# INSTITUT DE MATHEMATIQUES DE BOURGOGNE

UMR 5584

## Publications 2016

Dernières parutions

### [hal-01736228] Rational solutions to the KPI equation of order 7 depending on 12 parameters

16 mars 2018

We construct in this paper, rational solutions as a quotient of two determinants of order 2N = 14 and we obtain what we call solutions of order N = 7 to the Kadomtsev-Petviashvili equation (KPI) as a quotient of 2 polynomials of degree 112 in x, y and t depending on 12 parameters. The maximum (...)

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### [hal-01721845] Working Notes on the Time Minimal Saturation of a Pair of Spins and Application in Magnetic Resonance Imaging

16 mars 2018

In this article, we analyse the time minimal control for the saturation of a pair of spins of the same species but with inhomogeneities of the applied RF-magnetic field, in relation with the contrast problem in Magnetic Resonance Imaging. We make a complete analysis based on geometric control (...)

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### [hal-01720871] Optimality of 1-norm regularization among weighted 1-norms for sparse recovery : a case study on how to find optimal regularizations

7 mars 2018

The 1-norm was proven to be a good convex regularizer for the recovery of sparse vectors from under-determined linear measurements. It has been shown that with an appropriate measurement operator, a number of measurements of the order of the sparsity of the signal (up to log factors) is (...)

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### [hal-01721845] Working Notes on the Time Minimal Saturation of a Pair of Spins and Application in Magnetic Resonance Imaging

2 mars 2018

In this article, we analyse the time minimal control for the saturation of a pair of spins of the same species but with inhomogeneities of the applied RF-magnetic field, in relation with the contrast problem in Magnetic Resonance Imaging. We make a complete analysis based on geometric control (...)

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### [hal-01720871] Optimality of 1-norm regularization among weighted 1-norms for sparse recovery : a case study on how to find optimal regularizations

2 mars 2018

The 1-norm was proven to be a good convex regularizer for the recovery of sparse vectors from under-determined linear measurements. It has been shown that with an appropriate measurement operator, a number of measurements of the order of the sparsity of the signal (up to log factors) is (...)

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### [hal-01718345] Singularities of min time affine control systems

27 février 2018

Affine control problems arise naturally from controlled mechanical systems. Building on previous results [2, 8], we go one step further and prove that the extremal flow given by Pontrjagin maximum principle can be stratified. We also study the regularity of this flow in terms of (...)

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### [hal-01708905] Convergence of a relaxed inertial proximal algorithm for maximally monotone operators

16 février 2018

In a Hilbert space $\mathcal H$, given $A:\mathcal H\to 2^\mathcal H$ a maximally monotone operator, we study the convergence properties of a general class of relaxed inertial proximal algorithms. This study aims to extend to the case of the general monotone inclusion $Ax \ni 0$ the (...)

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### [hal-01388054] Darboux integrable system with a triple point and pseudo-abelian integrals

6 février 2018

We study pseudo-abelian integrals associated with polynomial perturbations of Dar-boux integrable system with a triple point. Under some assumptions we prove the local boundedness of the number of their zeros. Assuming that this is the only non-genericity, we prove that the number of zeros of (...)

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

5 février 2018

We consider the orbital stability of relative equilibria of Hamiltonian dynamical systems on Banach spaces, in the presence of a multi-dimensional invariance group for the dynamics. We prove a persistence result for such relative equilibria, present a generalization of the Vakhitov-Kolokolov (...)

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### [hal-01679261] Non-integrability of the minimum-time kepler problem

10 janvier 2018

We prove that the minimum-time controlled Kepler problem is not meromorphically Liouville integrable on the Riemann surface of its Hamiltonian.

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### [hal-01653901] Sub-Riemannian geometry, Hamiltonian dynamics, micro-swimmers, Copepod nauplii and Copepod robot

4 janvier 2018

This article deals with relation between sub-Riemannian geometry, Hamiltonian dynamics and micro-swimmers. Sub-Riemannian geometry is developed in the framework of geometric optimal control and following the Maximum Principle, the geodesics are solutions of an Hamiltonian differential equation. (...)

