourite to win a prospective open Wimbledon. Mulloy had beaten both Hoad and Gonzales in singles competition. Max Robertson, tennis author and commentator, rated Hoad as the best post-war Wimbledon player, followed by Gonzales and Laver, in his 1977 book Wimbledon 1877–1977. In the second edition (1981) his list was unchanged but in the third edition (1987) he listed Hoad second behind Boris Becker. In The Encyclopedia of Tennis (1973) sportswriters Allison Danzig and Lance Tingay as well as tennis coach and former player Harry Hopman listed their ten greatest players. Only Tingay included Hoad in his list, ranking him in fifth position. In 100 Greatest of All Time, a 2012 television series broadcast by the Tennis Channel, Hoad was ranked the 19th greatest male player. With his movie-star good looks, powerful physique, and outgoing personality, Hoad became a tennis icon in the 1950s. As Kramer says, "Everybody loved Hoad, even Pancho Gonzales. They should put that on Lew's tombstone as the ultimate praise for the man.... Even when Hoad was clobbering Gonzales, Gorgo wanted his respect and friendship." In a 1975 issue of Sports Illustrated, Arthur Ashe was quoted as relating a remark which Pancho Gonzales had said to him, "If there was ever a Universe Davis Cup, and I had to pick one man to represent Planet Earth, I would pick Lew Hoad in his prime." Rod Laver in 2012 rated Hoad as the greatest player of the 'past champions' era of tennis. Laver described his strengths of "power, volleying and explosiveness" as justification of his accolade. In a January 2019 interview, Laver stated that Hoad was "the best player who ever held a racquet. He had every shot in the book and he could overpower anyone. He was so strong." Pancho Gonzales made a similar assessment, "He was such a strong ****...when he tried, you just couldn't beat him. He hit the ball harder than anyone I ever played." Personal life Hoad proposed to his girlfriend, Australian tennis player Jenny Staley, on her 21st birthday party in March 1955 and they planned to announce their engagement in June in London while both were on an overseas tour. After arrival in London Jenny discovered that she was pregnant and the couple decided to get married straight away. The marriage took place the following day on 18 June 1955 at St Mary's Church, Wimbledon in London on the eve of Wimbledon fortnight. They have two daughters and a son. After announcing his retirement in 1967, due to persistent back problems, Hoad moved to Fuengirola, Spain, near Málaga, where he and his wife operated a tennis resort, Lew Hoad's Campo de Tenis, for more than thirty years entertaining personal friends such as actors Stewart Granger, Sean Connery, Deborah Kerr and her husband, Kirk Douglas, and saxophonist Stan Getz. In 1978, Hoad's back problem was successfully treated with spinal fusion surgery, and he was relieved of pain. There had been two ruptured discs and a herniation. The doctor asked one of Hoad's friends, "How on earth did this man walk, let alone play tennis?" Hoad was diagnosed with a rare and incurable form of leukemia on 13 January 1994 which caused his death on 3 July 1994. Press reports of a heart attack were incorrect. Hoad's personal physician specialist was his own son-in-law Dr. Manuel Benavides, who explained the cause of death. A book co-written with Jack Pollard and titled My Game ("The Lew Hoad story" in the USA) was published in 1958. In 2002, Pollard teamed up with his widow, Jenny, to write My Life With Lew. Hoad was inducted into the International Tennis Hall of Fame in Newport, in 1980 and this was followed in December 1985 by his induction into the Sport Australia Hall of Fame. In January 1995 he was posthumously inducted into the Tennis Australia Hall of Fame together with friend and rival Ken Rosewall. The ITF organizes a seniors tournament in his honor called The Lew Hoad Memorial ITF Veterans Tournament. The Kooyong Classic at Kooyong Stadium, the principal warm-up event for the Australian Open, awards the Lew Hoad Memorial Trophy to the winner of the men's singles. Kooyong stadium was the site of some of Hoad's greatest victories. Grand Slam and Pro Slam finals Singles Grand Slam finals (4–2) Pro Slam finals (0–7) Doubles: 13 (8 titles, 5 runner-ups) Mixed doubles: 4 (1 title, 3 runner-ups) Other significant finals Performance timeline Singles Hoad joined the professional tennis circuit in 1957 and as a consequence was banned from competing in the amateur Grand Slams until the start of the Open Era at the 1968 French Open. See also Overall tennis records – Men's Singles Notes References Sources Biographies External links Hoad vs. Rosewall, 1955 NSW final, White City, Sydney-newsreel Hoad vs. Sirola, 1956 German final, Hamburg, at 8:20-newsreel Hoad df. Rosewall, 1959 Roland Garros 3rd place-newsreel Lew Hoad Tennis and Paddle Club Category:Australian Championships (tennis) champions Category:Australian Championships (tennis) junior champions Category:Australian expatriates in Spain Category:Australian male tennis players Category:French Championships (tennis) champions Category:People from Fuengirola Category:Sportspeople from Sydney Category:Tennis people from New South Wales Category:International Tennis Hall of Fame inductees Category:United States National champions (tennis) Category:Wimbledon champions (pre-Open Era) Category:1934 births Category:1994 deaths Category:Grand Slam (tennis) champions in men's singles Category:Grand Slam (tennis) champions in mixed doubles Category:Grand Slam (tennis) champions in men's doubles Category:Deaths from leukemia Category:Professional tennis players before the Open Era Category:Grand Slam (tennis) champions in boys' singles Category:Grand Slam (tennis) champions in boys' doubles

Q: UltraDateTimeEditor - MinDate set to future date results in odd behavior If you set the MinDate on an UltraDateTimeEditor to a date that is today or in the past and then type in a date that is before the MinDate, the control clears the date (desired outcome). If you set a MinDate that is in the future and type in a date that is before the MinDate value, the control acts oddly. Example MinDate = 1/29/2014 Type in = 1/1/2014 Tab out of the control Date control shows 1/1/2020 After some trial and error, it appears that the control is taking the first two spaces in the year (2014) and treating it like a 2-digit version of the year (20). If you type in 1/1/1500, you get 1/1/2015. If you type in 1/1/1900 you get 1/1/2019. Is this a known issue (I couldn't find anything on it)? Is there a workaround that allows both the limiting of the dates on the dropdown, but also won't result in the odd behavior when a user tries to type a date in? A: I made a quick test using version 12.1 with the latest available service release - 12.1.20121.2135 and I could confirm that the issue is fixed. Please try to upgrade to latest available service release of version 12.1 or to one of latest versions (for example 13.1 or 13.2) where the issue is fixed. Let me know if you have any questions

An AirAsia airliner has overshot the runway at an airport in the Philippines forcing passengers to make an urgent exit on emergency slides, it has been claimed. The incident occured at Kalibo Airport in Aklan province and involved an Airbus A320-216 carrying 153 passengers and crew from the Filipino capital Manila. Local journalist Jet Damazo-Santos was on board the plane and uploaded photographs to Twitter showing chaotic scenes as passengers were forced to disembark the aircraft on emergency slides. 'Engine was shut immediately, we were told to leave bags, deplane asap. Firetruck was waiting,' she said, adding that there appeared to be no injuries despite the plane coming to an 'abrupt stop'. The incident comes just hours after six bodies and wreckage were recovered from the sea off the Indonesian coast of Borneo Island following the disappearance of Air Asia flight 8501 on Sunday. Scroll down for video Escape: Local journalist Jet Damazo-Santos was on board the plane and uploaded photographs to Twitter showing chaotic scenes as passengers were forced to disembark the aircraft on emergency slides Care: Elderly patients were pictured having their blood pressure checked in the aftermath of the incident Describing the terrifying incident, Ms Damazo-Santos said: 'Nobody seems to be hurt. Weather was bad because of #senangph [sic]. Plane came to a very abrupt stop.' Her mention of bad weather refers to tropical storm Seniang, which has been battering the Philippines for several days. She updated her Twitter account with a number of photographs taken in the aftermath of the incident, including images of elderly patients having their blood pressure checked and shoeless members of cabin standing on the runway, having removed their footwear to use the inflatable slide. Ms Damazo-Santos said that her flight had been delayed by two hours after the poor weather at Kalibo Airport had earlier forced a plane from Cebu Pacific airlines to turn back to Manila. With all passengers said to be safe, Ms Damazo-Santos said they now face a long wait to reclaim their luggage as officials insist the plane is towed to a parking area before it can be unloaded. The journalist later wrote about her experience for the Filipino news website Rappler. In a statement AirAsia said: 'AirAsia Philippines confirms flight Z2 272 from Manila skidded off the Kalibo International Airport runway at 5:43PM upon landing. All 153 passengers and crew were able to disembark safely, no injuries reported.' 'All passengers are now at a hotel assisted by AirAsia staff,' they added. Chaotic scenes: Shoeless members of AirAsia cabin crew stand on the runway at Kalibo Airport, having removed their footwear to use the plane's inflatable slide Firefighters on the scene: The incident occured at Kalibo Airport in Aklan province and involved an Airbus A320-216 carrying 153 passengers and crew from the Filipino capital Manila The incident comes just hours after six bodies were recovered from the Java Sea following the disappearance of AirAsia flight 8501 on Sunday. 162 people were on board the flight when it disappeared from radars 42 minutes into its flight from Surabaya in Indonesia to Singapore. Poor weather has been suggested a likely factor in that crash after it emerged the pilot requested to deviate from its flight plan and climb above bad weather. By the time permission to do so was granted, the plane had already vanished from radars. Officials have confirmed that bodies and debris found in Java Sea off Indonesia are from AirAsia flight 8501, and a naval spokesman said the rescuers remain 'very busy' retrieving the victims. Scores of bodies were discovered alongside luggage, a plane door and an emergency slide floating in the water 100 miles off the coast of Borneo Island earlier today after three days of searching. The recovery of six bodies came as devastated relatives of AirAsia crash victims collapsed in grief and were taken to hospital after an Indonesian television station showed disturbing uncensored footage of the corpses floating in the sea.

Everything you need for any type of training. In three diverse colourways with a distinct design, the Running Shorts offer freedom and coverage as you run, squat or jump.Gymshark | Be a visionary.10/01/19All Productsfilter-colour: Bluefilter-size:smain-colour: 82bed6 | Dusky TealMensShortssize:lsize:msize:ssize:xlsize:xxl2019-01-10

""" Definition of urls for DjangoWebProject1. """ from datetime import datetime from django.conf.urls import patterns, include, url from django.contrib import admin from app.forms import BootstrapAuthenticationForm admin.autodiscover() urlpatterns = patterns('', url(r'^', include('app.urls', namespace="app")), url(r'^contact$', 'app.views.contact', name='contact'), url(r'^about', 'app.views.about', name='about'), url(r'^seed', 'app.views.seed', name='seed'), url(r'^login/$', 'django.contrib.auth.views.login', { 'template_name': 'app/login.html', 'authentication_form': BootstrapAuthenticationForm, 'extra_context': { 'title':'Log in', 'year':datetime.now().year, } }, name='login'), url(r'^logout$', 'django.contrib.auth.views.logout', { 'next_page': '/', }, name='logout'), url(r'^admin/', include(admin.site.urls)), )

Q: insert duplicate keys to hash map I have created hash map and when I debug it I saw that I have duplicte keys. I didnt override the hashCode() & equals(Object obj) in the key - Object1 and i wonder how will it affect the performance of the map search? private HashMap<Object1,Object2> map = new HashMap<Object1,Object2>(); A: It is not possible to have duplicate keys in a Map, you have different keys that "appear" the same (Maybe based on their toString()? )because you have not overridden equals() and hashCode(), but in reality the keys are different. This means that in order to get all values from your Map you need to keep every key you created and store it somewhere, which to me defeats the purpose of the Map. Summary: Override equals() and hashCode(), then put your key/value pairs into the Map.

I listened to a fascinating program last night about Julian Rotter who is an eminent Clinical Psychologist. He wrote and studied a great deal about what he termed ‘The Locus of Control’ and posited that it was either Internal or External. An Internal Locus of Control means you are taking responsibility for the fact that you have an influence over everything in your life, and External Locus of Control means that things happen to you which you can’t control. In NLP we call this the ‘Cause and Effect’ equation. The problem with being at the Effect side is that you are not in control of things, you become a victim to life. Now I realise that shit happens! Of course I do… bad things have happened to me too – here’s an example: My Business Was Insolvent 3 Years Ago. ‘Effect’ thinking says: When I bought the business I was conned and paid too much When the person I bought off left they told me nothing about how to run a business There is a recession on I can’t find the staff nowadays ‘Cause’ thinking says: When I bought the business I didn’t do enough research, so next time I am going to ensure that I research all investments thoroughly When I bought the business I didn’t ask the right questions, so next time I will ensure that I am curious and I’ll seek the advice of professionals People are not prepared to spend money, so what can I do to change my ‘offering’ and my marketing to be relevant for the times The right people for my business are out there, so how can I communicate better so that I find them (FYI – this business is now back doing exceptionally well!) Being at ‘Cause’ does not mean that you blame yourself for things, it means you accept that you have had an effect, no matter how tiny, on everything that happens. This is a VERY empowering thing to think and believe. “What am I learning NOW about how I might do things BETTER and differently in the future?” Listen to the program on BBC iPlayer, it’ll open your eyes to the power of controlling your mind and why we all need to think differently. The only thing the program doesn’t talk about is how to change… and that’s where NLP comes in! Happy Listening,,,, Comments Coaching Academy… Coming soon A new Coaching Academy is coming soon, with subscriptions as low as £25 per month it'll be the perfect way to access ongoing business coaching. Enter your details below to receive VIP early access. [expected live January 2020]

God Bless The Mother That Has Lost A Child Viewed: 3170 Posted by: Steve Hardwick Date: May 14 2017 1:39 PM GOD BLESS THE MOTHER God Bless The Mother who has lost part of herself now..Her child is gone..and yet she knows she must go on somehow.She will never be who she was onceBefore her child was taken and some days she can’t help but feel that her heart has been forsaken. They say that you give the hardest tasks to those who are strongBut her task is so painful, Lord..it’s one that lasts lifelong.Please help her rise each time she falls, give courage for her fears.Have Angels hover over near to dry her endless tears. Keep her close, within your arms each moment they are apart.Please give her comfort while she grieves...God soothe her aching heart.In God’s name we pray, Amen

Welcome to Miro St Constantin Hotel Facilities A lobby and a reception are available to guests. The upper floors are easily accessible using the lift. Amenities include a baggage storage service, a safe and currency exchange facilities. Internet access and wireless internet access are available in the public areas. Gastronomic options include a restaurant and a bar. Guests can visit the supermarket to purchase daily necessities. Shopping facilities are available. The grounds of the holiday complex feature a playground and an attractive garden. A TV room is also among the amenities at the apartment complex. Guests arriving in their own vehicles can park in the car park. Additional services include a babysitting service, a childcare service, car hire, room service, a wake-up service and a laundry. Rooms Special family rooms are available for families with children. All rooms feature air conditioning and a bathroom. A balcony or terrace can be found in most rooms, offering additional comfort. Each accommodation unit features separate bedrooms, a double bed or a sofa-bed. A safe is also available. The kitchenettes of the accommodation units are appointed with a fridge and tea and coffee making equipment. Internet access, a telephone, a TV and wireless internet access are provided as standard. Guests will also find slippers provided. In each of the bathrooms, guests will find a shower, a bathtub, a hairdryer and bathrobes. Sports/Entertainment A refreshing dip in the indoor or outdoor pool can be pleasantly cooling on hot days. A terrace, sun loungers and parasols are available. There is also a poolside snack bar. Those wishing to enjoy sports whilst on holiday can have fun on-site with golf. The apartment complex also offers sports enthusiasts a wide range of indoor facilities and activities, including a gym, table tennis, pool/billiards and darts. Additional leisure options available to guests include an entertainment programme, a disco and a nightclub. Meals The apartment complex offers a wide range of bookable meals and board options, including breakfast, lunch, dinner and All-inclusive. In addition, picnics and snacks are available. The show cooking is a particular attraction. Alcohol-free drinks and alcoholic drinks are served at the establishment. Payment The apartment complex accepts payment by VISA.

