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    We prove that every distinguished variety in the symmetrized polydisc $\mathbb G_n$ has complex dimension $1$ and can be represented as \beginalign\labeleqn:1 \Lambda= &{ (s_1,\dots,s_n-1,p)∈\mathbb G_n \,: \nonumber \\& \quad (s_1,\dots,s_n-1) ∈\sigma_T(F_1^*+pF_n-1\,,\u2009F_2^*+pF_n-2\,,\,\dots\,, F_n-1^*+pF_1) }, \endalign where $F_1,\dots,F_{n-1}$ are commuting square matrices of same order satisfying \beginitemize \item[(i)] $[F_i^*,F_{n-j}]=[F_j^*,F_{n-i}]$ for $1\leq i<j\leq n-1$, \item[(ii)] $\sigma_T(F_1,\dots,F_{n-1})\subseteq \mathbb G_{n-1}$. \enditemize The converse also holds, i.e, a set of the form (\refeqn:1) is always a distinguished variety in $\mathbb G_n$. We show that for a tuple of commuting operators $\Sigma = (S_1,\dots,S_{n-1},P)$ having $\Gamma_n$ as a spectral set, there is a distinguished variety $\Lambda_{\Sigma}$ in $\mathbb G_n$ such that the von-Neumann's inequality holds on $\overline{\Lambda_{\Sigma}}$, i.e, \[ \|f(S_1,\dots,S_n-1,P)\|≤\sup_(s_1,\dots,s_n-1,p)∈\Lambda_\Sigma\u2009|f(s_1,\dots,s_n-1,p)|, \]for any holomorphic polynomial $f$ in $n$ variables, provided that $P^n\rightarrow 0$ strongly as $n\rightarrow \infty$. The variety $\Lambda_\Sigma$ has been shown to have representation like (\refeqn:1), where $F_i$ is the unique solutions of the operator equation \[ S_i-S_n-i^*P=(I-P^*P)^\frac12X_i(I-P^*P)^\frac12\,,\u2009i=1,\dots,n-1. \]We provide some operator theory on $\Gamma_n$. We produce an explicit dilation and a concrete functional model for such a triple $(S_1,\dots,S_{n-1},P)$ and the unique operators $F_1,\dots,F_{n-1}$ play central role in this model. Also for $n\geq 3$, we describe a connection between distinguished varieties in $\mathbb G_n$ and $\mathbb G_{n-1}$.
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    Let $p$ be an odd prime such that $2^p-1$ is not a $p$th power (mod $p^2$). Then we prove that the inverse limit of Galois groups over $\mathbb{Q}(\zeta_p)$ of iterates of $\varphi_p(z)=(z-1)^p+2-\zeta_p$ is an infinite wreath product of cyclic groups. In particular, this statement holds for all $p\leq10000$ not equal to the Wieferich primes $1093$ and $3511$.
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    In today's cyber-enabled smart grids, high penetration of uncertain renewables, purposeful manipulation of meter readings, and the need for wide-area situational awareness, call for fast, accurate, and robust power system state estimation. The least-absolute-value (LAV) estimator is known for its robustness relative to the weighted least-squares (WLS) one. However, due to nonconvexity and nonsmoothness, existing LAV solvers based on linear programming are typically slow, hence inadequate for real-time system monitoring. This paper develops two novel algorithms for efficient LAV estimation, which draw from recent advances in composite optimization. The first is a deterministic linear proximal scheme that handles a sequence of convex quadratic problems, each efficiently solvable either via off-the-shelf algorithms or through the alternating direction method of multipliers. Leveraging the sparse connectivity inherent to power networks, the second scheme is stochastic, and updates only \empha few entries of the complex voltage state vector per iteration. In particular, when voltage magnitude and (re)active power flow measurements are used only, this number reduces to one or two, \emphregardless of the number of buses in the network. This computational complexity evidently scales well to large-size power systems. Furthermore, by carefully \emphmini-batching the voltage and power flow measurements, accelerated implementation of the stochastic iterations becomes possible. The developed algorithms are numerically evaluated using a variety of benchmark power networks. Simulated tests corroborate that improved robustness can be attained at comparable or markedly reduced computation times for medium- or large-size networks relative to the "workhorse" WLS-based Gauss-Newton iterations.
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    In coding for distributed storage systems, efficient data reconstruction and repair through accessing a predefined number of arbitrarily chosen storage nodes is guaranteed by regenerating codes. Traditionally, code parameters, specially the number of helper nodes participating in a repair process, are predetermined. However, depending on the state of the system and network traffic, it is desirable to adapt such parameters accordingly in order to minimize the cost of repair. In this work a class of regenerating codes with minimum storage is introduced that can simultaneously operate at the optimal repair bandwidth, for a wide range of exact repair mechanisms, based on different number of helper nodes.
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    We introduce a generalised multivariate Polya process for document language modelling. The framework outlined here generalises a number of statistical language models used in information retrieval for modelling document generation. In particular, we show that the choice of replacement matrix M ultimately defines the type of random process and therefore defines a particular type of document language model. We show that a particular variant of the general model is useful for modelling term-specific burstiness. Furthermore, via experimentation we show that this variant significantly improves retrieval effectiveness over a strong baseline on a number of small test collections.
  • Aug 22 2017 cs.LO arXiv:1708.06010v1
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    A universal process of a process calculus is one that, given the Gödel index of a process of a certain type, produces a process equivalent to the encoded process. This paper demonstrates how universal processes can be formally defined and how a universal process of the value-passing calculus can be constructed. The existence of such a universal process in a process model can be explored to implement higher order communications, security protocols, and programming languages in the process model. A process version of the S-m-n theorem is stated to showcase how to embed the recursion theory in a process calculus.
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    With $G = \mathbb{Z}/p$, $p$ prime, we calculate the ordinary $G$-cohomology (with Burnside ring coefficients) of $\mathbb{C}P_G^\infty = B_G U(1)$, the complex projective space, a model for the classifying space for $G$-equivariant complex line bundles. The $RO(G)$-graded ordinary cohomology was calculated by Gaunce Lewis, but here we extend to a larger grading in order to capture a more natural set of generators, including the Euler class of the canonical bundle, as well as a significantly simpler set of relations.