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### [hal-01226734] Geometric and Numerical Optimal Control with Application to Swimming at Low Reynolds Number and Magnetic Resonance Imaging.

3 janvier 2018

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-01672815] Super-rigid Affine Fano Varieties

27 décembre 2017

We study a wide class of affine varieties, which we call affine Fano varieties. By analogy with birationally super-rigid Fano varieties, we define super-rigidity for affine Fano varieties, and provide many examples and non-examples of super-rigid affine Fano (...)

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### [hal-01662926] Mass transportation on sub-Riemannian structures of rank two in dimension four

13 décembre 2017

This paper is concerned with the study of the Monge optimal transport problem in sub-Riemannian manifolds where the cost is given by the square of the sub-Riemannian distance. Our aim is to extend previous results on existence and uniqueness of optimal transport maps to cases of sub-Riemannian (...)

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### [hal-01660062] RATE OF CONVERGENCE OF INERTIAL GRADIENT DYNAMICS WITH TIME-DEPENDENT VISCOUS DAMPING COEFFICIENT

11 décembre 2017

In a Hilbert space $\mathcal H$, we study the convergence properties when $t \to + \infty$ of the trajectories of the second-order differential equation \beginequation* \mbox(IGS)_\gamma \quad \quad \ddotx(t) + \gamma(t) \dotx(t) + \nabla \Phi (x(t))=0, \endequation* where $\nabla\Phi$ is the (...)

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### [hal-01658494] Recurrence of Multidimensional Persistent Random Walks. Fourier and Series Criteria

8 décembre 2017

The recurrence features of persistent random walks built from variable length Markov chains are investigated. We observe that these stochastic processes can be seen as Lévy walks for which the persistence times depend on some internal Markov chain: they admit Markov random walk skeletons. A (...)

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### [hal-01653901] Sub-Riemannian geometry, Hamiltonian dynamics, micro-swimmers, Copepod nauplii and Copepod robot

6 décembre 2017

This article deals with relation between sub-Riemannian geometry, Hamiltonian dynamics and micro-swimmers. Sub-Riemannian geometry is developed in the framework of geometric optimal control and following the Maximum Principle, the geodesics are solutions of an Hamiltonian differential equation. (...)

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### [hal-01653901] Sub-Riemannian geometry, Hamiltonian dynamics, micro-swimmers, Copepod nauplii and Copepod robot

5 décembre 2017

This article deals with relation between sub-Riemannian geometry, Hamiltonian dynamics and micro-swimmers. Sub-Riemannian geometry is developed in the framework of geometric optimal control and following the Maximum Principle, the geodesics are solutions of an Hamiltonian differential equation. (...)

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### [hal-01226734] Geometric and Numerical Optimal Control with Application to Swimming at Low Reynolds Number and Magnetic Resonance Imaging.

28 novembre 2017

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-01648383] Convergence of damped inertial dynamics governed by regularized maximally monotone operators

28 novembre 2017

In a Hilbert space setting, we study the asymptotic behavior, as time $t$ goes to infinity, of the trajectories of a second-order differential equation governed by the Yosida regularization of a maximally monotone operator with time-varying positive index $\lambda(t)$. The dissipative and (...)

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### [hal-01648248] Families of rational solutions of order $6$ to the KPI equation depending on 10 parameters.

27 novembre 2017

Here we constuct rational solutions of order 6 to the Kadomtsev-Petviashvili equation (KPI) as a quotient of 2 polynomials of degree 84 in x, y and t depending on 10 parameters. We verify that the maximum of modulus of these solutions at order 6 is equal to 2(2N + 1) 2 = 338. We study the (...)

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### [hal-01326790] Optimal strokes at low Reynolds number : a geometric and numerical study of Copepod and Purcell swimmers

23 novembre 2017

In this article, we provide a comparative geometric and numerical analysis of optimal strokes for two different rigid links swimmer models at low Reynolds number: the Copepod swimmer (a symmetric swimmer recently introduced by [31]) and the long-standing three-link Purcell swimmer [29]. The (...)

