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Unusual Corrections to Scaling and Convergence of Universal Renyi Properties at Quantum Critical PointsSep 01 2015At a quantum critical point, bipartite entanglement entropies have universal quantities which are subleading to the ubiquitous area law. For Renyi entropies, these terms are known to be similar to the von Neumann entropy, while being much more amenable ... More

Point defect states emergence in a plasmonic crystalAug 30 2019Plasmonic crystals are well known to have band structure including a bandgap, enabling the control of surface plasmon propagation and confinement. The band dispersion relation of bulk crystals has been generally measured by momentum-resolved spectroscopy ... More

Convex cones and SAGBI bases of permutation invariantsJul 17 2006Let G be a permutation group acting on {1,...,n}, and < be any admissible term order on the polynomial ring K[x_1,...,x_n]. We prove that the invariant ring K[x_1,...,x_n]^G of G has a finite SAGBI basis if, and only if, G is generated by reflections. ... More

Separation choosability and dense bipartite induced subgraphsFeb 11 2018Dec 04 2018We study a restricted form of list colouring, for which every pair of lists that correspond to adjacent vertices may not share more than one colour. The optimal list size such that a proper list colouring is always possible given this restriction, we ... More

Geometric mutual information at classical critical pointsDec 13 2013Mar 27 2014A practical use of the entanglement entropy in a 1d quantum system is to identify the conformal field theory describing its critical behavior. It is exactly $(c/3)\ln \ell$ for an interval of length $\ell$ in an infinite system, where $c$ is the central ... More

Entanglement in gapless resonating valence bond statesJul 16 2012Jan 21 2013We study resonating-valence-bond (RVB) states on the square lattice of spins and of dimers, as well as SU(N)-invariant states that interpolate between the two. These states are ground states of gapless models, although the SU(2)-invariant spin RVB state ... More

Compilation for QCSPJul 17 2013We propose in this article a framework for compilation of quantified constraint satisfaction problems (QCSP). We establish the semantics of this formalism by an interpretation to a QCSP. We specify an algorithm to compile a QCSP embedded into a search ... More

EPTAS for Max Clique on Disks and Unit BallsMar 05 2018Apr 11 2018We propose a polynomial-time algorithm which takes as input a finite set of points of $\mathbb R^3$ and compute, up to arbitrary precision, a maximum subset with diameter at most $1$. More precisely, we give the first randomized EPTAS and deterministic ... More

Conformal Field Theory for Inhomogeneous One-dimensional Quantum Systems: the Example of Non-Interacting Fermi GasesJun 14 2016In spite of the tremendous successes of conformal field theory (CFT) in describing large-scale, universal, effects in one-dimensional (1D) systems at quantum critical points, its applicability in condensed matter physics has been limited to situations ... More

A Multivariate Extreme Value Theory Approach to Anomaly Clustering and VisualizationJul 17 2019In a wide variety of situations, anomalies in the behaviour of a complex system, whose health is monitored through the observation of a random vector X = (X1,. .. , X d) valued in R d , correspond to the simultaneous occurrence of extreme values for certain ... More

Perfect graphs of arbitrarily large clique-chromatic numberJun 29 2015Jun 30 2015We prove that there exist perfect graphs of arbitrarily large clique-chromatic number. These graphs can be obtained from cobipartite graphs by repeatedly gluing along cliques. This negatively answers a question raised by Duffus, Sands, Sauer, and Woodrow ... More

On Recent Advances in Supervised Ranking for Metabolite ProfilingFeb 05 2014This paper focuses on data arising from the field of metabolomics, a rapidly developing area concerned by the analysis of the chemical fingerprints (i.e. the metabolite profile). The metabolite profile is left by specific chemical processes occurring ... More

Free fermions at the edge of interacting systemsJan 09 2019Jan 16 2019We study the edge behavior of inhomogeneous one-dimensional quantum systems, such as Lieb-Liniger models in traps or spin chains in spatially varying magnetic fields. For free systems these fall into several universality classes, the most generic one ... More

Edge Growth in Graph CubesSep 02 2010We show that for every connected graph $G$ of diameter $\ge 3$, the graph $G^3$ has average degree $\ge 7/4 \delta(G)$. We also provide an example showing that this bound is best possible. This resolves a question of Hegarty \cite{PH}.

