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Prépublications (HAL)

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Une partie des prépublications de l’Institut de Mathématiques de Bourgogne est disponible sur la plateforme HAL :

[hal-01308641] Towards a symplectic version of the Chevalley restriction theorem

1er mars 2017

If (G,V) is a polar representation with Cartan subspace c and Weyl group W, it is shown that there is a natural morphism of Poisson schemes (c+c*)/W->(V+V*)///G. This morphism is conjectured to be an isomorphism of the underlying reduced varieties if (G,V) is visible. The conjecture is (...)

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[hal-01342210] An algebraic continuous time parameter estimation for a sum of sinusoidal waveform signals

26 janvier 2017

In this paper, a novel algebraic method is proposed to estimate amplitudes, frequencies, and phases of a biased and noisy sum of complex exponential sinusoidal signals. The resulting parameter estimates are given by original closed formulas, constructed as integrals acting as time-varying (...)

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[hal-01415014] Affine-ruled varieties without the Laurent cancellation property

12 décembre 2016

We describe a method to construct hypersurfaces of the complex affine n-space with isomorphic C*-cylinders. Among these hypersurfaces, we find new explicit counterexamples to the Laurent cancellation problem, that is, hypersurfaces that are nonisomorphic, although their C*-cylinders are (...)

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[hal-01414966] Normal forms and embeddings for power-log transseries

12 décembre 2016

Dulac series are asymptotic expansions of first return maps in a neighborhood of a hyperbolic polycycle. In this article, we consider two algebras of power-log transseries (generalized series) which extend the algebra of Dulac series. We give a formal normal form and prove a formal embedding (...)

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[hal-01414891] Center Manifolds for Partially Hyperbolic Sets Without Strong Unstable Connections

12 décembre 2016

We consider compact sets which are invariant and partially hyperbolic under the dynamics of a diffeomorphism of a manifold. We prove that such a set K is contained in a locally invariant center submanifold if and only if each strong stable and strong unstable leaf intersects K at exactly one (...)

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[hal-01414874] Connectedness of the space of smooth actions of on the interval

12 décembre 2016

We prove that the spaces of C-infinity orientation preserving actions of Z(n) on [0, 1] and non-free actions of Z(2) on the circle are connected.

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[hal-01414829] Computing higher Frobenius–Schur indicators in fusion categories constructed from inclusions of finite groups

12 décembre 2016

We consider a subclass of the class of group-theoretical fusion categories: To every finite group G and subgroup H one can associate the category of G-graded vector spaces with a two-sided H-action compatible with the grading. We derive a formula that computes higher Frobenius-Schur indicators (...)

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[hal-01414815] Completeness number of families of subsets of convergence spaces

12 décembre 2016

Compactoid and compact families generalize both convergent filters and compact sets. This concept turned out to be useful in various quests, like Scott topologies, triquotient maps and extensions of the Choquet active boundary theorem. The completeness number of a family in a convergence space (...)

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[hal-01414773] A simple solution to the word problem for virtual braid groups

12 décembre 2016

We show a simple and easily implementable solution to the word problem for virtual braid groups.

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[hal-01414713] Characterizations of convex approximate subdifferential calculus in Banach spaces

12 décembre 2016

We establish subdifferential calculus rules for the sum of convex functions defined on normed spaces. This is achieved by means of a condition relying on the continuity behaviour of the inf-convolution of their corresponding conjugates, with respect to any given topology intermediate between (...)

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[hal-01414661] Homological projective duality for determinantal varieties

12 décembre 2016

In this paper we prove Homological Projective Duality for categorical resolutions of several classes of linear determinantal varieties. By this we mean varieties that are cut out by the minors of a given rank of a m x n matrix of linear forms on a given projective space. As applications, we (...)

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[hal-01414596] Fredholm and Wronskian representations of solutions to the KPI equation and multi-rogue waves

12 décembre 2016

We construct solutions to the Kadomtsev-Petviashvili equation (KPI) in terms of Fredholm determinants. We deduce solutions written as a quotient of Wronskians of order 2N. These solutions, called solutions of order N, depend on 2N - 1 parameters. When one of these parameters tends to zero, we (...)

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[hal-01414575] Frobenius-Schur Indicators for Some Fusion Categories Associated to Symmetric and Alternating Groups

12 décembre 2016

We calculate Frobenius-Schur indicator values for some fusion categories obtained from inclusions of finite groups , where more concretely G is symmetric or alternating, and H is a symmetric, alternating or cyclic group. Our work is strongly related to earlier results by (...)

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[hal-01414555] An ocean drum : quasi-geostrophic energetics from a Riemann geometry perspective

12 décembre 2016

We revisit the discussion of the energetics of quasi-geostrophic flows from a geometric perspective based on the introduction of an effective metric, built in terms of the flow stratification and the Coriolis parameter. In particular, an appropriate notion of normal modes is defined through a (...)

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[hal-01413451] Harmonic measures and the foliated geodesic flow for foliations with negatively curved leaves

9 décembre 2016

In this paper we define a notion of Gibbs measure for the geodesic flow tangent to a foliation with negatively curved leaves and associated to a particular potential H. We prove that there is a canonical bijective correspondence between these measures and Garnett's harmonic (...)

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[hal-01413440] Estimating the geometric median in Hilbert spaces with stochastic gradient algorithms : L-p and almost sure rates of convergence

9 décembre 2016

The geometric median, also called L-1-median, is often used in robust statistics. Moreover, it is more and more usual to deal with large samples taking values in high dimensional spaces. In this context, a fast recursive estimator has been introduced by Cardot et al. (2013). This work aims at (...)

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[hal-01413416] A spectral-like decomposition for transitive Anosov flows in dimension three

9 décembre 2016

Given a (transitive or non-transitive) Anosov vector field X on a closed three dimensional manifold M, one may try to decompose (M, X) by cutting M along tori and Klein bottles transverse to X. We prove that one can find a finite collection of pairwise disjoint, pairwise non-parallel tori and (...)

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[hal-01413426] Multidomain spectral method for Schrödinger equations

9 décembre 2016

A multidomain spectral method with compactified exterior domains combined with stable second and fourth order time integrators is presented for Schrodinger equations. The numerical approach allows high precision numerical studies of solutions on the whole real line. At examples for the linear (...)

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[hal-01413281] Moduli spaces of rank two aCM bundles on the Segre product of three projective lines

9 décembre 2016

Let F subset of C P-7 be the image of the Segre embedding of P-1 x P-1 x P-1. In the present paper we deal with the moduli spaces of locally free sheaves epsilon of rank 2 with h(i)(F, epsilon(t)) = 0 for i = 1,2 and t is an element of Z, on F. (C) 2015 Elsevier B.V. All rights (...)

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[hal-01413263] Antiperiodic dynamical 6-vertex model by separation of variables II : functional equations and form factors

9 décembre 2016

We pursue our study of the antiperiodic dynamical 6-vertex model using Sklyanin's separation of variables approach, allowing in the model new possible global shifts of the dynamical parameter. We show in particular that the spectrum and eigenstates of the antiperiodic transfer matrix are (...)

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[hal-01413233] Integration of a Dirac comb and the Bernoulli polynomials

9 décembre 2016

For any positive integer n, we consider the ordinary differential equations of the form y((n)) = 1 - III + F where III denotes the Dirac comb distribution and F is a piecewise-C-infinity periodic function with null average integral. We prove the existence and uniqueness of periodic solutions of (...)

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[hal-01413224] Motives of quadric bundles

9 décembre 2016

This article is about motives of quadric bundles. In the case of odd dimensional fibers and where the basis is of dimension two we give an explicit relative Chow-Kunneth decomposition. This relative Chow-Kunneth decomposition shows that the motive of the quadric bundle is isomorphic to the (...)

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[hal-01413213] Double Ramification Cycles and Quantum Integrable Systems

9 décembre 2016

In this paper, we define a quantization of the Double Ramification Hierarchies of Buryak (Commun Math Phys 336:1085-1107, 2015) and Buryak and Rossi (Commun Math Phys, 2014), using intersection numbers of the double ramification cycle, the full Chern class of the Hodge bundle and psi-classes (...)

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[hal-01413200] Asymptotics of correlation functions of the Heisenberg-Ising chain in the easy-axis regime

9 décembre 2016

We analyse the long-time large-distance asymptotics of the longitudinal correlation functions of the Heisenberg-Ising chain in the easy-axis regime. We show that in this regime the leading asymptotics of the dynamical two-point functions is entirely determined by the two-spinon contribution to (...)

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[hal-01413158] Analysis of a slow–fast system near a cusp singularity

9 décembre 2016

This paper studies a slow fast system whose principal characteristic is that the slow manifold is given by the critical set of the cusp catastrophe. Our analysis consists of two main parts: first, we recall a formal normal form suitable for systems as the one studied here; afterwards, taking (...)

