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The chromatic class and the chromatic number of the planar conjugated triangulationJul 30 2013This material is dedicated to the estimation of the chromatic number and chromatic class of the conjugated triangulation (first conversion) and also of the second conversion of the planar triangulation. Also this paper introduces some new hypotheses, ... More

Left-invariant almost nearly Kähler structures on $SU(2)\times SU(2)$ in the tetrahedron visualization for $CP^3$Aug 29 2006Jun 04 2008The set of maximal non-integrable structures $(SU(2)\times SU(2),B,I)$, where $B$ is Killing-Cartan metric is described as subset of $\mathbb{CP}^3$. The visualization of complex projective space $\mathbb{CP}^3$ as tetrahedron which edges and faces are ... More

On connection between division sequences and presentations of a free groupMay 20 2010May 24 2010This paper describes a simple method for estimating lower bounds on the number of classes of equivalence for a special kind of integer sequences, called division sequences. The method is based on adding group structure to classes of equivalence and studying ... More

K-theory of locally finite graph $C^*$-algebrasJul 22 2010Apr 24 2013We calculate the K-theory of the Cuntz-Krieger algebra ${\cal O}_E$ associated with an infinite, locally finite graph, via the Bass-Hashimoto operator. The formulae we get express the Grothendieck group and the Whitehead group in purely graph theoretic ... More

Almost nilpotency of an associative algebra with an almost nilpotent fixed-point subalgebraNov 26 2017Let A be an associative algebra of arbitrary dimension over a field F and G a finite soluble group of automorphisms of A oforder n, prime to the characteristic of F. We prove that if the fixed-point subalgebra of A under the action of G contains a two-sided ... More

Experimental Realization of the Deutsch-Jozsa Algorithm with a Six-Qubit Cluster StateMar 24 2010We describe the first experimental realization of the Deutsch-Jozsa quantum algorithm to evaluate the properties of a 2-bit boolean function in the framework of one-way quantum computation. For this purpose a novel two-photon six-qubit cluster state was ... More

Maltese cross coupling to cold atoms in free spaceFeb 08 2019We demonstrate a novel geometry for strong coupling of light and matter in free space, i.e., without the use of optical cavities. Guided by optical metrology tools, we use a manual pick-and-place technique to precisely and stably position four high numerical ... More

Micro and Macro Fractals generated by multi-valued dynamical systemsApr 28 2013Given a multi-valued function $\Phi$ on a topological space $X$ we study the properties of its fixed fractal, which is defined as the closure of the orbit $\Phi^\omega(Fix(\Phi))=\bigcup_{n\in\omega}\Phi^n(Fix(\Phi))$ of the set $Fix(\Phi)=\{x\in X:x\in\Phi(x)\}$ ... More

Strong law of large numbers on graphs and groupsApr 06 2009Jun 29 2010We consider (graph-)group-valued random element $\xi$, discuss the properties of a mean-set $\ME(\xi)$, and prove the generalization of the strong law of large numbers for graphs and groups. Furthermore, we prove an analogue of the classical Chebyshev's ... More

Direct and inverse spectral problems for a class of non-selfadjoint band matricesApr 19 2013The spectral properties of a class of band matrices are investigated. The reconstruction of matrices of this special class from given spectral data is also studied. Necessary and sufficient conditions for that reconstruction are found. The obtained results ... More

Kleinian orbifolds uniformized by RP groups with an elliptic and a hyperbolic generatorMar 31 2009We consider non-elementary Kleinian groups \Gamma, without invariant plane, generated by an elliptic and a hyperbolic element with their axes lying in one plane. We find presentations and a complete list of orbifolds uniformized by such \Gamma.

Extremes of multidimensional stationary Gaussian random fieldsOct 10 2016May 11 2018Let $\{X(\mathbf{t}):\mathbf{t}=(t_1, t_2, \ldots, t_d)\in[0,\infty)^d\}$ be a centered stationary Gaussian field with almost surely continuous sample paths, unit variance and correlation function $r$ satisfying conditions $r(\mathbf{t})<1$ for every ... More

Pulsed source of spectrally uncorrelated and indistinguishable photons at telecom wavelengthsMar 26 2014We report on the generation of indistinguishable photon pairs at telecom wavelengths based on a type-II parametric down conversion process in a periodically poled potassium titanyl phosphate (PPKTP) crystal. The phase matching, pump laser characteristics ... More