Return probability after a quench from a domain wall initial state in the spin-1/2 XXZ chainJul 20 2017Aug 24 2017We study the return probability and its imaginary ($\tau$) time continuation after a quench from a domain wall initial state in the XXZ spin chain, focusing mainly on the region with anisotropy $|\Delta|< 1$. We establish exact Fredholm determinant formulas ... More

An SIR Graph Growth Model for the Epidemics of Communicable DiseasesDec 09 2013Feb 05 2014It is the main purpose of this paper to introduce a graph-valued stochastic process in order to model the spread of a communicable infectious disease. The major novelty of the SIR model we promote lies in the fact that the social network on which the ... More

On Tree-based Methods for Similarity LearningJun 21 2019In many situations, the choice of an adequate similarity measure or metric on the feature space dramatically determines the performance of machine learning methods. Building automatically such measures is the specific purpose of metric/similarity learning. ... More

Edge-decomposing graphs into coprime forestsMar 09 2018The Barat-Thomassen conjecture, recently proved in [Bensmail et al.: A proof of the Barat-Thomassen conjecture. J. Combin. Theory Ser. B, 124:39-55, 2017.], asserts that for every tree T, there is a constant $c_T$ such that every $c_T$-edge connected ... More

Emptiness formation probability, Toeplitz determinants, and conformal field theoryMar 22 2013Mar 24 2014We revisit the study of the emptiness formation probability, the probability of forming a sequence of $\ell$ spins with the same ferromagnetic orientation in the ground-state of a quantum spin chain. We focus on two different examples, exhibiting strikingly ... More

Shannon and Rényi mutual information in quantum critical spin chainsMar 24 2014Jul 31 2014We study the Shannon mutual information in one-dimensional critical spin chains, following a recent conjecture (Phys. Rev. Lett. 111, 017201 (2013)), as well as R\'enyi generalizations of it. We combine conformal field theory arguments with numerical ... More

Functional Bipartite Ranking: a Wavelet-Based Filtering ApproachDec 18 2013It is the main goal of this article to address the bipartite ranking issue from the perspective of functional data analysis (FDA). Given a training set of independent realizations of a (possibly sampled) second-order random function with a (locally) smooth ... More

Learning Reputation in an Authorship NetworkNov 25 2013The problem of searching for experts in a given academic field is hugely important in both industry and academia. We study exactly this issue with respect to a database of authors and their publications. The idea is to use Latent Semantic Indexing (LSI) ... More

Ranking the best instancesNov 06 2006Feb 14 2007We formulate the local ranking problem in the framework of bipartite ranking where the goal is to focus on the best instances. We propose a methodology based on the construction of real-valued scoring functions. We study empirical risk minimization of ... More

Free fermions at the edge of interacting systemsJan 09 2019Apr 24 2019We study the edge behavior of inhomogeneous one-dimensional quantum systems, such as Lieb-Liniger models in traps or spin chains in spatially varying magnetic fields. For free systems these fall into several universality classes, the most generic one ... More

Convexly independent subsets of Minkowski sums of convex polygonsMar 27 2019We show that there exist convex $n$-gons $P$ and $Q$ such that the largest convex polygon in the Minkowski sum $P+Q$ has size $\Theta(n\log n)$. This matches an upper bound of Tiwary.

