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Gaussian Prototypical Networks for Few-Shot Learning on OmniglotAug 09 2017We propose a novel architecture for $k$-shot classification on the Omniglot dataset. Building on prototypical networks, we extend their architecture to what we call Gaussian prototypical networks. Prototypical networks learn a map between images and embedding ... More

Towards understanding feedback from supermassive black holes using convolutional neural networksDec 02 2017Supermassive black holes at centers of clusters of galaxies strongly interact with their host environment via AGN feedback. Key tracers of such activity are X-ray cavities -- regions of lower X-ray brightness within the cluster. We present an automatic ... More

The Goldilocks zone: Towards better understanding of neural network loss landscapesJul 06 2018Nov 12 2018We explore the loss landscape of fully-connected and convolutional neural networks using random, low-dimensional hyperplanes and hyperspheres. Evaluating the Hessian, $H$, of the loss function on these hypersurfaces, we observe 1) an unusual excess of ... More

Large Scale Structure of Neural Network Loss LandscapesJun 11 2019There are many surprising and perhaps counter-intuitive properties of optimization of deep neural networks. We propose and experimentally verify a unified phenomenological model of the loss landscape that incorporates many of them. High dimensionality ... More

Exploring the cooperative regimes in a model of agents without memory or "tags": indirect reciprocity vs. selfish incentivesNov 15 2002The self-organization in cooperative regimes in a simple mean-field version of a model based on "selfish" agents which play the Prisoner's Dilemma (PD) game is studied. The agents have no memory and use strategies not based on direct reciprocity nor 'tags'. ... More

Stiffness: A New Perspective on Generalization in Neural NetworksJan 28 2019We investigate neural network training and generalization using the concept of stiffness. We measure how stiff a network is by looking at how a small gradient step on one example affects the loss on another example. In particular, we study how stiffness ... More

Adaptive Quantum State Tomography with Neural NetworksDec 17 2018Quantum State Tomography is the task of determining an unknown quantum state by making measurements on identical copies of the state. Current algorithms are costly both on the experimental front -- requiring vast numbers of measurements -- as well as ... More

Cooperation and Self-Regulation in a Model of Agents Playing Different GamesJun 23 2003A simple model for cooperation between "selfish" agents, which play an extended version of the Prisoner's Dilemma(PD) game, in which they use arbitrary payoffs, is presented and studied. A continuous variable, representing the probability of cooperation, ... More

On Evolutionary Spatial Heterogeneous GamesDec 20 2007How coperation between self-interested individuals evolve is a crucial problem, both in biology and in social sciences, that is far from being well understood. Evolutionary game theory is a useful approach to this issue. The simplest model to take into ... More

Fixed boundary conditions and phase transitions in pure gauge compact QEDJun 02 1994We have simulated the pure gauge compact QED with fixed boundary conditions, on lattices from $6^4$ to $16^4$. We argue that a lattice with this fixed boundary imposition corresponds actually to a lattice with spherical topology. We have found the presence ... More

The Effect of Large Amplitude Fluctuations in the Ginzburg-Landau Phase TransitionOct 09 2000The lattice Ginzburg-Landau model in d=3 and d=2 is simulated, for different values of the coherence length $\xi$ in units of the lattice spacing $a$, using a Monte Carlo method. The energy, specific heat, vortex density $v$, helicity modulus $\Gamma_\mu$ ... More

Evolutionary Markovian Strategies in 2 x 2 Spatial GamesJun 07 2006Evolutionary spatial 2 x 2 games between heterogeneous agents are analyzed using different variants of cellular automata (CA). Agents play repeatedly against their nearest neighbors 2 x 2 games specified by a rescaled payoff matrix with two parameteres. ... More

Weak lensing at the limit of the sky background noiseAug 16 1996Recent weak lensing observations have pushed the use of 4 meter-class telescopes to the limits of their capabilities with exposure times exceeding several hours. The leading idea is that the surface density of faint galaxies up to very faint magnitude ... More

Fractional Statistics in Three Dimensions: Compact Maxwell-Higgs SystemSep 21 1995We show that a (3+1)-dimensional system composed of an open magnetic vortex and an electrical point charge exhibits the phenomenon of Fermi-Bose transmutation. In order to provide the physical realization of this system we focus on the lattice compact ... More

