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Effect of structural disorder on quantum oscillations in graphiteFeb 06 2017We have studied the effect of structural disorder on the de Haas van Alphen (dHvA) and Shubnikov de Haas (SdH) quantum oscillations measured in single-crystal and highly oriented pyrolytic graphite samples at temperatures down to 30 mK and at magnetic ... More

Unstable and elusive superconductorsMay 28 2015We briefly review earlier and report original experimental results in the context of metastable or possible superconducting materials. We show that applied electric field induces conducting state in Copper Chloride (CuCl) whose characteristics resemble ... More

Submillimeter - sized proximity effect in graphite and bismuthFeb 08 2019In this work, we probe the electrical properties of macroscopic graphite and bismuth in which the electrical current is injected via superconducting electrodes, few millimeters apart from each other. Results reveal the induction of a partial superconducting-like ... More

Partial Order on the set of Boolean Regulatory FunctionsJan 22 2019Logical models have been successfully used to describe regulatory and signaling networks without requiring quantitative data. However, existing data is insufficient to adequately define a unique model, rendering the parametrization of a given model a ... More

Taming the magnetoresistance anomaly in graphiteJul 03 2018At low temperatures, graphite presents a magnetoresistance anomaly which manifests as a transition to a high-resistance state (HRS) above a certain critical magnetic field $\text{B}_\text{c}$. Such HRS is currently attributed to a c-axis charge-density-wave ... More

Equicontinuity of maps on dendritesNov 12 2018Given a dendrite $X$ and a continuous map $f\colon X\to X$, we show the following are equivalent: (i) $\omega_f$ is continuous and $\overline{\mathrm{Per}(f)}=\bigcap_{n\in\mathbb{N}}f^n(X)$; (ii) $\omega(x,f)=\Omega(x,f)$ for each $x\in X$; and (iii) ... More

The stability of extended Floater-Hormann interpolantsSep 09 2014Jul 25 2016We present a new analysis of the stability of extended Floater-Hormann interpolants, in which both noisy data and rounding errors are considered. Contrary to what is claimed in the current literature, we show that the Lebesgue constant of these interpolants ... More

On the backward stability of the second barycentric formula for interpolationOct 09 2013Aug 14 2014We present a new stability analysis for the second barycentric formula for interpolation, showing that this formula is backward stable when the relevant Lebesgue constant is small.

Deep learning generalizes because the parameter-function map is biased towards simple functionsMay 22 2018Sep 28 2018Deep neural networks generalize remarkably well without explicit regularization even in the strongly over-parametrized regime. This success suggests that some form of implicit regularization must be at work. In this paper we argue that a strong intrinsic ... More

1/f noise in grapheneSep 13 2013We present a novel and comprehensive model of 1/f noise in nanoscale graphene devices that accounts for the unusual and so far unexplained experimental characteristics. We find that the noise power spectral density versus carrier concentration of single-layer ... More

A finite set of local moves for Kirby calculusFeb 07 2011Aug 21 2012We exhibit a finite set of local moves that connect any two surgery presentations of the same 3-manifold via framed links in the three-sphere. The moves are handle-slides and blow-downs/ups of a particular simple kind.

Four-manifolds with shadow-complexity zeroSep 01 2009We prove that a closed 4-manifold has shadow-complexity zero if and only if it is a kind of 4-dimensional graph manifold, which decomposes into some particular blocks along embedded copies of S^2 x S^1, plus some complex projective spaces. We deduce a ... More

Superrigidity In Infinite Dimension And Finite Rank Via Harmonic MapsJun 09 2012We prove geometric superrigidity for actions of cocompact lattices in semisimple Lie groups of higher rank on infinite dimensional Riemannian manifolds of nonpositive curvature and finite telescopic dimension.

