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1001.0334 | We report new observations of the 110-111 (6 cm) and 211-212 (2 cm) transitions of ortho-formaldehyde (o-H2CO) in absorption at z=0.68466 toward the gravitational lens system B0218+357. Radiative transfer modeling indicates that both transitions are anti-inverted relative to the 4.6 K cosmic microwave background (CMB), regardless of the source covering factor, with excitation temperatures of ~1 K and 1.5-2 K for the 110-111 and 211-212 lines, respectively. Using these observations and a large velocity gradient radiative transfer model that assumes a gradient of 1 km s^-1 pc^-1, we obtain a molecular hydrogen number density of 2x10^3 cm^-3 < n(H2) < 1x10^4 cm^-3 and a column density of 2.5x10^13 cm^-2 < N(o-H2CO) < 8.9x10^13 cm^-2, where the allowed ranges conservatively include the range of possible source covering factors in both lines. The measurements suggest that H2CO excitation in the absorbing clouds in the B0218+357 lens is analogous to that in Galactic molecular clouds: it would show H2CO absorption against the CMB if it were not illuminated by the background quasar or if it were viewed from another direction. | [
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1001.0335 | We propose a novel way to communicate signals in the form of waves across a d - dimensional lattice. The mechanism is based on quantum search algorithms and makes it possible to both search for marked positions in a regular grid and to communicate between two (or more) points on the lattice. Remarkably, neither the sender nor the receiver needs to know the position of each other despite the fact that the signal is only exchanged between the contributing parties. This is an example of using wave interference as a resource by controlling localisation phenomena effectively. Possible experimental realisations will be discussed. | [
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1001.0336 | A search for depletion of the combined flux of active neutrino species over a 735 km baseline is reported using neutral-current interaction data recorded by the MINOS detectors in the NuMI neutrino beam. Such a depletion is not expected according to conventional interpretations of neutrino oscillation data involving the three known neutrino flavors. A depletion would be a signature of oscillations or decay to postulated non-interacting "sterile" neutrinos, scenarios not ruled out by existing data. From an exposure of 3.18x10^{20} protons on target in which neutrinos of energies between ~500 MeV and 120 GeV are produced predominantly as nu_mu, the visible energy spectrum of candidate neutral-current reactions in the MINOS far detector is reconstructed. Comparison of this spectrum to that inferred from a similarly selected near detector sample shows that of the portion of the nu_mu flux observed to disappear in charged-current interaction data, the fraction that could be converting to a sterile state is less than 52% at 90% confidence level (C.L.). The hypothesis that active neutrinos mix with a single sterile neutrino via oscillations is tested by fitting the data to various models. In the particular four-neutrino models considered, the mixing angles theta_{24} and theta_{34} are constrained to be less than 11 degrees and 56 degrees at 90% C.L., respectively. The possibility that active neutrinos may decay to sterile neutrinos is also investigated. Pure neutrino decay without oscillations is ruled out at 5.4 standard deviations. For the scenario in which active neutrinos decay into sterile states concurrently with neutrino oscillations, a lower limit is established for the neutrino decay lifetime tau_3/m_3 > 2.1x10^{-12} s/eV at 90% C.L.. | [
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1001.0337 | Aim of this communication is to describe the first results of a work-in-progress regarding the chemical properties of gas and stars in the circumnuclear regions of nearby galaxies. Different techniques have been employed to estimate the abundances of chemical elements in the gaseous and stellar components of nuclear surroundings in different classes of galaxies according to the level of activity of the nucleus (normal or passive, star forming galaxies and AGNs). | [
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1001.0338 | Given a simplicial complex with weights on its simplices, and a nontrivial cycle on it, we are interested in finding the cycle with minimal weight which is homologous to the given one. Assuming that the homology is defined with integer coefficients, we show the following : For a finite simplicial complex $K$ of dimension greater than $p$, the boundary matrix $[\partial_{p+1}]$ is totally unimodular if and only if $H_p(L, L_0)$ is torsion-free, for all pure subcomplexes $L_0, L$ in $K$ of dimensions $p$ and $p+1$ respectively, where $L_0$ is a subset of $L$. Because of the total unimodularity of the boundary matrix, we can solve the optimization problem, which is inherently an integer programming problem, as a linear program and obtain integer solution. Thus the problem of finding optimal cycles in a given homology class can be solved in polynomial time. This result is surprising in the backdrop of a recent result which says that the problem is NP-hard under $\mathbb{Z}_2$ coefficients which, being a field, is in general easier to deal with. One consequence of our result, among others, is that one can compute in polynomial time an optimal 2-cycle in a given homology class for any finite simplicial complex embedded in $\mathbb{R}^3$. Our optimization approach can also be used for various related problems, such as finding an optimal chain homologous to a given one when these are not cycles. | [
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1001.0339 | This paper presents several novel theoretical results regarding the recovery of a low-rank matrix from just a few measurements consisting of linear combinations of the matrix entries. We show that properly constrained nuclear-norm minimization stably recovers a low-rank matrix from a constant number of noisy measurements per degree of freedom; this seems to be the first result of this nature. Further, the recovery error from noisy data is within a constant of three targets: 1) the minimax risk, 2) an oracle error that would be available if the column space of the matrix were known, and 3) a more adaptive oracle error which would be available with the knowledge of the column space corresponding to the part of the matrix that stands above the noise. Lastly, the error bounds regarding low-rank matrices are extended to provide an error bound when the matrix has full rank with decaying singular values. The analysis in this paper is based on the restricted isometry property (RIP) introduced in [6] for vectors, and in [22] for matrices. | [
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1001.0341 | The problem of motif detection can be formulated as the construction of a discriminant function to separate sequences of a specific pattern from background. In computational biology, motif detection is used to predict DNA binding sites of a transcription factor (TF), mostly based on the weight matrix (WM) model or the Gibbs free energy (FE) model. However, despite the wide applications, theoretical analysis of these two models and their predictions is still lacking. We derive asymptotic error rates of prediction procedures based on these models under different data generation assumptions. This allows a theoretical comparison between the WM-based and the FE-based predictions in terms of asymptotic efficiency. Applications of the theoretical results are demonstrated with empirical studies on ChIP-seq data and protein binding microarray data. We find that, irrespective of underlying data generation mechanisms, the FE approach shows higher or comparable predictive power relative to the WM approach when the number of observed binding sites used for constructing a discriminant decision is not too small. | [
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1001.0342 | It is shown, by considering the case of the harmonic oscillator, that quantum fluctuations may be the most significant contribution to the random walk of a single molecule. From this point, the controversy on the existence of a standard quantum limit (SQL) is addressed and settled on the experimental ground. Comparisons to the experimental data yet avalaible in the literature provide a new estimate of the reduced Planck constant yielding \hbar = (1.1 \pm 0.2) ~ 10^{-34} J.s. | [
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1001.0343 | We investigate the relationship between multipartite entanglement and symmetry, focusing on permutation symmetric states. We use the Majorana representation, where these states correspond to points on a sphere. Symmetry of the representation under rotation is equivalent to symmetry of the states under products of local unitaries. The geometric measure of entanglement is thus phrased entirely as a geometric optimisation, and a condition for the equivalence of entanglement measures written in terms of point symmetries. Finally we see that different symmetries of the states correspond to different types of entanglement with respect to SLOCC interconvertibility. | [
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1001.0344 | We study zero-temperature stability of topological phases of matter under weak time-independent perturbations. Our results apply to quantum spin Hamiltonians that can be written as a sum of geometrically local commuting projectors on a D-dimensional lattice with certain topological order conditions. Given such a Hamiltonian H_0 we prove that there exists a constant threshold \epsilon>0 such that for any perturbation V representable as a sum of short-range bounded-norm interactions the perturbed Hamiltonian H=H_0+\epsilon V has well-defined spectral bands originating from O(1) smallest eigenvalues of H_0. These bands are separated from the rest of the spectrum and from each other by a constant gap. The band originating from the smallest eigenvalue of H_0 has exponentially small width (as a function of the lattice size). Our proof exploits a discrete version of Hamiltonian flow equations, the theory of relatively bounded operators, and the Lieb-Robinson bound. | [
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1001.0345 | Atomic magnetometers have very high absolute precision and sensitivity to magnetic fields but suffer from a fundamental problem: the vectorial or tensorial interaction of light with atoms leads to "dead zones", certain orientations of magnetic field where the magnetometer loses its sensitivity. We demonstrate a simple polarization modulation scheme that simultaneously creates coherent population trapping (CPT) in orientation and alignment, thereby eliminating dead zones. Using $^{87}$Rb in a 10 Torr buffer gas cell we measure narrow, high-contrast CPT transparency peaks in all orientations and also show absence of systematic effects associated with non-linear Zeeman splitting. | [
