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The Cosmic Dust Analyzer onboard Cassini: ten years of discoveriesFeb 13 2018The interplanetary space probe Cassini/Huygens reached Saturn in July 2004 after seven years of cruise phase. The Cosmic Dust Analyzer (CDA) measures the interplanetary, interstellar and planetary dust in our solar system since 1999 and provided unique ... More

A Class of Zielonka Automata with a Decidable Controller Synthesis ProblemJan 20 2016Feb 02 2016The decidability of the distributed version of the Ramadge and Wonham control problem (Ramadge and Wonham 1989), where both the plant and the controllers are modelled as Zielonka au-tomata (Zielonka 1987; Diekert and Rozenberg 1995) is a challenging open ... More

Computing Jacobi's $θ$ in quasi-linear timeNov 13 2015Jacobi's $\theta$ function has numerous applications in mathematics and computer science; a naive algorithm allows the computation of $\theta(z,\tau)$, for $z, \tau$ verifying certain conditions, with precision $P$ in $O(\mathcal{M}(P) \sqrt{P})$ bit ... More

Hamiltonian finite-temperature quantum field theory from its vacuum on partially compactified spaceApr 21 2016The partition function of a relativistic invariant quantum field theory is expressed by its vacuum energy calculated on a spatial manifold with one dimension compactified to a 1-sphere $S^1 (\beta)$, whose circumference $\beta$ represents the inverse ... More

Genetic cellular neural networks for generating three-dimensional geometryMar 28 2016There are a number of ways to procedurally generate interesting three-dimensional shapes, and a method where a cellular neural network is combined with a mesh growth algorithm is presented here. The aim is to create a shape from a genetic code in such ... More

Comment on "Towards a large deviation theory for strongly correlated systems"Sep 12 2012Jan 14 2013I comment on a recent paper by Ruiz and Tsallis [Phys. Lett. A 376, 2451 (2012)] claiming to have found a '$q$-exponential' generalization of the large deviation principle for strongly correlated random variables. I show that the basic scaling results ... More

The large deviation approach to statistical mechanicsApr 02 2008Aug 20 2009The theory of large deviations is concerned with the exponential decay of probabilities of large fluctuations in random systems. These probabilities are important in many fields of study, including statistics, finance, and engineering, as they often yield ... More

Relationships between p-unit constructions for real quadratic fieldsApr 10 2010Let $K$ be a real quadratic field and let $p$ be a prime number which is inert in $K$. Let $K_p$ be the completion of $K$ at $p$. In a previous paper, we constructed a $p$-adic invariant $u_C\in K_p$, and we proved a $p$-adic Kronecker limit formula relating ... More

Simple closed geodesics and the study of Teichmüller spacesDec 08 2009The goal of the chapter is to present certain aspects of the relationship between the study of simple closed geodesics and Teichm\"uller spaces.

Optimal DVB-S2 spectral efficiency with hierarchical modulationNov 19 2014We study the design of a DVB-S2 system in order to maximise spectral efficiency. This task is usually challenging due to channel variability. The solution adopted in modern satellite communications systems such as DVB-SH and DVB-S2 relies mainly on a ... More

Setting new Cosmology constraints with ALMAMar 06 2014Mar 17 2014I make a short revision of Cosmology questions which ALMA was built to address. Without diving into much detail, I point out the ALMA specifications and strategies which are expected to provide a better handle of: the temperature evolution of the Cosmic ... More

Glass and jamming transition of simple liquids: static and dynamic theoryJul 15 2013We study the glass and jamming transition of finite-dimensional models of simple liquids: hard- spheres, harmonic spheres and more generally bounded pair potentials that modelize frictionless spheres in interaction. At finite temperature, we study their ... More

$GL_2$-real analytic Eisenstein series twisted by parameter matrices and multiplicative integral quasi-charactersJul 11 2016In this monograph, we study in detail a special class of $GL_2$-real analytic Eisenstein series.