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### [hal-01442880] Sub-Riemannian geometry and swimming at low Reynolds number : the Copepod case

23 novembre 2017

Based on copepod observations, Takagi proposed a model to interpret the swimming behavior of these microorganisms using sinusoidal paddling or sequential paddling followed by a recovery stroke in unison, and compares them invoking the concept of efficiency. Our aim is to provide an (...)

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### [hal-01504996] On codimension two embeddings up to link-homotopy

31 octobre 2017

We consider knotted annuli in 4–space, called 2–string-links, which are knotted surfaces in codi-mension two that are naturally related, via closure operations, to both 2–links and 2–torus links. We classify 2–string-links up to link-homotopy by means of a 4–dimensional version of Milnor invariants. (...)

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### [hal-01622447] Deformations of $\mathbb{A}^1$-cylindrical varieties

27 octobre 2017

An algebraic variety is called $\mathbbA^1$-cylindrical if it contains an $\mathbbA^1$-cylinder, i.e. a Zariski open subset of the form $Z\times\mathbbA^1$ for some algebraic variety $Z$. We show that the generic fiber of a family $f:X\rightarrow S$ of normal $\mathbbA^1$-cylindrical varieties (...)

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### [hal-01619911] Symbolic Computations of First Integrals for Polynomial Vector Fields

23 octobre 2017

In this article we show how to generalize to the Darbouxian, Liouvillian and Riccati case the extactic curve introduced by J. Pereira. With this approach, we get new algorithms for computing , if it exists, a rational, Darbouxian, Liouvillian or Riccati first integral with bounded degree of a (...)

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### [hal-01620406] Automorphisms of $\mathbb{P}^1$-bundles over rational surfaces

20 octobre 2017

In this paper we provide the complete classification of $\mathbbP^1$-bundles over smooth projective rational surfaces whose neutral component of the automorphism group is maximal. Our results hold over any algebraically closed field of characteristic (...)

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### [hal-01620368] Stability conditions and related filtrations for $(G,h)$-constellations

20 octobre 2017

Given an infinite reductive algebraic group $G$, we consider $G$-equivariant coherent sheaves with prescribed multiplicities, called $(G,h)$-constellations, for which two stability notions arise. The first one is analogous to the $\theta$-stability defined for quiver representations by King and (...)

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### [hal-01620380] Horospherical stacks

20 octobre 2017

We prove structure theorems for algebraic stacks with a reductive group action and a dense open substack isomorphic to a horospherical homogeneous space, and thereby obtain new examples of algebraic stacks which are global quotient stacks. Our results partially generalize the work of (...)

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### [hal-01598396] Rational solutions of order 5 to the KPI equation depending on 8 parameters

5 octobre 2017

In this paper, we go on with the study of rational solutions to the Kadomtsev-Petviashvili equation (KPI). We construct here rational solutions of order 5 as a quotient of 2 polynomials of degree 60 in x, y and t depending on 8 parameters. The maximum modulus of these solutions at order 5 is (...)

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### [hal-01467144] Topological classification of Morse-Smale diffeomorphisms without heteroclinic curves on 3-manifolds

28 septembre 2017

We show that, up to topological conjugation, the equivalence class of a Morse-Smale diffeomorphism without heteroclinic curves on 3-manifold is completely defined by an em- bedding of two-dimensional stable and unstable heteroclinic laminations to a characteristic (...)

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### [hal-01592583] Note on residual finiteness of Artin groups

25 septembre 2017

Let A be an Artin group. A partition P of the set of standard generators of A is called admissible if, for all X, Y ∈ P , X = Y , there is at most one pair (s, t) ∈ X × Y which has a relation. An admissible partition P determines a quotient Coxeter graph Γ/P. We prove that, if Γ/P is either a (...)

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### [hal-01591187] Predictive control based on nonlinear observer for muscular force and fatigue model

21 septembre 2017

The Functional Electrical Stimulation (FES) is used in the case of neurological disorders (paralyzed muscles) or the muscle reinforcement (sportsmen). A recent model was proposed coupling a force model and a fatigue model. Based on the specific structure of the model, we present a predictive (...)

