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Kirwan map and moduli space of flat connectionsJun 24 2003Dec 15 2003If $K$ is a compact Lie group and $g\geq 2$ an integer, the space $K^{2g}$ is endowed with the structure of a Hamiltonian space with a Lie group valued moment map $\Phi$. Let $\beta$ be in the centre of $K$. The reduction $\Phi^{-1}(\beta)/K$ is homeomorphic ... More

Quasi-Poisson actions and massive non-rotating BTZ black holesSep 29 2004Using ideas from an article of P. Bieliavsky, M. Rooman and Ph. Spindel on BTZ black holes, I construct a family of interesting examples of quasi-Poisson actions as defined by A. Alekseev and Y. Kosmann-Schwarzbach. As an application, I obtain a genuine ... More

Quantisation of Lie-Poisson manifoldsNov 03 2004In quantum physics, the operators associated with the position and the momentum of a particle are unbounded operators and $C^*$-algebraic quantisation does therefore not deal with such operators. In the present article, I propose a quantisation of the ... More

Differentiable Game MechanicsMay 13 2019Deep learning is built on the foundational guarantee that gradient descent on an objective function converges to local minima. Unfortunately, this guarantee fails in settings, such as generative adversarial nets, that exhibit multiple interacting losses. ... More

The Mechanics of n-Player Differentiable GamesFeb 15 2018Jun 06 2018The cornerstone underpinning deep learning is the guarantee that gradient descent on an objective converges to local minima. Unfortunately, this guarantee fails in settings, such as generative adversarial nets, where there are multiple interacting losses. ... More

Towards a Definition of Disentangled RepresentationsDec 05 2018How can intelligent agents solve a diverse set of tasks in a data-efficient manner? The disentangled representation learning approach posits that such an agent would benefit from separating out (disentangling) the underlying structure of the world into ... More

Woulda, Coulda, Shoulda: Counterfactually-Guided Policy SearchNov 15 2018Learning policies on data synthesized by models can in principle quench the thirst of reinforcement learning algorithms for large amounts of real experience, which is often costly to acquire. However, simulating plausible experience de novo is a hard ... More

Comment on " Gain coefficient method for amplified spontaneous emission in thin waveguided film of a conjugated polymer " [APL 93, 163307 (2008)]Feb 24 2009Comment on " Gain coefficient method for amplified spontaneous emission in thin waveguided film of a conjugated polymer " [APL 93, 163307 (2008)]

Shelah's eventual categoricity conjecture in universal classes. Part IIFeb 08 2016Sep 06 2016We prove that a universal class categorical in a high-enough cardinal is categorical on a tail of cardinals. As opposed to other results in the literature, we work in ZFC, do not require the categoricity cardinal to be a successor, do not assume amalgamation, ... More

Spectral triples for finitely presented groups, index 1Nov 19 2010May 26 2015Using a Cayley complex (generalizing the Cayley graph) and Clifford algebras, we are able to give, for a large class of finitely presented groups, a uniform construction of spectral triples with $D_{+}$ of index 1.

Shelah's eventual categoricity conjecture in universal classes. Part IJun 23 2015Nov 30 2015We prove: $\mathbf{Theorem}$ Let $K$ be a universal class. If $K$ is categorical in cardinals of arbitrarily high cofinality, then $K$ is categorical on a tail of cardinals. The proof stems from ideas of Adi Jarden and Will Boney, and also relies on a ... More

An analytical comparison of coalescent-based multilocus methods: The three-taxon caseJul 17 2012Incomplete lineage sorting (ILS) is a common source of gene tree incongruence in multilocus analyses. A large number of methods have been developed to infer species trees in the presence of ILS. Here we provide a mathematical analysis of several coalescent-based ... More

Logarithmic fluctuations for the Internal Diffusion Limited AggregationNov 23 2001Feb 02 2005This paper has been withdrawn by the author due to an error in the computation of E(n,x) on page 6 which appears to be essential for the result. The author is currently trying to correct this proof