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1001.0346 | In this paper, we quantify the benefits of employing relay station in large-coverage cognitive radio systems which opportunistically access the licensed spectrum of some small-coverage primary systems scattered inside. Through analytical study, we show that even a simple decode-and-forward (SDF) relay, which can hold only one packet, offers significant path-loss gain in terms of the spatial transmission opportunities and link reliability. However, such scheme fails to capture the spatial-temporal burstiness of the primary activities, that is, when either the source-relay (SR) link or relay-destination (RD) link is blocked by the primary activities, the cognitive spectrum access has to stop. To overcome this obstacle, we further propose buffered decode-and-forward (BDF) protocol. By exploiting the infinitely long buffer at the relay, the blockage time on either SR or RD link is saved for cognitive spectrum access. The buffer gain is shown analytically to improve the stability region and average end-to-end delay performance of the cognitive relay system. | [
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1001.0347 | To a maximal torus in a quasi-split semi-simple simply-connected group over a local field of characteristic 0, Langlands and Shelstad construct a cohomological invariant called the splitting invariant, which is an important component of their endoscopic transfer factors. We study this invariant in the case of a split real group and prove a decomposition theorem which expresses this invariant for a general torus as a product of the corresponding invariants for simple tori. We also show how this reduction formula allows for the comparison of splitting invariants between different tori in the given real group. | [
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1001.0348 | Harmonic numbers $H_k=\sum_{0<j\le k}1/j (k=0,1,2,...)$ arise naturally in many fields of mathematics. In this paper we initiate the study of congruences involving both harmonic numbers and Lucas sequences. One of our three theorems is as follows: Let u_0=0, u_1=1, and u_{n+1}=u_n-4u_{n-1} for n=1,2,3,.... Then, for any prime p>5 we have $$\sum_{k=0}^{p-1}u_{k+\delta}H_k/2^k=0 (mod p),$$ where $\delta=0$ if p=1,2,4,8 (mod 15), and $\delta=1$ otherwise. | [
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] |
1001.0349 | The Kepler Mission began its 3.5-year photometric monitoring campaign in May 2009 on a select group of approximately 150,000 stars. The stars were chosen from the ~half million in the field of view that are brighter than 16th magnitude. The selection criteria are quantitative metrics designed to optimize the scientific yield of the mission with regards to the detection of Earth-size planets in the habitable zone. This yields more than 90,000 G-type stars on or close to the Main Sequence, >20,000 of which are brighter than 14th magnitude. At the temperature extremes, the sample includes approximately 3,000 M-type dwarfs and a small sample of O and B-type MS stars <200. Small numbers of giants are included in the sample which contains ~5,000 stars with surface gravities log(g) < 3.5. We present a brief summary of the selection process and the stellar populations it yields in terms of surface gravity, effective temperature, and apparent magnitude. In addition to the primary, statistically-derived target set, several ancillary target lists were manually generated to enhance the science of the mission, examples being: known eclipsing binaries, open cluster members, and high proper-motion stars. | [
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1001.0351 | High contrast imaging can find and characterize gas giant planets around nearby young stars and the closest M stars, complementing radial velocity and astrometric searches by exploring orbital separations inaccessible to indirect methods. Ground-based coronagraphs are already probing within 25 AU of nearby young stars to find objects as small as ~ 3 Jupiter masses. This paper compares near-term and future ground-based capabilities with high contrast imaging modes of the James Webb Space Telescope (JWST). Monte Carlo modeling reveals that JWST can detect planets with masses as small as 0.2 MJup across a broad range of orbital separations. We present new calculations for planet brightness as a function of mass and age for specific JWST filters and extending to 0.1 MJup. | [
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1001.0352 | The Kepler Mission was launched on March 6, 2009 to perform a photometric survey of more than 100,000 dwarf stars to search for terrestrial-size planets with the transit technique. Follow-up observations of planetary candidates identified by detection of transit-like events are needed both for identification of astrophysical phenomena that mimic planetary transits and for characterization of the true planets and planetary systems found by Kepler. We have developed techniques and protocols for detection of false planetary transits and are currently conducting observations on 177 Kepler targets that have been selected for follow-up. A preliminary estimate indicates that between 24% and 62% of planetary candidates selected for follow-up will turn out to be true planets. | [
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1001.0353 | Pulsars are among the most mysterious astrophysical objects in the Universe and are believed to be rotating neutron stars formed in supernova explosions. They are unique testing grounds of dense matter theories and gravitational physics and also provide links among nuclear physics, particle physics and General Relativity. Neutron stars may exhibit some of the most extreme and exotic characteristics that could not be found elsewhere in the Universe. Their properties are largely determined by the equation of state (EOS) of neutron-rich matter, which is the chief ingredient in calculating neutron star structure and properties of related phenomena, such as gravitational wave emission from deformed pulsars. Presently, the EOS of neutron-rich matter is still very uncertain mainly due to the poorly known density dependence of the nuclear symmetry energy especially at supra-saturation densities. Nevertheless, significant progress has been made recently in constraining the density dependence of the nuclear symmetry energy mostly at sub-saturation densities using terrestrial nuclear reactions. While there are still some uncertainties especially at supra-saturation densities, these constraints could provide useful information on the limits of the global properties of pulsars and the gravitational waves to be expected from them. Here we review our recent work on constraining properties of pulsars and gravitational radiation with data from terrestrial nuclear laboratories. | [
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1001.0354 | In this paper we give a quantum statistical interpretation for the bracket polynomial state sum <K> and for the Jones polynomial. We use this quantum mechanical interpretation to give a new quantum algorithm for computing the Jones polynomial. This algorithm is useful for its conceptual simplicity, and it applies to all values of the polynomial variable that lie on the unit circle in the complex plane. Letting C(K) denote the Hilbert space for this model, there is a natural unitary transformation U from C(K) to itself such that <K> = <F|U|F> where |F> is a sum over basis states for C(K). The quantum algorithm arises directly from this formula via the Hadamard Test. We then show that the framework for our quantum model for the bracket polynomial is a natural setting for Khovanov homology. The Hilbert space C(K) of our model has basis in one-to-one correspondence with the enhanced states of the bracket state summmation and is isomorphic with the chain complex for Khovanov homology with coefficients in the complex numbers. We show that for the Khovanov boundary operator d defined on C(K) we have the relationship dU + Ud = 0. Consequently, the unitary operator U acts on the Khovanov homology, and we therefore obtain a direct relationship between Khovanov homology and this quantum algorithm for the Jones polynomial. The formula for the Jones polynomial as a graded Euler characteristic is now expressed in terms of the eigenvalues of U and the Euler characteristics of the eigenspaces of U in the homology. The quantum algorithm given here is inefficient, and so it remains an open problem to determine better quantum algorithms that involve both the Jones polynomial and the Khovanov homology. | [
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1001.0355 | We study the entropy of the distribution of the set R_n of vertices visited by a simple random walk on a graph with bounded degrees in its first n steps. It is shown that this quantity grows linearly in the expected size of R_n if the graph is uniformly transient, and sublinearly in the expected size if the graph is uniformly recurrent with subexponential volume growth. This in particular answers a question asked by Benjamini, Kozma, Yadin and Yehudayoff (arXiv:0903.3179v1). | [
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1001.0356 | We present 7 sequential weekly observations of NGC 5548 conducted in 2007 with the \textit{Suzaku} X-ray Imaging Spectrometer (XIS) in the 0.2-12 keV band and Hard X-ray Detector (HXD) in 10-600 keV band. The iron K$\alpha$ line is well detected in all seven observations and K$\beta$ line is also detected in four observations. In this paper, we investigate the origin of the Fe K lines using both the width of the line and the reverberation mapping method. With the co-added XIS and HXD spectra, we identify Fe K$\alpha$ and K$\beta$ line at 6.396$_{-0.007}^{+0.009}$ keV and 7.08$_{-0.05}^{+0.05}$ keV, respectively. The width of line obtained from the co-added spectra is 38$_{-18}^{+16}$ eV ($\textrm{FWHM}=4200_{-2000}^{+1800}$ km/s) which corresponds to a radius of 20$_{-10}^{+50}$ light days, for the virial production of $1.220\times10^7$ M$_{\odot}$ in NCG 5548. To quantitatively investigate the origin of the narrow Fe line by the reverberation mapping method, we compare the observed light curves of Fe K$\alpha$ line with the predicted ones, which are obtained by convolving the continuum light curve with the transfer functions in a thin shell and an inclined disk. The best-fit result is given by the disk case with $i=30^\circ$ which is better than a fit to a constant flux of the Fe K line at the 92.7% level (F-test). We find that the emitting radius obtained from the light curve is 25-37 light days, which is consistent with the radius derived from the Fe K line width. Combining the results of the line width and variation, the most likely site for the origin of the narrow iron lines is 20-40 light days away from the central engine, though other possibilities are not completely ruled out. (abridged) | [
