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Let $p$ and $l$ be rational primes such that $l$ is odd and the order of $p$ modulo $l$ is even. For such primes $p$ and $l$, and for $e=l, 2l$, we consider the non-singular projective curves $aY^e = bX^e + cZ^e$ ($abc \neq 0$) defined over finite fields $\mathbf{F}_q$ such that $q=p^\alpha \equiv 1(\bmod {e})$. We see that the Fermat curves correspond precisely to those curves among each class (for $e=l,2l$), that are maximal or minimal over $\mathbf{F}_q$. We observe that each Fermat prime gives rise to explicit maximal and minimal curves over finite fields of characteristic 2. For $e=2l$, we explicitly determine the $\zeta$-function(s) for this class of curves, over $\mathbf{F}_q$, as rational functions in the variable $t$, for distinct cases of $a,b$, and $c$, in $\mathbf{F}_q^*$. The $\zeta$-function in each case is seen to satisfy the Weil conjectures (now theorems) for this concrete class of curves. | Zeta function of the projective curve $\pmb{aY^{2 l} = bX^{2 l} + cZ^{2 l}}$ over a class of finite fields, for odd primes $\pmb{l}$ |
We propose a new scanning transmission electron microscopy (STEM) technique that can realize the three-dimensional (3D) characterization of vacancies, lighter and heavier dopants with high precision. Using multislice STEM imaging and diffraction simulations of beta-Ga2O3 and SrTiO3, we show that selecting a small range of low scattering angles can make the contrast of the defect-containing atomic columns substantially more depth-dependent. The origin of the depth-dependence is the de-channeling of electrons due to the existence of a point defect in the atomic column, which creates extra ripples at low scattering angles. We show that, by capturing the de-channeling signal with narrowly selected annular dark field angles (e.g. 20-40 mrad), the contrast of a column containing a point defect in the image can be significantly enhanced. The effect of sample thickness, crystal orientation, probe convergence angle, and experimental uncertainty will also be discussed. Our new technique can therefore create new opportunities for highly precise 3D structural characterization of individual point defects in functional materials. | Three-Dimensional Imaging of Individual Point Defects Using Selective Detection Angles in Annular Dark Field Scanning Transmission Electron Microscopy |
Fundamental astrophysical parameters have been derived for Be 55 open cluster based on UBVI CCD photometric data, observed with the AZT-22 1.5m telescope at Maidanak Astronomical Observatory in Uzbekistan. The mean reddening is obtained as E(B-V)=1.77+-0.10 mag from early type members. The zero age main sequence fitting in the Q(VA)- Q0 diagrams indicates the distance modulus, (V0 - MV)=12.4+-0.20 mag (d=3.02+-0.28 kpc). This photometric distance is consistent with the distances of Gaia EDR3 (d=3.09+-0.16 kpc) and period-luminosity relation (d=2.78+-0.32 kpc) of its Cepheid S5 within the uncertainties. This distance also locates the cluster near the Perseus spiral arm. The Geneva isochrone fittings to the Hertzsprung-Russell diagram and observational colourmagnitude diagrams derive turn-off age, 85+-13 Myr, by taking care five red supergiants/bright giants. The possible inconsistences on the locations of the bright giants with the rotating/non-rotating isochrones may be due to both the age spread of stars in young open clusters and the diversity in rotational velocities. | UBVI CCD Photometry of Berkeley 55 Open Cluster |
In this paper the existence of a smooth density is proved for the solution of an SDE, with locally Lipschitz coefficients and semi-monotone drift, under H\"ormander condition. We prove the nondegeneracy condition for the solution of the SDE, from it an integration by parts formula would result in the Wiener space. To this end we construct a sequence of SDEs with globally Lipschitz coefficients whose solutions converge to the original one and use some Lyapunov functions to show the uniformly boundedness of the p-moments of the solutions and their Malliavin derivatives. | Smooth density for the Solution of Scalar SDEs with Locally Lipschitz Coefficients under H\"ormander Condition |
Supplying the missing necessary conditions, we complete the characterisation of the $L^p\to L^q$ boundedness of commutators $[b,T]$ of pointwise multiplication and Calder\'on-Zygmund operators, for arbitrary pairs of $1<p,q<\infty$ and under minimal non-degeneracy hypotheses on $T$. For $p\leq q$ (and especially $p=q$), this extends a long line of results under more restrictive assumptions on $T$. In particular, we answer a recent question of Lerner, Ombrosi, and Rivera-R\'ios by showing that $b\in BMO$ is necessary for the $L^p$-boundedness of $[b,T]$ for any non-zero homogeneous singular integral $T$. We also deal with iterated commutators and weighted spaces. For $p>q$, our results are new even for special classical operators with smooth kernels. As an application, we show that every $f\in L^p(R^d)$ can be represented as a convergent series of normalised Jacobians $Ju=\det\nabla u$ of $u\in \dot W^{1,dp}(R^d)^d$. This extends, from $p=1$ to $p>1$, a result of Coifman, Lions, Meyer and Semmes about $J:\dot W^{1,d}(R^d)^d\to H^1(R^d)$, and supports a conjecture of Iwaniec about the solvability of the equation $Ju=f\in L^p(R^d)$. | The L^p-to-L^q boundedness of commutators with applications to the Jacobian operator |
We show that the non-perturbative dynamics of $\mathcal{N}=2$ super Yang-Mills theories in a self-dual $\Omega$-background and with an arbitrary simple gauge group is fully determined by studying renormalization group equations of vevs of surface operators generating one-form symmetries. The corresponding system of equations is a {\it non-autonomous} Toda chain, the time being the RG scale. We obtain new recurrence relations which provide a systematic algorithm computing multi-instanton corrections from the tree-level one-loop prepotential as the asymptotic boundary condition of the RGE. We exemplify by computing the $E_6$ and $G_2$ cases up to two-instantons. | Instantons to the people: the power of one-form symmetries |
Purpose: To assess the utility of deep learning in the detection of geographic atrophy (GA) from color fundus photographs; secondary aim to explore potential utility in detecting central GA (CGA). Design: A deep learning model was developed to detect the presence of GA in color fundus photographs, and two additional models to detect CGA in different scenarios. Participants: 59,812 color fundus photographs from longitudinal follow up of 4,582 participants in the AREDS dataset. Gold standard labels were from human expert reading center graders using a standardized protocol. Methods: A deep learning model was trained to use color fundus photographs to predict GA presence from a population of eyes with no AMD to advanced AMD. A second model was trained to predict CGA presence from the same population. A third model was trained to predict CGA presence from the subset of eyes with GA. For training and testing, 5-fold cross-validation was employed. For comparison with human clinician performance, model performance was compared with that of 88 retinal specialists. Results: The deep learning models (GA detection, CGA detection from all eyes, and centrality detection from GA eyes) had AUC of 0.933-0.976, 0.939-0.976, and 0.827-0.888, respectively. The GA detection model had accuracy, sensitivity, specificity, and precision of 0.965, 0.692, 0.978, and 0.584, respectively. The CGA detection model had equivalent values of 0.966, 0.763, 0.971, and 0.394. The centrality detection model had equivalent values of 0.762, 0.782, 0.729, and 0.799. Conclusions: A deep learning model demonstrated high accuracy for the automated detection of GA. The AUC was non-inferior to that of human retinal specialists. Deep learning approaches may also be applied to the identification of CGA. The code and pretrained models are publicly available at https://github.com/ncbi-nlp/DeepSeeNet. | A deep learning approach for automated detection of geographic atrophy from color fundus photographs |
Obreshkov-like numerical integrators have been widely applied to power system transient simulation. Misuse of the numerical integrators as numerical differentiators may lead to numerical oscillation or bias. Criteria for Obreshkov-like numerical integrators to be used as numerical differentiators are proposed in this paper to avoid these misleading phenomena. The coefficients of a numerical integrator for the highest order derivative turn out to determine its suitability. Some existing Obreshkov-like numerical integrators are examined under the proposed criteria. It is revealed that the notorious numerical oscillations induced by the implicit trapezoidal method cannot always be eliminated by using the backward Euler method for a few time steps. Guided by the proposed criteria, a frequency response optimized integrator considering second order derivative is put forward which is suitable to be used as a numerical differentiator. Theoretical observations are demonstrated in time domain via case studies. The paper points out how to properly select the numerical integrators for power system transient simulation and helps to prevent their misuse. | Proper Selection of Obreshkov-Like Numerical Integrators Used as Numerical Differentiators for Power System Transient Simulation |
Charged hadron production in the $e^{+}e^{-}$ annihilations at 91 to 206 GeV in full phase space and in $\overline{p}p$ collisions at 200 to 900~GeV collision energies are studied using non-extensive Tsallis and stochastic Weibull probability distributions.~The Tsallis distribution shows better description of the data than the Weibull distribution. The 2-jet modification of the statistical distribution is applied to describe $e^{+}e^{-}$ data.~The main features of these distributions can be described by a two-component model with soft, collective interactions at low transverse energy and hard, constituent interactions dominating at high transverse energy.~This modification is found to give much better description than a full-sample fit, and again Tsallis function is found to better describe the data than the Weibull one pointing at the non-extensive character of the multiparticle production process. | Multiplicity spectra in $e^{+}e^{-}$ and $\overline{p}p$ collisions in terms of Tsallis and Weibull distributions |
Autoregressive generative models of images tend to be biased towards capturing local structure, and as a result they often produce samples which are lacking in terms of large-scale coherence. To address this, we propose two methods to learn discrete representations of images which abstract away local detail. We show that autoregressive models conditioned on these representations can produce high-fidelity reconstructions of images, and that we can train autoregressive priors on these representations that produce samples with large-scale coherence. We can recursively apply the learning procedure, yielding a hierarchy of progressively more abstract image representations. We train hierarchical class-conditional autoregressive models on the ImageNet dataset and demonstrate that they are able to generate realistic images at resolutions of 128$\times$128 and 256$\times$256 pixels. We also perform a human evaluation study comparing our models with both adversarial and likelihood-based state-of-the-art generative models. | Hierarchical Autoregressive Image Models with Auxiliary Decoders |