Complements of nearly perfect graphsApr 10 2013A class of graphs closed under taking induced subgraphs is $\chi$-bounded if there exists a function $f$ such that for all graphs $G$ in the class, $\chi(G) \leq f(\omega(G))$. We consider the following question initially studied in [A. Gy{\'a}rf{\'a}s, ... More

The complex chemistry of hot cores in Sagittarius B2(N): Influence of cosmic-ray ionization and thermal historyJun 11 2019As the number of complex organic molecules (COMs) detected in the interstellar medium increases, it becomes important to place meaningful constraints on the formation pathways of these species. The molecular cloud SgrB2(N) is host to several hot molecular ... More

Dynamics and level statistics of interacting fermions in the Lowest Landau LevelMay 18 2018We consider the unitary dynamics of interacting fermions in the lowest Landau level, on spherical and toroidal geometries. The dynamics are driven by the interaction Hamiltonian which, viewed in the basis of single-particle Landau orbitals, contains correlated ... More

Wave-vortex interactionApr 21 2009We present an experimental study on the effect of a electromagneticaly generated vortex flow on parametrically amplified waves at the surface of a fluid. The underlying vortex flow, generated by a periodic Lorentz force, creates spatio-temporal fluctuations ... More

VC-dimension and Erdős-Pósa propertyDec 04 2014Let $G=(V,E)$ be a graph. A $k$-neighborhood in $G$ is a set of vertices consisting of all the vertices at distance at most $k$ from some vertex of $G$. The hypergraph on vertex set $V$ which edge set consists of all the $k$-neighborhoods of $G$ for all ... More

On Tail Index Estimation based on Multivariate DataFeb 03 2014Apr 09 2014This article is devoted to the study of tail index estimation based on i.i.d. multivariate observations, drawn from a standard heavy-tailed distribution, i.e. of which 1-d Pareto-like marginals share the same tail index. A multivariate Central Limit Theorem ... More

Edge-partitioning 3-edge-connected graphs into pathsJul 26 2019We show that for every l, there exists d_l such that every 3-edge-connected graph with minimum degree d_l can be edge-partitioned into paths of length l (provided that its number of edges is divisible by l). This improves a result asserting that 24-edge-connectivity ... More

Coloring dense graphs via VC-dimensionJul 09 2010The Vapnik-\v{C}ervonenkis dimension is a complexity measure of set-systems, or hypergraphs. Its application to graphs is usually done by considering the sets of neighborhoods of the vertices (cf. Alon et al. (2006) and Chepoi, Estellon, and Vaxes (2007)), ... More

Universal terms in the overlap of the ground state of the spin-1/2 XXZ chain with the Néel stateMay 23 2017Aug 05 2017We analyze universal terms that appear in the large system size scaling of the overlap between the N\'eel state and the ground state of the spin-1/2 XXZ chain in the antiferromagnetic regime. In a critical theory, the order one term of the asymptotics ... More

Logarithmic corrections to the free energy from sharp corners with angle $2π$Mar 14 2013Jul 25 2013We study subleading corrections to the corner free energy in classical two-dimensional critical systems, focusing on a generic boundary perturbation by the stress-tensor of the underlying conformal field theory (CFT). In the particular case of an angle ... More

Full counting statistics in the Haldane-Shastry chainAug 24 2016We present analytical and numerical results regarding the magnetization full counting statistics (FCS) of a subsystem in the ground-state of the Haldane-Shastry chain. Exact Pfaffian expressions are derived for the cumulant generating function, as well ... More

Spatial and spectral dynamics in STEM hyperspectral imaging using random scan patternsSep 17 2019The evolution of the scanning modules for scanning transmission electron microscopes (STEM) has realized the possibility to generate arbitrary scan pathways, an approach currently explored to improve acquisition speed and to reduce electron dose effects. ... More

Enhanced Eshelby Twist on Thin Wurtzite InP Nanowires and Measurement of Local Crystal RotationSep 11 2014We have performed a detailed study of the lattice distortions of InP wurtzite nanowires containing an axial screw dislocation. Eshelby predicted that this kind of system should show a crystal rotation due to the dislocation induced torque. We have measured ... More