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    We review Boltzmann machines and energy-based models. A Boltzmann machine defines a probability distribution over binary-valued patterns. One can learn parameters of a Boltzmann machine via gradient based approaches in a way that log likelihood of data is increased. The gradient and Laplacian of a Boltzmann machine admit beautiful mathematical representations, although computing them is in general intractable. This intractability motivates approximate methods, including Gibbs sampler and contrastive divergence, and tractable alternatives, namely energy-based models.
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    We study quantum Brownian motion (QBM) models of a particle in a dissipative environment coupled to a periodic potential. We review QBM for a particle in a one-dimensional periodic potential and extend the study to that of a particle in two-dimensional periodic potentials of four Bravais lattice types: square, rectangular, triangular (hexagonal), and centered rectangular. We perform perturbative renormalization group analyses to derive the flow diagrams and phase boundaries for a particle in these lattice potentials, and observe localization behavior dependent on the anisotropy of the lattice parameters.
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    The Kardar-Parisi-Zhang (KPZ) fixed point is a Markov process, recently introduced by Matetski, Quastel, Remenik (arXiv:1701.00018), that describes the limit fluctuations of the height function associated to the totally asymmetric simple exclusion process (TASEP), and it is conjectured to be at the centre of the KPZ universality class. Our main result is that the KPZ incremental process converges weakly to its invariant measure, given by a two-sided Brownian motion with zero drift and diffusion coefficient 2. The heart of the proof is the coupling method that allows us to compare the TASEP height function with its invariant process, which under the KPZ scaling turns into uniform estimates for the KPZ fixed point.
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    We study the crossover from low- to high-temperature fluctuations including critical fluctuations in confined isotropic O$(n)$-symmetric systems on the basis of a finite-size renormalization-group approach at fixed dimension $d$ introduced previously [V. Dohm, Phys. Rev. Lett. \bf 110, 107207 (2013)]. Our theory is formulated within the $\varphi^4$ lattice model in a $d$-dimensional block geometry with periodic boundary conditions. We derive the finite-size scaling functions $F^{\text ex}$ and $X$ of the excess free energy density and of the thermodynamic Casimir force, respectively, for $1\leq n \leq \infty$, $2<d<4$. Applications are given for $ L_\parallel^{d-1} \times L$ slab geometries with a finite aspect ratio $\rho=L/L_\parallel$ as well as for the film limit $\rho \to 0$ at fixed $L$. For $n=1$ and $\rho=0$ the low-temperature limits of $F^{\text ex}$ and $X$ vanish whereas they are finite for $n\geq 2$ and $\rho = 0$ due to the effect of the Goldstone modes. For $n=1$ and $\rho>0$ we find a finite low-temperature limit of $F^{\text ex}$ which deviates from that of the the Ising model. We attribute this deviation to the nonuniversal difference between the $\varphi^4$ model with continuous variables $\varphi$ and the Ising model with discrete spin variables $s=\pm1$. For $n\geq 2$ and $\rho>0$, a logarithmic divergence of $F^{\text ex}$ in the low-temperature limit is predicted, in excellent agreement with Monte Carlo (MC) data for the $d=3$ $XY$ model. For $2\leq n \leq \infty$ and $0\leq \rho<\rho_0=0.8567$ the Goldstone modes generate a negative (attractive) low-temperature Casimir force that vanishes for $\rho = \rho_0$ and becomes positive (repulsive) for $\rho > \rho_0$. Our predictions are compared with MC data for Ising, $XY$, and Heisenberg models in slab geometries with $0.01\leq\rho\leq1$. Good overall agreement is found.
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    We review Boltzmann machines extended for time-series. These models often have recurrent structure, and back propagration through time (BPTT) is used to learn their parameters. The per-step computational complexity of BPTT in online learning, however, grows linearly with respect to the length of preceding time-series (i.e., learning rule is not local in time), which limits the applicability of BPTT in online learning. We then review dynamic Boltzmann machines (DyBMs), whose learning rule is local in time. DyBM's learning rule relates to spike-timing dependent plasticity (STDP), which has been postulated and experimentally confirmed for biological neural networks.
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    We use the transfer matrix formulation of scattering theory in two-dimensions to treat the scattering problem for a potential of the form $v(x,y)=\zeta\,\delta(ax+by)g(bx-ay)$ where $\zeta,a$, and $b$ are constants, $\delta(x)$ is the Dirac $\delta$ function, and $g$ is a real- or complex-valued function. We map this problem to that of $v(x,y)=\zeta\,\delta(x)g(y)$ and give its exact and analytic solution for the following choices of $g(y)$: i) A linear combination of $\delta$-functions, in which case $v(x,y)$ is a finite linear array of two-dimensional $\delta$-functions; ii) A linear combination of $e^{i\alpha_n y}$ with $\alpha_n$ real; iii) A general periodic function that has the form of a complex Fourier series. In particular we solve the scattering problem for a potential consisting of an infinite linear periodic array of two-dimensional $\delta$-functions. We also prove a general theorem that gives a sufficient condition for different choices of $g(y)$ to produce the same scattering amplitude within specific ranges of values of the wavelength $\lambda$. For example, we show that for arbitrary real and complex parameters, $a$ and $\mathfrak{z}$, the potentials $ \mathfrak{z} \sum_{n=-\infty}^\infty\delta(x)\delta(y-an)$ and $a^{-1}\mathfrak{z}\delta(x)[1+2\cos(2\pi y/a)]$ have the same scattering amplitude for $a< \lambda\leq 2a$.
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    Exploring weakly perturbed Keplerian motion within the restricted three-body problem, Lidov (1962) and, independently, Kozai (1962) discovered coupled oscillations of eccentricity and inclination (the KL-cycles). Their classical studies were based on an integrable model of the secular evolution, obtained by double averaging of the disturbing function approximated with its first non-trivial term. This was the quadrupole term in the series expansion with respect to the ratio of the semimajor axis of the disturbed body to that of the disturbing body. If the next (octupole) term is kept in the expression for the disturbing function, long-term modulation of the KL-cycles can established (Ford et al., 2000, Naoz et al., 2011, Katz et al., 2011). Specifically, flips between the prograde and retrograde orbits become possible. Since such flips are observed only when the perturber has a non-zero eccentricity, the term "Eccentric Kozai-Lidov Effect" (or EKL-effect) was proposed by Lithwick and Naoz (2011) to specify such behaviour. We demonstrate that the EKL-effect can be interpreted as a resonance phenomenon. To this end, we write down the equations of motion in terms of "action-angle" variables emerging in the integrable Kozai-Lidov model. It turns out that for some initial values the resonance is degenerate and the usual "pendulum" approximation is insufficient to describe the evolution of the resonance phase. Analysis of the related bifurcations allows us to estimate the typical time between the successive flips for different parts of the phase space.