Gravitational Lensing and Tests of the Cosmological ConstantFeb 01 1998The case for a flat Cold Dark Matter model with a positive cosmological constant $\Lambda$ has been recently strongly advocated by some theoreticians. In this paper we give the observers point of view to the light of the most recent observations with ... More

Limit theorems for some adaptive MCMC algorithms with subgeometric kernelsJul 18 2008Sep 03 2009This paper deals with the ergodicity and the existence of a strong law of large numbers for adaptive Markov Chain Monte Carlo. We show that a diminishing adaptation assumption together with a drift condition for positive recurrence is enough to imply ... More

Highly ionized absorbers at high redshiftJun 28 2005We investigate the existence of a metal-rich OVI population in 10 high spectral resolution quasar spectra and define observational criteria for this class of absorbers. The low temperatures of nearly half of all OVI absorbers (redshifts 2.0 to 2.6), implied ... More

Formation of Cooper Pairs as a Consequence of Exchange InteractionJan 15 2015Aug 03 2016Analyzing the exchange energy of two conduction electrons in the crystal at a many-body approach we find, that the exchange energy may be negative and, thus, the singlet state may be favorable. A full overlap in the real space of the wave functions of ... More

Uniform bounds for robust mean estimatorsDec 09 2018Dec 29 2018Median-of-means technique is an elegant and general method for estimating the expectation of a random variable that provides strong non-asymptotic guarantees under minimal assumptions on the underlying distribution. We consider generalizations of the ... More

Landau dispersion relationship in self-consistent field theoryMar 05 2019The spectral problem is studied associated with Maxwell-Boltzmann equations describing collisionless plasma. Formula for instability index is obtained and effective conditions of two-stream instability are given.

Critical percolation in the planeSep 24 2009We study scaling limits and conformal invariance of critical site percolation on triangular lattice. We show that some percolation-related quantities are harmonic conformal invariants, and calculate their values in the scaling limit. As a particular case ... More

Matter Fields in the Loop Representation of the Partition FunctionFeb 17 1994We present the extension of the Lagrangian $loop$ representation in such a way to introduce matter fields. The partition function of lattice compact U(1) Gauge-Higgs model is expressed as a sum over closed as much as open surfaces. These surfaces correspond ... More

Loop Action for Lattice U(1) Gauge TheoryFeb 11 1994It is showed that the very recently introduced Lagrangian $loop$ formulation of the lattice Maxwell theory is equivalent to the Villain form in 2+1 dimensions. A transparent description of the classical $loop$ action is given in pure geometrical terms ... More

Limit theorems for some adaptive MCMC algorithms with subgeometric kernels: Part IINov 02 2009We prove a central limit theorem for a general class of adaptive Markov Chain Monte Carlo algorithms driven by sub-geometrically ergodic Markov kernels. We discuss in detail the special case of stochastic approximation. We use the result to analyze the ... More

Loop Representation of the Partition Function of Lattice U(1) Gauge TheoryFeb 17 1994We introduce in a natural and straigthforward way the $loop$ (Lagrangian) $representation$ for the partition function of pure compact lattice QED. The corresponding classical lattice loop action is proportional to the quadratic area of the loop world ... More

Smoothed quantile regression processes for binary response modelsFeb 22 2013In this paper, we consider binary response models with linear quantile restrictions. Considerably generalizing previous research on this topic, our analysis focuses on an infinite collection of quantile estimators. We derive a uniform linearization for ... More

Towards conformal invariance of 2D lattice modelsJul 31 2007Many 2D lattice models of physical phenomena are conjectured to have conformally invariant scaling limits: percolation, Ising model, self-avoiding polymers, ... This has led to numerous exact (but non-rigorous) predictions of their scaling exponents and ... More

Cyclically regular semigroupsMar 16 2011We study varieties of semigroups related to completely 0-simple semigroup. We present here an algorithmic descriptions of these varieties interms of "forbidden" semigroups.

