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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

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

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

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

Quasideterminant solutions of a non-Abelian Hirota-Miwa equationFeb 09 2007A non-Abelian version of the Hirota-Miwa equation is considered. In an earlier paper [Nimmo (2006) J. Phys. A: Math. Gen. \textbf{39}, 5053-5065] it was shown how solutions expressed as quasideterminants could be constructed for this system by means of ... More

Linearization of the box-ball system: an elementary approachSep 28 2017Dec 30 2017Kuniba, Okado, Takagi and Yamada have found that the time-evolution of the Takahashi-Satsuma box-ball system can be linearized by considering rigged configurations associated with states of the box-ball system. We introduce a simple way to understand ... 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.

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

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

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

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

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

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

An asymptotically stable scheme for diffusive coagulation-fragmentation modelsAug 23 2007This paper is devoted to the analysis of a numerical scheme for the coagulation and fragmentation equation with diffusion in space. A finite volume scheme is developed, based on a conservative formulation of the space nonhomogeneous coagulation-fragmentation ... 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

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

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

Irrationality proofs for zeta values, moduli spaces and dinner partiesDec 19 2014A simple geometric construction on the moduli spaces $\mathcal{M}_{0,n}$ of curves of genus $0$ with $n$ ordered marked points is described which gives a common framework for many irrationality proofs for zeta values. This construction yields Ap\'ery's ... More

Functional Programming is FreeApr 02 2015A paper has recently been published in SIAM-JC. This paper is faulty: 1) The standard requirements about the definition of an algorithm are not respected, 2) The main point in the complexity study, namely the functional programming component, is absent. ... 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

Recent developments in heavy flavor probes in lattice QCDOct 29 2015The analysis of heavy flavor lattice correlation functions to obtain insights into transport phenomena and bound state dissociation patterns is a difficult and interesting challenge from the point of view of lattice QCD spectroscopy. In this contribution ... More

The highest energy neutrinos: first evidence for cosmic originNov 25 2013Developments in neutrino astronomy have been to a great extent motivated by the search for the sources of the cosmic rays, leading at a very early stage to the concept of a cubic kilometer neutrino detector. Almost four decades later such an instrument, ... More

The Lutz-Kelker ParadoxJun 25 2014Jul 11 2014The Lutz-Kelker correction is intended to give an unbiased estimate for stellar parallaxes and magnitudes, but it is shown explicitly that it does not. This paradox results from the application of an argument about sample statistics to the treatment of ... More

Sharp analysis of low-rank kernel matrix approximationsAug 09 2012May 22 2013We consider supervised learning problems within the positive-definite kernel framework, such as kernel ridge regression, kernel logistic regression or the support vector machine. With kernels leading to infinite-dimensional feature spaces, a common practical ... More

Integral points on curves, the unit equation, and motivic periodsApr 03 2017This paper recasts some of the recent literature on Kim's extension of Chabauty's method for bounding points on curves in the language of motivic periods. A variant of the higher Albanese manifolds is defined which is equipped with a canonical de Rham ... More

IceCube: Neutrino Physics from GeV - PeVAug 14 2013An update on recent discoveries by the IceCube project, which transforms approximately one cubic kilometer of natural Antarctic ice into a Cherenkov detector. This paper will be submitted to SLAC for inclusion in the Snowmass2013 proceedings

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.

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

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

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

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

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

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

From the Deligne-Ihara conjecture to Multiple Modular ValuesMar 30 2019This is the write-up of a talk given in honour of Prof. Ihara's 80th Birthday conference in Kyoto in 2018. After briefly reviewing the work of Ihara on the projective line minus 3 points, I outline the main ideas in the proof of the Deligne-Ihara conjecture ... 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

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

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

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

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

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

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

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.

A multi-variable version of the completed Riemann zeta function and other $L$-functionsMar 30 2019We define a generalisation of the completed Riemann zeta function in several complex variables. It satisfies a functional equation, shuffle product identities, and has simple poles along finitely many hyperplanes, with a recursive structure on its residues. ... 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

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

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

On indicated coloring of some classes of graphsFeb 01 2018Indicated coloring is a type of game coloring in which two players collectively color the vertices of a graph in the following way. In each round the first player (Ann) selects a vertex, and then the second player (Ben) colors it properly, using a fixed ... More

How Traders enter the Market through the BookMar 05 2001Simulation of the trading activity based on the implementation of the book.

