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Results for "Loïc Vial"

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Comparison of Global Algorithms in Word Sense DisambiguationApr 07 2017This article compares four probabilistic algorithms (global algorithms) for Word Sense Disambiguation (WSD) in terms of the number of scorer calls (local algo- rithm) and the F1 score as determined by a gold-standard scorer. Two algorithms come from the ... More
Improving the Coverage and the Generalization Ability of Neural Word Sense Disambiguation through Hypernymy and Hyponymy RelationshipsNov 02 2018In Word Sense Disambiguation (WSD), the predominant approach generally involves a supervised system trained on sense annotated corpora. The limited quantity of such corpora however restricts the coverage and the performance of these systems. In this article, ... More
Sense Vocabulary Compression through the Semantic Knowledge of WordNet for Neural Word Sense DisambiguationMay 14 2019In this article, we tackle the issue of the limited quantity of manually sense annotated corpora for the task of word sense disambiguation, by exploiting the semantic relationships between senses such as synonymy, hypernymy and hyponymy, in order to compress ... More
Pure motives with representable Chow groupsNov 15 2011Let $k$ be an algebraically closed field. We show using Kahn's and Sujatha's theory of birational motives that a Chow motive over $k$ whose Chow groups are all representable belongs to the full and thick subcategory of motives generated by the twisted ... More
Remarks on motives of abelian typeDec 05 2011Jul 27 2015A motive over a field $k$ is of abelian type if it belongs to the thick and rigid subcategory of Chow motives spanned by the motives of abelian varieties over $k$. This paper contains three sections of independent interest. First, we show that a motive ... More
Infinitary Intersection Types as Sequences: a New Answer to Klop's QuestionOct 20 2016We provide a type-theoretical characterization of weakly-normalizing terms in an infinitary lambda-calculus. We adapt for this purpose the standard quantitative (with non-idempotent intersections) type assignment system of the lambda-calculus to our infinite ... More
Operations in Milnor K-theoryDec 02 2008We show that operations in Milnor K-theory mod $p$ of a field are spanned by divided power operations. After giving an explicit formula for divided power operations and extending them to some new cases, we determine for all fields $k$ and all prime numbers ... More
Projectors on the intermediate algebraic JacobiansJul 21 2009Nov 15 2011Let $X$ be a complex smooth projective variety of dimension $d$. Under some assumption on the cohomology of $X$, we construct mutually orthogonal idempotents in $CH_d(X \times X) \otimes \Q$ whose action on algebraically trivial cycles coincides with ... More
Niveau and coniveau filtrations on cohomology groups and Chow groupsJul 21 2009Dec 04 2012The Bloch-Beilinson-Murre conjectures predict the existence of a descending filtration on Chow groups of smooth projective varieties which is functorial with respect to the action of correspondences and whose graded parts depend solely on the topology ... More
The Collapse of the Sequential Intersection Type System on the Multiset Intersection Type is SurjectiveOct 20 2016We show that every (finite or not) typing derivation of system M, using non-idempotent intersection, which is the infinitary version of de Carvalho's system M_0 , can be represented in a rigid, non-idempotent intersection type system S. Namely, whereas ... More
The Fourier transform for certain hyperKaehler fourfoldsSep 23 2013Jun 03 2014Using a codimension-$1$ algebraic cycle obtained from the Poincar\'e line bundle, Beauville defined the Fourier transform on the Chow groups of an abelian variety $A$ and showed that the Fourier transform induces a decomposition of the Chow ring $CH^*(A)$. ... More
Personalized PageRank dimensionality and algorithmic implicationsApr 09 2018Many systems, including the Internet, social networks, and the power grid, can be represented as graphs. When analyzing graphs, it is often useful to compute scores describing the relative importance or distance between nodes. One example is Personalized ... More