Interrogating surface length spectra and quantifying isospectralityNov 07 2016This article is about inverse spectral problems for hyperbolic surfaces and in particular how length spectra relate to the geometry of the underlying surface. A quantitative answer is given to the following: how many questions do you need to ask a length ... More

Approaching the Gaussian channel capacity with APSK constellationsMar 16 2015We consider the Gaussian channel with power constraint P. A gap exists between the channel capacity and the highest achievable rate of equiprobable uniformly spaced signal. Several approaches enable to overcome this limitation such as constellations with ... More

Kissing numbers for surfacesNov 15 2011The so-called {\it kissing number} for hyperbolic surfaces is the maximum number of homotopically distinct systoles a surface of given genus $g$ can have. These numbers, first studied (and named) by Schmutz Schaller by analogy with lattice sphere packings, ... More

A multiwavelength study of near- and mid-infrared selected galaxies at high redshift: ERGs, AGN-identification and the contribution from dustOct 12 2011Nov 17 2011The main focus of this thesis is the IR spectral regime, which since the 70's and 80's has revolutionised our understanding of the Universe. A multi-wavelength analysis on Extremely Red Galaxy populations is first presented in one of the most intensively ... More

A basic introduction to large deviations: Theory, applications, simulationsJun 21 2011Feb 29 2012The theory of large deviations deals with the probabilities of rare events (or fluctuations) that are exponentially small as a function of some parameter, e.g., the number of random components of a system, the time over which a stochastic system is observed, ... More

Simple spin models with non-concave entropiesApr 01 2005Jan 24 2008Two simple spin models are studied to show that the microcanonical entropy can be a non-concave function of the energy, and that the microcanonical and canonical ensembles can give non-equivalent descriptions of the same system in the thermodynamic limit. ... More

The homology systole of hyperbolic Riemann surfacesOct 02 2010Apr 07 2011The main goal of this note is to show that the study of closed hyperbolic surfaces with maximum length systole is in fact the study of surfaces with maximum length homological systole. The same result is shown to be true for once-punctured surfaces, and ... More

Repeated Binomial Coefficients and High-Degree CurvesNov 15 2014We consider the problem of characterizing solutions in $(x, y)$ to the equation ${x \choose y}={{x-a} \choose {y+b}}$ in terms of $a$ and $b$. We obtain one simple result which allows the determination of a ratio in terms of $a$ and $b$ which the ratio ... More

Numerical Simulations of Galactic Outflows and Evolution of the IGMOct 05 2011Galactic outflows play a major role in the evolution of galaxies and the intergalactic medium (IGM). The energy deposited into the interstellar medium by supernovae and active galactic nuclei can accelerate the gas past the escape velocity, and eject ... More

On the controller synthesis problem for distributed systems with causal memoryJan 20 2016Oct 25 2016The decidability of the distributed version of the Ramadge and Wonham controller synthesis problemwhere both the plant and the controllers are modelled as Zielonka automataand the controllers have causal memoryis a challenging open problem.There exists ... More

Generation of Gaussian Density FieldsJun 22 2005Jul 15 2005This document describes analytical and numerical techniques for the generation of Gaussian density fields, which represent cosmological density perturbations. The mathematical techniques involved in the generation of density harmonics in k-space, the ... More

Methods for calculating nonconcave entropiesMar 01 2010Apr 28 2010Five different methods which can be used to analytically calculate entropies that are nonconcave as functions of the energy in the thermodynamic limit are discussed and compared. The five methods are based on the following ideas and techniques: i) microcanonical ... More

Comment on "First-order phase transitions: equivalence between bimodalities and the Yang-Lee theorem"Mar 02 2005I discuss the validity of a result put forward recently by Chomaz and Gulminelli [Physica A 330 (2003) 451] concerning the equivalence of two definitions of first-order phase transitions. I show that distributions of zeros of the partition function fulfilling ... More

Equivalence and nonequivalence of ensembles: Thermodynamic, macrostate, and measure levelsMar 26 2014Feb 13 2015We present general and rigorous results showing that the microcanonical and canonical ensembles are equivalent at all three levels of description considered in statistical mechanics - namely, thermodynamics, equilibrium macrostates, and microstate measures ... More

Fixed point free involutions on Riemann surfacesApr 06 2005Jul 09 2005Involutions without fixed points on hyperbolic closed Riemann surface are discussed. For an orientable surface $X$ of even genus with an arbitrary Riemannian metric $d$ admitting an involution $\tau$, it is known that $\min_{p\in X}d(p,\tau(p))$ is bounded ... More

A short note on short pantsApr 28 2013May 22 2013It is a theorem of Bers that any closed hyperbolic surface admits a pants decomposition consisting of curves of bounded length where the bound only depends on the topology of the surface. The question of the quantification of the optimal constants has ... More

