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New insights on Titan's interior from its obliquityMar 10 2014We constructed a 6-degrees of freedom rotational model of Titan as a 3-layer body consisting of a rigid core, a fluid global ocean, and a floating ice shell. The ice shell exhibits partially-compensated lateral thickness variations in order to simultaneously ... More

Ocean tidal heating in icy satellites with solid shellsApr 20 2018As a long-term energy source, tidal heating in subsurface oceans of icy satellites can influence their thermal, rotational, and orbital evolution, and the sustainability of oceans. We present a new theoretical treatment for tidal heating in thin subsurface ... More

Impact-induced melting during accretion of the EarthMar 29 2016Because of the high energies involved, giant impacts that occur during planetary accretion cause large degrees of melting. The depth of melting in the target body after each collision determines the pressure and temperature conditions of metal-silicate ... More

On solutions to the non-Abelian Hirota-Miwa equation and its continuum limitsSep 23 2008In this paper, we construct grammian-like quasideterminant solutions of a non-Abelian Hirota-Miwa equation. Through continuum limits of this non-Abelian Hirota-Miwa equation and its quasideterminant solutions, we construct a cascade of noncommutative ... More

Yang-Baxter Maps from the Discrete BKP EquationNov 13 2009Mar 31 2010We construct rational and piecewise-linear Yang-Baxter maps for a general N-reduction of the discrete BKP equation.

Darboux dressing and undressing for the ultradiscrete KdV equationMar 18 2019We solve the direct scattering problem for the ultradiscrete Korteweg de Vries (udKdV) equation, over $\mathbb R$ for any potential with compact (finite) support, by explicitly constructing bound state and non-bound state eigenfunctions. We then show ... More

Bolasso: model consistent Lasso estimation through the bootstrapApr 08 2008We consider the least-square linear regression problem with regularization by the l1-norm, a problem usually referred to as the Lasso. In this paper, we present a detailed asymptotic analysis of model consistency of the Lasso. For various decays of the ... More

Matching of Wilson loop eigenvalue densities in 1+1, 2+1 and 3+1 dimensionsMay 14 2007We investigate the matching of eigenvalue densities of Wilson loops in SU(N) lattice gauge theory: the eigenvalue densities in 1+1, 2+1 and 3+1 dimensions are nearly identical when the traces of the loops are equal. We show that the matching is present ... More

Multiple Modular Values for SL_2(Z)Jul 19 2014Multiple modular values are a common generalisation of multiple zeta values and periods of modular forms, and are periods of a hypothetical Tannakian category of mixed modular motives. They are given by regularised iterated integrals on the upper half ... More

An Extension of the Bianchi-Egnell Stability Estimate to Bakry, Gentil, and Ledoux's Generalization of the Sobolev Inequality to Continuous DimensionsDec 17 2015This paper extends a stability estimate of the Sobolev Inequality established by G. Bianchi and H. Egnell in their paper "A note on the Sobolev Inequality." Bianchi and Egnell's Stability Estimate answers the question raised by H. Brezis and E. H. Lieb: ... More

Breaking the Curse of Dimensionality with Convex Neural NetworksDec 30 2014Oct 31 2016We consider neural networks with a single hidden layer and non-decreasing homogeneous activa-tion functions like the rectified linear units. By letting the number of hidden units grow unbounded and using classical non-Euclidean regularization tools on ... More

Boundary conditions and subelliptic estimates for geometric Kramers-Fokker-Planck operators on manifolds with boundariesSep 19 2013Feb 03 2014This article is concerned with maximal accretive realizations of geometric Kramers-Fokker-Planck operators on manifolds with boundaries. A general class of boundary conditions is introduced which ensures the maximal accretivity and some global subelliptic ... More

Cybernetic Principles of Aging and Rejuvenation: the buffering-challenging strategy for life extensionMar 31 2014Aging is analyzed as the spontaneous loss of adaptivity and increase in fragility that characterizes dynamic systems. Cybernetics defines the general regulatory mechanisms that a system can use to prevent or repair the damage produced by disturbances. ... More

CosPA2013: OutlookFeb 28 2014Outlook talk presented at the 10th International Symposium on Cosmology and Particle Astrophysics (CosPA2013)

Duality between subgradient and conditional gradient methodsNov 27 2012Oct 18 2013Given a convex optimization problem and its dual, there are many possible first-order algorithms. In this paper, we show the equivalence between mirror descent algorithms and algorithms generalizing the conditional gradient method. This is done through ... More

Single-valued periods and multiple zeta valuesSep 20 2013The values at 1 of single-valued multiple polylogarithms span a certain subalgebra of multiple zeta values. In this paper, the properties of this algebra are studied from the point of view of motivic periods.