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[hal-01412829] Local analytic regularity in the linearized Calderón problem

8 décembre 2016

We show that the linearized local Dirichlet-to-Neumann map at a real-analytic potential for measurements made at an analytic open subset of the boundary is injective.

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[hal-01412826] Large- x Analysis of an Operator-Valued Riemann–Hilbert Problem

8 décembre 2016

The purpose of this paper is to push forward the theory of operator-valued Riemann-Hilbert problems and demonstrate their effectiveness in respect to the implementation of a non-linear steepest descent method a la Deift-Zhou. In this paper, we demonstrate that the operator-valued (...)

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[hal-01412806] Finite size spectrum of SU(N) principal chiral field from discrete Hirota dynamics

8 décembre 2016

Using recently proposed method of discrete Hirota dynamics for integrable (1 + 1)D quantum field theories on a finite space circle of length L we derive and test numerically a finite system of nonlinear integral equations for the exact spectrum of energies of SU(N) x SU(N) principal chiral (...)

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[hal-01412778] Characterization of regularity for a connected Abelian action

8 décembre 2016

Let V be a finite dimensional real vector space, let g be the real span of a finite set of commuting endomorphisms of V, and G = exp g. We study the orbit structure in elements of a finite partition of V into explicit G-invariant connected sets. In particular, we prove that either there is an (...)

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[hal-01333295] CLEAR : Covariant LEAst-square Re-fitting with applications to image restoration

8 décembre 2016

In this paper, we propose a new framework to remove parts of the systematic errors affecting popular restoration algorithms, with a special focus for image processing tasks. Generalizing ideas that emerged for l1 regularization, we develop an approach re-fitting the results of standard methods (...)

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[hal-01412059] Characterizing the maximum parameter of the total-variation denoising through the pseudo-inverse of the divergence

8 décembre 2016

We focus on the maximum regularization parameter for anisotropic total-variation denoising. It corresponds to the minimum value of the regularization parameter above which the solution remains constant. While this value is well know for the Lasso, such a critical value has not been investigated (...)

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[hal-01287290] Optimal Control of an Ensemble of Bloch Equations with Applications in MRI

8 décembre 2016

The optimal control of an ensemble of Bloch equations describing the evolution of an ensemble of spins is the mathematical model used in Nuclear Resonance Imaging and the associated costs lead to consider Mayer optimal control problems. The Maximum Principle allows to parameterize the optimal (...)

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[hal-01410978] Numerical study of the Kerr solution in rotating coordinates

6 décembre 2016

The Kerr solution in coordinates corotating with the horizon is studied as a testbed for a spacetime with a helical Killing vector in the Ernst picture. The solution is numerically constructed by solving the Ernst equation with a spectral method and a Newton iteration. We discuss convergence of (...)

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[hal-01410977] On critical behaviour in generalized Kadomtsev-Petviashvili equations

6 décembre 2016

An asymptotic description of the formation of dispersive shock waves in solutions to the generalized Kadomtsev-Petviashvili (KP) equation is conjectured. The asymptotic description based on a multiscales expansion is, given in terms of a special solution to an ordinary differential equation of (...)

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[hal-01410973] On determinant representations of scalar products and form factors in the SoV approach : the XXX case

6 décembre 2016

In the present article we study the form factors of quantum integrable lattice models solvable by the separation of variables (SoVs) method. It was recently shown that these models admit universal determinant representations for the scalar products of the so-called separate states (a class (...)

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[hal-01410931] On tensor factorizations of Hopf algebras

6 décembre 2016

We prove a variety of results on tensor product factorizations of finite dimensional Hopf algebras (more generally Hopf algebras satisfying chain conditions in suitable braided categories). The results are analogs of well-known results on direct product factorizations of finite groups (or (...)

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[hal-01410920] On the Links-Gould invariant and the square of the Alexander polynomial

6 décembre 2016

This paper gives a connection between well-chosen reductions of the Links-Gould invariants of oriented links and powers of the Alexander-Conway polynomial. This connection is obtained by showing the representations of the braid groups we derive the specialized Links-Gould polynomials from can (...)

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[hal-01410903] Partially hyperbolic diffeomorphisms with a uniformly compact center foliation : the quotient dynamics

6 décembre 2016

We show that a partially hyperbolic C-1-diffeomorphism f : M -> M with a uniformly compact f-invariant center foliation F-c is dynamically coherent. Further, the induced homeomorphism F : M/F-c -> M/F-c on the quotient space of the center foliation has the shadowing property, i. e. for (...)

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[hal-01410535] Polarities and Generalized Extremal Convolutions

6 décembre 2016

A reflection on the inceptive role of Moreau in various studies is presented. Gustave Choquet (1915-2006), Jean Jacques Moreau (1923-2014) and Ennio De Giorgi (1928-1996) inspired developments of variational analysis. I had the fortune to know them all and to follow their tracks. Jean Jacques (...)

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[hal-01410406] PT-symmetry and Schrodinger operators. The double well case

6 décembre 2016

We study a class of PT-symmetric semiclassical Schrodinger operators, which are perturbations of a selfadjoint one. Here, we treat the case where the unperturbed operator has a double-well potential. In the simple well case, two of the authors have proved in [6] that, when the potential is (...)

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[hal-01410258] Toward a Classification of Quasirational Solutions of the Nonlinear Schrodinger Equation

6 décembre 2016

Based on a representation in terms of determinants of the order 2N, we attempt to classify quasirational solutions of the one-dimensional focusing nonlinear Schrodinger equation and also formulate several conjectures about the structure of the solutions. These solutions can be written as a (...)

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[hal-01410308] Rational solutions to the KPI equation and multi rogue waves

6 décembre 2016

We construct here rational solutions to the Kadomtsev-Petviashvili equation (KPI) as a quotient of two polynomials in x, y and t depending on several real parameters. This method provides an infinite hierarchy of rational solutions written in terms of polynomials of degrees 2N (N + 1) in x, y (...)

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[hal-01410190] Unfoldings of saddle-nodes and their Dulac time

6 décembre 2016

In this paper we study unfoldings of saddle-nodes and their Dulac time. By unfolding a saddle-node, saddles and nodes appear. In the first result (Theorem A) we give a uniform asymptotic expansion of the trajectories arriving at the node. Uniformity is with respect to all parameters including (...)

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[hal-01287290] Optimal Control of an Ensemble of Bloch Equations with Applications in MRI

6 décembre 2016

The optimal control of an ensemble of Bloch equations describing the evolution of an ensemble of spins is the mathematical model used in Nuclear Resonance Imaging and the associated costs lead to consider Mayer optimal control problems. The Maximum Principle allows to parameterize the optimal (...)

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[hal-01407992] Rationally integrable vector fields and rational additive group actions

2 décembre 2016

We characterize rational actions of the additive group on algebraic varieties defined over a field of characteristic zero in terms of a suitable integrability property of their associated velocity vector fields. This extends the classical correspondence between regular actions of the additive (...)

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[hal-01407979] Recursion Relations for Double Ramification Hierarchies

2 décembre 2016

In this paper we study various properties of the double ramification hierarchy, an integrable hierarchy of hamiltonian PDEs introduced in Buryak (Commun Math Phys 336(3): 1085-1107, 2015) using intersection theory of the double ramification cycle in the moduli space of stable curves. In (...)

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[hal-01407967] Robust Criterion for the Existence of Nonhyperbolic Ergodic Measures

2 décembre 2016

We give explicit C (1)-open conditions that ensure that a diffeomorphism possesses a nonhyperbolic ergodic measure with positive entropy. Actually, our criterion provides the existence of a partially hyperbolic compact set with one-dimensional center and positive topological entropy on which (...)

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[hal-01407869] Shock formation in the dispersionless Kadomtsev-Petviashvili equation

2 décembre 2016

The dispersionless Kadomtsev-Petviashvili (dKP) equation (u(t) + uu(x))(x)= u(yy) is one of the simplest nonlinear wave equations describing two-dimensional shocks. To solve the dKP equation numerically we use a coordinate transformation inspired by the method of characteristics for the (...)

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[hal-01407785] Solutions of the Ablowitz-Kaup-Newell-Segur Hierarchy Equations of the "Rogue Wave" Type : A Unified Approach

2 décembre 2016

We describe a unified structure of solutions for all equations of the Ablowitz-Kaup-Newell-Segur hierarchy and their combinations. We give examples of solutions that satisfy different equations for different parameter values. In particular, we consider a rank-2 quasirational solution that can (...)

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[hal-01407485] Positively alpha-Far Sets and Existence Results for Generalized Perturbed Sweeping Processes

2 décembre 2016

We consider the general class of positively alpha-far sets, introduced in [29], which contains strictly the class of uniformly prox-regular sets and the class of uniformly subsmooth sets. We provide some conditions to assure the uniform subsmoothness, and thus the positive alpha-farness, of the (...)