Localising Relational Degrees of Freedom in Quantum MechanicsFeb 13 2006This thesis presents a wide-ranging study of localising relational degrees of freedom. Three physical systems are studied in depth, each built upon a simple measurement-based process. For each physical system - light from independent sources leaking onto ... More

Central Limit Theorem and Large Deviation Principle for Continuous Time Open Quantum WalksOct 05 2016Open Quantum Walks (OQWs), originally introduced by S. Attal, are quantum generalizations of classical Markov chains. Recently, natural continuous time models of OQW have been developed by C. Pellegrini. These models, called Continuous Time Open Quantum ... More

Topological contributions to fermionic correlators and nonperturbative aspects of QCD in two dimensionsJun 27 1998We analyze the formation of fermionic condensates in two dimensional quantum chromodynamics for matter in the fundamental representation of the gauge group. We show that a topological regular instanton background is crucial in order to obtain nontrivial ... More

Ensemble equivalence for general many-body systemsJun 15 2011Nov 15 2011It has been proved for a class of mean-field and long-range systems that the concavity of the thermodynamic entropy determines whether the microcanonical and canonical ensembles are equivalent at the level of their equilibrium states, i.e., whether they ... More

Temperature fluctuations and mixtures of equilibrium states in the canonical ensembleDec 12 2002Dec 12 2002It has been suggested recently that `$q$-exponential' distributions which form the basis of Tsallis' non-extensive thermostatistical formalism may be viewed as mixtures of exponential (Gibbs) distributions characterized by a fluctuating inverse temperature. ... More

When is a quantity additive, and when is it extensive?Jan 09 2002The difference between the terms additivity and extensivity, as well as their respective negations, is critically analyzed and illustrated with a few examples. The concepts of subadditivity, pseudo-additivity, and pseudo-extensivity are also defined.

Comment on "Entropy Generation in Computation and the Second law of Thermodynamics", by S. Ishioka and N. FuchikamiFeb 19 1999This brief note argues that, contrary to the claim of Ishioka and Fuchikami (chao-dyn/9902012), Landauer's principle is concerned a priori with entropy generation in computing processes. The concept of heat, in this principle, is only relevant when a ... More

Leading order QCD in Coulomb gaugeNov 30 2011Coulomb gauge QCD in the first order formalism can be written in terms of a ghost-free, nonlocal action that ensures total color charge conservation via Gauss' law. Making an Ansatz whereby the nonlocal term (the Coulomb kernel) is replaced by its expectation ... More

Leading order infrared quantum chromodynamics in Coulomb gaugeNov 25 2011A truncation scheme for the Dyson-Schwinger equations of quantum chromodynamics in Coulomb gauge within the first order formalism is presented. The truncation is based on an Ansatz for the Coulomb kernel occurring in the action. Results at leading loop ... More

Nuclear State Preparation via Landau-Zener-Stueckelberg transitions in Double Quantum DotsNov 21 2008Jun 04 2009We theoretically model a nuclear-state preparation scheme that increases the coherence time of a two-spin qubit in a double quantum dot. The two-electron system is tuned repeatedly across a singlet-triplet level-anticrossing with alternating slow and ... More

Light Propagation in Inhomogeneous Universes. V. Gravitational Lensing of Distant SupernovaeOct 29 2007Nov 22 2007We use a series of ray-tracing experiments to determine the magnification distribution of high-redshift sources by gravitational lensing. We determine empirically the relation between magnification and redshift, for various cosmological models. We then ... 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

The Stefan-Boltzmann law: SU(2) versus SO(3) lattice gauge theoryJan 11 2000We investigate the high temperature limit of SU(2) and SO(3) lattice gauge theory, respectively. In particular, we study the Stefan-Boltzmann constant in both cases. As is well known, the Stefan-Boltzmann constant extracted from SU(2) lattice gauge theory ... More

A Note on the Hitchin System in a Background B-fieldJul 20 1998Jul 21 1998The space of solutions to the Hitchin equations on the dual torus with punctures determines the Higgs branch of certain impurity theories. An alternative description of this Higgs branch is provided, in terms of the proper deformation of Hitchin system ... More

Generalized Subjective Lexicographic Expected Utility RepresentationMay 24 2016We provide foundations for decisions in face of unlikely events by extending the standard framework of Savage to include preferences indexed by a family of events. We derive a subjective lexicographic expected utility representation which allows for infinitely ... More