Two problems from the Polishchuk and Positselski book on Quadratic algebrasJun 28 2016In the book 'Quadratic algebras' by Polishchuk and Positselski [23] algebras with a small number of generators (n=2,3) are considered. For some number r of relations possible Hilbert series are listed, and those appearing as series of Koszul algebras ... More

Constrained minimum Riesz and Green energy problems for vector measures associated with a generalized condenserFeb 19 2018For a finite collection $\mathbf A=(A_i)_{i\in I}$ of locally closed sets in $\mathbb R^n$, $n\geqslant3$, with the sign $\pm1$ prescribed such that the oppositely charged plates are mutually disjoint, we consider the minimum energy problem relative to ... More

Adaptive variable selection in nonparametric sparse additive modelsAug 26 2015We consider the problem of recovery of an unknown multivariate signal $f$ observed in a $d$-dimensional Gaussian white noise model of intensity $\varepsilon$. We assume that $f$ belongs to a class of smooth functions ${\cal F}^d\subset L_2([0,1]^d)$ and ... More

Homology of non-$k$-overlapping discsMar 04 2014In this paper we describe the homology and cohomology of some natural bimodules over the little discs operad, whose components are configurations of non-$k$-overlapping discs. At the end we briefly explain how this algebraic structure intervenes in the ... More

Adaptive density estimation based on a mixture of GammasMay 26 2016We consider the problem of Bayesian density estimation on the positive semiline for possibly unbounded densities. We propose a hierarchical Bayesian estimator based on the gamma mixture prior which can be viewed as a location mixture. We study convergence ... More

The Hidden Magnetic Field of The Young Neutron Star in Kesteven 79Oct 14 2011Mar 16 2012Recent observations of the central compact object in the Kesteven 79 supernova remnant show that this neutron star (NS) has a weak dipole magnetic field (a few x 10^{10} G) but an anomalously large (~ 64%) pulse fraction in its surface X-ray emission. ... More

Complete Characterization of K-Theory for C*-algebras Associated to Locally Finite Unoriented GraphsDec 29 2015In this paper we give a complete description of K-theory groups for Cuntz-Krieger C*-algebras associated to general locally-finite (topologically connected) graphs via Bass-Hashimoto operator. Our result generalizes the one obtained by the second author ... More

Additivity of on-line decision complexity is violated by a linear term in the length of a binary stringAug 31 2009We show that there are infinitely many binary strings z, such that the sum of the on-line decision complexity of predicting the even bits of z given the previous uneven bits, and the decision complexity of predicting the uneven bits given the previous ... More

Infinite dimensional Riemannian symmetric spaces with fixed-sign curvature operatorApr 26 2012Oct 04 2014We associate to any Riemannian symmetric space (of finite or infinite dimension) a L$^*$-algebra, under the assumption that the curvature operator has a fixed sign. L$^*$-algebras are Lie algebras with a pleasant Hilbert space structure. The L$^*$-algebra ... More

On the existence of stable compact leaves for transversely holomorphic foliationsMar 31 2012A transversely holomorphic foliation on a compact complex manifold, exhibits a compact stable leaf if and only if the set of compact leaves is not a zero measure subset of the manifold.

Quelques calculs de sommes de GaussAug 13 2011We observe that the Galois action on local constants associated to Galois representations of a local field yields information on their arithmetic nature, for example provides an upper bound to their order when they are roots of unity. It also yields information ... More

Around Quillen's theorem AAug 11 2011Jul 02 2014New version, including a variant of Quillen's proof of the Solomon-Tits theorem.

On the generalised Tate conjecture for products of elliptic curves over finite fieldsJan 10 2011We prove the generalised Tate conjecture for H^3 of products of elliptic curves over finite fields, by slightly modifying an argument of M. Spiess concerning the Tate conjecture. We prove it fully if the elliptic curves run among at most 3 isogeny classes. ... More

Number of points of function fields over finite fieldsOct 14 2002Oct 30 2002This is a revised and slightly expanded version. We point out that in the previous summary, "without cohomology" should really read "almost without cohomology" because of the proof of Lemma 2, that the idea to consider effective motives divisible by the ... More

Absence of spontaneous magnetic order at non-zero temperature in one- and two-dimensional Heisenberg and XY systems with long-range interactionsMay 06 2001May 27 2002The Mermin-Wagner theorem is strengthened so as to rule out magnetic long-range order at T>0 in one- or two-dimensional Heisenberg and XY systems with long-range interactions decreasing as R^{-alpha} with a sufficiently large exponent alpha. For oscillatory ... More