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1001.0357 | For a two-user Gaussian multiple access channel (GMAC), frequency division multiple access (FDMA), a well known orthogonal-multiple-access (O-MA) scheme has been preferred to non-orthogonal-multiple-access (NO-MA) schemes since FDMA can achieve the sum-capacity of the channel with only single-user decoding complexity [\emph{Chapter 14, Elements of Information Theory by Cover and Thomas}]. However, with finite alphabets, in this paper, we show that NO-MA is better than O-MA for a two-user GMAC. We plot the constellation constrained (CC) capacity regions of a two-user GMAC with FDMA and time division multiple access (TDMA) and compare them with the CC capacity regions with trellis coded multiple access (TCMA), a recently introduced NO-MA scheme. Unlike the Gaussian alphabets case, it is shown that the CC capacity region with FDMA is strictly contained inside the CC capacity region with TCMA. In particular, for a given bandwidth, the gap between the CC capacity regions with TCMA and FDMA is shown to increase with the increase in the average power constraint. Also, for a given power constraint, the gap between the CC capacity regions with TCMA and FDMA is shown to decrease with the increase in the bandwidth. Hence, for finite alphabets, a NO-MA scheme such as TCMA is better than the well known O-MAC schemes, FDMA and TDMA which makes NO-MA schemes worth pursuing in practice for a two-user GMAC. | [
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1001.0358 | Rank invariants are a parametrized version of Betti numbers of a space multi-filtered by a continuous vector-valued function. In this note we give a sufficient condition for their finiteness. This condition is sharp for spaces embeddable in R^n. | [
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1001.0359 | Circular null geodesic orbits, in extremal Reissner-Nordstrom spacetimes, are examined with regard to their stability, and compared with similar orbits in the near-extremal situation. Extremization of the effective potential for null circular orbits shows the existence of a stable circular geodesic in the extremal spacetime, precisely {\it on} the event horizon, which coincides with its null geodesic generator. Such an orbit also emerges as a global minimum of the effective potential for circular {\it timelike} orbits. This type of geodesic is of course absent in the corresponding near-extremal spacetime, as we show here, testifying to differences between the extremal limit of a generic RN spacetime and the exactly extremal geometry. | [
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1001.0361 | Articles whose authors make them Open Access (OA) by self-archiving them online are cited significantly more than articles accessible only to subscribers. Some have suggested that this "OA Advantage" may not be causal but just a self-selection bias, because authors preferentially make higher-quality articles OA. To test this we compared self-selective self-archiving with mandatory self-archiving for a sample of 27,197 articles published 2002-2006 in 1,984 journals. The OA Advantage proved just as high for both. Logistic regression showed that the advantage is independent of other correlates of citations (article age; journal impact factor; number of co-authors, references or pages; field; article type; or country) and greatest for the most highly cited articles. The OA Advantage is real, independent and causal, but skewed. Its size is indeed correlated with quality, just as citations themselves are (the top 20% of articles receive about 80% of all citations). The advantage is greater for the more citeable articles, not because of a quality bias from authors self-selecting what to make OA, but because of a quality advantage, from users self-selecting what to use and cite, freed by OA from the constraints of selective accessibility to subscribers only. | [
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1001.0362 | An interaction of a photon with $^3H$ is invstigated based on a three dimensional Faddeev approach. In this approach the three-nucleon Faddeev equations with two-nucleon interactions are formulated with consideration of the magnitude of the vector Jacobi momenta and the angle between them with the inclusion of the spin-isospin quantum numbers, without employing a partial wave decomposition. In this formulation the two body t-matrices and triton wave function are calculated in the three dimensional approach using AV18 potential. In the first step we use the standard single nucleon current in this article. | [
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1001.0363 | A self consistant and manifestly covariant theory for the dynamics of four charges (masses) (namely electric, magnetic, gravitational, Heavisidian) has been developed in simple, compact and consistent manner. Starting with an invariant Lagrangian density and its quaternionic representation, we have obtained the consistent field equation for the dynamics of four charges. It has been shown that the present reformulation reproduces the dynamics of individual charges (masses) in the absence of other charge (masses) as well as the generalized theory of dyons (gravito - dyons) in the absence gravito - dyons (dyons). key words: dyons, gravito - dyons, quaternion PACS NO: 14.80Hv | [
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] |
1001.0364 | The temperature dependence of the lifetime of the thermally isolated metastable N8 cubane up to its decay into N2 molecules has been calculated by the molecular dynamics method. It has been demonstrated that this dependence significantly deviates from the Arrhenius law. The applicability of the finite heat bath theory to the description of thermally isolated atomic clusters has been proved using statistical analysis of the results obtained. | [
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1001.0365 | We use the screened Coulomb potential with $r$-dependent coupling constant and the non--perturbative quark--antiquark potential derived within Field Correlator Method (FCM) to calculate $J/\psi$ and $\Upsilon$ binding energies and melting temperatures in the deconfined phase of quark-gluon plasma. | [
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1001.0366 | A new understanding of the notion of the stable solution to ill-posed problems is proposed. The new notion is more realistic than the old one and better fits the practical computational needs. A method for constructing stable solutions in the new sense is proposed and justified. The basic point is: in the traditional definition of the stable solution to an ill-posed problem $Au=f$, where $A$ is a linear or nonlinear operator in a Hilbert space $H$, it is assumed that the noisy data $\{f_\delta, \delta\}$ are given, $||f-f_\delta||\leq \delta$, and a stable solution $u_\d:=R_\d f_\d$ is defined by the relation $\lim_{\d\to 0}||R_\d f_\d-y||=0$, where $y$ solves the equation $Au=f$, i.e., $Ay=f$. In this definition $y$ and $f$ are unknown. Any $f\in B(f_\d,\d)$ can be the exact data, where $B(f_\d,\d):=\{f: ||f-f_\delta||\leq \delta\}$.The new notion of the stable solution excludes the unknown $y$ and $f$ from the definition of the solution. | [
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1001.0367 | Let $G(k)=\int_0^1g(x)e^{kx}dx$, $g\in L^1(0,1)$. The main result of this paper is the following theorem. {\bf Theorem}. {\it If $\limsup_{k\to +\infty}|G(k)|<\infty$, then $g=0$. There exists $g\not\equiv 0$, $g\in L^1(0,1)$, such that $G(k_j)=0$, $k_j<k_{j+1}$, $\lim_{j\to \infty}k_j=\infty$, $\lim_{k\to \infty}|G(k)|$ does not exist, $\limsup_{k\to +\infty}|G(k)|=\infty$. This $g$ oscillates infinitely often in any interval $[1-\delta, 1]$, however small $\delta>0$ is.} | [
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1001.0368 | Let $F(u)=h$ be an operator equation in a Banach space $X$, $\|F'(u)-F'(v)\|\leq \omega(\|u-v\|)$, where $\omega\in C([0,\infty))$, $\omega(0)=0$, $\omega(r)>0$ if $r>0$, $\omega(r)$ is strictly growing on $[0,\infty)$. Denote $A(u):=F'(u)$, where $F'(u)$ is the Fr\'{e}chet derivative of $F$, and $A_a:=A+aI.$ Assume that (*) $\|A^{-1}_a(u)\|\leq \frac{c_1}{|a|^b}$, $|a|>0$, $b>0$, $a\in L$. Here $a$ may be a complex number, and $L$ is a smooth path on the complex $a$-plane, joining the origin and some point on the complex $a-$plane, $0<|a|<\epsilon_0$, where $\epsilon_0>0$ is a small fixed number, such that for any $a\in L$ estimate (*) holds. It is proved that the DSM (Dynamical Systems Method) \bee \dot{u}(t)=-A^{-1}_{a(t)}(u(t))[F(u(t))+a(t)u(t)-f],\quad u(0)=u_0,\ \dot{u}=\frac{d u}{dt}, \eee converges to $y$ as $t\to +\infty$, where $a(t)\in L,$ $F(y)=f$, $r(t):=|a(t)|$, and $r(t)=c_4(t+c_2)^{-c_3}$, where $c_j>0$ are some suitably chosen constants, $j=2,3,4.$ Existence of a solution $y$ to the equation $F(u)=f$ is assumed. It is also assumed that the equation $F(w_a)+aw_a-f=0$ is uniquely solvable for any $f\in X$, $a\in L$, and $\lim_{|a|\to 0,a\in L}\|w_a-y\|=0.$ | [
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] |
1001.0369 | We investigate the interplay of quark and meson degrees of freedom in a physical state representing a near-threshold resonance for the case of a single continuum channel. We demonstrate that such a near-threshold resonance may possess quite peculiar properties if both quark and meson dynamics generate weakly coupled near-threshold poles in the S-matrix. In particular, the scattering t-matrix may possess zeros in this case. We also discuss possible implications for production reactions as well as studies within lattice QCD. | [
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1001.0371 | We derive a new acoustic black hole metric from the Abelian Higgs model. In the non-relativistic limit, while the Abelian Higgs model becomes the Ginzburg-Landau model, the metric reduces to an ordinary Unruh type. We investigate the possibility of using (type I and II) superconductors as the acoustic black holes. We propose to realize experimental acoustic black holes by using spiral vortices solutions from the Navier-stokes equation in the non-relativistic classical fluids. | [
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1001.0372 | In the paper we obtain equations for large-scale fluctuations of the mean field (the field of magnetization and quadrupole moments) in a magnetic system realized by a square (cubic) lattice of atoms with spin s >= 1 at each site. We use the generalized Heisenberg Hamiltonian with biquadratic exchange as a quantum model. A quantum thermodynamical averaging gives classical effective models, which are interpreted as Hamiltonian systems on coadjoint orbits of Lie group SU(3). | [
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] |