Solving Local Equivalence Problems with the Equivariant Moving Frame MethodApr 05 2013Given a Lie pseudo-group action, an equivariant moving frame exists in the neighborhood of a submanifold jet provided the action is free and regular. For local equivalence problems the freeness requirement cannot always be satisfied and in this paper ... More

Unfriendly or weakly unfriendly partitions of graphsFeb 01 2014For each infinite cardinal $\kappa $ and each graph $G=(V,E)$, we say that a partition $\pi :V\rightarrow \left\{ 0,1\right\} $ is $\kappa $-unfriendly if, for each $x\in V$, $\left| \left\{ y\in V\mid \left\{ x,y\right\} \in E\text{ and }\pi (y)\neq ... More

Point transformations in invariant difference schemesJul 17 2005In this paper, we show that when two systems of differential equations admitting a symmetry group are related by a point transformation it is always possible to generate invariant schemes, one for each system, that are also related by the same transformation. ... More

Depth-graded motivic multiple zeta valuesJan 14 2013We study the depth filtration on motivic multiple zeta values, and its relation to modular forms. Using period polynomials for cusp forms for PSL_2(Z), we construct an explicit Lie algebra of solutions to the linearized double shuffle equations over the ... More

Multiple Modular Values and the relative completion of the fundamental group of $M_{1,1}$Jul 19 2014Jun 19 2017Multiple modular values are a common generalisation of multiple zeta values and periods of modular forms, and are periods of a hypothetical Tannakian category of mixed modular motives. They are given by regularised iterated integrals on the upper half ... More

Self-avoiding and plane-filling properties for terdragons and other triangular folding curvesDec 27 2017We consider $n$-folding triangular curves, or $n$-folding t-curves, obtained by folding $n$ times a strip of paper in $3$, each time possibly left then right or right then left, and unfolding it with $\pi /3$ angles. An example is the well known terdragon ... More

Locally Contractive Maps on Perfect Polish Ultrametric SpacesFeb 12 2015May 01 2015In this paper we present a result concerning locally contractive maps defined on subsets of perfect Polish ultrametric spaces (i.e. separable complete ultrametric spaces). Specifically, we show that a perfect compact ultrametric space cannot be contained ... More

On deterministic approximation of the Boltzmann equation in a bounded domainJun 06 2011In this paper we present a fully deterministic method for the numerical solution to the Boltzmann equation of rarefied gas dynamics in a bounded domain for multi-scale problems. Periodic, specular reflection and diffusive boundary conditions are discussed ... More

The tangent complex and Hochschild cohomology of E_n-ringsApr 01 2011Aug 29 2013In this work, we study the deformation theory of $\cE_n$-rings and the $\cE_n$ analogue of the tangent complex, or topological Andr\'e-Quillen cohomology. We prove a generalization of a conjecture of Kontsevich, that there is a fiber sequence $A[n-1] ... More

Constraints on higher-dimensional gravity from the cosmic shear three-point correlation functionSep 09 2004With the developments of large galaxy surveys or cosmic shear surveys it is now possible to map the dark matter distribution at truly cosmological scales. Detailed examinations of the statistical properties of the dark matter distribution reveal the detail ... More

Self-concordant analysis for logistic regressionOct 24 2009Most of the non-asymptotic theoretical work in regression is carried out for the square loss, where estimators can be obtained through closed-form expressions. In this paper, we use and extend tools from the convex optimization literature, namely self-concordant ... More

Weak disorder for low dimensional polymers: The model of stable lawsMar 16 2006In this paper, we consider directed polymers in random environment with long range jumps in discrete space and time. We extend to this case some techniques, results and classifications known in the usual short range case. However, some properties are ... More