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### [hal-01583550] Ping-pong configurations and circular orders on free groups

7 septembre 2017

We discuss actions of free groups on the circle with “ping-pong” dynamics, i.e. dynamics determined by a finite amount of combinatorial data. As a natural extension of the work started in (Mann, Rivas, 2016), we show that the free group $F_n$ admits an isolated circular order if and only if n is (...)

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### [hal-01578348] Algebraic models of the real affine plane

29 août 2017

We introduce a new invariant, the real (logarithmic)-Kodaira dimension, that allows to distinguish smooth real algebraic surfaces up to birational diffeomorphism. As an application, we construct infinite families of smooth rational real algebraic surfaces with trivial homology groups, whose (...)

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### [hal-01573708] Morita equivalence of pointed fusion categories of small rank

22 août 2017

We classify pointed fusion categories C(G, ω) up to Morita equivalence for 1 < |G| < 32. Among them, the cases |G| = 2 3 , 2 4 and 3 3 are emphasized. Although the equivalence classes of such categories are not distinguished by their Frobenius-Schur indicators, their categorical Morita (...)

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### [hal-01525384] From Fredholm and Wronskian representations to rational solutions to the KPI equation depending on 2N − 2 parameters, the structure of the solutions and the case of fourth order

21 août 2017

We have already constructed solutions to the Kadomtsev-Petviashvili equation (KPI) in terms of Fredholm determinants and wronskians of order 2N. These solutions have been called solutions of order N and they depend on 2N − 1 parameters. We construct here N-order rational solutions. We prove that (...)

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### [hal-01573708] Morita equivalence of pointed fusion categories of small rank

11 août 2017

We classify pointed fusion categories C(G, ω) up to Morita equivalence for 1 < |G| < 32. Among them, the cases |G| = 2 3 , 2 4 and 3 3 are emphasized. Although the equivalence classes of such categories are not distinguished by their Frobenius-Schur indicators, their categorical Morita (...)

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### [hal-01573376] Modular categories are not determined by their modular data

9 août 2017

Arbitrarily many pairwise inequivalent modular categories can share the same modular data. We exhibit a family of examples that are module categories over twisted Drinfeld doubles of finite groups, and thus in particular integral modular (...)

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### [hal-01570874] Injective homomorphisms of mapping class groups of non-orientable surfaces

1er août 2017

Let N be a compact, connected, non-orientable surface of genus ρ with n boundary components, with ρ ≥ 5 and n ≥ 0, and let M(N) be the mapping class group of N. We show that, if G is a finite index subgroup of M(N) and ϕ : G → M(N) is an injective homomorphism, then there exists f ∈ M(N) such that (...)

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### [hal-01569445] Equivariant extensions of Ga-torsors over punctured surfaces

27 juillet 2017

Motivated by the study of the structure of algebraic actions the additive group on affine threefolds X, we consider a special class of such varieties whose algebraic quotient morphisms X → X//Ga restrict to principal homogeneous bundles over the complement of a smooth point of the quotient. We (...)

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### [hal-01568278] Generalized Johnson homomorphisms for extended N-series

25 juillet 2017

The Johnson filtration of the mapping class group of a compact, oriented surface is the descending series consisting of the kernels of the actions on the nilpotent quotients of the fundamental group of the surface. Each term of the Johnson filtration admits a Johnson homomorphism, whose kernel (...)

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### [hal-01226734] Working Examples In Geometric Optimal Control

24 juillet 2017

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-01542608] Hyperbolicity as an obstruction to smoothability for one-dimensional actions

18 juillet 2017

Ghys and Sergiescu proved in the $80$s that Thompson's groups $F$ and $T$ admit actions by $C^\infty$ diffeomorphisms of the interval. They proved that the standard actions of these groups are topologically conjugate to a group of $C^\infty$ diffeomorphisms. Monod defined a family of groups of (...)

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### [hal-01178641] Groups with infinitely many ends acting analytically on the circle

17 juillet 2017

This article is inspired by two milestones in the study of non-minimal group actions on the circle: Duminy's theorem about the number of ends of semi-exceptional leaves, and Ghys' freeness result in real-analytic regularity. Our first result concerns groups of real-analytic diffeomorphisms with (...)