Multi-height Scattering Phase Shifts From Sunspots And Phase Differences Between Photospheric Heights With SDO/HMI and AIA DataJul 12 2013Following Couvidat (2013), we analyze data from the Helioseismic and Magnetic Imager (HMI) and the Atmospheric Imaging Assembly (AIA) instruments onboard the Solar Dynamics Observatory: Doppler velocity and continuum intensity at 6173 A as well as intensity ... More

Quasiminimal abstract elementary classesNov 22 2016We propose the notion of a quasiminimal abstract elementary class (AEC). This is an AEC satisfying four semantic conditions: countable L\"owenheim-Skolem-Tarski number, existence of a prime model, closure under intersections, and uniqueness of nonalgebraic ... More

Ore's theorem on subfactor planar algebrasApr 03 2017Mar 22 2018This paper proves that an irreducible subfactor planar algebra with a distributive biprojection lattice admits a minimal 2-box projection generating the identity biprojection. It is a generalization of a theorem of Ore on intervals of finite groups, conjectured ... More

Indiscernible extraction and Morley sequencesMar 23 2014Jun 14 2014We present a new proof of the existence of Morley sequences in simple theories. We avoid using the Erd\H{o}s-Rado theorem and instead use only Ramsey's theorem and compactness. The proof shows that the basic theory of forking in simple theories can be ... More

Downward categoricity from a successor inside a good frameOct 13 2015Oct 03 2016We use orthogonality calculus to prove a downward transfer from categoricity in a successor in abstract elementary classes (AECs) that have a good frame (a forking-like notion for types of singletons) on an interval of cardinals: $\mathbf{Theorem}$ Let ... More

Shelah's eventual categoricity conjecture in tame AECs with primesSep 14 2015Jan 20 2017A new case of Shelah's eventual categoricity conjecture is established: $\mathbf{Theorem}$ Let $K$ be an AEC with amalgamation. Write $H_2 := \beth_{\left(2^{\beth_{\left(2^{\text{LS} (K)}\right)^+}}\right)^+}$. Assume that $K$ is $H_2$-tame and $K_{\ge ... More

Ore's theorem for cyclic subfactor planar algebras and applicationsMay 25 2015Jul 03 2016This paper introduces the cyclic subfactors, generalizing the cyclic groups as the subfactors generalize the groups, and generalizing the natural numbers as the maximal subfactors generalize the prime numbers. On one hand, a theorem of O. Ore states that ... More

Higher dimensional Zariski decompositionsApr 29 2002Using currents with minimal singularities, we construct pointwise minimal multiplicities for a real pseudo-effective $(1,1)$-class $\alpha$ on a compact complex $n$-fold $X$, which are the local obstructions to the numerical effectivity of $\alpha$. The ... More

New High Proper Motion Stars from the Digitized Sky Survey. III. Stars with proper motions 0.45<mu<2.0''/yr south of Decl.=-30Jan 13 2005Jun 07 2005We report the discovery of 182 new southern stars with proper motion larger than 0.45''/yr. The stars were found in an expansion of the SUPERBLINK proper motion survey to 8,980 square degrees south of Decl.=-30. The new high proper motion stars include ... More

Local limit theorem for symmetric random walks in Gromov-hyperbolic groupsSep 14 2012Completing a strategy of Gou\"ezel and Lalley, we prove a local limit theorem for the random walk generated by any symmetric finitely supported probability measure on a non-elementary Gromov-hyperbolic group: denoting by $R$ the inverse of the spectral ... More

Characterization of weak convergence of Birkhoff sums for Gibbs-Markov mapsSep 03 2008Jul 08 2009We investigate limit theorems for Birkhoff sums of locally H\"older functions under the iteration of Gibbs-Markov maps. Aaronson and Denker have given sufficient conditions to have limit theorems in this setting. We show that these conditions are also ... More