Spectrum of magnetohydrodynamic turbulenceNov 10 2005Feb 24 2006We propose a phenomenological theory of strong incompressible magnetohydrodynamic turbulence in the presence of a strong large-scale external magnetic field. We argue that in the inertial range of scales, magnetic-field and velocity-field fluctuations ... More

Framed moduli spaces and tuples of operatorsMar 14 2012In this work we address the classical problem of classifying tuples of linear operators and linear functions on a finite dimensional vector space up to base change. Having adopted for the situation considered a construction of framed moduli spaces of ... More

Moduli space of symmetric connectionsDec 28 2001The action of origin-preserving diffeomorphisms on a space of jets of symmetric connections is considered. Dimensions of moduli spaces of generic connections are calculated. Poincar\'e series of the geometric structure of symmetric connection is constructed, ... More

Kolmogorov-Burgers Model for Star Forming TurbulenceAug 18 2001Oct 23 2001The process of star formation in interstellar molecular clouds is believed to be controlled by driven supersonic magnetohydrodynamic turbulence. We suggest that in the inertial range such turbulence obeys the Kolmogorov law, while in the dissipative range ... More

Hypercyclic operators on topological vector spacesAug 19 2010Bonet, Frerick, Peris and Wengenroth constructed a hypercyclic operator on the locally convex direct sum of countably many copies of the Banach space $\ell_1$. We extend this result. In particular, we show that there is a hypercyclic operator on the locally ... More

The Connection between the Quantum Frequency of Radiation and Frequencies of Circling of the Electron in Atom of HydrogenFeb 04 2002The connection between the quantum frequency of radiation by the transition of the electron from orbit n to orbit k and frequencies of circling of electron in these orbits for the atom of hydrogen is determined.

B-spline normal multi-scale transforms for planar curvesNov 18 2013Normal multi-scale transform [4] is a nonlinear multi-scale transform for representing geometric objects that has been recently investigated [1, 7, 10]. The restrictive role of the exact order of polynomial reproduction $P_e$ of the approximating subdivision ... More

Sub-Gaussian estimators of the mean of a random matrix with heavy-tailed entriesMay 23 2016Jun 29 2016Estimation of the covariance matrix has attracted a lot of attention of the statistical research community over the years, partially due to important applications such as Principal Component Analysis. However, frequently used empirical covariance estimator ... More

Discrete Complex Analysis and ProbabilitySep 30 2010We discuss possible discretizations of complex analysis and some of their applications to probability and mathematical physics, following our recent work with Dmitry Chelkak, Hugo Duminil-Copin and Cl\'ement Hongler.

Conformal invariance in random cluster models. I. Holomorphic fermions in the Ising modelJul 31 2007We construct discrete holomorphic observables in the Ising model at criticality and show that they have conformally covariant scaling limits (as mesh of the lattice tends to zero). In the sequel those observables are used to construct conformally invariant ... More

Norm attaining operators and pseudospectrumSep 06 2012It is shown that if $1<p<\infty$ and $X$ is a subspace or a quotient of an $\ell_p$-direct sum of finite dimensional Banach spaces, then for any compact operator $T$ on $X$ such that $\|I+T\|>1$, the operator $I+T$ attains its norm. A reflexive Banach ... More

Dimension of quasicirclesApr 07 2009We introduce canonical antisymmetric quasiconformal maps, which minimize the quasiconformality constant among maps sending the unit circle to a given quasicircle. As an application we prove Astala's conjecture that the Hausdorff dimension of a $k$-quasicircle ... More

Grafting Seiberg-Witten monopolesOct 26 2001Feb 23 2003We demonstrate that the operation of taking disjoint unions of J-holomorphic curves (and thus obtaining new J-holomorphic curves) has a Seiberg-Witten counterpart. The main theorem asserts that, given two solutions (A_i, psi_i), i=0,1 of the Seiberg-Witten ... More

Framed moduli and Grassmannians of submodulesOct 22 2010Dec 20 2010In this work we study a realization of moduli spaces of framed quiver representations as Grassmannians of submodules devised by Marcus Reineke. Obtained is a generalization of this construction for finite dimensional associative algebras and for quivers ... More

Aproximation of periodical function in weighted Orlicz spacesJan 12 2015In this paper we obtained some direct and inverse theorems of approximation theory for $\psi$-differentiable functions in the metric weighted Orlicz spaces with weights, which belong to the class of Muckenhoupt.