1001.0373 | We study ordered states and topological excitations in a quasi-two-dimensional magnet, modeled by a square lattice with spins $s {=} 1$ at all sites, and the Hamiltonian with biquadratic exchange interaction between nearest neighbor sites. We propose two effective Hamiltonians for description of large-scale excitations in the two-dimensional case. They describe excitations of the mean field in a nematic phase and a mixed ferromagnetic-nematic phase. It is shown that the effective Hamiltonians are minimized on configurations with fixed topological charge. These topological excitations can arise at low temperatures and cause a destruction of a long-range order in the two-dimensional system. | [
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1001.0374 | Using data collected with the ISTRA+ spectrometer at U70 proton synchrotron of IHEP, we report the first measurement of the destructive interference in the radiative kaon cecay K- -->mu-nugamma. We find the difference of the vector and axial form factors Fv-Fa=0.126+/-0.027+/-0.043. The measured value is two standard deviations above the O(p**4) ChPT prediction equal to 0.055. Inclusion of exotic tensor interaction gives Fv-Fa=0.144+/-0.044+/-0.035 and Ft=-0.0079+/-0.0113+/-0.0073, i.e. -0.03<Ft<0.01 at 90% CL,consistent both with zero and with recent theoretical prediction equal to |Ft|=0.022. | [
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1001.0375 | We construct a class of topological excitations of a mean field in a two-dimensional spin system represented by a quantum Heisenberg model with high powers of exchange interaction. The quantum model is associated with a classical one (the continuous classical analogue) that is based on a Landau-Lifshitz like equation, and describes large-scale fluctuations of the mean field. On the other hand, the classical model is a Hamiltonian system on a coadjoint orbit of the unitary group SU($2s {+} 1$) in the case of spin $s$. We have found a class of mean field configurations that can be interpreted as topological excitations, because they have fixed topological charges. Such excitations change their shapes and grow preserving an energy. | [
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1001.0376 | We propose a general scheme for separation of variables in the integrable Hamiltonian systems on orbits of the loop algebra $\mathfrak{sl}(2,\Complex)\times \mathcal{P}(\lambda,\lambda^{-1})$. In particular, we illustrate the scheme by application to modified Korteweg--de Vries (MKdV), sin(sinh)-Gordon, nonlinear Schr\"odinger, and Heisenberg magnetic equations. | [
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1001.0377 | The Jacobian elliptic functions are generalized and applied to a nonlinear eigenvalue problem with $p$-Laplacian. The eigenvalue and the corresponding eigenfunction are represented in terms of common parameters, and a complete description of the spectra and a closed form representation of the corresponding eigenfunctions are obtained. As a by-product of the representation, it turns out that a kind of solution is also a solution of another eigenvalue problem with $p/2$-Laplacian. | [
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1001.0378 | $L^{\infty}$ estimates in the integrability by compensation result of H. Wente fail in dimension larger than two when Sobolev spaces are replaced by the ad-hoc Morrey spaces. However, in this paper we prove that $L^{\infty}$ estimates hold in arbitrary dimension when Morrey spaces are replaced by their Littlewood Paley counterparts: Besov-Morrey spaces. As an application we prove the existence of conservation laws to solution of elliptic systems of the form $-\Delta u= \Omega \cdot \nabla u$ where $\Omega$ is antisymmetric and both $\nabla u$ and $\Omega$ belong to these Besov-Morrey spaces for which the system is critical. | [
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1001.0379 | The paper gives the complete characterization of all graded nilpotent Lie algebras with infinite-dimensional Tanaka prolongation as extensions of graded nilpotent Lie algebras of lower dimension by means of a commutative ideal. We introduce a notion of weak characteristics of a vector distribution and prove that if a bracket-generating distribution of constant type does not have non-zero complex weak characteristics, then its symmetry algebra is necessarily finite-dimensional. The paper also contains a number of illustrative algebraic and geometric examples including the proof that any metabelian Lie algebra with a 2-dimensional center always has an infinite-dimensional Tanaka prolongation. | [
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1001.0381 | Exact wormhole solutions, while eagerly sought after, often have the appearance of being overly specialized or highly artificial. A case for the possible existence of traversable wormholes would be more compelling if an abundance of solutions could be found. It is shown in this note that for many of the wormhole geometries in the literature, the exact solutions obtained imply the existence of large sets of additional solutions. | [
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1001.0382 | The radiative viscosity of superfluid $npe$ matter is studied, and it is found that to the lowest order of $\delta \mu/T$ the ratio of radiative viscosity to bulk viscosity is the same as that of the normal matter. | [
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1001.0383 | The Graph Isomorphism problem restricted to graphs of bounded treewidth or bounded tree distance width are known to be solvable in polynomial time [Bod90],[YBFT99]. We give restricted space algorithms for these problems proving the following results: - Isomorphism for bounded tree distance width graphs is in L and thus complete for the class. We also show that for this kind of graphs a canon can be computed within logspace. - For bounded treewidth graphs, when both input graphs are given together with a tree decomposition, the problem of whether there is an isomorphism which respects the decompositions (i.e. considering only isomorphisms mapping bags in one decomposition blockwise onto bags in the other decomposition) is in L. - For bounded treewidth graphs, when one of the input graphs is given with a tree decomposition the isomorphism problem is in LogCFL. - As a corollary the isomorphism problem for bounded treewidth graphs is in LogCFL. This improves the known TC1 upper bound for the problem given by Grohe and Verbitsky [GroVer06]. | [
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1001.0384 | The present paper is a review of the current state of Graph-Link Theory (graph-links are also closely related to homotopy classes of looped interlacement graphs), dealing with a generalisation of knots obtained by translating the Reidemeister moves for links into the language of intersection graphs of chord diagrams. In this paper we show how some methods of classical and virtual knot theory can be translated into the language of abstract graphs, and some theorems can be reproved and generalised to this graphical setting. We construct various invariants, prove certain minimality theorems and construct functorial mappings for graph-knots and graph-links. In this paper, we first show non-equivalence of some graph-links to virtual links. | [
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1001.0385 | This article extends the previous paper in "M.W. Yuen, \textit{Stabilities for Euler-Poisson Equations in Some Special Dimensions}, J. Math. Anal. Appl. \textbf{344} (2008), no. 1, 145--156.", from the Euler-Poisson equations for attractive forces to the repulsive ones in $R^{N}$ $(N\geq2)$. The similar stabilities of the system are studied. Additionally, we explain that it is impossible to have the density collapsing solutions with compact support to the system with repulsive forces for $\gamma>1$. | [
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1001.0386 | We regularized the 3D Navier-Stokes equations by adding a fourth-order viscosity term. We study the upper semicontinuity, of the global attractors of the Leray-Hopf weak solutions of the regularized 3D Navier-Stokes equations, as the artificial dissipation goes to 0. We also consider applications of obtained results to the regularized problem by allowing the family of forcing functions to vary with epsilon, for epsilon >0. | [
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1001.0387 | We prove that the basic intersection cohomology $ {I H}^{^{*}}_{_{\bar{p}}}{(M/\mathcal{F})}, $ where $\mathcal{F}$ is the singular foliation determined by an isometric action of a Lie group $G$ on the compact manifold $M$, is finite dimensional. | [
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1001.0388 | We construct a Gysin sequence associated to any smooth ${\mathbb S}^3$-action on a smooth manifold. | [
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1001.0389 | The total tau hadronic width can be accurately calculated using analyticity and the operator product expansion. The result turns out to be very sensitive to the value of alpha_s(m_tau^2), providing a precise determination of the strong coupling constant. The theoretical description of this observable is updated, including the recently computed O(alpha_s^4) contributions. The experimental determination of alpha_s(m_tau^2) and its actual uncertainties are discussed. | [
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1001.0391 | The micromagnetic distribution in a dielectric nanoparticle is theoretically considered. It is shown that the existence of inhomogeneous magnetoelectric interaction in magnetic dielectrics provides the possibility to stabilize the vortex and antivortex state. The estimation of the critical voltage necessary for vortex/antivortex nucleation in bismuth ferrite and iron garnet nanoparticles yields a value of +/-150 V. This system can be considered as electrically switchable two state-logic magnetic element. | [
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1001.0392 | Ten days of commissioning data (Quarter 0) and thirty-three days of science data (Quarter 1) yield instrumental flux timeseries of ~150,000 stars that were combed for transit events, termed Threshold Crossing Events (TCE), each having a total detection statistic above 7.1-sigma. TCE light curves are modeled as star+planet systems. Those returning a companion radius smaller than 2R_J are assigned a KOI (Kepler Object of Interest) number. The raw flux, pixel flux, and flux-weighted centroids of every KOI are scrutinized to assess the likelihood of being an astrophysical false-positive versus the likelihood of a being a planetary companion. This vetting using Kepler data is referred to as data validation. Herein, we describe the data validation metrics and graphics used to identify viable planet candidates amongst the KOIs. Light curve modeling tests for a) the difference in depth of the odd- versus even-numbered transits, b) evidence of ellipsoidal variations, and c) evidence of a secondary eclipse event at phase=0.5. Flux-weighted centroids are used to test for signals correlated with transit events with a magnitude and direction indicative of a background eclipsing binary. Centroid timeseries are complimented by analysis of images taken in-transit versus out-of-transit, the difference often revealing the pixel contributing the most to the flux change during transit. Examples are shown to illustrate each test. Candidates passing data validation are submitted to ground-based observers for further false-positive elimination or confirmation/characterization. | [