Quantum field theory on rotating black hole spacetimesSep 25 2015This thesis is concerned with the development of a general method to compute renormalised local observables for quantum matter fields, in a given quantum state, on a rotating black hole spacetime. The rotating black hole may be surrounded by a Dirichlet ... More

Bethe-Salpeter equation at leading order in Coulomb gaugeNov 19 2012The Bethe-Salpeter equation and leptonic decay constants for pseudoscalar and vector quark-antiquark mesons with arbitrary quark masses are studied in Coulomb gauge, under a leading order truncation. As input, we use a pure linear rising potential, supplemented ... More

SymmetriesJul 07 2014Classical mathematics are founded within set theory, but sets don't have \emph{symmetries}. We conjecture that if we allow sets with symmetries, then many problems such as \emph{Mirror symmetry} or \emph{Homological mirror symmetry} can be explained. ... More

The effective potential of the confinement order parameter in the Hamiltonian ApproachDec 18 2013The effective potential of the order parameter for confinement is calculated within the variational approach to the Hamilton formulation of Yang-Mills theory. Compactifying one spatial dimension and using a background gauge fixing this potential is obtained ... More

The Explicit Construction of Orders on SurfacesJun 30 2011We implement a noncommutative analogue of the well-known commutative cyclic covering trick and implement it to explicitly construct a vast collection of numerically Calabi-Yau orders, noncommutative analogues of surfaces of Kodaira dimension 0. We construct ... More

Hamiltonian Approach to QCD: The effective potential of the Polyakov loopJan 11 2013The effective potential of the order parameter for confinement is calculated within the Hamiltonian approach to Yang--Mills theory. Compactifying one spatial dimension and using a background gauge fixing this potential is obtained by minimizing the energy ... More

New existence and symmetry results for least energy positive solutions of Schrödinger systems with mixed competition and cooperation termsDec 14 2014In this paper we focus on existence and symmetry properties of solutions to the cubic Schr\"odinger system \[ -\Delta u_i +\lambda_i u_i = \sum_{j=1}^d \beta_{ij} u_j^2 u_i \quad \text{in $\Omega \subset \mathbb{R}^N$},\qquad i=1,\dots d \] where $d\geq ... More

Sign-changing solutions of competition-diffusion elliptic systems and optimal partition problemsMay 27 2011In this paper we prove the existence of infinitely many sign-changing solutions for the system of $m$ Schr\"odinger equations with competition interactions $$ -\Delta u_i+a_i u_i^3+\beta u_i \sum_{j\neq i} u_j^2 =\lambda_{i,\beta} u_i \quad u_i\in H^1_0(\Omega), ... More

Symplectic integrators in the realm of Hofer's geometryDec 31 2011Symplectic integrators constructed from Hamiltonian and Lie formalisms are obtained as symplectic maps whose flow follows the exact solution of a "sourrounded" Hamiltonian K = H + h^k H_1. Those modified Hamiltonians depends virtually on the time by h. ... More

Information-theoretic approach to the study of control systemsApr 02 2001May 16 2003We propose an information-theoretic framework for analyzing control systems based on the close relationship of controllers to communication channels. A communication channel takes an input state and transforms it into an output state. A controller, similarly, ... More

Variational and optimal control representations of conditioned and driven processesJun 17 2015Nov 22 2015We have shown recently that a Markov process conditioned on rare events involving time-integrated random variables can be described in the long-time limit by an effective Markov process, called the driven process, which is given mathematically by a generalization ... More

Standard transmutation operators for the one dimensional Schrödinger operator with a locally integrable potentialAug 23 2016We study a special class of operators T satisfying the transmutation relation (Tu)"-qTu=Tu" in the sense of distributions, where q is a locally integrable function, and u belongs to a suitable space of distributions depending on the smoothness properties ... More

Topological order and the vacuum of Yang-Mills theoriesDec 04 2014Jan 14 2015We study, for $SU(2)$ Yang-Mills theories discretized on a lattice, a non-local topological order parameter, the center flux ${{z}}$. We show that: i) well defined topological sectors classified by $\pi_1(SO(3))=\mathbb{Z}_2$ can only exist in the ordered ... More