A class of non-holomorphic modular forms III: real analytic cusp forms for $\mathrm{SL}_2(\mathbb{Z})$Oct 22 2017Nov 06 2017We define canonical real analytic versions of modular forms of integral weight for the full modular group, generalising real analytic Eisenstein series. They are harmonic Maass waveforms with poles at the cusp, whose Fourier coefficients involve periods ... More

Peano-Gosper curves and the local isomorphism propertyMay 02 2017We consider unbounded curves without endpoints. Isomorphism is equivalence up to translation. Self-avoiding plane-filling curves cannot be periodic, but they can satisfy the local isomorphism property: We obtain a set $\Omega $ of coverings of the plane ... More

Centralizers in the Hecke algebras of complex reflection groupsJul 18 2007How far can the elementary description of centralizers of parabolic subalgebras of Hecke algebras of finite real reflection groups be generalized to the complex reflection group case? In this paper we begin to answer this question by establishing results ... More

Exploring Large Feature Spaces with Hierarchical Multiple Kernel LearningSep 09 2008For supervised and unsupervised learning, positive definite kernels allow to use large and potentially infinite dimensional feature spaces with a computational cost that only depends on the number of observations. This is usually done through the penalization ... More

Graph kernels between point cloudsDec 20 2007Point clouds are sets of points in two or three dimensions. Most kernel methods for learning on sets of points have not yet dealt with the specific geometrical invariances and practical constraints associated with point clouds in computer vision and graphics. ... More

Model-Consistent Sparse Estimation through the BootstrapJan 21 2009We consider the least-square linear regression problem with regularization by the $\ell^1$-norm, a problem usually referred to as the Lasso. In this paper, we first present a detailed asymptotic analysis of model consistency of the Lasso in low-dimensional ... More

A Schlafli-type formula for convex cores of hyperbolic 3-manifoldsApr 30 1997In 3-dimensional hyperbolic geometry, the classical Schlafli formula expresses the variation of the volume of a hyperbolic polyhedron in terms of the length of its edges and of the variation of its dihedral angles. We prove a similar formula for the variation ... More

Variations of the boundary geometry of 3--dimensional hyperbolic convex coresApr 30 1997A fundamental object in a hyperbolic 3-manifold M is its convex core C(M), defined as the smallest closed non-empty convex subset of M. We investigate the way the geometry of the boundary S of C(M) varies as we vary the hyperbolic metric of M. Thurston ... More

Mixed Tate motives over $\Z$Feb 07 2011We prove that the category of mixed Tate motives over $\Z$ is spanned by the motivic fundamental group of $\Pro^1$ minus three points. We prove a conjecture by M. Hoffman which states that every multiple zeta value is a $\Q$-linear combination of $\zeta(n_1,..., ... More

Adaptivity of averaged stochastic gradient descent to local strong convexity for logistic regressionMar 25 2013Mar 16 2014In this paper, we consider supervised learning problems such as logistic regression and study the stochastic gradient method with averaging, in the usual stochastic approximation setting where observations are used only once. We show that after $N$ iterations, ... More

The number of paperfolding curves in a covering of the planeAug 13 2014Jul 14 2015These results complete our paper in Hiroshima Mathematical Journal, vol. 42, pp. 37-75. Let C be a covering of the plane by disjoint complete folding curves which satisfies the local isomorphism property. We show that C is locally isomorphic to an essentially ... More

A class of non-holomorphic modular forms IJul 05 2017Oct 26 2017This introductory paper studies a class of real analytic functions on the upper half plane satisfying a certain modular transformation property. They are not eigenfunctions of the Laplacian and are quite distinct from Maass forms. These functions are ... More

Mode coupling evolution in arbitrary inflationary backgroundsMar 18 2010Nov 25 2010The evolution of high order correlation functions of a test scalar field in arbitrary inflationary backgrounds is computed. Whenever possible, exact results are derived from quantum field theory calculations. Taking advantage of the fact that such calculations ... More

The Statistics of the large-scale Velocity FieldJan 15 1996A lot of predictions for the statistical properties of the cosmic velocity field at large-scale have been obtained recently using perturbation theory. In this contribution I report the outcomes of a set of numerical tests that aim to check these results. ... More