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    The Recurrent Chinese Restaurant Process (RCRP) is a powerful statistical method for modeling evolving clusters in large scale social media data. With the RCRP, one can allow both the number of clusters and the cluster parameters in a model to change over time. However, application of the RCRP has largely been limited due to the non-conjugacy between the cluster evolutionary priors and the Multinomial likelihood. This non-conjugacy makes inference di cult and restricts the scalability of models which use the RCRP, leading to the RCRP being applied only in simple problems, such as those that can be approximated by a single Gaussian emission. In this paper, we provide a novel solution for the non-conjugacy issues for the RCRP and an example of how to leverage our solution for one speci c problem - the social event discovery problem. By utilizing Sequential Monte Carlo methods in inference, our approach can be massively paralleled and is highly scalable, to the extent it can work on tens of millions of documents. We are able to generate high quality topical and location distributions of the clusters that can be directly interpreted as real social events, and our experimental results suggest that the approaches proposed achieve much better predictive performance than techniques reported in prior work. We also demonstrate how the techniques we develop can be used in a much more general ways toward similar problems.
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    We study a problem of fundamental importance to ICNs, namely, minimizing routing costs by jointly optimizing caching and routing decisions over an arbitrary network topology. We consider both source routing and hop-by-hop routing settings. The respective offline problems are NP-hard. Nevertheless, we show that there exist polynomial time approximation algorithms producing solutions within a constant approximation from the optimal. We also produce distributed, adaptive algorithms with the same approximation guarantees. We simulate our adaptive algorithms over a broad array of different topologies. Our algorithms reduce routing costs by several orders of magnitude compared to prior art, including algorithms optimizing caching under fixed routing.
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    In this paper, we demonstrate a connection between the group structure and Neron-Tate pairing on elliptic curves in an elliptic fibration with section on a K3 surface, and the structure of the ample cone for the K3 surface. Part of the result can be thought of as a case of the specialization theorem.
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    Training large vocabulary Neural Network Language Models (NNLMs) is a difficult task due to the explicit requirement of the output layer normalization, which typically involves the evaluation of the full softmax function over the complete vocabulary. This paper proposes a Batch Noise Contrastive Estimation (B-NCE) approach to alleviate this problem. This is achieved by reducing the vocabulary, at each time step, to the target words in the batch and then replacing the softmax by the noise contrastive estimation approach, where these words play the role of targets and noise samples at the same time. In doing so, the proposed approach can be fully formulated and implemented using optimal dense matrix operations. Applying B-NCE to train different NNLMs on the Large Text Compression Benchmark (LTCB) and the One Billion Word Benchmark (OBWB) shows a significant reduction of the training time with no noticeable degradation of the models performance. This paper also presents a new baseline comparative study of different standard NNLMs on the large OBWB on a single Titan-X GPU.
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    In what is being dubbed as the great American solar eclipse, on 21 August 2017, a total solar eclipse will sweep across the continental Unites States. Given the path of the eclipse and the length of totality available for eclipse observations, this eclipse will offer unprecedented opportunities for observations of the Sun's coronal structure and diagnostics of the coronal magnetic field. The Sun's coronal magnetic field is notoriously difficult to constrain and theoretical computational models must be relied upon for gaining insight on the coronal structure. Well-constrained solar coronal field models are crucial for understanding the origin of, and predicting solar storms that generate severe space weather. Here we present a technique for predicting and inferring the structure of the coronal field based on a data driven solar surface flux transport model which is forward run to 21 August 2017 to predict the Sun's surface field distribution. The predicted solar surface field is subsequently used as input in a potential field source surface model to generate the coronal structure during the imminent solar eclipse. Our results -- which can be verified during the 21 August 2017 eclipse observations -- indicate the presence of two helmet streamers, one each in the eastern and western limb on the southern solar hemisphere and significant radial open-flux at the poles indicating the accumulation of unipolar, polar fields in the build-up to the minimum of sunspot cycle 24. The South (open) polar flux appears to be stronger indicating an asymmetric sunspot cycle 25 with stronger activity in the southern hemisphere. The CESSI prediction of the coronal field expected during the 21 August, 2017 great American solar eclipse, accompanying images and data is available at the CESSI prediction website: http://www.cessi.in/solareclipse2017.
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    A Fermi liquid model for hadrons has been suggested for the hadrons in medium. The hadrons are supposed to behave like quasi particle as Fermi excitation while in the medium and the effective mass of the hadrons have been estimated using Fermi liquid model. Considering a momentum dependent potential inside the medium to describe the interaction, the effective masses of the hadrons are estimated. The temperature dependence of effective masses has also been studied. The possibility of describing masses of the quarks as Fermi excitation has been investigated. Compressibility, specific heats, density of states in medium has been studied. The potential depth for light and singly heavy baryons in medium has been extracted. The results are found to be very interesting and compared with the other studies available in literature.