Non-quantized Dirac monopoles and strings in the Berry phase of anisotropic spin systemsApr 26 2004Aug 31 2004The Berry phase of an anisotropic spin system that is adiabatically rotated along a closed circuit C is investigated. It is shown that the Berry phase consists of two contributions: (i) a geometric contribution which can be interpreted as the flux through ... More

Interlayer exchange coupling: Preasymptotic correctionsAug 10 1998Sep 03 1999In the asymptotic limit, the interlayer exchange coupling decays as $D^{-2}$, where $D$ is the spacer thickness. A systematic procedure for calculating the preasymptotic corrections, i.e., the terms of order $D^{-n}$ with $n \ge 3$, is presented. The ... More

Performance Bounds for Lambda Policy Iteration and Application to the Game of TetrisNov 05 2007Oct 11 2011We consider the discrete-time infinite-horizon optimal control problem formalized by Markov Decision Processes. We revisit the work of Bertsekas and Ioffe, that introduced $\lambda$ Policy Iteration, a family of algorithms parameterized by $\lambda$ that ... More

Nonstandard Intuitionistic InterpretationsDec 22 2015We present a notion of realizability and a functional interpretation in the context of intuitionistic logic, both incorporating nonstandard principles. The functional interpretation that we present corresponds to the intuitionistic counterpart of an interpretation ... More

Lévy mixing related to distributed order calculus, subordinators and slow diffusionsJun 18 2014May 19 2015The study of distributed order calculus usually concerns about fractional derivatives of the form $\int_0^1 \partial^\alpha u \, m(d\alpha)$ for some measure $m$, eventually a probability measure. In this paper an approach based on L\'evy mixing is proposed. ... More

Motifs et adjointsJun 28 2015Nov 23 2015We show in many cases the existence of adjoints to extension of scalars on categories of motivic nature, in the framework of field extensions. This is to be contrasted with the more classical situation where one deals with a finite type morphism of schemes. ... More

Approximate Policy Iteration Schemes: A ComparisonMay 12 2014We consider the infinite-horizon discounted optimal control problem formalized by Markov Decision Processes. We focus on several approximate variations of the Policy Iteration algorithm: Approximate Policy Iteration, Conservative Policy Iteration (CPI), ... More

Operationalization of Basic Observables in MechanicsApr 10 2015Dec 03 2015This novel approach to the foundation of the physical theory begins with Hermann von Helmholtz fundamental analysis of basic measurements. We explain the mathematical formalism from the operationalization of basic observables. According to Leibniz resp. ... More

Signal-wise performance attribution for constrained portfolio optimisationApr 18 2014Aug 06 2014Performance analysis, from the external point of view of a client who would only have access to returns and holdings of a fund, evolved towards exact attribution made in the context of portfolio optimisation, which is the internal point of view of a manager ... More

Cubical informal type theory: the higher groupoid structureJun 22 2018Following a project of developing conventions and notations for informal type theory carried out in the homotopy type theory book for a framework built out of an augmentation of constructive type theory with axioms governing higher-dimensional constructions ... More

Singular integrals and Hardy type spaces for the inverse Gauss measureJan 26 2018Let $\gamma_{-1}$ be the absolutely continuous measure on $\mathbb{R}^n$ whose density is the reciprocal of a Gaussian and consider the natural weighted Laplacian $\mathcal{A}$ on $L^2(\gamma_{-1})$. In this paper, we prove boundedness and unboundedness ... More

Constructing a class of solutions for the Hamilton-Jacobi equation in field theorySep 12 2007A new approach leading to the formulation of the Hamilton-Jacobi equation for field theories is investigated within the framework of jet-bundles and multi-symplectic manifolds. An algorithm associating classes of solutions to given sets of boundary conditions ... More

Heat Kernels and CyclesMay 26 2005We use the heat kernel (on differential forms) on a compact Riemannian manifold to assign a real number to a k-tuple of cycles on the manifold satisfying certain conditions. If k is 2, this number is the ordinary topological linking number, an integer ... More

La théorie des invariants des formes quadratiques ternaires revisitéeMay 27 2008The simultaneous invariants of 2, 3, 4 and 5 ternary quadratic forms under the group $\SL(3, {\Bbb C})$ were given by several authors (P. Gordan, C. Ciamberlini, H.W. Turnbull, J.A Todd), utilizing the symbolic method. Using the Jordan algebra structure ... More