[Detection and identification of Mycobacteria with polymerase chain reaction-restriction fragment length polymorphism (PCR-RFLP) from patients with Mycobacterial skin infections]. To establish a rapid approach to the detection and identification of Mycobacteria from lesions of patients with suspected Mycobacterial infections. Specimens were obtained from five patients suspected to have Mycobacterial infections. DNA extracted from clinical samples was amplified by nested PCR. The PCR products were digested with HhaI, MboI, and BstUI restriction enzymes and applied to PAGE. The species of Mycobacteria were determined by restriction fragment length polymorphism (RFLP) analysis. Identification of Mycobacteria culture was also performed in 3 patients. M. marinum was found in two patients diagnosed as swimming pool granuloma. M. tuberculosis was found in one patient diagnosed as infectious skin granuloma. All these 3 Mycobacteria were confirmed by Mycobacteria culture. A strain of M. tuberculosis and a strain of M. fortuitum were detected in remain two patients. The results above indicate that PCR-RFLP analysis is rapid and reliable in detection and identification of different Mycobacteria species from skin tissues. Application of this method will be helpful for early diagnosis and treatment of Mycobacteria skin infections.

CORCORAN, Calif. — A follower of Charles Manson has been arrested for allegedly trying to smuggle a cell phone inside a California prison where the mass murderer is housed. California Department of Corrections spokeswoman Terry Thornton says 63-year-old Craig Carlisle Hammond was arrested Sunday for investigation of conspiracy, possession of an illegal communication device and attempting to bring a cell phone into a prison. Hammond was taken to jail and is scheduled to be in court next month.

Scroll compressors in each of which a compression mechanism including an orbiting scroll and a fixed scroll is housed in a casing have been known to date. The compression mechanism includes a compression chamber formed by engaging the fixed scroll and the orbiting scroll with each other. As shown in Patent Document 1, some of such scroll compressors reduce separation between the orbiting scroll and the fixed scroll by utilizing a pressure rise in the compression chamber. The scroll compressor shown in Patent Document 1 is connected to a refrigeration circuit of an air conditioning system. A compression mechanism of this scroll compressor has a suction port that is open at a suction position of the compression chamber, a discharge port that is open at a discharge position of the compression chamber, and an intermediate port that is open at an intermediate position between the suction position and the discharge position in the compression chamber. The suction port communicates with a low-pressure line of the refrigeration circuit, and the discharge port communicates with a high-pressure line of the refrigeration circuit. This configuration can press an orbiting scroll against a fixed scroll by utilizing the pressure of a fluid introduced through the intermediate port from the compression chamber at the intermediate position into the back pressure space. In this manner, application of a pressing force to the orbiting scroll can reduce separation of the orbiting scroll from the fixed scroll.

Минулого тижня в місті Каневі, або, як його іноді називають, «Мецці українського народу», відбулася символічна і вкрай непересічна подія. У музеї на Чернечій горі — саме біля могили Тараса Шевченка — у рамках проекту «Славетний Кобзар очима китайських митців» було представлено виставку «Нев’януча слава. Слава Тарасу Шевченку». Зазначимо, що це вже четвертий спільний китайсько-український виставковий проект, повністю профінансований китайською стороною. Як наголосив співорганізатор події проректор Національної академії образотворчого мистецтва та архітектури Остап Ковальчук, найіменитіші художники півторамільярдного Китаю, відомі в усьому світі, пропустили крізь себе творчість українського письменника та представили своє бачення у вигляді портретів Тараса Григоровича, ілюстрацій до «Кобзаря» та ієрогліфів у різних стилях китайської каліграфії — найбільш поцінованого китайцями виду мистецтва. «Тут Джі Лон — 79-річний пекінський маестро, академік, багато працював на літературній ниві як ілюстратор і тепер не полишає пензля — він написав портрет кобзаря Остапа Вересая, ілюстрацію до «Катерини», — зазначив Ковальчук. — Художник вник у нашу історію, був в Україні, малює її. Інша картина — «Українська хатка у селі Моринці», яку написав академік, зірка китайського мистецтва і телебачення Дун Хао». «Як гармонійно і красиво писалася каліграфія, яка є не фоном, а величезним мистецтвом, яким займалися всі — від імператора до Мао. Каліграфію на даній виставці представляє ректор Центральної академії, голова Спілки художників КНР — уявіть який розголос ця тема мала у Китаї!» — наголосив пан Остап і додав, що загалом завдяки цьому проекту, якому сприяли посольства України у Китаї і Китаю в Україні, Міністерству культури, МЗС, «ми у культурних відносинах із КНР на прекрасному рівні». «СВОБОДА БУЛА ОСНОВНИМ ПОКЛИКАННЯМ ШЕВЧЕНКА» Головним організатором та куратором виставки з китайської сторони був віце-президент Китайської академії живопису та каліграфії Алан Юй. «Тарас Шевченко — це дух України, борець за свободу українського народу і обличчя української нації. Зараз він є тим «мостом», який поєднує Китай та Україну, — зазначив Юй під час візиту до Канева. — На сьогодні Тарас Шевченко — це не лише українець, він також китаєць і взагалі людина світу, яка об’єднує всіх нас. Свобода була основним покликанням у його житті». Віце-президент китайської академії також подякував організаторам за можливість провести дану виставку у найбільш знакових культурних місцях України — у місті Каневі — на батьківщині українського поета, а раніше, у травні цього року, — у Національному музеї ім. Тараса Шевченка у Києві. «Шевченко є знаковою фігурою як для Китаю, так і для мене особисто», — говорить Юй. ТАКИМ ШЕВЧЕНКА МИ ЩЕ НЕ БАЧИЛИ. КИТАЙСЬКІ МИТЦІ ПО-СВОЄМУ ЗОБРАЗИЛИ «БОРЦЯ ЗА СВОБОДУ УКРАЇНСЬКОГО НАРОДУ І ОБЛИЧЧЯ УКРАЇНСЬКОЇ НАЦІЇ» Звідки ж у китайців такий живий інтерес до України і до одного з найбільших її символів — Тараса Григоровича Шевченка? В 1920-х рр. китайський письменник і літературний критик Мао Дунь вперше опублікував життєвий шлях і вибрані твори Шевченка китайською мовою у «Щомісячному журналі розповідей». Надалі про Шевченка у Китаї дізнавалися завдяки «культурному обміну» між КНР та СРСР. «Китайські митці, які намалювали дані ілюстрації до «Кобзаря» — в основному 30—40-х рр. народження, тому вони чули про Шевченка ще за радянських часів. До того ж багато китайських художників є вихідцями зі школи Максимова та Тетяни Яблонської — китайські художники є учнями радянських митців, тому вони знають про Україну», — говорить Алан Юй. Востаннє ж «Кобзар» видавався у Китаї у 1982 році і був перекладений з російської. Але його перекладач 73-річний Ге Баоцюань на цьому не зупинився і розпочав спеціально вивчати українську мову, аби зробити найбільш наближений переклад збірки. Загалом він зробив 130 перекладів віршів з української. Планувалося, що саме для цього видання китайські митці, які є професорами і викладачами Китайської академії живопису та каліграфії, мали намалювати ілюстрації. В серпні 2015 року вони вперше завітали до України та із супроводом головного зберігача Національного музею Тараса Шевченка Юлії Шиленко відвідали музеї, серед яких Національний музей народної архітектури та побуту України у Пирогові, Національний художній музей. ПІСЛЯ НЕЯКІСНОЇ РЕКОНСТРУКЦІЇ МУЗЕЮ (2003—2010 рр.) СИРІСТЬ, ПЛІСНЯВА ТА ГРИБОК РУЙНУЮТЬ ШТУКАТУРКУ У ПРИМІЩЕННЯХ І РОБЛЯТЬ ВСЕ БІЛЬШЕ ВИСТАВКОВИХ ЗАЛ НЕПРИДАТНИМИ ДЛЯ ВИКОРИСТАННЯ. ОДНА ІЗ НИХ ПЕРЕТВОРИЛАСЯ НА «СКЛАД НЕПОТРІБНИХ РЕЧЕЙ» «Художники тричі були в Україні, відвідували Київ, Канів, Моринці, де народився Шевченко, — розповідає китайський керівник проекту Алан Юй. — Також їм було продемонстровано багато картин з усього світу — як художники малювали українського письменника. Вони дивилися на монументи Шевченка у різних країнах. Кожен з них мав «Кобзаря» китайською, тому міг прочитати і знайти натхнення для робіт. Виходячи з цього, кожен китайський митець отримував розуміння, що він хоче малювати — портрет, уривок з твору Шевченка чи ієрогліфи». «НОВИЙ ПОГЛЯД НА КОБЗАРЯ» Цілий рік китайські митці під проводом Алана Юя працювали над своїми витворами. Проте далі виникли певні проблеми, оскільки вдова перекладача Ге Баоцюаня, яка мала права на його переклади, з якихось причин не захотіла втілювати цей проект. Тож дані картини були випущені у форматі виставки, а до її каталогу було вписано ті самі переклади Ге Баоцюаня. До кожної ілюстрації художники написали свої коментарі. «Виявилося, що у деяких китайських митців набагато глибше, об’ємніше уявлення та розуміння творів Тараса Шевченка, — ділиться враженнями співорганізатор виставки, головний хранитель Національного музею Т. Шевченка Юлія Шиленко. — В Україні Шевченко, якого за багато років зробили чимось «обов’язковим» та розтиражованим, іноді сприймається достатньо поверхово і без розуміння глибини його творчості. Китайці ж дуже пройнялися ним і з нового боку подивилися на Кобзаря». ДАНА ВИСТАВКА — ЦЕ МОЖЛИВІСТЬ РАЗОМ ІЗ КИТАЙЦЯМИ ПЕРЕОСМИСЛИТИ ТВОРЧІСТЬ ТАРАСА ШЕВЧЕНКА, СПРИЙМАЮЧИ ЙОГО У «СХІДНОМУ» КОНТЕКСТІ «Тож результат роботи виявився очікувано чудовим. «Для шевченкіани, шевченкознавства, для наших музеїв і для нашої країни відкриття цієї виставки і взагалі цей проект із «Кобзарем» надзвичайно велика подія, — говорить Юлія Шиленко. — У наш час, коли триває війна, гроші на культуру не виділяють, втілити якийсь проект надзвичайно складно. І раптом китайська сторона, після мандрівки Україною протягом місяця, перейнялася цим, вклала немалі кошти в розвиток нашої культури, щоб просувати її в світі. Весь світ і ми самі зможемо зрозуміти Тараса Шевченка краще лише тоді, коли сприйматимемо його не вузько, а в контексті. Його потрібно «підтягнути» до зрозумілих категорій для всіх народів — даний проект саме це і робить. Так само наступного року ми разом із іспанцями робитимемо проект «Гойя і Шевченко» — один іспанський художник, що перейнявся цією ідеєю, вкладатиме в нього свої кошти — українських коштів знов не буде ні копійки. На жаль, в українському уряді нас не чують». Розповідаючи «Дню» про перспективу китайсько-українських культурних відносин, віце-президент китайської академії Алан Юй зазначив, що вже цього вересня у центрі Пекіна в Музеї світу триватиме виставка даних робіт за мотивами творів Шевченка із рушниками та скатертинами із колекції Віктора Ющенка. «Це буде поєднання України та Китаю», — зазначив Алан Юй. «Китайці продовжуватимуть співпрацю, в тому числі культурну, із Україною, — продовжує Юй. — Місяць тому український та китайський уряди домовилися про полегшення процедури оформлення віз для китайців. Раніше китайцям було легше поїхати до країн Європи, аніж отримати українську візу. Тепер є надія на розширення зв’язків та взагалі на перспективне майбутнє». ЗРУЙНОВАНА «УКРАЇНСЬКА МЕККА» Як поділилися організатори виставки «Нев’януча слава. Слава Тарасу Шевченку», після згаданої події планується здійснення глобального задуму — відкриття музею Тараса Шевченка у Пекіні. Достойний крок для розвитку китайсько-українських взаємин та для підтримки української культури. І з цього приводу хотілося б зазначити і про контрасти даної виставки. Заходячи під високу стелю ззовні розкішної будівлі Канівського музею Тараса Шевченка, перебуваючи у просторій і світлій залі, де триває виставка, одразу і не здогадаєшся, що сусідні приміщення у цій самій будівлі у жахливому напівзруйнованому стані. Реконструкція музею, яка відбувалася з 2003 по 2010 рік і до якої доклали руку «менеджери» Януковича, була виконана абияк, без достатнього рівня гідроізоляції будівлі, тож кожен дощ призводить до затоплення виставкових залів, а сирість, пліснява та грибок знищують штукатурку і роблять все більше приміщень непридатними для використання. І це, як було сказано на початку, — в «українській Мецці»! Якщо українці таким чином ставляться до власної «Мекки», то годі вже говорити про менш культові місця. Окрім того, як після такого ставитимуться до України та її культури іноземці — скажімо, китайці чи поляки? Йдеться про позиціонування держави. «На нещодавній конференції міжнародного об’єднання музеїв та професійних музейних працівників в Італії одним зі спікерів був професор Економічного університету з Австралії Девід Тросбі, — коментує Юлія Шиленко. — Ще в 90-х рр. він написав книжку «Економіка та культура», в якій зазначив, що культура є основним чинником економічного зростання держави. Тоді його тезу сприйняли скептично, але вже у 2002 році на засіданні Світового банку було прийнято цю доктрину як основну: інвестиція грошей у культуру повертається економічним зростанням держави. Люди вже давно довели цю тезу науково — державне ж керівництво України досі не зрозуміло пріоритетів, які потрібно обирати при управлінні державою. Культура — це наша ідентичність і особливість, яка нас вирізняє з-поміж інших народів. Вкладаючи в неї кошти, ми інвестуємо в майбутнє. У мене ж виникає враження, що останнім часом фінансування культури в Україні припиняється». Тож чи інвестує сьогодні держава у своє майбутнє? Таке враження, що за неї це роблять інші суб’єкти міжнародної політики.