Foncteurs de Mackey à réciprocitéOct 29 2012This text was written 20 years ago, inspired by M. Somekawa's paper on K-groups attached to semi-abelian varieties (K-Theory 4 (1990), 105--119) and before Voevodsky's theory of presheaves with transfers. The reason why it only had a limited circulation ... More

Comment on "Space-Time Crystals of Trapped Ions": And Yet it Moves Not !Nov 20 2012A Comment on "Space-Time Crystals of Trapped ions", by Tongcang Li et al. (PRL 109, 163001 (2012); arXiv:1206.4772

Berry phase, topology, and diabolicity in quantum nano-magnetsNov 18 2005A topological theory of the diabolical points (degeneracies) of quantum magnets is presented. Diabolical points are characterized by their diabolicity index, for which topological sum rules are derived. The paradox of the the missing diabolical points ... More

Exchange interaction parameters and adiabatic spin-wave spectra of ferromagnets: A "renormalized magnetic force theorem"Jul 24 2002Aug 31 2004The ``magnetic force theorem'' is frequently used to compute exchange interaction parameters and adiabatic spin-wave spectra of ferromagnets. The interest of this approach is that it allows to obtain these results from a non-self-consistent calculation ... More

Equivalence rationnelle, equivalence numerique et produits de courbes elliptiques sur un corps finiMay 14 2002Jul 20 2002This is an update of the first version. We clarify that the main results apply to more general smooth projective varieties X than products of elliptic curves (briefly: X is of "abelian type", e.g. an abelian variety or a product of curves, and the Tate ... More

Should one compute the Temporal Difference fix point or minimize the Bellman Residual? The unified oblique projection viewNov 19 2010We investigate projection methods, for evaluating a linear approximation of the value function of a policy in a Markov Decision Process context. We consider two popular approaches, the one-step Temporal Difference fix-point computation (TD(0)) and the ... More

Fly-automata for checking MSO 2 graph propertiesNov 27 2015Dec 22 2015A more descriptive but too long title would be : Constructing fly-automata to check properties of graphs of bounded tree-width expressed by monadic second-order formulas written with edge quantifications. Such properties are called MSO2 in short. Fly-automata ... More

Superradiance: Classical, Relativistic and Quantum AspectsApr 13 2014Jul 12 2014Several physical systems can be treated as a scattering process, and, for these processes, a natural observed quantity arises: the ratio between the reflected and incident intensities, known as the reflection coefficient. This dissertation is concerned ... More

Analysis of a malaria model with mosquito host choice and bed-net controlNov 13 2013A malaria model is formulated which includes the enhanced attractiveness of infectious humans to mosquitoes, as result of host manipulation by malaria parasite, and the human behavior, represented by insecticide-treated bed nets usage. The occurrence ... More

The 1-loop vacuum polarization for a graphene-like medium in an external magnetic field; corrections to the Coulomb potentialSep 06 2016I calculate the 1-loop vacuum polarization $\Pi_{\mu\nu}(k,B,a)$ for a photon of momentum $k=(\hat k,k_3)$ interacting with the electrons of a thin medium of thickness $2a$ simulating graphene, in the presence of a constant and uniform external magnetic ... More

Search for a high mass diphoton resonance using the ATLAS detectorNov 10 2016A search for new spin-0 resonances decaying into two photons in the ATLAS experiment at the LHC is described. The analysis is based on $pp$ collision data at $\sqrt{s}$=13 TeV corresponding to integrated luminosities of 3.2/fb and 12.2/fb recorded in ... More

An Introduction to Geometric TopologyOct 08 2016This book provides a self-contained introduction to the topology and geometry of surfaces and three-manifolds. The main goal is to describe Thurston's geometrisation of three-manifolds, proved by Perelman in 2002. The book is divided into three parts: ... More

Symmetrization for fractional Neumann problemsJan 27 2016Sep 01 2016In this paper we complement the program concerning the application of symmetrization methods to nonlocal PDEs by providing new estimates, in the sense of mass concentration comparison, for solutions to linear fractional elliptic and parabolic PDEs with ... More

Quantum Spin Systems after DLS1978Mar 06 2006Mar 08 2006In their 1978 paper, Dyson, Lieb, and Simon (DLS) proved the existence of Ne'el order at positive temperature for the spin-S Heisenberg antiferromagnet on the d-dimensional hypercubic lattice when either S >= 1 and d >= 3 or S=1/2 and d is sufficiently ... More

Van Lambalgen's theorem fails for some computable measureSep 09 2015Mar 13 2016Van Lambalgen's theorem states that a pair $(\alpha,\beta)$ of bitsequences is Martin-L\"of random if and only if $\alpha$ is Martin-L\"of random and $\beta$ is Martin-L\"of random relative to $\alpha$. In [Information and Computation 209.2 (2011): 183-197, ... More

Dirac physical measures for generic diffeomorphismsSep 13 2016We prove that, for a $C^1$ generic diffeomorphism, the only Dirac physical measures with dense statistical basin are those supported on sinks.