Global smoothness estimation of a Gaussian process from regular sequence designsNov 12 2012Jan 09 2014We consider a real Gaussian process $X$ having a global unknown smoothness $(r_{\scriptscriptstyle 0},\beta_{\scriptscriptstyle 0})$, $r_{\scriptscriptstyle 0}\in \mathds{N}_0$ and $\beta_{\scriptscriptstyle 0} \in]0,1[$, with $X^{(r_{\scriptscriptstyle ... More
On the Chow ring of Cynk-Hulek Calabi-Yau varieties and Schreieder varietiesDec 08 2017Apr 18 2019This note is about certain locally complete families of Calabi-Yau varieties constructed by Cynk and Hulek, and certain varieties constructed by Schreieder. We prove that the cycle class map on the Chow ring of powers of these varieties admits a section, ... More
Assessing extrema of empirical principal component functionsAug 01 2006The difficulties of estimating and representing the distributions of functional data mean that principal component methods play a substantially greater role in functional data analysis than in more conventional finite-dimensional settings. Local maxima ... More
The motive of the Hilbert cubeMar 03 2015Oct 05 2016The Hilbert scheme $X^{[3]}$ of length-$3$ subschemes of a smooth projective variety $X$ is known to be smooth and projective. We investigate whether the property of having a multiplicative Chow-Kuenneth decomposition is stable under taking the Hilbert ... More
Homogenization of periodic and random ferroelectric-dielectric compositesOct 08 2018Apr 01 2019We investigate the homogenized permittivity of ferroelectric-dielectric mixtures under a static electric field. A refined model is used to take into account the coupling between the electrostatic problem and the electric field dependent permittivity of ... More
Non-idempotent types for classical calculi in natural deduction styleFeb 15 2018Nov 07 2018In the first part of this paper, we define two resource aware typing systems for the $\lambda\mu$-calculus based on non-idempotent intersection and union types. The non-idempotent approach provides very simple combinatorial arguments --based on decreasing ... More
A coupling model for quasi-normal modes of photonic resonatorsApr 08 2016Aug 17 2016We develop a model for the coupling of quasi-normal modes in open photonic systems consisting of two resonators. By expressing the modes of the coupled system as a linear combination of the modes of the individual particles, we obtain a generalized eigenvalue ... More
Non-idempotent types for classical calculi in natural deduction styleFeb 15 2018Apr 05 2019In the first part of this paper, we define two resource aware typing systems for the $\lambda\mu$-calculus based on non-idempotent intersection and union types. The non-idempotent approach provides very simple combinatorial arguments --based on decreasing ... More
On the role of clustering in Personalized PageRank estimationJun 04 2017Jul 23 2018Personalized PageRank (PPR) is a measure of the importance of a node from the perspective of another (we call these nodes the $\textit{target}$ and the $\textit{source}$, respectively). PPR has been used in many applications, such as offering a Twitter ... More
Parameter tuning in pointwise adaptation using a propagation approachAug 25 2009This paper discusses the problem of adaptive estimation of a univariate object like the value of a regression function at a given point or a linear functional in a linear inverse problem. We consider an adaptive procedure originated from Lepski [Theory ... More
Connecting Gröbner Bases Programs with Coq to do Proofs in Algebra, Geometry and ArithmeticsJul 21 2010We describe how we connected three programs that compute Groebner bases to Coq, to do automated proofs on algebraic, geometrical and arithmetical expressions. The result is a set of Coq tactics and a certificate mechanism (downloadable at http://www-sop.inria.fr/marelle/Loic.Pottier/gb-keappa.tgz). ... More
Algebraic-based nonstandard time-stepping schemesSep 13 2015In this preliminary work, we present nonstandard time-stepping strategies to solve differential equations based on the algebraic estimation method applied to the estimation of time-derivative, which provides interesting properties of "internal" filtering. ... More