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[hal-01404663] Persistent random walks. II. Functional Scaling Limits

1er décembre 2016

We give a complete and unified description – under some stability assumptions – of the functional scaling limits associated with some persistent random walks for which the recurrent or transient type is studied in [1]. As a result, we highlight a phase transition phenomenon with respect to the (...)

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[hal-01406266] Solving chance-constrained optimal control problems in aerospace engineering via Kernel Density Estimation

30 novembre 2016

The goal of this paper is to show how non-parametric statistics can be used to solve chance-constrained optimization and optimal control problems by reformulating them into deterministic ones, focusing on the details of the algorithmic approach. We use the Kernel Density Estimation method to (...)

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[hal-01405724] Approximation by filtering in optimal control and applications

30 novembre 2016

Minimum time control of slow-fast systems is considered. In the case of only one fast angle, averaging techniques are available for such systems. The approach introduced in Dargent (2014) and Bombrun et al. (2013) is recalled, then extended to time dependent systems by means of a suitable (...)

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[hal-01405354] The NSLUC property and Klee envelope

29 novembre 2016

A notion called norm subdifferential local uniform convexity (NSLUC) is introduced and studied. It is shown that the property holds for all subsets of a Banach space whenever the norm is either locally uniformly convex or k-fully convex. The property is also valid for all subsets of the Banach (...)

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[hal-01405314] Twenty Parameters Families of Solutions to the NLS Equation and the Eleventh Peregrine Breather

29 novembre 2016

The Peregrine breather of order eleven (P-11 breather) solution to the focusing one-dimensional nonlinear Schrodinger equation (NLS) is explicitly constructed here. Deformations of the Peregrine breather of order 11 with 20 real parameters solutions to the NLS equation are also given: when all (...)

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[hal-01405169] Recent Advances in Celestial and Space Mechanics

29 novembre 2016

This book presents recent advances in space and celestial mechanics, with a focus on the N-body problem and astrodynamics, and explores the development and application of computational techniques in both areas. It highlights the design of space transfers with various modes of propulsion, like (...)

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[hal-01404050] Coxeter groups, symmetries, and rooted representations

28 novembre 2016

Let $(W,S)$ be a Coxeter system, let $G$ be a group of symmetries of $(W,S)$ and let $f : W \to \GL (V)$ be the linear representation associated with a root basis $(V, \langle .,. \rangle, \Pi)$. We assume that $G \subset \GL (V)$, and that $G$ leaves invariant $\Pi$ and $\langle .,. \rangle$. (...)

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[tel-01402516] Geometric and numerical methods in optimal control and application to orbit transfer and swimming at low Reynolds number

25 novembre 2016

The first part of this work is devoted to the study of the swimming at low Reynolds number. We deal with two models of microswimmers: one is a symmetric 2-link swimmer introduced by D. Takagi to model the movement of an abundant variety of zooplankton called Copepod and the seminal model (...)

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[hal-01363539] Equidistribution of jellium energy for Coulomb and Riesz Interactions

22 novembre 2016

For general dimension $d$ we prove the equidistribution of energy at the micro-scale in $\mathbb R^d$, for the optimal point configurations appearing in Coulomb gases at zero temperature. At the microscopic scale, i.e. after blow-up at the scale corresponding to the interparticle distance, in (...)

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[hal-01394595] Affine lines in the complement of a smooth plane conic

10 novembre 2016

We classify closed curves isomorphic to the affine line in the complement of a smooth rational projective plane conic Q. Over a field of characteristic zero, we show that up to the action of the subgroup of the Cremona group of the plane consisting of birational endomorphisms restricting to (...)

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[hal-01388054] DARBOUX INTEGRABLE SYSTEM WITH A TRIPLE POINT AND PSEUDO-ABELIAN INTEGRALS

3 novembre 2016

In this paper we consider the degeneracies of the third type. More exact, the perturbations of the Darboux integrable foliation with a triple point, i.e. the case where three of the curves P i = 0 meet at one point, are considered. Assuming that this is the only non-genericity, we prove that (...)

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[hal-01389493] Cut-off method for endogeny of recursive tree processes

28 octobre 2016

Given a solution to a recursive distributional equation, a natural (and non-trivial) question is whether the corresponding recursive tree process is endogenous. That is, whether the random environment almost surely defines the tree process. We propose a new method of proving endogeny, which (...)

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[hal-01387423] Optimal control theory and the efficiency of the swimming mechanism of the Copepod Zooplankton

28 octobre 2016

In this article, the model of swimming at low Reynolds number introduced by D. Takagi (2015) to analyze the displacement of an abundant variety of zooplankton is used as a testbed to analyze the motion of symmetric microswimmers in the framework of optimal control theory assuming that the (...)

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[hal-01388054] DARBOUX INTEGRABLE SYSTEM WITH A TRIPLE POINT AND PSEUDO-ABELIAN INTEGRALS

27 octobre 2016

In this paper we consider the degeneracies of the third type. More exact, the perturbations of the Darboux integrable foliation with a triple point, i.e. the case where three of the curves P i = 0 meet at one point, are considered. Assuming that this is the only non-genericity, we prove that (...)

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[hal-01387423] Optimal control theory and the efficiency of the swimming mechanism of the Copepod Zooplankton

25 octobre 2016

In this article, the model of swimming at low Reynolds number introduced by D. Takagi (2015) to analyze the displacement of an abundant variety of zooplankton is used as a testbed to analyze the motion of symmetric microswimmers in the framework of optimal control theory assuming that the (...)

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[hal-01387443] Optimal Control Theory and the Swimming Mechanism of the Copepod Zooplankton

25 octobre 2016

In this article, the model of swimming at low Reynolds number introduced by D. Takagi (2015) to analyze the displacement of an abundant variety of zooplankton is used as a testbed to analyze the motion of symmetric microswimmers in the framework of optimal control theory assuming that the (...)

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[hal-01386683] Mise en scéne et origine perçue des voix hallucinées dans des discours de patients schizophrènes

24 octobre 2016

Ce travail qui s’inscrit dans la perspective des travaux de Lagache (1934) et de la phénoménologie étudie la mise en récit par des patients schizophrènes de leurs hallucinations auditives. La méthodologie repose sur l’analyse des différents types de « discours rapportés » utilisés par les patients (...)

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[hal-01286602] A Numerical Approach to the Optimal Control and Efficiency of the Copepod Swimmer

24 octobre 2016

This article presents a geometric and numerical approach to compute the optimal swimming strokes of a larval copepod. A simplified model of locomotion at low Reynolds number is analyzed in the framework of Sub-Riemannian geometry. Both normal and abnormal geodesics are considered along which (...)

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[hal-01287290] Optimal Control of an Ensemble of Bloch Equations with Applications in MRI

24 octobre 2016

The optimal control of an ensemble of Bloch equations describing the evolution of an ensemble of spins is the mathematical model used in Nuclear Resonance Imaging and the associated costs lead to consider Mayer optimal control problems. The Maximum Principle allows to parameterize the optimal (...)

Lire la suite

[tel-01379106] Problème de centre tangentiel et problème de monodromie pour certains Hamiltoniens non-génériques

13 octobre 2016

Dans le cas générique Yu. S. Ilyashenko a donné une solution pour le problème tangentielle du centre et le probème de la monodromie. Néanmoins, on ne connaît pas la solution pour tous les cas non-génériques. Dans cette thèse on étudie une famille des équations hamiltoniennes non-génériques dont (...)

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[hal-01380365] Initial-boundary value problem for the heat equation - A stochastic algorithm

13 octobre 2016

The Initial-Boundary Value Problem for the heat equation is solved by using a new algorithm based on a random walk on heat balls. Even if it represents a sophisticated generalization of the Walk on Spheres (WOS) algorithm introduced to solve the Dirich-let problem for Laplace's equation, its (...)

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[tel-01379106] Problème de centre tangentiel et problème de monodromie pour certains Hamiltoniens non-génériques

12 octobre 2016

Dans le cas générique Yu. S. Ilyashenko a donné une solution pour le problème tangentielle du centre et le probème de la monodromie. Néanmoins, on ne connaît pas la solution pour tous les cas non-génériques. Dans cette thèse on étudie une famille des équations hamiltoniennes non-génériques dont (...)

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[hal-01374364] Families of exotic affine 3-spheres

5 octobre 2016

We construct algebraic families of exotic affine 3-spheres, that is, smooth affine threefolds diffeomorphic to a non-degenerate smooth complex affine quadric of dimension 3 but non algebraically isomorphic to it. We show in particular that for every smooth topologically contractible affine (...)