Los cuadros de Ernesto "Che" Guevara y Juan Domingo Perón serán retirados del principal patio de la Casa Rosada y serán trasladados a la ex ESMA. La misma suerte correrán 40 retratos pintados al óleo de próceres latinoamericanos que había colocado la ex presidenta Cristina Kirchner y que conformaban la Galería de los Patriotas Latinoamericanos. Serán descolgados antes de fin de mes y enviados a una muestra permanente en lo que fue la Escuela de Mecánica de la Armada (ex ESMA), donde ahora funciona el Espacio de la Memoria y los Derechos Humanos, también creado durante la gestión del kirchnerista. "Se va a mantener toda la colección de cuadros junta, porque fueron donaciones de gobiernos de otros países latinoamericanos, pero en una muestra permanente en la ex ESMA, donde el acceso es abierto para todo el público y serán vistos por más gente", dijo a LA NACION un funcionario cercano al secretario general de la Presidencia, Fernando De Andreis, que dirige este proyecto de reordenamiento de la Casa Rosada. En el principal patio interno de la planta baja del palacio, donde fueron velados los restos del ex presidente Néstor Kirchner el 27 de octubre de 2010, conviven los cuadros de Juan Domingo Perón, el Che Guevara, Eva Perón, Hipólito Yrigoyen y el recordado ex presidente de Chile Salvador Allende, depuesto y muerto en 1973. En otro patio adyacente, donde está el ingreso mismo de Balcarce 50, conviven los libertadores de América José de San Martín y Simón Bolívar, pintura esta donada por el gobierno de Venezuela. Para no hacer discriminaciones enojosas, el gobierno de Mauricio Macri resolvió sacar a todos los cuadros. "En realidad las paredes de los patios y pasillos de la Casa Rosada no deben funcionar como una galería de pintura o muestra de cuadros y menos tan sesgada. No tiene sentido que estén allí", dijo uno de los organizadores del inminente traslado. Incluso, añadió que una vez instalada la muestra en la ex ESMA posiblemente se agregarían otros cuadros de próceres argentinos y de otros países no tan emparentados con el ideario kirchnerista para emparejar el contenido histórico. Igualmente la muestra podría mantener el nombre de Patriotas Latinoamericanos, tal como es ahora. Entre los retratos que sobresalen, además de Peron, Evita, Allende, Yrigoyen, Rosas, San Martín, Bolivar y el Che Guevara, están los del recordado obispo Oscar Romero, de El Salvador, el cuatro veces presidente de Brasil Getulio Vargas, o Víctor Raúl Haya de la Torre, fundador en Perú de la Alianza Popular Revolucionaria Americana y líder histórico del Partido Aprista. En otros pasillos están las pinturas del caudillo indígena Tupac Amaru, del prócer del a independencia chilena Bernardo O’ Higgins, el uruguayo José Artigas, el caudillo indígena aymara boliviano Tupaj Katari, o el paraguayo Francisco Solano Lopez y Benito Juárez y Pancho Villa, donados por México. Este nuevo recambio en la Casa Rosada forma parte del proceso de deskirchnerización de los lugares públicos e institucionales que está llevando adelante el gobierno de Mauricio Macri.

Após os sites americanos anunciarem que ‘Vingadores: Ultimato‘ voltará aos cinemas dos EUA no dia 28 de Junho com uma cena pós-créditos, muitos fãs brasileiros nos enviaram mensagem perguntando se o filme também seria relançado por aqui. O CinePOP entrou em contato com a Walt Disney do Brasil, que nos CONFIRMOU o relançamento nos cinemas nacionais. Porém, a data ainda não foi definida. Fiquem ligados no CinePOP para mais novidades! A nova versão terá 188 minutos de duração, seis minutos a mais que o original. A nova versão não trará um corte drasticamente diferente do filme, já que os minutos extras virão em forma de uma cena pós-créditos. “Não é uma versão estendida, mas haverá uma versão entrando nos cinemas com um empurrão de marketing que trará algumas novidades no final do filme. Se você ficar e assistir ao filme, após os créditos, haverá uma cena deletada, um pequeno tributo e algumas surpresas. O lançamento acontece no próximo fim de semana.”, afirmou Kevin Feige. Com o relançamento, a Disney tenta passar os US$ 46 milhões que separam a bilheteria mundial de ‘Vingadores: Ultimato‘ (US$ 2,74 bilhões) e ‘Avatar‘ (US$ 2,78 bilhões). Aproveite para assistir: Não foi revelado se o filme será relançado no Brasil. Assista nossa crítica:

Q: Printf waiting for enter int kr=0; int ss =0; while ((kr=getchar()) != EOF){ if(kr != '\n') { ss++; } printf("%d\n",ss); } With this code , printf is waiting until i press enter then printing all the sequential ss values at the same time like in this . Can somebody explain this behavior ? A: printf is not waiting it is getchar instead. getchar uses a buffer behind the scene. When that buffer is empty, getchar will read 1 line from stdin and then return the first caracter. If it is not empty, it will return the next caracter from the buffer immediatly. That means that the getchar will wait the first time you call it. And thus your printf is never executed until you press enter

People often wonder- what really is CrossFit? How exactly does it work so well? We explain our training philosophy one piece at a time illustrated as the pyramid of CrossFit. CrossFit is a Strength and Conditioning Program that focuses on improving General Physical... We know many of you travel for work- below you will find two lists for you. The first list is for workouts you can do inside a hotel gym (thanks to Jason Khalipa of Norcal Crossfit). The second list is what you can do inside your hotel room (thanks to Steele Creek...

# gbRNAs.sql was originally generated by the autoSql program, which also # generated gbRNAs.c and gbRNAs.h. This creates the database representation of # an object which can be loaded and saved from RAM in a fairly # automatic way. #Genbank RNA genes CREATE TABLE gbRNAs ( bin int unsigned not null, chrom varchar(255) not null, # chromosome chromStart int unsigned not null, # Start position in chromosome chromEnd int unsigned not null, # End position in chromosome name varchar(255) not null, # gene name score int unsigned not null, # Score from 900-1000. 1000 is best strand char(1) not null, # Value should be + or - product varchar(255) not null, # Description of RNA gene intron varchar(255) not null, # Coordinates of intron in RNA gene #Indices PRIMARY KEY(name) );

1. Introduction {#sec1} =============== In cardiac anesthesia BIS monitoring is increasingly used to monitor anesthesia depth as well monitoring cerebral ischemia, which may be particularly important during cardiopulmonary bypass (CPB) \[[@B1], [@B2]\] and cardiopulmonary resuscitation \[[@B3], [@B4]\]. We describe a patient who, while being monitored with BIS, suffered a transient ischemic attack (TIA) of the brainstem. 2. Case Report {#sec2} ============== A 76-year-old man was scheduled for a three-vessel coronary artery grafting (CAG) using CPB. His medical history included hypertension, a minor inferior myocardial infarction, amaurosis fugax, surgical resection of a vocal cord carcinoma, and an eyelid correction. Physical examination showed a 70 kg, 1.69 m tall patient with a blood pressure of 170/70 mmHg and a pulse of 52. A bruit was heard over the heart, both carotid arteries and femoral arteries consistent with an aortic valve sclerosis. Cardiac ultrasound showed a hypokinetic inferior left ventricular wall, a good left and right ventricular function and an aortic valve sclerosis with minor aortic valve insufficiency. Coronary angiogram showed occlusion of the RCA, 90% occlusion of the LAD and 70% occlusion of the RCX. Patient took acetylsalicylic acid, chlortalidone, amlodipine, atorvastatin, metoprolol, isosorbide mononitrate, and isosorbide dinitrate. The patient was scheduled for a coronary bypass and premedicated with paracetamol 1000 mg and midazolam 7.5 mg, orally. Once in the operating theatre the patient was prepared for the operation with an 14 G IV infusion and a 20 G arterial cannula in the left radial artery as well as standard monitoring with a 5 lead ECG, pulsoximetry, and a noninvasive blood pressure band on the right arm. A BIS Quatro Sensor (XP) was placed and the monitor (Aspect Medical Systems, Inc. model A-2000 BIS Monitor) started. During this period the patient was alert and communicative. Without provocation, the patient suddenly complained of dizziness, stopped breathing, became unresponsive, and his eyes deviated upwards en laterally. The BIS monitor then gave its first reading of 60. We initially ventilated the patient by mask and gave naloxone to rule out an accidental sufentanil bolus. Subsequently the patient was intubated without medication. We requested an emergency neurological consultation. During this period the blood pressure and pulse remained stable at around 170/85 with a pulse of 55. Neurological examination showed a Glasgow Coma Score (GCS) of E-1, M-1, and V-T: eyes closed, no motor response to painful stimuli, and no sounds. He had pinpoint pupils and pupillary reactions showed minimal constriction to light. Corneal reflexes were present while oculocephalic reflexes were absent. Both eyes were deviated upwards and to the left. Tendon reflexes were increased on the left side, with bilateral extensor plantar responses. We performed a CT-scan, which showed central and cortical atrophy with subthalamic and periventricular hypodensities consistent with older vascular damage. The CT-angiogram showed generalized atherosclerotic changes in all brachiocephalic vessels, especially in the common and internal carotid arteries and a slight stenosis of the origin of the left vertebral artery. After the CT-scan, we restarted the BIS monitoring which still showed the BIS value at about 50 to 60. Eleven minutes after resuming BIS monitoring the patient opened his eyes, started breathing and responding to voice commands, and BIS values increased to around 80--85. The patient was extubated and wanted to know the result of the operation. On neurological examination, the patient was alert and responded adequately. There was a bilateral downbeat nystagmus in downgaze. Tendon reflexes remained increased on the left side, while both plantar responses were flexor. Based on the neurological examination, the transient nature of the neurological deficit, and the CT-scan, we concluded that the patient had suffered a transient ischemic attack of the brainstem. During the whole event which lasted 102 minutes the patient had remained hemodynamically stable. He was transferred to the neurological intensive care where the rest of his stay remained unremarkable, and he recovered without any neurological deficit. 3. Discussion {#sec3} ============= The primary reason to use an EEG monitor in anesthesia is to prevent awareness. Indeed, individuals suffering from this experience can have serious mental disorders. Awareness in a general population was found to be just below 0,2% and in a high-risk population just below 1% \[[@B5], [@B6]\]. Two large scale prospective trials (SAFE trial and B-Aware trial \[[@B5], [@B6]\]) demonstrated a reduction of 80% in the incidence of awareness using the BIS monitor. Furthermore, BIS and other EEG devices can be used to titrate anesthetics towards a desired level of hypnosis, with the aim to prevent exaggerated plasma concentration, which could lead to hemodynamic instability and prolonged awakening. There are some clinical conditions where BIS is unusually low. These are conditions were the cerebral functions are impaired by hypoperfusion, ischemia, hypoglycaemia, and hypothermia \[[@B7]\]. Patients with a neurological disease can present with unusual BIS values and anticonvulsant drugs may reduce BIS values. BIS may also detect microembolic injury \[[@B8]\]. In our case, BIS monitoring coincided with the clinical findings of reduced cerebral activity and later the return of consciousness. The BIS value is derived from two frontal leads. As such it will primarily monitor frontal lobe cortical electrical activity and indirectly frontal cerebral perfusion. As there was no change in blood pressure and pulse rate we think that the overall cerebral perfusion pressure was not reduced during the ischemic attack. Therefore, together with the diagnosis of brainstem TIA, we think that the BIS value is decreased by another mechanism then a perfusion disturbance. The cerebral cortex receives extensive afferent projections from brainstem nuclei. There is a long list of pathological brain conditions known to affect the EEG. Ischaemia is one of these conditions. Ischaemia of the lower brainstem (with a clinical picture characterized by coma, respiratory abnormalities, and pinpoint pupils) results in diffuse low-voltage activity and bilateral slowing of the EEG although a posterior alpha rhythm may be preserved. Hence a logical explanation for the significant decrease in the BIS signal observed in our patient may be the decrease in frontal cortical activity during ischemia of the brainstem. However, people using the BIS should be aware that the simplifying algorithm built in to the monitor limits its diagnostic possibilities and there are many factors, unknown to the user, which can alter the BIS value. The BIS monitoring did not lead to a change in treatment policy. Brainstem TIAs are supposedly a rare occurrence. The timing of our patients attack was quite spectacular: 20 minutes earlier and he would have been found asphyxiated in his bed and his death would most likely have been attributed to a coronary event. Thirty seconds later he would have been under anesthesia and subjected to hypothermia, hypotension, and full heparinization from the CPB. We can only speculate what the neurological outcome would have been. If the neurological outcome had been bad, it would have been labeled as a complication of the CPB. It begs the question how often the brainstem TIAs really happen in our cardio vascular-compromised population. 4. Summary {#sec4} ========== This 76-year-old patient suffered a brainstem TIA before cardiac surgery. The TIA was registered on BIS and resulted in a drop in BIS to a value of 60. When consciousness returned spontaneously, the BIS increased to 85. We believe that the lack of input from the brainstem to the frontal cortex resulted in the reduced cortical electrical activity as registered with the BIS. [^1]: Academic Editor: Michael G. Irwin

Impacting health through the worksite. The achievement of the Healthy People 2010 objectives will require community involvement of health care providers. The worksite remains the best place to access the adult population for health promotion and disease prevention. In addition, it is essential that non-worksite primary care services be attuned to the effects of work on health and illness. Given the frequency and duration of exposure, the significance of a worksite health history for the primary care provider cannot be overstated. To effectively serve clients, health histories should include assessment for the presence of hazardous worksite exposures and consideration of organizational climate. Further, when considering the provision of health promotion programs in the community, offering programs at the worksites within the community can be particularly effective. There should be increased efforts by health care providers to promote lifestyle modification through client and community interventions. The worksite offers an excellent setting as well as an opportunity to collaborate with employers to facilitate health promotion programs. Recognizing the significance of the occupational environment, an increasing number of worksite intervention studies have been reported. However, continued growth in this area is still needed. Research on worksite health promotion and disease prevention intervention is still in its infancy. Nurses can make a unique contribution to research on worksite lifestyle modification programs, and in enhancing the health status of the nation.

