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Constraint Categorial GrammarsJul 04 1995Although unification can be used to implement a weak form of $\beta$-reduction, several linguistic phenomena are better handled by using some form of $\lambda$-calculus. In this paper we present a higher order feature description calculus based on a typed ... More

On simple Filippov superalgebras of type A(m,n)Aug 04 2010It is proved that there exist no simple finite-dimensional Filippov superalgebras of type A(m,n) over an algebraically closed field of characteristic 0.

Cleaning tasks knowledge transfer between heterogeneous robots: a deep learning approachMar 13 2019Nowadays, autonomous service robots are becoming an important topic in robotic research. Differently from typical industrial scenarios, with highly controlled environments, service robots must show an additional robustness to task perturbations and changes ... More

Master curves for the stress tensor invariants in stationary states of static granular beds. Implications for the thermodynamic phase spaceMay 24 2011Sep 07 2011We prepare static granular beds under gravity in different stationary states by tapping the system with pulsed excitations of controlled amplitude and duration. The macroscopic state---defined by the ensemble of static configurations explored by the system ... More

A bounded coarse structure for families of pseudometricsOct 10 2014Oct 13 2014We define the bounded coarse structure attached to a family of pseudometrics and give some counterexamples to conjectures that arise naturally.

Dugundji's Canonical Covers, asymptotic and covering dimensionJun 24 2013Given a nowheredense closed subset $X$ of a metrizable compact space $\tx$, we characterize the dimension of $X$ in terms of the multiplicity of the canonicals covers of the complementary of $X$, specially in some particular cases, like when $\tx$ is ... More

A $C_0$ coarse structure for families of pseudometrics and the Higson-Roe functorOct 10 2014This paper deepens into the relations between coarse spaces and compactifications, by defining a $C_0$ coarse structure attached to a family of pseudometrics. This definition allow us to give a more topological point of view on the relations between coarse ... More

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

Physical Determination of the ActionJun 28 2013Dec 04 2015The objective is a foundation of physics from the operationalization of its basic observables. We begin with classical and relativistic kinematics. Seizing on a programmatic proposal by Heinrich Hertz we arrive via quantification of energy-momentum at ... More

Operationalization of Relativistic MotionMay 11 2012Dec 03 2015We demonstrate the definition of basic observables from physical operations, the key to overcome hidden stumbling blocks and apparent paradoxes from unscrutinized (classical) formalisms. We develop Helmholtz program of basic measurements for relativistic ... More

Thermo-Rotational Instability in Plasma Disks Around Compact ObjectsFeb 12 2008Differentially rotating plasma disks, around compact objects, that are imbedded in a ``seed'' magnetic field are shown to develop vertically localized ballooning modes that are driven by the combined radial gradient of the rotation frequency and vertical ... 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

The permanent spatial decomposition of the wave functionOct 26 2009Permanent spatial decomposition (PSD) is the (hypothesized) property of the wave function of a macroscopic system of decomposing into localized permanently non-overlapping parts when it spreads over a macroscopic region. The typical example of this phenomenon ... 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

Symmetry and Complete Regularity: Kopperman's duality {\it à la quantale}Nov 02 2016Nearly three decades from his celebrated result, we study a modern refinement and strengthening of Kopperman's full metrisabilty of all topological spaces. Within this new theory of \emph{V-spaces}, developed by Flagg and Weiss, we investigate several ... More

Uniform van Lambalgen's theorem fails for computable randomnessOct 02 2015Feb 02 2018We show that there exists a bitsequence that is not computably random for which its odd bits are computably random and its even bits are computably random relative to the odd bits. This implies that the uniform variant of van Lambalgen's theorem fails ... More

Effective multiplicity for the Einstein-scalar field Lichnerowicz equationJul 09 2013We prove the stability of the Einstein-scalar field Lichnerowicz equation under subcritical perturbations of the critical nonlinearity in dimensions 3, 4 and 5. As a consequence, we obtain the existence of a second solution to the equation in several ... 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

Bounded harmonic functions for the Heckman--Opdam LaplacianSep 24 2008Oct 21 2008We describe the set of bounded harmonic functions for the Heckman--Opdam Laplacian, when the multiplicity function is larger than 1/2. We prove that this set is a vector space of dimension the cardinality of the Weyl group. We give some consequences in ... More

Albanese kernels and Griffiths groupsNov 12 2017Apr 29 2018We describe the Griffiths group of the product of a curve $C$ and a surface $S$ as a quotient of the Albanese kernel of $S$ over the function field of $C$. When $C$ is a hyperplane section of $S$ varying in a Lefschetz pencil, we prove the nonvanishing ... More