Infinite dimensional non-positively curved symmetric spaces of finite rankSep 02 2011Sep 26 2011This paper concerns a study of three families of non-compact type symmetric spaces of infinite dimension. Although they have infinite dimension they have finite rank. More precisely, we show they have finite telescopic dimension. We also show the existence ... More

The Einstein-scalar field constraint system in the positive caseJan 24 2013We prove the existence of solutions to the conformal Einstein-scalar constraint system of equations for closed compact Riemannian manifolds in the positive case. Our results apply to the vacuum case with positive cosmological constant and to the massive ... More

Teaching an Old Elephant New TricksSep 09 2009In recent years, column stores (or C-stores for short) have emerged as a novel approach to deal with read-mostly data warehousing applications. Experimental evidence suggests that, for certain types of queries, the new features of C-stores result in orders ... More

Koszul duality for PROPsFeb 13 2004The notion of PROP models the operations with multiple inputs and multiple outputs, acting on some algebraic structures like the bialgebras or the Lie bialgebras. We prove a Koszul duality theory for PROPs generalizing the one for associative algebras ... More

Uniformly Generating Distribution Functions for Discrete Random VariablesNov 03 2000Dec 13 2001An algorithm is presented which, with optimal efficiency, solves the problem of uniform random generation of distribution functions for an n-valued random variable.

Discrete Morse Theory for Manifolds with BoundaryJul 19 2010Oct 02 2010We introduce a version of discrete Morse theory specific for manifolds with boundary. The idea is to consider Morse functions for which all boundary cells are critical. We obtain "Relative Morse Inequalities" relating the homology of the manifold to the ... More

Analysis of Microprocessor Based Protective Re-lay's (MBPR) Differential Equation AlgorithmsJun 23 2010This paper analyses and explains from the systems point of view, microprocessor based protective relay (MBPR) systems with emphasis on differential equation algorithms. Presently, the application of protective relaying in power systems, using MBPR systems, ... More

Free monoid in monoidal abelian categoriesNov 24 2004Apr 29 2008We give an explicit construction of the free monoid in monoidal abelian categories when the monoidal product does not necessarily preserve coproducts. We apply it to several new monoidal categories that appeared recently in the theory of Koszul duality ... More

A Koszul duality for propsNov 24 2004Apr 13 2007The notion of prop models the operations with multiple inputs and multiple outpus, acting on some algebraic structures like the bialgebras or the Lie bialgebras. In this paper, we generalize the Koszul duality theory of associative algebras and operads ... More

Classes de cycles motiviques étalesFeb 02 2011Jul 25 2011Let X be a smooth variety over a field k, and l be a prime number invertible in k. We study the (\'etale) unramified H^3 of X with coefficients Q_l/Z_l(2) in the style of Colliot-Th\'el\`ene and Voisin. If k is separably closed, finite or p-adic, this ... More

On the multiplicities of a motiveOct 14 2006Feb 05 2007We study the multiplicities of pure motives modulo numerical equivalence, which are defined as scalars comparing the tannakian trace with the ring-theoretic trace. Our general set-up is that of a rigid semi-simple tensor category such that End(1) is a ... More

Comment on "Quantum Time Crystals": a new paradigm or just another proposal of perpetuum mobile?Oct 15 2012A Comment on Frank Wilczek's paper "Quantum Time Crystals" (Phys. Rev. Lett. 109, 160401 (2012); arXiv:1202.2539).