Agnel Philip The Republic | azcentral.com A former Phoenix police officer who pleaded guilty to stealing more than 2,000 narcotic pills that were in police custody was sentenced to nearly four years in prison by a Maricopa County Superior Court judge on Friday. William B. McCartney, 40, will serve three years and nine months in the Department of Corrections followed by three years of probation, according to the sentence Superior Court Judge Peter Reinstein handed down Friday morning. Reinstein will recommend to the Department of Corrections that McCartney be transferred to an out-of-state prison to serve his sentence. McCartney was arrested in 2011 after an internal audit showed that bags containing prescription painkillers, like oxycodone, that were handled by him were tampered with and replaced with over-the-counter medication. McCartney said during the hearing that he stole the painkillers because he was addicted to them. He said his addiction stemmed from an operation on his hand that he injured while on duty. "I know what I did was wrong, horrible and unethical," McCartney said. McCartney and his lawyer, David Cantor, asked the judge for the minimum sentence stipulated in his plea agreement of three years due to his achievements as a police officer and his contributions to society. But prosecutor Edward Leiter asked for a five-year sentence and said other police officers need to learn from McCartney's experience. "The message needs to be sent, frankly, to all police officers that if you engage in this type of activity … you will be appropriately punished," Leiter said. Five or six cases were directly impacted by McCartney's theft, but no cases were dismissed, Leiter said. McCartney's actions were a direct breach of public trust, Leiter said. Three members of McCartney's family spoke during the hearing. They said McCartney was a good man whose life spiraled out of control due to his addiction to painkillers. "We will all continue to love, support and be here for him," his brother, Ken McCartney, said as he cried at the podium. McCartney was extradited from Pennsylvania in July 2012 after being arrested in June. He had previously been arrested in 2011, but was released soon afterward as the case was further investigated. McCartney had been in the Phoenix Police Department since 1999 before his 2011 arrest, according to court documents. He resigned shortly after being arrested in 2011 and moved with his family to Pennsylvania. The defendant's family made impassioned pleas to Reinstein. They said they acknowledged the severity of the crime, but pointed to McCartney's record as a citizen and police officer. "He has always been a generous person," Ken McCartney said. The lead detective on the case, Theron Quass, said during the hearing that McCartney had legal ways to treat his pain and get counselling for his addiction but chose to steal the drugs instead. "He was clearly not honest, clearly addicted to drugs," Cantor said in reply to Quass' statements. Linda Staley, McCartney's sister, said his addiction was hidden from family members, doctors and friends. She said he has made an attempt to become clean after he realized he had a drug problem. "I am proud, as a sister, that he is here today," Staley said in reference to him taking responsibility by pleading guilty. Reinstein said McCartney's history as a police officer and good family man were mitigating factors in his sentencing, and he said McCartney was lucky to have his family support him. However, Reinstein also said he betrayed the trust of the people by stealing the narcotics.

Content Marketing is a Long Game I just got back from having coffee with a client. We were talking about content, its importance, and the fact that you simply can’t game the system (by system I mean Google). We were also lamenting the fact that honest and effective SEO companies are not always the ones that “win the bid.” The client will not always want to hear what these SEO providers have to say. Instead what they want to hear is “we will get you 100s of leads overnight for next to nothing.” Sure, we all like to dream. We all like to get the best deal. But, remember, you get what you pay for. I’m not just talking about money here. I’m also talking about time. Because, time is money. Everything Google does is geared towards delivering the best search results to its users. Think about that. What is a good search result in your industry? What are your clients looking for? I’ve gotten into debates in the past with less than stellar SEO companies about their efforts to game the system. For example, one company wanted to create a series of pages for every location the client served… each having the same content! I warned them that Google was warning against this. Their answer… “well, it works great right now.” I think you can see where this is headed. Content marketing, “a marketing technique of creating and distributing valuable, relevant and consistent content to attract and acquire a clearly defined audience – with the objective of driving profitable customer action,” is another piece of this strategy. It’s a long game. What does this mean? It means that marketing with content (good utility content) will not convert right away. You can’t expect to write a blog post, like this one, and get a sale from it tomorrow. You might, and it doesn’t hurt to ask, but it isn’t the point. The point of content marketing is build trust in your brand. You’re working to become THE resource in your industry. The go-to. To do this, you need to consistently provide value, answer questions, and solve problems… expecting nothing in return. This might seem crazy to some. But, think about it this way. You could “sell, sell, sell” right out of the gates and maybe get a few leads. But, how many people have you turned off in the process? And how many people will refer you to their contacts based on this approach? Not many. Why would they? You haven’t given them anything. And that’s the way it works today. Jon-Mikel Bailey - Before co-founding Wood Street in 2002, Jon worked in sales, marketing and business development for technology and marketing firms. A popular speaker, he gives seminars on marketing, internet marketing, branding and web design to chambers of commerce, trade associations and colleges. He has a BFA in Photography from Frostburg State University and still shoots photos for Wood Street clients. For almost 60 years our company has been manufacturing reliable construction equipment. The trust in the EDCO brand comes from decades of superior face-to-face customer service and training. To grow, we needed to expose more people to our high-quality service. Obviously, an upgraded Internet presence was the best way to reach new audiences. We had lots of online training ideas, but our outdated website prevented us from realizing them. We brought big ideas to Wood St who created an entirely new website based on... Read More

13-cis-retinoic acid plus interferon-alpha: a phase II clinical study in squamous cell carcinoma of the lung and the head and neck. Retinoids and interferon-alpha (IFN-alpha) have been shown to have a synergetic antiproliferative and differentiative effect on many cell lines, and in combination they have already been tested with some success in the treatment of some tumors. We investigated the tolerance and efficacy of high dose 13-cis-retinoic acid (2 mg/kg/day) and IFN-alpha in the treatment of advanced squamous cell carcinoma of the lung and of the head and neck. No partial or complete response was observed in the 10 patients treated. The toxicity was unusual and mild to moderate considering the dose of retinoid given. This observation leads us to suspect that IFN-alpha may alleviate some of the side effects of the retinoid, and is of interest in the design of future clinical trials.

Fitzmaurice, Saskatchewan Fitzmaurice is an unincorporated area in the rural municipality of Garry No. 245, in the Canadian province of Saskatchewan. Fitzmaurice is located North of Highway 52 & West of Highway 617 in eastern Saskatchewan. See also List of communities in Saskatchewan List of rural municipalities in Saskatchewan References External links Saskatchewan City & Town Maps Saskatchewan Gen Web - One Room School Project Post Offices and Postmasters - ArchiviaNet - Library and Archives Canada Saskatchewan Gen Web Region Online Historical Map Digitization Project GeoNames Query 2006 Community Profiles Category:Ghost towns in Saskatchewan Category:Insinger No. 275, Saskatchewan Category:Unincorporated communities in Saskatchewan

Remove JPanel Components Hi im triying to remove all the components ina JPanle and replace it with new ones. The JPanel is running on an applet, every time I remove all components the apllet just crashes. I also tryed revalidate and repaint and the applet still dies. here is the last code I tried: Well, generally you want to call "validate()", not "revalidate()", on a container whose contents you've changed while it's visible. Without seeing more of your code, that'd be the first thing I'd recommend. Haroldo Level Greenhorn Joined: Feb 17, 2005 Posts: 6 posted Feb 18, 2005 14:13:00 0 I tried validate also and it didn't work, here is the complete code... public class ChatRoom extends Applet implements ActionListener, KeyListener { public static final int chatPort=3737;

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package vpx import "errors" func Error(err CodecErr) error { switch err { case CodecOk: return nil case CodecError: return ErrCodecUnknownError case CodecMemError: return ErrCodecMemError case CodecABIMismatch: return ErrCodecABIMismatch case CodecIncapable: return ErrCodecIncapable case CodecUnsupBitstream: return ErrCodecUnsupBitstream case CodecUnsupFeature: return ErrCodecUnsupFeature case CodecCorruptFrame: return ErrCodecCorruptFrame case CodecInvalidParam: return ErrCodecInvalidParam default: return ErrCodecUnknownError } } var ( ErrCodecUnknownError = errors.New("vpx: unknown error") ErrCodecMemError = errors.New("vpx: memory error") ErrCodecABIMismatch = errors.New("vpx: ABI mismatch") ErrCodecIncapable = errors.New("vpx: incapable") ErrCodecUnsupBitstream = errors.New("vpx: unsupported bitstream") ErrCodecUnsupFeature = errors.New("vpx: unsupported feature") ErrCodecCorruptFrame = errors.New("vpx: corrupt frame") ErrCodecInvalidParam = errors.New("vpx: invalid param") )

Shabir Ahmad Bhat was one of the most prominent faces of the BJP in Jammu and Kashmir's Pulwama district. He was killed by militants on 22 August despite having security. Pulwama: As threats against mainstream political workers and leaders increases in South Kashmir, Reyaz Ahmad, a low-key member of the Bharatiya Janata Party (BJP), has been exploring the possibility of migrating to the relatively safer Srinagar, the summer capital of Jammu and Kashmir. At the same time, Ahmad has been pushing the inevitable, trying to assure his family members that the "situation is getting better", and that his two children, who are enrolled in a government-run school in South Kashmir, cannot be admitted to another school in the city mid-session. However, the recent killing of one of the most prominent faces of the BJP in Pulwama district, Shabir Ahmad Bhat, allegedly by militants, despite having security, has spread terror through the ranks and files of the party. "He (Bhat) was provided security by the government, yet he was killed. We don't have security, which makes it scarier," said Ahmad, a resident of Pulwama's Pinglan village. "Before this, party general secretary Gulzar Ahmad Nangroo was fired upon by militants, but his personal security officer fired back and saved him in Pulwama town." On Sunday afternoon, he borrowed a car from a neighbour and quietly set out for Srinagar with his wife and two children without informing anyone in his locality. "When the sun would set, I could hear myself breathing because there was so much silence in our home every evening," he said. There was a time in Kashmir when being a BJP worker was taboo and nearly impossible for any Kashmiri. The first BJP leader to fall prey to the bullets was Tika Lal Taploo, a Kashmiri Pandit who was killed by militants in 1989, just when insurgency began to plague the Valley. The party gradually built a tiny base in the villages of Kashmir, albeit behind closed doors. But South Kashmir was one region that had a formidable presence of BJP workers. It was here that the BJP first held its roadshows. Party workers had launched a door-to-door campaign in Anantnag town before the 2014 Assembly elections in Jammu and Kashmir. It was a given that the BJP would not win any seats, but its mere presence was an indicator of the changing politics of the Valley. Those were the days when new-age militancy had yet to take centrestage in Jammu and Kashmir, with no spillover from Hizbul Mujahideen commander Burhan Wani's killing. Mohammad Rafiq Wani, who fought the last Assembly elections on a BJP ticket and is the party chief in South Kashmir's Anantnag district, said there is fear among the workers of all political parties in the state, more so among BJP workers. While many have already resigned, we held a meeting for them on Monday, which around 300 of them attended. "It is a close-knit society, and everyone knows everyone. Even if someone resigns from the BJP, few would believe it, assuming they will be back after things cool down," he said. A day after Bhat's killing on 22 August, at least two dozen BJP workers met in a small house in Pulwama and decided to migrate from their villages. A majority of them were either Bhat's associates or had participated in small meetings organised by the BJP in Pulwama district. "Living in our houses is like inviting militants to kill us," Arshad, another BJP worker, said at the meeting. "It is better to move to safer areas than wait for death." Party leader Altaf Ahmad Thakur said the BJP has "around 30,000 members in just one district of Pulwama" and "around 12,000 of them live in the periphery" of the town. They are the card-holders of the party, but providing security to all is out of question, he said, adding that the BJP had "around 4.3 lakh members in 2016" in Kashmir, a majority of them in the southern region. "Eleven thousand of them are active members of the party who participate in the BJP's day-to-day activities," Thakur said. Bhat is often given the credit for the BJP's strengthened foothold in Pulwama district, but surprisingly, one of his security guards was withdrawn only a few days before he was killed, making him more vulnerable. BJP national vice-president and Jammu and Kashmir in-charge Avinash Rai Khanna, who visited Bhat's house in Pulwama after his death, said there is mounting concern over the security of party workers in the Valley. "Our workers are targeted to lower their morale, but these dastardly acts won't deter us from carrying out the work for which we are here," he said. However, Khanna's words of assurance will hardly help BJP workers and leaders on the ground. Recently, several party workers in the far-flung villages of Pulwama visited mosques to seek forgiveness. But as militant ranks swelled in these regions, the mainstream activists who participated in political activities began to feel insecure. In the last few months, as the situation improved after Jammu and Kashmir was brought under Governor's Rule, several of BJP's mainstream activists and leaders returned to their homes. Now, Bhat's murder has forced them to leave home once again. Bhat's was the third killing of a BJP political worker since November. The first to be targeted in the last two years was BJP youth leader Gowhar Ahmad Bhat, who was killed by suspected militants in Shopian district. Militants then ambushed Ghulam Nabi Patel, who was earlier associated with the Congress and Peoples Democratic Party, at Rajpora market in April. In South Kashmir, the assassination of Ghulam Hyder Noorani in 1999 is one of the better-known incidents of a BJP leader being attacked. Militants killed Noorani and his three workers during a campaign trail after he was nominated as the party's candidate for the Anantnag parliamentary seat. "People made fun of us at one time. They would boo us and crack jokes at our expense," said Sofi Yousuf, a BJP MLC who joined the party around the same time Noorani was killed. "This too shall pass. We will live here, and we will die her. We aren’t going anywhere."