Smoothing discrete Morse theoryDec 04 2012Dec 10 2014After surveying classical notions of PL topology of the Seventies, we clarify the relation between Morse theory and its discretization by Forman. We show that PL handles theory and discrete Morse theory are equivalent, in the sense that every discrete ... More

Hilbert functions and geometryApr 06 2004Apr 13 2004This note is devoted to the study of the links between the Hilbert function of a subscheme X of the projective space, and its geometric properties. We will assume that X is arithmetically Cohen-Macaulay, which allows us to characterize its Hilbert function ... More

Weak hamiltonian Wilson Coefficients from Lattice QCDDec 26 2017In this work we present a calculation of the Wilson Coefficients $C_1$ and $C_2$ of the Effective Weak Hamiltonian to all-orders in $\alpha_s$, using lattice simulations. Given the current availability of lattice spacings we restrict our calculation to ... More

Spectral GeometryDec 16 2017The goal of these lectures is to present the few fundamentals of noncommutative geometry looking around its spectral approach. Strongly motivated by physics, in particular by relativity and quantum mechanics, Chamseddine and Connes have defined an action ... More

Hodge loci and atypical intersections: conjecturesNov 26 2017We present a conjecture on the geometry of the Hodge locus of a (graded polarizable, admissible) variation of mixed Hodge structure over a complex smooth quasi-projective base, generalizing to this context the Zilber-Pink Conjecture for mixed Shimura ... More

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

Projected site-occupation embedding theory: a rigorous embedding combining wavefunction theory and density functional theoryFeb 15 2019Site-occupation embedding theory (SOET) [B. Senjean et al., Theo. Chem. Acc. (2018) 137:169] is an in-principle exact embedding method combining wavefunction theory and density functional theory that yields promising results when applied to the one-dimensional ... More

Almost homogeneous curves over an arbitrary fieldMar 28 2017We classify the pairs $(C,G)$ where $C$ is a seminormal curve over an arbitrary field $k$ and $G$ is a smooth connected algebraic group acting faithfully on $C$ with a dense orbit, and we determine the equivariant Picard group of $C$. We also give a partial ... More

Multiplicative properties of the multiplicative groupJun 08 2017Nov 02 2017We give a few properties equivalent to the Bloch-Kato conjecture (now the norm residue isomorphism theorem).

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

An approach between the multiplicative and additive structure of a Jordan ringApr 18 2018Let J and J' be Jordan rings. We prove under some conditions that if J contains a nontrivial idempotent, then n-multiplicative maps and n-multiplicative derivations from J to J' are additive maps.

A Tauberian theorem for nonexpansive operators and applications to zero-sum stochastic gamesJan 26 2015Feb 23 2015We prove a Tauberian theorem for nonexpansive operators, and apply it to the model of zero-sum stochastic game. Under mild assumptions, we prove that the value of the lambda-discounted game v_{lambda} converges uniformly when lambda goes to 0 if and only ... More

General limit value in zero-sum stochastic gamesOct 20 2014Nov 11 2015Bewley and Kohlberg (1976) and Mertens and Neyman (1981) have proved, respectively, the existence of the asymptotic value and the uniform value in zero-sum stochastic games with finite state space and finite action sets. In their work, the total payoff ... More

Homotopy theory of homotopy algebrasNov 20 2014Feb 07 2016This paper studies the homotopy theory of algebras and homotopy algebras over an operad. It provides an exhaustive description of their higher homotopical properties using the more general notion of morphisms called infinity-morphisms. The method consists ... More

Lieb-Robinson bounds and the existence of infinite system dynamicsSep 15 2009We present a recent result on the existence of the dynamics in the thermodynamic limit of a class of anharmonic quantum oscillator lattices, which was obtained using Lieb--Robinson bounds.

Divisibility properties of motivic cohomologyJan 18 2018We extend results of Colliot-Th\'el\`ene and Raskind on the $\mathcal{K}_2$-cohomology of smooth projective varieties over a separably closed field $k$ to the \'etale motivic cohomology of smooth, not necessarily projective, varieties over $k$. Some consequences ... More

Linear Differential Equations as a Data-StructureNov 21 2018A lot of information concerning solutions of linear differential equations can be computed directly from the equation. It is therefore natural to consider these equations as a data-structure, from which mathematical properties can be computed. A variety ... 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.