Realization of aperiodic subshifts and uniform densities in groupsJul 13 2015Feb 17 2016A theorem of Gao, Jackson and Seward, originally conjectured to be false by Glasner and Uspenskij, asserts that every countable group admits a $2$-coloring. A direct consequence of this result is that every countable group has a strongly aperiodic subshift ... More

Clique versus Independent SetJan 11 2013Jun 27 2014Yannakakis' Clique versus Independent Set problem (CL-IS) in communication complexity asks for the minimum number of cuts separating cliques from stable sets in a graph, called CS-separator. Yannakakis provides a quasi-polynomial CS-separator, i.e. of ... More

Isolating highly connected induced subgraphsJun 06 2014We prove that any graph $G$ of minimum degree greater than $2k^2-1$ has a $(k+1)$-connected induced subgraph $H$ such that the number of vertices of $H$ that have neighbors outside of $H$ is at most $2k^2-1$. This generalizes a classical result of Mader, ... More

Graphs with large chromatic number induce $3k$-cyclesAug 10 2014Answering a question of Kalai and Meshulam, we prove that graphs without induced cycles of length $3k$ have bounded chromatic number. This implies the very first case of a much broader question asserting that every graph with large chromatic number induces ... More

Online Matrix Completion Through Nuclear Norm RegularisationJan 10 2014It is the main goal of this paper to propose a novel method to perform matrix completion on-line. Motivated by a wide variety of applications, ranging from the design of recommender systems to sensor network localization through seismic data reconstruction, ... More

Observation of intermittency in wave turbulenceDec 29 2006Mar 07 2007We report the observation of intermittency in gravity-capillary wave turbulence on the surface of mercury. We measure the temporal fluctuations of surface wave amplitude at a given location. We show that the shape of the probability density function of ... More

Scaling-up Empirical Risk Minimization: Optimization of Incomplete U-statisticsJan 12 2015Apr 19 2016In a wide range of statistical learning problems such as ranking, clustering or metric learning among others, the risk is accurately estimated by $U$-statistics of degree $d\geq 1$, i.e. functionals of the training data with low variance that take the ... More

Realization of aperiodic subshifts and uniform densities in groupsJul 13 2015Mar 23 2018A theorem of Gao, Jackson and Seward, originally conjectured to be false by Glasner and Uspenskij, asserts that every countable group admits a $2$-coloring. A direct consequence of this result is that every countable group has a strongly aperiodic subshift ... More

A Short Review of Ethical Challenges in Clinical Natural Language ProcessingMar 29 2017Clinical NLP has an immense potential in contributing to how clinical practice will be revolutionized by the advent of large scale processing of clinical records. However, this potential has remained largely untapped due to slow progress primarily caused ... More

Sparse Representation of Multivariate Extremes with Applications to Anomaly RankingMar 31 2016Extremes play a special role in Anomaly Detection. Beyond inference and simulation purposes, probabilistic tools borrowed from Extreme Value Theory (EVT), such as the angular measure, can also be used to design novel statistical learning methods for Anomaly ... More

The Erdős-Hajnal Conjecture for Paths and AntipathsMar 21 2013Jun 26 2014We prove that for every k, there exists $c_k>0$ such that every graph G on n vertices not inducing a path $P_k$ and its complement contains a clique or a stable set of size $n^{c_k}$.

