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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

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

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

Exceptional collections, and the Neron-Severi lattice for surfacesApr 07 2015Jul 13 2016We work out properties of smooth projective varieties over a (not necessarily algebraically closed) field that admit collections of objects in the bounded derived category of coherent sheaves that are either full exceptional, or numerically exceptional ... 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

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

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

Chow-Kuenneth decomposition for 3- and 4-folds fibred by varieties with small Chow group of zero-cyclesNov 15 2011Dec 04 2012Let $k$ be a field and let $\Omega$ be a universal domain over $k$. Let $f:X \r S$ be a dominant morphism defined over $k$ from a smooth projective variety $X$ to a smooth projective variety $S$ of dimension $\leq 2$ such that the general fibre of $f_\Omega$ ... More

Chow groups of smooth varieties fibred by quadricsMar 12 2012Let $f : X \rightarrow B$ be a proper flat dominant morphism between two smooth quasi-projective complex varieties $X$ and $B$. Assume that there exists an integer $l$ such that all closed fibres $X_b$ of $f$ satisfy $CH_j(X_b) = \Q$ for all $j \leq l$. ... More

Algebraic cycles and fibrationsMar 12 2012Sep 24 2013Let $f : X -> B$ be a projective surjective morphism between quasi-projective varieties. The goal of this paper is the study of the Chow groups of $X$ in terms of the Chow groups of $B$ and of the fibers of $f$. One of the applications concerns quadric ... 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

Non-idempotent types for classical calculi in natural deduction styleFeb 15 2018Jun 14 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

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

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

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

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

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

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

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

Local non-Bayesian social learning with stubborn agentsApr 29 2019In recent years, people have increasingly turned to social networks like Twitter and Facebook for news. In contrast to traditional news sources, these platforms allow users to simultaneously read news articles and share opinions with other users. Among ... 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

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

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

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

An example of a topologically non-rigid foliation of the complex projective planeOct 12 2009Nov 12 2012We give here an explicit example of an algebraic family of foliations of CP^{2} which is topologically trivial but not analytically trivial. This example underlines the necessity of some assumptions in Y. Ilyashenko's rigidity theorem.

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

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

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

Restart perturbations for lazy, reversible Markov chains: trichotomy and pre-cutoff equivalenceJul 05 2019Given a lazy, reversible Markov chain with $n$ states and transition matrix $P_n$, a distribution $\sigma_n$ over the states, and some $\alpha_n \in (0,1)$, we consider restart perturbations, which take the following form: with probability $1-\alpha_n$, ... 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

Restart perturbations for lazy, reversible Markov chains: trichotomy and pre-cutoff equivalenceJul 05 2019Jul 08 2019Given a lazy, reversible Markov chain with $n$ states and transition matrix $P_n$, a distribution $\sigma_n$ over the states, and some $\alpha_n \in (0,1)$, we consider restart perturbations, which take the following form: with probability $1-\alpha_n$, ... 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

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

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

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

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

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

Twisted bialgebras, cofreeness and cointeractionMay 24 2019We study twisted bialgebras and double twisted bialgebras, that is to say bialgebras in the category of linear species, or in the category of species in the category of coalgebras. We define the notion of cofree twisted coalgebra and generalize Hoffman's ... More

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

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.

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

Realizations of Hopf algebras of graphs by alphabetsMay 24 2019We here give polynomial realizations of various Hopf algebras or bialgebras on Feynman graphs, graphs, posets or quasi-posets, that it to say injections of these objects into polynomial algebras generated by an alphabet. The alphabet here considered are ... 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

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.

Exact Bayesian inference for off-line change-point detection in tree-structured graphical modelsMar 25 2016Jun 16 2016We consider the problem of change-point detection in multivariate time-series. The multivariate distribution of the observations is supposed to follow a graphical model, whose graph and parameters are affected by abrupt changes throughout time. We demonstrate ... 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

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

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

Bounds for the state-modulated resolvent of a linear Boltzmann generatorOct 04 2011We study a generalized resolvent for the generator of a Markovian semigroup. The Markovian generator appears in a linear Boltzmann equation modeling a one-dimensional test particle in a periodic potential and colliding elastically with particles from ... 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

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

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

Neutral Hydrogen and its Emission Lines in the Solar CoronaSep 16 2016Since the Lalpha rocket observations of (Gabriel, Solar Phys. 21, 392, 1971), it has been realized that the hydrogen (H) lines could be observed in the corona and offer an interesting diagnostic for the temperature, density, and radial velocity of the ... More

High order finite element calculations for the deterministic Cahn-Hilliard equationMar 04 2010In this work, we propose a numerical method based on high degree continuous nodal elements for the Cahn-Hilliard evolution. The use of the p-version of the finite element method proves to be very efficient and favorably compares with other existing strategies ... 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

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

Existence of non-algebraic singularities of differential equationFeb 17 2009May 31 2010An algebraizable singularity is a germ of a singular holomorphic foliation which can be defined in some appropriate local chart by a differential equation with algebraic coefficients. We show that there exists at least countably many saddle-node singularities ... More

Using polarimetry to retrieve the cloud coverage of Earth-like exoplanetsAug 23 2017Context. Clouds have already been detected in exoplanetary atmospheres. They play crucial roles in a planet's atmosphere and climate and can also create ambiguities in the determination of atmospheric parameters such as trace gas mixing ratios. Knowledge ... More

Scaling limit of multitype Galton-Watson trees with infinitely many typesMay 15 2014Oct 31 2015We introduce a certain class of 2-type Galton-Watson trees with edge lengths. We prove that, after an adequate rescaling, the weighted height function of a forest of such trees converges in law to the reflected Brownian motion. We then use this to deduce ... More

The entrance law of the excursion measure of the reflected process for some classes of Lévy processesJan 25 2019We provide integral formulae for the Laplace transform of the entrance law of the reflected excursions for symmetric L\'evy processes in terms of their characteristic exponent. For subordinate Brownian motions and stable processes we express the density ... More

Explicit versions of the prime ideal theorem for Dedekind zeta functions under GRH, IIFeb 10 2016Mar 27 2017We have proved recently several explicit versions of the prime ideal theorem under GRH. Here we prove a version with optimal asymptotic behaviour.