Mulitgraded Dyson-Schwinger systemsNov 21 2015We study systems of combinatorial Dyson-Schwinger equations with an arbitrary number $N$ of coupling constants. The considered Hopf algebra of Feynman graphs is $\mathbb{N}^N$-graded, and we wonder if the graded subalgebra generated by the solution is ... More
A prelie algebra associated to a linear endomorphism and related algebraic structuresSep 20 2013Dec 23 2014We attach to any linear endomorphism f of any vector space V a structure of prelie algebra on the shuffle algebra T(V); we describe its enveloping algebra, the dual Hopf algebra and the associated group of characters. For f=Id\_V, we find the algebra ... More
Chromatic polynomials and bialgebras of graphsNov 14 2016The chromatic polynomial is characterized as the unique polynomial invariant of graphs, compatible with two interacting bialgebras structures: the first coproduct is given by partitions of vertices into two parts, the second one by a contraction-extraction ... More
Vitesse de Convergence dans le Théorème Limite Central pour Chaînes de Markov de Probabilité de Transition Quasi-CompacteSep 26 2006Let $Q$ be a transition probability on a measurable space $E$, let $(X\_n)\_n$ be a Markov chain associated to $Q$, and let $\xi$ be a real-valued measurable function on $E$, and $S\_n = \sum\_{k=1}^{n} \xi(X\_k)$. Under functional hypotheses on the action ... More
Online tuning of artificial neural networks using para-model algorithm -- A preliminary studyMay 06 2019In this preliminary work, we explore the possibilities of using a model-free based control law in order to adjust synaptic weights in artificial neural networks. In the supervised learning context, we consider the problem of tuning the weights as a feedback ... More
Universal aspects of critical percolation on random half-planar mapsDec 24 2014Dec 18 2015We study a large class of Bernoulli percolation models on random lattices of the half- plane, obtained as local limits of uniform planar triangulations or quadrangulations. We first compute the exact value of the site percolation threshold in the quadrangular ... More
Note on Pontryagin maximum principle with running state constraints and smooth dynamics -- Proof based on the Ekeland variational principleApr 14 2016In this note our aim is to give a proof of the Pontryagin maximum principle for a general optimal control problem with running state constraints and smooth dynamics. Our proof is based on the classical Ekeland variational principle. The main result (and ... More
Variational and symplectic approach of the model-free controlNov 18 2010We propose a theoretical development of the model-free control in order to extend its robustness capabilities. The proposed method is based on the auto-tuning of the model-free controller parameter using an optimal approach. Some examples are discussed ... More
Algebraic structures on double and plane posetsJan 27 2011Jun 04 2013We study the Hopf algebra of double posets and two of its Hopf subalgebras, the Hopf algebras of plane posets and of posets "without N". We prove that they are free, cofree, self-dual, and we give an explicit Hopf pairing on these Hopf algebras. We also ... More
Faà di Bruno subalgebras of the Hopf algebra of planar trees from combinatorial Dyson-Schwinger equationsJul 09 2007Nov 28 2007We consider the combinatorial Dyson-Schwinger equation X=B^+(P(X)) in the non-commutative Connes-KreimerHopf algebra of planar rooted trees H, where B^+ is the operator of grafting on a root, and P a formal series. The unique solution X of this equation ... More
Breadth first search coding of multitype forests with application to Lamperti representationOct 01 2014We obtain a bijection between some set of multidimensional sequences and this of $d$-type plane forests which is based on the breadth first search algorithm. This coding sequence is related to the sequence of population sizes indexed by the generations, ... More
The infinitesimal Hopf algebra and the poset of planar forestsFeb 04 2008We introduce an infinitesimal Hopf algebra of planar trees, generalising the construction of the non-commutative Connes-Kreimer Hopf algebra. A non-degenerate pairing and a dual basis are defined, and a combinatorial interpretation of the pairing in terms ... More