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    Kinematic correlations for pairs of beauty hadrons, produced in high energy proton-proton collisions, are studied. The data sample used was collected with the LHCb experiment at centre-of-mass energies of 7 and 8 TeV and corresponds to an integrated luminosity of 3 fb$^{-1}$. The measurement is performed using inclusive $b\rightarrow J/\psi X$ decays in the rapidity range $2<y^{J/\psi}<4.5$. The observed correlations are in good agreement with theoretical predictions.
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    Periodically driven (Floquet) systems have been under active theoretical and experimental investigations. This paper aims at a systematic study in the following aspects of Floquet systems: (I) A systematic formulation of topological invariants of Floquet systems based on the cooperation of topology and symmetries. Topological invariants are obtained for the ten symmetry classes in all spatial dimensions, for both homogeneous Floquet systems and Floquet topological defects. (II) A general theory of Floquet topological defects, based on the proposed topological invariants. (III) Models and proposals of Floquet topological defects in low dimensions. Among them are Floquet Majorana zero modes and Majorana Pi modes in vortices of topologically trivial superconductors under a periodic driving. In addition, we also clarified several notable issues about Floquet topological invariants. Among other issues, we prove the equivalence between the effective-Hamiltonian-based band topological invariants and the frequency-domain band topological invariants.
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    In this paper, the problem of recovery of morphological information lost in abbreviated forms is addressed with a focus on highly inflected languages. Evidence is presented that the correct inflected form of an expanded abbreviation can in many cases be deduced solely from morphosyntactic tags of the context. The prediction model is a deep bidirectional LSTM network with tag embedding. The network is trained on over 10 million words from the Polish Sejm Corpus and achieves 74.2\% prediction accuracy on a smaller, but more general National Corpus of Polish. Analysis of errors suggests that performance in this task may improve if some prior knowledge about the abbreviated word is incorporated into the model.
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    In 1997 B. Weiss introduced the notion of measurably entire functions and proved that they exist on every arbitrary free C- action defined on standard probability space. In the same paper he asked about the minimal possible growth of measurably entire functions. In this work we show that for every arbitrary free C- action defined on a standard probability space there exists a measurably entire function whose growth does not exceed exp (exp[log^p |z|]) for any p > 3. This complements a recent result by Buhovski, Glücksam, Logunov, and Sodin (arXiv:1703.08101) who showed that such functions cannot grow slower than exp (exp[log^p |z|]) for any p < 2.
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    We provide a novel and simple description of Schellekens' seventy-one affine Kac-Moody structures of self-dual vertex operator algebras of central charge 24 by utilizing cyclic subgroups of the glue codes of the Niemeier lattices with roots. We also discuss a possible uniform construction procedure of the self-dual vertex operator algebras of central charge 24 starting from the Leech lattice. This also allows us to consider the uniqueness question for all non-trivial affine Kac-Moody structures. We finally discuss our description from a Lorentzian viewpoint.
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    The main purpose of this work is to provide a non-local approach to study aspects of structural stability of 3D Filippov systems. We introduce a notion of semi-local structural stability which detects when a piecewise smooth vector field is robust around the whole switching manifold and we give a complete characterization of such systems. In particular, we present some methods in the qualitative theory of piecewise smooth vector fields, emphasizing a geometrical analysis of the foliations generated by their orbits. Such approach displays surprisingly a rich dynamical behaviour that has been studied in details in this work. It is worth to say that this subject has not been treated recently from a non-local point of view, and we hope that the approach adopted in this work contributes to the understanding of the structural stability for piecewise-smooth vector fields in its most global sense.
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    Propagated acoustic waves, which generate radiation pressure, exert a non-contact force on a remote object. By suitably designing the wave field, remote tweezers are produced that stably levitate particles in the air without any mechanical contact forces. Recent works have revealed that holographic traps can levitate particles even with a single-sided wave source. However, the levitatable objects in the previous studies were limited to particles smaller than the wavelength, or flat parts placed near a rigid wall. Here, we achieve a stable levitation of a macroscopic rigid body by a holographic design of acoustic field without any dynamic control. The levitator models the acoustic radiation force and torque applied to a rigid body by discretising the body's surface, as well as the acoustic wave sources, and optimizes the acoustic field on the body surface to achieve the Lyapunov stability so that the field can properly respond to the fluctuation of the body position and rotation. In an experiment, a 40 kHz (8.5 mm wavelength) ultrasonic phased array levitated a polystyrene sphere and a regular octahedron with a size of ~50 mm located 200 mm away from acoustic elements in the air. This method not only expands the variety of levitatable objects but also contributes to microscopic contexts, such as in-vivo micromachines, since shorter-wavelength ultrasound than the size of target objects can be used to achieve higher controllability and stability.
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    PESQ and POLQA , are standards are standards for automated assessment of voice quality of speech as experienced by human beings. The predictions of those objective measures should come as close as possible to subjective quality scores as obtained in subjective listening tests. Wavenet is a deep neural network originally developed as a deep generative model of raw audio wave-forms. Wavenet architecture is based on dilated causal convolutions, which exhibit very large receptive fields. In this short paper we suggest using the Wavenet architecture, in particular its large receptive filed in order to learn PESQ algorithm. By doing so we can use it as a differentiable loss function for speech enhancement.