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1001.0393 | Identical products being sold at different prices in different locations is a common phenomenon. Price differences might occur due to various reasons such as shipping costs, trade restrictions and price discrimination. To model such scenarios, we supplement the classical Fisher model of a market by introducing {\em transaction costs}. For every buyer $i$ and every good $j$, there is a transaction cost of $\cij$; if the price of good $j$ is $p_j$, then the cost to the buyer $i$ {\em per unit} of $j$ is $p_j + \cij$. This allows the same good to be sold at different (effective) prices to different buyers. We provide a combinatorial algorithm that computes $\epsilon$-approximate equilibrium prices and allocations in $O\left(\frac{1}{\epsilon}(n+\log{m})mn\log(B/\epsilon)\right)$ operations - where $m$ is the number goods, $n$ is the number of buyers and $B$ is the sum of the budgets of all the buyers. | [
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1001.0394 | We describe brane configurations that interpolate between the N=6 AdS4xCP3 background of Type IIA supergravity and the N=0 AdS4xCP3 background of massive Type IIA supergravity. Using the T-dual Type IIB configurations we prove that this leads to unequal Chern-Simons levels in the dual gauge theory, and find the precise relation between the parameters of the gauge theory and the RR fluxes of the background. This provides further evidence for the conjecture of Gaiotto and Tomasiello about the CFT dual of the massive Type IIA background. | [
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] |
1001.0395 | We compute the finite temperature density response function of nonrelativistic cold fermions with an isotropic condensate. The pair-breaking contribution to the response function is evaluated in the limit of small three-momentum transfers q within an effective theory which exploits series expansion in powers of small q/p_F, where p_F is the Fermi momentum. The leading order O(q^2) contribution is universal and depends only on two fundamental scales, the Fermi energy and the pairing gap. The particle-hole Landau Fermi-liquid interaction contributes first at the next-to-leading-order O(q^4). The scattering contribution to the polarization tensor is nonperturbative (in the above sense) and is evaluated numerically. The spectral functions of density fluctuations are constructed and the relevance of the q^2 scaling for the pair-breaking neutrino emission from neutron stars is discussed. | [
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1001.0396 | At present there are two vastly different ab initio approaches to the description of the the many-body dynamics: the Density Functional Theory (DFT) and the functional integral (path integral) approaches. On one hand, if implemented exactly, the DFT approach can allow in principle the exact evaluation of arbitrary one-body observable. However, when applied to Large Amplitude Collective Motion (LACM) this approach needs to be extended in order to accommodate the phenomenon of surface-hoping, when adiabaticity is strongly violated and the description of a system using a single (generalized) Slater determinant is not valid anymore. The functional integral approach on the other hand does not appear to have such restrictions, but its implementation does not appear to be straightforward endeavor. However, within a functional integral approach one seems to be able to evaluate in principle any kind of observables, such as the fragment mass and energy distributions in nuclear fission. These two radically approaches can likely be brought brought together by formulating a stochastic time-dependent DFT approach to many-body dynamics. | [
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1001.0397 | We analyze the decoherence induced on a single qubit by the interaction with a two-level boson system with critical internal dynamics. We explore how the decoherence process is affected by the presence of quantum phase transitions in the environment. We conclude that the dynamics of the qubit changes dramatically when the environment passes through a continuous excited state quantum phase transition. If the system-environment coupling energy equals the energy at which the environment has a critical behavior, the decoherence induced on the qubit is maximal and the fidelity tends to zero with finite size scaling obeying a power-law. | [
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1001.0398 | The decoherence induced on a single qubit by its interaction with the environment is studied. The environment is modelled as a scalar two-level boson system that can go through either first order or continuous excited state quantum phase transitions, depending on the values of the control parameters. A mean field method based on the Tamm-Damkoff approximation is worked out in order to understand the observed behaviour of the decoherence. Only the continuous excited state phase transition produces a noticeable effect in the decoherence of the qubit. This is maximal when the system-environment coupling brings the environment to the critical point for the continuous phase transition. In this situation, the decoherence factor (or the fidelity) goes to zero with a finite size scaling power law. | [
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1001.0399 | Oscillating stars in binary systems are among the most interesting stellar laboratories, as these can provide information on the stellar parameters and stellar internal structures. Here we present a red giant with solar-like oscillations in an eclipsing binary observed with the NASA Kepler satellite. We compute stellar parameters of the red giant from spectra and the asteroseismic mass and radius from the oscillations. Although only one eclipse has been observed so far, we can already determine that the secondary is a main-sequence F star in an eccentric orbit with a semi-major axis larger than 0.5 AU and orbital period longer than 75 days. | [
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1001.0401 | This article deals with the numerical resolution of Markovian backward stochastic differential equations (BSDEs) with drivers of quadratic growth with respect to $z$ and bounded terminal conditions. We first show some bound estimates on the process $Z$ and we specify the Zhang's path regularity theorem. Then we give a new time discretization scheme with a non uniform time net for such BSDEs and we obtain an explicit convergence rate for this scheme. | [
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1001.0402 | We present a new algorithm to compute the classical modular polynomial Phi_n in the rings Z[X,Y] and (Z/mZ)[X,Y], for a prime n and any positive integer m. Our approach uses the graph of n-isogenies to efficiently compute Phi_n mod p for many primes p of a suitable form, and then applies the Chinese Remainder Theorem (CRT). Under the Generalized Riemann Hypothesis (GRH), we achieve an expected running time of O(n^3 (log n)^3 log log n), and compute Phi_n mod m using O(n^2 (log n)^2 + n^2 log m) space. We have used the new algorithm to compute Phi_n with n over 5000, and Phi_n mod m with n over 20000. We also consider several modular functions g for which Phi_n^g is smaller than Phi_n, allowing us to handle n over 60000. | [
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1001.0403 | We report on the discovery of a new extremely short period transiting extrasolar planet, WASP-19b. The planet has mass Mpl = 1.15 \pm 0.08 MJ, radius Rpl = 1.31 \pm 0.06 RJ, and orbital period P = 0.7888399 \pm 0.0000008 days. Through spectroscopic analysis, we determine the host star to be a slightly super-solar metallicity ([M/H] = 0.1 \pm 0.1 dex) G-dwarf with Teff = 5500 \pm 100 K. In addition, we detect periodic, sinusoidal flux variations in the light curve which are used to derive a rotation period for the star of Prot = 10.5 \pm 0.2 days. The relatively short stellar rotation period suggests that either WASP-19 is somewhat young (~ 600 Myr old) or tidal interactions between the two bodies have caused the planet to spiral inward over its lifetime resulting in the spin-up of the star. Due to the detection of the rotation period, this system has the potential to place strong constraints on the stellar tidal quality factor, Q's, if a more precise age is determined. | [
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1001.0404 | Extending previous results of Oh--Zumbrun and Johnson--Zumbrun, we show that spectral stability implies linearized and nonlinear stability of spatially periodic traveling-wave solutions of viscous systems of conservation laws for systems of generic type, removing a restrictive assumption that wave speed be constant to first order along the manifold of nearby periodic solutions. | [
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1001.0405 | In this paper we consider the problem of reconstructing a hidden weighted hypergraph of constant rank using additive queries. We prove the following: Let $G$ be a weighted hidden hypergraph of constant rank with n vertices and $m$ hyperedges. For any $m$ there exists a non-adaptive algorithm that finds the edges of the graph and their weights using $$ O(\frac{m\log n}{\log m}) $$ additive queries. This solves the open problem in [S. Choi, J. H. Kim. Optimal Query Complexity Bounds for Finding Graphs. {\em STOC}, 749--758,~2008]. When the weights of the hypergraph are integers that are less than $O(poly(n^d/m))$ where $d$ is the rank of the hypergraph (and therefore for unweighted hypergraphs) there exists a non-adaptive algorithm that finds the edges of the graph and their weights using $$ O(\frac{m\log \frac{n^d}{m}}{\log m}). $$ additive queries. Using the information theoretic bound the above query complexities are tight. | [
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1001.0406 | Rigorous quantum electrodynamical calculation is presented for energy levels of the 1^1S, 2^1S, 2^3S, 2^1P_1, and 2^3P_{0,1,2} states of helium-like ions with the nuclear charge Z=3...12. The calculational approach accounts for all relativistic, quantum electrodynamical, and recoil effects up to orders m\alpha^6 and m^2/M\alpha^5, thus advancing the previously reported theory of light helium-like ions by one order in \alpha. | [