Looking back at superfluid heliumMar 26 2003A few years after the discovery of Bose Einstein condensation in several gases, it is interesting to look back at some properties of superfluid helium. After a short historical review, I comment shortly on boiling and evaporation, then on the role of ... More

Shelah's eventual categoricity conjecture in tame AECs with primesSep 14 2015Oct 03 2016A new case of Shelah's eventual categoricity conjecture is established: $\mathbf{Theorem}$ Let $K$ be an AEC with amalgamation. Write $H_2 := \beth_{\left(2^{\beth_{\left(2^{\text{LS} (K)}\right)^+}}\right)^+}$. Assume that $K$ is $H_2$-tame and $K_{\ge ... More

Weak turbulence theory for rotating magnetohydrodynamics and planetary dynamosMay 16 2014A weak turbulence theory is derived for magnetohydrodynamics under rapid rotation and in the presence of a large-scale magnetic field. The angular velocity $\Omega_0$ is assumed to be uniform and parallel to the constant Alfv\'en speed ${\bf b_0}$. Such ... More

Wave turbulence in magnetohydrodynamicsJan 06 2012This chapter reviews the recent progress made mainly during the last two decades on wave turbulence in magnetized plasmas (MHD, Hall MHD and electron MHD) in the incompressible and compressible cases. The emphasis is made on homogeneous and anisotropic ... More

Statistical Study of Short Quiescent Times Between FlaresMar 28 2000Dec 10 2000The study of the statistical distribution of short quiescent times ($\le$ 30 minutes) between solar flares has been investigated on a 1D MHD model. A power law behaviour is found which indicates the existence of sympathetic flaring. This prediction is ... More

Theory for helical turbulence under fast rotationFeb 26 2014Recent numerical simulations have shown the strong impact of helicity on \ADD{homogeneous} rotating hydrodynamic turbulence. The main effect can be summarized through the following law, $n+\tilde n = -4$, where $n$ and $\tilde n$ are respectively the ... More

Dual Ore's theorem on distributive intervals of finite groupsAug 08 2017Mar 20 2018This paper gives a self-contained group-theoretic proof of a dual version of a theorem of Ore on distributive intervals of finite groups. We deduce a bridge between combinatorics and representations in finite group theory.

Initial conditions in hybrid inflation: exploration by MCMC techniqueJun 23 2010In hybrid inflation, initial field values leading to sufficiently long inflation were thought be fine-tuned in a narrow band along the inflationary valley. A re-analysis of this problem has shown that there exists a non negligible proportion of successful ... More

Convergence of a finite volume scheme for the incompressible fluidsApr 05 2007We consider a finite volume scheme for the two-dimensional incompressible Navier-Stokes equations. We use a triangular mesh. The unknowns for the velocity and pressure are respectively piecewise constant and affine. We use a projection method to deal ... More

Tameness from two successive good framesJul 27 2017Mar 25 2019We show, assuming a mild set-theoretic hypothesis, that if an abstract elementary class (AEC) has a superstable-like forking notion for models of cardinality $\lambda$ and a superstable-like forking notion for models of cardinality $\lambda^+$, then orbital ... More

The lazy model theoretician's guide to Shelah's eventual categoricity conjecture in universal classesOct 28 2015Nov 30 2015We give a short overview of the proof of Shelah's eventual categoricity conjecture in universal classes with amalgamation in arXiv:1506.07024 .