Structured sparsity-inducing norms through submodular functionsAug 25 2010Nov 12 2010Sparse methods for supervised learning aim at finding good linear predictors from as few variables as possible, i.e., with small cardinality of their supports. This combinatorial selection problem is often turned into a convex optimization problem by ... More

Consistency of trace norm minimizationOct 15 2007Regularization by the sum of singular values, also referred to as the trace norm, is a popular technique for estimating low rank rectangular matrices. In this paper, we extend some of the consistency results of the Lasso to provide necessary and sufficient ... More

Learning with Submodular Functions: A Convex Optimization PerspectiveNov 28 2011Oct 08 2013Submodular functions are relevant to machine learning for at least two reasons: (1) some problems may be expressed directly as the optimization of submodular functions and (2) the lovasz extension of submodular functions provides a useful set of regularization ... More

Shaping Level Sets with Submodular FunctionsDec 07 2010Jun 10 2011We consider a class of sparsity-inducing regularization terms based on submodular functions. While previous work has focused on non-decreasing functions, we explore symmetric submodular functions and their \lova extensions. We show that the Lovasz extension ... More

High-Dimensional Non-Linear Variable Selection through Hierarchical Kernel LearningSep 04 2009We consider the problem of high-dimensional non-linear variable selection for supervised learning. Our approach is based on performing linear selection among exponentially many appropriately defined positive definite kernels that characterize non-linear ... More

Consistency of the group Lasso and multiple kernel learningJul 23 2007Jan 28 2008We consider the least-square regression problem with regularization by a block 1-norm, i.e., a sum of Euclidean norms over spaces of dimensions larger than one. This problem, referred to as the group Lasso, extends the usual regularization by the 1-norm ... More

Motivic periods and the projective line minus three pointsJul 19 2014This is a review of the theory of the motivic fundamental group of the projective line minus three points, and its relation to multiple zeta values.

Tilings and associated relational structuresFeb 19 2009Feb 19 2010In the present paper, as we did previously in [7], we investigate the relations between the geometric properties of tilings and the algebraic properties of associated relational structures. Our study is motivated by the existence of aperiodic tiling systems. ... More

Paperfolding sequences, paperfolding curves and local isomorphismJun 06 2008Jun 29 2010For each integer n, an n-folding curve is obtained by folding n times a strip of paper in two, possibly up or down, and unfolding it with right angles. Generalizing the usual notion of infinite folding curve, we define complete folding curves as the curves ... More

HST/ACS Observations of Europa's Atmospheric UV Emission at Eastern ElongationJun 07 2011Jun 15 2011We report results of a Hubble Space Telescope (HST) campaign with the Advanced Camera for Surveys to observe Europa at eastern elongation, i.e. Europa's leading side, on 2008 June 29. With five consecutive HST orbits, we constrain Europa's atmospheric ... More

Gravity and non-gravity mediated couplings in multiple-field inflationMar 15 2010Mechanisms for the generation of primordial non-Gaussian metric fluctuations in the context of multiple-field inflation are reviewed. As long as kinetic terms remain canonical, it appears that nonlinear couplings inducing non-gaussianities can be split ... More

Convex Analysis and Optimization with Submodular Functions: a TutorialOct 20 2010Nov 14 2010Set-functions appear in many areas of computer science and applied mathematics, such as machine learning, computer vision, operations research or electrical networks. Among these set-functions, submodular functions play an important role, similar to convex ... More

Notes on Motivic PeriodsDec 20 2015The second part of a set of notes based on lectures given at the IHES in 2015 on Feynman amplitudes and motivic periods.

The massless higher-loop two-point functionApr 10 2008We introduce a new method for computing massless Feynman integrals analytically in parametric form. An analysis of the method yields a criterion for a primitive Feynman graph $G$ to evaluate to multiple zeta values. The criterion depends only on the topology ... More

Dedekind Zeta motives for totally real fieldsApr 10 2008Jan 14 2013Let $k$ be a totally real number field. For every odd $n\geq 3$, we construct a Dedekind zeta motive in the category $\MT(k)$ of mixed Tate motives over $k$. By directly calculating its Hodge realisation, we prove that its period is a rational multiple ... More

Feynman Amplitudes and Cosmic Galois groupDec 20 2015Feb 17 2016The first part of a set of notes based on lectures given at the IHES in May 2015 on Feynman amplitudes and motivic periods.