Quantum geometric phase in Majorana's stellar representation: Mapping onto a many-body Aharonov-Bohm phaseApr 11 2012Jun 13 2012The (Berry-Aharonov-Anandan) geometric phase acquired during a cyclic quantum evolution of finite-dimensional quantum systems is studied. It is shown that a pure quantum state in a (2J+1)-dimensional Hilbert space (or, equivalently, of a spin-J system) ... More

Long-range magnetic interaction due to the Casimir effectFeb 01 2002May 27 2002The zero-point quantum fluctuations of the electromagnetic field in vacuum are known to give rise to a long-range attractive force between metal plates (Casimir effect). For ferromagnetic layers separated by vacuum, it is shown that the interplay of the ... More

Theory of interlayer exchange interactions in magnetic multilayersJul 27 1999Dec 20 1999This paper presents a review of the phenomenon of interlayer exchange coupling in magnetic multilayers. The emphasis is put on a pedagogical presentation of the mechanism of the phenomenon, which has been successfully explained in terms of a spin-dependent ... More

Algèbres de Jordan et théorie des invariantsJun 30 2009Mar 13 2011If V is a simple complex euclidean Jordan algebra and G the subgroup of GL(V) fixing the determinant of V, we give a unified description of the invariant algebras C[pV]^G, for p not greater than three.

Charge Distributions in Metallic Alloys: a Charge Excess Functional theory approachDec 17 2002Charge Distributions in Metallic Alloys: a Charge Excess Functional theory approach

The 1-loop self-energy of an electron in a strong external magnetic field revisitedOct 12 2015May 02 2016I calculate the 1-loop self-energy of the lowest Landau level an electron of mass m in a strong, constant and uniform external magnetic field B, beyond its always used truncation at (ln L)^2, L=|e|B/m^2. This is achieved by evaluating the integral deduced ... More

Measurement of properties of the Higgs boson in bosonic decay channels using the ATLAS detectorSep 15 2014The properties of the Higgs boson measured in bosonic decay channels ($H \rightarrow \gamma\gamma$, $H \rightarrow ZZ^* \rightarrow 4\ell$, $H \rightarrow WW^{*} \rightarrow \ell\nu\ell\nu$, $H \rightarrow Z\gamma$) with 25 fb$^{-1}$ of pp collision data ... More

Relativistic Bohmian mechanics without a preferred foliationSep 11 2015Oct 15 2015In non-relativistic Bohmian mechanics the universe is represented by a probability space whose sample space is composed of the Bohmian trajectories. In relativistic Bohmian mechanics an entire class of empirically equivalent probability spaces can be ... More

Meagerness of the set of compact leaves for transversely holomorphic foliationsSep 15 2014A transversely holomorphic foliation on a compact complex manifold, exhibits a compact stable leaf if and only if the set of compact leaves is not a meager subset of the manifold.

Waveform Optimization for SWIPT with Nonlinear Energy Harvester ModelingFeb 02 2016Simultaneous Wireless Information and Power Transfer (SWIPT) has attracted significant attention in the communication community. The problem of waveform design for SWIPT has however never been addressed so far. In this paper, a novel SWIPT transceiver ... More

On the Dolbeault cohomology of projective varieties and locally residual currentsMay 03 2005Let $X$ be a projective manifold. Let $Y_1,...,Y_{p+1}$ be $p+1$ ample hypersurfaces in complete intersection position on $X$, each defined by the global section of an ample Cartier divisor. We show in this note that for $i\le p+1$, the cohomology groups ... More

Non-linear model equation for three-dimensional Bunsen flamesJul 10 2006The non linear description of laminar premixed flames has been very successful, because of the existence of model equations describing the dynamics of these flames. The Michelson Sivashinsky equation is the most well known of these equations, and has ... More

Deviation probability bounds for fractional martingales and related remarksApr 19 2012In this paper we prove exponential inequalities (also called Bernstein's inequality) for fractional martingales. As an immediate corollary, we will discuss weak law of large numbers for fractional martingales under divergence assumption on the $\beta-$variation ... More

Links, two-handles, and four-manifoldsDec 28 2004Nov 14 2005We show that only finitely many links in a closed 3-manifold share the same complement, up to twists along discs and annuli. Using the same techniques, we prove that by adding 2-handles on the same link we get only finitely many smooth cobordisms between ... More

Octonion multiplication and Heawood's mapJun 29 2011In this note, the octonion multiplication table is recovered from a regular tesselation of the "equilateral" two dimensional torus by seven hexagons, also known as Heawood's map.