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[hal-01333295] CLEAR : Covariant LEAst-square Re-fitting with applications to image restoration

15 septembre 2016

In this paper, we propose a new framework to remove parts of the systematic errors affecting popular restoration algorithms, with a special focus for image processing tasks. Generalizing ideas that emerged for l1 regularization, we develop an approach re-fitting the results of standard methods (...)

Lire la suite

[hal-01363539] Equidistribution of jellium energy for Coulomb and Riesz Interactions

13 septembre 2016

For general dimension $d$ we prove the equidistribution of energy at the micro-scale in $\mathbb R^d$, for the optimal point configurations appearing in Coulomb gases at zero temperature. At the microscopic scale, i.e. after blow-up at the scale corresponding to the interparticle distance, in (...)

Lire la suite

[hal-01359037] Regularization of chattering phenomena via bounded variation controls

2 septembre 2016

In control theory, the term chattering is used to refer to strong oscillations of controls, such as an infinite number of switchings over a compact interval of times. In this paper we focus on three typical occurences of chattering: the Fuller phenomenon, referring to situations where an (...)

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[hal-01246830] Un astronome bourguignon : Alexandre Véronnet (1876-1951)

30 août 2016

Qui est donc Alexandre Véronnet ? Nous allons voir qu'Alexandre Véronnet est un scientifique tout à fait étonnant ayant eu un parcours particulièrement original. Prêtre, il quitte l’Eglise à la fin de la Première Guerre mondiale. Il soutient une thèse en Astronomie en 1912. Le premier conflit mondial, (...)

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[hal-01326790] Optimal strokes at low Reynolds number : a geometric and numeric study using the Copepod and Purcell swimmers

3 août 2016

In this article, we make a comparative geometric and numeric analysis of the optimal strokes at low Reynolds number using two specific rigid links swimmers: the Copepod swimmer, a symmetric swimmer introduced recently 30 and the historical three-link Pur-cell swimmer 27 where the cost to (...)

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[hal-01348445] Generic Properties of Dynamical Systems

1er août 2016

The state of a concrete system (from physics, chemistry, ecology, or other sciences) is described using (finitely many, say n) observable quantities (e.g., positions and velocities for mechanical systems, population densities for echological systems, etc.). Hence, the state of a system may be (...)

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[hal-01346532] Accelerated Alternating Descent Methods for Dykstra-like problems

22 juillet 2016

This paper extends recent results by the first author and T. Pock (ICG, TU Graz, Austria) on the acceleration of alternating minimization techniques for quadratic plus nons-mooth objectives depending on two variables. We discuss here the strongly convex situation, and how " fast " (...)

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[hal-01342901] THE LINKS-GOULD INVARIANT AS A CLASSICAL GENERALIZATION OF THE ALEXANDER POLYNOMIAL ?

8 juillet 2016

In this paper we conjecture that the Links-Gould invariant of links, that we know is a generalization of the Alexander-Conway polynomial, shares some of its classical features. In particular it seems to give a lower bound for the genus of links and to provide a criterion for fiberedness of (...)

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[hal-01340990] Cylinders in del Pezzo fibrations

4 juillet 2016

We show that a del Pezzo fibration π : V → W of degre d contains a vertical open cylinder, that is, an open subset whose intersection with the generic fiber of π is isomorphic to Z × A 1 K for some quasi-projective variety Z defined over the function field K of W , if and only if d ≥ 5 and π : V → (...)

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[hal-01339879] Numerical study of the stability of the Peregrine breather

30 juin 2016

The Peregrine breather is widely discussed as a model for rogue waves in deep water. We present here a detailed numerical study of perturbations of the Peregrine breather as a solution to the nonlinear Schr\"odinger (NLS) equations. We first address the modulational instability of the (...)

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[hal-01336325] Convexity of injectivity domains on the ellipsoid of revolution : The oblate case

24 juin 2016

We characterize the convexity properties of the tangent injectivity domain on an the ellipsoid of revolution in the oblate case.

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[hal-01330610] Fredholm representations of solutions to the KPI equation, their wronkian versions and rogue waves

20 juin 2016

We construct solutions to the Kadomtsev-Petviashvili equation (KPI) in terms of Fredholm determinants. We deduce solutions written as a quotient of wronskians of order 2N. These solutions called solutions of order N depend on 2N − 1 parameters. When one of these parameters tends to zero, we (...)

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[hal-01333882] Heteroclinic Structure of Parametric Resonance in the Nonlinear Schrödinger Equation

20 juin 2016

We show that the nonlinear stage of modulational instability induced by parametric driving in the defocusing nonlinear Schrödinger equation can be accurately described by combining mode truncation and averaging methods, valid in the strong driving regime. The resulting integrable oscillator (...)

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[hal-01333295] CLEAR : Covariant LEAst-square Re-fitting with applications to image restoration

20 juin 2016

In this paper, we propose a new framework to remove parts of the systematic errors affecting popular restoration algorithms, with a special focus for image processing tasks. Extending ideas that emerged for l1 regularization, we develop an approach that can help re-fitting the results of (...)

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[hal-01326790] Optimal strokes at low Reynolds number : a geometric and numeric study using the Copepod and Purcell swimmers

10 juin 2016

In this article, we make a comparative geometric and numeric analysis of the optimal strokes at low Reynolds number using two specific rigid links swimmers: the Copepod swimmer, a symmetric swimmer introduced recently 28 and the historical three-link Pur-cell swimmer 25 where the cost to (...)

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[hal-01329298] Other quantum relatives of the Alexander polynomial through the Links-Gould invariants

9 juin 2016

Oleg Viro studied in arXiv:math/0204290 two interpretations of the (multivariable) Alexander polynomial as a quantum link invariant: either by considering the quasi triangular Hopf algebra associated to $U_q sl(2)$ at fourth roots of unity, or by considering the super Hopf algebra $U_q (...)

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[hal-00933198] Simulation of hitting times for Bessel processes with non integer dimension

17 mai 2016

In this paper we pursue and complete the study of the simulation of the hitting time of some given boundaries for Bessel processes. These problems are of great interest in many application fields as finance and neurosciences. In a previous work \citeDeaconu-Herrmann, the authors introduced a (...)

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[hal-01312534] Orbital stability via the energy-momentum method : the case of higher dimensional symmetry groups

9 mai 2016

We consider the orbital stability of the relative equilibria of Hamiltonian dynamical systems on Banach spaces, in the presence of a multi-dimensional invariance group for the dynamics. We present a generalization of the Vakhitov-Kolokolov slope condition to this higher dimensional setting, and (...)

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[hal-01287290] Optimal Control of an Ensemble of Bloch Equations with Applications in MRI

4 mai 2016

The optimal control of an ensemble of Bloch equations describing the evolution of an ensemble of spins is the mathematical model used in Nuclear Resonance Imaging and the associated costs lead to consider Mayer optimal control problems. The Maximum Principle allows to parameterize the optimal (...)

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[hal-01307073] Determinantal sets, singularities and application to optimal control in medical imagery

3 mai 2016

Control theory has recently been involved in the field of nuclear magnetic resonance imagery. The goal is to control the magnetic field optimally in order to improve the contrast between two biological matters on the pictures. Geometric optimal control leads us here to analyze mero-morphic (...)

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[hal-01307073] Determinantal sets, singularities and application to optimal control in medical imagery

2 mai 2016

Control theory has recently been involved in the field of nuclear magnetic resonance imagery. The goal is to control the magnetic field optimally in order to improve the contrast between two biological matters on the pictures. Geometric optimal control leads us here to analyze mero-morphic (...)

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[hal-01307073] Determinantal sets, singularities and application to optimal control in medical imagery

26 avril 2016

Control theory has recently been involved in the field of nuclear magnetic resonance imagery. The goal is to control the magnetic field optimally in order to improve the contrast between two biological matters on the pictures. Geometric optimal control leads us here to analyze mero-morphic (...)

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[hal-01300631] Antiperiodic dynamical 6-vertex model by separation of variables II : Functional equations and form factors

11 avril 2016

We pursue our study of the antiperiodic dynamical 6-vertex model using Sklyanin's separation of variables approach, allowing in the model new possible global shifts of the dynamical parameter. We show in particular that the spectrum and eigenstates of the antiperiodic transfer matrix are (...)

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[hal-01293978] Higher Frobenius-Schur indicators for Drinfeld doubles of finite groups through characters of centralizers

8 avril 2016

We present a new approach to calculating the higher Frobenius-Schur indicators for the simple modules over the Drinfeld double of a finite group. In contrast to the formula by Kashina-Sommerhäuser-Zhu that involves a sum over all group elements satisfying a certain condition, our formula (...)

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[hal-01299469] Families of deformations of the twelfth Peregrine breather solutions to the NLS equation with twenty two parameters

7 avril 2016

The twelfth Peregrine breather (P12 breather) solution to the focusing one dimensional nonlinear Schrödinger equation (NLS) with its twenty two real parameters deformations solutions to the NLS equation are explicitly constructed here. New families of quasi-rational solutions of the NLS equation (...)