We compile a large sample of 120 Seyfert 2 galaxies (Sy2s) which contains 49 hidden broad-line region (HBLR) Sy2s and 71 non-HBLR Sy2s. From the difference in the power sources between two groups, we test if HBLR Sy2s are dominated by active galactic nuclei (AGNs), and if non-HBLR Sy2s are dominated by starbursts. We show that: (1) HBLR Sy2s have larger accretion rates than non-HBLR Sy2s; (2) HBLR Sy2s have larger \Nev $\lambda 14.32$/\Neii $\lambda 12.81$ and \oiv $\lambda 25.89$/\Neii $\lambda 12.81$ line ratios than non-HBLR Sy2s; (3) HBLR Sy2s have smaller $IRAS$ $f_{60}/f_{25}$ flux ratio which shows the relative strength of the host galaxy and nuclear emission than non-HBLR Sy2s. So we suggest that HBLR Sy2s and non-HBLR Sy2s are AGN-dominated and starburst-dominated, respectively. In addition, non-HBLR Sy2s can be classified into the luminous ($L_{\rm [O III]}>10^{41} \rm ergs s^{-1}$) and less luminous ($L_{\rm [O III]}<10^{41} \rm ergs s^{-1}$) samples, when considering only their obscuration. We suggest that: (1) the invisibility of polarized broad lines (PBLs) in the luminous non-HBLR Sy2s depends on the obscuration; (2) the invisibility of PBLs in the less luminous non-HBLR Sy2s depends on the very low Eddington ratio rather than the obscuration. | The Different Nature in Seyfert 2 Galaxies With and Without Hidden Broad-Line Regions |
In ultrarelativistic heavy-ion experiments, one estimates the centrality of a collision by using a single observable, say $n$, typically given by the transverse energy or the number of tracks observed in a dedicated detector. The correlation between $n$ and the impact parameter, $b$, of the collision is then inferred by fitting a specific model of the collision dynamics, such as the Glauber model, to experimental data. The goal of this paper is to assess precisely which information about $b$ can be extracted from data without any specific model of the collision. Under the sole assumption that the probability distribution of $n$ for a fixed $b$ is Gaussian, we show that the probability distribution of the impact parameter in a narrow centrality bin can be accurately reconstructed up to $5\%$ centrality. We apply our methodology to data from the Relativistic Heavy Ion Collider and the Large Hadron Collider. We propose a simple measure of the precision of the centrality determination, which can be used to compare different experiments. | Relating centrality to impact parameter in nucleus-nucleus collisions |
A study of the temperature (T) and density (n_s) dependence of conductivity \sigma(n_s,T) of a highly disordered, two-dimensional (2D) electron system in Si demonstrates scaling behavior consistent with the existence of a metal-insulator transition (MIT). The same critical exponents are found when the Coulomb interaction is screened by the metallic gate and when it is unscreened or long range. The results strongly suggest the existence of a disorder-dominated 2D MIT, which is not directly affected by the range of the Coulomb interactions. | Critical Behavior of a Strongly Disordered 2D Electron System: The Cases of Long-Range and Screened Coulomb Interactions |
We analyze a model problem representing a multi-electronic molecule sitting on a metal surface. Working with a reduced configuration interaction Hamiltonian, we show that one can extract very accurate ground state wavefunctions as compared with the numerical renormalization group theory (NRG) -- even in the limit of weak metal-molecule coupling strength but strong intramolecular electron-electron repulsion. Moreover, we extract what appear to be meaningful excitation energies as well. Our findings should lay the groundwork for future {\em ab initio} studies of charge transfer processes and bond making/breaking processes on metal surfaces. | Electronic Structure for Multielectronic Molecules Near a Metal Surface |
We analyze thermodynamic bounds on equilibrium fluctuations of an order parameter, which are analogous to relations, which have been derived recently in the context of non-equilibrium fluctuations of currents. We discuss the case of {\it global} fluctuations when the order parameter is measured in the full system of interest, and {\it local} fluctuations, when the order parameter is evaluated only in a sub-part of the system. Using isometric fluctuation theorems, we derive thermodynamic bounds on the fluctuations of the order parameter in both cases. These bounds could be used to infer the value of symmetry breaking field or the relative size of the observed sub-system to the full system from {\it local} fluctuations. | Thermodynamic bounds on equilibrium fluctuations of a global or local order parameter |
The present status of theoretical expectations of studies of single photons from relativistic heavy ion collisions is discussed. It is argued that the upper limit of single photon radiation from S+Au collisions at CERN SPS obtained by the WA80 collaboration perhaps rules out any reasonable description of the collision process which does not involve a phase transition to quark gluon plasma. Predictions for single photons from the quark-matter likely to be created in collision of two lead nuclei at RHIC and LHC energies are given with a proper accounting of chemical equilibration and transverse expansion. Finally, it is pointed out that, contrary to the popular belief of a quadrilateral dependence of electromagnetic radiations ($N_\gamma$) from such collisions on the number of charged particles ($N_{ch})$, we may only have $N_\gamma \propto N_{ch}^{1.2}$. | Single Photons from Relativistic Heavy Ion Collisions and Quark-Hadron Phase Transition |
Plasmonic nanoparticles provide an ideal environment for the enhancement of fluorescent emission. On the one hand, they locally amplify the electromagnetic fields, increasing the emitter excitation rate, and on the other hand, they provide a high local density of states that accelerates spontaneous emission. However, when the emitter is placed in close proximity to a single metal nanoparticle, the number of nonradiative states increases dramatically, causing the fluorescence to quench. It has been predicted theoretically that, through a judicious placing of the emitter, fluorescence in plasmonic nanocavities can be increased at monotonically. In this article, we show that such monotonic increase is due to the use of local response approximation in the description of the plasmonic response of metal nanoparticles. We demonstrate that taking into account the electron tunneling and the nonlocality of the surrounding system via the quantum hydrodynamic theory results eventually in a quenching of fluorescence enhancement also when the emitter is placed in a nanocavity, as opposed to local response and Thomas-Fermi hydrodynamic theory results. This outcome marks the importance of considering the quantum effects, in particular, the electron tunneling to correctly describe the emission effects in plasmonic systems at nanoscale. | Fluorescence quenching in plasmonic dimers due to electron tunneling |
We obtain strong coloring theorems at successors of singular cardinals from failures of certain instances of simultaneous reflection of stationary sets. Along the way, we establish new results in club-guessing and in the general theory of ideals. | Club-guessing, stationary reflection, and coloring theorems |
In this short note, a companion of [20], we discuss several families of $q$-series identities in connection to false and mock theta functions, characters of modules of vertex algebras, and "sum of tails". | Further $q$-series identities and conjectures relating false theta functions and characters |
In TDD reciprocity-based massive MIMO it is essential to be able to compute the downlink precoding matrix over all OFDM resource blocks within a small fraction of the uplink-downlink slot duration. Early implementation of massive MIMO are limited to the simple Conjugate Beamforming (ConjBF) precoding method, because of such computation latency limitation. However, it has been widely demonstrated by theoretical analysis and system simulation that Regularized Zero-Forcing (RZF) precoding is generally much more effective than ConjBF for a large but practical number of transmit antennas. In order to recover a significant fraction of the gap between ConjBF and RZF and yet meeting the very strict computation latency constraints, truncated polynomial expansion (TPE) methods have been proposed. In this paper we present a novel TPE method that outperforms all previously proposed methods in the general non-symmetric case of users with arbitrary antenna correlation. In addition, the proposed method is significantly simpler and more flexible than previously proposed methods based on deterministic equivalents and free probability in large random matrix theory. We consider power allocation with our TPE approach, and show that classical system optimization problems such as min-sum power and max-min rate can be easily solved. Furthermore, we provide a detailed computation latency analysis specifically targeted to a highly parallel FPGA hardware architecture. | Truncated Polynomial Expansion Downlink Precoders and Uplink Detectors for Massive MIMO |
Saturation is considered the state-of-the-art method for computing fixpoints with decision diagrams. We present a relatively simple decision diagram operation called REACH that also computes fixpoints. In contrast to saturation, it does not require a partitioning of the transition relation. We give sequential algorithms implementing the new operation for both binary and multi-valued decision diagrams, and moreover provide parallel counterparts. We implement these algorithms and experimentally compare their performance against saturation on 692 model checking benchmarks in different languages. The results show that the REACH operation often outperforms saturation, especially on transition relations with low locality. In a comparison between parallelized versions of REACH and saturation we find that REACH obtains comparable speedups up to 16 cores, although falls behind saturation at 64 cores. Finally, in a comparison with the state-of-the-art model checking tool ITS-tools we find that REACH outperforms ITS-tools on 29% of models, suggesting that REACH can be useful as a complementary method in an ensemble tool. | A Decision Diagram Operation for Reachability |
We consider concurrent stochastic games played on graphs with reachability and safety objectives. These games can be solved by value iteration as well as strategy iteration, each of them yielding a sequence of under-approximations of the reachability value and a sequence of over-approximation of the safety value, converging to it in the limit. For both approaches, we provide the first (anytime) algorithms with stopping criteria. The stopping criterion for value iteration is based on providing a convergent sequence of over-approximations, which then allows to estimate the distance to the true value. For strategy iteration, we bound the error by complementing the strategy iteration algorithm for reachability by a new strategy iteration algorithm under-approximating the safety-value. | Stopping Criteria for Value and Strategy Iteration on Concurrent Stochastic Reachability Games |
In this work we explore the thermodynamic aspects of dark energy for late future time universe in two different scenarios: as a perfect fluid with constant and variable equation of state parameter; and as dissipative fluid described by a barotropic equation of state with bulk viscosity in the framework of the Eckart theory and the full Israel-Stewart theory. We explore cosmological solutions for a flat, homogeneous and isotropic universe; and we assume the late future time behavior when the dark energy dominates the cosmic evolution. When modeled as a perfect fluid with a dynamical equation of state, $p=w(a)\rho$, the dark energy has an energy density, temperature and entropy well defined and an interesting result is that there is no entropy production even though been dynamical. For dissipative dark energy, in the Eckart theory two cases are studied: $\xi=const.$ and $\xi =(\beta/\sqrt{3}) \rho^{1/2}$; it is found that the entropy grows exponentially for the first case and as a power-law for the second. In the Israel-Stewart theory we consider a $\xi =\xi_0 \rho^{1/2}$ and a relaxation time $\tau = \xi/\rho$; an analytical Big Rip solution is obtained with a power-law entropy. In all cases a power-law relation between temperature and energy density is obtained. In order to maintain the second law of thermodynamics theoretical constraints for the equation of state are found in the different dark energy models studied. A barotropic dark fluid with $w<-1$ is thermodynamically difficult to support, but the overall effect of bulk viscosity in certain cases allows a phantom regime without thermodynamic anomalies. | Thermodynamics of viscous dark energy for the late future time universe |