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    Here we discuss the physics of electro-optic modulators deploying 2D materials. We include a scaling laws analysis showing how energy-efficiency and speed change for three underlying cavity systems as a function of critical device length scaling. A key result is that the energy-per-bit of the modulator is proportional to the volume of the device, thus making the case for submicron-scale modulators possible deploying a plasmonic optical mode. We then show how Graphenes Pauli-blocking modulation mechanism is sensitive to the device operation temperature, whereby a reduction of the temperature enables a 10x reduction in modulator energy efficiency. Furthermore, we show how the high index tunability of Graphene is able to compensate for the small optical overlap factor of 2D-based material modulators, which is unlike classical Silicon-based dispersion devices. Lastly we demonstrate a novel method towards a 2D material printer suitable for cross-contamination free and on-demand printing. The latter paves the way to integrate 2D materials seamlessly into taped-out photonic chips.
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    Oscillation modes of isolated compact stars can, in principle, be a fingerprint of the equation of state (EoS) of dense matter. We study the non-radial high-frequency l=2 spheroidal modes of neutron stars and strange quark stars, adopting a two-component model (core and crust) for these two types of stars. Using perturbed fluid equations in the relativistic Cowling approximation, we explore the effect of a strangelet or hadronic crust on the oscillation modes of strange stars. The results differ from the case of neutron stars with a crust. In comparison to fluid-only configurations, we find that a solid crust on top of a neutron star increases the p-mode frequency slightly with little effect on the f-mode frequency, whereas for strange stars, a strangelet crust on top of a quark core significantly increases the f-mode frequency with little effect on the p-mode frequency.
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    Pump-probe experiments have turned out as a powerful tool in order to study the dynamics of competing orders in a large variety of materials. The corresponding analysis of the data often relies on standard linear-response theory generalized to non-equilibrium situations. Here we examine the validity of such an approach within the attractive Hubbard model for which the dynamics of pairing and charge-density wave orders is computed using the time-dependent Hartree-Fock approximation (TDHF). Our calculations reveal that the `linear-response assumption' is justified for small to moderate non-equilibrium situations (i.e., pump pulses) when the symmetry of the pump-induced state differs from that of the external field. This is the case, when we consider the pairing response in a charge-ordered state or the charge-order response in a superconducting state. The situation is very different when the non-equilibrium state and the external probe field have the same symmetry. In this case, we observe significant changes of the response in magnitude but also due to mode coupling when moving away from an equilibrium state, indicating the failure of the linear-response assumption.
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    This paper continues the study of combinatorial properties of binary functions --- that is, functions $f:2^E\rightarrow\mathbb{C}$ such that $f(\emptyset)=1$, where $E$ is a finite set. Binary functions have previously been shown to admit families of transforms that generalise duality, including a trinity transform, and families of associated minor operations that generalise deletion and contraction, with both these families parameterised by the complex numbers. Binary function representations exist for graphs (via the indicator functions of their cutset spaces) and indeed arbitrary matroids (as shown by the author previously). In this paper, we characterise degenerate elements --- analogues of loops and coloops --- in binary functions, with respect to any pair of minor operations from our complex-parameterised family. We then apply this to study the relationship between binary functions and Tutte's alternating dimaps, which also support a trinity transform and three associated minor operations. It is shown that only the simplest alternating dimaps have binary representations of the form we consider, which seems to be the most direct type of representation. The question of whether there exist other, more sophisticated types of binary function representations for alternating dimaps is left open.
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    In this paper, we compute the slice genus for many low-crossing virtual knots. For instance, we show that 1295 out of 92800 virtual knots with 6 or fewer crossings are slice, and that all but 248 of the rest are not slice. Key to these results are computations of Turaev's graded genus, which we show extends to give an invariant of virtual knot concordance. The graded genus is remarkably effective as a slice obstruction, and we develop an algorithm that applies virtual unknotting operations to determine the slice genus of many virtual knots with 6 or fewer crossings.
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    The family of unitary non-equivalent Weyl-Stratonovich kernels determining the Wigner probability distribution function of an arbitrary N-level quantum system is constructed.
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    This paper proposes a network architecture to perform variable length semantic video generation using captions. We adopt a new perspective towards video generation where we allow the captions to be combined with the long-term and short-term dependencies between video frames and thus generate a video in an incremental manner. Our experiments demonstrate our network architecture's ability to distinguish between objects, actions and interactions in a video and combine them to generate videos for unseen captions. The network also exhibits the capability to perform spatio-temporal style transfer when asked to generate videos for a sequence of captions. We also show that the network's ability to learn a latent representation allows it generate videos in an unsupervised manner and perform other tasks such as action recognition.
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    Corner detection is a vital operation in numerous computer vision applications. The Chord-to-Point Distance Accumulation (CPDA) detector is recognized as the contour-based corner detector producing the lowest localization error while localizing corners in an image. However, in our experiment part, we demonstrate that CPDA detector often misses some potential corners. Moreover, the detection algorithm of CPDA is computationally costly. In this paper, We focus on reducing localization error as well as increasing average repeatability. The preprocessing and refinements steps of proposed process are similar to CPDA. Our experimental results will show the effectiveness and robustness of proposed process over CPDA.