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[hal-01286602] A Numerical Approach to the Optimal Control and Efficiency of the Copepod Swimmer

7 avril 2016

— The objective of this article is to make a geometric and numerical analysis about the optimal displacements of a larval copepod swimming at low Reynolds number. A simplified model of locomotion is analyzed in the framework of Sub-Riemannian geometry. In particular, the role of both normal and (...)

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[hal-01226734] Working Examples In Geometric Optimal Control

25 mars 2016

This series of notes have their origin into accelerated course in optimal control given to multidisciplinary Phd students in Mathematics, Physics or Control Engineering and the purpose is to present the seminal results of this theory in view of applications to concrete problems. For that we (...)

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[hal-01277412] Special issue on New trends in optimal control

21 mars 2016

This special volume gathers a number of new contributions addressing various topics related to the field of optimal control theory and sensitivity analysis. The field has a rich and varied mathematical theory, with a long tradition and a vibrant body of applications. It has attracted a growing (...)

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[hal-01287290] Optimal Control of an Ensemble of Bloch Equations with Applications in MRI

15 mars 2016

The optimal control of an ensemble of Bloch equations describing the evolution of an ensemble of spins is the mathematical model used in Nuclear Resonance Imaging and the associated costs lead to consider Mayer optimal control problems. The Maximum Principle allows to parameterize the optimal (...)

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[hal-01143763] The Purcell Three-link swimmer : some geometric and numerical aspects related to periodic optimal controls

14 mars 2016

The maximum principle combined with numerical methods is a powerful tool to compute solutions for optimal control problems. This approach turns out to be extremely useful in applications, including solving problems which require establishing periodic trajectories for Hamiltonian systems, (...)

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[hal-01285853] Persistent random walks, variable length Markov chains and piecewise deterministic Markov processes *

14 mars 2016

A classical random walk (S t , t ∈ N) is defined by S t := t n=0 X n , where (X n) are i.i.d. When the increments (X n) n∈N are a one-order Markov chain, a short memory is introduced in the dynamics of (S t). This so-called " persistent " random walk is nolonger Markovian and, under (...)

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[hal-01284275] Convergence Rates for Persistence Diagram Estimation in Topological Data Analysis

12 mars 2016

Computational topology has recently seen an important development toward data analysis, giving birth to the field of topological data analysis. Topological persistence, or persistent homology, appears as a fundamental tool in this field. In this paper, we study topological persistence in (...)

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[hal-01286602] A Numerical Approach to the Optimal Control and Efficiency of the Copepod Swimmer

12 mars 2016

The objective of this article is to make a geometric and numerical analysis about the optimal displacements of a larval copepod swimming at low Reynolds number. A simplified model of locomotion is analyzed in the framework of Sub-Riemannian geometry. In particular, the role of both normal and (...)

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[hal-01164543] A simple solution to the word problem for virtual braid groups

8 mars 2016

We show a simple and easily implementable solution to the word problem for virtual braid groups.

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[hal-01280499] QUADRATIC AND PINCZON ALGEBRAS

2 mars 2016

Given a symmetric non degenerated bilinear form b on a vector space V , G. Pinczon and R. Ushirobira defined a bracket , on the space of multilinear skewsymmetric forms on V. With this bracket, the quadratic Lie algebra structure equation on (V, b) becomes simply Ω, Ω = 0. We characterize (...)

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[hal-00969285] Integrability methods in the time minimal coherence transfer for Ising chains of three spins

26 février 2016

The objective of this article is to analyze the integrability proper-ties of extremal solutions of Pontryagin Maximum Principle in the time min-imal control of a linear spin system with Ising coupling in relation with con-jugate and cut loci computations. Restricting to the case of three spins, (...)

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[hal-01197123] Generalized stochastic Lagrangian paths for the Navier-Stokes equation

24 février 2016

In the note added in proof of the seminal paper [Groups of diffeomorphisms and the motion of an incompressible fluid, Ann. of Math. 92 (1970), 102-163], Ebin and Marsden introduced the so-called correct Laplacian for the Navier-Stokes equation on a compact Riemannian manifold. In the spirit of (...)

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[hal-01276394] Patterns of deformations of P 3 and P 4 breathers solutions to the NLS equation

24 février 2016

In this article, one gives a classification of the solutions to the one dimensional nonlinear focusing Schrödinger equation (NLS) by considering the modulus of the solutions in the (x, t) plan in the cases of orders 3 and 4. For this, we use a representation of solutions to NLS equation as a (...)

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[hal-01159255] Autoregressive Functions Estimation in Nonlinear Bifurcating Autoregressive Models

16 février 2016

Bifurcating autoregressive processes, which can be seen as an adaptation of au-toregressive processes for a binary tree structure, have been extensively studied during the last decade in a parametric context. In this work we do not specify any a priori form for the two autoregressive functions (...)

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[hal-01254200] Adaptive Estimation for Bifurcating Markov Chains

13 février 2016

In a first part, we prove Bernstein-type deviation inequalities for bifurcating Markov chains (BMC) under a geometric ergodicity assumption, completing former results of Guyon and Bitseki Penda, Djellout and Guillin. These preliminary results are the key ingredient to implement nonparametric (...)

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[hal-01017350] Homotopy classification of ribbon tubes and welded string links

11 février 2016

Ribbon 2-knotted objects are locally flat embeddings of surfaces in 4-space which bound immersed 3-manifolds with only ribbon singularities. They appear as topological realizations of welded knotted objects, which is a natural quotient of virtual knot theory. In this paper, we consider ribbon (...)

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[hal-01270913] On determinant representations of scalar products and form factors in the SoV approach : the XXX case

9 février 2016

In the present article we study the form factors of quantum integrable lattice models solvable by the separation of variables (SoV) method. It was recently shown that these models admit universal determinant representations for the scalar products of the so-called separate states (a class which (...)

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[hal-01251594] ADAPTIVE ESTIMATION FOR BIFURCATING MARKOV CHAINS

12 janvier 2016

In a first part, we prove Bernstein-type deviation inequalities for bifurcating Markov chains (BMC) under a geometric ergodicity assumption, completing former results of Guyon and Bitseki Penda, Djellout and Guillin. These preliminary results are the key ingredient to implement nonparametric (...)

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[tel-01250596] Topological characterization of virtual braids

12 janvier 2016

The purpose of this thesis is to give a topological characterization of virtual braids. Virtual braids are equivalence classes of planar braid-like diagrams identified up to isotopy, Reidemeister and virtual Reidemeister moves. The set of virtual braids admits a group structure and is called (...)

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[hal-01100918] Blowing-up of locally monomially foliated space

12 janvier 2016

In this paper, we prove that the blowing-up preserve the local monomiality of foliated space.

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[hal-01099283] LND-FILTRATIONS AND SEMI-RIGID DOMAINS

12 janvier 2016

We investigate the filtration corresponding to the degree function induced by a non-zero locally nilpotent derivation and its associated graded algebra. We show that this kind of filtration, referred to as the LND-filtration, is the ideal candidate to study the structure of semi-rigid (...)

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[hal-01108702] Local monomialization conjecture of a singular foliation of Darboux type

12 janvier 2016

After the nice result introduced by Belotto in [1] concerning the local monomialization of a singular foliation given by n first integrals, this work is a continuation in the same spirit. In this paper, we introduce a important conjecture about local monomialization of a singular foliation of (...)

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[hal-01246830] Un astronome bourguignon : Alexandre Véronnet (1876-1951) (document de travail, version 1)

22 décembre 2015

Qui est donc Alexandre Véronnet ? C'est à cette question que nous allons répondre. Nous allons voir que Alexandre Véronnet est un scientifique tout à fait étonnant ayant eu un parcours particulièrement original.

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[tel-01244646] Motifs des fibrés en quadriques et jacobiennes intermédiaires relatives des paires K3-Fano

18 décembre 2015

Cette thèse comporte deux parties. Dans la première partie on étudie le motif de Chow d’un fibré en quadriques de dimension relative impaire sur une surface. On montre que ce motif admet une décomposition qui fait intervenir le motif de Prym du revêtement double de la courbe discriminante. Dans la (...)

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[hal-01224526] The eleventh Peregrine breather and twenty parameters families of solutions to the NLS equation

15 décembre 2015

The Peregrine breather of order eleven (P11 breather) solution to the focusing one dimensional nonlinear Schrödinger equation (NLS) is explicitly constructed here. Deformations of the Peregrine breather of order 11 with 20 real parameters solutions to the NLS equation are also given : when all (...)

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[hal-01231875] An attempt to classification of the quasi rational solutions to the NLS equation

15 décembre 2015

Based on a representation in terms of determinants of order 2N , an attempt to classification of quasi rational solutions to the one dimensional focusing nonlinear Schrödinger equation (NLS) is given and several conjectures about the structure of the solutions are also formulated. These (...)