We obtain the asymptotic behaviour of the longest increasing/non-decreasing subsequences in a random uniform multiset permutation in which each element in {1,...,n} occurs k times, where k may depend on n. This generalizes the famous Ulam-Hammersley problem of the case k=1. The proof relies on poissonization and a connection with variants of the Hammersley-Aldous-Diaconis particle system. | The Ulam-Hammersley problem for multiset permutations |
We present a new numerical method for transporting arbitrary sets in a velocity field. The method computes a deformation mapping of the domain and advects particular sets by function composition with the map. This also allows for the transport of multiple sets at low computational cost. Our strategy is to separate the computation of short time advection from the storage and representation of long time deformation maps, employing appropriate grid resolution for each of these two parts. We show through numerical experiments that the resulting algorithm is accurate and exhibits significant reductions in computational time over other methods. Results are presented in two and three dimensions, and accuracy and efficiency are studied. | The Characteristic Mapping Method for the Linear Advection of Arbitrary Sets |
We consider the semilinear heat equation in large dimension $d\geq 11$ $$ \partial_t u =\Delta u+|u| ^{p-1}u, \ \ p=2q+1, \ \ q\in \mathbb N $$ on a smooth bounded domain $\Omega\subset \mathbb R^d$ with Dirichlet boundary condition. In the supercritical range $p\geq p(d)>1+\frac{4}{d-2}$ we prove the existence of a countable family $(u_\ell)_{\ell \in \mathbb N}$ of solutions blowing-up at time $T>0$ with type II blow up: $$ \parallel u_{\ell}(t) \parallel_{L^{\infty}} \sim C (T-t)^{-c_\ell} $$ with blow-up speed $c_\ell>\frac{1}{p-1}$. They concentrate the ground state $Q$ being the only radially and decaying solution of $\Delta Q+Q^p=0$: $$ u(x,t)\sim \frac{1}{\lambda (t)^{\frac{2}{p-1}}}Q\left(\frac{x-x_0}{\lambda (t)} \right), \ \lambda\sim C(u_n)(T-t)^{\frac{c_\ell(p-1)}{2}} $$ at some point $x_0\in \Omega$. The result generalizes previous works on the existence of type II blow-up solutions, which only existed in the radial setting. The present proof uses robust nonlinear analysis tools instead, based on energy methods and modulation techniques. This is the first non-radial construction of a solution blowing up by concentration of a stationary state in the supercritical regime, and provides a general strategy to prove similar results for dispersive equations or parabolic systems and to extend it to multiple blow ups. | Non radial type II blow up for the energy supercritical semilinear heat equation |
We propose a general approach to the question of how biological rhythms spontaneously self-regulate, based on the concept of ``stochastic feedback''. We illustrate this approach by considering the neuroautonomic regulation of the heart rate. The model generates complex dynamics and successfully accounts for key characteristics of cardiac variability, including the $1/f$ power spectrum, the functional form and scaling of the distribution of variations, and correlations in the Fourier phases. Our results suggest that in healthy systems the control mechanisms operate to drive the system away from extreme values while not allowing it to settle down to a constant output. | Stochastic Feedback and the Regulation of Biological Rhythms |
In the present paper we introduce a new attack on NTRU-HPS cryptosystem using lattice theory and Babai's Nearest Plane Algorithm. This attack has many similarities with the classic CVP attack on NTRU, but in our case we use a different lattice, instead of the classic lattice which is constructed with the public key. Finally, the attack is illustrated by many examples. | Message recovery attack to NTRU using a lattice independent from the public key |
We study the $I$-$V$ characteristics of S$_{\text{T}}$/n/N contacts, where S$_{\text{T}}$ is a BCS superconductor S with a built-in exchange field $h$, n represents a normal metal wire, and N---a normal metal reservoir. The superconductor S$_{\text{T}}$ is separated from the n-wire by a spin filter which allows the passage of electrons with a certain spin direction so that only fully polarized triplet Cooper pairs penetrate into the n-wire. We show that both the subgap conductance $\sigma_{\text{sg}}$ and the excess current $I_{\text{exc}}$, which occur in conventional S/n/N contacts due to Andreev reflection (AR), exist also in the considered system. In our case, they are caused by unconventional AR that is not accompanied by spin flip. The excess current $I_{\text{exc}}$ exists only if $h$ exceeds a certain magnitude $h_{\text{c}}$. At ${h < h_{\text{c}}}$ the excess current is converted into a deficit current $I_\text{{def}}$. The dependencies of the differential conductance and the current $I_{\text{exc}}$ are presented as a function of voltage and $h$. | Excess current in ferromagnet-superconductor structures with fully polarized triplet component |
An approach by J.Wu describes homotopy groups $\pi_{n}(S^2)$ of the standard 2-sphere as isotopy classes of spherical $n+1$--strand Brunnian braids is investigated in the case $n=3$ for applications. | A remark on the Hopf invariant for spherical 4-braids |
Hamiltonian mechanics of field theory can be formulated in a generally covariant and background independent manner over a finite dimensional extended configuration space. The physical symplectic structure of the theory can then be defined over a space G of three-dimensional surfaces without boundary, in the extended configuration space. These surfaces provide a preferred over-coordinatization of phase space. I consider the covariant form of the Hamilton-Jacobi equation on G, and a canonical function S on G which is a preferred solution of the Hamilton-Jacobi equation. The application of this formalism to general relativity is equivalent to the ADM formalism, but fully covariant. In the quantum domain, it yields directly the Ashtekar-Wheeler-DeWitt equation. Finally, I apply this formalism to discuss the partial observables of a covariant field theory and the role of the spin networks --basic objects in quantum gravity-- in the classical theory. | Covariant hamiltonian formalism for field theory: Hamilton-Jacobi equation on the space G |
Tilting mutation is a way of producing new tilting complexes from old ones replacing only one indecomposable summand. In this paper, we give a purely combinatorial procedure for performing tilting mutation of suitable algebras. As an application, we recreate a result due to Ladkani, which states that the path algebra of a quiver shaped like a line (with certain relations) is derived equivalent to the path algebra of a quiver shaped like a rectangle. We will do this by producing an explicit series of tilting mutations going between the two algebras. | A combinatorial procedure for tilting mutation |
Wireless sensor networks (WSNs) suffers from the hot spot problem where the sensor nodes closest to the base station are need to relay more packet than the nodes farther away from the base station. Thus, lifetime of sensory network depends on these closest nodes. Clustering methods are used to extend the lifetime of a wireless sensor network. However, current clustering algorithms usually utilize two techniques; selecting cluster heads with more residual energy, and rotating cluster heads periodically to distribute the energy consumption among nodes in each cluster and lengthen the network lifetime. Most of the algorithms use random selection for selecting the cluster heads. Here, we propose a Fault Tolerant Trajectory Clustering (FTTC) technique for selecting the cluster heads in WSNs. Our algorithm selects the cluster heads based on traffic and rotates periodically. It provides the first Fault Tolerant Trajectory based clustering technique for selecting the cluster heads and to extenuate the hot spot problem by prolonging the network lifetime. | A Fault Tolerant Trajectory Clustering (FTTC) for selecting cluster heads inWireless Sensor Networks |
During the last decade, lattice-Boltzmann (LB) simulations have been improved to become an efficient tool for determining the permeability of porous media samples. However, well known improvements of the original algorithm are often not implemented. These include for example multirelaxation time schemes or improved boundary conditions, as well as different possibilities to impose a pressure gradient. This paper shows that a significant difference of the calculated permeabilities can be found unless one uses a carefully selected setup. We present a detailed discussion of possible simulation setups and quantitative studies of the influence of simulation parameters. We illustrate our results by applying the algorithm to a Fontainebleau sandstone and by comparing our benchmark studies to other numerical permeability measurements in the literature. | Quantitative analysis of numerical estimates for the permeability of porous media from lattice-Boltzmann simulations |
Waveguide integrated optical modulators in the mid-infrared (mid-IR) wavelength range are of significant interest for molecular spectroscopy in one hand, as on-chip synchronous detection can improve the performance of detection systems, and for free-space communications on the other hand, where optical modulators working in the atmospheric transparency windows are crucially missing. Here we report for the first time the demonstration of optical modulation in mid-IR photonic circuit reaching wavelengths larger than 8 um. Moreover, optical modulation in an unprecedented wavelength range, from 5.5 to 11 um wavelength is shown, relying on a broadband Ge-rich graded-SiGe platform. This first demonstration is used as a proof of concept, to experimentally confirm the free-carrier absorption effect modeling. These results pave the way towards efficient high-performance electrically-driven integrated optical modulators in the mid-IR wavelength range. | Optical modulation in Ge-rich SiGe waveguides in the mid-IR wavelength range up to 11 um |
Randomisation is used in experimental design to reduce the prevalence of unanticipated confounders. Complete randomisation can however create unbalanced designs, for example, grouping all samples of the same condition in the same batch. Block randomisation is an approach that can prevent severe imbalances in sample allocation with respect to both known and unknown confounders. This feature provides the reader with an introduction to blocking and randomisation, insights into how to effectively organise samples during experimental design, with special considerations with respect to proteomics. | On the importance of block randomisation when designing proteomics experiments |