On the decomposition of motivic multiple zeta valuesFeb 07 2011Feb 08 2011We review motivic aspects of multiple zeta values, and as an application, we give an exact-numerical algorithm to decompose any (motivic) multiple zeta value of given weight into a chosen basis up to that weight.

Discretizations preserving all Lie point symmetries of the Korteweg-de Vries equationJul 15 2005We show how to descritize the Korteweg-de Vries equation in such a way as to preserve all the Lie point symmetries of the continuous differential equation. It is shown that, for a centered implicit scheme, there are at least two possible ways of doing ... More

Periods and Feynman amplitudesDec 31 2015Feynman amplitudes in perturbation theory form the basis for most predictions in particle collider experiments. The mathematical quantities which occur as amplitudes include values of the Riemann zeta function and relate to fundamental objects in number ... More

Feynman Amplitudes and Cosmic Galois groupDec 20 2015Feb 01 2017The first part of a set of notes based on lectures given at the IHES in May 2015 on Feynman amplitudes and motivic periods.

Submodular Functions: from Discrete to Continous DomainsNov 02 2015Feb 23 2016Submodular set-functions have many applications in combinatorial optimization, as they can be minimized and approximately maximized in polynomial time. A key element in many of the algorithms and analyses is the possibility of extending the submodular ... More

Notes on Motivic PeriodsDec 20 2015Feb 22 2017The second part of a set of notes based on lectures given at the IHES in 2015 on Feynman amplitudes and motivic periods.

Convex relaxations of structured matrix factorizationsSep 12 2013We consider the factorization of a rectangular matrix $X $ into a positive linear combination of rank-one factors of the form $u v^\top$, where $u$ and $v$ belongs to certain sets $\mathcal{U}$ and $\mathcal{V}$, that may encode specific structures regarding ... More

The Anisotropies and Origins of Ultrahigh Energy Cosmic RaysOct 04 2018IceCube detects more than 100,000 neutrinos per year in the GeV- to PeV-energy range. Among those, we have isolated a flux of high-energy cosmic neutrinos. I will discuss the instrument, the analysis of the data, the significance of the discovery of cosmic ... More

The evolution of the large-scale structure of the universe: beyond the linear regimeNov 12 2013Dec 01 2013These lecture notes introduce analytical tools, methods and results describing the growth of cosmological structure beyond the linear regime. The presentation is focused on the single flow regime of the Vlasov-Poisson equation describing the development ... More

Two Topological Uniqueness Theorems for Spaces of Real NumbersOct 03 2012A 1910 theorem of Brouwer characterizes the Cantor set as the unique totally disconnected, compact metric space without isolated points. A 1920 theorem of Sierpinski characterizes the rationals as the unique countable metric space without isolated points. ... More

On the topology of components of some Springer fibers and their relation to Kazhdan-Lusztig theoryApr 18 2002We describe the irreducible components of Springer fibers for hook and two-row nilpotent elements of gl_n(C) as iterated bundles of flag manifolds and Grassmannians. We then relate the topology (in particular, the intersection homology Poincare' polynomials) ... More

Zeta elements in depth 3 and the fundamental Lie algebra of a punctured elliptic curveApr 18 2015This paper draws connections between the double shuffle equations and structure of associators; universal mixed elliptic motives as defined by Hain and Matsumoto; and the Rankin-Selberg method for modular forms for $SL_2(\mathbb{Z})$. We write down explicit ... More

Miraculous cancellations for quantum $SL_2$Aug 25 2017Sep 22 2017In earlier work, Helen Wong and the author discovered certain "miraculous cancellations" for the quantum trace map connecting the Kauffman bracket skein algebra of a surface to its quantum Teichmueller space, occurring when the quantum parameter $q$ is ... More

Well-posedness results for the 3D Zakharov-Kuznetsov equationNov 11 2011We prove the local well-posedness of the three-dimensional Zakharov-Kuznetsov equation $\partial_tu+\Delta\partial_xu+ u\partial_xu=0$ in the Sobolev spaces $H^s(\R^3)$, $s>1$, as well as in the Besov space $B^{1,1}_2(\R^3)$. The proof is based on a sharp ... More