Life in the Stockmarket - a Realistic Model for TradingAug 31 2000We propose a frustrated and disordered many-body model of a stockmarket in which independent adaptive traders can trade a stock subject to the economic law of supply and demand. We show that the typical scaling properties and the correlated volatility ... More

Stochastic Variance Reduction Methods for Saddle-Point ProblemsMay 20 2016We consider convex-concave saddle-point problems where the objective functions may be split in many components, and extend recent stochastic variance reduction methods (such as SVRG or SAGA) to provide the first large-scale linearly convergent algorithms ... More

Tau Neutrino Appearance with a 1000 Megaparsec BaselineApr 21 1998A high-energy neutrino telescope, such as the operating AMANDA detector, may detect neutrinos produced in sources, possibly active galactic nuclei or gamma-ray bursts, distant by a thousand megaparsecs. These sources produce mostly nu_e or nu_mu neutrinos. ... More

A Rescaling Velocity Method for Dissipative Kinetic Equations - Applications to Granular MediaApr 24 2012Apr 18 2013We present a new numerical algorithm based on a relative energy scaling for collisional kinetic equations allowing to study numerically their long time behavior, without the usual problems related to the change of scales in velocity variables. It is based ... More

Analysis of an Asymptotic Preserving Scheme for Relaxation SystemsMay 13 2011We study the convergence of a class of asymptotic preserving numerical schemes initially proposed by F. Filbet & S. Jin \cite{filb1} and G. Dimarco & L. Pareschi \cite{DimarcoP} in the context of nonlinear and stiff kinetic equations. Here, our analysis ... More

The Continuum Slopes of Optically Selected QSOsJul 29 1996Quasi-simultaneous optical/near-IR photometry is presented for a sample of 37 luminous optically selected QSOs drawn from the Large Bright QSO Survey. Most of the QSOs have decreased in brightness since discovery; this is expected in flux-limited samples. ... More

Data-driven calibration of linear estimators with minimal penaltiesSep 10 2009Sep 13 2011This paper tackles the problem of selecting among several linear estimators in non-parametric regression; this includes model selection for linear regression, the choice of a regularization parameter in kernel ridge regression, spline smoothing or locally ... More

Mean field propagation of infinite dimensional Wigner measures with a singular two-body interaction potentialNov 25 2011Jun 25 2014We consider the quantum dynamics of many bosons systems in the mean field limit with a singular pair-interaction potential, including the attractive or repulsive Coulombic case in three dimensions. By using a measure transportation technique, we show ... More

Electrical conductivity and thermal dilepton rate from quenched lattice QCDSep 19 2011We report on a continuum extrapolation of the vector current correlation function for light valence quarks in the deconfined phase of quenched QCD. This is achieved by performing a systematic analysis of the influence of cut-off effects on light quark ... More

Gamma Ray Astronomy With IceCubeMay 13 2003We demonstrate that the South Pole kilometer-scale neutrino observatory IceCube can detect multi-TeV gamma rays continuously over a large fraction of the southern sky. While not as sensitive as pointing atmospheric Cerenkov telescopes, IceCube can roughly ... More

The vacant set of two-dimensional critical random interlacement is infiniteJun 18 2016For the model of two-dimensional random interlacements in the critical regime (i.e., $\alpha=1$), we prove that the vacant set is a.s.\ infinite, thus solving an open problem from arXiv:1502.03470. Also, we prove that the entrance measure of simple random ... More

Direct products and elementary equivalence of polycyclic-by-finite groupsSep 10 2013Aug 13 2014We give an algebraic characterization of elementary equivalence for polycyclic-by-finite groups. Using this characterization, we investigate the relations between their elementary equivalence and the elementary equivalence of the factors in their decompositions ... More

A p-adaptive local discontinuous galerkin level set method for Willmore flowMar 14 2016The level set method is often used to capture interface behavior in two or three dimensions. In this paper, we present a combination of local discontinuous Galerkin (LDG) method and level set method for simulating Willmore flow. The LDG scheme is energy ... More

Non-strongly-convex smooth stochastic approximation with convergence rate O(1/n)Jun 10 2013We consider the stochastic approximation problem where a convex function has to be minimized, given only the knowledge of unbiased estimates of its gradients at certain points, a framework which includes machine learning methods based on the minimization ... More

On the importance of nonlinear couplings in large-scale neutrino streamsMar 19 2015Jul 15 2015We propose a procedure to evaluate the impact of nonlinear couplings on the evolution of massive neutrino streams in the context of large-scale structure growth. Such streams can be described by general nonlinear conservation equations, derived from a ... More

Describing massive neutrinos in cosmology as a collection of independent flowsNov 21 2013A new analytical approach allowing to account for massive neutrinos in the non-linear description of the growth of the large-scale structure of the universe is proposed. Unlike the standard approach in which neutrinos are described as a unique hot fluid, ... More

Concentration Fluctuations from Multinomial Probability Theory and the possible role in continuum Microkinetic Rate TheoryJan 18 2019Recently, continuum Microkinetic Rate Theory (cMRT) has been advanced as a method of studying rates of systems, where deviations between observation and cMRT theory have been found, and it hypothesized that these deviations are linked either to oscillations ... More

Spanning forest polynomials and the transcendental weight of Feynman graphsOct 28 2009We give combinatorial criteria for predicting the transcendental weight of Feynman integrals of certain graphs in $\phi^4$ theory. By studying spanning forest polynomials, we obtain operations on graphs which are weight-preserving, and a list of subgraphs ... More

The metric space of geodesic laminations on a surface II: small surfacesAug 28 2003May 28 2005We continue our investigation of the space of geodesic laminations on a surface, endowed with the Hausdorff topology. We determine the topology of this space for the once-punctured torus and the 4-times-punctured sphere. For these two surfaces, we also ... More