Why Miley Cyrus *Isn’t* The Worst Role Model For Kids Miley Cyrus has just topped the list of worst celebrity role models for kids. And we totally don’t agree with the verdict. According to a new survey on Vouchercloud, the Wrecking Ball singer has been ranked to the top spot by British parents. Yahoo reports that the survey asked parents who had at least one child under the age 10 if there were any pop icons they would hate for their children to idolise. Both male and female celebrities were presented to them, and a whopping 78% placed Miley in first place. . Miley’s first place spot is probably owed to her seemingly wild child ways. Granted, she shocked a lot of people when she emerged with a rockin’ new look, having shed her Hannah Montana image. But when you dig a little deeper, Miley’s actually a pretty solid role model in our eyes. Her passion in these areas can’t be questioned, having founded the Happy Hippie Foundation – a nonprofit that works to help homeless and LGBT kids – and of course there was that spectacular time that she invited a homeless man onto the stage to accept an award on her behalf, giving him a platform to tell his story. 2. Miley promotes a positive body image In a world where most parents worry about the influences over their children’s view of their own body, Miley publically stands to promote a balanced and healthy view. She recently spoke out about the ‘body dysmorphia’ she experienced during her time as Hannah Montana. She also opened up to Marie Claire: ‘When you look at retouched, perfect photos, you feel like s**t’, she said. ‘They lighten black girls’ skin. They smooth out wrinkles. Even when I get stuck on Instagram wondering, “Why don’t I look like that?” It’s a total bummer. It’s crazy what people have decided we’re all supposed to be.’ We’re sure this is something that most of us – children or not – can relate to. 3. Miley champions the idea of accepting every sexuality Be true to yourself. It’s ok. Speaking with TIME, she revealed: ‘I hope more kids don’t do what I did and sit in their room and cry, thinking “I just don’t know what I’m supposed to be,'” she said. ‘But when I tell kids sometimes, “Just be yourself,” I feel like, “I hope you can do that. Can you really do that?'” Miley openly talks about her relationships with both men and women, and the struggles and insecurities she has experienced through each and every relationship. 4. Miley is a strong, independent woman The star preaches strength and independence: “It has a lot to do with being a feminist, but I’m finally O.K. with being alone. I think that’s something we have to talk about more: that you can be alone. “There are times in my life where I’ve had boyfriends or girlfriends. And there are times where I just love being with myself and don’t want to give part of myself away to someone else … I think that’s a new freedom for women, especially. I don’t know that my mother would have been able to be 22 and secure in being alone. But my future doesn’t rely on having a partner.”

! Copyright (C) 2002-2013 Free Software Foundation, Inc. ! Contributed by Paul Brook <paul@nowt.org> ! !This file is part of the GNU Fortran 95 runtime library (libgfortran). ! !GNU libgfortran is free software; you can redistribute it and/or !modify it under the terms of the GNU General Public !License as published by the Free Software Foundation; either !version 3 of the License, or (at your option) any later version. !GNU libgfortran is distributed in the hope that it will be useful, !but WITHOUT ANY WARRANTY; without even the implied warranty of !MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the !GNU General Public License for more details. ! !Under Section 7 of GPL version 3, you are granted additional !permissions described in the GCC Runtime Library Exception, version !3.1, as published by the Free Software Foundation. ! !You should have received a copy of the GNU General Public License and !a copy of the GCC Runtime Library Exception along with this program; !see the files COPYING3 and COPYING.RUNTIME respectively. If not, see !<http://www.gnu.org/licenses/>. ! !This file is machine generated. #include "config.h" #include "kinds.inc" #include "c99_protos.inc" #if defined (HAVE_GFC_REAL_10) #ifdef HAVE_ASINHL elemental function _gfortran_specific__asinh_r10 (parm) real (kind=10), intent (in) :: parm real (kind=10) :: _gfortran_specific__asinh_r10 _gfortran_specific__asinh_r10 = asinh (parm) end function #endif #endif

El cambio de rumbo en RTVE es un hecho especialmente constatable este lunes 10 de septiembre, en el que la cadena pública ha recogido como noticia principal la exclusiva desvelada por eldiario.es de que la ministra de Sanidad del Gobierno socialista, Carmen Montón, obtuvo un máster en la Rey Juan Carlos plagado de irregularidades. El Telediario Matinal de las 8:00 horas ha incluido la información en sus titulares principales, y 'Los Desayunos' de Xabier Fortes directamente han abierto con ella. Algo que recientemente no hizo TVE con dos casos similares como los másters de Cristina Cifuentes y de Pablo Casado, que fueron relegados e incluso ocultados pese a centrar la actualidad informativa en el resto de medios. Mientras continúan los cambios en la Corporación pública, con el PP denunciando "purgas" y "depuraciones sociatas" y antiguos responsables de TVE como Carmen Sastre asegurando que ha sido "un quítate tú que ya vengo yo", la cadena pública no ha obviado la importancia informativa de la noticia aunque su protagonista sea un miembro del actual Gobierno. Tercer titular en el Telediario Matinal de TVE En eldiario.es, la información ha sido publicada a las 6 de la mañana. TVE la ha recogido en su bucle informativo desde las 6:30 horas, y ya en el informativo editado y presentado por Inma Gómez Lobo, la noticia ha sido presentada como tercer titular, tras la apertura del año judicial y la candidatura de Carmena a su reelección en Madrid. "Otro máster en duda. La ministra Carmen Montón curó uno en la Rey Juan Carlos e incurrió en presuntas irregularidades. Eso es lo que dice eldiario.es, que asegura que la ministra tuvo muy buenas notas a pesar de que se incorpora a mitad de curso y no trató con los profesores. Montón ha dicho en Twitter que dará explicaciones esta mañana", ha explicado la presentadora, mientras en formato de "colas" se veía en pantalla imágenes de la exclusiva de eldiario.es y una imagen de la ministra. En el minuto 9:30 del informativo, por lo tanto a las 8:09 horas de la mañana y ya presentados todos los titulares, el Telediario Matinal ha desarrollado algo más la noticia con una entradilla a cámara de Inma Gómez Lobo, y luego nuevamente con un formato de "colas" en las que podían verse imágenes de la web de eldiario.es y de la ministra, a lo largo de unos 45 segundos. Noticia principal de apertura en 'Los Desayunos' El programa matinal de Xabier Fortes había anunciado como punto fuerte para este lunes 10 de septiembre su entrevista con la exministra Ana Pastor, pero se ha adaptado a la actualidad para abrir con este nuevo caso de un máster en duda de un político. Citando nuevamente a la fuente, el presentador ha realizado una entradilla a cámara para explicar más detalladamente la información, mientras se ofrecían imágenes de la web de eldiario.es. Sin detenerse, se ha mostrado también el tuit de la ministra Montón prometiendo dar explicaciones en rueda de prensa, y se ha dado paso a un análisis de los tertulianos Marisa Cruz (El Mundo), Elsa García de Blas (El País), Bieito Rubido (ABC) y Jesús Maraña (Infolibre). También se han recogido las declaraciones al respecto del Secretario General del PP, Teodoro García Egea, en RNE. Todo ello ha ocupado los primeros 6 minutos del programa, hasta las 8:42, y el debate se ha alargado a este respecto situando la noticia así como la más importante del día y asunto de apertura. 'La Mañana' no emite la rueda de prensa, el 24H sí A las 11 de la mañana, la ministra Montón ha convocado a la prensa para dar explicaciones y contar su versión de la polémica desatada, sobre la que ya había opinado Pablo Casado: "Yo no voy a hacer lo que hicieron conmigo, confío en sus explicaciones". La comparecencia de prensa ya se incluía en tiempo de 'La Mañana', que no ha cortado su parrilla habitual para conectar en directo con el acto. Sí que lo ha hecho el Canal 24H, aunque con algo de retraso, por lo que no ha ofrecido la comparecencia de Montón desde el primer segundo, sino que ha llegado unos minutos después. Como explican a Vertele fuentes del Consejo de Informativos, este órgano de control ya ha enviado preguntas a la dirección de informativos para averiguar por qué han entrado tarde en TVE, perdiéndose la primera parte de la comparecencia de Montón. En concreto, en La 1 se ha conectado 8 minutos tarde y solo se ha emitido una parte de la rueda de prensa, volviendo luego a la programación normal antes de que terminara. El Canal 24 horas, aunque ya ha conectado con la comparecencia empezada, ha emitido la rueda completa. Por su parte, la Dirección ya se ha puesto en contacto con ellos para tratar de aclarar lo ocurrido. Noticia principal en 'Más Desayunos', con Escolar en directo Concluido el tiempo de 'La Mañana', ya en el segundo espacio de Fortes en La 1 de TVE, 'Más Desayunos', el programa ha vuelto a situar su foco en esta noticia como una de las principales del día. Por primera vez, TVE ha querido contar directamente con una de las voces de eldiario.es que firman la exclusiva, en este caso la del director Nacho Escolar. En el caso de Cifuentes, ningún periodista de eldiario.es fue invitado o contactado para explicar la noticia de primera mano. Así actuó TVE con el máster de Cifuentes El tratamiento informativo ha sido muy diferente al que, hace unos meses, TVE dio al escándalo por el máster fraudulento de Cristina Cifuentes, que acabó provocando la dimisión de la por entonces Presidenta de la Comunidad de Madrid. El 21 marzo, eldiario.es destapó en exclusiva la información, y pese a ser publicada también a las 6 de la mañana, durante toda su franja despertador TVE no informó sobre ello. No lo hizo ni en su bucle informativo, ni en el Telediario Matinal de Jerónimo Fernández (que ha protestado tras ser cesado de su puesto). En 'Los Desayunos' de Sergio Martín: La primera mención al respecto la hizo Sergio Martín en 'Los Desayunos', presentándola como un "run run en los pasillos del Congreso" y diciendo: "Ya hay reacciones políticas y por eso se lo tengo que contar" para dar paso a la información. Martín citó a eldiario.es y el programa incluyó un pantallazo con la portada del medio, del mismo modo que este lunes ha realizado Inma Gómez Lobo. El tertuliano Miguel Ángel Liso, director editorial del Grupo Zeta, al que Martín pedía una valoración, reclamaba "cautela" ante la noticia e insistía en la idea de que Cifuentes había sido "contundente" en "defender su honorabilidad". El colaborador decía que había de esperarse a tener "pruebas fehacientes que demuestren una regularidad" antes de emitir un juicio. Más allá del breve resumen que hacía el presentador en este momento, Los Desayunos no profundizó más ni alteró sus contenidos del día. Durante el resto del caso, la cobertura superficial se repitió en Los Desayunos, que sí informó de él cuando había novedades importantes, recogiendo las informaciones. Sin embargo, ningún periodista de eldiario.es fue invitado a la tertulia en la que sí participaron periodistas de otros medios para explicar la información de primera mano, por lo que los análisis se realizaron siempre sin dar voz directa al medio que destapó la exclusiva, ni siquiera por vía telefónica. En el Telediario 1 de Pilar García Muñiz: En el Telediario 1 de la cadena, la noticia también tuvo presencia, aunque con un polémico tratamiento y presentación: sin contar el contenido de la noticia, abriéndola con el desmentido del rector de la Rey Juan Carlos, Javier Ramos, dando por ciertas las explicaciones sin pruebas de que todo fue "un error de transcripcción" y sin citar al medio, al que solo se ha referido como "un diario digital". ▶ Repasa lo más destacado de nuestro # TD1 en cuatro minutoshttps://t.co/CpUM13KEwlpic.twitter.com/bkewF85Udh — Telediarios de TVE (@telediario_tve) 21 de marzo de 2018 Pilar García Muñiz locutaba de la siguiente manera estas primeras imágenes al respecto. "La Universidad Rey Juan Carlos atribuye a un error de transcripción que en dos asignaturas del máster que Cristina Cifuentes cursó hace seis años figurase como no presentada. Cifuentes aprobó las dos asignaturas según ha confirmado el rector. La oposición pide explicaciones. El gobierno regional defiende la honorabilidad del comportamiento de la presidenta". Para encontrar la noticia en la escaleta del Telediario hubo que esperar 15 minutos: "La Universidad Rey Juan Carlos niega cualquier irregularidad en el máster de Cristina Cifuentes", leyó la presentadora. El espacio eludió citar a eldiario.es como responsable de la noticia, refiriéndose a éste como "un diario digital" que "sostiene que la presidenta regional obtuvo la titulación con notas falsificadas". Días después, el Telediario 1 de TVE eludió informar sobre las "irregularidades" del título universitario de la presidenta regional y obvió mencionar que el anuncio de su querella criminal contra Ignacio Escolar y Raquel Ejerique se realizó a través de un plasma sin preguntas. En 'Informe semanal' de Jenaro Castro: Los intentos de TVE por ocultar y restar importancia a la información sobre Cifuentes, que acabó produciendo su dimisión, fueron aún más evidentes en el 'Informe semanal' de Jenaro Castro. Primero lo ignoraron. Luego lo despacharon en un minuto dentro de otra pieza que alababa los presupuestos del Gobierno. Y, 25 días después de destaparse, llegó el día en el que Informe Semanal decidió dedicar uno de sus reportajes al Máster de Cifuentes, escándalo que había copado las portadas de todos los medios y el tiempo de los programas informativos del resto de cadenas. El reportaje no solo silenció la opinión del medio que dio en exclusiva la información y la de sus periodistas, si no que borró cualquier referencia al periódico digital, mostrando capturas de pantalla de las noticias de eldiario.es sin que en ningún momento se viera su logo o su cabecera. El tratamiento provocó que el Consejo de Informativos de TVE iniciase una investigación al respecto, extrañado por el tiempo que habían tardado en recoger el caso, y que se hubiese silenciado al medio que lo destapó: "Es como si quieres hacer un reportaje sobre el Watergate y no contactas con Bernstein y Woodward". El máster de Casado también fue relegado en TVE La situación se repitió meses después, cuando el 9 de abril El País destapó un caso similar sobre el máster de Pablo Casado, que el ahora líder del PP logró sin pisar el aula pese a que en teoría se exigía ir a clase. El proceso se encuentra desde el 6 de agosto en manos del Tribunal Supremo, después de que la jueza lo elevase tras apreciar que existen indicios de delito y que el título fue "un regalo académico". Nuevamente, el Telediario Matinal no hizo ni una sola mención a la información. Y en este caso, tampoco recogieron la noticia Los Desayunos, pese a que buena parte de su entrega versó en torno a la situación del Máster de Cifuentes y a la Convención del PP. El Telediario 1 tampoco hizo mención a la noticia. En el caso de 'Informe Semanal', el programa tuvo un antes y un después a la llegada de Rosa María Mateo y la salida de Jenaro Castro. Primero, el director y presentador del programa se puso a sí mismo al frente de una entrevista al recién proclamado líder del PP, en la que apenas le preguntó por su máster. Después de que la investigación se trasladase al Tribunal Supremo, apenas cuatro días después, el 10 de agosto, el programa con Jerónimo Fernández al frente trató sobre el máster de Casado con una postura alejada de la del PP. "La actualidad de España nos conduce al Tribunal Supremo, que decidirá en las próximas semanas qué hacer con el caso del máster de Pablo Casado, si archivarlo o investigarlo y abrir juicio. La juez que ha elevado la causa al alto tribunal aprecia los cohechos impropio y prevaricación administrativa. En las 54 páginas de que consta la exposición motivada, la juez Carmen Rodríguez-Medel describe lo más parecido a una fábrica de regalar másters. El líder del PP insiste en que ha actuado correctamente y no dimitirá", introdujo el presentador.