The Poisson boundary of triangular matrices in a number fieldDec 11 2006Sep 19 2008The aim of this note is to describe the Poisson boundary of the group of invertible triangular matrices with coefficients in a number field. It generalizes to any dimension and to any number field a result of Brofferio concerning the Poisson boundary ... More

Random walk on a building of type $\tilde{A}_r$ and Brownian motion of the Weyl chamberNov 17 2006May 25 2009In this paper we study a random walk on an affine building of type $\tilde{A}_r$, whose radial part, when suitably normalized, converges to the Brownian motion of the Weyl chamber. This gives a new discrete approximation of this process, alternative to ... More

Tauberian theorems for general iterations of operators: applications to zero-sum stochastic gamesSep 07 2016This paper proves several Tauberian theorems for general iterations of operators, and provides two applications to zero-sum stochastic games where the total payoff is a weighted sum of the stage payoffs. The first application is to provide conditions ... More

Type Ia SupernovaeMar 22 2000Type Ia Supernovae are in many aspects still enigmatic objects. Recent years have witnessed a bonanza of supernova observations. The increased samples from dedicated searches have allowed the statistical investigation of Type Ia Supernovae as a class. ... More

On the equivalence between minimal sufficient statistics, minimal typical models and initial segments of the Halting sequenceNov 23 2009It is shown that the length of the algorithmic minimal sufficient statistic of a binary string x, either in a representation of a finite set, computable semimeasure, or a computable function, has a length larger than the computational depth of x, and ... More

Algebra+Homotopy=OperadFeb 15 2012This survey provides an elementary introduction to operads and to their applications in homotopical algebra. The aim is to explain how the notion of an operad was prompted by the necessity to have an algebraic object which encodes higher homotopies. We ... More

Dualite de Koszul des PROPsMay 04 2004In this thesis, we generalize the Koszul duality for associative algebras and operads to PROPs. The operads are algebraic objects that represent the operations with multiple inputs but only one output acting on a certain type of algebras. A PROP models ... More

Complexity of PL-manifoldsOct 30 2008Apr 14 2009We extend Matveev's complexity of 3-manifolds to PL compact manifolds of arbitrary dimension, and we study its properties. The complexity of a manifold is the minimum number of vertices in a simple spine. We study how this quantity changes under the most ... More

Light output response of the LVD liquid scintillator to neutron-induced nuclear recoilsApr 13 2013The organic liquid scintillator used in the LVD experiment (INFN Gran Sasso National Laboratory) has been exposed to an Am-Be neutron source to measure the light response function for neutron energies in the region from about 4 to 11 MeV. A full Monte ... More

Order and chaos in quantum irregular scattering: Wigner's time delayMar 12 1993Recent developments in the semiclassical analysis of chaotic systems are reviewed and illustrated for Wigner's time delay in elastic scattering of a point particle from three disks in the plane. The convergence of the cycle expanded periodic orbit expression ... More

Search for the Standard Model Higgs boson decaying to four lepton (muon, electron) final states with the ATLAS experiment at the LHC colliderAug 01 2008The search for the Standard Model Higgs boson in the four lepton (electron and muon) final state with the ATLAS detector at the LHC is presented. The analysis strategy and the efficiency for selecting the signal and rejecting the background are discussed, ... More

The full faithfulness conjectures in characteristic pSep 19 2012We present a triangulated version of the conjectures of Tate and Beilinson on algebraic cycles over a finite field. This sheds a new light on Lichtenbaum's Weil-etale cohomology.

Algebraic tori as Nisnevich sheaves with transfersJul 25 2011Mar 13 2012We relate R-equivalence on tori with Voevodsky's theory of homotopy invariant Nisnevich sheaves with transfers and effective motivic complexes.

A sheaf-theoretic reformulation of the Tate conjectureJan 06 1998Let p be a prime number. We give a conjecture of a sheaf-theoretic nature which is equivalent to the strong form of the Tate conjecture for smooth, projective varieties X over F_p: for all n>0, the order of pole of the Hasse-Weil zeta function of X at ... More

Somekawa's K-groups and Voevodsky's Hom groups (preliminary version)Sep 23 2010We construct a surjective homomorphism from Somekawa's K-group associated to a finite collection of semi-abelian varieties over a perfect field to a corresponding Hom group in Voevodsky's triangulated category of effective motivic complexes.