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### [hal-01557228] LOCAL BANDWIDTH SELECTION FOR KERNEL DENSITY ESTIMATION IN BIFURCATING MARKOV CHAIN MODEL

13 juillet 2017

We propose an adaptive estimator for the stationary distribution of a bifurcating Markov Chain on R d. Bifurcating Markov chains (BMC for short) are a class of stochastic processes indexed by regular binary trees. A kernel estimator is proposed whose bandwidth is selected by a method inspired (...)

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### [hal-01556806] Algebraic-geometric techniques for the feedback classification and robustness of the optimal control of a pair of Bloch equations with application to Magnetic Resonance Imaging

5 juillet 2017

The aim of this article is to classify the singular trajectories associated with the optimal control problems of a pair of controlled Bloch equations. The motivation is to analyze the robustness of the optimal solutions to the contrast and the time-minimal saturation problem, in magnetic (...)

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### [hal-01544680] A sharp oracle inequality for Graph-Slope

29 juin 2017

Following recent success on the analysis of the Slope estimator, we provide a sharp oracle inequality in term of prediction error for Graph-Slope, a generalization of Slope to signals observed over a graph. In addition to improving upon best results obtained so far for the Total Variation (...)

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### [hal-01542608] Hyperbolicity as an obstruction to smoothability for one-dimensional actions

20 juin 2017

Ghys and Sergiescu proved in the $80$s that Thompson's groups $F$ and $T$ admit actions by $C^\infty$ diffeomorphisms of the interval. They proved that the standard actions of these groups are topologically conjugate to a group of $C^\infty$ diffeomorphisms. Monod defined a family of groups of (...)

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### [hal-01531275] Ordering Garside groups

2 juin 2017

We introduce a condition on Garside groups that we call Dehornoy structure. An iteration of such a structure leads to a left order on the group. We show conditions for a Garside group to admit a Dehornoy structure, and we apply these criteria to prove that the Artin groups of type A and I 2 (...)

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### [hal-01525384] From Fredholm and Wronskian representations to rational solutions to the KPI equation depending on 2N − 2 parameters, the structure of the solutions and the case of fourth order

22 mai 2017

We have already constructed solutions to the Kadomtsev-Petviashvili equation (KPI) in terms of Fredholm determinants and wronskians of order 2N. These solutions have been called solutions of order N and they depend on 2N − 1 parameters. We construct here N-order rational solutions. We prove that (...)

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### [hal-01524814] Exact simulation of the first-passage time of diffusions

19 mai 2017

Since diffusion processes arise in so many different fields, efficient tech-nics for the simulation of sample paths, like discretization schemes, represent crucial tools in applied probability. Such methods permit to obtain approximations of the first-passage times as a by-product. For (...)

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### [hal-01522437] Poly-freeness of even Artin groups of FC type

16 mai 2017

We prove that even Artin groups of FC type are poly-free and residually finite.

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### [hal-01442880] Sub-Riemannian geometry and swimming at low Reynolds number : the Copepod case

25 avril 2017

Based on copepod observations, Takagi proposed a model to interpret the swimming behavior of these microorganisms using sinusoidal paddling or sequential paddling followed by a recovery stroke in unison, and compares them invoking the concept of efficiency. Our aim is to provide an (...)

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### [hal-01507551] $\mathbb{A}^2$ -Fibrations between affine spaces are trivial $\mathbb{A}^2$-bundles

14 avril 2017

We give a criterion for a flat fibration with affine plane fibers over a smooth scheme defined over a field of characteristic zero to be a Zariski locally trivial $\mathbbA^2$-bundle. An application is a positive answer to a version of the Dolgachev-Weisfeiler Conjecture for such fibrations: a (...)

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### [hal-01507063] Solving chance constrained optimal control problems in aerospace via Kernel Density Estimation

12 avril 2017

The goal of this paper is to show how non-parametric statistics can be used to solve some chance constrained optimization and optimal control problems. We use the Kernel Density Estimation method to approximate the probability density function of a random variable with unknown distribution , (...)