One part of the Department of Defense is hard at work researching technology that is alternately amazing, bizarre, and downright scary. You may not be familiar with the Defense Advanced Research Projects Agency, more commonly known as "DARPA," but the robotic creations it brings under the wing of the U.S. defense budget are often on the cutting-edge of weird. In honor of Skynet Day, we bring you some of the craziest DARPA robots that may someday be our new overlords. DARPA was founded in 1958 as a response to the Soviet launch of the Sputnik satellite and has since funded "revolutionary, high-payoff research" to keep the Pentagon supplied with the latest in defense-flavored tech. From a fluttering hummingbird-shaped spy drone to more than a few motorized automatons that move in ways uncanny, these projects should help you sleep at night...in theory. 1. BigDog BigDog, developed by BostonDynamics, is quadruped robot intended to haul, climb, and carry its way over rough terrain. While the buzzing noise that BigDog emits makes this robotic beast all the more unsettling, the real kicker is watching BigDog recover from a fall on slippery ice. 2. Nano hummingbird drone This robotic ornithopter might not take the most inconspicuous shape, but it can hover aloft to fulfill your spying needs for 8 minutes straight, darting off at a brisk 11 miles an hour if any onlooker becomes the wiser. Developed by AeroVironment, this little fella has a contract with DARPA for its reconnaissance and surveillance applications. 3. LittleDog LittleDog may not have the raw, unsettling oomphof its big brother, but its beetle-like form and successful rock-climbing (scrabbling?) skills make it no less impressive. 4. RiSE climbing robot We're not sure what kind of surveillance opportunities await the RiSE robot, developed by a team at Carnegie Mellon, but we do know we wouldn't want to run into one of these things scaling its way up...well, anything. The RiSE is a "bioinspired climbing robot" intended to walk on land and climb vertically, two activities it seems to execute with eery aplomb. 5. PetMan PetMan is the bipedal sibling of BigDog, reportedly developed to test chemical protection suits for the U.S. Army. PetMan simulates both human movement mechanics and human physiology precisely - it will can even sweat in hot environments. 6. Crusher unmanned ground vehicle The Crusher is an autonomous, unmanned off-road vehicle that takes after a tank more than most of these other more biologically-inclined robots. Developed at Carnegie Mellon, it weighs 6.4 tons and packs plenty of on-board electronics - like laser range-finders and an advanced GPS system - to help it navigate over rough terrain. 7. BigDog weaponized...with horns If BigDog's eerily sophisticated mechanical abilities and ominous buzzing sound have you a little on edge, maybe this lo-tech "weaponized" version of BigDog will make you feel better? Then again, maybe not. This post originally appeared on Tecca, which helps you get the best from the personal technology in your life.

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Lack of correlation between the induction of donor class I and class II major histocompatibility complex antigens and graft rejection. The induction of donor major histocompatibility complex (MHC) antigens on nonrejected and rejected rat renal allografts was compared at various times after transplantation in two strain combinations, DA-to-PVG and LEW-to-DA. Graft rejection was prevented by preoperative donor-specific blood transfusion (DST). Quantitative absorption analysis and immunohistology were performed using monoclonal antibodies specific for donor class I and class II MHC antigens. A significant increase in the expression of donor MHC antigens, both class I and class II, was demonstrated on nonrejected as well as rejected kidneys after transplantation. A kinetic analysis showed that induction of donor class I antigens was accelerated on the nonrejected grafts, and by day 5 the nonrejected kidneys showed increased expression of class I antigen when compared with the rejected grafts (a 37- vs. a 25-fold increase in expression). Increased expression of donor class I antigens persisted on the nonrejected grafts and was still detectable on long-term-surviving kidneys, 50 days after transplantation. The magnitude of class II antigen induction was similar on both rejected and nonrejected grafts (8-fold by 5 days after transplantation). Immunohistology demonstrated that class I and class II antigens were induced on identical structures in the kidney in both situations. In particular the vessel endothelia, which do not express class II antigens in normal kidney, become strongly positive in both rejected and nonrejected grafts 5 days after transplantation. Although renal allograft rejection is completely suppressed in rats given a single donor-specific blood transfusion before transplantation, graft survival cannot be explained by the lack of induction of donor MHC antigens. Donor MHC antigens are induced on these nonrejected kidney grafts, and therefore they could act as target molecules for the effector cells that mediate graft destruction. Thus the induction of donor MHC antigens on tissue allografts should not be considered as indicative of a rejection response resulting in graft destruction.