Motivic zeta functions of motivesJun 17 2006Let K be a field of characteristic 0 and A be a rigid tensor K-linear category. Let M be a finite-dimensional object of A in the sense of Kimura-O'Sullivan. We prove that the "motivic" zeta function of M with coefficients in K\_0(A) has a functional equation. ... More

Impossibility of Spontaneously Rotating Time-Crystals: A No-Go TheoremJun 26 2013Aug 19 2013I present arguments indicating the impossibility of spontaneously rotating quantum timecrystals, as recently proposed by Frank Wilczek [arXiv:1202.2539]. In particular, I prove a No-Go Theorem, rigorously ruling out the possibility of spontaneous ground-state ... More

Berry phase effects in magnetismJun 13 2005Lecture notes published in ''Magnetism goes nano'', Lecture Manuscripts of the 36th Spring School of the Institute of Solid State Research, edited by Stefan Bluegel, Thomas Brueckel, and Claus M. Schneider (Forschungszentrum Juelich, 2005).

Theory of interlayer exchange couplingMay 03 1999This paper contains the notes of lectures on the theory of interlayer exchange coupling presented at the 30-th Ferienschule of the Institut fuer Festkoerperforschung, Forschungszentrum Juelich, March 1999.

Portfolio management under risk contraints - Lectures given at MITACS-PIMS-UBC Summer School in Risk Management and Risk SharingJun 30 2013The aim of these lectures at MITACS-PIMS-UBC Summer School in Risk Man- agement and Risk Sharing is to discuss risk controlled approaches for the pricing and hedging of financial risks. We will start with the classical dual approach for financial markets, ... More

New insights into abelian topologically massive gauge theoriesMay 23 2007Abelian topologically massive gauge theories (TMGT) provide a topological mechanism to generate mass for any p-tensor boson in any dimension. Within the Hamiltonian formulation, the embedded topological field theory (TFT) is not made manifest. We therefore ... More

On the Performance Bounds of some Policy Search Dynamic Programming AlgorithmsJun 03 2013We consider the infinite-horizon discounted optimal control problem formalized by Markov Decision Processes. We focus on Policy Search algorithms, that compute an approximately optimal policy by following the standard Policy Iteration (PI) scheme via ... More

Modular self-organizationSep 26 2006The aim of this paper is to provide a sound framework for addressing a difficult problem: the automatic construction of an autonomous agent's modular architecture. We combine results from two apparently uncorrelated domains: Autonomous planning through ... More

Pathological and Omega-transitive Representations of Free GroupsApr 25 2012Nov 13 2013Given a linear order $\Omega$ its automorphism group $\Aut(\Omega)$ forms a lattice-ordered group via pointwise order. Assuming the continuum to be a regular cardinal, we show that \emph{pathological} and \emph{$\omega$-transitive} (i.e. highly transitive) ... More

Complexity of 3-manifoldsMay 13 2004Jan 31 2005We give a summary of known results on Matveev's complexity of compact 3-manifolds. The only relevant new result is the classification of all closed orientable irreducible 3-manifolds of complexity 10.

Quantum Spin SystemsSep 02 2004This article is a short introduction to the general topic of quantum spin systems. After a brief sketch of the history of the subject, the standard mathematical framework for formulating problems and results in quantum spin systems is described. Then, ... More

No-arbitrage in discrete-time markets with proportional transaction costs and general information structureJan 04 2005We discuss the no-arbitrage conditions in a general framework for discrete-time models of financial markets with proportional transaction costs and general information structure. We extend the results of Kabanov and al. (2002), Kabanov and al. (2003) ... More

Fonctions zêta et $L$ de variétés et de motifsDec 31 2015Sep 04 2016R\'edaction d'un cours de M2 donn\'e \`a Jussieu au printemps 2013. This is the write-up of a Masters course given at Jussieu in Spring 2013.

m-sophisticationJan 26 2010The m-sophistication of a finite binary string x is introduced as a generalization of some parameter in the proof that complexity of complexity is rare. A probabilistic near sufficient statistic of x is given which length is upper bounded by the m-sophistication ... More

Influence tests I: ideal composite hypothesis tests, and causal semimeasuresDec 14 2009Ratios of universal enumerable semimeasures corresponding to hypotheses are investigated as a solution for statistical composite hypotheses testing if an unbounded amount of computation time can be assumed. Influence testing for discrete time series is ... More

