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The model of the ideal rotary element of MoritaDec 28 2010Jan 05 2011Reversible computing is a concept reflecting physical reversibility. Until now several reversible systems have been investigated. In a series of papers Kenichi Morita defines the rotary element RE, that is a reversible logic element. By reversibility, ... More

A finiteness result for $p$-adic families of Bianchi modular formsFeb 08 2019We study $p$-adic families of cohomological automorphic forms for ${\mathrm{GL}}(2)$ over imaginary quadratic fields and prove that families interpolating a Zariski-dense set of classical cuspidal automorphic forms only occur under very restrictive conditions. ... More

An Infinitesimal $p$-adic Multiplicative Manin-Mumford ConjectureJul 05 2016Dec 13 2018Our results concern analytic functions on the open unit $p$-adic poly-disc in $\mathbb{C}^n_p$ centered at the multiplicative unit and we prove that such functions only vanish at finitely many $n$-tuples of roots of unity $(\zeta_1-1,\ldots,\zeta_n-1)$ ... More

An Infinitesimal $p$-adic Multiplicative Manin-Mumford ConjectureJul 05 2016Our results concern analytic functions on the open unit $p$-adic poly-disc in $\mathbb{C}^n_p$ centered at the multiplicative unit and we prove that such functions only vanish at finitely many $n$-tuples of roots of unity $(\zeta_1-1,\ldots,\zeta_n-1)$ ... More

The intersection and the union of the asynchronous systemsOct 20 2006The asynchronous systems $f$ are the models of the asynchronous circuits from digital electrical engineering. They are multi-valued functions that associate to each input $u:\mathbf{R}\to \{0,1\}^{m}$ a set of states $x\in f(u),$ where $x:\mathbf{R}\to ... More

Some first thoughts on the stability of the asynchronous systemsOct 29 2004The (non-initialized, non-deterministic) asynchronous systems (in the input-output sense) are multi-valued functions from m-dimensional signals to sets of n-dimensional signals, the concept being inspired by the modeling of the asynchronous circuits. ... More

The Delay-Insensitivity, the Hazard-Freedom, the Semi-Modularity and the Technical Condition of Good Running of the Discrete Time Asynchronous AutomataOct 31 2001The paper studies some important properties of the asynchronous (=timed) automata: the delay-insensitivity, the hazard-freedom, the semi-modularity and the technical condition of good running. Time is discrete.

Selected Topics in Asynchronous AutomataOct 31 2001The paper is concerned with defining the electrical signals and their models. The delays are discussed, the asynchronous automata - which are the models of the asynchronous circuits - and the examples of the clock generator and of the R-S latch are given. ... More

On the serial connection of the regular asynchronous systemsJun 20 2012The asynchronous systems f are multi-valued functions, representing the non-deterministic models of the asynchronous circuits from the digital electrical engineering. In real time, they map an 'admissible input' function u:R\rightarrow{0,1}^{m} to a set ... More

Examples of Models of the Asynchronous CircuitsFeb 17 2004We define the delays of a circuit, as well as the properties of determinism, order, time invariance, constancy, symmetry and the serial connection.

The dependence on the initial states and the transitivity of the regular autonomous asynchronous systemsDec 28 2010The asynchronous systems are non-deterministic real time, binary valued models of the asynchronous circuits from electronics. Autonomy means that there is no input and regularity means analogies with the (real) dynamical systems. We introduce the concepts ... More

Topics in asynchronous systemsSep 13 2004In the paper we define and characterize the asynchronous systems from the point of view of their autonomy, determinism, order, non-anticipation, time invariance, symmetry, stability and other important properties. The study is inspired by the models of ... More

Defining the symmetry of the universal semi-regular autonomous asynchronous systemsJun 20 2012Jul 20 2013The regular autonomous asynchronous systems are the non-deterministic Boolean dynamical systems and universality means the greatest in the sense of the inclusion. The paper gives four definitions of symmetry of these systems in a slightly more general ... More

The decomposition of the regular asynchronous systems as parallel connection of regular asynchronous systemsJun 20 2012The asynchronous systems are the non-deterministic models of the asynchronous circuits from the digital electrical engineering, where non-determinism is a consequence of the fact that modelling is made in the presence of unknown and variable parameters. ... More

Binary signals: a note on the prime period of a pointDec 22 2012The 'nice' $x:\mathbf{R}\rightarrow\{0,1\}^{n}$ functions from the asynchronous systems theory are called signals. The periodicity of a point of the orbit of the signal x is defined and we give a note on the existence of the prime period.