Non shifted calculus of variations on time scales with Nabla-differentiable SigmaFeb 14 2013Jan 13 2016In calculus of variations on general time scales, an integral Euler-Lagrange equation is usually derived in order to characterize the critical points of non shifted Lagrangian functionals, see e.g. [R.A.C. Ferreira and co-authors, Optimality conditions ... More
A class of fractional optimal control problems and fractional Pontryagin's systems. Existence of a fractional Noether's theoremMar 07 2012In this paper, we study a class of fractional optimal control problems. A necessary condition for the existence of an optimal control is provided in the literature. It is commonly given as the existence of a solution of a fractional Pontryagin's system ... More
Commutative and non-commutative bialgebras of quasi-posets and applications to Ehrhart polynomialsMay 26 2016Nov 14 2016To any poset or quasi-poset is attached a lattice polytope, whose Ehrhart polynomial we study from a Hopf-algebraic point of view. We use for this two interacting bialgebras on quasi-posets. The Ehrhart polynomial defines a Hopf algebra morphism taking ... More
Examples of Com-PreLie Hopf algebrasJan 26 2015We gives examples of Com-PreLie bialgebras, that is to say bialgebras with a preLie product satisfying certain compatibilities. Three families are defined on shuffle algebras: one associated to linear endomorphisms, one associated to linear form, one ... More
Analyticity in spaces of convergent power series and applicationsAug 29 2013May 27 2015We study the analytic structure of the space of germs of an analytic function at the origin of \ww C^{\times m} , namely the space \germ{\mathbf{z}} where \mathbf{z}=\left(z\_{1},\cdots,z\_{m}\right) , equipped with a convenient locally convex topology. ... More
Extending to the complex line Dulac's corner maps of non-degenerate planar singularitiesJan 08 2013Aug 28 2015We study the complex Dulac map for a holomorphic foliation of the complex plane, near a non-degenerate singularity (both eigenvalues of the linearization are nonzero) with two separatrices. Following the well-known results of Y. Il'yashenko we provide ... More
Bidendriform bialgebras, trees, and free quasi-symmetric functionsMay 11 2005We introduce bidendriform bialgebras, which are bialgebras such that both product and coproduct can be split into two parts satisfying good compatibilities. For example, the Malvenuto-Reutenauer Hopf algebra and the non-commutative Connes-Kreimer Hopf ... More
An explicit Berry-Esséen bound for uniformly expanding maps on the intervalOct 28 2009For uniformly expanding maps on the interval, analogous versions of the Berry-Ess\'een theorem are known but only with an unexplicit upper bound in $O(1/\sqrt{n})$ without any constants being specified. In this paper, we use the recent complex cone technique ... More
Bruhat order on plane posets and applicationsNov 23 2012A plane poset is a finite set with two partial orders, satisfying a certain incompatibility condition. The set PP of isoclasses of plane posets owns two products, and an infinitesimal Hopf algebra structure is defined on the vector space H_PP generated ... More
Free and cofree Hopf algebrasOct 26 2010Jun 22 2011We first prove that a graded, connected, free and cofree Hopf algebra is always self-dual; then that two graded, connected, free and cofree Hopf algebras are isomorphic if, and only if, they have the same Poincar\'e-Hilbert formal series. If the characteristic ... More
Plane posets, special posets, and permutationsSep 06 2011Apr 05 2013We study the self-dual Hopf algebra $\h_{\SP}$ of special posets introduced by Malvenuto and Reutenauer and the Hopf algebra morphism from $\h_{\SP}$ to to the Hopf algebra of free quasi-symmetric functions $\FQSym$ given by linear extensions. In particular, ... More
Ordered forests and parking functionsJul 09 2010Mar 01 2011We prove that the Hopf algebra of parking functions and the Hopf algebra of ordered forests are isomorphic, using a rigidity theorem for a particular type of bialgebras.