Non-linear model equation for three-dimensional Bunsen flamesJul 10 2006The non linear description of laminar premixed flames has been very successful, because of the existence of model equations describing the dynamics of these flames. The Michelson Sivashinsky equation is the most well known of these equations, and has ... More

Supernovae and CosmologyFeb 28 2008The extreme luminosity and their fairly unique temporal behaviour have made supernovae a superb tool to measure distances in the universe. As complex astrophysical events they provide interesting insights into explosion physics, explosive nucleosynthesis, ... More

TYPE Ib/c SUPERNOVAE AND THEIR RELATION TO BINARY STARSMar 01 1995The present understanding of type Ib/c supernovae and their connection to interacting binaries is reviewed. The problems of the classification and the lack of well-observed events exclude direct inference of progenitor characteristics. The absence of ... 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

Analysis of Microprocessor Based Protective Re-lay's (MBPR) Differential Equation AlgorithmsJun 23 2010This paper analyses and explains from the systems point of view, microprocessor based protective relay (MBPR) systems with emphasis on differential equation algorithms. Presently, the application of protective relaying in power systems, using MBPR systems, ... 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

Echoes in classical dynamical systemsOct 28 2002Echoes arise when external manipulations to a system induce a reversal of its time evolution that leads to a more or less perfect recovery of the initial state. We discuss the accuracy with which a cloud of trajectories returns to the initial state in ... More

Classes de cycles motiviques étalesFeb 02 2011Jul 25 2011Let X be a smooth variety over a field k, and l be a prime number invertible in k. We study the (\'etale) unramified H^3 of X with coefficients Q_l/Z_l(2) in the style of Colliot-Th\'el\`ene and Voisin. If k is separably closed, finite or p-adic, this ... More

On the multiplicities of a motiveOct 14 2006Feb 05 2007We study the multiplicities of pure motives modulo numerical equivalence, which are defined as scalars comparing the tannakian trace with the ring-theoretic trace. Our general set-up is that of a rigid semi-simple tensor category such that End(1) is a ... More

Comment on "Quantum Time Crystals": a new paradigm or just another proposal of perpetuum mobile?Oct 15 2012A Comment on Frank Wilczek's paper "Quantum Time Crystals" (Phys. Rev. Lett. 109, 160401 (2012); arXiv:1202.2539).

Quantum geometric phase in Majorana's stellar representation: Mapping onto a many-body Aharonov-Bohm phaseApr 11 2012Jun 13 2012The (Berry-Aharonov-Anandan) geometric phase acquired during a cyclic quantum evolution of finite-dimensional quantum systems is studied. It is shown that a pure quantum state in a (2J+1)-dimensional Hilbert space (or, equivalently, of a spin-J system) ... More

Long-range magnetic interaction due to the Casimir effectFeb 01 2002May 27 2002The zero-point quantum fluctuations of the electromagnetic field in vacuum are known to give rise to a long-range attractive force between metal plates (Casimir effect). For ferromagnetic layers separated by vacuum, it is shown that the interplay of the ... More

Theory of interlayer exchange interactions in magnetic multilayersJul 27 1999Dec 20 1999This paper presents a review of the phenomenon of interlayer exchange coupling in magnetic multilayers. The emphasis is put on a pedagogical presentation of the mechanism of the phenomenon, which has been successfully explained in terms of a spin-dependent ... More

Algèbres de Jordan et théorie des invariantsJun 30 2009Mar 13 2011If V is a simple complex euclidean Jordan algebra and G the subgroup of GL(V) fixing the determinant of V, we give a unified description of the invariant algebras C[pV]^G, for p not greater than three.

Charge Distributions in Metallic Alloys: a Charge Excess Functional theory approachDec 17 2002Charge Distributions in Metallic Alloys: a Charge Excess Functional theory approach

Quantum field theory without divergence: the method of the interaction operatorsJul 13 2016Aug 08 2016The recently proposed interior boundary conditions approach [S. Teufel and R. Tumulka: Avoiding Ultraviolet Divergence by Means of Interior Boundary Conditions, arXiv:1506.00497] is a method for defining Hamiltonians without UV divergence for quantum ... More

Hyperbolic four-manifoldsDec 11 2015Dec 30 2015This is a short survey on finite-volume hyperbolic four-manifolds. We describe some general theorems and focus on the concrete examples that we found in the literature. The paper contains no new result.