Discrete Morse Theory Is At Least As Perfect As Morse TheoryOct 04 2010Jul 09 2014In bounding the homology of a manifold, Forman's Discrete Morse theory recovers the full precision of classical Morse theory: Given a PL triangulation of a manifold that admits a Morse function with c_i critical points of index i, we show that some subdivision ... More

Additivity of on-line decision complexity is violated by a linear term in the length of a binary stringAug 31 2009We show that there are infinitely many binary strings z, such that the sum of the on-line decision complexity of predicting the even bits of z given the previous uneven bits, and the decision complexity of predicting the uneven bits given the previous ... More

On the existence of stable compact leaves for transversely holomorphic foliationsMar 31 2012A transversely holomorphic foliation on a compact complex manifold, exhibits a compact stable leaf if and only if the set of compact leaves is not a zero measure subset of the manifold.

Quelques calculs de sommes de GaussAug 13 2011We observe that the Galois action on local constants associated to Galois representations of a local field yields information on their arithmetic nature, for example provides an upper bound to their order when they are roots of unity. It also yields information ... More

Around Quillen's theorem AAug 11 2011Jul 02 2014New version, including a variant of Quillen's proof of the Solomon-Tits theorem.

On the generalised Tate conjecture for products of elliptic curves over finite fieldsJan 10 2011We prove the generalised Tate conjecture for H^3 of products of elliptic curves over finite fields, by slightly modifying an argument of M. Spiess concerning the Tate conjecture. We prove it fully if the elliptic curves run among at most 3 isogeny classes. ... More

Number of points of function fields over finite fieldsOct 14 2002Oct 30 2002This is a revised and slightly expanded version. We point out that in the previous summary, "without cohomology" should really read "almost without cohomology" because of the proof of Lemma 2, that the idea to consider effective motives divisible by the ... More

Absence of spontaneous magnetic order at non-zero temperature in one- and two-dimensional Heisenberg and XY systems with long-range interactionsMay 06 2001May 27 2002The Mermin-Wagner theorem is strengthened so as to rule out magnetic long-range order at T>0 in one- or two-dimensional Heisenberg and XY systems with long-range interactions decreasing as R^{-alpha} with a sufficiently large exponent alpha. For oscillatory ... More

Non-quantized Dirac monopoles and strings in the Berry phase of anisotropic spin systemsApr 26 2004Aug 31 2004The Berry phase of an anisotropic spin system that is adiabatically rotated along a closed circuit C is investigated. It is shown that the Berry phase consists of two contributions: (i) a geometric contribution which can be interpreted as the flux through ... More

Interlayer exchange coupling: Preasymptotic correctionsAug 10 1998Sep 03 1999In the asymptotic limit, the interlayer exchange coupling decays as $D^{-2}$, where $D$ is the spacer thickness. A systematic procedure for calculating the preasymptotic corrections, i.e., the terms of order $D^{-n}$ with $n \ge 3$, is presented. The ... More

Collapses, products and LC manifoldsNov 24 2009May 16 2010Durhuus and Jonsson (1995) introduced the class of "locally constructible" (LC) triangulated manifolds and showed that all the LC 2- and 3-manifolds are spheres. We show here that for each d>3 some LC d-manifolds are not spheres. We prove this result ... More

Performance Bounds for Lambda Policy Iteration and Application to the Game of TetrisNov 05 2007Oct 11 2011We consider the discrete-time infinite-horizon optimal control problem formalized by Markov Decision Processes. We revisit the work of Bertsekas and Ioffe, that introduced $\lambda$ Policy Iteration, a family of algorithms parameterized by $\lambda$ that ... More

Interfaces and droplets in quantum lattice modelsSep 18 2000This paper is a short review of recent results on interface states in the Falicov-Kimball model and the ferromagnetic XXZ Heisenberg model. More specifically, we discuss the following topics: 1) The existence of interfaces in quantum lattice models that ... More

Nonstandard Intuitionistic InterpretationsDec 22 2015We present a notion of realizability and a functional interpretation in the context of intuitionistic logic, both incorporating nonstandard principles. The functional interpretation that we present corresponds to the intuitionistic counterpart of an interpretation ... More

Stochastic homogenization of nonconvex Hamilton-Jacobi equations: a counterexampleDec 20 2015Sep 07 2016We provide an example of a Hamilton-Jacobi equation in which stochastic homogenization does not occur. The Hamiltonian involved in this example satisfies the standard assumptions of the literature, except that it is not convex.