--- abstract: 'We give the emission function of the axially symmetric Buda-Lund hydro model and present its simultaneous, high quality fits to identified particle spectra, two-particle Bose-Einstein or HBT correlations and charged particle pseudorapidity distributions as measured by BRAHMS and PHENIX in 0-30 % central, $\sqrt{s_{\NN}} = 200$ GeV Au+Au collisions at RHIC. The best fit is achieved when the most central region of the particle emitting volume is superheated to $T_0 = 200 \pm 9$ MeV $ \ge T_c =172 \pm 3$ MeV, a preliminary, 3 $\sigma$ effect.' author: - | M. Csanád$^1$, T. Csörgő$^2$, B. Lörstad$^3$ and A. Ster$^2$\ $^1$Dept. Atomic Phys., ELTE, H-1117 Budapest, Pázmány P. 1/a, Hungary\ $^2$MTA KFKI RMKI, H - 1525 Budapest 114, P.O.Box 49, Hungary\ $^3$Dept. Physics, University of Lund, S - 22362 Lund, Sweden title: | [**A hint at quark deconfinement\ in 200 GeV Au+Au data at RHIC**]{} --- Introduction ============ The Buda-Lund hydro model is successful in describing the identified single particle spectra and the transverse mass dependent Bose-Einstein or HBT radii as well as the pseudorapidity distribution of charged particles in Au + Au collisions at $\sqrt{s_{\NN}} = 130 $ GeV [@ster-ismd03], as measured by the BRAHMS, PHENIX, PHOBOS and STAR collaborations. The result of the simultaneous fit to all these datasets indicate the existence of a very hot region, with a temperature significantly greater than 170 MeV [@mate-ell1]. Recently, Fodor and Katz calculated the phase diagram of lattice QCD at finite net barion density [@Fodor:2001pe]. These lattice results, obtained with light quark masses four times heavier than the physical value, indicated that in the $0 \le \mu_B \le 700$ MeV region the transition from confined to deconfined matter is a cross-over, with $T_c \simeq 172 \pm 3$ MeV. This value is, within one standard deviation, independent of the bariochemical potential in the $0 \le \mu_B \le 300$ MeV region. The Buda-Lund fits, combined with these lattice results, provide an indication for quark deconfinement in Au + Au collisions with $\sqrt{s_{\NN}} = 130 $ GeV colliding energies at RHIC. This observation was confirmed [@mate-ell1] by the analysis of the transverse momentum and rapidity dependence of the elliptic flow as measured by the PHENIX and PHOBOS collaborations. Here we investigate what happens if a similar analysis is performed on the final, published Au+Au collision data at RHIC at the maximum, $\sqrt{s_{\NN}} = 200$ GeV bombarding energies. The emission function of the Buda-Lund hydro model ================================================== The Buda-Lund hydro model was introduced in refs. [@Csorgo:1995bi; @Csorgo:1995vf]. This model was defined in terms of its emission function $S(x,k)$, for axial symmetry, corresponding to central collisions of symmetric nuclei. The observables are calculated analytically, see refs. [@cs-rev; @ster-ismd03] for details and key features. Here we summarize the Buda-Lund emission function in terms of its fit parameters. The presented form is equivalent to the original shape proposed in refs. [@Csorgo:1995bi; @Csorgo:1995vf], however, it is easier to fit and interpret it. The single particle invariant momentum distribution, $N_1(k_1)$, is obtained as N\_1(k\_1) = \^4 x S(x,k\_1). For chaotic (thermalized) sources, in case of the validity of the plane-wave approximation, the two-particle invariant momentum distribution $N_2(k_1,k_2) $ is also determined by $S(x,k)$, the single particle emission function, if non-Bose-Einstein correlations play negligible role or can be corrected for, see ref. [@cs-rev] for a more detailed discussion. Then the two-particle Bose-Einstein correlation function, $ C_2 (k_1,k_2) = { N_2(k_1,k_2)}/\left[{ N_1(k_1) N_1(k_2) }\right] $ can be evaluated in a core-halo picture [@Csorgo:1994in], where the emission function is a sum of emission functions characterizing a hydrodynamically evolving core and a surrounding halo of decay products of long-lived resonances, $S(x,k) = S_c(x,k) + S_h(x,k)$. Consequently, the single particle spectra can also be given as a sum, $N_1(k) = N_{1,c}(k) + N_{1,h}(k)$. In the correlation function, an effective intercept parameter $\lambda \equiv \lambda_*(K)$ appears and its relative momentum dependence can be calculated directly from the emission function of the core, C\_2 (k\_1,k\_2) = 1+ 1+\_[\*]{}(K), where the relative and the momenta are $q = k_1-k_2$, $K = 0.5 (k_1+k_2)$, and the Fourier-transformed emission function is defined as $\tilde S(q,K) = \int \d^4 x S(x,K) \exp(i q x).$ The measured $\lambda_*$ parameter of the correlation function is utilized to correct the core spectrum for long-lived resonance decays [@Csorgo:1994in]: $ N_1(k) = N_c(k)/{\sqrt{\lambda_{*}(k)}}. $ The emission function of the core is assumed to have a hydrodynamical form, $$S_c(x,k) d^4 x = \frac{g}{(2 \pi)^3} \frac{ k^\nu d^4\Sigma_\nu(x)}{B(x,k) +s_q},$$ where $g$ is the degeneracy factor ($g = 1$ for pseudoscalar mesons, $g = 2$ for spin=1/2 barions). The particle flux over the freeze-out layers is given by a generalized Cooper–Frye factor: the freeze-out hypersurface depends parametrically on the freeze-out time $\tau$ and the probability to freeze-out at a certain value is proportional to $H(\tau)$, $ k^\nu d^4\Sigma_\nu(x) = m_t \cosh(\eta - y) H(\tau) d\tau \, \tau_0 d\eta \, dr_x \, dr_y. $ Here $\eta = 0.5 \log[(t + r_z)/(t-r_z)]$, $\tau=\sqrt{t^2 - r_z^2}$, $ y = 0.5 \log[(E + k_z)/(E-k_z)]$ and $m_t=\sqrt{E^2 - k_z^2}$. The freeze-out time distribution $H(\tau)$ is approximated by a Gaussian, $ H(\tau) = \frac{1}{(2 \pi \Delta\tau^2)^{3/2}} \exp\left[-\frac{(\tau - \tau_0)^2} {2 \Delta \tau^2} \right], $ where $\tau_0$ is the mean freeze-out time, and the $\Delta\tau$ is the duration of particle emission, satisfying $\Delta\tau \ll \tau_0$. The (inverse) Boltzmann phase-space distribution, $B(x,k)$ is given by $$B(x,k)= \exp\left( \frac{ k^\nu u_\nu(x)}{T(x)} -\frac{\mu(x)}{T(x)} \right),$$ and the term $s_q$ is $ 0$, $-1$, and $+1$ for Boltzmann, Bose-Einstein and Fermi-Dirac statistics, respectively. The flow four-velocity, $u^\nu(x)$, the chemical potential, $\mu(x)$, and the temperature, $T(x)$ distributions for axially symmetric collisions were determined from the principles of simplicity, analyticity and correspondence to hydrodynamical solutions in the limits when such solutions were known [@Csorgo:1995bi; @Csorgo:1995vf]. Recently, the Buda-Lund hydro model lead to the discovery of a number of new, exact analytic solutions of hydrodynamics, both in the relativistic [@relsol-cyl; @relsol-ell] and in the non-relativistic domain [@nr-sol; @nr-ell; @nr-inf]. The expanding matter is assumed to follow a three-dimensional, relativistic flow, characterized by transverse and longitudinal Hubble constants, u\^(x) = ( , H\_t r\_x, H\_t r\_y, H\_z r\_z ), where $\gamma$ is given by the normalization condition $u^\nu(x) u_\nu(x) = 1$. In the original form, this four-velocity distribution $u^\nu(x)$ was written as a linear transverse flow, superposed on a scaling longitudinal Bjorken flow . The strength of the transverse flow was characterized by its value $\langle u_t\rangle$ at the “geometrical" radius $R_G$, see refs. [@Csorgo:1995bi; @Chapman:1994ax; @Ster:1998hu]: u\^(x) & = & ( , , , ),\ & = & r\_t / R\_G, with $ r_t = (r_x^2 + r_y^2)^{1/2}$. Such a flow profile, with a time-dependent radius parameter $R_G$, was recently shown to be an exact solution of the equations of relativistic hydrodynamics of a perfect fluid at a vanishing speed of sound, see refs. [@Biro:1999eh; @Biro:2000nj]. The Buda-Lund hydro model characterizes the inverse temperature $1/T(x)$, and fugacity, $\exp\left[\mu(x)/T(x)\right]$ distributions of an axially symmetric, finite hydrodynamically expanding system with the mean and the variance of these distributions, in particular & = & - -[ (- y\_0)\^2 2 \^2 ]{}, \[e:mu\]\ [1 T(x)]{} & = & [1 T\_0 ]{} ( 1 + [r\_t\^2 2 R\_s\^2]{} ) ( 1 + [(- \_0)\^2 2 \_s\^2 ]{} ). Here $R_G$ and $\Delta\eta$ characterize the spatial scales of variation of the fugacity distribution, $\exp\left[\mu(x)/T(x)\right]$, that control particle densities. Hence these scales are referred to as geometrical lengths. These are distinguished from the scales on which the inverse temperature distribution changes, the temperature drops to half if $r_x = r_y = R_s$ or if $\tau = \tau_0 + \sqrt{2} \Delta\tau_s$. These parameters can be considered as second order Taylor expansion coefficients of these profile functions, restricted only by the symmetry properties of the source, and can be trivially expressed by re-scaling the earlier fit parameters. The above is the most direct form of the Buda-Lund model. However, different combinations may also be used to measure the flow, temperature and fugacity profiles [@Csorgo:1995bi; @cs-rev]: $ H_t \equiv {b}/{\tau_0} \, = \, \ave{u_t} / R_G \, = \, \ave{u_t^\prime} / R_s$ , $H_l \equiv \gamma_t /\tau_0$, where $ \gamma_t = \sqrt{ 1 + H_t^2 r_t^2}$ is evaluated at the point of maximal emittivity, and & = & = \_r = ,\ & = & = \_s = . Buda-Lund fits to Au+Au data at $\sqrt{s_{\NN}}= 200$ GeV ========================================================== In this section, we present new fit results to BRAHMS data on charged particle pseudorapidity distributions [@Bearden:2001qq], and PHENIX data on identified particle momentum distributions and Bose-Einstein (HBT) radii [@Adler:2003cb; @Adler:2004rq] in Au+Au collisions at $\sqrt{s_{\NN}}= 200$ GeV. The analysis codes and methods are identical to the ones used to fit the BRAHMS [@Bearden:2001xw], PHENIX [@Adcox:2001mf; @Adcox:2002uc], PHOBOS [@Back:2001bq], and STAR [@Adler:2001zd] data in 0- 5% most central Au+Au collisions at $\sqrt{s_{\NN}} = 130$ GeV, see ref. [@ster-ismd03]. The applied Buda-Lund 1.5 fitting package can be downloaded, together with the detailed fit results, from ref. [@Csorgo-blhome]. This calculation determines the position of the saddle point exactly in the beam direction, but in the transverse direction, the saddle point equations are solved only approximately, as summarized in ref. [@cs-rev]. The new results for $\sqrt{s_{\NN}} = 200$ GeV Au+Au collisions in the 0-30% centrality class are shown in the first column of Table 1. For comparison, we also show the results of an identical fit to $\sqrt{s_{\NN}} = 130$ GeV Au+Au collisions in the 0- 5% centrality class. ------------------------------ ------ ----------- ------- ----------- -- -- -- -- Buda-Lund v1.5 0 - 30 % 0 - 5(6) % $T_0$ \[MeV\] 200 $\pm$ 9 214 $\pm$ 7 $T_{\mbox{\rm e}}$ \[MeV\] 127 $\pm$ 13 102 $\pm$ 11 $\mu_B$ \[MeV\] 61 $\pm$ 40 77 $\pm$ 38 $R_{G}$ \[fm\] 13.2 $\pm$ 1.3 28.0 $\pm$ 5.5 $R_{s}$ \[fm\] 11.6 $\pm$ 1.0 8.6 $\pm$ 0.4 $\langle u_t^\prime \rangle$ 1.5 $\pm$ 0.1 1.0 $\pm$ 0.1 $\tau_0$ \[fm/c\] 5.7 $\pm$ 0.2 6.0 $\pm$ 0.2 $\Delta\tau$ \[fm/c\] 1.9 $\pm$ 0.5 0.3 $\pm$ 1.2 $\Delta\eta$ 3.1 $\pm$ 0.1 2.4 $\pm$ 0.1 $\chi^2/\mbox{\rm NDF}$ 132 / 208 158.2 / 180 ------------------------------ ------ ----------- ------- ----------- -- -- -- -- : The first column shows the source parameters from simultaneous fits of final BRAHMS and PHENIX data for 0 - 30 % most central $Au+Au$ collisions at $\sqrt{s_{\NN}} = 200$ GeV, as shown in Figs. 1 and 2, as obtained with the Buda-Lund hydro model, version 1.5. The errors on these parameters are still preliminary. The second column is the result of an identical analysis of BRAHMS, PHENIX, PHOBOS and STAR data for 0 - 5 % most central Au+Au collisions at $\sqrt{s_{\NN}}=130$ GeV, ref. [@ster-ismd03]. []{data-label="tab:results"} ![ \[fig:spectra\] [Solid line shows the simultaneous Buda-Lund v1.5 fit to final Au+Au data at $\sqrt{s_{\NN}} = 200$ GeV. The transverse mass distributions of identified particles are measured by PHENIX [@Adler:2003cb] the pseudorapidity distributions of charged particles are measured by BRAHMS [@Bearden:2001qq], the transverse mass dependence of the radius parameters are data of PHENIX [@Adler:2004rq]. Note that the identified particle spectra are published in more detailed centrality classes, but we recombined the 0-30% most central collisions so that the fitted spectra and radii be obtained in the same centrality class.]{} ](fig1.eps "fig:"){width="2.7in"} ![ \[fig:spectra\] [Solid line shows the simultaneous Buda-Lund v1.5 fit to final Au+Au data at $\sqrt{s_{\NN}} = 200$ GeV. The transverse mass distributions of identified particles are measured by PHENIX [@Adler:2003cb] the pseudorapidity distributions of charged particles are measured by BRAHMS [@Bearden:2001qq], the transverse mass dependence of the radius parameters are data of PHENIX [@Adler:2004rq]. Note that the identified particle spectra are published in more detailed centrality classes, but we recombined the 0-30% most central collisions so that the fitted spectra and radii be obtained in the same centrality class.]{} ](fig2.eps "fig:"){width="2.7in"} ![ \[fig:radii\] [Top row shows the transverse mass dependence of the side, out and longitudinal HBT radii, the central line shows their pairwise ratio (usually only $R_{\mbox{\rm out}}/R_{\mbox{\rm side}}$ is shown) together with the Buda-Lund fits, vers. 1.5. The bottom line shows the inverse of the squared radii. The intercept of the curves in this row is within errors zero for the two transverse components, so the fugacity is within errors independent of the transverse coordinates. However, the intercept is nonzero in the longitudinal direction, which makes the fugacity (hence particle ratios) rapidity dependent. See also ref. [@ster-ismd03] for a similar plot at $\sqrt{s_{\NN}} = 130$ GeV.]{} ](fig3.eps){width="4.3in"} Let us clarify first the meaning of the parameters shown in Table 1. The temperature at the center of the fireball at the mean freeze-out time is denoted by $T_0 \equiv T(r_x=r_y=0, \tau=\tau_0)$. The surface temperature is also a characteristic, kind of an average temperature, and its value is always $T_s \equiv T(r_x=r_y=R_s, \tau=\tau_0) = T_0/2$. In fact this relationship defines the “surface" radius $R_s$. During the particle emission, the system may cool due to evaporation and expansion, this is measured by the “post-evaporation temperature" $T_e \equiv T(r_x=r_y=0, \tau = \tau_0 + \sqrt{2} \Delta\tau)$. In the presented cases, the strength of the transverse flow is measured by $\ave{u_t^\prime}$, its value at the “surface radius" $R_s$. The “mean freeze-out time" parameter is denoted by $\tau_0$ and the “duration" of particle emission, or the width of the freeze-out time distribution is measured by $\Delta\tau$. The fugacity distribution varies on the characteristic transverse scale given by the “geometrical radius" $R_G$. Finally, the width of the space-time rapidity distribution, or the longitudinal variation scale of the fugacity distribution is measured by the parameter $\Delta\eta$. Perhaps it could be more appropriate to directly fit the transverse Hubble constant, $H_t = \ave{u_t^\prime}/R_s$ to the data, as this value is not sensitive to the length-scale chosen to evaluate the “average" transverse flow $\ave{u_t^\prime}$. In the case of parameters shown in Table 1, the density drop in the transverse direction is dominated by the cooling of the local temperature distribution in the transverse direction, and not so much by the change of the fugacity distribution. That is why we fitted here $\ave{u_t^\prime}$ at the “surface radius" $R_s$. Note also that $\tau_0$ could more properly be interpreted as the inverse of the longitudinal Hubble constant $H_l$, which is only an order of magnitude estimate of the mean freeze-out time, similarly to how the inverse of the present value of the Hubble constant in astrophysics provides only an order of magnitude estimate of the life-time of our Universe. The feasibility of directly fitting the transverse and longitudinal Hubble constants to data will be investigated in a subsequent publication. Let us also note, that we have fitted the absolute normalized spectra for identified particles, and the normalization conditions were given by central chemical potentials $\mu_0$ that were taken as free normalization parameters for each particle species. All these directly fitted parameters are made public at [@Csorgo-blhome]. From these values, we have determined the net bariochemical potential as $\mu_B = \mu_p - \mu_{\overline{p}}$. Although this parameter is not directly fitted but calculated, we have included $\mu_B$ in Table 1, so that our results could be compared with other successful models of two-particle Bose-Einstein correlations at RHIC, namely the AMPT cascade [@Lin:2002gc], Tom Humanic’s cascade [@Humanic:2002iw], the blast-wave model [@Retiere:2003qb; @Retiere:2003kf], the Hirano-Tsuda numerical hydro [@Hirano:2002hv] and the Cracow “single freeze-out thermal model"  [@Broniowski:2002wp; @Florkowski:2002wn; @Broniowski:2001we]. Now, we are ready for the discussion of the results in Table 1. In case of more central collisions at the lower RHIC energies, a well defined minimum was found, with accurate error matrix and a statistically acceptable fit quality, $\chi^2$/NDF= 158/180, that corresponds to a confidence level of 88 %. (These fit results were shown graphically on Figs. 1 and 2 of ref. [@ster-ismd03], and the parameters are summarized in the second column of Table 1.) In the case of the less central but more energetic Au+Au collisions, the obtained $\chi^2/\mbox{\rm NDF}$ fit is [*too small*]{}. Note that in these fits we added the systematic and statistical errors in quadrature, and this procedure is preliminary and has to be revisited before we can report on the final values of the fit parameters and determine their error bars. It could also be advantageous to analyze a more central data sample, or the centrality dependence of the radius parameters and the pseudorapidity distributions, or to fit additional data of STAR and PHOBOS too, so that the parameters of the Buda-Lund hydro model could be determined with smaller error bars. At present, we find that $T_0 > T_c = 172 \pm 3$ MeV [@Fodor:2001pe] by 3 $\sigma$ in case of the 0-30 % most central Au+Au data at $\sqrt{s_{\NN}} = 200$ GeV, while $T_0 > T_c$ by more than 5 $\sigma$ in case of the 0-5(6) % most central Au+Au data at $\sqrt{s_{\NN}} = 130 $ GeV. Thus this signal of a cross-over transition to quark deconfinement is not yet significant in the more energetic but less central Au+Au data sample, while it is significant at the more central, but less energetic sample. In this latter case of 130 GeV Au+Au data, $R_G$ obviously became an irrelevant parameter, with $1/R_G\approx 0.$ . This is explicitly visible in Fig. 2 of ref. [@ster-ismd03], where the last row indicates that the correlation radii are in the scaling limit and the fugacity distribution, $\exp\left[\mu(x)/T(x)\right]$ is independent of the transverse coordinates. The Buda-Lund model predicted, see eqs. (53-58) in ref. [@Csorgo:1995bi] and also eqs. (26-28) in [@nr-inf], that the linearity of the inverse radii as a function of $m_t$ can be connected to the Hubble flow and the temperature gradients. The slopes are the same for side, out and longitudinal radii if the Hubble flow (and the temperature inhomogeneities) become direction independent. The intercepts of the linearly extrapolated $m_t$ dependent inverse squared radii at $m_t=0$ determine $1/R_G^2$, or the magnitude of corrections from the finite geometrical source sizes, that stem from the $\exp[\mu(x)/T(x)]$ terms. We can see on Fig. 2, that these corrections within errors vanish also in $\sqrt{s_{\NN}} = 200$ Au+Au collisions at RHIC. This result is important, because it explains, why thermal and statistical models are successful at RHIC: if $\exp[\mu(x)/T(x)] = \exp(\mu_0/T_0)$, then this factor becomes an overall normalization factor, proportional to the particle abundances. Indeed, we found that when the finite size in the transverse direction is generated by the $T(x)$ distribution, the quality of the fit increased and we had no degenerate parameters in the fit any more. This is also the reason, why we interpret $R_s$, given by the condition that $T(r_x=r_y=R_s) = T_0/2$, as a “surface" radius: this is the scale where particle density drops. Note that we have obtained similarly good description of these data if we require that the four-velocity field is a fully developed, three-dimensional Hubble flow, with $u^\nu = x^\nu/\tau$, however, we cannot elaborate on this point here due to the space limitations [@mate-ell1]. Conclusions =========== Table 1, Figures 1 and 2 indicate that the Buda-Lund hydro model works well both at the lower and the higher RHIC energies, and gives a good quality description of the transverse mass dependence of the HBT radii. For the dynamical reason, see refs. [@nr-inf] and [@Csorgo:1995bi]. In fact, even the time evolution of the entrophy density can be solved from the fit results, $s(\tau) = s_0 (\tau_0/\tau)^3$, which is the consequence of the Hubble flow, $u^\nu = x^\nu/\tau$, a well known solution of relativistic hydrodynamics, see also ref. [@relsol-ell]. This is can be considered as the resolution of the RHIC HBT “puzzle", although a careful search of the literature indicates that this “puzzle" was only present in models that were not tuned to CERN SPS data [@Csorgo:2002ry]. We also observe that the central temperature is $T_0 = 214 \pm 7$ MeV in the most central Au+Au collisions at $\sqrt{s_{\NN}} = 130$ GeV, and we find here a net bariochemical potential of $\mu_B = 77 \pm 38$ MeV. Recent lattice QCD results indicate [@Fodor:2001pe], that the critical temperature is within errors a constant of $T_c = 172 \pm 3$ MeV in the $0 \le \mu_B \le 300$ MeV interval. Our results clearly indicate $(T,\mu_B)$ values above this critical line, which is a significant, more than 5 $\sigma$ effect. The present level of precision and the currently fitted PHENIX and BRAHMS data set does not yet allow a firm conclusion about such an effect at $\sqrt{s_{\NN}} = 200$ GeV, however, a similar behavior is seen on a 3 standard deviation level. This can be interpreted as a hint at quark deconfinement at $\sqrt{s_{\NN}} = 200$ GeV at RHIC. Finding similar parameters from the analysis of the pseudorapidity dependence of the elliptic flow, it was estimated in ref. [@mate-ell1] that 1/8th of the total volume is above the critical temperature in Au+Au collisions at $\sqrt{s_{\NN}} = 130$ GeV, at the time when pions are emitted from the source. We interpret this result as an indication for quark deconfinement and a cross-over transition in Au+Au collisions at $\sqrt{s_{\NN}} = 130 $ GeV at RHIC. This result was signaled first in ref. [@Csorgo:2002ry] in a Buda-Lund analysis of the final PHENIX and STAR data on midrapidity spectra and Bose-Einstein correlations, but only at a three standard deviation level. By including the pseudorapidity distributions of BRAHMS and PHOBOS, the $T_0 \gg T_c$ effect became significant in most central Au+Au collisions at $\sqrt{s_{\NN}} = 130 $ GeV. We are looking forward to observe, what happens with the present signal in Au+Au collisions at $\sqrt{s_{\NN}} = 200$ GeV, if we include STAR and PHOBOS data to the fitted sample. The above observation of temperatures, that are higher than the critical one, is only an indication, with other words, an indirect proof for the production of a new phase, as the critical temperature is not extracted directly from the data, but taken from recent lattice QCD calculations. More data are needed to clarify the picture of quark deconfinement at the maximal RHIC energies, for example the centrality dependence of the Bose-Einstein (HBT) radius parameters could provide very important insights. Acknowledgments {#acknowledgments .unnumbered} =============== T. Cs. and M. Cs. would like to the Organizers for their kind hospitality and for their creating an inspiring and fruitful meeting. The support of the following grants are gratefully acknowledged: OTKA T034269, T038406, the OTKA-MTA-NSF grant INT0089462, the NATO PST.CLG.980086 grant and the exchange program of the Hungarian and Polish Academy of Sciences. [99]{} M. Csanád, T. Csörgő, B. Lörstad, A. Ster, Act. Phys. Pol. B[**35**]{}, 191 (2004), nucl-th/0311102. M. Csanád, T. Csörgő and B. Lörstad, nucl-th/0310040. Z. Fodor and S. D. Katz, JHEP [**0203**]{} (2002) 014 T. Csörgő and B. Lörstad, Phys. Rev. C [**54**]{} (1996) 1390 T. Csörgő and B. Lörstad, Nucl. Phys. A [**590**]{} (1995) 465C T. Csörgő, Heavy Ion Phys.  [**15**]{} (2002) 1, hep-ph/0001233. T. Csörgő, B. Lörstad and J. Zimányi, Z. Phys. C [**71**]{} (1996) 491 T. Csörgő, F. Grassi, Y. Hama, T. Kodama, Phys. Lett. B[**565**]{}, 107 (2003) T. Csörgő, L. Csernai, Y. Hama, T. Kodama, nucl-th/0306004. T. Csörgő, nucl-th/9809011. T. Csörgő, hep-ph/0111139. T. Csörgő and J. Zimányi, Heavy Ion Phys.  [**17**]{}, 281 (2003), nucl-th/0206051. S. Chapman, P. Scotto and U. Heinz, Heavy Ion Phys.  [**1**]{} (1995) 1, hep-ph/9409349. A. Ster, T. Csörgő and J. Beier, Heavy Ion Phys.  [**10**]{} (1999) 85, hep-ph/9810341. T. S. Biró, Phys. Lett. B [**474**]{} (2000) 21 T. S. Biró, Phys. Lett. B [**487**]{} (2000) 133 S. S. Adler [*et al.*]{} \[PHENIX Collaboration\], \[arXiv:nucl-ex/0307022\]. I. G. Bearden [*et al.*]{} \[BRAHMS Collaboration\], Phys. Rev. Lett.  [**88**]{} (2002) 202301 S. S. Adler \[PHENIX Collaboration\], arXiv:nucl-ex/0401003. I. G. Bearden [*et al.*]{} \[BRAHMS Collaborations\], Phys. Lett. B [**523**]{} (2001) 227 B. B. Back [*et al.*]{} \[PHOBOS Collaboration\], Phys. Rev. Lett.  [**87**]{} (2001) 102303 K. Adcox [*et al.*]{} \[PHENIX Collaboration\], Phys. Rev. Lett.  [**88**]{} (2002) 242301 K. Adcox [*et al.*]{} \[PHENIX Collaboration\], Phys. Rev. Lett.  [**88**]{} (2002) 192302 C. Adler [*et al.*]{} \[STAR Collaboration\], Phys. Rev. Lett.  [**87**]{} (2001) 082301 Z. W. Lin, C. M. Ko and S. Pal, Phys. Rev. Lett.  [**89**]{} (2002) 152301, T. J. Humanic, Nucl. Phys. A [**715**]{} (2003) 641 F. Retiere, J. Phys. G [**30**]{} (2004) S335 F. Retiere and M. A. Lisa, arXiv:nucl-th/0312024. T. Hirano and K. Tsuda, Nucl. Phys. A [**715**]{} (2003) 821 W. Broniowski, A. Baran and W. Florkowski, AIP Conf. Proc.  [**660**]{} (2003) 185 W. Florkowski and W. Broniowski, AIP Conf. Proc.  [**660**]{} (2003) 177 W. Broniowski and W. Florkowski, Phys. Rev. Lett.  [**87**]{} (2001) 272302 T. Csörgő and A. Ster, Heavy Ion Phys.  [**17**]{} (2003) 295, nucl-th/0207016.