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[hal-01237039] Online Learning and Game Theory. A quick overview with recent results and applications

9 décembre 2015

We study one of the main concept of online learning and sequential decision problem known as regret minimization. We investigate three different frameworks, whether data are generated accordingly to some i.i.d. process, or when no assumption whatsoever are made on their generation and, finally, (...)

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[hal-01238192] Volatile and Organic Compositions of Sedimentary Rocks in Yellowknife Bay, Gale Crater, Mars

4 décembre 2015

H2O, CO2, SO2, O2, H2, H2S, HCl, chlorinated hydrocarbons, NO, and other trace gases were evolved during pyrolysis of two mudstone samples acquired by the Curiosity rover at Yellowknife Bay within Gale crater, Mars. H2O/OH-bearing phases included 2:1 phyllosilicate(s), bassanite, akaganeite, (...)

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[hal-01165480] ON THE LINKS-GOULD INVARIANT AND THE SQUARE OF THE ALEXANDER POLYNOMIAL

1er décembre 2015

This paper gives a connection between well chosen reductions of the Links-Gould invariants of oriented links and powers of the Alexander-Conway polynomial. We prove these formulas by showing the representations of the braid groups we derive the specialized Links-Gould polynomials from can be (...)

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[hal-01231875] An attempt to classification of the quasi rational solutions to the NLS equation

1er décembre 2015

Based on a representation in terms of determinants of order 2N , an attempt to classification of quasi rational solutions to the one dimensional focusing nonlinear Schrödinger equation (NLS) is given and several conjectures about the structure of the solutions are also formulated. These (...)

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[hal-01226734] Working Examples In Geometric Optimal Control

13 novembre 2015

This series of notes have their origin into accelerated course in optimal control given to multidisciplinary Phd students in Mathematics, Physics or Control Engineering and the purpose is to present the seminal results of this theory in view of applications to concrete problems. For that we (...)

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[hal-01224526] The eleventh Peregrine breather and twenty parameters families of solutions to the NLS equation

6 novembre 2015

The Peregrine breather of order eleven (P11 breather) solution to the focusing one dimensional nonlinear Schrödinger equation (NLS) is explicitly constructed here. Deformations of the Peregrine breather of order 11 with 20 real parameters solutions to the NLS equation are also given : when all (...)

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[hal-01220278] Celestial and Space Mechanics

30 octobre 2015

The objective of this book is to present recent advances in celestial and space mechanics written by contributors from both academic institutions and space agencies. It is organized in seven complementary articles, two devoted to celestial mechanics and five dedicated to orbital mechanics. One (...)

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[tel-01219892] Spectral properties of random non-self-adjoint operators

26 octobre 2015

In this thesis we are interested in the spectral properties of random non-self-adjoint operators. Weare going to consider primarily the case of small random perturbations of the following two types of operators: 1. a class of non-self-adjoint h-differential operators Ph, introduced by M. Hager (...)

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[hal-01217945] On forbidden moves and the delta move

21 octobre 2015

We consider the quotient of welded knotted objects under several equivalence relations, generated respectively by self-crossing changes, ∆ moves, self-virtualizations and forbidden moves. We prove that for welded objects up to forbidden moves or classical objects up to ∆ moves, the notions of (...)

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[hal-01217085] On forbidden moves and the delta move

20 octobre 2015

We consider the quotient of welded knotted objects under several equivalence relations, generated respectively by self-crossing changes, ∆ moves, self-virtualizations and forbidden moves. We prove that for welded objects up to forbidden moves or classical objects up to ∆ moves, the notions of (...)

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[hal-00931816] The walk on moving spheres : a new tool for simulating Brownian motion’s exit time from a domain

16 octobre 2015

In this paper we introduce a new method for the simulation of the exit time and position of a $\delta$-dimensional Brownian motion from a domain. The main interest of our method is that it avoids splitting time schemes as well as inversion of complicated series. The idea is to use the connexion (...)

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[tel-01213952] Actions hyperboliques du groupe multiplicatif sur des variétés affines : espaces exotiques et structures locales

13 octobre 2015

Cette thèse est consacré à l'étude des T-variétés affines à l'aide de la présentation due à Altmann et Hausen. On s'intéresse plus particulièrement au cas des actions hyperboliques du groupe multiplicatif Gm. Dans une première partie, on étudie les espaces affines exotiques, c'est-à-dire des variétés (...)

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[hal-01143763] The Purcell Three-link swimmer : some geometric and numerical aspects related to periodic optimal controls

6 octobre 2015

The maximum principle combined with numerical methods is a powerful tool to compute solutions for optimal control problems. This approach turns out to be extremely useful in applications, including solving problems which require establishing periodic trajectories for Hamiltonian systems, (...)

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[hal-01211211] Hyperbolic geometry in the work of J. H. Lambert

4 octobre 2015

The memoir ``Theorie der Parallellinien" (1766) by Johann Heinrich Lambert is one of the founding texts of hyperbolic geometry, even though its author's aim was, like many of his predecessors', to prove that such a geometry does not exist. In fact, Lambert developed his theory with the (...)

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[hal-01210378] Influence du profil de croissance des génisses Prim Holstein sur leurs performances laitières en première lactation

3 octobre 2015

L’âge au 1er vêlage est un indicateur couramment utilisé pour décrire la stratégie de renouvellement en élevage laitier. Pour un même âge et/ou un poids donné au 1er vêlage, il peut exister des objectifs de croissance de génisses différents entre les élevages. Mais même avec des objectifs similaires, les (...)

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[tel-01206493] Solution of XXZ and XYZ spin chains with boundaries by separation of variables

29 septembre 2015

In this thesis we give accounts on the solution of the open XXZ and XYZ quantum spin-1/2 chains with the most generic integrable boundary terms. By using the the Separation of Variables method (SoV), due to Sklyanin, we are able, in the inhomogeneous case, to build the complete set of (...)

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[tel-01206319] Contribution to variational analysis : stability of tangent and normal cones and convexity of Chebyshev sets

29 septembre 2015

The aim of this thesis is to study the following three problems: 1) We are concerned with the behavior of normal cones and subdifferentials with respect to two types of convergence of sets and functions: Mosco and Attouch-Wets convergences. Our analysis is devoted to proximal, Fréchet, and (...)

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[hal-01205277] Affine-ruled varieties without the Laurent cancellation property

25 septembre 2015

We describe a method to construct hypersurfaces of the complex affine $n$-space with isomorphic $\mathbbC^*$-cylinders. Among these hypersurfaces, we find new explicit counterexamples to the Laurent Cancellation Problem, i.e. hypersurfaces that are non isomorphic, although their (...)

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[hal-01201838] COPULA’S APPROXIMATIONS : APPLICATION TO QUANTILE ESTIMATION

22 septembre 2015

Estimating high level quantiles of aggregated variables (mainly sums or weighted sums) is crucial in risk management for many application fields such as finance, insurance, environment... This question has been widely treated but new efficient methods are always welcome; especially if they (...)

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[hal-01135794] Persistent random walks

13 septembre 2015

We consider a walker that at each step keeps the same direction with a probability that depends on the time already spent in the direction the walker is currently moving. In this paper, we study some asymptotic properties of this persistent random walk and give the conditions of recurrence or (...)

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[hal-01197123] Generalized stochastic Lagrangian paths for the Navier-Stokes equation

11 septembre 2015

The purpose of this work is to establish a counterpart for the Navier-Stokes equation of Brenier's generalized flows for the Euler equation. We introduce a class of semi-martingales on a compact Riemannian manifold which will be generalized solutions of the Navier-Stokes equation. We prove that (...)

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[hal-01192831] A note on Constantin and Iyer’s representation formula for the Navier–Stokes equations

4 septembre 2015

The purpose of this note is to establish a probabilistic representation formula for Navier–Stokes equations on a compact Riemannian manifold. To this end, we first give a geometric interpretation of Constantin and Iyer's representation formula for the Navier–Stokes equation, then extend it to a (...)

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[hal-01192833] Remarks on spectral gaps on the Riemannian path space

4 septembre 2015

In this paper, we will give some remarks on links between the spectral gap of the Ornstein-Uhlenbeck operator on the Riemannian path space with lower and upper bounds of the Ricci curvature on the base manifold; this work was motivated by a recent work of A. Naber on the characterization of the (...)

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[hal-01188470] REAL FRONTIERS OF FAKE PLANES

1er septembre 2015

In [8], we define and partially classify fake real planes, that is, minimal complex surfaces with conjugation whose real locus is diffeomorphic to the euclidean real plane $\mathbbR^2$. Classification results are given up to biregular isomorphisms and up to birational diffeomorphisms. In this (...)