The geometric mean of two matrices from a computational viewpointDec 30 2011The geometric mean of two matrices is considered and analyzed from a computational viewpoint. Some useful theoretical properties are derived and an analysis of the conditioning is performed. Several numerical algorithms based on different properties and ... More

Distributions vectorielles homogènes sur une algèbre de JordanMay 15 2007We study distributions on a Euclidean Jordan algebra V with values in a finite dimensional representation space for the identity component G of the structure group of V and homogeneous equivariance condition. We show that such distributions exist if and ... More

Bounds on the mass gap of the ferromagnetic XXZ chainJan 20 1995We prove rigorous lower and upper bounds for the mass gap of the ferromagnetic spin 1/2 XXZ chain. The two bounds coincide asymptotically in the Ising limit $\Delta\to\infty$. Near the isotropic point, $\Delta=1$, the estimates are good enough to determine ... More

Homology of generalized partition posetsMay 16 2004Aug 31 2006We define a poset of partitions associated to an operad. We prove that the operad is Koszul if and only if the poset is Cohen-Macaulay. In one hand, this characterisation allows us to compute the homology of the poset. This homology is given by the Koszul ... More

Discussion of: Brownian distance covarianceOct 05 2010Discussion on "Brownian distance covariance" by G\'abor J. Sz\'ekely and Maria L. Rizzo [arXiv:1010.0297]

Periodic Orbit TheoryMar 23 1993[[ RM: A review paper on cycle expansions. I quote the introduction: in section (2) ]] I will summarize Gutzwiller's theory for the spectrum of eigenenergies and extend it to diagonal matrix elements as well. The derivation of the associated zeta function ... More

Transversely projective holomorphic foliations with singularitiesDec 02 2004Oct 07 2010We study codimension one holomorphic foliations on complex projective spaces and compact manifolds under the assumption that the foliation has a projective transverse structure in the complement of some invariant codimension one analytic subset. The basic ... More

Geometrically constrained magnetic wallApr 26 1999Sep 20 1999The structure and properties of a geometrically constrained magnetic wall in a constriction separating two wider regions are investigated theoretically. They are shown to differconsiderably from those of an unconstrained wall, so that the geometrically ... More

Improved and Generalized Upper Bounds on the Complexity of Policy IterationJun 03 2013Feb 10 2016Given a Markov Decision Process (MDP) with $n$ states and a totalnumber $m$ of actions, we study the number of iterations needed byPolicy Iteration (PI) algorithms to converge to the optimal$\gamma$-discounted policy. We consider two variations of PI: ... More

On the Use of Non-Stationary Policies for Infinite-Horizon Discounted Markov Decision ProcessesMar 25 2012Mar 30 2012We consider infinite-horizon $\gamma$-discounted Markov Decision Processes, for which it is known that there exists a stationary optimal policy. We consider the algorithm Value Iteration and the sequence of policies $\pi_1,...,\pi_k$ it implicitely generates ... More

Stability and instability of the Einstein-Lichnerowicz constraint systemFeb 14 2015We investigate the relevance of the conformal method by investigating stability issues for the Einstein-Lichnerowicz conformal constraint system in a nonlinear scalar-field setting. We prove the stability of the system with respect to arbitrary perturbations ... More

Exact high temperature expansion of the one-loop thermodynamic potential with complex chemical potentialNov 11 2013Jan 10 2014We present a derivation of an exact high temperature expansion for a one-loop thermodynamic potential $\Omega(\tilde{\mu})$ with complex chemical potential $\tilde{\mu}$. The result is given in terms of a single sum the coefficients of which are analytical ... More

A conjectured class of scale-invariant distances on inner product spacesJan 07 2014Jan 09 2014Let $V$ be an inner product space, and $x, y \in V$; the conjecture is made that, for any $p \in [1, \infty]$, the function $d_p(x, y):=\|x-y\|/(\|x\|^p+ \|y\|^p)^{1/p}$ is a distance on $V$.