Smart cities are revolutionizing the transportation infrastructure by the integration of technology. However, ensuring that various transportation system components are operating as expected and in a safe manner is a great challenge. In this work, we propose the use of formal methods as a means to specify and reason about the traffic network's complex properties. Formal methods provide a flexible tool to define the safe operation of the traffic network by capturing non-conforming behavior, exploring various possible states of the traffic scene, and detecting any inconsistencies within it. Hence, we develop specification-based monitoring for the analysis of traffic networks using the formal language, Signal Temporal Logic. We develop monitors that identify safety-related behavior such as conforming to speed limits and maintaining appropriate headway. The framework is tested using a calibrated micro-simulated highway scenario and offline specification-based monitoring is applied to individual vehicle trajectories to understand whether they violate or satisfy the defined safety specifications. Statistical analysis of the outputs show that our approach can differentiate violating from conforming vehicle trajectories based on the defined specifications. This work can be utilized by traffic management centers to study the traffic stream properties, identify possible hazards, and provide valuable feedback for automating the traffic monitoring systems. | Towards formalization and monitoring of microscopic traffic parameters using temporal logic |
The summation of logarithmic contributions to perturbative radiative corrections in physical processes through use of the renormalization group equation has proved to be a useful way of enhancing the information one can obtain from explicit calculation. However, it has proved difficult to perform this summation when massive fields are present. In this note we point out that if the masses involved are quite large, the decoupling theorem of Symanzik and of Appelquist and Carazzone can be used to make the summation of logarithms possible. | Renormalization Group Summation with Heavy Fields |
Network alignment, or the task of finding corresponding nodes in different networks, is an important problem formulation in many application domains. We propose CAPER, a multilevel alignment framework that Coarsens the input graphs, Aligns the coarsened graphs, Projects the alignment solution to finer levels and Refines the alignment solution. We show that CAPER can improve upon many different existing network alignment algorithms by enforcing alignment consistency across multiple graph resolutions: nodes matched at finer levels should also be matched at coarser levels. CAPER also accelerates the use of slower network alignment methods, at the modest cost of linear-time coarsening and refinement steps, by allowing them to be run on smaller coarsened versions of the input graphs. Experiments show that CAPER can improve upon diverse network alignment methods by an average of 33% in accuracy and/or an order of magnitude faster in runtime. | CAPER: Coarsen, Align, Project, Refine - A General Multilevel Framework for Network Alignment |
Many mathematical models involve input parameters, which are not precisely known. Global sensitivity analysis aims to identify the parameters whose uncertainty has the largest impact on the variability of a quantity of interest (output of the model). One of the statistical tools used to quantify the influence of each input variable on the output is the Sobol sensitivity index. We consider the statistical estimation of this index from a finite sample of model outputs. We study asymptotic and non-asymptotic properties of two estimators of Sobol indices. These properties are applied to significance tests and estimation by confidence intervals. | Statistical inference for Sobol pick freeze Monte Carlo method |
This paper has been withdrawn by the author in favor of a stronger result proven by the author with R. Frank and T. Weidl in arXiv:0707.0998 | Critical Lieb-Thirring bounds for one-dimensional Schrodinger operators and Jacobi matrices with regular ground states |
We present results of the multicolour UBVR photometry of the high-amplitude EC14026-type star, Balloon 090100001. The data span over a month and consist of more than a hundred hours of observations. Fourier analysis of these data led us to the detection of at least 30 modes of pulsation of which 22 are independent. The frequencies of 13 detected modes group in three narrow ranges, around 2.8, 3.8 and 4.7 mHz, where the radial fundamental mode, the first and second overtones are likely to occur. Surprisingly, we also detect 9 independent modes in the low-frequency domain, between 0.15 and 0.4 mHz. These modes are typical for pulsations found in PG1716+426-type stars, discovered recently among cool B-type subdwarfs. The modes found in these stars are attributed to the high-order g modes. As both kinds of pulsations are observed in Balloon 090100001, it represents a link between the two classes of pulsating hot subdwarfs. At present, it is probably the most suitable target for testing evolutionary scenarios and internal constitution models of these stars by means of asteroseismology. Three of the modes we discovered form an equidistant frequency triplet which can be explained by invoking rotational splitting of an $\ell$ = 1 mode. The splitting amounts to about 1.58 $\mu$Hz, leading to a rotation period of 7.1 $\pm$ 0.1 days. | Multicolour photometry of Balloon 090100001: linking the two classes of pulsating hot subdwarfs |
We present a theoretical study of degeneracy breaking due to short-ranged impurities in finite, single-wall, metallic carbon nanotubes. The effective mass model is used to describe the slowly varying spatial envelope wavefunctions of spinless electrons near the Fermi level at two inequivalent valleys (K-points) in terms of the four component Dirac equation for massless fermions, with the role of spin assumed by pseudospin due to the relative amplitude of the wave function on the sublattice atoms (``A'' and ``B''). Using boundary conditions at the ends of the tube that neither break valley degeneracy nor mix pseudospin eigenvectors, we use degenerate perturbation theory to show that the presence of impurities has two effects. Firstly, the position of the impurity with respect to the spatial variation of the envelope standing waves results in a sinusoidal oscillation of energy level shift as a function of energy. Secondly, the position of the impurity within the hexagonal graphite unit cell produces a particular 4 by 4 matrix structure of the corresponding effective Hamiltonian. The symmetry of this Hamiltonian with respect to pseudospin flip is related to degeneracy breaking and, for an armchair tube, the symmetry with respect to mirror reflection in the nanotube axis is related to pseudospin mixing. | Degeneracy breaking and intervalley scattering due to short-ranged impurities in finite single-wall carbon nanotubes |
Substitution of nickel by copper in the heavy fermion system CeNi$_{9-x}$Cu$_x$Ge$_4$ alters the local crystal field environment of the Ce$^{3+}$-ions. This leads to a quantum phase transition near $x\approx0.4$, which is not only driven by the competition between Kondo effect and RKKY interaction, but also by a reduction of an effectively fourfold to a twofold degenerate crystal field ground state. To study the consequences of a changing crystal field in CeNi$_8$CuGe$_4$ on its Kondo properties, inelastic neutron scattering (INS) experiments were performed. Two well-defined crystal field transitions were observed in the energy-loss spectra at 4 K. The crystal field level scheme determined by neutron spectroscopy is compared with results from specific heat measurements. | Crystal field studies on the heavy fermion compound CeNi$_8$CuGe$_4$ |
The stellarator-type storage ring for accumulation of multi- Ampere proton and ion beams with energies in the range of $100~AkeV$ to $1~AMeV$ is designed at Frankfurt university. The main idea for beam confinement with high transversal momentum acceptance was presented in EPAC2006. This ring is typically suited for experiments in plasma physics and nuclear astrophysics. The accumulator ring with a closed longitudinal magnetic field is foreseen with a strength up to $6-8~T$. The experiments with two room temperature 30 degree toroids are needed. The beam transport experiments in toroidal magnetic fields were first described in EPAC2008 within the framework of a proposed low energy ion storage ring. The test setup aims on developing a ring injection system with two beam lines representing the main beam line and the injection line. The primary beam line for the experiments was installed and successfully commissioned in 2009. A special diagnostics probe for \textit{"in situ"} ion beam detection was installed.This modular technique allows online diagnostics of the ion beam along the beam path. In this paper, we present new results on beam transport experiments and discuss transport and transverse beam injection properties of that system. | Experiments with low energy ion beam transport into toroidal magnetic fields |
Lattice-based investigations of two fundamental QCD quantities are described, namely the gluon and quark propagators in Landau gauge. We have studied the Landau gauge gluon propagator using a variety of lattices with spacings from a = 0.17 to 0.41 fm. We demonstrate that it is possible to obtain scaling behavior over a very wide range of momenta and lattice spacings and to explore the infinite volume and continuum limits. These results confirm that the Landau gauge gluon propagator is infrared finite. We study the Landau gauge quark propagator in quenched QCD using two forms of the O(a)-improved propagator and we find good agreement between these. The extracted value of the infrared quark mass in the chiral limit is found to be 300 +/- 30 MeV. We conclude that the momentum regime where the transition from nonperturbative to perturbative QCD occurs is Q^2 approx 4GeV^2. | Gluons, quarks, and the transition from nonperturbative to perturbative QCD |
We give a decomposition of the equivariant Kasparov category for discrete quantum group with torsions. As an outcome, we show that the crossed product by a discrete quantum group in a certain class preserves the UCT. We then show that quasidiagonality of a reduced C*-algebra of a countable discrete quantum group $\Gamma$ implies that $\Gamma$ is amenable, and deduce from the work of Tikuisis, White and Winter, and the results in the first part of the paper, the converse (i.e. the quantum Rosenberg Conjecture) for a large class of countable discrete unimodular quantum groups. We also note that the unimodularity is a necessary condition. | On the Baum--Connes conjecture for discrete quantum groups with torsion and the quantum Rosenberg Conjecture |
In this paper, we propose a new approach to train Generative Adversarial Networks (GANs) where we deploy a double-oracle framework using the generator and discriminator oracles. GAN is essentially a two-player zero-sum game between the generator and the discriminator. Training GANs is challenging as a pure Nash equilibrium may not exist and even finding the mixed Nash equilibrium is difficult as GANs have a large-scale strategy space. In DO-GAN, we extend the double oracle framework to GANs. We first generalize the players' strategies as the trained models of generator and discriminator from the best response oracles. We then compute the meta-strategies using a linear program. For scalability of the framework where multiple generators and discriminator best responses are stored in the memory, we propose two solutions: 1) pruning the weakly-dominated players' strategies to keep the oracles from becoming intractable; 2) applying continual learning to retain the previous knowledge of the networks. We apply our framework to established GAN architectures such as vanilla GAN, Deep Convolutional GAN, Spectral Normalization GAN and Stacked GAN. Finally, we conduct experiments on MNIST, CIFAR-10 and CelebA datasets and show that DO-GAN variants have significant improvements in both subjective qualitative evaluation and quantitative metrics, compared with their respective GAN architectures. | DO-GAN: A Double Oracle Framework for Generative Adversarial Networks |