The equations of the ideal latchesApr 05 2008The latches are simple circuits with feedback from the digital electrical engineering. We have included in our work the C element of Muller, the RS latch, the clocked RS latch, the D latch and also circuits containing two interconnected latches: the edge ... More

Asynchronous pseudo-systemsMay 14 2005The paper introduces the concept of asynchronous pseudo-system. Its purpose is to correct/generalize/continue the study of the asynchronous systems (the models of the asynchronous circuits) that has been started in [1], [2].

The equations of the ideal latchesNov 05 2004Nov 08 2004The latches are simple circuits with feedback from the digital electrical engineering. We have included in our work the C element of Muller, the RS latch, the clocked RS latch, the D latch and also circuits containing two interconnected latches: the edge ... More

An Asynchronous Automata Approach to the Semantics of Temporal LogicOct 31 2001The paper presents the differential equations that characterize an asynchronous automaton and gives their solution x:R->{0,1}x...x{0,1}. Remarks are made on the connection between the continuous time and the discrete time of the approach. The continuous ... More

Universal regular autonomous asynchronous systems: omega-limit sets, invariance and basins of attractionDec 28 2010The asynchronous systems are the non-deterministic real time-binary models of the asynchronous circuits from electrical engineering. Autonomy means that the circuits and their models have no input. Regularity means analogies with the dynamical systems, ... More

On the Inertia of the Asynchronous CircuitsFeb 17 2004We present the bounded delays, the absolute inertia and the relative inertia.

Applications of the Differential Calculus in the Study of the Timed Automata: the Inertial Delay BufferOct 31 2001We write the relations that characterize the simpliest timed automaton, the inertial delay buffer, in two versions: the non-deterministic and the deterministic one, by making use of the derivatives of the R->{0,1} functions.

Introductory Topics in Binary Set FunctionsOct 31 2001Let X be a non-empty set and U a ring of subsets of X. The countable additive functions U->{0,1} are called measures. The paper gives some definitions (derivable measures, the Lebesgue-Stieltjes measures) and properties of these functions, its purpose ... More

On the basins of attraction of the regular autonomous asynchronous systemsJun 20 2012Jul 20 2013The Boolean autonomous dynamical systems, also called regular autonomous asynchronous systems are systems whose 'vector field' is a function {\Phi}:{0,1}^{n}{\to}{0,1}^{n} and time is discrete or continuous. While the synchronous systems have their coordinate ... More

Universal Regular Autonomous Asynchronous Systems: Fixed Points, Equivalencies and Dynamic BifurcationsJun 20 2012Jul 20 2013The asynchronous systems are the non-deterministic models of the asynchronous circuits from the digital electrical engineering. In the autonomous version, such a system is a set of functions x:R{\to}{0,1}^{n} called states (R is the time set). If an asynchronous ... More

Binary periodic signals and flowsNov 21 2014The concept of boolean autonomous deterministic regular asynchronous system has its origin in switching theory, the theory of modeling the switching circuits from the digital electrical engineering. The attribute boolean vaguely refers to the Boole algebra ... More

Defining the Delays of the Asynchronous CircuitsFeb 17 2004We define the delays of a circuit, as well as the properties of determinism, order, time invariance, constancy, symmetry and the serial connection.

Towards a Mathematical Theory of the Delays of the Asynchronous CircuitsFeb 17 2004The inequations of the delays of the asynchronous circuits are written, by making use of pseudo-Boolean differential calculus. We consider these efforts to be a possible starting point in the semi-formalized reconstruction of the digital electrical engineering ... More

Introductory Topics in Distributions over Binary Test FunctionsOct 31 2001We note with B2 the Boole algebra with two elements. We define for the R->B2 functions the limits, the derivatives, the differentiability, the test functions, the integrals. We also define the distributions over the space of these test functions, the ... More

Real Time Models of the Asynchronous Circuits: The Delay TheoryDec 17 2004The chapter from the book introduces the delay theory, whose purpose is the modeling of the asynchronous circuits from digital electrical engineering with ordinary and differential pseudo-boolean equations.