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[hal-00918633] Time Versus Energy in the Averaged Optimal Coplanar Kepler Transfer towards Circular Orbits

23 août 2015

The aim of this note is to compare the averaged optimal coplanar transfer towards circular orbits when the costs are the transfer time transfer and the energy consumption. While the energy case leads to analyze a 2D Riemannian metric using the standard tools of Riemannian geometry (curvature (...)

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[hal-01184044] The Lyapunov tortoise and the dyadic hare

13 août 2015

We study a gcd algorithm directed by Least Significant Bits, the so―called LSB algorithm, and provide a precise average―case analysis of its main parameters [number of iterations, number of shifts, etc\ldots]. This analysis is based on a precise study of the dynamical systems which provide a (...)

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[hal-01183351] Explicit biregular/birational geometry of affine threefolds : completions of A^3 into del Pezzo fibrations and Mori conic bundles

8 août 2015

We study certain pencils of del Pezzo surfaces generated by a smooth del Pezzo surface S of degree less or equal to 3 anti-canonically embedded into a weighted projective space P and an appropriate multiple of a hyperplane H. Our main observation is that every minimal model program relative to (...)

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[tel-01131399] Contrôle optimal et métriques de Clairaut-Liouville avec applications

24 juillet 2015

Le travail de cette thèse porte sur l'étude des lieux conjugué et de coupure de métriques riemanniennes ou pseudo-riemanniennes en dimension 2. On se place du point de vue du contrôle optimal pour appliquer le principe du maximum de Pontryagin afin de caractériser les extrémales des problèmes (...)

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[hal-01179229] AUTOMORPHISM GROUPS OF KORAS-RUSSELL THREEFOLDS OF THE SECOND KIND

23 juillet 2015

We determine the automorphism groups of Koras-Russell threefolds of the second kind. In particular we show that these groups are semi-direct products of two subgroups, one given by the multiplicative group and the other isomorphic to a polynomial ring in two variables with the addition law. We (...)

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[hal-01178953] Rigid affine surfaces with isomorphic A2-cylinders

22 juillet 2015

We construct families of smooth affine surfaces with pairwise non isomorphic A 1-cylinders but whose A 2-cylinders are all isomorphic. These arise as complements of cuspidal hyperplane sections of smooth projective cubic surfaces.

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[tel-01150953] Local monomialization of generalized real analytic functions

20 juillet 2015

Generalized power series extend the notion of formal power series by considering exponents ofeach variable ranging in a well ordered set of positive real numbers. Generalized analytic functionsare defined locally by the sum of convergent generalized power series with real coe cients. Weprove a (...)

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[hal-01176073] On usual, virtual and welded knotted objects up to homotopy

17 juillet 2015

We consider several classes of knotted objects, namely usual, virtual and welded pure braids and string links, and two equivalence relations on those objects, induced by either self-crossing changes or self-virtualizations. We provide a number of results which point out the differences between (...)

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[hal-01176009] La méthode d’itération rationnelle de Georges Lemaître (document de travail)

17 juillet 2015

En 1942, le célèbre astronome et physicien belge Georges Lemaître (1894-1966) publie dans le Bulletin de la classe des sciences de l'Académie Royale de Belgique, un article dans lequel il formule une méthode qu'il nomme itération rationnelle. Il redécouvre à la fois le processus du Delta 2 de Aitken et (...)

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[hal-01175667] A note on the restricted universal enveloping algebra of a restricted Lie-Rinehart Algebra

12 juillet 2015

Lie-Rinehart algebras, also known as Lie algebroids, give rise to Hopf algebroids by a universal enveloping algebra construction, much as the universal enveloping algebra of an ordinary Lie algebra gives a Hopf algebra, of infinite dimension. In finite characteristic, the universal enveloping (...)

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[hal-01175154] Fake Real Planes : exotic affine algebraic models of $\mathbb{R}^{2}$

11 juillet 2015

We study real rational models of the euclidean affine plane $\mathbbR^2$ up to isomorphisms and up to birational diffeomorphisms. The analogous study in the compact case, that is the classification of real rational models of the real projective plane $\mathbbR\mathbbP^2$ is well known: up to (...)

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[hal-01107470] Hausdorff volume in non equiregular sub-Riemannian manifolds

2 juillet 2015

In this paper we study the Hausdorff volume in a non equiregular sub-Riemannian manifold and we compare it with a smooth volume. We first give the Lebesgue decomposition of the Hausdorff volume. Then we study the regular part, show that it is not commensurable with the smooth volume, and give (...)

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[hal-01169229] METHODS TO COMPUTE RING INVARIANTS AND APPLICATIONS : A NEW CLASS OF EXOTIC THREEFOLDS

30 juin 2015

We develop some methods to compute the Makar-Limanov and Derksen invariants, isomorphism classes and automorphism groups for k-domains B, which are constructed from certain Russell k-domains. We propose tools and techniques to distinguish between k-domains with the same Makar-Limanov and (...)

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[hal-01162407] A note about the geometric optimal control of the copepod swimmer

20 juin 2015

The objective of this note is to made preliminary remarks concerning the optimal locomotion of the Copepod swimmer described by a simple model concerning swimming at low Reynolds number, in the framework of Sub-Riemannian geometry. In particular the role of both normal and abnormal geodesics is (...)

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[hal-01165480] ON THE LINKS-GOULD INVARIANT AND THE SQUARE OF THE ALEXANDER POLYNOMIAL

20 juin 2015

This paper gives a connection between well chosen reductions of the Links-Gould invariants of oriented links and powers of the Alexander-Conway polynomial. We prove these formulas by showing the representations of the braid groups we derive the specialized Links-Gould polynomials from can be (...)

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[hal-01165324] Tenth order solutions to the NLS equation with eighteen parameters

20 juin 2015

We present here new solutions of the focusing one dimensional non linear Schrödinger equation which appear as deformations of the Peregrine breather of order 10 with 18 real parameters. With this method, we obtain new families of quasi-rational solutions of the NLS equation, and we obtain (...)

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[hal-01145681] ON THE NUMBER OF ISOLATED ZEROS OF PSEUDO-ABELIAN INTEGRALS : DEGENERACIES OF THE CUSPIDAL TYPE

20 juin 2015

We consider a multivalued function of the form $H_\varepsilon=P_\varepsilon^\alpha_0\prod^k_i=1P_i^\alpha_i, P_i\in\mathbbR[x,y], \alpha_i\in\mathbbR^\ast_+$, which is a Darboux first integral of polynomial one-form $\omega=M_\varepsilon\fracdH_\varepsilonH_\varepsilon=0, (...)

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[hal-00940106] Virtual braids from a topological viewpoint

20 juin 2015

Virtual braids are a combinatorial generalization of braids. We present abstract braids as equivalence classes of braid diagrams on a surface, joining two distinguished boundary components. They are identified up to isotopy, compatibility, stability and Reidemeister moves. We show that virtual (...)

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[hal-01164543] A simple solution to the word problem for virtual braid groups

18 juin 2015

We show a simple and easily implementable solution to the word problem for virtual braid groups.

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[hal-01145780] Families of solutions of order nine to the NLS equation with sixteen parameters

15 juin 2015

We construct new deformations of the Peregrine breather (P9) of order 9 with 16 real parameters. With this method, we obtain explicitly new families of quasi-rational solutions to the NLS equation in terms of a product of an exponential depending on t by a ratio of two polynomials of degree 90 (...)

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[hal-01160563] Empirical and theoretical study of atelostomate (Echinoidea, Echinodermata) plate architecture : using graph analysis to reveal structural constraints.

6 juin 2015

Describing patterns of connectivity among organs is essential for identifying anatomical homologies among taxa. It is also critical for revealing morphogenetic processes and the associated constraints that control the morphological diversification of clades. This is particularly relevant for (...)

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[hal-00521135] Genèse et diffusion d’un théorème de Robert de Montessus de Ballore sur les fractions continues alg\’ebriques.

30 mai 2015

En 1902, Robert de Montessus de Ballore démontre la convergence d'une fraction continue algébrique associée à une fonction analytique à l'origine et méromorphe dans un domaine contenant l'origine. Aujourd'hui ce théorème est encore cité. Et le nom Montessus de Ballore sert à nommer des généralisations (...)

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[hal-01109143] Higher order Peregrine breathers solutions to the NLS equation

27 mai 2015

The solutions to the one dimensional focusing nonlinear Schrödinger equation (NLS) can be written as a product of an exponential depending on t by a quotient of two polynomials of degree N (N + 1) in x and t. These solutions depend on 2N − 2 parameters : when all these parameters are equal to 0, (...)

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[hal-01111000] Homological Projective Duality for Determinantal Varieties

26 mai 2015

In this paper we prove Homological Projective Duality for crepant categorical resolutions of several classes of linear determinantal varieties. By this we mean varieties that are cut out by the minors of a given rank of a n x m matrix of linear forms on a given projective space. As (...)