Pointwise universal trigonometric seriesSep 06 2012A series $S_a=\sum\limits_{n=-\infty}^\infty a_nz^n$ is called a {\it pointwise universal trigonometric series} if for any $f\in C(\T)$, there exists a strictly increasing sequence $\{n_k\}_{k\in\N}$ of positive integers such that $\sum\limits_{j=-n_k}^{n_k} ... More

Remarks on common hypercyclic vectorsSep 06 2012We treat the question of existence of common hypercyclic vectors for families of continuous linear operators. It is shown that for any continuous linear operator $T$ on a complex Fr\'echet space $X$ and a set $\Lambda\subseteq \R_+\times\C$ which is not ... More

The signature of an even symmetric form with vanishing associated linking formApr 23 2012Apr 25 2012We prove that the signature of an even, symmetric form on a finite rank integral lattice, has signature divisible by 8, provided its associated linking form vanishes in the Witt group of linking forms. Our result generalizes the well know fact that an ... More

Partial fractioning reduction of perturbative amplitudesDec 23 2011A new method is presented for the simplification of loop integrals in one particle irreducible diagrams with large numbers of external lines, based on the partial fractioning of products of propagators. Whenever a loop diagram in $d$ dimensions has $d+1$ ... More

Top Quark Properties at the TevatronFeb 11 2017I report on the status of the studies of top-quark properties carried out by the Tevatron experiments CDF and D0.

Adaptive quantum tomographyOct 10 2016We provide a review of the experimental and theoretical research in the field of quantum tomography with an emphasis on recently developed adaptive protocols. Several statistical frameworks for adaptive experimental design are discussed. We argue in favor ... More

Inferring hierarchical structure of spatial and generic complex networks through a modeling frameworkDec 15 2017Our recent paper [Grauwin et al. Sci. Rep. 7 (2017)] demonstrates that community and hierarchical structure of the networks of human interactions largely determines the least and should be taken into account while modeling them. In the present proof-of-concept ... More

The Spectral Problem and Algebras Associated with Extended Dynkin GraphsApr 06 2009The Spectral Problem is to describe possible spectra $\sigma (A_j)$ for an irreducible $n$-tuple of Hermitian operators s.t. $A_1+...+A_n$ is a scalar operator. In case when $m_j= | \sigma (A_j)|$ are finite and a rooted tree ${\rm T}_{m_1,..., m_n}$ ... More

A complete locally convex space of countable dimension admitting an operator with no invariant subspacesSep 14 2010We construct a complete locally convex topological vector space $X$ of countable algebraic dimension and a continuous linear operator $T:X\to X$ such that $T$ has no non-trivial closed invariant subspaces.

Hypercyclic tuples of operators on $C^n$ and $R^n$Aug 20 2010A tuple $(T_1,\dots,T_n)$ of continuous linear operators on a topological vector space $X$ is called hypercyclic if there is $x\in X$ such that the the orbit of $x$ under the action of the semigroup generated by $T_1,\dots,T_n$ is dense in $X$. This concept ... More

Self-detection of x-ray Fresnel transmissivity using photoelectron-induced gas ionizationMay 27 2015Jan 18 2016Electric response of an x-ray mirror enclosed in a gas flow ionization chamber was studied under the conditions of total external reflection for hard x-rays. It is shown that the electric response of the system as a function of the incidence angle is ... More

Painleve Classification of Polynomial Ordinary Differential Equations of Arbitrary Order and Second DegreeOct 09 2014The problem of Painleve classification of ordinary differential equations lasting since the end of XIX century saw significant advances for the limited equation order, however not that much for the equations of higher orders. In this work we propose the ... More

On the Spectrum of Magnetohydrodynamic TurbulenceMar 02 2005Jun 17 2005We propose a phenomenological model for incompressible magnetohydrodynamic turbulence. We argue that nonlinear-wave interaction weakens as the energy cascade proceeds to small scales, however, the anisotropy of fluctuations along the large-scale magnetic ... More

Powers of sets in free groupsMay 11 2010Nov 23 2012We prove that |A^n| > c_n |A|^{[\frac{n+1}{2}]} for any finite subset A of a free group if A contains at least two noncommuting elements, where c_n>0 are constants not depending on A. Simple examples show that the order of these estimates are the best ... More

Operators commuting with the Volterra operator are not weakly supercyclicMar 10 2009We prove that any bounded linear operator on $L_p[0,1]$ for $1\leq p<\infty$, commuting with the Volterra operator $V$, is not weakly supercyclic, which answers affirmatively a question raised by L\'eon-Saavedra and Piqueras-Lerena. It is achieved by ... More