Effective potential (in)stability and lower bounds on the scalar (Higgs) massMar 24 2005It is widely believed that the top loop corrections to the Higgs effective potential destabilise the electroweak (EW) vacuum and that, imposing stability, lower bounds on the Higgs mass can be derived. With the help of a scalar-Yukawa model, we show that ... More

A game theoretic bound for minmax regret optimization problems with interval dataFeb 04 2016In this paper, we provide a generic anytime lower bounding procedure for minmax regret optimization problems. We show that the lower bound obtained is always at least as accurate as the lower bound recently proposed by Chassein and Goerigk (2015). The ... More

Classification of Sets using Restricted Boltzmann MachinesMar 25 2011We consider the problem of classification when inputs correspond to sets of vectors. This setting occurs in many problems such as the classification of pieces of mail containing several pages, of web sites with several sections or of images that have ... More

Spiked solutions for Schrödinger systems with Sobolev critical exponent: the cases of competitive and weakly cooperative interactionsMay 12 2016In this paper we deal with the nonlinear Schr\"odinger system \[ -\Delta u_i =\mu_i u_i^3 + \beta u_i \sum_{j\neq i} u_j^2 + \lambda_i u_i, \qquad u_1,\ldots, u_m\in H^1_0(\Omega) \] in dimension 4, a problem with critical Sobolev exponent. In the competitive ... More

Chiral symmetry breaking in Hamiltonian QCD in Coulomb gaugeJul 26 2011Spontaneous breaking of chiral symmetry is investigated in the Hamiltonian approach to QCD in Coulomb gauge. The quark wave functional is determined by the variational principle using an ansatz which goes beyond the commonly used BCS-type of wave functionals ... More

Checking $2 \times M$ separability via semidefinite programmingJan 14 2003In this paper we propose a sequence of tests which gives a definitive test for checking $2\times M$ separability. The test is definitive in the sense that each test corresponds to checking membership in a cone, and that the closure of the union of all ... More

Blackwell-Optimal Strategies in Priority Mean-Payoff GamesJun 08 2010We examine perfect information stochastic mean-payoff games - a class of games containing as special sub-classes the usual mean-payoff games and parity games. We show that deterministic memoryless strategies that are optimal for discounted games with ... More

What are single photons good for?Feb 02 2012In a long-held preconception, photons play a central role in present-day quantum technologies. But what are sources producing photons one by one good for precisely? Well, in opposition to what many suggest, we show that single-photon sources are not helpful ... More

Anomalous structural evolution of soft particles: Equibrium liquid state theoryDec 14 2009We use the hyper-netted chain approximation of liquid state theory to analyze the evolution with density of the pair correlation function in a model of soft spheres with harmonic repulsion. As observed in recent experiments on jammed soft particles, theory ... More

Optical homodyne tomography with polynomial series expansionJul 04 2011Nov 11 2011We present and demonstrate a method for optical homodyne tomography based on the inverse Radon transform. Different from the usual filtered back-projection algorithm, this method uses an appropriate polynomial series to expand the Wigner function and ... More

The Coulomb gauge ghost Dyson-Schwinger equationJul 15 2010Nov 21 2010A numerical study of the ghost Dyson-Schwinger equation in Coulomb gauge is performed and solutions for the ghost propagator found. As input, lattice results for the spatial gluon propagator are used. It is shown that in order to solve completely, the ... More

Solving Simple Stochastic Games with Few Random VerticesDec 11 2007May 25 2009Simple stochastic games are two-player zero-sum stochastic games with turn-based moves, perfect information, and reachability winning conditions. We present two new algorithms computing the values of simple stochastic games. Both of them rely on the existence ... More

Generalized Random Phase Approximation and Gauge TheoriesJun 24 2003Mean-field treatments of Yang-Mills theory face the problem of how to treat the Gauss law constraint. In this paper we try to face this problem by studying the excited states instead of the ground state. For this purpose we extend the operator approach ... More

The Diagonalized Newton Algorithm for Nonnegative Matrix FactorizationJan 15 2013Mar 18 2013Non-negative matrix factorization (NMF) has become a popular machine learning approach to many problems in text mining, speech and image processing, bio-informatics and seismic data analysis to name a few. In NMF, a matrix of non-negative data is approximated ... More