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1001.0407 | We construct a kinetic equation simulating the behavior of degenerate quantum Bose gases with the collision rate proportional to the molecule velocity. We obtain an analytic solution of the half--space boundary--value Smoluchowski problem of the temperature jump at the interface between the degenerate Bose gas and the condensed phase. | [
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1001.0408 | We have carried out calculations of current-voltage characteristics for the electron tunnel current through a junction with a thin insulating ferroelectric barrier assuming that interface transmissions for the left and right interfaces noticeably differ due to dissimilarity of the interfaces. Obtained conductance versus voltage and current versus voltage curves exhibit well distinguishable asymmetric hysteresis. We show that the asymmetry in the hysteretic effects could originate from the asymmetric bias voltage profile inside the junction. In particular, we analyze the hysteresis asymmetries occurring when the bias voltage distribution is low sensitive to the spontaneous polarization reversal. | [
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] |
1001.0409 | C. F. Gauss discovered a beautiful formula for the number of irreducible polynomials of a given degree over a finite field. Assuming just a few elementary facts in field theory and the exclusion-inclusion formula, we show how one see the shape of this formula and its proof instantly. | [
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1001.0411 | Due to quantum fluctuations, probed at small scales, spacetime is very complicated -- something akin in complexity to a turbulent froth which the late John Wheeler dubbed quantum foam, aka spacetime foam. Our recent work suggests that (1) we may be close to being able to detect quantum foam with extragalactic sources once the Very Large Telescope Interferometers (VLTI) are fully operational; (2) dark energy is arguably a cosmological manifestation of quantum foam, the constituents of which obey infinite statistics; (3) in the gravitational context, turbulence is closely related to holographic quantum foam, partly validating Wheeler's picture of a turbulent spacetime. | [
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] |
1001.0412 | The identification of individual stars in crowded environments using photometric information alone is confounded by source confusion. However, with the addition of spectroscopic information it is possible to distinguish between blends and areas where the light is dominated by a single star using the widths of absorption features. We describe a procedure for identifying locations in kinematically hot environments where the light is dominated by a single star, and apply this method to spectra with 0.1 arcsec angular resolution covering the 2.1 - 2.3 micron interval in the central regions of M32. Targets for detailed investigation are selected as areas of localized brightness enhancement. Three locations where at least 60% of the K-band light comes from a single bright star, and another with light that is dominated by two stars with very different velocities, are identified. The dominant stars are evolving near the tip of the asymptotic giant branch (AGB), and have M5 III spectral type. The lack of a dispersion in spectral-type suggests that the upper AGB within the central arcsec of M32 has a dispersion in J-K of only a few hundreths of a magnitude, in agreement with what is seen at larger radii. One star has weaker atomic absorption lines than the others, such that [M/H] is 0.2 dex lower. Such a difference in metallicity is consistent with the metallicity dispersion inferred from the width of the AGB in M32. The use of line width to distinguish between blends involving many relatively faint stars, none of which dominate the light output, and areas that are dominated by a single intrinsically bright star could be extended to crowded environments in other nearby galaxies. | [
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1001.0413 | We present an analysis of the early Kepler observations of the previously discovered transiting planet HAT-P-7b. The light curve shows the transit of the star, the occultation of the planet, and the orbit phase-dependent light from the planet. In addition, phase-dependent light from the star is present, known as "ellipsoidal variations". The very nearby planet (only 4 stellar radii away) gravitationally distorts the star and results in a flux modulation twice per orbit. The ellipsoidal variations can confuse interpretation of the planetary phase curve if not self-consistently included in the modeling. We fit the light curve using the Roche potential approximation and derive improved planet and orbit parameters. | [
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1001.0414 | The Kepler mission provides an exciting opportunity to study the lightcurves of stars with unprecedented precision and continuity of coverage. This is the first look at a large sample of stars with photometric data of a quality that has heretofore been only available for our Sun. It provides the first opportunity to compare the irradiance variations of our Sun to a large cohort of stars ranging from vary similar to rather different stellar properties, at a wide variety of ages. Although Kepler data is in an early phase of maturity, and we only analyze the first month of coverage, it is sufficient to garner the first meaningful measurements of our Sun's variability in the context of a large cohort of main sequence stars in the solar neighborhood. We find that nearly half of the full sample is more active than the active Sun, although most of them are not more than twice as active. The active fraction is closer to a third for the stars most similar to the Sun, and rises to well more than half for stars cooler than mid K spectral types. | [
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1001.0415 | An important question arising from the Frobenius Coin Problem is to decide whether or not a given monetary sum S can be obtained from N coin denominations. We develop a new Generating Function G(x), where the coefficient of x^i is equal to the number of ways in which coins from the given denominations can be arranged as a stack whose total monetary worth is i. We show that the Recurrence Relation for obtaining G(x), is linear, enabling G(x) to be expressed as a rational function, that is, G(x) = P(x)/Q(x), where both P(x) and Q(x) are Polynomials whose degrees are bounded by the largest coin denomination. | [
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1001.0416 | We report the discovery and the Rossiter-McLaughlin effect of Kepler-8b, a transiting planet identified by the NASA Kepler Mission. Kepler photometry and Keck-HIRES radial velocities yield the radius and mass of the planet around this F8IV subgiant host star. The planet has a radius RP = 1.419 RJ and a mass, MP = 0.60 MJ, yielding a density of 0.26 g cm^-3, among the lowest density planets known. The orbital period is P = 3.523 days and orbital semima jor axis is 0.0483+0.0006/-0.0012 AU. The star has a large rotational v sin i of 10.5 +/- 0.7 km s^-1 and is relatively faint (V = 13.89 mag), both properties deleterious to precise Doppler measurements. The velocities are indeed noisy, with scatter of 30 m s^-1, but exhibit a period and phase consistent with the planet implied by the photometry. We securely detect the Rossiter-McLaughlin effect, confirming the planet's existence and establishing its orbit as prograde. We measure an inclination between the projected planetary orbital axis and the projected stellar rotation axis of lambda = -26.9 +/- 4.6 deg, indicating a moderate inclination of the planetary orbit. Rossiter-McLaughlin measurements of a large sample of transiting planets from Kepler will provide a statistically robust measure of the true distribution of spin-orbit orientations for hot jupiters in general. | [
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1001.0417 | We present the first results of our analyses of selected RR Lyrae stars for which data have been obtained by the Kepler Mission. As expected, we find a significant fraction of the RRab stars to show the Blazhko effect, a still unexplained phenomenon that manifests itself as periodic amplitude and phase modulations of the light curve, on time scales of typically tens to hundreds of days. The long time span of the Kepler Mission of 3.5 yrs, and the unprecedentedly high precision of its data provide a unique opportunity for the study of RR Lyrae stars. Using data of a modulated star observed in the first roll as a showcase, we discuss the data, our analyses, findings, and their implications for our understanding of RR Lyrae stars and the Blazhko effect. With at least 40% of the RR Lyrae stars in our sample showing modulation, we confirm the high incidence rate that was only found in recent high-precision studies. Moreover, we report the occurrence of additional frequencies, beyond the main pulsation mode and its modulation components. Their half-integer ratio to the main frequency is reminiscent of a period doubling effect caused by resonances, observed for the first time in RR Lyrae stars. | [
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1001.0418 | The advent of Web 3.0, claiming for personalization in interactive systems (Lassila & Hendler, 2007), and the need for systems capable of interacting in a more natural way in the future society flooded with computer systems and devices (Harper et al., 2008) show that great advances in HCI should be done. This chapter presents some contributions of LIA for the future of HCI, defending that using common sense knowledge is a possibility for improving HCI, especially because people assign meaning to their messages based on their common sense and, therefore, the use of this knowledge in developing user interfaces can make them more intuitive to the end-user. Moreover, as common sense knowledge varies from group to group of people, it can be used for developing applications capable of giving different feedback for different target groups, as the applications presented along this chapter illustrate, allowing, in this way, interface personalization taking into account cultural issues. For the purpose of using common sense knowledge in the development and design of computer systems, it is necessary to provide an architecture that allows it. This chapter presents LIAs approaches for common sense knowledge acquisition, representation and use, as well as for natural language processing, contributing with those ones who intent to get into this challenging world to get started. | [
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1001.0419 | For a countable amenable group \Gamma and an element f in the integral group ring Z\Gamma being invertible in the group von Neumann algebra of \Gamma, we show that the entropy of the shift action of \Gamma on the Pontryagin dual of the quotient of Z\Gamma by its left ideal generated by f is the logarithm of the Fuglede-Kadison determinant of f. For the proof, we establish an \ell^p-version of Rufus Bowen's definition of topological entropy, addition formulas for group extensions of countable amenable group actions, and an approximation formula for the Fuglede-Kadison determinant of f in terms of the determinants of perturbations of the compressions of f. | [