Operators Similar to Contractions and Their Similarity to a Normal OperatorNov 10 2001It is proved recently by Benamara-Nikolski that a contraction having finite defects and spectrum not filling in the closed unit disc, is similar to a normal operator if and only if it has the so-called linear resolvent growth property. We obtain results ... More

On The Painleve Property For A Class Of Quasilinear Partial Differential EquationsSep 11 2018The last decades saw growing interest across multiple disciplines in nonlinear phenomena described by partial differential equations (PDE). Integrability of such equations is tightly related with the Painleve property - solutions being free from moveable ... More

Effect of slip boundary conditions on interfacial stability of two-layer viscous fluids under shearJun 06 2015Jun 09 2015The traditional approach in the study of hydrodynamic stability of stratified fluids includes the stick boundary conditions between layers. However, this rule may be violated in polymer systems and as a consequence various instabilities may arise. The ... More

Positivstellensatz and flat functionals on path *-algebrasApr 06 2009Jun 07 2009We consider the class of non-commutative *-algebras which are path algebras of doubles of quivers with the natural involutions. We study the problem of extending positive truncated functionals on such *-algebras. An analog of the solution of the truncated ... More

Finite Size Analysis of the U(1) Phase Transition using the World-sheet FormulationJul 31 1998We present a high statistics analysis of the pure gauge compact U(1) lattice theory using the the world-sheet or Lagrangian loop representation. We have applied a simulation method that deals directly with (gauge invariant) integer variables on plaquettes. ... More

The SDSS Damped Lya Survey: Data Release 1Mar 16 2004Apr 28 2004We present the results from an automated search for damped Lya (DLA) systems in the quasar spectra of Data Release 1 from the Sloan Digital Sky Survey (SDSS-DR1). At z~2.5, this homogeneous dataset has greater statistical significance than the previous ... More

Worldsheet Formulation for Lattice Staggered FermionsJul 22 1996Sep 09 1997The worldsheet formulation is introduced for lattice gauge theories with dynamical fermions. The partition function of lattice compact QED with staggered fermions is expressed as a sum over surfaces with border on self-avoiding fermionic paths. The surfaces ... More

Probing dark matter caustics with weak lensingJun 02 2005Mar 16 2006Caustics are high-density structures that form frequently in collisionless media. Under self-gravity, cold dark matter flows focus onto caustics which are yet to be resolved in numerical simulations and or observed in the real world. If detected, caustics ... More

Smoothed quantile regression processes for binary response modelsFeb 22 2013Apr 04 2019In this paper, we consider binary response models with linear quantile restrictions. Considerably generalizing previous research on this topic, our analysis focuses on an infinite collection of quantile estimators. We derive a uniform linearisation for ... More

Orbits of coanalytic Toeplitz operators and weak hypercyclicityOct 11 2012We prove a new criterion of weak hypercyclicity of a bounded linear operator on a Banach space. Applying this criterion, we solve few open questions. Namely, we show that if $G$ is a region of $\C$ bounded by a smooth Jordan curve $\Gamma$ such that $G$ ... More

Compact operators without extended eigenvaluesSep 07 2012A complex number $\lambda$ is called an extended eigenvalue of a bounded linear operator $T$ on a Banach space $\B$ if there exists a non-zero bounded linear operator $X$ acting on $\B$ such that $XT=\lambda TX$. We show that there are compact quasinilpotent ... More

On Some Extensions of Bernstein's Inequality for Self-adjoint OperatorsDec 22 2011Apr 14 2017We present some extensions of Bernstein's concentration inequality for random matrices. This inequality has become a useful and powerful tool for many problems in statistics, signal processing and theoretical computer science. The main feature of our ... More

Moduli space of Fedosov structuresOct 30 2003We consider the space of germs of Fedosov structures at a point, together with the group of origin-preserving diffeomorphisms acting on it. We calculate dimensions of moduli spaces of $k$-jets of generic structures and construct Poincar\'e series. It ... More