Building prime models in fully good abstract elementary classesSep 23 2015May 10 2016We show how to build primes models in classes of saturated models of abstract elementary classes (AECs) having a well-behaved independence relation: $\mathbf{Theorem.}$ Let $K$ be an almost fully good AEC that is categorical in $\text{LS} (K)$ and has ... More

Infinitary stability theoryDec 10 2014Feb 24 2016We introduce a new device in the study of abstract elementary classes (AECs): Galois Morleyization, which consists in expanding the models of the class with a relation for every Galois type of length less than a fixed cardinal $\kappa$. We show: $\mathbf{Theorem}$ ... More

The categoricity spectrum of large abstract elementary classesMay 10 2018Sep 19 2018The categoricity spectrum of a class of structures is the collection of cardinals in which the class has a single model up to isomorphism. Assuming that cardinal exponentiation is injective (a weakening of the generalized continuum hypothesis, GCH), we ... More

Quasiminimal abstract elementary classesNov 22 2016Jun 12 2017We propose the notion of a quasiminimal abstract elementary class (AEC). This is an AEC satisfying four semantic conditions: countable L\"owenheim-Skolem-Tarski number, existence of a prime model, closure under intersections, and uniqueness of the generic ... More

On the volume of a line bundleJan 05 2002Using a result of Fujita on approximate Zariski decompositions and the singular version of Demailly's holomorphic Morse inequalities as obtained by Bonavero, we express the volume of a line bundle in terms of the absolutely continuous parts of all the ... More

The invariant Quot schemeNov 02 2005Given an affine scheme X with an action of a reductive group G and a G-linearized coherent sheaf M, we construct the ``invariant Quot scheme'' that parametrizes the quotients of M whose space of global sections is a direct sum of simple G-modules with ... More

On the Kahler-Einstein metric at strictly pseudoconvex pointsJan 05 2018Jul 05 2018We prove a local boundary regularity result for the complete Kahler-Einstein metrics of negative Ricci curvature near strictly pseudoconvex boundary point. We also study the asymptotic behaviour of their holomorphic bisectional curvatures near such points. ... More

Sharp polynomial estimates for the decay of correlationsFeb 15 2002We generalize a method developed by Sarig to obtain polynomial lower bounds for correlation functions for maps with a countable Markov partition. A consequence is that LS Young's estimates on towers are always optimal. Moreover, we show that, for functions ... More

Deformations of cones of primitive vectorsJun 08 2005Nov 22 2005For a complex connected reductive group G, we classify the simple modules whose cone of primitive vectors admits a nontrivial G-invariant deformation. We relate this classification to that of simple Jordan algebras, and to that (due to Akhiezer) of smooth ... More

Learning and Querying Fast Generative Models for Reinforcement LearningFeb 08 2018A key challenge in model-based reinforcement learning (RL) is to synthesize computationally efficient and accurate environment models. We show that carefully designed generative models that learn and operate on compact state representations, so-called ... More

Chiral symmetry and spectrum of Euclidean Dirac operatorNov 09 1999After recalling some connections between the Spontaneous Breakdown of Chiral Symmetry (SBChS) and the spectrum of the Dirac operator for Euclidean QCD on a torus, we use this tool to reconsider two related issues : the Zweig rule violation in the scalar ... More

Getting DNA twist rigidity from single molecule experimentsFeb 17 2004We use an elastic rod model with contact to study the extension versus rotation diagrams of single supercoiled DNA molecules. We reproduce quantitatively the supercoiling response of overtwisted DNA and, using experimental data, we get an estimation of ... More

A 26 ps RMS time-to-digital converter core for Spartan-6 FPGAsMar 27 2013We have designed, implemented and tested a time-to-digital converter core in a low-cost Spartan-6 FPGA. Our design exploits the finite propagation speed in carry chains to realize a delay line in which the propagation distance of the incoming signal's ... More

Tameness from two successive good framesJul 27 2017Aug 02 2018We show, assuming a mild set-theoretic hypothesis, that if an abstract elementary class (AEC) has a superstable-like forking notion for models of cardinality $\lambda$ and a superstable-like forking notion for models of cardinality $\lambda^+$, then orbital ... More

On the variance of internode distance under the multispecies coalescentDec 20 2018We consider the problem of estimating species trees from unrooted gene tree topologies in the presence of incomplete lineage sorting, a common phenomenon that creates gene tree heterogeneity in multilocus datasets. One popular class of reconstruction ... More