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1001.0421 | Integer factorization is a very hard computational problem. Currently no efficient algorithm for integer factorization is publicly known. However, this is an important problem on which it relies the security of many real world cryptographic systems. I present an implementation of a fast factorization algorithm on MapReduce. MapReduce is a programming model for high performance applications developed originally at Google. The quadratic sieve algorithm is split into the different MapReduce phases and compared against a standard implementation. | [
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1001.0422 | We develop a theory of cooperative emission of light by an ensemble of emitters, such as fluorescing molecules or semiconductor quantum dots, located near a metal nanostructure supporting surface plasmon. The primary mechanism of cooperative emission in such systems is resonant energy transfer between emitters and plasmons rather than the Dicke radiative coupling between emitters. We identify two types of plasmonic coupling between the emitters, (i) plasmon-enhanced radiative coupling and (ii) plasmon-assisted nonradiative energy transfer, the competition between them governing the structure of system eigenstates. Specifically, when emitters are removed by more than several nm from the metal surface, the emission is dominated by three superradiant states with the same quantum yield as a single emitter, resulting in a drastic reduction of ensemble radiated energy, while at smaller distances cooperative behavior is destroyed by nonradiative transitions. The crossover between two regimes can be observed in distance dependence of ensemble quantum efficiency. Our numerical calculations incorporating direct and plasmon-assisted interactions between the emitters indicate that they do not destroy the plasmonic Dicke effect. | [
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1001.0423 | Dense random packings of hard particles are useful models of granular media and are closely related to the structure of nonequilibrium low-temperature amorphous phases of matter. Most work has been done for random jammed packings of spheres, and it is only recently that corresponding packings of nonspherical particles (e.g., ellipsoids) have received attention. Here we report a study of the maximally random jammed (MRJ) packings of binary superdisks and monodispersed superballs whose shapes are defined by |x_1|^2p+...+|x_2|^2p<=1 with d = 2 and 3, respectively, where p is the deformation parameter with values in the interval (0, infinity). We find that the MRJ densities of such packings increase dramatically and nonanalytically as one moves away from the circular-disk and sphere point. Moreover, the disordered packings are hypostatic and the local arrangements of particles are necessarily nontrivially correlated to achieve jamming. We term such correlated structures "nongeneric". The degree of "nongenericity" of the packings is quantitatively characterized by determining the fraction of local coordination structures in which the central particles have fewer contacting neighbors than average. We also show that such seemingly special packing configurations are counterintuitively not rare. As the anisotropy of the particles increases, the fraction of rattlers decreases while the minimal orientational order increases. These novel characteristics result from the unique rotational symmetry breaking manner of the particles. | [
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1001.0424 | We construct a family of purely infinite $C^*$-algebras, $\mathcal{Q}^\lambda$ for $\lambda\in (0,1)$ that are classified by their $K$-groups. There is an action of the circle $\T$ with a unique ${\rm KMS}$ state $\psi$ on each $\mathcal{Q}^\lambda.$ For $\lambda=1/n,$ $\mathcal{Q}^{1/n}\cong O_n$, with its usual $\T$ action and ${\rm KMS}$ state. For $\lambda=p/q,$ rational in lowest terms, $\mathcal{Q}^\lambda\cong O_n$ ($n=q-p+1$) with UHF fixed point algebra of type $(pq)^\infty.$ For any $n>0,$ $\mathcal{Q}^\lambda\cong O_n$ for infinitely many $\lambda$ with distinct KMS states and UHF fixed-point algebras. For any $\lambda\in (0,1),$ $\mathcal{Q}^\lambda\neq O_\infty.$ For $\lambda$ irrational the fixed point algebras, are NOT AF and the $\mathcal{Q}^\lambda$ are usually NOT Cuntz algebras. For $\lambda$ transcendental, $K_1\cong K_0\cong\Z^\infty$, so that $\mathcal{Q}^\lambda$ is Cuntz' $\mathcal Q_{\N}$, \cite{Cu1}. If $\lambda^{\pm 1}$ are both algebraic integers, the {\bf only} $O_n$ which appear satisfy $n\equiv 3(mod 4).$ For each $\lambda$, the representation of $\mathcal{Q}^\lambda$ defined by the KMS state $\psi$ generates a type ${\rm III}_\lambda$ factor. These algebras fit into the framework of modular index (twisted cyclic) theory of \cite{CPR2,CRT} and \cite{CNNR}. | [
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1001.0425 | We study ordinary solitons and gap solitons (GSs) in the effectively one-dimensional Gross-Pitaevskii equation, with a combination of linear and nonlinear lattice potentials. The main points of the analysis are effects of the (in)commensurability between the lattices, the development of analytical methods, viz., the variational approximation (VA) for narrow ordinary solitons, and various forms of the averaging method for broad solitons of both types, and also the study of mobility of the solitons. Under the direct commensurability (equal periods of the lattices, the family of ordinary solitons is similar to its counterpart in the free space. The situation is different in the case of the subharmonic commensurability, with L_{lin}=(1/2)L_{nonlin}, or incommensurability. In those cases, there is an existence threshold for the solitons, and the scaling relation between their amplitude and width is different from that in the free space. GS families demonstrate a bistability, unless the direct commensurability takes place. Specific scaling relations are found for them too. Ordinary solitons can be readily set in motion by kicking. GSs are mobile too, featuring inelastic collisions. The analytical approximations are shown to be quite accurate, predicting correct scaling relations for the soliton families in different cases. The stability of the ordinary solitons is fully determined by the VK (Vakhitov-Kolokolov) criterion, while the stability of GS families follows an inverted ("anti-VK") criterion, which is explained by means of the averaging approximation. | [
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] |
1001.0426 | Based on the semi-classical theory, we investigate the thermodynamic properties of a dipolar Fermi gas. Through a self-consistent procedure, we numerically obtain the phase space distribution function at finite temperature. We show that the deformations in both momentum and real space becomes smaller and smaller as one increases the temperature. For homogeneous case, we also calculate pressure, entropy, and heat capacity. In particular, at low temperature limit and in weak interaction regime, we obtain an analytic expression for the entropy, which agrees qualitatively with our numerical result. The stability of a trapped gas at finite temperature is also explored. | [
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1001.0427 | The principal filtration of the infinite-dimensional odd Contact Lie superalgebra over a field of characteristic $p>2$ is proved to be invariant under the automorphism group by investigating ad-nilpotent elements and determining certain invariants such as subalgebras generated by some ad-nilpotent elements. Then, it is proved that two automorphisms coincide if and only if they coincide on the -1 component with respect to the principal grading. Finally, all the odd Contact superalgebras are classified up to isomorphisms. | [
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1001.0428 | All-loop Finite Unified Theories (FUTs) are very interesting N=1 supersymmetric Grand Unified Theories (GUTs) which not only realise an old field theoretic dream but also have a remarkable predictive power due to the required reduction of couplings. The reduction of the dimensionless couplings in N=1 GUTs is achieved by searching for renormalization group invariant (RGI) relations among them holding beyond the unification scale. Finiteness results from the fact that there exist RGI relations among dimensionless couplings that guarantee the vanishing of all beta-functions in certain N=1 GUTs even to all orders. Furthermore developments in the soft supersymmetry breaking sector of N=1 GUTs and FUTs lead to exact RGI relations, i.e. reduction of couplings, in this dimensionful sector of the theory too. Based on the above theoretical framework phenomenologically consistent FUTS have been constructed. Here we present FUT models based on the SU(5) and SU(3)^3 gauge groups and their predictions. Of particular interest is the Higgs mass prediction of one of the models which is expected to be tested at the LHC. | [
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] |
1001.0429 | Solution to the reduced matrix model of IKKT type is studied with non-zero fermion fields. A suggestion is made that our universe is made of rational numbers rather than being a continuum. To substantiate this proposal, the reduced Yang-Mills equation is written in the form of an elliptic curve. The normalization of the solution can be expressed in terms of the Weierstrass function generically or in terms of the Dedekind function in the case of 3-brane. A way to define the gravitational field in the matrix model is proposed with some new interpretation of the cosmological constant. The (first) quantization of the system is done within the framework of non-commutative geometry. | [
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1001.0431 | We use Green's function method to study the Heisenberg model of LaFeAsO with the striped antiferromagnetic collinear spin structure. In addition to the intra-layer spin couplings $J_{1a},J_{1b},J_2$ and the inter-layer coupling $J_c$, we further consider the contributions of the single-ion anisotropy $J_s$. The analytical expressions for the magnetic phase-transition temperature $T_N$ and the spin spectrum gap $\Delta$ are obtained. According to the experimental temperature $T_N=138$K and the previous estimations of the coupling interactions, we make a further discussion about the magnitude and the effects of the single-ion anisotropy $J_s$. We find that the magnitudes of $J_s$ and $J_c$ can compete. The dependences of the transition temperature $T_N$, the zero-temperature average spin and the spin spectrum gap on the single-ion anisotropy are investigated. We find they both increase as $J_s$ increases. The spin spectrum gap at low temperature $T\to0$ is calculated as a function of $J_s$, the result of which is a useful reference for the future experimental researches. | [