Electrodynamics of accelerated charges or Why electron does not radiate in Rutherford's atomMar 20 2000It is shown, that the radiation of the charge, moving with uniform acceleration or uniformly moving round a circle and also freely moving in a gravitational field, contradicts the principle of equivalence. It is also shown, that the interaction of the ... More

Moduli Space of General ConnectionsOct 25 2010We consider local invariants of general connections (with torsion). The group of origin-preserving diffeomorphisms acts on a space of jets of general connections. Dimensions of moduli spaces of generic connections are calculated. Poincar\'e series of ... More

Chaotic Banach algebrasAug 19 2010We construct an infinite dimensional non-unital Banach algebra $A$ and $a\in A$ such that the sets $\{za^n:z\in\C,\ n\in\N\}$ and $\{({\bf 1}+a)^na:n\in\N\}$ are both dense in $A$, where $\bf 1$ is the unity in the unitalization $A^{\#}=A\oplus \spann\{{\bf ... More

Forest fires on $\Z_+$ with ignition only at 0Jul 10 2009Sep 15 2009We consider a version of the forest fire model on graph $G$, where each vertex of a graph becomes occupied with rate one. A fixed vertex $v_0$ is hit by lightning with the same rate, and when this occurs, the whole cluster of occupied vertices containing ... More

Stokes Theorem for Lipschitz forms on a smooth manifoldMay 27 2008Stokes theorem holds for Lipschitz forms on a smooth manifold.

Complex network representation through multi-dimensional node projectionJun 10 2018Complex network topology might get pretty complicated challenging many network analysis objectives, such as community detection for example. This however makes common emergent network phenomena such as scale-free topology or small-world property even ... More

Nice Banach Modules and Invariant SubspacesSep 05 2012Let $\A$ be a semisimple unital commutative Banach algebra. We say that a Banach $\A$-module $M$ is nice if every proper closed submodule of $M$ is contained in a closed submodule of $M$ of codimension 1. We provide examples of nice and non-nice modules. ... More

Heegaard Floer genus bounds for Dehn surgeries on knotsFeb 20 2012Jul 22 2013We provide a new obstruction for a rational homology 3-sphere to arise by Dehn surgery on a given knot in the 3-sphere. The obstruction takes the form of an inequality involving the genus of the knot, the surgery coefficient, and a count of L-structures ... More

Research into Orbital Motion Stability in System of Two Magnetically Interacting BodiesJan 17 2011The stability of the orbital motion of two long cylindrical magnets interacting exclusively with magnetic forces is described. To carry out analytical studies a model of magnetically interacting symmetric tops [1] is used. The model was previously developed ... More

On orbits of truncated convolution operatorsAug 20 2010We prove that a semigroup generated by a finitely many truncated convolution operators on $L^p[0,1]$ with $1\leq p<\infty$ is non-supercyclic. On the other hand, there is a truncated convolution operator, which possesses irregular vectors.

Semi-invariants of 2-representations of quiversSep 24 2009In this work we obtain a version of the Procesi-Rasmyslov Theorem for the algebra of semi-invariants of representations of an arbitrary quiver with dimension vector (2,2,...,2).

A dichotomy for some elementarily generated modal logicsJun 22 2014Feb 27 2015In this paper we consider the normal modal logics of elementary classes defined by first-order formulas of the form $\forall x_0 \exists x_1 \dots \exists x_n \bigwedge x_i R_\lambda x_j$. We prove that many properties of these logics, such as finite ... More

A deformed conifold with a cosmological constantApr 08 2015Jul 14 2015We find a new regular solution of six-dimensional Einstein's equations with a positive cosmological constant. It has the same isometry group as the (deformed) conifold geometry, and the superpotential approach is used to solve the equations of motion. ... More

The geometry of a deformation of the standard addition on the integral latticeJan 15 2013Let $\mathfrak A_n$ be the subset of the standard integer lattice $\mathbb Z^n$, $\mathfrak A_n\subset\mathbb Z^n$ which is defined by the condition $\mathfrak A_n=((a_1,...,a_n)\in\mathbb Z^n | a_i\not\equiv a_j\mod n, \forall i,j\in {1,... n})$. It ... More

A Solvable Model for Nonlinear Mean Field DynamoMay 21 2001We formulate a solvable model that describes generation and saturation of mean magnetic field in a dynamo with kinetic helicity, in the limit of large magnetic Prandtl number. This model is based on the assumption that the stochastic part of the velocity ... More