On the singular p-Laplacian system under Navier slip type boundary conditions. The gradient-symmetric caseDec 24 2012We consider the p-Laplacian system of N equations in n space variables, 1< p\leq 2, under the homogeneous Navier slip boundary condition. Furthermore, the gradient of the velocity is replaced by the, more physical, symmetric gradient. We prove W^{2, q} ... More

Divergence of the correlation length for critical planar FK percolation with $1\le q\le4$ via parafermionic observablesAug 18 2012Sep 23 2012Parafermionic observables were introduced by Smirnov for planar FK percolation in order to study the critical phase $(p,q)=(p_c(q),q)$. This article gathers several known properties of these observables. Some of these properties are used to prove the ... More

ProvGen: generating synthetic PROV graphs with predictable structureJun 10 2014This paper introduces provGen, a generator aimed at producing large synthetic provenance graphs with predictable properties and of arbitrary size. Synthetic provenance graphs serve two main purposes. Firstly, they provide a variety of controlled workloads ... More

Two-Player Perfect-Information Shift-Invariant Submixing Stochastic Games Are Half-PositionalJan 25 2014Oct 08 2015We consider zero-sum stochastic games with perfect information and finitely many states and actions. The payoff is computed by a payoff function which associates to each infinite sequence of states and actions a real number. We prove that if the the payoff ... More

Quark gap equation in an external magnetic fieldOct 22 2013The nonperturbative quark gap equation under the rainbow truncation and with two versions of a phenomenological one-gluon exchange interaction is studied in the presence of a uniform external magnetic field, with emphasis on the small field limit. The ... More

Toward a strictification theorem for co-Segal categoriesJul 27 2013Aug 01 2013We show that for a monoidal model category $\M=(\ul{M}, \otimes, I)$, certain co-Segal $\M$-categories are equivalent to strict ones.

Renormalized vacuum polarization of rotating black holesFeb 04 2015May 05 2015Quantum field theory on rotating black hole spacetimes is plagued with technical difficulties. Here, we describe a general method to renormalize and compute the vacuum polarization of a quantum field in the Hartle-Hawking state on rotating black holes. ... More

Conference ImpressionDec 22 1999This paper gives a personal impression of the conference ``Asymmetrical PNe II: From Origins to Microstructures'', flags some of the highlights, gathers together some facts and terminology, and indicates some promising future lines of work in this field. ... More

Effective potential for the order parameter of the SU(2) Yang-Mills deconfinement transitionSep 16 1997The Polyakov loop variable serves as an order parameter to characterize the confined and deconfined phases of Yang-Mills theory. By integrating out the vector fields in the SU(2) Yang-Mills partition function in one-loop approximation, an effective action ... More

Monopoles contra vortices in SU(2) lattice gauge theory?Mar 18 1997We show that the scenario of vortex induced confinement of center--projected SU(2) lattice gauge theory is not necessarily in conflict with the findings in the positive plaquette model.

Teaching introductory STEM with the Marble GameOct 12 2012Oct 22 2012Recently there have been multiple calls for curricular reforms to develop new pathways to the science, technology, engineering and math (STEM) disciplines. The Marble Game answers these calls by providing a conceptual framework for quantitative scientific ... More

Minimal length of two intersecting simple closed geodesicsAug 02 2006Aug 14 2006On a hyperbolic Riemann surface, given two simple closed geodesics that intersect $n$ times, we address the question of a sharp lower bound $L_n$ on the length attained by the longest of the two geodesics. We show the existence of a surface $S_n$ on which ... More

Filling sets of curves on punctured surfacesAug 14 2015We study filling sets of simple closed curves on punctured surfaces. In particular we study lower bounds on the cardinality of sets of curves that fill and that pairwise intersect at most k times on surfaces with given genus and number of punctures. We ... More

Exceptional times for percolation under exclusion dynamicsMay 16 2016May 27 2016We analyse in this paper a conservative analogue of the celebrated model of dynamical percolation introduced by H\"aggstr\"om, Peres and Steif in [HPS97]. It is simply defined as follows: start with an initial percolation configuration $\omega(t=0)$. ... More

Ground States for a nonlinear Schrödinger system with sublinear coupling termsApr 17 2015We study the existence of ground states for the coupled Schr\"odinger system \begin{equation} \left\{\begin{array}{lll} \displaystyle -\Delta u_i+\lambda_i u_i= \mu_i |u_i|^{2q-2}u_i+\sum_{j\neq i}b_{ij} |u_j|^q|u_i|^{q-2}u_i \\ u_i\in H^1(\mathbb{R}^n), ... More