The consistency, the composition and the causality of the asynchronous flowsApr 21 2015Let $\Phi:\{0,1\}^{n}\longrightarrow\{0,1\}^{n}$. The asynchronous flows are (discrete time and real time) functions that result by iterating the coordinates $\Phi_{i}$ independently on each other. The purpose of the paper is that of showing that the ... More

Some properties of the regular asynchronous systemsApr 13 2008The asynchronous systems are the models of the asynchronous circuits from the digital electrical engineering. An asynchronous system f is a multi-valued function that assigns to each admissible input u a set f(u) of possible states x in f(u). A special ... More

The non-anticipation of the asynchronous systemsApr 12 2008The asynchronous systems are the models of the asynchronous circuits from the digital electrical engineering and non-anticipation is one of the most important properties in systems theory. Our present purpose is to introduce several concepts of non-anticipation ... More

Relatively inertial delaysNov 05 2006The paper studies the relatively inertial delays that represent one of the most important concepts in the modeling of the asynchronous circuits.

Sobolev-Lorentz spaces in the Euclidean setting and counterexamplesMay 27 2016This paper studies the inclusions between different Sobolev-Lorentz spaces $W^{1,(p,q)}(\Omega)$ defined on open sets $\Omega \subset {\mathbf{R}^n},$ where $n \ge 1$ is an integer, $1<p<\infty$ and $1 \le q \le \infty.$ We prove that if $1 \le q<r \le ... More

A noncommutative version of the Julia-Wolff-Caratheodory TheoremOct 19 2015Jan 25 2016The classical Julia-Wolff-Carath{\'e}odory Theorem characterizes the behaviour of the derivative of an analytic self-map of a unit disc or of a half-plane of the complex plane at certain boundary points. We prove a version of this result that applies ... More

Interaction of Magnetization and Heat Dynamics for Pulsed Domain Wall Movement with Joule HeatingJun 25 2016Sep 27 2016Pulsed domain wall movement is studied here in Ni80Fe20 nanowires on SiO2, using a fully integrated electrostatic, thermoelectric, and micromagnetics solver based on the Landau-Lifshitz-Bloch equation, including Joule heating, anisotropic magneto-resistance, ... More

Effective Field Model of Roughness in Magnetic StructuresAug 18 2015An effective field model is introduced here within the micromagnetics formulation, to study roughness in magnetic structures, by considering sub-exchange length roughness levels as a perturbation on a smooth structure. This allows the roughness contribution ... More

The coefficients of the period polynomialsFeb 16 2014A general description of the Vi\`ete coefficients of the gaussian period polynomials is given, in terms of certain symmetric representations of the subgroups and the corresponding quotient groups of the multiplicative group \mathbf{F}_{p}^{*} of a finite ... More

2d random Dirac fermions: large N approachJan 03 2002We study the symmetry classes for the random Dirac fermions in 2 dimensions. We consider $N_f$ species of fermions, coupled by different types of disorder. We analyse the renormalisation group flow at the order of one loop. At $N_f$ large, the disorder ... More

Sobolev-Lorentz spaces in the Euclidean setting and counterexamplesMay 27 2016Jan 29 2017This paper studies the inclusions between different Sobolev-Lorentz spaces $W^{1,(p,q)}(\Omega)$ defined on open sets $\Omega \subset {\mathbf{R}^n},$ where $n \ge 1$ is an integer, $1<p<\infty$ and $1 \le q \le \infty.$ We prove that if $1 \le q<r \le ... More

Quasiparticles in the multicomponenet Zhang-Hansson-Kivelson modelOct 19 2000Apr 26 2001We study the vortex solutions in a multicomponent Zhang-Hansson-Kivelson model for the fractional quantum Hall effect, at the self-dual point. Vortices with minimal free energy represent Laughlin quasiholes. We find at least two classes of solutions, ... More

Glauber Dynamics On The Cycle Is MonotoneMay 03 2003We study heat-bath Glauber dynamics for the ferromagnetic Ising model on a finite cycle (a graph where every vertex has degree two). We prove that the relaxation time $\tau_2$ is an increasing function of any of the couplings $J_{xy}$. We also prove some ... More