Goal-Oriented Reduction of Automata NetworksAug 19 2016We consider networks of finite-state machines having local transitions conditioned by the current state of other automata. In this paper, we depict a reduction procedure tailored for a given reachability property of the form ``from global state s there ... More
Existence of a weak solution for fractional Euler-Lagrange equationsMar 07 2012Jan 13 2016In this paper, we state with a variational method a general theorem providing the existence of a weak solution $u$ for fractional Euler-Lagrange equations of the type: $$ \dfrac{\partial L}{\partial x} (u,D^\alpha_- u,t) + D^\alpha_+ (\dfrac{\partial ... More
Dynamical system-based robot reaching motions by para-model control approach - A preliminary studyOct 03 2016In this report, we apply the proposed "para-model" framework in order to control the trajectory of a dynamical system-based robot. The optimization of the dynamical performances in closed-loop is performed using a derivative-free optimization algorithm. ... More
Germes de feuilletages présentables du plan complexeMar 12 2013Nov 26 2013Let F be a germ of a singular foliation of the complex plane. Assuming that F is a generalized curve D. Marin and J.-F. Mattei proved the incompressibility of the foliation in a neighborhood from which a finite set of analytic curves is removed. We show ... More
How does the photon's spin affect Gravitational Wave measurements?Apr 19 2019We study the effect of the polarization of light beams on the time delay measured in Gravitational Wave experiments. To this end, we consider the Mathisson-Papapetrou-Dixon equations in a gravitational wave background, with two of the possible supplementary ... More
The infinitesimal Hopf algebra and the operads of planar forestsJan 15 2009We introduce two operads which own the set of planar forests as a basis. With its usual product and two other products defined by different types of graftings, the algebra of planar rooted trees H becomes an algebra over these operads. The compatibility ... More
Free brace algebras are free prelie algebrasSep 17 2008Jun 23 2009Let g be a free brace algebra. This structure implies that g is also a prelie algebra and a Lie algebra. It is already known that g is a free Lie algebra. We prove here that g is also a free prelie algebra, using a description of g with the help of planar ... More
L'algèbre des invariants d'un groupe de Coxeter agissant sur un mutiple de sa représentation standardNov 28 2007Let G be a Coxeter group of type A_n, B_n, D_n or I_2(N), or a complex reflection group of type G(de,e,n). Let V be its standard representation and let k be an integer greater than 2. Then G acts on S(V)^{\otimes k}. We show that the algebra of invariants ... More
Free quadri-algebras and dual quadri-algebrasApr 23 2015We study quadri-algebras and dual quadri-algebras. We describe the free quadri-algebra on one generator as a subobject of the Hopf algebra of permutations FQSym, proving a conjecture due to Aguiar and Loday, using that the operad of quadri-algebras can ... More
Deformation of the Hopf algebra of plane posetsApr 14 2012Nov 23 2012We describe and study a four parameters deformation of the two products and the coproduct of the Hopf algebra of plane posets. We obtain a family of braided Hopf algebras, generally self-dual. We also prove that in a particular case (when the second parameter ... More
General Dyson-Schwinger equations and systemsDec 12 2011We classify combinatorial Dyson-Schwinger equations giving a Hopf subalgebra of the Hopf algebra of Feynman graphs of the considered Quantum Field Theory. We first treat single equations with an arbitrary number (eventually infinite) of insertion operators. ... More
The Hopf algebra of Fliess operators and its dual pre-Lie algebraApr 05 2013Feb 21 2014We study the Hopf algebra H of Fliess operators coming from Control Theory in the one-dimensional case. We prove that it admits a graded, finte-dimensional, connected gradation. Dually, the vector space IR is both a pre-Lie algebra for the pre-Lie product ... More
Commutative and non-commutative bialgebras of quasi-posets and applications to Ehrhart polynomialsMay 26 2016To any poset or quasi-poset is attached a lattice polytope, whose Ehrhart polynomial we study from a Hopf-algebraic point of view. We use for this two interacting bialgebras on quasi-posets. The Ehrhart polynomial defines a Hopf algebra morphism with ... More
Variational integrator for fractional Pontryagin's systems. Existence of a discrete fractional Noether's theoremMar 08 2012Fractional Pontryagin's systems emerge in the study of a class of fractional optimal control problems but they are not resolvable in most cases. In this paper, we suggest a numerical approach for these fractional systems. Precisely, we construct a variational ... More
A para-model agent for dynamical systemsFeb 21 2012Oct 03 2016Consider a dynamical system $u \mapsto x, \dot{x} = f_{nl}(x,u)$ where $f_{nl}$ is a nonlinear (convex or nonconvex) function, or a combination of nonlinear functions that can eventually switch. We present, in this preliminary work, a generalization of ... More
Model-free control of non-minimum phase systems and switched systemsJun 09 2011This brief presents a simple derivation of the standard model-free control for the non-minimum phase systems. The robustness of the proposed method is studied in simulation considering the case of switched systems.