An introduction to inflation after Planck: from theory to observationsJan 02 2015These lecture notes have been written for a short introductory course on the status of inflation after Planck and BICEP2, given at the Xth Modave School of Mathematical Physics. The first objective is to give an overview of the theory of inflation: motivations, ... More

Hybrid inflation along waterfall trajectoriesJun 23 2010Feb 28 2011We identify a new inflationary regime for which more than 60 e-folds are generated classically during the waterfall phase occuring after the usual hybrid inflation. By performing a bayesian Monte-Carlo-Markov-Chain analysis, this scenario is shown to ... More

Saturation and solvability in abstract elementary classes with amalgamationApr 26 2016Apr 14 2017$\mathbf{Theorem.}$ Let $K$ be an abstract elementary class (AEC) with amalgamation and no maximal models. Let $\lambda > \text{LS} (K)$. If $K$ is categorical in $\lambda$, then the model of cardinality $\lambda$ is Galois-saturated. This answers a question ... More

Stability of a colocated finite volume scheme for the incompressible Navier-Stokes equationsApr 05 2007We introduce a finite volume scheme for the two-dimensional incompressible Navier-Stokes equations. We use a triangular mesh. The unknowns for the velocity and pressure are both piecewise constant (colocated scheme). We use a projection (fractional-step) ... More

Stability of a finite volume scheme for the incompressible fluidsApr 05 2007Nov 20 2007We introduce a finite volume scheme for the two-dimensional incompressible Navier-Stokes equations. We use a triangular mesh. The unknowns for the velocity and pressure are respectively piecewise constant and affine. We use a projection method to deal ... More

Statistical properties of a skew product with a curve of neutral pointsNov 12 2003We study a skew product with a curve of neutral points. We show that there exists a unique absolutely continuous invariant probability measure, and that the Birkhoff averages of a sufficiently smooth observable converge to a normal law or a stable law, ... More

Central limit theorem and stable laws for intermittent mapsNov 06 2002Dec 06 2002In the setting of abstract Markov maps, we prove results concerning the convergence of renormalized Birkhoff sums to normal laws or stable laws. They apply to one-dimensional maps with a neutral fixed point at 0 of the form $x+x^{1+\alpha}$, for $\alpha\in ... More

Berry-Esseen theorem and local limit theorem for non uniformly expanding mapsOct 24 2003Dec 13 2004We prove that, in Young towers with sufficiently small tails, the speed in the central limit theorem is O(1/\sqrt{n}), and the local limit theorem holds. This implies the same results for many non uniformly expanding dynamical systems, namely those for ... More

New High Proper Motion Stars from the Digitized Sky Survey. IV. Completion of the Southern Survey and 170 Additional Stars with pm>0.45 arcsec/yrMar 28 2008May 30 2008Completion of the SUPERBLINK proper motion survey in the southern celestial hemisphere has turned up 170 new stars with proper motion 0.45 arcsec/yr < pm < 2.0 arcsec/yr. This fourth and final installment completes the all-sky, data-mining of the Digitized ... More

The type III manufactoryJan 14 2011May 26 2015Using unusual objects in the theory of von Neumann algebra, as the chinese game Go or the Conway game of life (generalized on finitely presented groups), we are able to build, by hands, many type III factors.

A numerical lower bound for the spectral radius of random walks on surface groupsOct 16 2013Jun 06 2014Estimating numerically the spectral radius of a random walk on a nonamenable graph is complicated, since the cardinality of balls grows exponentially fast with the radius. We propose an algorithm to get a bound from below for this spectral radius in Cayley ... More

Spectral triples for finitely generated groups, index 0Oct 25 2010May 26 2015Using Cayley graphs and Clifford algebras, we are able to give, for every finitely generated groups, a uniform construction of spectral triples with a generically non-trivial phase for the Dirac operator. Unfortunatly $D_{+}$ is index $0$, but we are ... More