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    We consider a wide range of regularized stochastic minimization problems with two regularization terms, one of which is composed with a linear function. This optimization model abstracts a number of important applications in artificial intelligence and machine learning, such as fused Lasso, fused logistic regression, and a class of graph-guided regularized minimization. The computational challenges of this model are in two folds. On one hand, the closed-form solution of the proximal mapping associated with the composed regularization term or the expected objective function is not available. On the other hand, the calculation of the full gradient of the expectation in the objective is very expensive when the number of input data samples is considerably large. To address these issues, we propose a stochastic variant of extra-gradient type methods, namely \textsfStochastic Primal-Dual Proximal ExtraGradient descent (SPDPEG), and analyze its convergence property for both convex and strongly convex objectives. For general convex objectives, the uniformly average iterates generated by \textsfSPDPEG converge in expectation with $O(1/\sqrt{t})$ rate. While for strongly convex objectives, the uniformly and non-uniformly average iterates generated by \textsfSPDPEG converge with $O(\log(t)/t)$ and $O(1/t)$ rates, respectively. The order of the rate of the proposed algorithm is known to match the best convergence rate for first-order stochastic algorithms. Experiments on fused logistic regression and graph-guided regularized logistic regression problems show that the proposed algorithm performs very efficiently and consistently outperforms other competing algorithms.
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    We exhibit infinitely many examples of edge-regular graphs that have regular cliques and that are not strongly regular. This answers a question of Neumaier from 1981.
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    In this note we construct a series of small subsets containing a non-d-th power element in a finite field by applying certain bounds on incomplete character sums. Precisely, let $h=\lfloor q^{\delta}\rfloor>1$ and $d\mid q^h-1$. If $q^h-1$ has a prime divisor $r$ with $r=O((h\log q)^c)$, then there is a constant $0<\epsilon<1$ such that for a ratio at least $\frac 1 {q^{\epsilon h}}$ of $\alpha\in \mathbb{F}_{q^{h}} \backslash\mathbb{F}_{q}$, the set $S=\{ \alpha-x^t, x\in\mathbb{F}_{q}\}$ of cardinality $O(q^{\frac 12 +\delta_c})$ contains a non-d-th power in $\mathbb{F}_{q^{\lfloor q^\delta\rfloor}}$, where $t$ is the largest power of $r$ such that $t<\sqrt{q}/h$. For odd $q$, the choice of $\delta=\frac 12-d, d=o(1)>0$ shows that there exists an explicit subset of cardinality $q^{1-d}=O(\log^{2+\epsilon'}(q^h))$ containing a non-quadratic element in $\mathbb{F}_{q^h}$. On the other hand, the choice of $h=2$ shows that for any odd prime power $q$, there is an explicit subset of cardinality $O(\sqrt{q})$ containing a non-quadratic element in $\mathbb{F}_{q^2}$, essentially improving a $O(q)$ construction by Coulter and Kosick \citeCK. In addition, we obtain a similar construction for small sets containing a primitive element. The construction works well provided $\phi(q^h-1)$ is very small, where $\phi$ is the Euler's totient function.
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    The KdV equation can be derived in the shallow water limit of the Euler equations. Over the last few decades, this equation has been extended to include higher order effects. Although this equation has only one conservation law, exact periodic and solitonic solutions exist. Khare and Saxena \citeKhSa,KhSa14,KhSa15 demonstrated the possibility of generating new exact solutions by combining known ones for several fundamental equations (e.g., Korteweg - de Vries, Nonlinear Schrödinger). Here we find that this construction can be repeated for higher order, non-integrable extensions of these equations. Contrary to many statements in the literature, there seems to be no correlation between integrability and the number of nonlinear one variable wave solutions.
  • PDF
    This paper presents a sparse representation-based classification approach with a novel dictionary construction procedure. By using the constructed dictionary sophisticated prior knowledge about the spatial nature of the image can be integrated. The approach is based on the assumption that each image patch can be factorized into characteristic spatial patterns, also called shapelets, and patch-specific spectral information. A set of shapelets is learned in an unsupervised way and spectral information are embodied by training samples. A combination of shapelets and spectral information are represented in an undercomplete spatial-spectral dictionary for each individual patch, where the elements of the dictionary are linearly combined to a sparse representation of the patch. The patch-based classification is obtained by means of the representation error. Experiments are conducted on three well-known hyperspectral image datasets. They illustrate that our proposed approach shows superior results in comparison to sparse representation-based classifiers that use only limited spatial information and behaves competitively with or better than state-of-the-art classifiers utilizing spatial information and kernelized sparse representation-based classifiers.
  • PDF
    We report an unexpected positive hydrostatic pressure derivative of the superconducting transition temperature in the doped topological insulator \NBS via $dc$ SQUID magnetometry in pressures up to 0.6 GPa. This result is contrary to reports on the homologues \CBS and \SBS where smooth suppression of $T_c$ is observed. Our results are consistent with recent Ginzburg-Landau theory predictions of a pressure-induced enhancement of $T_c$ in the nematic multicomponent $E_u$ state proposed to explain observations of rotational symmetry breaking in doped Bi$_2$Se$_3$ superconductors.
  • PDF
    We prove that every $\mathbb{Z}^{k}$-action $(X,\mathbb{Z}^{k},T)$ of mean dimension less than $D/2$ admitting a factor $(Y,\mathbb{Z}^{k},S)$ of Rokhlin dimension not greater than $L$ embeds in $(([0,1]^{(L+1)D})^{\mathbb{Z}^{k}}\times Y,\sigma\times S)$, where $D\in\mathbb{N}$, $L\in\mathbb{N}\cup\{0\}$ and $\sigma$ is the shift on the Hilbert cube $([0,1]^{(L+1)D})^{\mathbb{Z}^{k}}$; in particular, when $(Y,\mathbb{Z}^{k},S)$ is an irrational $\mathbb{Z}^{k}$-rotation on the $k$-torus, $(X,\mathbb{Z}^{k},T)$ embeds in $(([0,1]^{2^kD+1})^{\mathbb{Z}^k},\sigma)$, which is compared to a previous result by the first named author, Lindenstrauss and Tsukamoto. Moreover, we give a complete and detailed proof of Takens' embedding theorem with a continuous observable for $\mathbb{Z}$-actions and deduce the analogous result for $\mathbb{Z}^{k}$-actions. Lastly, we show that the Lindenstrauss--Tsukamoto conjecture for $\mathbb{Z}$-actions holds generically, discuss an analogous conjecture for $\mathbb{Z}^{k}$-actions appearing in a forthcoming paper by the first two authors and Tsukamoto and verify it for $\mathbb{Z}^{k}$-actions on finite dimensional spaces.