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### [hal-01504996] On codimension two embeddings up to link-homotopy

12 avril 2017

We consider knotted annuli in 4–space, called 2–string-links, which are knotted surfaces in codi-mension two that are naturally related, via closure operations, to both 2–links and 2–torus links. We classify 2–string-links up to link-homotopy by means of a 4–dimensional version of Milnor invariants. (...)

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### [hal-01492325] The thirteenth Peregrine breather and its deformations depending on twenty four parameters solutions to the NLS equation.

24 mars 2017

We go on with the study of the solutions to the focusing one dimensional nonlinear Schrödinger equation (NLS). We construct here the thirteen's Peregrine breather (P13 breather) with its twenty four real parameters, creating deformation solutions to the NLS equation. New families of (...)

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### [hal-01452778] On measures in sub-Riemannian geometry

8 mars 2017

In \citegjha we give a detailed analysis of spherical Hausdorff measures on sub-Riemannian manifolds in a general framework, that is, without the assumption of equiregularity. The present paper is devised as a complement of this analysis, with both new results and open questions. The first aim (...)

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### [hal-01452778] On measures in sub-Riemannian geometry

16 février 2017

In \citegjha we give a detailed analysis of spherical Hausdorff measures on sub-Riemannian manifolds in a general framework, that is, without the assumption of equiregularity. The present paper is devised as a complement of this analysis, with both new results and open questions. The first aim (...)

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### [hal-01467965] Maximal Solutions of Sparse Analysis Regularization

16 février 2017

This paper deals with the non-uniqueness of the solutions of an analysis-Lasso regularization. Most of previous works in this area is concerned with the case where the solution set is a singleton, or to derive guarantees to enforce uniqueness. Our main contribution consists in providing a (...)

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### [hal-01467144] Topological classification of Morse-Smale diffeomorphisms without heteroclinic curves on 3-manifolds

16 février 2017

We show that, up to topological conjugation, the equivalence class of a Morse-Smale diffeomorphism without heteroclinic curves on 3-manifold is completely defined by an em- bedding of two-dimensional stable and unstable heteroclinic laminations to a characteristic (...)

Lire la suite

### [hal-01452778] On measures in sub-Riemannian geometry

15 février 2017

In \citegjha we give a detailed analysis of spherical Hausdorff measures on sub-Riemannian manifolds in a general framework, that is, without the assumption of equiregularity. The present paper is devised as a complement of this analysis, with both new results and open questions. The first aim (...)

Lire la suite

### [hal-01452778] On measures in sub-Riemannian geometry

6 février 2017

In \citegjha we give a detailed analysis of spherical Hausdorff measures on sub-Riemannian manifolds in a general framework, that is, without the assumption of equiregularity. The present paper is devised as a complement of this analysis, with both new results and open questions. The first aim (...)

Lire la suite

### [hal-01326790] Optimal strokes at low Reynolds number : a geometric and numerical study of Copepod and Purcell swimmers

30 janvier 2017

In this article, we provide a comparative geometric and numerical analysis of optimal strokes for two different rigid links swimmer models at low Reynolds number: the Copepod swimmer (a symmetric swimmer recently introduced by [31]) and the long-standing three-link Purcell swimmer [29]. The (...)

Lire la suite

26 janvier 2017

[...]

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### [hal-01442880] Optimal control theory, sub-Riemannian geometry and swimming of copepod

23 janvier 2017

In [17], based on the observation of copepods, Takagi proposed a model to analyze the swimming of microorganisms using sinusoidal paddling or sequential paddling followed by a recovery stroke in unison, and they are compared with the concept of efficiency. Our aim is to provide an (...)

Lire la suite

### [hal-01429264] The equivariant Jacobian Conjecture fails for pseudo-planes

7 janvier 2017

A smooth complex variety satisfies the Generalized Jacobian Conjecture if all its etale endomorphisms are proper. We study the equivariant version of the conjecture for ℚ-acyclic surfaces of negative Kodaira dimension and infinite algebraic groups. We show that it holds for groups other than ℂ∗, (...)

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

1er décembre 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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30 novembre 2016

[...]

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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-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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### [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-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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### [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 (...)

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### [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 (...)

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### [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-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-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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9 juin 2016

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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-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-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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