Bernstein-based polynomial approach to study the stability of switched systems and formal verification using HOL LightOct 15 2014In this preliminary work, we propose to use a polynomial approach in order to study the stability of switched systems. The proposed strategy is based on the Bernstein interpolation method that may transform a switched system into a polynomial expression ... More
Semi-explicit Parareal method based on convergence acceleration techniqueDec 19 2012Feb 14 2014The Parareal algorithm is used to solve time-dependent problems considering multiple solvers that may work in parallel. The key feature is a initial rough approximation of the solution that is iteratively refined by the parallel solvers. We report a derivation ... More
Chromatic polynomials and bialgebras of graphsNov 14 2016Nov 30 2016The chromatic polynomial is characterized as the unique polynomial invariant of graphs, compatible with two interacting bialgebras structures: the first coproduct is given by partitions of vertices into two parts, the second one by a contraction-extraction ... More
On the law of the supremum of Lévy processesNov 18 2010May 31 2013We show that the law of the overall supremum $\bar{X}_t=\sup_{s\le t}X_s$ of a L\'evy process $X$ before the deterministic time $t$ is equivalent to the average occupation measure $\mu_t(dx)=\int_0^t\p(X_s\in dx)\,ds$, whenever 0 is regular for both open ... More
The operads of planar forests are KoszulMar 09 2009We describe the Koszul dual of two quadratic operads on planar forests introduced to study the infinitesimal Hopf algebra of planar rooted trees and prove that these operads are Koszul.
Systems of Dyson-Schwinger equationsSep 02 2009Mar 02 2010We consider systems of combinatorial Dyson-Schwinger equations (briefly, SDSE) X_1=B^+_1(F_1(X_1,...,X_N))...X_N=B^+_N(F_N(X_1,...,X_N)) in the Connes-Kreimer Hopf algebra H_I of rooted trees decorated by I={1,...,N},where B^+_i is the operator of grafting ... More
Left ideals in an enveloping algebra, prelie products and applications to simple complex Lie algebrasJan 06 2010We characterize prelie algebras in words of left ideals of the enveloping algebras and in words of modules, and use this result to prove that a simple complex finite-dimensional Lie algebra is not prelie, with the possible exception of f4.
On quadri-algebrasNov 24 2014Nov 25 2014WWe describe the Koszul dual of the operad Quad of quadri-algebras, show the koszularity of Quad and give the formal series of Quad and its dual, which proves a conjecture due to Aguiar and Loday. A notion of quadri-bialgebra is also introduced, with ... More
Overcoming model simplifications when quantifying predictive uncertaintyMar 21 2017It is generally accepted that all models are wrong -- the difficulty is determining which are useful. Here, a useful model is considered as one that is capable of combining data and expert knowledge, through an inversion or calibration process, to adequately ... More
The Ly<alpha> and Ly<beta> profiles in solar prominences and prominence fine structureOct 07 2007We present the first combined Ly<alpha> and Ly<beta> profiles in solar prominences obtained by the SOHO/SUMER instrument and discuss their important spatial variability with respect to predictions from 1D and multithread models.