Lévy mixing related to distributed order calculus, subordinators and slow diffusionsJun 18 2014May 19 2015The study of distributed order calculus usually concerns about fractional derivatives of the form $\int_0^1 \partial^\alpha u \, m(d\alpha)$ for some measure $m$, eventually a probability measure. In this paper an approach based on L\'evy mixing is proposed. ... More

Motifs et adjointsJun 28 2015Nov 23 2015We show in many cases the existence of adjoints to extension of scalars on categories of motivic nature, in the framework of field extensions. This is to be contrasted with the more classical situation where one deals with a finite type morphism of schemes. ... More

Approximate Policy Iteration Schemes: A ComparisonMay 12 2014We consider the infinite-horizon discounted optimal control problem formalized by Markov Decision Processes. We focus on several approximate variations of the Policy Iteration algorithm: Approximate Policy Iteration, Conservative Policy Iteration (CPI), ... More

Tauberian theorems for general iterations of operators: applications to zero-sum stochastic gamesSep 07 2016This paper proves several Tauberian theorems for general iterations of operators, and provides two applications to zero-sum stochastic games where the total payoff is a weighted sum of the stage payoffs. The first application is to provide conditions ... More

Jordan derivations on triangular matrix ringsOct 26 2014Oct 28 2014Guided by the research line introduced by Martindale III in [1] on the study of the additivity of maps, this article aims establish condi- tions on triangular matrix rings in order that an map ' satisfying '(ab + ba) = '(a)b + a'(b) + '(b)a + b'(a) for ... More

Propositional dynamic logic for searching games with errorsJan 28 2014We investigate some finitely-valued generalizations of propositional dynamic logic with tests. We start by introducing the (n+1)-valued Kripke models and a corresponding language based on a modal extension of {\L}ukasiewicz many-valued logic. We illustrate ... More

Operationalization of Basic Observables in MechanicsApr 10 2015Dec 03 2015This novel approach to the foundation of the physical theory begins with Hermann von Helmholtz fundamental analysis of basic measurements. We explain the mathematical formalism from the operationalization of basic observables. According to Leibniz resp. ... More

Uniform van Lambalgen's theorem fails for computable randomnessOct 02 2015We show that there exists a bitsequence that is not computably random for which its odd bits are computably random and its even bits are computably random relative to the odd bits. This implies that the uniform variant of van Lambalgen's theorem fails ... More

Bounded-degree factors of lacunary multivariate polynomialsDec 11 2014Jan 29 2016In this paper, we present a new method for computing bounded-degree factors of lacunary multivariate polynomials. In particular for polynomials over number fields, we give a new algorithm that takes as input a multivariate polynomial f in lacunary representation ... More

Computing low-degree factors of lacunary polynomials: a Newton-Puiseux approachJan 19 2014Jun 24 2014We present a new algorithm for the computation of the irreducible factors of degree at most $d$, with multiplicity, of multivariate lacunary polynomials over fields of characteristic zero. The algorithm reduces this computation to the computation of irreducible ... More

On the Abel-Radon transform of locally residual currentsFeb 22 2010First we recall the definition of locally residual currents and their basic properties. We prove in this first section a trace theorem, that we use later. Then we define the Abel-Radon transform of a current ${\cal R}(\alpha)$, on a projective variety ... More

A family of $ω_1$ many topological types of locally finite treesApr 15 2016Two rooted locally finite trees are considered equivalent if both can be embedded into each other as topological minors by means of tree-order preserving mappings. By exploiting Nash-William's Theorem, Matthiesen provided a non-constructive proof of the ... More

Signal-wise performance attribution for constrained portfolio optimisationApr 18 2014Aug 06 2014Performance analysis, from the external point of view of a client who would only have access to returns and holdings of a fund, evolved towards exact attribution made in the context of portfolio optimisation, which is the internal point of view of a manager ... More

The critical random barrier for the survival of branching random walk with absorptionNov 11 2009We study a branching random walk on $\r$ with an absorbing barrier. The position of the barrier depends on the generation. In each generation, only the individuals born below the barrier survive and reproduce. Given a reproduction law, Biggins et al. ... More

Constructing a class of solutions for the Hamilton-Jacobi equation in field theorySep 12 2007A new approach leading to the formulation of the Hamilton-Jacobi equation for field theories is investigated within the framework of jet-bundles and multi-symplectic manifolds. An algorithm associating classes of solutions to given sets of boundary conditions ... More