Phase Transition in Distance-Based Phylogeny ReconstructionAug 29 2011We introduce a new distance-based phylogeny reconstruction technique which provably achieves, at sufficiently short branch lengths, a logarithmic sequence-length requirement---improving significantly over previous polynomial bounds for distance-based ... More

Sequence-Length Requirement of Distance-Based Phylogeny Reconstruction: Breaking the Polynomial BarrierAug 14 2009We introduce a new distance-based phylogeny reconstruction technique which provably achieves, at sufficiently short branch lengths, a polylogarithmic sequence-length requirement -- improving significantly over previous polynomial bounds for distance-based ... More

Saturation and solvability in abstract elementary classes with amalgamationApr 26 2016May 11 2016$\mathbf{Theorem.}$ Let $K$ be an abstract elementary class (AEC) with amalgamation and no maximal models. Let $\lambda > \text{LS} (K)$. If $K$ is categorical in $\lambda$, then the model of cardinality $\lambda$ is Galois-saturated. This answers a question ... More

Oscillation Power in Sunspots and Quiet Sun from Hankel Analysis Performed on SDO/HMI and SDO/AIA DataSep 07 2012The Helioseismic and Magnetic Imager (HMI) and the Atmospheric Imaging Assembly (AIA) instruments onboard the Solar Dynamics Observatory satellite produce Doppler velocity and continuum intensity at 6173 A as well as intensity maps at 1600 A and 1700 ... More

Mechanical behavior of steels: from fundamental mechanisms to macroscopic deformationJan 08 2014My scientific activities aim at understand and predict the mechanical behaviour of steels, from fundamental mechanisms to macroscopic deformation. This manuscript is dedicated to the TWIP effect (TWinning Induced Plasticity) of high manganese austenitic ... More

Physical collisions of moonlets and clumps with the Saturn's F-ring coreJan 05 2009Since 2004, observations of Saturn's F ring have revealed that the ring's core is surrounded by structures with radial scales of hundreds of kilometers, called "spirals" and "jets". Gravitational scattering by nearby moons was suggested as a potential ... More

Toward a stability theory of tame abstract elementary classesSep 12 2016Oct 26 2016We initiate a systematic investigation of the abstract elementary classes that have amalgamation, satisfy tameness (a locality property for orbital types), and are stable (in terms of the number of orbital types) in some cardinal. We define a cardinal ... More

Mathematical and numerical analysis of a model for anti-angiogenic therapy in metastatic cancersSep 16 2010We introduce and analyze a phenomenological model for anti-angiogenic therapy in the treatment of metastatic cancers. It is a structured transport equation with a nonlocal boundary condition describing the evolution of the density of metastasis that we ... More

Asymptotic behavior of the complete Kahler-Einstein metric in tube domainsJul 05 2018Aug 30 2018We study the complete Kahler-Einstein metric in tube domains. We obtain estimates of this metric and its holomorphic bisectional curvatures near the weakly pseudoconvex boundary points.

Characters of the irreducible representations with fundamental highest weight for the symplectic group in characteristic pDec 14 2005Let K be an algebraically closed field of characteristic p>0 and let Sp(2m) be the symplectic group of rank m over K. The main theorem of this article gives the character of the rational simple Sp(2m)-modules with fundamental highest weight as an explicit ... More

Toward a stability theory of tame abstract elementary classesSep 12 2016May 21 2018We initiate a systematic investigation of the abstract elementary classes that have amalgamation, satisfy tameness (a locality property for orbital types), and are stable (in terms of the number of orbital types) in some cardinal. Assuming the singular ... More

Forking and superstability in tame AECsMay 29 2014Jun 30 2015We prove that any tame abstract elementary class categorical in a suitable cardinal has an eventually global good frame: a forking-like notion defined on all types of single elements. This gives the first known general construction of a good frame in ... More

Spectral triples for finitely generated groups, index 0Oct 25 2010Nov 08 2016Using Cayley graphs and Clifford algebras, we are able to give, for every finitely generated groups, a uniform construction of spectral triples with a generically non-trivial phase for the Dirac operator. Unfortunatly $D_{+}$ is index $0$, but we are ... More

Dual Ore's theorem for distributive intervals of small indexOct 24 2016This paper proves a dual version of a theorem of Oystein Ore for every distributive interval of finite groups [H,G] of index |G:H|<9720, and for every boolean interval of rank <7. It has applications to representation theory for every finite group.