The metric space of geodesic laminations on a surface: IAug 28 2003Mar 19 2004We consider the space of geodesic laminations on a surface, endowed with the Hausdorff metric d_H and with a variation of this metric called the d_log metric. We compute and/or estimate the Hausdorff dimensions of these two metrics. We also relate these ... More

Chiral Koszul dualityMar 30 2011Aug 11 2011We extend the theory of chiral and factorization algebras, developed for curves by Beilinson and Drinfeld in \cite{bd}, to higher-dimensional varieties. This extension entails the development of the homotopy theory of chiral and factorization structures, ... More

Cosmological Large-scale Structures beyond Linear Theory in Modified GravityFeb 09 2011We consider the effect of modified gravity on the growth of large-scale structures at second order in perturbation theory. We show that modified gravity models changing the linear growth rate of fluctuations are also bound to change, although mildly, ... More

Zero-pointed manifoldsSep 09 2014Feb 08 2015We formulate a theory of pointed manifolds, accommodating both embeddings and Pontryagin-Thom collapse maps, so as to present a common generalization of Poincar\'e duality in topology and Koszul duality in $\mathcal{E}_n$-algebra.

IceHEP High Energy Physics at the South PoleOct 31 2005Mar 10 2006With the solar and SN87 neutrino observations as proofs of concepts, the kilometer-scale neutrino experiment IceCube will scrutinize its data for new particle physics. In this paper we review the prospects for the realization of such a program. We begin ... More

Poincaré/Koszul dualitySep 08 2014Nov 16 2015We prove a duality for factorization homology which generalizes both usual Poincar\'e duality for manifolds and Koszul duality for $\mathcal{E}_n$-algebras. The duality has application to the Hochschild homology of associative algebras and enveloping ... More

Casimir scaling of domain wall tensions in the deconfined phase of D=3+1 SU(N) gauge theoriesMay 26 2005We perform lattice calculations of the spatial 't Hooft k-string tensions in the deconfined phase of SU(N) gauge theories for N=2,3,4,6. These equal (up to a factor of T) the surface tensions of the domain walls between the corresponding (Euclidean) deconfined ... More

Lattice String Field TheorySep 22 2010String field theory is a candidate for a full non-perturbative definition of string theory. We aim to define string field theory on a space-time lattice to investigate its behaviour at the quantum level. Specifically, we look at string field theory in ... More

Strong to weak coupling transitions of SU(N) gauge theories in 2+1 dimensionsOct 02 2006We find a strong-to-weak coupling cross-over in D=2+1 SU(N) lattice gauge theories that appears to become a third-order phase transition at N=\infty, in a similar way to the Gross-Witten transition in the D=1+1 SU(N\to\infty) lattice gauge theory. There ... More

The Demographics of Long-Period CometsSep 05 2005The absolute magnitude and perihelion distributions of long-period comets are derived, using data from the Lincoln Near-Earth Asteroid Research (LINEAR) survey. The results are surprising in three ways. Firstly, the flux of comets through the inner solar ... More

Kauffman brackets, character varieties, and triangulations of surfacesSep 01 2010A Kauffman bracket on a surface is an invariant for framed links in the thickened surface, satisfying the Kauffman skein relation and multiplicative under superposition. This includes representations of the skein algebra of the surface. We show how an ... More

A law of large numbers for random walks in random mixing environmentsMay 28 2002We prove a law of large numbers for a class of multidimensional random walks in random environments where the environment satisfies appropriate mixing conditions, which hold when the environment is a weak mixing field in the sense of Dobrushin and Shlosman. ... More

Variation of the Liouville measure of a hyperbolic surfaceMar 11 2002Sep 16 2002For a compact riemannian manifold of negative curvature, the geodesic foliation of its unit tangent bundle is independent of the negatively curved metric, up to Holder bicontinuous homeomorphism. However, the riemannian metric defines a natural transverse ... More

Mean field propagation of Wigner measures and BBGKY hierarchies for general bosonic statesMar 10 2010May 07 2010Contrary to the finite dimensional case, Weyl and Wick quantizations are no more asymptotically equivalent in the infinite dimensional bosonic second quantization. Moreover neither the Weyl calculus defined for cylindrical symbols nor the Wick calculus ... More