Soft threshold factorization has been used extensively to study hadronic collisions. It is derived in the limit where the momentum fractions $x_{a,b}$ of both incoming partons approach $x_{a,b}\to 1$. We present a generalized threshold factorization theorem for color-singlet processes, which holds in the weaker limit of only $x_a \to 1$ for generic $x_b$ (or vice versa), corresponding to the limit of large rapidity but generic invariant mass of the produced color singlet. It encodes the complete soft and/or collinear singular structure in the partonic momentum fractions to all orders in perturbation theory, including in particular flavor-nondiagonal partonic channels at leading power. It provides a more powerful approximation than the classic soft threshold limit, capturing a much larger set of contributions. We demonstrate this explicitly for the Z and Higgs rapidity spectrum to NNLO, and we use it to predict a nontrivial set of its N3LO contributions. Our factorization theorem provides the relevant resummation of large-$x$ logarithms in the rapidity spectrum required for resummation-improved PDF fits. One of our factorization ingredients is a new beam function closely related to the N-jettiness beam function. As a byproduct, we identify the correct soft threshold factorization for rapidity spectra among the differing results in the literature. | Generalized Threshold Factorization with Full Collinear Dynamics |
This paper introduces likelihood-based and feature-based modulation recognition methods. In the feature-based modulation simulation part, instantaneous feature, cyclic spectrum, high-order cumulants, and wavelet transform features are used as the entry point, and six digital signals including 2ASK, 4ASK, BPSK, QPSK, 2FSK and 4FSK are simulated, showing the difference of signals in multiple dimensions | Feature Extraction, Modulation and Recognition of Mixed Signal Based on SVM |
In this comment we show that the avian compass entanglement considerations of J. Cai, G. G. Guerreschi and H. J. Briegel (Phys. Rev. Lett. 104, 220502 (2010)) result in unphysical predictions on the magnetic sensitivity of this biochemical sensor. As well known from a series of papers on precision measurements and detailed derivations of standard quantum limits, not taking into account decoherence results in an overestimate of the entanglement lifetime, and this is the case at hand. The entanglement lifetime is wrongly assumed by the authors to be independent of the reaction time (the inverse of the recombination rate) and hence it is grossly overestimated. This is so because the spin coherence lifetime is limited by the reaction time, and the entanglement lifetime cannot be any longer. | Comment on "Quantum Control and Entanglement in a Chemical Compass" |
We study optimal simple second-order cone representations (a particular subclass of second-order cone representations) for weighted geometric means, which turns out to be closely related to minimum mediated sets. Several lower and upper bounds on the size of optimal simple second-order cone representations are proved. In the case of bivariate weighted geometric means (equivalently, one dimensional mediated sets), we are able to prove the exact size of an optimal simple second-order cone representation and give an algorithm to compute one. In the genenal case, fast heuristic algorithms and traversal algorithms are proposed to compute an approximately optimal simple second-order cone representation. Finally, applications to polynomial optimization, matrix optimization, and quantum information are provided. | Weighted Geometric Mean, Minimum Mediated Set, and Optimal Simple Second-Order Cone Representation |
Bluetooth Low Energy (BLE) has become one of the most popular wireless communication protocols and is used in billions of smart devices. Despite several security features, the hardware and software limitations of these devices makes them vulnerable to man-in-the-middle (MITM) attacks. Due to the use of these devices in increasingly diverse and safety-critical applications, the capability to detect MITM attacks has become more critical. To address this challenge, we propose the use of the response time behavior of a BLE device observed in relation to select read and write operations and introduce an activeMITM attack detection system that identifies changes in response time. Our measurements on several BLE devices show that theirresponse time behavior exhibits very high regularity, making it a very reliable attack indicator that cannot be concealed by an attacker. Test results show that our system can very accurately and quickly detect MITM attacks while requiring a simple learning approach. | BLEKeeper: Response Time Behavior Based Man-In-The-Middle Attack Detection |
It has been conjectured that transport in integrable one-dimensional (1D) systems is necessarily ballistic. The large diffusive response seen experimentally in nearly ideal realizations of the S=1/2 1D Heisenberg model is therefore puzzling and has not been explained so far. Here, we show that, contrary to common belief, diffusion is universally present in interacting 1D systems subject to a periodic lattice potential. We present a parameter-free formula for the spin-lattice relaxation rate which is in excellent agreement with experiment. Furthermore, we calculate the current decay directly in the thermodynamic limit using a time-dependent density matrix renormalization group algorithm and show that an anomalously large time scale exists even at high temperatures. | Diffusion and ballistic transport in one-dimensional quantum systems |
This paper studies Gaussian random fields with Mat\'ern covariance function with smooth parameter $\nu>2$. Two cases of parameter spaces, the Euclidean space and $N$-dimensional sphere, are considered. For such smooth Gaussian fields, we have derived the explicit formulae for the expected Euler characteristic of the excursion set, the expected number and height distribution of critical points. The results are valuable for approximating the excursion probability and computing p-values for peak inference. | Smooth Mat\'ern Gaussian Random Fields: Euler Characteristic, Expected Number and Height Distribution of Critical Points |
We consider the problem of learning a graph from a finite set of noisy graph signal observations, the goal of which is to find a smooth representation of the graph signal. Such a problem is motivated by the desire to infer relational structure in large datasets and has been extensively studied in recent years. Most existing approaches focus on learning a graph on which the observed signals are smooth. However, the learned graph is prone to overfitting, as it does not take the unobserved signals into account. To address this issue, we propose a novel graph learning model based on the distributionally robust optimization methodology, which aims to identify a graph that not only provides a smooth representation of but is also robust against uncertainties in the observed signals. On the statistics side, we establish out-of-sample performance guarantees for our proposed model. On the optimization side, we show that under a mild assumption on the graph signal distribution, our proposed model admits a smooth non-convex optimization formulation. We then develop a projected gradient method to tackle this formulation and establish its convergence guarantees. Our formulation provides a new perspective on regularization in the graph learning setting. Moreover, extensive numerical experiments on both synthetic and real-world data show that our model has comparable yet more robust performance across different populations of observed signals than existing non-robust models according to various metrics. | Distributionally Robust Graph Learning from Smooth Signals under Moment Uncertainty |
Modeling attention in neural multi-source sequence-to-sequence learning remains a relatively unexplored area, despite its usefulness in tasks that incorporate multiple source languages or modalities. We propose two novel approaches to combine the outputs of attention mechanisms over each source sequence, flat and hierarchical. We compare the proposed methods with existing techniques and present results of systematic evaluation of those methods on the WMT16 Multimodal Translation and Automatic Post-editing tasks. We show that the proposed methods achieve competitive results on both tasks. | Attention Strategies for Multi-Source Sequence-to-Sequence Learning |
We study the magnetic properties of single crystals of rutile TiO2 implanted with cobalt for various fluences. The temperature variation of zero field cooled(ZFC) and field cooled (FC) magnetization shows a much higher blocking temperature (TB) along [1-10]. Similarly the scaling of magnetization isotherms above TB is seen only when the field is parallel to [1-10] direction. With field along this direction, the magnetization shows near saturation at a much smaller field compared to that of[001] direction. The Co nanoclusters possess an "easy" and "hard axis" of magnetization coupled by the magneto crystalline anisotropy of secondary phases of cobalt with TiO2. In addition, at T=2 K we observe a crossover in the magnetization vs field isotherms between the two field directions in the samples which has been attributed to the anisotropic paramagnetism arising from cobalt present in 2+ ionic state with S = 3/2. | Anisotropic super-paramagnetism in cobalt implanted rutile-TiO2 single crystals |
Neural network calibration is an essential task in deep learning to ensure consistency between the confidence of model prediction and the true correctness likelihood. In this paper, we propose a new post-processing calibration method called Neural Clamping, which employs a simple joint input-output transformation on a pre-trained classifier via a learnable universal input perturbation and an output temperature scaling parameter. Moreover, we provide theoretical explanations on why Neural Clamping is provably better than temperature scaling. Evaluated on CIFAR-100 and ImageNet image recognition datasets and a variety of deep neural network models, our empirical results show that Neural Clamping significantly outperforms state-of-the-art post-processing calibration methods. | Neural Clamping: Joint Input Perturbation and Temperature Scaling for Neural Network Calibration |
We carry on a general study on axially symmetric, static fluids admitting a conformal Killing vector (CKV). The physical relevance of this kind of symmetry is emphasized. Next, we investigate all possible consequences derived from the imposition of such a symmetry. Special attention is paid to the problem of symmetry inheritance. Several families of solutions endowed with a CKV are exhibited. | Self-similarity in static axially symmetric relativistic fluids |
Two-dimensional electrophoresis of proteins has preceded, and accompanied, the birth of proteomics. Although it is no longer the only experimental scheme used in modern proteomics, it still has distinct features and advantages. The purpose of this tutorial paper is to guide the reader through the history of the field, then through the main steps of the process, from sample preparation to in-gel detection of proteins, commenting the constraints and caveats of the technique. Then the limitations and positive features of two-dimensional electrophoresis are discussed (e.g. its unique ability to separate complete proteins and its easy interfacing with immunoblotting techniques), so that the optimal type of applications of this technique in current and future proteomics can be perceived. This is illustrated by a detailed example taken from the literature and commented in detail. This Tutorial is part of the International Proteomics Tutorial Programme (IPTP 2). | Two-dimensional gel electrophoresis in proteomics: A tutorial |