Sobolev-Lorentz capacity and its regularity in the Euclidean settingJul 26 2017Feb 18 2018This paper studies the Sobolev-Lorentz capacity and its regularity in the Euclidean setting for $n \ge 1$ integer. We extend here our previous results on the Sobolev-Lorentz capacity obtained for $n \ge 2.$ Moreover, for $n \ge 2$ integer we obtain a ... More

Generative Deep Neural Networks for Dialogue: A Short ReviewNov 18 2016Researchers have recently started investigating deep neural networks for dialogue applications. In particular, generative sequence-to-sequence (Seq2Seq) models have shown promising results for unstructured tasks, such as word-level dialogue response generation. ... More

A Survey of Available Corpora for Building Data-Driven Dialogue SystemsDec 17 2015Dec 22 2015During the past decade, several areas of speech and language understanding have witnessed substantial breakthroughs from the use of data-driven models. In the area of dialogue systems, the trend is less obvious, and most practical systems are still built ... More

Lower bounds for the density of locally elliptic Itô processesFeb 28 2007We give lower bounds for the density $p_T(x,y)$ of the law of $X_t$, the solution of $dX_t=\sigma (X_t) dB_t+b(X_t) dt,X_0=x,$ under the following local ellipticity hypothesis: there exists a deterministic differentiable curve $x_t, 0\leq t\leq T$, such ... More

On Area Comparison and Rigidity Involving the Scalar CurvatureSep 04 2013We prove a splitting theorem for Riemannian n-manifolds with scalar curvature bounded below by a negative constant and containing certain area-minimising hypersurfaces (Theorem 3). Thus we generalise [25,Theorem 3] by Nunes. This splitting result follows ... More

Saturation and Condensate Fraction Reduction of Cold Alpha MatterSep 09 2009Sep 15 2009The ground state energy of ideal alpha-matter at T=0 is analyzed within the framework of variational theory of Bose quantum liquids. Calculations are done for three local alpha-alpha potentials with positive volume integrals and two-body correlation functions ... More

Random soups, carpets and fractal dimensionsSep 24 2010We study some properties of a class of random connected planar fractal sets induced by a Poissonian scale-invariant and translation-invariant point process. Using the second-moment method, we show that their Hausdorff dimensions are deterministic and ... More

Sensitivity Analysis for Hybrid Systems and Systems with MemoryApr 18 2019We present an adjoint sensitivity method for hybrid discrete -- continuous systems, extending previously published forward sensitivity methods. We treat ordinary differential equations and differential-algebraic equations of index up to two (Hessenberg) ... More

Trajectory trapping and the evolution of drift turbulence beyond the quasilinear stageSep 10 2012Test modes on turbulent magnetized plasmas are studied taking into account the ion trapping that characterizes the E x B drift in the background turbulence. We show that trappyng provides the physical mechanism for the formation of large scale potential ... More

The Quantum Liquid of Alpha ClustersDec 16 2010Within the variational approach of Bose liquids we analyze the g.s. energy of charge neutral alpha matter at $T$=0. As a prerequisite for such calculation we take from the literature or propose new $\alp-\alp$ potentials that are particularly suitable ... More

Planar N=4 gauge theory and the Inozemtsev long range spin chainJan 09 2004Apr 05 2004We investigate whether the (planar, two complex scalar) dilatation operator of N=4 gauge theory can be, perturbatively and, perhaps, non-perturbatively, described by an integrable long range spin chain with elliptic exchange interaction. Such a chain ... More

Spectral properties of polynomials in independent Wigner and deterministic matricesNov 22 2016Sep 19 2017On the one hand, we prove that almost surely, for large dimension, there is no eigenvalue of a Hermitian polynomial in independent Wigner and deterministic matrices, in any interval lying at some distance from the supports of a sequence of deterministic ... More

Hindrance of ^{16}O+^{208}Pb fusion at extreme sub-barrier energiesNov 20 2007We analyze the fusion data for $^{16}$O+$^{208}$Pb using coupled-channels calculations. We include couplings to the low-lying surface excitations of the projectile and target and study the effect of the ($^{16}$O,$^{17}$O) one-neutron pickup. The hindrance ... More

The Lebesgue decomposition of the free additive convolution of two probability distributionsMar 03 2006Aug 22 2007We prove that the free additive convolution of two Borel probability measures supported on the real line can have a component that is singular continuous with respect to the Lebesgue measure on the real line only if one of the two measures is a point ... More