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] |
1001.0432 | The present notes are based on a course on Cherednik algebras given by the first author at MIT in the Fall of 2009. Their goal is to give an introduction to Cherednik algebras, and to review the web of connections between them and other mathematical objects. | [
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] |
1001.0433 | We construct a kinetic equation modeling the behavior of degenerate quantum Bose gases whose collision rate depends on the momentum of elementary excitations. We consider the case where the phonon component is the decisive factor in the elementary excitations. We analytically solve the half-space boundary value problem of the temperature jump at the boundary of the degenerate Bose gas in the presence of a Bose -- Einstein condensate. | [
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1001.0434 | We update phenomenological constraints on a Two Higgs Doublet Model with lepton flavour non-conserving Yukawa couplings. We review that $\tan \beta$ is ambiguous in such "Type III" models, and define it from the $\tau$ Yukawa coupling. The neutral scalars $\phi$ could be searched for at hadron colliders in $ \phi \to \tau \bar{\mu}$, and are constrained by the rare decay $\tau \to \mu \gamma$. The Feynman diagrams for the collider process, with Higgs production via gluon fusion, are similar to the two-loop "Barr-Zee" diagrams which contribute to $\tau \to \mu \gamma$. Some "tuning" is required to obtain a collider cross-section of order the Standard Model expectation for $\sigma (gg \to h_{SM} \to \tau^+ \tau^-)$, while agreeing with the current bound from $\tau \to \mu \gamma$. | [
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1001.0435 | We present a construction of Donaldson-Thomas invariants for three-dimensional projective Calabi-Yau Deligne-Mumford stacks. We also study the structure of these invariants for etale gerbes over such stacks. | [
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1001.0436 | We study the design of truthful mechanisms that do not use payments for the generalized assignment problem (GAP) and its variants. An instance of the GAP consists of a bipartite graph with jobs on one side and machines on the other. Machines have capacities and edges have values and sizes; the goal is to construct a welfare maximizing feasible assignment. In our model of private valuations, motivated by impossibility results, the value and sizes on all job-machine pairs are public information; however, whether an edge exists or not in the bipartite graph is a job's private information. We study several variants of the GAP starting with matching. For the unweighted version, we give an optimal strategyproof mechanism; for maximum weight bipartite matching, however, we show give a 2-approximate strategyproof mechanism and show by a matching lowerbound that this is optimal. Next we study knapsack-like problems, which are APX-hard. For these problems, we develop a general LP-based technique that extends the ideas of Lavi and Swamy to reduce designing a truthful mechanism without money to designing such a mechanism for the fractional version of the problem, at a loss of a factor equal to the integrality gap in the approximation ratio. We use this technique to obtain strategyproof mechanisms with constant approximation ratios for these problems. We then design an O(log n)-approximate strategyproof mechanism for the GAP by reducing, with logarithmic loss in the approximation, to our solution for the value-invariant GAP. Our technique may be of independent interest for designing truthful mechanisms without money for other LP-based problems. | [
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1001.0437 | Kepler's primary mission is a search for earth-size exoplanets in the habitable zone of late-type stars using the transit method. To effectively accomplish this mission, Kepler orbits the Sun and stares nearly continuously at one field-of-view which was carefully selected to provide an appropriate density of target stars. The data transmission rates, operational cycles, and target management requirements implied by this mission design have been optimized and integrated into a comprehensive plan for science operations. The commissioning phase completed all critical tasks and accomplished all objectives within a week of the pre-launch plan. Since starting science, the nominal data collection timeline has been interrupted by two safemode events, several losses of fine point, and some small pointing adjustments. The most important anomalies are understood and mitigated, so Kepler's technical performance metrics have improved significantly over this period and the prognosis for mission success is excellent. The Kepler data archive is established and hosting data for the science team, guest observers, and public. The first data sets to become publicly available include the monthly full-frame images, dropped targets, and individual sources as they are published. Data are released through the archive on a quarterly basis; the Kepler Results Catalog will be released annually starting in 2011. | [
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1001.0438 | It is proposed that primary nucleation of amorphous microspherulites of hydrated silica in natural proto-precious-opal can be followed by a long range superlattice ordering process by means of electrostatic self-assembly. Necessary conditions in the thermodynamics are a high surface charge density on microspherulite surfaces, a long Debye length and an appropriate number density of nucleation centres. A further chemical requirement is a high alkaline environmental pH from 9 to 10. It is also proposed that the characteristic concentric spherical shell-like structure of spherulites, centred on primary nuclei, are due to sequential deposition of intrinsic salts which precipitate out when the corresponding solubility limits in the liquid are successively exceeded. It can be that the better-known sedimentation of microspherulites under gravity only plays part in the final stabilization period of overall growth. | [
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] |
1001.0439 | We present a theory of backward stochastic differential equations in continuous time with an arbitrary filtered probability space. No assumptions are made regarding the left continuity of the filtration, of the predictable quadratic variations of martingales or of the measure integrating the driver. We present conditions for existence and uniqueness of square-integrable solutions, using Lipschitz continuity of the driver. These conditions unite the requirements for existence in continuous and discrete time and allow discrete processes to be embedded with continuous ones. We also present conditions for a comparison theorem and hence construct time consistent nonlinear expectations in these general spaces. | [
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1001.0441 | Dance video is one of the important types of narrative videos with semantic rich content. This paper proposes a new meta model, Dance Video Content Model (DVCM) to represent the expressive semantics of the dance videos at multiple granularity levels. The DVCM is designed based on the concepts such as video, shot, segment, event and object, which are the components of MPEG-7 MDS. This paper introduces a new relationship type called Temporal Semantic Relationship to infer the semantic relationships between the dance video objects. Inverted file based index is created to reduce the search time of the dance queries. The effectiveness of containment queries using precision and recall is depicted. Keywords: Dance Video Annotations, Effectiveness Metrics, Metamodeling, Temporal Semantic Relationships. | [
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1001.0442 | Dance videos are interesting and semantics-intensive. At the same time, they are the complex type of videos compared to all other types such as sports, news and movie videos. In fact, dance video is the one which is less explored by the researchers across the globe. Dance videos exhibit rich semantics such as macro features and micro features and can be classified into several types. Hence, the conceptual modeling of the expressive semantics of the dance videos is very crucial and complex. This paper presents a generic Dance Video Semantics Model (DVSM) in order to represent the semantics of the dance videos at different granularity levels, identified by the components of the accompanying song. This model incorporates both syntactic and semantic features of the videos and introduces a new entity type called, Agent, to specify the micro features of the dance videos. The instantiations of the model are expressed as graphs. The model is implemented as a tool using J2SE and JMF to annotate the macro and micro features of the dance videos. Finally examples and evaluation results are provided to depict the effectiveness of the proposed dance video model. Keywords: Agents, Dance videos, Macro features, Micro features, Video annotation, Video semantics. | [
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1001.0443 | Educational media mining is the process of converting raw media data from educational systems to useful information that can be used to design learning systems, answer research questions and allow personalized learning experiences. Knowledge discovery encompasses a wide range of techniques ranging from database queries to more recent developments in machine learning and language technology. Educational media mining techniques are now being used in IT Services research worldwide. Multi-modal Lecture Recordings is one of the important types of educational media and this paper explores the research challenges for mining lecture recordings for the efficient personalized learning experiences. Keywords: Educational Media Mining; Lecture Recordings, Multimodal Information System, Personalized Learning; Online Course Ware; Skills and Competences; | [
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1001.0444 | We study an inflation model that inflaton field is non-minimally coupled to the induced scalar curvature on the Randall-Sundrum (RS) II brane. We investigate the effects of the non-minimal coupling on the inflationary dynamics of this braneworld model. Our study shows that the number of e-folds decreases by increasing the value of the non-minimal coupling. We compare our model parameters with the minimal case and also with recent observational data. In comparison with recent observation, we obtain a constraint on the values that the non-minimal coupling attains. | [
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