La théorie des invariants des formes quadratiques ternaires revisitéeMay 27 2008The simultaneous invariants of 2, 3, 4 and 5 ternary quadratic forms under the group $\SL(3, {\Bbb C})$ were given by several authors (P. Gordan, C. Ciamberlini, H.W. Turnbull, J.A Todd), utilizing the symbolic method. Using the Jordan algebra structure ... More

Random walk on a building of type $\tilde{A}_r$ and Brownian motion of the Weyl chamberNov 17 2006May 25 2009In this paper we study a random walk on an affine building of type $\tilde{A}_r$, whose radial part, when suitably normalized, converges to the Brownian motion of the Weyl chamber. This gives a new discrete approximation of this process, alternative to ... More

The Poisson boundary of triangular matrices in a number fieldDec 11 2006Sep 19 2008The aim of this note is to describe the Poisson boundary of the group of invertible triangular matrices with coefficients in a number field. It generalizes to any dimension and to any number field a result of Brofferio concerning the Poisson boundary ... More

Comparison between Laplace-Lagrange Secular Theory and Numerical SimulationJun 08 2018The large increase in exoplanet discoveries in the last two decades showed a variety of systems whose stability is not clear. In this work we chose the $\upsilon$ Andromedae system as the basis of our studies in dynamical stability. This system has a ... More

$r$-Stable Hypersurfaces in Conformally Stationary SpacetimesMar 01 2010In this paper we study the r-stability of closed spacelike hypersurfaces with constant $r$-th mean curvature in conformally stationary spacetimes of constant sectional curvature. In this setting, we obtain a characterization of $r-$stability through the ... More

Anomalies in Bottom from new physics in TopMay 13 2018Aug 06 2018We analyze the possibility to accommodate current $b \to s \ell^+ \ell^-$ anomalies with TeV-scale mediators that couple to right-handed top quarks and muons, contributing to $b \to s \ell^+ \ell^-\,$ at the one-loop level. We use the Standard Model Effective ... More

m-sophisticationJan 26 2010The m-sophistication of a finite binary string x is introduced as a generalization of some parameter in the proof that complexity of complexity is rare. A probabilistic near sufficient statistic of x is given which length is upper bounded by the m-sophistication ... More

Influence tests I: ideal composite hypothesis tests, and causal semimeasuresDec 14 2009Ratios of universal enumerable semimeasures corresponding to hypotheses are investigated as a solution for statistical composite hypotheses testing if an unbounded amount of computation time can be assumed. Influence testing for discrete time series is ... More

The geometric mean of two matrices from a computational viewpointDec 30 2011The geometric mean of two matrices is considered and analyzed from a computational viewpoint. Some useful theoretical properties are derived and an analysis of the conditioning is performed. Several numerical algorithms based on different properties and ... More

Distributions vectorielles homogènes sur une algèbre de JordanMay 15 2007We study distributions on a Euclidean Jordan algebra V with values in a finite dimensional representation space for the identity component G of the structure group of V and homogeneous equivariance condition. We show that such distributions exist if and ... More

Bounds on the mass gap of the ferromagnetic XXZ chainJan 20 1995We prove rigorous lower and upper bounds for the mass gap of the ferromagnetic spin 1/2 XXZ chain. The two bounds coincide asymptotically in the Ising limit $\Delta\to\infty$. Near the isotropic point, $\Delta=1$, the estimates are good enough to determine ... More

Homology of generalized partition posetsMay 16 2004Aug 31 2006We define a poset of partitions associated to an operad. We prove that the operad is Koszul if and only if the poset is Cohen-Macaulay. In one hand, this characterisation allows us to compute the homology of the poset. This homology is given by the Koszul ... More

Discussion of: Brownian distance covarianceOct 05 2010Discussion on "Brownian distance covariance" by G\'abor J. Sz\'ekely and Maria L. Rizzo [arXiv:1010.0297]

Lieb-Robinson bounds and the existence of infinite system dynamicsSep 15 2009We present a recent result on the existence of the dynamics in the thermodynamic limit of a class of anharmonic quantum oscillator lattices, which was obtained using Lieb--Robinson bounds.