Plasma diagnostic of a solar prominence from hydrogen and helium resonance linesSep 23 2006We present the first comparison of profiles of H et He resonance lines observed by SUMER with theoretical profiles computed with our non-LTE radiative transfer code. We use the H I Lyman-beta, H I Lyman-epsilon, and He I 584 A lines. Our code allows us ... More
Effect of motions in prominences on the helium resonance lines in the extreme ultravioletAug 10 2006Dec 08 2006We aim at studying the effect of radial motions on the spectrum emitted by moving prominences in the helium resonance lines and at facilitating the interpretation of observations, in order to improve our understanding of these dynamic structures. We develop ... More
On descending cohomology geometricallyOct 20 2014Oct 26 2016In this paper, motivated by a problem posed by Barry Mazur, we show that for smooth projective varieties over the rationals, the odd cohomology groups of degree less than or equal to the dimension can be modeled by the cohomology of an abelian variety, ... More
Existence of nodal solutions for Dirac equations with singular nonlinearitiesAug 12 2012Jan 18 2013We prove, by a shooting method, the existence of infinitely many solutions of the form $\psi(x^0,x) = e^{-i\Omega x^0}\chi(x)$ of the nonlinear Dirac equation {equation*} i\underset{\mu=0}{\overset{3}{\sum}} \gamma^\mu \partial_\mu \psi- m\psi - F(\bar{\psi}\psi)\psi ... More
Out-of-equilibrium properties and non-linear effects for interacting quantum impurity systems in their strong coupling regimeMar 29 2013Jun 19 2014We provide an exact description of out-of-equilibrium fixed points in quantum impurity systems, that is able to treat time-dependent forcing. Building on this, we then show that analytical out-of-equilibrium results, that exactly treat interactions, can ... More
Pontryagin Maximum Principle for finite dimensional nonlinear optimal control problems on time scalesFeb 14 2013In this article we derive a strong version of the Pontryagin Maximum Principle for general nonlinear optimal control problems on time scales in finite dimension. The final time can be fixed or not, and in the case of general boundary conditions we derive ... More
Zeros of Dedekind zeta functions under GRHJul 05 2014Sep 17 2015Assuming GRH, we prove an explicit upper bound for the number of zeros of a Dedekind zeta function having imaginary part in $[T-a,T+a]$. We also prove a bound for the multiplicity of the zeros.
Invariance principles for random walks conditioned to stay positiveFeb 14 2006Apr 10 2008Let $\{S_n\}$ be a random walk in the domain of attraction of a stable law $\mathcal{Y}$, i.e. there exists a sequence of positive real numbers $(a_n)$ such that $S_n/a_n$ converges in law to $\mathcal{Y}$. Our main result is that the rescaled process ... More
First- and second-order phase transitions in scale-free networksJun 26 2002Oct 24 2002We study first- and second-order phase transitions of ferromagnetic lattice models on scale-free networks, with a degree exponent $\gamma$. Using the example of the $q$-state Potts model we derive a general self-consistency relation within the frame of ... More
Uniform infinite half-planar quadrangulations with skewnessDec 27 2016We introduce a one-parameter family of random infinite quadrangulations of the half-plane, which we call the uniform infinite half-planar quadrangulations with skewness (UIHPQ$_p$ for short, with $p\in[0,1/2]$ measuring the skewness). They interpolate ... More
Seq2Biseq: Bidirectional Output-wise Recurrent Neural Networks for Sequence ModellingApr 09 2019Apr 16 2019During the last couple of years, Recurrent Neural Networks (RNN) have reached state-of-the-art performances on most of the sequence modelling problems. In particular, the "sequence to sequence" model and the neural CRF have proved to be very effective ... More
On $\mathbb{R}^d$-valued multi-self-similar Markov processesSep 06 2018An $\mathbb{R}^d$-valued Markov process $X^{(x)}_t=(X^{1,x_1}_t,\dots,X^{d,x_d}_t)$, $t\ge0,x\in\mathbb{R}^d$ is said to be multi-self-similar with index $(\alpha_1,\dots,\alpha_d)\in[0,\infty)^d$ if the identity in law \[(c_iX_t^{i,x_i/c_i};i=1,\dots,d)_{t\ge0}\ed(X_{ct}^{(x)})_{t\ge0}\,,\] ... More
The Helium spectrum in erupting solar prominencesSep 18 2006Even quiescent solar prominences may become active and sometimes erupt. These events are occasionally linked to coronal mass ejections. However we know very little about the plasma properties during the activation and eruption processes. We present new ... More