Prisoner's Dilemma cellular automata revisited: evolution of cooperation under environmental pressureDec 20 2005Jun 06 2006We propose an extension of the evolutionary Prisoner's Dilemma cellular automata, introduced by Nowak and May \cite{nm92}, in which the pressure of the environment is taken into account. This is implemented by requiring that individuals need to collect ... More

Subgeometric rates of convergence of f-ergodic strong Markov processesMay 31 2006We provide a condition for f-ergodicity of strong Markov processes at a subgeometric rate. This condition is couched in terms of a supermartingale property for a functional of the Markov process. Equivalent formulations in terms of a drift inequality ... More

Performance of a Distributed Stochastic Approximation AlgorithmMar 07 2012Dec 02 2013In this paper, a distributed stochastic approximation algorithm is studied. Applications of such algorithms include decentralized estimation, optimization, control or computing. The algorithm consists in two steps: a local step, where each node in a network ... More

Success and Failure of Adaptation-Diffusion Algorithms for Consensus in Multi-Agent NetworksOct 25 2014This paper investigates the problem of distributed stochastic approximation in multi-agent systems. The algorithm under study consists of two steps: a local stochastic approximation step and a diffusion step which drives the network to a consensus. The ... More

The Lagrangian Loop Representation of Lattice U(1) Gauge TheoryJul 26 1994It is showed how the Hamiltonian lattice $loop$ $representation$ can be cast straightforwardly in the Lagrangian formalism. The procedure is general and here we present the simplest case: pure compact QED. This connection has been shaded by the non canonical ... More

Viral quasispecies profiles as the result of the interplay of competition and cooperationMay 11 2010Viral quasispecies can be regarded as a swarm of genetically related mutants or a quasispecies (QS). A common formalism to approach QS is the replicator-mutator equation (RME). However, a problem with the RME is how to quantify the interaction coefficients ... More

Subgeometric rates of convergence in Wasserstein distance for Markov chainsFeb 19 2014Jul 14 2015In this paper, we provide sufficient conditions for the existence of the invariant distribution and for subgeometric rates of convergence in Wasserstein distance for general state-space Markov chains which are (possibly) not irreducible. Compared to previous ... More

Adaptive Equi-Energy Sampler : Convergence and IllustrationJul 03 2012Feb 04 2013Markov chain Monte Carlo (MCMC) methods allow to sample a distribution known up to a multiplicative constant. Classical MCMC samplers are known to have very poor mixing properties when sampling multimodal distributions. The Equi-Energy sampler is an interacting ... More

Nanoroughened plasmonic films for enhanced biosensing detectionJul 26 2013Although fluorescence is the prevailing labeling technique in biosensing applications, sensitivity improvement is still a striving challenge. We show that coating standard microscope slides with nanoroughened silver films provides a high fluorescence ... More

A note on Brill--Noether existence for graphs of low genusSep 07 2016In an influential 2008 paper, Baker proposed a number of conjectures relating the divisor theory of algebraic curves with an analogous combinatorial theory on finite graphs. In this note, we examine Baker's Brill--Noether existence conjecture for special ... More

Conformal invariance of boundary touching loops of FK Ising modelSep 29 2015In this article we show the convergence of a loop ensemble of interfaces in the FK Ising model at criticality, as the lattice mesh tends to zero, to a unique conformally invariant scaling limit. The discrete loop ensemble is described by a canonical tree ... More

Scintillations and Levy flights through the interstellar mediumApr 09 2002Temporal broadening of pulsar signals results from electron density fluctuations in the interstellar medium that cause the radiation to travel along paths of different lengths. The Gaussian theory of fluctuations predicts that the pulse temporal broadening ... More

Exotic solutions in string theoryJun 05 1999Solutions of classical string theory, correspondent to the world sheets, mapped in Minkowsky space with a fold, are considered. Typical processes for them are creation of strings from vacuum, their recombination and annihilation. These solutions violate ... More

Hermitian quasi-exactly solvable matrix Shroedinger operatorsDec 01 1998We construct six multi-parameter families of Hermitian quasi-exactly solvable matrix Schroedinger operators in one variable. The method for finding these operators relies heavily upon a special representation of the Lie algebra o(2,2) whose representation ... More