Dual Ore's theorem on distributive intervals of finite groupsAug 08 2017Mar 09 2019This paper gives a self-contained group-theoretic proof of a dual version of a theorem of Ore on distributive intervals of finite groups. We deduce a bridge between combinatorics and representations in finite group theory.

Ore's theorem on subfactor planar algebrasApr 03 2017Mar 26 2019This article proves that an irreducible subfactor planar algebra with a distributive biprojection lattice admits a minimal 2-box projection generating the identity biprojection. It is a generalization (conjectured in 2013) of a theorem of Oystein Ore ... More

Decay of correlations for nonuniformly expanding systemsJan 15 2004Dec 13 2004We estimate the speed of decay of correlations for general nonuniformly expanding dynamical systems, using estimates on the time the system takes to become really expanding. Our method can deal with fast decays, such as exponential or stretched exponential. ... More

A Borel-Cantelli lemma for intermittent interval mapsMar 09 2007We consider intermittent maps T of the interval, with an absolutely continuous invariant probability measure \mu. Kim showed that there exists a sequence of intervals A_n such that \sum \mu(A_n)=\infty, but \{A_n\} does not satisfy the dynamical Borel-Cantelli ... More

Accessible categories, set theory, and model theory: an invitationApr 25 2019We give a self-contained introduction to accessible categories and how they shed light on both model- and set-theoretic questions. We survey for example recent developments on the study of presentability ranks, a notion of cardinality localized to a given ... More

Preliminary results of charged pions cross-section in proton carbon interaction at 30 GeV measured with the NA61/SHINE detectorMay 20 2010As the intensity of neutrino beams produced at accelerators increases, important systematic errors due to poor knowledge of production cross sections for pions and kaons arise. Among other goals, the NA61/SHINE (SHINE=SPS Heavy Ion and Neutrino Experiment) ... More

Mathematical analysis of a two-dimensional population model of metastatic growth including angiogenesisSep 15 2010Angiogenesis is a key process in the tumoral growth which allows the cancerous tissue to impact on its vasculature in order to improve the nutrient's supply and the metastatic process. In this paper, we introduce a model for the density of metastasis ... More

Nearby stars from the LSPM-north Proper Motion Catalog. I. Main Sequence Dwarfs and Giants Within 33 Parsecs of the SunJun 07 2005A list of 4,131 dwarfs, subgiants, and giants located, or suspected to be located, within 33 parsecs of the Sun is presented. All the stars are drawn from the new LSPM-north catalog of 61,976 stars with annual proper motions larger than 0.15''/yr$. Trigonometric ... More

Toward a stability theory of tame abstract elementary classesSep 12 2016Oct 03 2016We initiate a systematic investigation of the abstract elementary classes that have amalgamation, satisfy tameness (a locality property for orbital types), and are stable (in terms of the number of orbital types) in some cardinal. We define a cardinal ... More

An interval map with a spectral gap on Lipschitz functions, but not on bounded variation functionsSep 03 2008We construct a uniformly expanding map of the interval, preserving Lebesgue measure, such that the corresponding transfer operator admits a spectral gap on the space of Lipschitz functions, but does not act continuously on the space of bounded variation ... More

The discovery of superfluidityNov 13 2006Superfluidity is a remarkable manifestation of quantum mechanics at the macroscopic level. This article describes the history of its discovery, which took place at a particularly difficult period of the twentieth century. A special emphasis is given to ... More