On Ideal Lattices and Gröbner BasesSep 27 2014In this paper, we draw a connection between ideal lattices and Gr\"{o}bner bases in the multivariate polynomial rings over integers. We study extension of ideal lattices in $\mathbb{Z}[x]/\langle f \rangle$ (Lyubashevsky \& Micciancio, 2006) to ideal ... More

Music-ripping: des pratiques qui provoquent la musicologieDec 24 2009Out of the scope of the usual positions of computing in the field of music and musicology, one notices the emergence of human-computer systems that do exist by breaking off. Though these singular systems take effect in the usual fields of expansion of ... More

Core compactness and diagonality in spaces of open setsNov 16 2010Dec 06 2010We investigate when the space $\mathcal O_X$ of open subsets of a topological space $X$ endowed with the Scott topology is core compact. Such conditions turn out to be related to infraconsonance of $X$, which in turn is characterized in terms of coincidence ... More

Angles, scales and parametric renormalizationDec 06 2011We decompose renormalized Feynman rules according to the scale and angle dependence of amplitudes. We use parametric representations such that the resulting amplitudes can be studied in algebraic geometry.

Multiple Gaussian Process ModelsOct 24 2011We consider a Gaussian process formulation of the multiple kernel learning problem. The goal is to select the convex combination of kernel matrices that best explains the data and by doing so improve the generalisation on unseen data. Sparsity in the ... More

On a three dimensional vision based collision avoidance modelJan 31 2017May 23 2017This paper presents a three dimensional collision avoidance approach for aerial vehicles inspired by coordinated behaviors in biological groups. The proposed strategy aims to enable a group of vehicles to converge to a common destination point avoiding ... More

Asymptotically preserving particle-in-cell methods for inhomogenous strongly magnetized plasmasJan 24 2017We propose a class of Particle-In-Cell (PIC) methods for the Vlasov-Poisson system with a strong and inhomogeneous external magnetic field with fixed direction, where we focus on the motion of particles in the plane orthogonal to the magnetic field (so-called ... More

Symmetry-preserving numerical schemesAug 08 2016Dec 06 2016In these lectures we review two procedures for constructing finite difference numerical schemes that preserve symmetries of differential equations. The first approach is based on Lie's infinitesimal symmetry generators, while the second method uses the ... More

A finite volume scheme for boundary-driven convection-diffusion equations with relative entropy structureJun 03 2016Apr 20 2017We propose a finite volume scheme for a class of nonlinear parabolic equations endowed with non-homogeneous Dirichlet boundary conditions and which admit relative en-tropy functionals. For this kind of models including porous media equations, Fokker-Planck ... More

Computability and Categoricity of Weakly Ultrahomogeneous StructuresAug 03 2016This paper investigates the effective categoricity of ultrahomogeneous structures. It is shown that any computable ultrahomogeneous structure is $\Delta^0_2$ categorical. A structure A is said to be weakly ultrahomogeneous if there is a finite (exceptional) ... More

On the asymptotic limit of the three dimensional Vlasov-Poisson system for large magnetic field : formal derivationMar 10 2016This paper establishes the long time asymptotic limit of the three dimensional Vlasov-Poisson equation with strong external magnetic field. The guiding center approximation is investigated in the three dimensional case with a non-constant magnetic field. ... More

Memetic evolution of art to distinct aestheticsJul 11 2015Humans have been using symbolic representation (i.e. art) as a creative cultural form indisputably for at least 80,000 years. A description of the processes central to the evolution of art from sculpted earthen forms early in human existence to paintings ... More

Charge coupling to anharmonic lattice excitations in a layered crystal at 800KMay 12 2015A study of charged particle and quasi-particle anharmonic lattice excitations in a meta-stable crystal of layered structure at high temperature has shown that a mobile lattice excitation called a quodon can bind securely to a hole or electron. Quodons ... More

On Ideal Lattices, Gröbner Bases and Generalized Hash FunctionsOct 08 2014Sep 08 2016In this paper, we draw connections between ideal lattices and multivariate polynomial rings over integers using Gr\"obner bases. Ideal lattices are ideals in the residue class ring, $\mathbb{Z}[x]/\langle f \rangle$ (here $f$ is a monic polynomial), and ... More