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[hal-01071400] Statistics of transitions for Markov chains with periodic forcing

26 mai 2015

The influence of a time-periodic forcing on stochastic processes can essentially be emphasized in the large time behaviour of their paths. The statistics of transition in a simple Markov chain model permits to quan-tify this influence. In particular a functional Central Limit Theorem can be (...)

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[hal-01110387] The first-passage time of the Brownian motion to a curved boundary : an algorithmic approach

26 mai 2015

Under some weak conditions, the first-passage time of the Brownian motion to a continuous curved boundary is an almost surely finite stopping time. Its probability density function (pdf) is explicitly known only in few particular cases. Several mathematical studies proposed to approximate the (...)

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[hal-01151427] EQUIVARIANTLY UNIFORMLY RATIONAL VARIETIES

14 mai 2015

Abstract. We introduce equivariant versions of uniform rationality: given an algebraic group G, a G-variety is called G-uniformly rational (resp. G-linearly uniformly rational) if every point has a G-invariant open neighborhood equivariantly isomorphic to a G-invariant open subset of the affine (...)

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[hal-01143763] The three links Purcell swimmer and some geometric problems related to periodic optimal controls

23 avril 2015

The maximum principle combined with numerical methods is a powerful tool to compute periodic optimal controls. We present some examples, in particular the three links Purcell swimmer and discuss some geometric problems related to such (...)

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[hal-01090977] Lunar perturbation of the metric associated to the averaged orbital transfer

23 avril 2015

In a series of previous article [1,2], we introduced a Riemannian metric associated to the energy minimizing orbital transfer with low propulsion. The aim of this article is to study the deformation of this metric due to a standard perturbation in space mechanics, the lunar attraction. Using (...)

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[hal-01144711] The dual and the double of a Hopf algebroid are Hopf algebroids

23 avril 2015

Let H be a ×-bialgebra in the sense of Takeuchi. We show that if H is ×-Hopf, and if H fulfills the finiteness condition necessary to define its skew dual, then the coopposite of the latter is ×-Hopf as well. If in addition the coopposite ×-bialgebra of H is ×-Hopf, then the coopposite of the (...)

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[hal-01115420] On tensor factorizations of Hopf algebras

22 avril 2015

We prove a variety results on tensor product factorizations of finite dimensional Hopf algebras (more generally Hopf algebras satisfying chain conditions in suitable braided categories). The results are analogs of well-known results on direct product factorizations of finite groups (or groups (...)

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[hal-01136676] L 1 -minimization for mechanical systems

7 avril 2015

Second order systems whose drift is defined by the gradient of a given potential are considered, and minimization of the L 1-norm of the control is addressed. An analysis of the extremal flow emphasizes the role of singular trajectories of order two [25, 29]; the case of the two-body potential (...)

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[tel-01136902] Some topics in variational analysis and optimization

3 avril 2015

In this thesis, we first study the theory of [gamma]-limits. Besides some basic properties of [gamma]-limits,expressions of sequential [gamma]-limits generalizing classical results of Greco are presented. These limits also give us a clue to a unified classification of derivatives and tangent (...)

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[hal-01135794] Persistent random walks

31 mars 2015

We consider a walker that at each step keeps the same direction with a probability that depends on the time already spent in the direction the walker is currently moving. In this paper, we study some asymptotic properties of this persistent random walk and give the conditions of recurrence or (...)

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[hal-01104428] Codimension one attracting sets in $\mathbb{P}^k(\mathbb{C})$

31 mars 2015

We are interested in attracting sets of $\mathbbP^k(\mathbbC)$ which are of small topological degree and of codimension $1.$ We first show that there exists a large family of examples. Then we study their ergodic and pluripotential theoretic (...)

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[hal-01136896] Geometric Numerical Methods and Results in the Control Imaging Problem in Nuclear Magnetic Resonance

31 mars 2015

The purpose of this paper is to present numerical methods and results about the contrast imaging problem in nuclear magnetic resonance which corresponds to a Mayer problem in optimal control. The candidates as minimizers are selected among a set of extremals, solutions of a Hamiltonian system (...)

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[tel-01136904] Mesures de GIBBS et mesures harmoniques pour les feuilletages aux feuilles courbées négativement

31 mars 2015

Dans ce travail de thèse, nous développons une notion de mesure de Gibbs pour le flot géodésique tangent aux feuilles d'un fibré feuilleté au dessus d'une base négativement courbée. Nous développons également une notion de mesure F-harmonique et prouvons qu'il existe une correspondance bijective entre (...)

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[hal-01135737] Multi-parametric solutions to the NLS equation

27 mars 2015

The structure of the solutions to the one dimensional focusing nonlin-ear Schrödinger equation (NLS) for the order N in terms of quasi rational functions is given here. We first give the proof that the solutions can be expressed as a ratio of two wronskians of order 2N and then two determinants (...)

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[hal-01117528] Online estimation of the geometric median in Hilbert spaces : non asymptotic confidence balls

25 mars 2015

Estimation procedures based on recursive algorithms are interesting and powerful techniques that are able to deal rapidly with (very) large samples of high dimensional data. The collected data may be contaminated by noise so that robust location indicators, such as the geometric median, may be (...)

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[hal-01131608] 2N+1 highest amplitude of the modulus of the N-th order AP breather and other 2N-2 parameters solutions to the NLS equation

19 mars 2015

We construct here new deformations of the AP breather (Akhmediev-Peregrine breather) of order N (or AP N breather) with 2N −2 real parameters. Other families of quasi-rational solutions of the NLS equation are obtained. We evaluate the highest amplitude of the modulus of AP breather of order N ; (...)

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[hal-01123965] Hyperbolic geometry in the work of Johann Heinrich Lambert

7 mars 2015

The memoir Theorie der Parallellinien (1766) by Johann Heinrich Lambert is one of the founding texts of hyperbolic geometry, even though its author's aim was, like many of his predecessors', to prove that such a geometry does not exist. In fact, Lambert developed his theory with the hope of (...)

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[hal-01122467] Frobenius-Schur indicators for some fusion categories associated to symmetric and alternating groups

5 mars 2015

We calculate Frobenius-Schur indicator values for some fusion categories obtained from inclusions of finite groups H⊂G, where more concretely G is symmetric or alternating, and H is a symmetric, alternating or cyclic group. Our work is strongly related to earlier results by (...)

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[hal-01116213] Rational reductions of the 2D-Toda hierarchy and mirror symmetry

13 février 2015

We introduce and study a two-parameter family of symmetry reductions of the two-dimensional Toda lattice hierarchy, which are characterized by a rational factorization of the Lax operator into a product of an upper diagonal and the inverse of a lower diagonal formal difference operator. They (...)

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[hal-01115411] A HIGHER FROBENIUS-SCHUR INDICATOR FORMULA FOR GROUP-THEORETICAL FUSION CATEGORIES

12 février 2015

Group-theoretical fusion categories are defined by data concerning finite groups and their cohomology: A finite group G endowed with a three-cocycle ω, and a subgroup H ⊂ G endowed with a two-cochain whose coboundary is the restriction of ω. The objects of the category are G-graded vector spaces (...)

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[hal-01115331] COMPUTING HIGHER FROBENIUS-SCHUR INDICATORS IN FUSION CATEGORIES CONSTRUCTED FROM INCLUSIONS OF FINITE GROUPS

12 février 2015

We consider a subclass of the class of group-theoretical fusion categories: To every finite group G and subgroup H one can associate the category of G-graded vector spaces with a two-sided H-action compatible with the grading. We derive a formula that computes higher Frobenius-Schur indicators (...)

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[hal-01115432] Braided bi-Galois theory II : The cocommutative case

12 février 2015

We study groups of bi-Galois objects over a Hopf algebra H in a braided monoidal category B. We assume H to be cocommutative in a certain sense; this does not mean that H is a cocommutative coalgebra with respect to the braiding given in B , but it is cocommutative with respect to a different (...)

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[hal-01115406] SOME QUASITENSOR AUTOEQUIVALENCES OF DRINFELD DOUBLES OF FINITE GROUPS

12 février 2015

We report on two classes of autoequivalences of the category of Yetter-Drinfeld modules over a finite group, or, equiv-alently the Drinfeld center of the category of representations of a finite group. Both operations are related to the r-th power opera-tion, with r relatively prime to the (...)

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[hal-01114188] Singular quadratic Lie superalgebras

11 février 2015

In this paper, we generalize some results on quadratic Lie algebras to quadratic Lie superalgebras, by applying graded Lie algebras tools. We establish a one-to-one correspondence between non-Abelian quadratic Lie superalgebra structures and nonzero even super-antisymmetric 3-forms satisfying a (...)

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