In this paper we initiate a study of non parametric contextual bandits under shape constraints on the mean reward function. Specifically, we study a setting where the context is one dimensional, and the mean reward function is isotonic with respect to this context. We propose a policy for this problem and show that it attains minimax rate optimal regret. Moreover, we show that the same policy enjoys automatic adaptation; that is, for subclasses of the parameter space where the true mean reward functions are also piecewise constant with $k$ pieces, this policy remains minimax rate optimal simultaneously for all $k \geq 1.$ Automatic adaptation phenomena are well-known for shape constrained problems in the offline setting; %The phenomenon of automatic adaptation of shape constrained methods is known to occur in offline problems; we show that such phenomena carry over to the online setting. The main technical ingredient underlying our policy is a procedure to derive confidence bands for an underlying isotonic function using the isotonic quantile estimator. The confidence band we propose is valid under heavy tailed noise, and its average width goes to $0$ at an adaptively optimal rate. We consider this to be an independent contribution to the isotonic regression literature. | Regret Minimization in Isotonic, Heavy-Tailed Contextual Bandits via Adaptive Confidence Bands |
Opposite-sign lepton pairs ($ee$,$e\mu$ and $\mu\mu$) from open charm decay are proposed as a measure of nuclear shadowing effects. Via an approximate scaling the ratio of the dilepton spectra from $p+A$ to those from $pp$ reflects the shadowing function well. We show that the required measurements are feasible at the Relativistic Heavy ion Collider (RHIC) by considering the backgrounds according to the proposed PHENIX detector geometry. | Nuclear gluon shadowing via dileptons from open charm decay in $p+A$ at $\sqrt s=200$ AGeV |
We employ a discrete integral-reflection representation of the double affine Hecke algebra of type $C^\vee C$ at the critical level q=1, to endow the open finite $q$-boson system with integrable boundary interactions at the lattice ends. It is shown that the Bethe Ansatz entails a complete basis of eigenfunctions for the commuting quantum integrals in terms of Macdonald's three-parameter hyperoctahedral Hall-Littlewood polynomials. | Completeness of the Bethe Ansatz for an open $q$-boson system with integrable boundary interactions |
It is shown that the problem of balancing a nonnegative matrix by positive diagonal matrices can be recast as a constrained nonlinear multiparameter eigenvalue problem. Based on this equivalent formulation some adaptations of the power method and Arnoldi process are proposed for computing the dominant eigenvector which defines the structure of the diagonal transformations. Numerical results illustrate that our novel methods accelerate significantly the convergence of the customary Sinkhorn-Knopp iteration for matrix balancing in the case of clustered dominant eigenvalues. | Accelerating the Sinkhorn-Knopp iteration by Arnoldi-type methods |
We extend the SHM analysis of hadron production results showing here consistency with the increased experimental data set, stability of the fit with regard to inclusion of finite resonance widths and 2-star hyperon resonances. We present new results on strangeness yield as a function of centrality and present their interpretation in terms of QGP inspired model of strangeness abundance in the hadronizing fireball. | Interpretation of strange hadron production at LHC |
The present study analyzes the changes in acceleration produced by swimmers before and after fatiguing effort. The subjects (n=15) performed a 25-meter crawl series at maximum speed without fatigue, and a second series with fatigue. The data were registered with a synchronized system that consisted in a position transducer (1 kHz) and a video photogrametry (50Hz). The acceleration (ms-2) was obtained by the derivative analysis of the variation of the position with time. The amplitude in the time domain was calculated with the root mean square (RMS); while the peak power (PP), the peak power frequency (PPF) and the spectrum area (SA) was calculated in the frequency domain with Fourier analysis. On one hand, the results of the temporal domain show that the RMS change percentage between series was 67.5% (p<0.001). On the other hand, PP, PPF, and SA show significant changes (p<0.001). PP and SA were reduced by 63.1% and 59.5%, respectively. Our results show that the acceleration analysis of the swimmer with Fourier analysis permits a more precise understanding of which propulsive forces contribute to the swimmer performance before and after fatigue appears. | Effect of fatigue on the intra-cycle acceleration in front crawl swimming: A time-frequency analysis |
To manipulate various types of physical signals in one single device has long captivated the attention of scientists and engineers. This however is very challenging, if not impossible, even for emerging metamaterials. Up to date, many artificial materials have been proposed, theoretically and (or) experimentally, for manipulating various waves/signals on a one-function-one-device basis. In this work, for the very first time, we employ undecorated natural materials to experimentally demonstrate a simultaneous camouflage for thermal current and electric dc current on the same device. It demonstrates how ingenuity can overcome the limitations of natural material systems without the need for complex decoration to impart inhomogeneous and (or) anisotropic properties, which was previously considered impossible to accomplish except by using metamaterials. | Invisible sensor: Simultaneous sensing and camouflaging in multiphysical fields |
In this paper we give sufficient conditions on a measurable function $p:(0,\infty)^n\rightarrow [1,\infty)$ in order that harmonic analysis operators (maximal operators, Riesz transforms, Littlewood--Paley functions and multipliers) associated with $\alpha$-Laguerre polynomial expansions are bounded on the variable Lebesgue space $L^{p(\cdot)} ((0,\infty)^n, \mu_\alpha)$, where $d\mu_\alpha (x)=2^n\prod_{j=1}^n \frac{x_j^{2\alpha_j+1} e^{-x_j^2}}{\Gamma(\alpha_j+1)} dx$, being $\alpha=(\alpha_1, \dots, \alpha_n)\in [0,\infty)^n$ and $x=(x_1,\dots,x_n)\in (0,\infty)^n$. | Harmonic analysis operators associated with Laguerre polynomial expansions on variable Lebesgue spaces |
Gamma-ray bursts (GRBs) of the long-duration class are the most luminous sources of electromagnetic radiation known in the Universe. They are generated by outflows of plasma ejected at near the speed of light by newly formed neutron stars or black holes of stellar mass at cosmological distances. Prompt flashes of MeV gamma rays are followed by longer-lasting afterglow emission from radio waves to GeV gamma rays, due to synchrotron radiation by energetic electrons in accompanying shock waves. Although emission of gamma rays at even higher, TeV energies by other radiation mechanisms had been theoretically predicted, it had never been detected previously. Here we report the clear detection of GRB 190114C in the TeV band, achieved after many years of dedicated searches for TeV emission from GRBs. Gamma rays in the energy range 0.2--1 TeV are observed from about 1 minute after the burst (at more than 50 standard deviations in the first 20 minutes). This unambiguously reveals a new emission component in the afterglow of a GRB, whose power is comparable to that of the synchrotron component. The observed similarity in the radiated power and temporal behaviour of the TeV and X-ray bands points to processes such as inverse Compton radiation as the mechanism of the TeV emission, while processes such as synchrotron emission by ultrahigh-energy protons are disfavoured due to their low radiative efficiency. | Teraelectronvolt emission from the $\gamma$-ray burst GRB 190114C |
While the squeezing of a propagating field can, in principle, be made arbitrarily strong, the cavity-field squeezing is subject to the well-known 3 dB limit, and thus has limited applications. Here, we propose the use of a fully quantum degenerate parametric amplifier (DPA) to beat this squeezing limit. Specifically, we show that by {\it simply} applying a two-tone driving to the signal mode, the pump mode can, {\it counterintuitively}, be driven by the photon loss of the signal mode into a squeezed steady state with, in principle, an {\it arbitrarily high} degree of squeezing. Furthermore, we demonstrate that this intracavity squeezing can increase the signal-to-noise ratio of longitudinal qubit readout {\it exponentially} with the degree of squeezing. Correspondingly, an improvement of the measurement error by {\it many orders of magnitude} can be achieved even for modest parameters. In stark contrast, using intracavity squeezing of the semiclassical DPA {\it cannot} practically increase the signal-to-noise ratio and thus improve the measurement error. Our results extend the range of applications of DPAs and open up new opportunities for modern quantum technologies. | Beating the 3 dB Limit for Intracavity Squeezing and Its Application to Nondemolition Qubit Readout |
We use the momentum space renormalization group to study the influence of phonons and the Coulomb interaction on the superconducting response function of armchair single-walled nanotubes. We do not find superconductivity in undoped single nanotubes. When doped, superconducting fluctuations can develop because of the phonons but remain small and are easily destroyed by the Coulomb interaction. The origin of superconductivity in ropes of nanotobes is most likely an intertube effect. Projections to zig-zag nanotubes indicate a more favorable disposition to superconducting fluctuations. | On superconductivity in armchair carbon nanotubes |
We calculate vacuum polarization corrections to the binding energies in neutral alkali atoms Na through to the superheavy element E119. We employ the relativistic Hartree-Fock method to demonstrate the importance of relaxation of the electronic core and the correlation potential method to study the effects of second and higher orders of perturbation theory. These many-body effects are sizeable for all orbitals, though particularly important for orbitals with angular momentum quantum number l>0. The orders of magnitude enhancement for d waves produces shifts that, for Rb and the heavier elements, are larger than those for p waves and only an order of magnitude smaller than the s-wave shifts. The many-body enhancement mechanisms that operate for vacuum polarization apply also to the larger self-energy corrections. | QED radiative corrections and many-body effects in atoms: vacuum polarization and binding energy shifts in alkali metals |
There has been an avalanche of recent research on multiple zeta values. We propose dividing identities for multiple zeta values into structural and specific types. Structural identities are valid for any generalized multiple zeta function, and we systematically investigate them through symmetric functions. Specific identities are only valid for a specific zeta function, and we show how these can be used in conjunction with structural identities to find closed form multiple zeta values. This allows us to interpret generalized multiple zeta values as the moments of a random variable, which we characterize in certain cases. We also evaluate certain multiple Bessel zeta values and multiple Hurwitz zeta values. | Structural identities for generalized multiple zeta values |