A note on the minimum distance of quantum LDPC codesApr 25 2014We provide a new lower bound on the minimum distance of a family of quantum LDPC codes based on Cayley graphs proposed by MacKay, Mitchison and Shokrollahi. Our bound is exponential, improving on the quadratic bound of Couvreur, Delfosse and Z\'emor. ... More

Multiresolution Analysis of Incomplete RankingsMar 08 2014Incomplete rankings on a set of items $\{1,\; \ldots,\; n\}$ are orderings of the form $a_{1}\prec\dots\prec a_{k}$, with $\{a_{1},\dots a_{k}\}\subset\{1,\dots,n\}$ and $k < n$. Though they arise in many modern applications, only a few methods have been ... More

Observation of gravity-capillary wave turbulenceOct 11 2006Mar 07 2007We report the observation of the cross-over between gravity and capillary wave turbulence on the surface of mercury. The probability density functions of the turbulent wave height are found to be asymmetric and thus non Gaussian. The surface wave height ... More

Ranking and empirical minimization of U-statisticsMar 05 2006The problem of ranking/ordering instances, instead of simply classifying them, has recently gained much attention in machine learning. In this paper we formulate the ranking problem in a rigorous statistical framework. The goal is to learn a ranking rule ... More

A Multiresolution Analysis Framework for the Statistical Analysis of Incomplete RankingsJan 04 2016Though the statistical analysis of ranking data has been a subject of interest over the past centuries, especially in economics, psychology or social choice theory, it has been revitalized in the past 15 years by recent applications such as recommender ... More

Disproving the normal graph conjectureAug 22 2015Mar 25 2016A graph $G$ is called normal if there exist two coverings, $\mathbb{C}$ and $\mathbb{S}$ of its vertex set such that every member of $\mathbb{C}$ induces a clique in $G$, every member of $\mathbb{S}$ induces an independent set in $G$ and $C \cap S \neq ... More

Discussion of ``2004 IMS Medallion Lecture: Local Rademacher complexities and oracle inequalities in risk minimization'' by V. KoltchinskiiAug 01 2007Discussion of ``2004 IMS Medallion Lecture: Local Rademacher complexities and oracle inequalities in risk minimization'' by V. Koltchinskii [arXiv:0708.0083]

Geometric entanglement of critical XXZ and Ising chains and Affleck-Ludwig boundary entropiesJul 23 2010We study the geometrical entanglement of the XXZ chain in its critical regime. Recent numerical simulations [Q.-Q. Shi, R. Or\'us, J. O. Fj\ae restad and H.-Q Zhou, New J. Phys. {\bf 12}, 025008 (2010)] indicate that it scales linearly with system size, ... More

Conflict Packing: an unifying technique to obtain polynomial kernels for editing problems on dense instancesJan 24 2011Jan 30 2014We develop a technique that we call Conflict Packing in the context of kernelization, obtaining (and improving) several polynomial kernels for editing problems on dense instances. We apply this technique on several well-studied problems: Feedback Arc ... More

A Probabilistic Theory of Supervised Similarity Learning for Pointwise ROC Curve OptimizationJul 18 2018The performance of many machine learning techniques depends on the choice of an appropriate similarity or distance measure on the input space. Similarity learning (or metric learning) aims at building such a measure from training data so that observations ... More

Symmetric Determinantal Representations in Characteristic 2Oct 22 2012May 15 2013This paper studies Symmetric Determinantal Representations (SDR) in characteristic 2, that is the representation of a multivariate polynomial P by a symmetric matrix M such that P=det(M), and where each entry of M is either a constant or a variable. We ... More

Learning the dependence structure of rare events: a non-asymptotic studyMay 23 2015Assessing the probability of occurrence of extreme events is a crucial issue in various fields like finance, insurance, telecommunication or environmental sciences. In a multivariate framework, the tail dependence is characterized by the so-called stable ... More

On Anomaly Ranking and Excess-Mass CurvesFeb 05 2015Learning how to rank multivariate unlabeled observations depending on their degree of abnormality/novelty is a crucial problem in a wide range of applications. In practice, it generally consists in building a real valued "scoring" function on the feature ... More

Ultra-Strong Light-Matter Coupling in Deeply Subwavelength THz LC resonatorsApr 14 2019The ultra-strong light-matter coupling regime has been demonstrated in a novel three-dimensional inductor-capacitor (LC) circuit resonator, embedding a semiconductor two-dimensional electron gas in the capacitive part. The fundamental resonance of the ... More