Non-vanishing at m -> 0 of the 1-loop self-mass of an electron of mass m propagating in a graphene-like medium in a constant external magnetic fieldJul 04 2016The 1-loop self-energy of a Dirac electron of mass m propagating in a thin medium simulating graphene in an external magnetic field B is investigated in Quantum Field Theory. Equivalence is shown with the so-called reduced QED_{3+1} on a 2-brane. Schwinger-like ... More

Characterization of transiting exoplanets: analyzing the impact of the host star on the planet parametersApr 13 2016In this PhD dissertation, I discuss issues of the Radial Velocities (RV) and transit methods. These techniques allow us to derive the mass and radius of an exoplanet, necessary to model its bulk structure and to have insight on its formation. To do this, ... More

Lacunaryx: Computing bounded-degree factors of lacunary polynomialsJun 11 2015Feb 18 2016In this paper, we report on an implementation in the free software Mathemagix of lacunary factorization algorithms, distributed as a library called Lacunaryx. These algorithms take as input a polynomial in sparse representation, that is as a list of nonzero ... More

Acceptable Complexity Measures of TheoremsSep 30 2009In 1931, G\"odel presented in K\"onigsberg his famous Incompleteness Theorem, stating that some true mathematical statements are unprovable. Yet, this result gives us no idea about those independent (that is, true and unprovable) statements, about their ... More

Potential model of a 2D Bunsen flameJul 10 2006The Michelson Sivashinsky equation, which models the non linear dynamics of premixed flames, has been recently extended to describe oblique flames. This approach was extremely successful to describe the behavior on one side of the flame, but some qualitative ... More

Stationary solutions and Neumann boundary conditions in the Sivashinsky equationApr 17 2006New stationary solutions of the (Michelson) Sivashinsky equation of premixed flames are obtained numerically in this paper. Some of these solutions, of the bicoalescent type recently described by Guidi and Marchetti, are stable with Neumann boundary conditions. ... More

Majorana's stellar representation for the local polarization of harmonic electromagnetic and gravitational wavesMar 20 2019The local polarization of electromagnetic (EMW) and gravitational waves (GW) is discussed from an operational point of view, in which all the relevant mathematical framework is constructed in terms of measurements of the power absorbed by a local detector. ... More

Théorème de Chebotarev effectifNov 22 2013Let K be a number field, and L be a finite normal extension of K with Galois group G. It is known that the number of Frobenius automorphisms corresponding to prime ideals, whose norms are less than x, is equivalent to the logarithmic integral as x tends ... More

Convergence of the solutions of the discounted Hamilton-Jacobi equation: a counterexampleJan 18 2018Jan 19 2018This paper provides a counterexample about the asymptotic behavior of the solutions of a discounted Hamilton-Jacobi equation, as the discount factor vanishes. The Hamiltonian of the equation is a 1-dimensional continuous and coercive Hamiltonian.

Topological properties of Wazewski dendrite groupsMar 13 2019Mar 28 2019Homeomorphism groups of generalized Wa\.zewski dendrites act on the infinite countable set of branch points of the dendrite and thus have a nice Polish topology. In this paper, we study them in the light of this Polish topology. The group of the universal ... More

Time-dependent configurations in the perturbative formalism of string theoryMar 01 2006In this thesis time-dependent configurations are studied in the formalism of first-quantized string. These configurations are exact: solutions of the corresponding two-dimensional conformal field theory can be found. We can compute perturbative string ... More

Modeling and Predicting the Growth and Death of Membership-based WebsitesJul 04 2013Jan 27 2014Driven by outstanding success stories of Internet startups such as Facebook and The Huffington Post, recent studies have thoroughly described their growth. These highly visible online success stories, however, overshadow an untold number of similar ventures ... More

Free monoid in monoidal abelian categoriesNov 24 2004Apr 29 2008We give an explicit construction of the free monoid in monoidal abelian categories when the monoidal product does not necessarily preserve coproducts. We apply it to several new monoidal categories that appeared recently in the theory of Koszul duality ... More

A Koszul duality for propsNov 24 2004Apr 13 2007The notion of prop models the operations with multiple inputs and multiple outpus, acting on some algebraic structures like the bialgebras or the Lie bialgebras. In this paper, we generalize the Koszul duality theory of associative algebras and operads ... More

A 0-1 law for vertex-reinforced random walks on $\mathbb{Z}$ with weight of order $k^α$, $α<1/2$Jul 13 2011Jun 14 2012We prove that Vertex Reinforced Random Walk on $\mathbb{Z}$ with weight of order $k^\alpha$, with $\alpha\in [0,1/2)$, is either almost surely recurrent or almost surely transient. This improves a previous result of Volkov who showed that the set of sites ... More