Georgia’s “stand your ground law” could come into play after a man shot and killed a suspected car thief who was trying to take his car from a gas station. The Atlanta Journal Constitution reports that Atlanta police are now securing murder warrants against 25-year-old Rasheem Scott, who allegedly opened fire against the car thieves. Witnesses tell WSB-TV that the man left his car running outside the gas station, when he saw a couple get in his car. The gas station owner says they watched as the man opened fire on a man who climbed into his black sedan, according to the television station. “I heard five shots, and I look back, and the girl is screaming, ‘Don’t shoot him no more,'” a witness told the television station, “She just screaming, ‘Don’t shoot him no more. Please don’t shoot him no more.'” Immediately after the incident, 25-year-old Scott walked back into the store and asked employees to call 911, WSBTV reports, he immediately turned himself into police custody. Atlanta police were securing murder warrants against him Sunday afternoon, according to The Atlanta Journal Constitution. Georgia’s stand your ground law was adopted from case law into legislation in 2006. Here is what it says: § 16-3-23.1. No duty to retreat prior to use of force in self-defense A person who uses threats or force in accordance with Code Section 16-3-21, relating to the use of force in defense of self or others, Code Section 16-3-23, relating to the use of force in defense of a habitation, or Code Section 16-3-24, relating to the use of force in defense of property other than a habitation, has no duty to retreat and has the right to stand his or her ground and use force as provided in said Code sections, including deadly force. It is not clear if the man’s case would fit into this category, but it is certainly something both prosecutors and defense will consider. [h/t and screengrab via WSB-TV] Have a tip we should know? [email protected]

Ethanol is a commonly encountered toxic substance. Methods for qualitative and quantitative determination of ethanol in body fluids, particularly human body fluids, are used in medicine and in law enforcement. In medicine, the level of ethanol in the blood is significant in diagnosing liver malfunction and alcoholism, as well as for understanding the reason for an emergency room patient being comatose. In law enforcement, such assays are used to determine whether or not an automobile operator is driving under the influence of alcohol. Ethanol testing can be accomplished using both enzymatic and nonenzymatic assays. The nonenzymatic assays have a number of disadvantages and are being widely replaced by enzymatic assays which are more accurate, highly specific, more sensitive and require less expensive procedures. Enzymatic assays are generally based on the use of alcohol dehydrogenase to catalyze the reaction of ethanol to acetaldehyde. This reaction can be used alone, or in combination with other reactions to produce a spectrophotometric signal which can be related to the amount of ethanol in the tested specimen. One enzymatic assay is based on the direct measurement of the reduced coenzyme (NADH), such as that described in U.S. Pat. No. 3,926,736 (Bucolo). This assay is carried out entirely in solution. Another enzymatic assay is described in EP-A-0464 942 (published Jan. 1, 1992) which uses nicotinamide adenine dinucleotide (NAD.sup.+) as a coenzyme with alcohol dehydrogenase to produce the reduced form of the coenzyme. The coenzyme, in turn, reacts with a tetrazolium salt to produce a detectable dye. The described assay is carried out in a multilayer analytical element containing tris(hydroxymethyl)aminomethane buffer and both crosslinked and uncrosslinked gelatin layers. One problem that has been encountered in developing a dry analytical element for the assay of ethanol is the strong interference by fluoride ion present in human serum. Fluoride ion is commonly used as a preservative in serum, and interferes in assays possibly by altering the equilibrium between ethanol and acetaldehyde, and causes the assay results to be biased positively compared to the true value of ethanol in the specimen. This problem has been effectively solved using a multilayer analytical element containing a high amount of buffer which is arranged in certain layers. Moreover, this element typically contains crosslinked gelatin as a binder for one or more of the reagent layers. Further details of such elements are found in U.S. application Ser. No. 08/005,683 (filed Jan. 19, 1993 by Detwiler) which is entitled MULTILAYER ANALYTICAL ELEMENT CONTAINING PRIMARY AMINE BUFFER AND METHOD FOR THE DETERMINATION OF ETHANOL. While the element just described can be used effectively to detect ethanol, coating its many layers requires multiple steps and causes manufacturing inefficiencies. It would be desirable to reduce the number of coating steps in preparing an element which is just as effective in the detection of ethanol, and thus provide manufacturing efficiencies needed in the highly competitive field of clinical chemistry.

Q: How to pass record id from row to Test method? I delete 1 record from table. How to pass into test method selectedMR(this record Id) and cover in test method from controller below? VF PAGE: <apex:repeat value={!mrItems} var="mrItem"> <apex:column> <apex:facet name="header">Deleting</apex:facet> <apex:commandButton value="Del" action="{!deleteMR}" reRender="form"> <apex:param name="mritemId" value="{!mrItem.id}" assignTo="{!selectedMR}"/> </apex:commandButton> </apex:column> </apex:repeat> CONTROLLER public void deleteMR() { if (selectedMR == null) { return; } TERF_MR__c tobeDeleted = null; for (TERF_MR__c mr : mrList) if (mr.Id == selectedMR) { if (mr.TERF_MR_Status__c != 'Approved') { tobeDeleted = mr; break; } else { ApexPages.addMessage(new ApexPages.Message(ApexPages.Severity.Info,'You can\'t delete approved month report')); } } if (tobeDeleted != null) { delete tobeDeleted; loadData(); } } TEST static testMethod void test1() { test.startTest(); TERF_MR__c MR = new TERF_MR__c(); Insert MR ; System.assert([SELECT Name FROM TERF_MR__c WHERE Id = :MR.Id].Name != null); PageReference testpage = new pageReference('/apex/TERF_Home'); testpage.getParameters().put('selectedMR', mr.Id); ApexPages.currentPage().getParameters().put('id', MR.id); TERF_Controller_Home contr = new TERF_Controller_Home(); contr.gotoTERF_CreateNew(); contr.deleteMR(); contr.goToSystem(); contr.save(); test.stopTest(); } A: For your test, set it directly on the controller: TERF_Controller_Home contr = new TERF_Controller_Home(); contr.selectedMR = mr.Id; ... contr.deleteMR(); Not sure, but you can probably also do it by naming the parameter to match this: <apex:param name="mritemId" value="{!mrItem.id}" assignTo="{!selectedMR}"/> i.e.: testpage.getParameters().put('mritemId', mr.Id);

A method for coronary artery calcium scoring using contrast-enhanced computed tomography. Limitations to the coronary calcium score include its requirement for noncontrast imaging and radiation exposure that approaches current methods for contrast-enhanced CT angiography. We sought to derive and validate a method of measuring the coronary artery calcium score (CACS) from standard contrast-enhanced CT, obviating the need for a second non-contrast calcium scan. The volume of intramural calcium of >320 HU in major coronary vessels was measured in 90 contrast-enhanced and traditional non-contrast calcium scan pairs. An empiric conversion factor was derived to convert the small voxel contrast-enhanced calcium volume to an Agatston calcium score. The accuracy of this technique was then prospectively validated in 120 consecutive patients undergoing clinical calcium scans and contrasted-enhanced coronary CT. Eleven patients were excluded from analysis because of the prespecified criteria of excessive noise in the contrast-enhanced CT or total coronary artery occlusion. The Pearson correlation of the contrast scan-derived calcium score with the measured CACS was r2 = 0.99. With standard CACS risk bands, agreement of the contrast-enhanced calcium score estimate with the measured CAC by quadratic weighted κ was 0.96. The 95% limits of agreement (Agatston units) were given by ±(3.2 + 0.14 × CACS + 4.44 mean square root of CACS). Inter-observer and intra-observer reliability with the intraclass correlation was 0.99. The calcium score can be accurately measured from contrast-enhanced cardiac CT scans with the use of a Hounsfield unit threshold of 320.

Q: HTML5 - Can it do this? Today? In HTML 5 is there any support for things which are really easy to do in Silverlight? For example, ripping a file (chosen by the user) into an array of bytes that can be base64 encoded and passed up to a web service? Or, creation/reading of an image and being able to manipulate the pixels and display this on screen? Or even save it to disk (location chosen by the user)? If so, which browsers would support this and are the APIs consistent? Thanks A: In HTML 5 is there any support for things which are really easy to do in Silverlight? See this For example, ripping a file (chosen by the user) into an array of bytes Yes. See this that can be base64 encoded Google and passed up to a web service? XMLHttpRequest still works. Or, creation/reading of an image and being able to manipulate the pixels and display this on screen? Yes. Combine FileReader with canvas. Or even save it to disk (location chosen by the user)? Sorry, not possible. No longer the case! See this. If so, which browsers would support this I know Firefox does, but try this on other browsers. See what works and what doesn't. and are the APIs consistent? Yes. These are called standards for a reason.