Comment on "Some non-conventional ideas about algorithmic complexity"Mar 16 2005We comment on a recent paper by D'Abramo [Chaos, Solitons & Fractals, 25 (2005) 29], focusing on the author's statement that an algorithm can produce a list of strings containing at least one string whose algorithmic complexity is greater than that of ... More

Information-Theoretic Limits of ControlMay 26 1999Fundamental limits on the controllability of physical systems are discussed in the light of information theory. It is shown that the second law of thermodynamics, when generalized to include information, sets absolute limits to the minimum amount of dissipation ... More

Violation of the PT-symmetry and structure formation in the dark matter-gravitational wave interactionSep 07 2016In flat spacetime, quantum fluctuations in dark matter, as described as a Bose-Einstein condensate, are stable and display a relativistic Bogoliubov dispersion relation. In the weak gravitational field limit, both relativistic and nonrelativistic models ... More

Catastrophic Phase Transitions and Early Warnings in a Spatial Ecological ModelOct 06 2009Gradual changes in exploitation, nutrient loading, etc. produce shifts between alternative stable states (ASS) in ecosystems which, quite often, are not smooth but abrupt or catastrophic. Early warnings of such catastrophic regime shifts are fundamental ... More

Nonconcave entropies in multifractals and the thermodynamic formalismJul 15 2005Dec 04 2006We discuss a subtlety involved in the calculation of multifractal spectra when these are expressed as Legendre-Fenchel transforms of functions analogous to free energy functions. We show that the Legendre-Fenchel transform of a free energy function yields ... More

Systoles and kissing numbers of finite area hyperbolic surfacesAug 26 2014Sep 29 2015We study the number and the length of systoles on complete finite area orientable hyperbolic surfaces. In particular, we prove upper bounds on the number of systoles that a surface can have (the so-called kissing number for hyperbolic surfaces). Our main ... More

Pure and Stationary Optimal Strategies in Perfect-Information Stochastic Games with Global PreferencesNov 25 2016We examine the problem of the existence of optimal deterministic stationary strategiesintwo-players antagonistic (zero-sum) perfect information stochastic games with finitely many states and actions.We show that the existenceof such strategies follows ... More

On some regularity results for $\,2-D\,$ Euler equations and linear elliptic b.v. problemsFeb 04 2015About thirty years ago we looked for "minimal assumptions" on the data which guarantee that solutions to the $\,2-D\,$ evolution Euler equations in a bounded domain are classical. Classical means here that all the derivatives appearing in the equations ... More

3D Polyominoes inscribed in a rectangular prismSep 24 2010We introduce a family of 3D combinatorial objects that we define as minimal 3D polyominoes inscribed in a rectanglar prism. These objects are connected sets of unitary cubic cells inscribed in a given rectangular prism and of minimal volume under this ... More

Disambiguating the role of noise correlations when decoding neural populations togetherAug 19 2016Objective: Integrating information from populations of correlated neurons can become too complex even for the human brain. Ignoring correlations may simplify the process but also cause an information loss. This loss has been quantified using many methods, ... More

Open problems concerning the Holder continuity of the direction of vorticity for the Navier-Stokes equationsApr 27 2016In these notes we consider solutions u to the evolution three dimensional Navier-Stokes equations in the whole space. Set w= curl u, the vorticity of u. Our study concerns mainly the relation between Holdercontinuity assumptions on the direction of the ... More

Short closed geodesics with self-intersectionsSep 01 2016Our main point of focus is the set of closed geodesics on hyperbolic surfaces. For any fixed integer $k$, we are interested in the set of all closed geodesics with at least $k$ (but possibly more) self-intersections. Among these, we consider those of ... More

Distances in domino flip graphsAug 25 2016This article is about measuring and visualizing distances between domino tilings. Given two tilings of a simply connected square tiled surface, we're interested in the minimum number of flips between two tilings. Given a certain shape, we're interested ... More

Resummed mean-field inference for strongly coupled dataOct 14 2015Oct 17 2016We present a resummed mean-field approximation for inferring the parameters of an Ising or a Potts model from empirical, noisy, one- and two-point correlation functions. Based on a resummation of a class of diagrams of the small correlation expansion ... More