Embedding theorems for actions on generalized trees, IMar 24 2010Sep 13 2010Using suitable deformations of simplicial trees and the duality theory for median sets, we show that every free action on a median set can be extended to a free and transitive one. We also prove that the category of median groups is a reflective full ... More

Conformal field theory and edge excitations for the principal series of quantum Hall fluidsDec 13 1999Apr 26 2001Motivated by recent experimental results, we reconsider the theory of the edge excitations for the fractional Hall effect at filling factors $\nu=p/(2np+1)$. We propose to modify the standard $u(1)\otimes su(p)$ edge theory for this series by introducing ... More

Spectral properties of polynomials in independent Wigner and deterministic matricesNov 22 2016On the one hand, we prove that almost surely, for large dimension, there is no eigenvalue of a Hermitian polynomial in independent Wigner and deterministic matrices, in any interval lying at some distance from the supports of a sequence of deterministic ... More

Arithmetic-arboreal residue structures induced by Prufer extensions : An axiomatic approachNov 03 2010We present an axiomatic framework for the residue structures induced by Prufer extensions with a stress upon the intimate connection between their arithmetic and arboreal theoretic properties. The main result of the paper provides an adjunction relationship ... More

Fast simulation of new coins from oldSep 13 2003Mar 31 2005Let S\subset (0,1). Given a known function f:S\to (0,1), we consider the problem of using independent tosses of a coin with probability of heads p (where p\in S is unknown) to simulate a coin with probability of heads f(p). We prove that if S is a closed ... More

Multiresolution Recurrent Neural Networks: An Application to Dialogue Response GenerationJun 02 2016Jun 14 2016We introduce the multiresolution recurrent neural network, which extends the sequence-to-sequence framework to model natural language generation as two parallel discrete stochastic processes: a sequence of high-level coarse tokens, and a sequence of natural ... More

Generating Factoid Questions With Recurrent Neural Networks: The 30M Factoid Question-Answer CorpusMar 22 2016May 29 2016Over the past decade, large-scale supervised learning corpora have enabled machine learning researchers to make substantial advances. However, to this date, there are no large-scale question-answer corpora available. In this paper we present the 30M Factoid ... More

A Survey of Available Corpora for Building Data-Driven Dialogue SystemsDec 17 2015Mar 21 2017During the past decade, several areas of speech and language understanding have witnessed substantial breakthroughs from the use of data-driven models. In the area of dialogue systems, the trend is less obvious, and most practical systems are still built ... More

The Bottleneck Simulator: A Model-based Deep Reinforcement Learning ApproachJul 12 2018Deep reinforcement learning has recently shown many impressive successes. However, one major obstacle towards applying such methods to real-world problems is their lack of data-efficiency. To this end, we propose the Bottleneck Simulator: a model-based ... More

A Hierarchical Latent Variable Encoder-Decoder Model for Generating DialoguesMay 19 2016Jun 14 2016Sequential data often possesses a hierarchical structure with complex dependencies between subsequences, such as found between the utterances in a dialogue. In an effort to model this kind of generative process, we propose a neural network-based generative ... More

Proceedings Second International Workshop on Algebraic Methods in Model-based Software EngineeringJun 29 2011Over the past years there has been quite a lot of activity in the algebraic community about using algebraic methods for providing support to model-driven software engineering. The aim of this workshop is to gather researchers working on the development ... More

Nonuniqueness of weak solutions to the Navier-Stokes equationSep 28 2017Oct 11 2018For initial datum of finite kinetic energy, Leray has proven in 1934 that there exists at least one global in time finite energy weak solution of the 3D Navier-Stokes equations. In this paper we prove that weak solutions of the 3D Navier-Stokes equations ... More

Regularization properties of the 2D homogeneous Boltzmann equation without cutoffNov 13 2009Nov 16 2009We consider the 2-dimensional spatially homogeneous Boltzmann equation for hard potentials. We assume that the initial condition is a probability measure that has some exponential moments and is not a Dirac mass. We prove some regularization properties: ... More

The filamentation of the laser beam as a labyrinth instabilityJun 13 2015At incident powers much higher than the threshold for filamentation a pulse from a high-power laser generates in the transversal plane a complex structure. It consists of randomly meandering stripes defining connected regions where the field intensity ... More