Wavelet families arise by scaling and translations of a prototype function, called the {\em {mother wavelet}}. The construction of wavelet bases for cardinal spline spaces is generally carried out within the multi-resolution analysis scheme. Thus, the usual way of increasing the dimension of the multi-resolution subspaces is by augmenting the scaling factor. We show here that, when working on a compact interval, the identical effect can be achieved without changing the wavelet scale but reducing the translation parameter. By such a procedure we generate a redundant frame, called a {\em{dictionary}}, spanning the same spaces as a wavelet basis but with wavelets of broader support. We characterise the correlation of the dictionary elements by measuring their `coherence' and produce examples illustrating the relevance of highly coherent dictionaries to problems of sparse signal representation. | From cardinal spline wavelet bases to highly coherent dictionaries |
A five dimensional model containing both left-right and quark-lepton symmetries is constructed, with the gauge group broken by a combination of orbifold compactification and the Higgs mechanism. An analysis of the gauge and scalar sectors is performed and it is shown that the 5d model admits a simpler scalar sector. Bounds on the relevant symmetry breaking scales are obtained and reveal that two neutral gauge bosons may appear in the TeV energy range to be explored by the LHC. Split fermions are employed to remove the mass relations implied by the quark-lepton symmetry and the necessary fermion localisation is achieved by introducing bulk scalars with kink vacuum profiles. The symmetries of the model constrain the Yukawa sector, which in turn severely constrains the extent to which realistic split fermion scenarios may be realized in the absence of Yukawa coupling hierarchies. Nevertheless we present two interesting one generation constructs. One of these provides a rationale for $m_t>m_b, m_{\tau}$ and $m_\nu\ll m_t$ with Yukawa parameters which vary by only a factor of five. The other also suppresses the proton decay rate by spatially separating quarks and leptons but requires a Yukawa parameter hierarchy of order $10^2$. | Combining Left-Right And Quark-Lepton Symmetries In 5D |
We discuss two independent constructions to introduce an N-extended Supersymmetric Quantum Mechanics. The first one makes use of the Fierz identities while the second one (divided into two subcases) makes use of the Schur lemma. The N supercharges Q_I are square roots of a free Hamiltonian H given by the tensor product of a D-dimensional Laplacian and a 2d-dimensional identity matrix operator. We present the mutual relations among N, D and d. The mod 8 Bott's periodicity of Clifford algebras is encoded, in the Fierz case, in the Radon-Hurwitz function and, in the Schur case, in an extra independent function. | Extended Supersymmetric Quantum Mechanics of Fierz and Schur Type |
The low-energy properties of a system at a critical point may have additional symmetries not present in the microscopic Hamiltonian. This letter presents the theory of a class of multicritical points that provide an interesting example of this in the phase diagrams of random antiferromagnetic spin chains. One case provides an analytic theory of the quantum critical point in the random spin-3/2 chain, studied in recent work by Refael, Kehrein and Fisher (cond-mat/0111295). | Permutation-Symmetric Multicritical Points in Random Antiferromagnetic Spin Chains |
Code cloning negatively affects industrial software and threatens intellectual property. This paper presents a novel approach to detecting cloned software by using a bijective matching technique. The proposed approach focuses on increasing the range of similarity measures and thus enhancing the precision of the detection. This is achieved by extending a well-known stable-marriage problem (SMP) and demonstrating how matches between code fragments of different files can be expressed. A prototype of the proposed approach is provided using a proper scenario, which shows a noticeable improvement in several features of clone detection such as scalability and accuracy. | An Extended Stable Marriage Problem Algorithm for Clone Detection |
Let $A$ and $B$ be unital semi-simple commutative Banach algebras. In this paper we study two-variable polynomials $p$ which satisfy the following property: a map $T$ from $A$ onto $B$ such that the equality \[ \sigma (p(Tf,Tg))=\sigma (p(f,g)), \quad f,g \in A \] holds is an algebra isomorphism. | Polynomially spectrum-preserving maps between commutative Banach algebras |
We prove the exponential stability of the zero solution of a stochastic differential equation with a H\"older noise, under the strong dissipativity assumption. As a result, we also prove that there exists a random pullback attractor for a stochastic system under a multiplicative fractional Brownian noise. | Asymptotic stability for stochastic dissipative systems with a H\"older noise |
The limiting shape of the random Young diagrams associated with an inhomogeneous random word is identified as a multidimensional Brownian functional. This functional is identical in law to the spectrum of a random matrix. The Poissonized word problem is also briefy studied, and the asymptotic behavior of the shape analyzed. | On the Limiting Shape of Young Tableaux Associated With Inhomogeneous Random Words |
We report the discovery of 1.97 ms period gamma-ray pulsations from the 75 minute orbital-period binary pulsar now named PSR J1653-0158. The associated Fermi Large Area Telescope gamma-ray source 4FGL J1653.6-0158 has long been expected to harbor a binary millisecond pulsar. Despite the pulsar-like gamma-ray spectrum and candidate optical/X-ray associations -- whose periodic brightness modulations suggested an orbit -- no radio pulsations had been found in many searches. The pulsar was discovered by directly searching the gamma-ray data using the GPU-accelerated Einstein@Home distributed volunteer computing system. The multi-dimensional parameter space was bounded by positional and orbital constraints obtained from the optical counterpart. More sensitive analyses of archival and new radio data using knowledge of the pulsar timing solution yield very stringent upper limits on radio emission. Any radio emission is thus either exceptionally weak, or eclipsed for a large fraction of the time. The pulsar has one of the three lowest inferred surface magnetic-field strengths of any known pulsar with $B_{\rm surf} \approx 4 \times 10^{7}\,$G. The resulting mass function, combined with models of the companion star's optical light curve and spectra, suggests a pulsar mass $\gtrsim 2\,M_{\odot}$. The companion is light-weight with mass $\sim 0.01\,M_{\odot}$, and the orbital period is the shortest known for any rotation-powered binary pulsar. This discovery demonstrates the Fermi Large Area Telescope's potential to discover extreme pulsars that would otherwise remain undetected. | Discovery of a Gamma-ray Black Widow Pulsar by GPU-accelerated Einstein@Home |
Low rank matrix approximation (LRMA), which aims to recover the underlying low rank matrix from its degraded observation, has a wide range of applications in computer vision. The latest LRMA methods resort to using the nuclear norm minimization (NNM) as a convex relaxation of the nonconvex rank minimization. However, NNM tends to over-shrink the rank components and treats the different rank components equally, limiting its flexibility in practical applications. We propose a more flexible model, namely the Weighted Schatten $p$-Norm Minimization (WSNM), to generalize the NNM to the Schatten $p$-norm minimization with weights assigned to different singular values. The proposed WSNM not only gives better approximation to the original low-rank assumption, but also considers the importance of different rank components. We analyze the solution of WSNM and prove that, under certain weights permutation, WSNM can be equivalently transformed into independent non-convex $l_p$-norm subproblems, whose global optimum can be efficiently solved by generalized iterated shrinkage algorithm. We apply WSNM to typical low-level vision problems, e.g., image denoising and background subtraction. Extensive experimental results show, both qualitatively and quantitatively, that the proposed WSNM can more effectively remove noise, and model complex and dynamic scenes compared with state-of-the-art methods. | Weighted Schatten $p$-Norm Minimization for Image Denoising and Background Subtraction |
In this paper, we present a polynomial dynamic programming algorithm that tests whether a $n$-vertex directed tree $T$ has an upward planar embedding into a convex point-set $S$ of size $n$. Further, we extend our approach to the class of outerplanar digraphs. This nontrivial and surprising result implies that any given digraph can be efficiently tested for an upward planar embedding into a given convex point set. | Upward Point Set Embeddability for Convex Point Sets is in $P$ |
Deep learning models have been the subject of study from various perspectives, for example, their training process, interpretation, generalization error, robustness to adversarial attacks, etc. A trained model is defined by its decision boundaries, and therefore, many of the studies about deep learning models speculate about the decision boundaries, and sometimes make simplifying assumptions about them. So far, finding exact points on the decision boundaries of trained deep models has been considered an intractable problem. Here, we compute exact points on the decision boundaries of these models and provide mathematical tools to investigate the surfaces that define the decision boundaries. Through numerical results, we confirm that some of the speculations about the decision boundaries are accurate, some of the computational methods can be improved, and some of the simplifying assumptions may be unreliable, for models with nonlinear activation functions. We advocate for verification of simplifying assumptions and approximation methods, wherever they are used. Finally, we demonstrate that the computational practices used for finding adversarial examples can be improved and computing the closest point on the decision boundary reveals the weakest vulnerability of a model against adversarial attack. | Investigating Decision Boundaries of Trained Neural Networks |
In this paper we briefly introduce the quantum methods for computations of the drag coefficients for flows around a body, using the flows around a rigid sphere as an example, and we aim for comparing the wake under quantized environment and the classical computational strategies for finding the drag force. This paper however doesn't provide discussion on the pressure distribution over the surfaces of a spherical body and neither the analytical solution for the flows around an airfoil due to the greatly limited computational capacities and resources. | Quantum method for computations of flows around a body with Data analysis |
We have applied the torus fitting procedure described in Ng & Romani (2004) to PWNe observations in the Chandra data archive. This study provides quantitative measurement of the PWN geometry and we characterize the uncertainties in the fits, with statistical errors coming from the fit uncertainties and systematic errors estimated by varying the assumed fitting model. The symmetry axis $\Psi$ of the PWN are generally well determined, and highly model-independent. We often derive a robust value for the spin inclination $\zeta$. We briefly discuss the utility of these results in comparison with new radio and high energy pulse measurements | Fitting Pulsar Wind Tori. II. Error Analysis and Applications |
We present an encoding technique that reduces the effects of noise on quantum spin systems whose operation is driven by Hamiltonian evolution. This technique is widely applicable, being most relevant to the scenarios where there are insufficient qubits to permit full scale error correction. Instead, our technique can be implemented over small numbers of qubits and still leads to noticeable improvements in the fidelity of operations. The encoding scheme is easy to implement, flexible with respect to choice of Hamiltonian, and close to optimal. | Noise reducing encoding strategies for spin chains |