  • PDF
    We study a sample of 19 galaxy clusters in the redshift range $0.15<z<0.30$ with highly complete spectroscopic membership catalogues (to $K < K^{\ast}(\rm z)+1.5$) from the Arizona Cluster Redshift Survey (ACReS); individual weak-lensing masses and near-infrared data from the Local Cluster Substructure Survey (LoCuSS); and optical photometry from the Sloan Digital Sky Survey (SDSS). We fit the scaling relations between total cluster luminosity in each of six bandpasses (${\it grizJK}$) and cluster mass, finding cluster luminosity to be a promising mass proxy with low intrinsic scatter $\sigma_{\ln L|M}$ of only $\sim 10-20$ per cent for all relations. At fixed overdensity radius, the intercept increases with wavelength, consistent with an old stellar population. The scatter and slope are consistent across all wavelengths, suggesting that cluster colour is not a function of mass. Comparing colour with indicators of the level of disturbance in the cluster, we find a narrower variety in the cluster colours of 'disturbed' clusters than of 'undisturbed' clusters. This trend is more pronounced with indicators sensitive to the initial stages of a cluster merger, e.g. the Dressler Schectman statistic. We interpret this as possible evidence that the total cluster star formation rate is 'standardised' in mergers, perhaps through a process such as a system-wide shock in the intracluster medium.
  • PDF
    In this paper, a data hiding scheme ready for Internet applications is proposed. An existing scheme based on chaotic iterations is improved, to respond to some major Internet security concerns, such as digital rights management, communication over hidden channels, and social search engines. By using Reed Solomon error correcting codes and wavelets domain, we show that this data hiding scheme can be improved to solve issues and requirements raised by these Internet fields.
  • PDF
    Handwritten character recognition has been the center of research and a benchmark problem in the sector of pattern recognition and artificial intelligence, and it continues to be a challenging research topic. Due to its enormous application many works have been done in this field focusing on different languages. Arabic, being a diversified language has a huge scope of research with potential challenges. A convolutional neural network model for recognizing handwritten numerals in Arabic language is proposed in this paper, where the dataset is subject to various augmentation in order to add robustness needed for deep learning approach. The proposed method is empowered by the presence of dropout regularization to do away with the problem of data overfitting. Moreover, suitable change is introduced in activation function to overcome the problem of vanishing gradient. With these modifications, the proposed system achieves an accuracy of 99.4\% which performs better than every previous work on the dataset.
  • PDF
    Motivated by observations of snap-through phenomena in buckled elastic strips subject to clamping and lateral end translations, we experimentally explore the multi-stability and bifurcations of thin bands of various widths and compare these results with numerical continuation of a perfectly anisotropic Kirchhoff rod. Our choice of boundary conditions is not easily satisfied by the anisotropic structures, forcing a cooperation between bending and twisting deformations. We find that, despite clear physical differences between rods and strips, a naive Kirchhoff model works surprisingly well as an organizing framework for the experimental observations. In the context of this model, we observe that anisotropy creates new states and alters the connectivity between existing states. Our results are a preliminary look at relatively unstudied boundary conditions for rods and strips that may arise in a variety of engineering applications, and may guide the avoidance of jump phenomena in such settings.
  • PDF
    We construct a canonical basis of two-cycles, on a $K3$ surface, in which the intersection form takes the canonical form $2E_8(-1) \oplus 3H$. The basic elements are realized by formal sums of smooth submanifolds.
  • PDF
    In this paper we propose an incremental learning strategy for import vector machines (IVM), which is a sparse kernel logistic regression approach. We use the procedure for the concept of self-training for sequential classification of hyperspectral data. The strategy comprises the inclusion of new training samples to increase the classification accuracy and the deletion of non-informative samples to be memory- and runtime-efficient. Moreover, we update the parameters in the incremental IVM model without re-training from scratch. Therefore, the incremental classifier is able to deal with large data sets. The performance of the IVM in comparison to support vector machines (SVM) is evaluated in terms of accuracy and experiments are conducted to assess the potential of the probabilistic outputs of the IVM. Experimental results demonstrate that the IVM and SVM perform similar in terms of classification accuracy. However, the number of import vectors is significantly lower when compared to the number of support vectors and thus, the computation time during classification can be decreased. Moreover, the probabilities provided by IVM are more reliable, when compared to the probabilistic information, derived from an SVM's output. In addition, the proposed self-training strategy can increase the classification accuracy. Overall, the IVM and the its incremental version is worthwhile for the classification of hyperspectral data.
  • PDF
    In this work, we consider the usage of wireless sensor networks (WSN) to monitor an area of interest, in order to diagnose on real time its state. Each sensor node forwards information about relevant features towards the sink where the data is processed. Nevertheless, energy conservation is a key issue in the design of such networks and once a sensor exhausts its resources, it will be dropped from the network. This will lead to broken links and data loss. It is therefore important to keep the network running for as long as possible by preserving the energy held by the nodes. Indeed, saving the quality of service (QoS) of a wireless sensor network for a long period is very important in order to ensure accurate data. Then, the area diagnosing will be more accurate. From another side, packet transmission is the phase that consumes the highest amount of energy comparing to other activities in the network. Therefore, we can see that the network topology has an important impact on energy efficiency, and thus on data and diagnosis accuracies. In this paper, we study and compare four network topologies: distributed, hierarchical, centralized, and decentralized topology and show their impact on the resulting estimation of diagnostics. We have used six diagnostic algorithms, to evaluate both prognostic and health management with the variation of type of topology in WSN.