Helicity fluctuation, generation of linking number and effect on resistivityDec 28 2006The energy of the stochastic magnetic field is bounded from below by a topological quantity expressing the degree of linkage of the field lines. When the bound is saturated one can assume that the storage of a certain magnetic energy requires a minimal ... More

Exact vortex solution of the Jacobs-Rebbi equation for ideal fluidsOct 06 2003The Jacobs-Rebbi equation arises in many contexts where vortical motion in two-dimensional ideal media is investigated. Alternatively, it can be derived in the Abelian Higgs field theory. It is considered non-integrable and numerical solutions have been ... More

On the nature of intermittency in weakly dissipative systemsAug 08 2002We propose a new perspective on the intermittency in weakly dissipative systems. It is focused on the elementary (burst-like) event separating states with different properties. This event is seen as a real-space-time manifestation of an instanton connecting ... More

Effect of density changes on tokamak plasma confinementFeb 21 2015Jul 10 2015A change of the particle density (by gas puff, pellets or impurity seeding) during the plasma discharge in tokamak produces a radial current and implicitly a torque and rotation that can modify the state of confinement. After ionization the newly born ... More

Larmor radius effects on impurity transport in turbulent plasmasAug 05 2004Test particle transport determined by the Lorentz force in turbulent magnetized plasmas is studied. The time dependent diffusion coefficient, valid for the whole range of parameters, is obtained by developing the decorrelation trajectory method. The effects ... More

Faster Fair Solution for the Reader-Writer ProblemSep 18 2013A fast fair solution for Reader-Writer Problem is presented.

Riesz transform and integration by parts formulas for random variablesNov 13 2009Apr 29 2010We use integration by parts formulas to give estimates for the $L^p$ norm of the Riesz transform. This is motivated by the representation formula for conditional expectations of functionals on the Wiener space already given in Malliavin and Thalmaier. ... More

Holder continuity for a drift-diffusion equation with pressureMar 19 2011We address the persistence of H\"older continuity for weak solutions of the linear drift-diffusion equation with nonlocal pressure \[ u_t + b \cdot \grad u - \lap u = \grad p,\qquad \grad\cdot u =0 \] on $[0,\infty) \times \R^{n}$, with $n \geq 2$. The ... More

Total variation distance between stochastic polynomials and invariance principlesMay 15 2017The goal of this paper is to estimate the total variation distance between two general stochastic polynomials. As a consequence one obtains an invariance principle for such polynomials. This generalizes known results concerning the total variation distance ... More

Regularity of probability laws by using an interpolation methodOct 31 2012We study the problem of the existence and regularity of a probability density in an abstract framework based on a "balancing" with approximating absolutely continuous laws. Typically, the absolutely continuous property for the approximating laws can be ... More

Aging processes in reversible reaction-diffusion systemsApr 11 2008Reversible reaction-diffusion systems display anomalous dynamics characterized by a power-law relaxation toward stationarity. In this paper we study in the aging regime the nonequilibrium dynamical properties of some model systems with reversible reactions. ... More

Almost global existence for the Prandtl boundary layer equationsFeb 15 2015Sep 25 2015We consider the Prandtl boundary layer equations on the half plane, with initial datum that lies in a weighted $H^1$ space with respect to the normal variable, and is real-analytic with respect to the tangential variable. The boundary trace of the horizontal ... More

Integration by parts formula with respect to jump times for stochastic differential equationsApr 19 2010We establish an integration by parts formula based on jumps times in an abstract framework in order to study the regularity of the law for processes solution of stochastic differential equations with jumps.

Results of the four-wave kinetic integral computation for spectra of special forms. The case of Zakharov spectraJan 11 2014With the aim to show explicitly the non stationarity of the Zakharov spectra, obtained analytically as the stationary solution of the four-wave kinetic equation for stochastic nonlinear surface gravity waves[1,2], we have calculated directly the proper ... More

Quantum cryptanalysis of symmetric, public-key and hash-based cryptographic schemesFeb 06 2019Quantum algorithms can break factoring and discrete logarithm based cryptography and weaken symmetric cryptography and hash functions. In order to estimate the real-world impact of these attacks, apart from tracking the development of fault-tolerant quantum ... More

Detecting Singleton Review Spammers Using Semantic SimilaritySep 09 2016Online reviews have increasingly become a very important resource for consumers when making purchases. Though it is becoming more and more difficult for people to make well-informed buying decisions without being deceived by fake reviews. Prior works ... More