We study the sample complexity of nondeterministically testable graph parameters and improve existing bounds on it by several orders of magnitude. The technique used would be also of independent interest. We also discuss the special case of weak nondeterministic testing for uniform hypergraphs of arbitrary order. | Complexity of Nondeterministic Graph Parameter Testing |
We present our initial results on the CO rotational spectral line energy distribution (SLED) of the $J$ to $J$$-$1 transitions from $J=4$ up to $13$ from Herschel SPIRE spectroscopic observations of 65 luminous infrared galaxies (LIRGs) in the Great Observatories All-Sky LIRG Survey (GOALS). The observed SLEDs change on average from one peaking at $J \le 4$ to a broad distribution peaking around $J \sim\,$6$-$7 as the IRAS 60-to-100 um color, $C(60/100)$, increases. However, the ratios of a CO line luminosity to the total infrared luminosity, $L_{\rm IR}$, show the smallest variation for $J$ around 6 or 7. This suggests that, for most LIRGs, ongoing star formation (SF) is also responsible for a warm gas component that emits CO lines primarily in the mid-$J$ regime ($5 \lesssim J \lesssim 10$). As a result, the logarithmic ratios of the CO line luminosity summed over CO (5$-$4), (6$-$5), (7$-$6), (8$-$7) and (10$-$9) transitions to $L_{\rm IR}$, $\log R_{\rm midCO}$, remain largely independent of $C(60/100)$, and show a mean value of $-4.13$ ($\equiv \log R^{\rm SF}_{\rm midCO}$) and a sample standard deviation of only 0.10 for the SF-dominated galaxies. Including additional galaxies from the literature, we show, albeit with small number of cases, the possibility that galaxies, which bear powerful interstellar shocks unrelated to the current SF, and galaxies, in which an energetic active galactic nucleus contributes significantly to the bolometric luminosity, have their $R_{\rm midCO}$ higher and lower than $R^{\rm SF}_{\rm midCO}$, respectively. | Warm Molecular Gas in Luminous Infrared Galaxies |
Let $G$ be a finite group. For a fixed element $g$ in $G$ and a given subgroup $H$ of $G$, the relative $g$-noncommuting graph of $G$ is a simple undirected graph whose vertex set is $G$ and two vertices $x$ and $y$ are adjacent if $x \in H$ or $y \in H$ and $[x,y] \neq g, g^{-1}$. We denote this graph by $\Gamma_{H, G}^g$. In this paper, we obtain computing formulae for degree of any vertex in $\Gamma_{H, G}^g$ and characterize whether $\Gamma_{H, G}^g$ is a tree, star graph, lollipop or a complete graph together with some properties of $\Gamma_{H, G}^g$ involving isomorphism of graphs. We also present certain relations between the number of edges in $\Gamma_{H, G}^g$ and certain generalized commuting probabilities of $G$ which give some computing formulae for the number of edges in $\Gamma_{H, G}^g$. Finally, we conclude this paper by deriving some bounds for the number of edges in $\Gamma_{H, G}^g$. | Relative g-noncommuting graph of finite groups |
Sparse Group LASSO (SGL) is a regularized model for high-dimensional linear regression problems with grouped covariates. SGL applies $l_1$ and $l_2$ penalties on the individual predictors and group predictors, respectively, to guarantee sparse effects both on the inter-group and within-group levels. In this paper, we apply the approximate message passing (AMP) algorithm to efficiently solve the SGL problem under Gaussian random designs. We further use the recently developed state evolution analysis of AMP to derive an asymptotically exact characterization of SGL solution. This allows us to conduct multiple fine-grained statistical analyses of SGL, through which we investigate the effects of the group information and $\gamma$ (proportion of $\ell_1$ penalty). With the lens of various performance measures, we show that SGL with small $\gamma$ benefits significantly from the group information and can outperform other SGL (including LASSO) or regularized models which do not exploit the group information, in terms of the recovery rate of signal, false discovery rate and mean squared error. | Asymptotic Statistical Analysis of Sparse Group LASSO via Approximate Message Passing Algorithm |
Materials Cloud is a platform designed to enable open and seamless sharing of resources for computational science, driven by applications in materials modelling. It hosts 1) archival and dissemination services for raw and curated data, together with their provenance graph, 2) modelling services and virtual machines, 3) tools for data analytics, and pre-/post-processing, and 4) educational materials. Data is citable and archived persistently, providing a comprehensive embodiment of the FAIR principles that extends to computational workflows. Materials Cloud leverages the AiiDA framework to record the provenance of entire simulation pipelines (calculations performed, codes used, data generated) in the form of graphs that allow to retrace and reproduce any computed result. When an AiiDA database is shared on Materials Cloud, peers can browse the interconnected record of simulations, download individual files or the full database, and start their research from the results of the original authors. The infrastructure is agnostic to the specific simulation codes used and can support diverse applications in computational science that transcend its initial materials domain. | Materials Cloud, a platform for open computational science |
Interior to the gaseous envelopes of Saturn, Uranus, and Neptune, there are high-density cores with masses larger than 10 Earth masses. According to the conventional sequential accretion hypothesis, such massive cores are needed for the onset of efficient accretion of their gaseous envelopes. However, Jupiter's gaseous envelope is more massive and core may be less massive than those of Saturn. In order to account for this structural diversity and the super-solar metallicity in the envelope of Jupiter and Saturn, we investigate the possibility that they may have either merged with other gas giants or consumed several Earth-mass proto-planetary embryos during or after the rapid accretion of their envelope. In general, impinging sub-Earth-mass planetesimals disintegrate in gas giants' envelopes deposit heavy elements well outside the cores and locally suppress the convection. Consequently, their fragments sediment to promote the growth of cores. Through a series of numerical simulations, we show that it is possible for colliding super-Earth-mass embryos to reach the cores of gas giants. Direct parabolic collisions also lead to the coalescence of gas giants and merging of their cores. In these cases, the energy released from the impact leads to vigorous convective motion throughout the envelope and the erosion of the cores. This dichotomy contributes to the observed dispersion in the internal structure and atmospheric composition between Jupiter and Saturn and other gas giant planets and elsewhere. | Embryo impacts and gas giant mergers I: Dichotomy of Jupiter and Saturn's core mass |
Particles states transforming in one of the infinite spin representations of the Poincar\'e group (as classified by E. Wigner) are consistent with fundamental physical principles, but local fields generating them from the vacuum state cannot exist. While it is known that infinite spin states localized in a spacelike cone are dense in the one-particle space, we show here that the subspace of states localized in any double cone is trivial. This implies that the free field theory associated with infinite spin has no observables localized in bounded regions. In an interacting theory, if the vacuum vector is cyclic for a double cone local algebra, then the theory does not contain infinite spin representations. We also prove that if a Doplicher-Haag-Roberts representation (localized in a double cone) of a local net is covariant under a unitary representation of the Poincar\'e group containing infinite spin, then it has infinite statistics. These results hold under the natural assumption of the Bisognano-Wichmann property, and we give a counter-example (with continuous particle degeneracy) without this property where the conclusions fail. Our results hold true in any spacetime dimension s+1 where infinite spin representations exist, namely s > 1. | Where Infinite Spin Particles Are Localizable |
In this paper we give a new, less restrictive condition for removability of singular sets, $E$, of smooth solutions to the m-Hessian equation (and also for more general fully nonlinear elliptic equations) in $\Omega \setminus E$, $\Omega \subset \mathbb R^n$. Besides the existence and regularity results for these equations, the proof only makes use of the classical elliptic theory, i.e. the classical maximum principles and a Hopf lemma. | Removable Singularities of $m$-Hessian Equations |
We develop a theory for the optical conductivity of doped multilayer graphene including the effects of electron-electron interactions. Applying the quantum kinetic formalism, we formulate a set of pseudospin Bloch equations that governs the dynamics of the nonequilibrium density matrix driven by an external \emph{a.c.} electric field under the influence of Coulomb interactions. These equations reveal a dynamical mechanism that couples the Drude and interband responses arising from the chirality of pseudospin textures in multilayer graphene systems. We demonstrate that this results in an interaction-induced enhancement of the Drude weight and plasmon frequency strongly dependent on the pseudospin winding number. Using bilayer graphene as an example, we also study the influence of higher-energy bands and find that they contribute considerable renormalization effects not captured by a low-energy two-band description. We argue that this enhancement of Drude weight and plasmon frequency occurs generally in materials characterized by electronic chirality. | Theory of interaction-induced renormalization of Drude weight and plasmon frequency in chiral multilayer graphene |
Ferromagnetic La3NiAlMnO9 (LNAMO) and La3CoAlMnO9 (LCAMO) triple-perovskite thin films are stabilized in the 750-860 oC temperature range in 100 to 900 mTorr O2 pressure range using pulsed-laser deposition. The LCAMO and LNAMO films exhibit ferromagnetism up to 190 K and 130 K respectively. The structural, optical and magnetic properties of these films demonstrate that the B-site 3d-cations, Al, Mn and Co or Ni ions, are structurally short-range ordered. The strong spin-lattice-polarization coupling in LCAMO is evidenced by the temperature dependence of the dielectric constant and the softening of the phonon frequencies starting in the vicinity of the ferromagnetic-to-paramagnetic phase transition mimicking the behaviours of La2CoMnO6 double perovskite. | Stabilization and functional properties of La3NiAlMnO9 and La3CoAlMnO9 magnetoelectric triple perovskites |
I searched for the ground state 6.8 and 9.2 GHz hyperfine transitions of rubidium and cesium toward M- and L-dwarfs that show Rb and Cs optical resonance lines. The optical lines can pump the hyperfine transitions, potentially forming masers. These spin-flip transitions of Rb and Cs are the principal transitions used in atomic clocks (the $^{133}$Cs hyperfine transition defines the second). If they are detected in stellar atmospheres, these transitions would provide exceptionally precise clocks that can be used as accelerometers, as exoplanet detectors, as probes of the predictions of general relativity, as probes of light propagation effects, and as a means to do fundamental physics with telescopes. Observations of 21 M- and L-dwarfs, however, show no evidence for Rb or Cs maser action, and a previous survey of giant stars made no Rb maser detections. | Atomic Clocks in Space: A Search for Rubidium and Cesium Masers in M- and L-Dwarfs |