A variational study of some hadron bag modelsJul 04 2012Jan 18 2013Quantum chromodynamics (QCD) is the theory of strong interaction and accounts for the internal structure of hadrons. Physicists introduced phe- nomenological models such as the M.I.T. bag model, the bag approximation and the soliton bag model to study ... More
Covert channel detection using Information TheoryFeb 28 2011This paper presents an information theory based detection framework for covert channels. We first show that the usual notion of interference does not characterize the notion of deliberate information flow of covert channels. We then show that even an ... More
A local limit theorem for densities of the additive component of a finite Markov Additive ProcessJun 22 2013In this paper, we are concerned with centered Markov Additive Processes $\{(X_t,Y_t)\}_{t\in\T}$ where the driving Markov process $\{X_t\}_{t\in\T}$ has a finite state space. Under suitable conditions, we provide a local limit theorem for the density ... More
General Cauchy-Lipschitz theory for shifted and non shifted Delta-Cauchy problems on time scalesDec 20 2012This article is devoted to completing some aspects of the classical Cauchy-Lipschitz (or Picard-Lindel\"of) theory for general nonlinear systems posed on time scales, that are closed subsets of the set of real numbers. Partial results do exist but do ... More
Explicit bounds for generators of the class groupJul 08 2016Oct 15 2016Assuming Generalized Riemann's Hypothesis, Bach proved that the class group $\mathcal C\!\ell_{\mathbf K}$ of a number field ${\mathbf K}$ may be generated using prime ideals whose norm is bounded by $12\mathcal L_{\mathbf K}^2$, and by $(4+o(1))\mathcal ... More
Asymptotically optimal prime ideal theorem under GRHFeb 10 2016Feb 11 2016We have proved recently several explicit versions of the prime ideal theorem under GRH. Here we prove a version with optimal asymptotic behaviour.
A computable bound of the essential spectral radius of finite range Metropolis--Hastings kernelsNov 23 2016Let $\pi$ be a positive continuous target density on $\mathbb{R}$. Let $P$ be the Metropolis-Hastings operator on the Lebesgue space $\mathbb{L}^2(\pi)$ corresponding to a proposal Markov kernel $Q$ on $\mathbb{R}$. When using the quasi-compactness method ... More
Goal-Driven Unfolding of Petri NetsNov 04 2016Unfoldings provide an efficient way to avoid the state-space explosion due to interleavings of concurrent transitions when exploring the runs of a Petri net. The theory of adequate orders allows one to define finite prefixes of unfoldings which contain ... More
On distributions determined by their upward, space-time Wiener-Hopf factorJan 31 2017Nov 27 2017According to the Wiener-Hopf factorization, the characteristic function $\varphi$ of any probability distribution $\mu$ on $\mathbb{R}$ can be decomposed in a unique way as \[1-s\varphi(t)=[1-\chi_-(s,it)][1-\chi_+(s,it)]\,,\;\;\;|s|\le1,\,t\in\mathbb{R}\,,\] ... More
Condensation in critical Cauchy Bienaymé-Galton-Watson treesApr 26 2018Nov 21 2018We are interested in the structure of large Bienaym\'e-Galton-Watson random trees whose offspring distribution is critical and falls within the domain of attraction of a stable law of index $\alpha=1$. In stark contrast to the case $\alpha \in (1,2]$, ... More
Helmholtz's inverse problem of the discrete calculus of variationsMar 06 2012Jan 13 2016We derive the discrete version of the classical Helmholtz condition. Precisely, we state a theorem characterizing second order finite differences equations admitting a Lagrangian formulation. Moreover, in the affirmative case, we provide the class of ... More
The Hopf algebra of finite topologies and T-partitionsJul 02 2014Oct 04 2014A noncommutative and noncocommutative Hopf algebra on finite topologies H_T is introduced and studied (freeness, cofreeness, self-duality...). Generalizing Stanley's definition of P-partitions associated to a special poset, we define the notion of T-partitions ... More
Meromorphic infinitesimal affine actions of the planeDec 12 2013We study complex Lie algebras spanned by pairs \left(Z,Y\right) of germs of a meromorphic vector field of the complex plane satisfying \left[Z,Y\right]=\delta Y for some \delta\in\ww C . This topic relates to Liouville-integrability of the differential ... More