Multicut is FPTOct 25 2010Nov 23 2010Let $G=(V,E)$ be a graph on $n$ vertices and $R$ be a set of pairs of vertices in $V$ called \emph{requests}. A \emph{multicut} is a subset $F$ of $E$ such that every request $xy$ of $R$ is cut by $F$, \i.e. every $xy$-path of $G$ intersects $F$. We show ... More

The Erdős-Hajnal Conjecture for Long Holes and Anti-holesAug 08 2014Erd\H{o}s and Hajnal conjectured that, for every graph $H$, there exists a constant $c_H$ such that every graph $G$ on $n$ vertices which does not contain any induced copy of $H$ has a clique or a stable set of size $n^{c_H}$. We prove that for every ... More

Efficient Eigen-updating for Spectral Graph ClusteringJan 07 2013Jan 27 2014Partitioning a graph into groups of vertices such that those within each group are more densely connected than vertices assigned to different groups, known as graph clustering, is often used to gain insight into the organisation of large scale networks ... More

A Rényi entropy perspective on topological order in classical toric code modelsJul 16 2015Concepts of information theory are increasingly used to characterize collective phenomena in condensed matter systems, such as the use of entanglement entropies to identify emergent topological order in interacting quantum many-body systems. Here we employ ... More

Using Distributed Representations to Disambiguate Biomedical and Clinical ConceptsAug 19 2016In this paper, we report a knowledge-based method for Word Sense Disambiguation in the domains of biomedical and clinical text. We combine word representations created on large corpora with a small number of definitions from the UMLS to create concept ... More

Evaluating Unsupervised Dutch Word Embeddings as a Linguistic ResourceJul 01 2016Word embeddings have recently seen a strong increase in interest as a result of strong performance gains on a variety of tasks. However, most of this research also underlined the importance of benchmark datasets, and the difficulty of constructing these ... More

Cyclic Orderings and Cyclic Arboricity of MatroidsDec 15 2009Jul 19 2011We prove a general result concerning cyclic orderings of the elements of a matroid. For each matroid $M$, weight function $\omega:E(M)\rightarrow\mathbb{N}$, and positive integer $D$, the following are equivalent. (1) For all $A\subseteq E(M)$, we have ... More

Empirical Risk Minimization under Random Censorship: Theory and PracticeJun 05 2019We consider the classic supervised learning problem, where a continuous non-negative random label $Y$ (i.e. a random duration) is to be predicted based upon observing a random vector $X$ valued in $\mathbb{R}^d$ with $d\geq 1$ by means of a regression ... More

Emergence of curved light-cones in a class of inhomogeneous Luttinger liquidsMay 01 2017Jul 12 2017The light-cone spreading of entanglement and correlation is a fundamental and ubiquitous feature of homogeneous extended quantum systems. Here we point out that a class of inhomogenous Luttinger liquids (those with a uniform Luttinger parameter $K$) at ... More

Parameterized algorithm for weighted independent set problem in bull-free graphsOct 23 2013Nov 21 2014The maximum stable set problem is NP-hard, even when restricted to triangle-free graphs. In particular, one cannot expect a polynomial time algorithm deciding if a bull-free graph has a stable set of size $k$, when $k$ is part of the instance. Our main ... More

Sparsity in Multivariate Extremes with Applications to Anomaly DetectionJul 21 2015Mar 14 2016Capturing the dependence structure of multivariate extreme events is a major concern in many fields involving the management of risks stemming from multiple sources, e.g. portfolio monitoring, insurance, environmental risk management and anomaly detection. ... More

On the complexity of partial derivativesJul 19 2016The method of partial derivatives is one of the most successful lower bound methods for arithmetic circuits. It uses as a complexity measure the dimension of the span of the partial derivatives of a polynomial. In this paper, we consider this complexity ... More