Recent comments

Māris Ozols Aug 03 2017 09:34 UTC

If I'm not mistaken, what you describe here is equivalent to the [QR decomposition][1]. The matrices $R_{ij}$ that act non-trivially only in a two-dimensional subspace are known as [Givens rotations][2]. The fact that any $n \times n$ unitary can be decomposed as a sequence of Givens rotations is ex

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gae Jul 26 2017 21:19 UTC

For those interested in the literature on teleportation simulation of quantum channels, a detailed and *comprehensive* review is provided in Supplementary Note 8 of https://images.nature.com/original/nature-assets/ncomms/2017/170426/ncomms15043/extref/ncomms15043-s1.pdf
The note describes well the t

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Maciej Malinowski Jul 26 2017 15:56 UTC

In what sense is the ground state for large detuning ordered and antiferromagnetic? I understand that there is symmetry breaking, but other than that, what is the fundamental difference between ground states for large negative and large positive detunings? It seems to be they both exhibit some order

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Stefano Pirandola Jul 26 2017 15:28 UTC

The performance of the memory assisted MDI-QKD with "quasi-EPR" sources is remarkable. It improves the key rate by 5 orders of magnitude over the PLOB bound at about 600 km (take a look at Figure 4).

Māris Ozols Jul 26 2017 11:07 UTC

Conway's list still has four other $1000 problems left:

https://oeis.org/A248380/a248380.pdf

SHUAI ZHANG Jul 26 2017 00:20 UTC

I am still working on improving this survey. If you have any suggestions, questions or find any mistakes, please do not hesitate to contact me: shuai.zhang@student.unsw.edu.au.

Alvaro M. Alhambra Jul 24 2017 16:10 UTC

This paper has just been updated and we thought it would be a good
idea to advertise it here. It was originally submitted a year ago, and
it has now been essentially rewritten, with two new authors added.

We have fixed some of the original results and now we:
-Show how some fundamental theorem

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Steve Flammia Jul 21 2017 13:43 UTC

Actually, there is even earlier work that shows this result. In [arXiv:1109.6887][1], Magesan, Gambetta, and Emerson showed that for any Pauli channel the diamond distance to the identity is equal to the trace distance between the associated Choi states. They prefer to phrase their results in terms

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Stefano Pirandola Jul 21 2017 09:43 UTC

This is very interesting. In my reading list!