Third-order Elsässer moments in axisymmetric MHD turbulenceOct 19 2010Incompressible MHD turbulence is investigated under the presence of a uniform magnetic field $\bb0$. Such a situation is described in the correlation space by a divergence relation which expresses the statistical conservation of the Els\"asser energy ... More

Quasiminimal abstract elementary classesNov 22 2016Nov 28 2016We propose the notion of a quasiminimal abstract elementary class (AEC). This is an AEC satisfying four semantic conditions: countable Lowenheim-Skolem-Tarski number, existence of a prime model, closure under intersections, and uniqueness of the generic ... More

Anamorphosis in hybrid inflation: How to avoid fine-tuning of initial conditions?Oct 20 2009In order to generate more than 60 e-folds of accelerated expansion in original hybrid inflation, 2-fields trajectories are usually required to be initially fine-tuned in a very narrow band along the inflationary valley or in some isolated points outside ... More

Quadratic centers defining elliptic surfacesApr 16 2007Jan 29 2008Let $X$ be a quadratic vector field with a center whose generic orbits are algebraic curves of genus one. To each $X$ we associate an elliptic surface (a smooth complex compact surface which is a genus one fibration). We give the list of all such vector ... More

Spectral triples for finitely presented groups, index 1Nov 19 2010Nov 08 2016Using a Cayley complex (generalizing the Cayley graph) and Clifford algebras, we are able to give, for a large class of finitely presented groups, a uniform construction of spectral triples with $D_{+}$ of index 1.

Shelah's eventual categoricity conjecture in universal classes: part IJun 23 2015Mar 05 2017We prove: $\mathbf{Theorem}$ Let $K$ be a universal class. If $K$ is categorical in cardinals of arbitrarily high cofinality, then $K$ is categorical on a tail of cardinals. The proof stems from ideas of Adi Jarden and Will Boney, and also relies on a ... More

On categoricity in successive cardinalsOct 23 2018Oct 31 2018We investigate, in ZFC, the behavior of abstract elementary classes (AECs) categorical in many successive small cardinals. We prove for example that a universal $\mathbb{L}_{\omega_1, \omega}$ sentence categorical on an end segment of cardinals below ... More

On the uniqueness property of forking in abstract elementary classesDec 19 2016Apr 25 2017In the setup of abstract elementary classes satisfying a local version of superstability, we prove the uniqueness property for $\mu$-forking, a certain independence notion arising from splitting. This had been a longstanding technical difficulty when ... More

Shelah's eventual categoricity conjecture in universal classes. Part IIFeb 08 2016Oct 26 2016We prove that a universal class categorical in a high-enough cardinal is categorical on a tail of cardinals. As opposed to other results in the literature, we work in ZFC, do not require the categoricity cardinal to be a successor, do not assume amalgamation, ... More

Building independence relations in abstract elementary classesMar 04 2015Mar 29 2016We study general methods to build forking-like notions in the framework of tame abstract elementary classes (AECs) with amalgamation. We show that whenever such classes are categorical in a high-enough cardinal, they admit a good frame: a forking-like ... More

Regularity of coboundaries for non uniformly expanding Markov mapsFeb 22 2005We prove that solutions $u$ of the equation $f=u-u\circ T$ are automatically Holder continuous when $f$ is Holder continuous, and $T$ is non uniformly expanding and Markov. This result applies in particular to Young towers and to intermittent maps.

The type III manufactoryJan 14 2011Nov 08 2016Using unusual objects in the theory of von Neumann algebra, as the chinese game Go or the Conway game of life (generalized on finitely presented groups), we are able to build, by hands, many type III factors.

Local limit theorem for nonuniformly partially hyperbolic skew-products, and Farey sequencesMar 22 2007We study skew-products of the form (x,\omega)\mapsto (Tx, \omega+\phi(x)) where T is a nonuniformly expanding map on a space X, preserving a (possibly singular) probability measure \tilde\mu, and \phi:X\to S^1 is a C^1 function. Under mild assumptions ... More