Capillary wave turbulence on a spherical fluid surface in low gravityAug 10 2007Feb 09 2009We report the observation of capillary wave turbulence on the surface of a fluid layer in a low-gravity environment. In such conditions, the fluid covers all the internal surface of the spherical container which is submitted to random forcing. The surface ... More

Coloring dense digraphsApr 24 2017The \emph{chromatic number} of a digraph $D$ is the minimum number of acyclic subgraphs covering the vertex set of $D$. A tournament $H$ is a \emph{hero} if every $H$-free tournament $T$ has chromatic number bounded by a function of $H$. Inspired by the ... More

On the Maximum Weight Independent Set Problem in graphs without induced cycles of length at least fiveMar 12 2019A hole in a graph is an induced cycle of length at least $4$, and an antihole is the complement of an induced cycle of length at least $4$. A hole or antihole is long if its length is at least $5$. For an integer $k$, the $k$-prism is the graph consisting ... More

ASPeRiX, a First Order Forward Chaining Approach for Answer Set ComputingMar 26 2015The natural way to use Answer Set Programming (ASP) to represent knowledge in Artificial Intelligence or to solve a combinatorial problem is to elaborate a first order logic program with default negation. In a preliminary step this program with variables ... More

Identifying codes in hereditary classes of graphs and VC-dimensionJul 22 2014Apr 22 2015An identifying code of a graph is a subset of its vertices such that every vertex of the graph is uniquely identified by the set of its neighbours within the code. We show a dichotomy for the size of the smallest identifying code in classes of graphs ... More

A Dictionary-based Approach to Racism Detection in Dutch Social MediaAug 31 2016We present a dictionary-based approach to racism detection in Dutch social media comments, which were retrieved from two public Belgian social media sites likely to attract racist reactions. These comments were labeled as racist or non-racist by multiple ... More

A tau-conjecture for Newton polygonsAug 10 2013May 13 2014One can associate to any bivariate polynomial P(X,Y) its Newton polygon. This is the convex hull of the points (i,j) such that the monomial X^i Y^j appears in P with a nonzero coefficient. We conjecture that when P is expressed as a sum of products of ... More

Domination and fractional domination in digraphsAug 01 2017Apr 27 2018In this paper, we investigate the relation between the (fractional) domination number of a digraph $G$ and the independence number of its underlying graph, denoted by $\alpha(G)$. More precisely, we prove that every digraph $G$ has fractional domination ... More

Coloring tournaments: from local to globalFeb 06 2017Mar 15 2017The \emph{chromatic number} of a directed graph $D$ is the minimum number of colors needed to color the vertices of $D$ such that each color class of $D$ induces an acyclic subdigraph. Thus, the chromatic number of a tournament $T$ is the minimum number ... More

A Linear Vertex Kernel for Maximum Internal Spanning TreeJul 20 2009Mar 03 2012We present a polynomial time algorithm that for any graph G and integer k >= 0, either finds a spanning tree with at least k internal vertices, or outputs a new graph G' on at most 3k vertices and an integer k' such that G has a spanning tree with at ... More

Gossip Dual Averaging for Decentralized Optimization of Pairwise FunctionsJun 08 2016In decentralized networks (of sensors, connected objects, etc.), there is an important need for efficient algorithms to optimize a global cost function, for instance to learn a global model from the local data collected by each computing unit. In this ... More

The Domination Number of GridsFeb 25 2011In this paper, we conclude the calculation of the domination number of all $n\times m$ grid graphs. Indeed, we prove Chang's conjecture saying that for every $16\le n\le m$, $\gamma(G_{n,m})=\lfloor\frac{(n+2)(m+2)}{5}\rfloor -4$.