Higher moments of arithmetic functions in short intervals: a geometric perspectiveApr 07 2016Dec 01 2016We study the geometry associated to the distribution of certain arithmetic functions, including the von Mangoldt function and the M\"obius function, in short intervals of polynomials over a finite field $\mathbb{F}_q$. Using the Grothendieck-Lefschetz ... More

Topological Entropy and Diffeomorphisms of Surfaces with Wandering DomainsOct 07 2009Let $M$ be a closed surface and $f$ a diffeomorphism of $M$. A diffeomorphism is said to permute a dense collection of domains, if the union of the domains are dense and the iterates of any one domain are mutually disjoint. In this note, we show that ... More

A Regularized Framework for Sparse and Structured Neural AttentionMay 22 2017Feb 23 2019Modern neural networks are often augmented with an attention mechanism, which tells the network where to focus within the input. We propose in this paper a new framework for sparse and structured attention, building upon a smoothed max operator. We show ... More

Rare Events Statistics in Reaction--Diffusion SystemsApr 09 2004Apr 20 2004We develop an efficient method to calculate probabilities of large deviations from the typical behavior (rare events) in reaction--diffusion systems. The method is based on a semiclassical treatment of underlying "quantum" Hamiltonian, encoding the system's ... More

On the analyticity and Gevrey class regularity up to the boundary for the Euler EquationsJul 13 2010We consider the Euler equations in a three-dimensional Gevrey-class bounded domain. Using Lagrangian coordinates we obtain the Gevrey-class persistence of the solution, up to the boundary, with an explicit estimate on the rate of decay of the Gevrey-class ... More

On a transport equation with nonlocal driftAug 05 2014In \cite{CordobaCordobaFontelos05}, C\'ordoba, C\'ordoba, and Fontelos proved that for some initial data, the following nonlocal-drift variant of the 1D Burgers equation does not have global classical solutions \[ \partial_t \theta +u \; \partial_x \theta ... More

The Domain of Analyticity of Solutions to the Three-Dimensional Euler Equations in a Half SpaceJul 13 2010We address the problem of analyticity up to the boundary of solutions to the Euler equations in the half space. We characterize the rate of decay of the real-analyticity radius of the solution $u(t)$ in terms of $\exp{\int_{0}^{t} \Vert \nabla u(s) \Vert_{L^\infty} ... More

Trajectory statistics and turbulence evolutionJul 29 2015The aim of this paper is to understand the tendency to organization of the turbulence in two-dimensional ideal fluids. We show that nonlinear processes as inverse cascade of the energy and vorticity concentration are essentially determined by trajectory ... More

Trapping, anomalous transport and quasi-coherent structures in magnetically confined plasmasMar 12 2009Strong electrostatic turbulence in magnetically confined plasmas is characterized by trapping or eddying of particle trajectories produced by the $E\times B$ stochastic drift. Trapping is shown to produce strong effects on test particles and on test modes. ... More

Self-duality of the asymptotic relaxation states of fluids and plasmasAug 08 2002The states of asymptotic relaxation of 2-dimensional fluids and plasma present a high degree of regularity and obey to the sinh-Poisson equation. We find that embedding the classical fluid description into a field-theoretical framework, the same equation ... More

Exact periodic solutions of the Liouville equation and the "snake" of density in JETAug 31 2004The "snake" is a persistent density perturbation at the rational q-surfaces after pellet injection. Together with other phenomena (density pinch and profile resiliancy) it can be traced back to the extremum of an action functional for line-vortices in ... More

Higher regularity of Holder continuous solutions of parabolic equations with singular drift velocitiesFeb 02 2011Motivated by an equation arising in magnetohydrodynamics, we prove that Holder continuous weak solutions of a nonlinear parabolic equation with singular drift velocity are classical solutions. The result is proved using the space-time Besov spaces introduced ... More

Benchmarking the quantum cryptanalysis of symmetric, public-key and hash-based cryptographic schemesFeb 06 2019Feb 07 2019Quantum algorithms can break factoring and discrete logarithm based cryptography and weaken symmetric cryptography and hash functions. In order to estimate the real-world impact of these attacks, apart from tracking the development of fault-tolerant quantum ... More