Extending Gossip Algorithms to Distributed Estimation of U-StatisticsNov 17 2015Efficient and robust algorithms for decentralized estimation in networks are essential to many distributed systems. Whereas distributed estimation of sample mean statistics has been the subject of a good deal of attention, computation of $U$-statistics, ... More

Shannon and entanglement entropies of one- and two-dimensional critical wave functionsJun 05 2009Oct 22 2009We study the Shannon entropy of the probability distribution resulting from the ground-state wave function of a one-dimensional quantum model. This entropy is related to the entanglement entropy of a Rokhsar-Kivelson-type wave function built from the ... More

Inhomogeneous field theory inside the arctic circleDec 09 2015Jun 09 2016Motivated by quantum quenches in spin chains, a one-dimensional toy-model of fermionic particles evolving in imaginary-time from a domain-wall initial state is solved. The main interest of this toy-model is that it exhibits the arctic circle phenomenon, ... More

Reversals of a large scale field generated over a turbulent backgroundFeb 02 2011We present a study of several systems in which a large scale field is generated over a turbulent background. These large scale fields usually break a symmetry of the forcing by selecting a direction. Under certain conditions, the large scale field displays ... More

Conformal Field Theory for Inhomogeneous One-dimensional Quantum Systems: the Example of Non-Interacting Fermi GasesJun 14 2016Nov 14 2016Conformal field theory (CFT) has been extremely successful in describing large-scale universal effects in one-dimensional (1D) systems at quantum critical points. Unfortunately, its applicability in condensed matter physics has been limited to situations ... More

Survey schemes for stochastic gradient descent with applications to M-estimationJan 09 2015In certain situations that shall be undoubtedly more and more common in the Big Data era, the datasets available are so massive that computing statistics over the full sample is hardly feasible, if not unfeasible. A natural approach in this context consists ... More

A stochastic SIR model with contact-tracing: large population limits and statistical inferenceJul 22 2008A stochastic epidemic model accounting for the effect of contact-tracing on the spread of an infectious disease is studied. Precisely, individuals identified as infected may contribute to detecting other infectious individuals by providing information ... More

On the complexity of partial derivativesJul 19 2016May 31 2017The method of partial derivatives is one of the most successful lower bound methods for arithmetic circuits. It uses as a complexity measure the dimension of the span of the partial derivatives of a polynomial. In this paper, we consider this complexity ... More

Quasi-polynomial time approximation schemes for the Maximum Weight Independent Set Problem in H-free graphsJul 10 2019In the Maximum Independent Set problem we are asked to find a set of pairwise nonadjacent vertices in a given graph with the maximum possible cardinality. In general graphs, this classical problem is known to be NP-hard and hard to approximate within ... More

Hitting and Harvesting PumpkinsMay 13 2011Dec 13 2013The "c-pumpkin" is the graph with two vertices linked by c>0 parallel edges. A c-pumpkin-model in a graph G is a pair A,B of disjoint subsets of vertices of G, each inducing a connected subgraph of G, such that there are at least c edges in G between ... More

Parameterized Complexity of Independent Set in H-Free GraphsOct 10 2018Feb 20 2019In this paper, we investigate the complexity of Maximum Independent Set (MIS) in the class of $H$-free graphs, that is, graphs excluding a fixed graph as an induced subgraph. Given that the problem remains $NP$-hard for most graphs $H$, we study its fixed-parameter ... More

On Computer-Intensive Simulation and Estimation Methods for Rare Event Analysis in Epidemic ModelsAug 27 2013This article focuses, in the context of epidemic models, on rare events that may possibly correspond to crisis situations from the perspective of Public Health. In general, no close analytic form for their occurrence probabilities is available and crude ... More

An Empirical Comparison of V-fold Penalisation and Cross Validation for Model Selection in Distribution-Free RegressionDec 08 2012Model selection is a crucial issue in machine-learning and a wide variety of penalisation methods (with possibly data dependent complexity penalties) have recently been introduced for this purpose. However their empirical performance is generally not ... More