Hyperbolic three-manifolds that embed geodesicallyOct 21 2015Mar 21 2016We prove that every complete finite-volume hyperbolic 3-manifold $M$ that is tessellated into right-angled regular polyhedra (dodecahedra or ideal octahedra) embeds geodesically in a complete finite-volume connected orientable hyperbolic 4-manifold $W$, ... More

Waveform and Transceiver Design for Simultaneous Wireless Information and Power TransferJul 19 2016Simultaneous Wireless Information and Power Transfer (SWIPT) has attracted significant attention in the communication community. The problem of waveform design has however never been addressed so far. In this paper, we first investigate how a communication ... More

The 1-loop self-energy of an electron in a strong external magnetic field revisitedOct 12 2015May 02 2016I calculate the 1-loop self-energy of the lowest Landau level an electron of mass m in a strong, constant and uniform external magnetic field B, beyond its always used truncation at (ln L)^2, L=|e|B/m^2. This is achieved by evaluating the integral deduced ... More

Relativistic Bohmian mechanics without a preferred foliationSep 11 2015Oct 15 2015In non-relativistic Bohmian mechanics the universe is represented by a probability space whose sample space is composed of the Bohmian trajectories. In relativistic Bohmian mechanics an entire class of empirically equivalent probability spaces can be ... More

Meagerness of the set of compact leaves for transversely holomorphic foliationsSep 15 2014A 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 meager subset of the manifold.

Waveform Optimization for SWIPT with Nonlinear Energy Harvester ModelingFeb 02 2016Simultaneous Wireless Information and Power Transfer (SWIPT) has attracted significant attention in the communication community. The problem of waveform design for SWIPT has however never been addressed so far. In this paper, a novel SWIPT transceiver ... More

Analyse des suites aléatoires engendrées par des automates cellulaires et applications à la cryptographieJul 15 2008This paper considers interactions between cellular automata and cryptology. It is known that non-linear elementary rule which is correlation-immune don't exist. This results limits the use of cellular automata as pseudo-random generators suitable for ... More

Topological properties of Wazewski dendrite groupsMar 13 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

On the Dolbeault cohomology of projective varieties and locally residual currentsMay 03 2005Let $X$ be a projective manifold. Let $Y_1,...,Y_{p+1}$ be $p+1$ ample hypersurfaces in complete intersection position on $X$, each defined by the global section of an ample Cartier divisor. We show in this note that for $i\le p+1$, the cohomology groups ... 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

Measurement of properties of the Higgs boson in bosonic decay channels using the ATLAS detectorSep 15 2014The properties of the Higgs boson measured in bosonic decay channels ($H \rightarrow \gamma\gamma$, $H \rightarrow ZZ^* \rightarrow 4\ell$, $H \rightarrow WW^{*} \rightarrow \ell\nu\ell\nu$, $H \rightarrow Z\gamma$) with 25 fb$^{-1}$ of pp collision data ... More

A note on multi-type cookie random walk on integersMar 11 2008Mar 25 2008We consider a random walk on integers where at the first visits to a site the walker gets a positive drift, but where after a certain number of visits the walker gets a negative drift. We prove that the walker is almost surely transient to the left with ... More

Maximal Hypoellipticity for Left-Invariant Differential Operators on Lie GroupsNov 12 2018Given a differential operator defined in terms of left-invariant vector fields on a Lie group, we prove that the local condition defining maximal hypoellipticity is equivalent to a global estimate if the operator is left invariant. As a consequence, we ... More

Enso: A general-purpose virtual machineMar 04 2019In this paper we introduce Enso, a virtual machine designed to be used as general-purpose state transition function in blockchains. This design allows the blockchain application logic to be coded into the state, instead of into the state transition function, ... More

Maxwell-Sylvester Multipoles and the Geometric Theory of Irreducible Tensor Operators of Quantum Spin SystemsMar 27 2018A geometric theory of the irreducible tensor operators of quantum spin systems. It is based upon the Maxwell-Sylvester geometric representation of the multipolar electrostatic potential. In the latter, an order-$\ell$ multipolar potential is represented ... More

A topological-like gravity model in a four dimensional space-timeMar 04 2018In this work we consider a model for gravity in 4-dimensional space-time originally proposed by A. Chamseddine which may be derived by a 5-dimensional Chern-Simons theory. Its topological origin makes it an interesting candidate for an easier quantization, ... More

Approximate light cone effects in a non-relativistic quantum field theory after a local quenchNov 15 2016We study the spreading of correlations after a local quench in a non-relativistic quantum field theory. We focus on noninteracting non-relativistic fermions and study the time evolution after two identical systems in their ground states are suddenly joined ... More

The knowledge paradox: why knowing more is knowing lessFeb 20 2017To provide an explanation of the evolution of scientific knowledge, I start from the assumption that knowledge is based on concepts, and propose that each concept about reality is affected by vagueness. This entails a paradox, which I term Knowledge Paradox ... More

A swift introduction to holomorphic foliations with singularitiesNov 19 2016These are the notes of a series of lectures delivered by the author at the Graduate School of Mathematics of the University of Tokyo, during the month of October 2015. They were meant to be as self-contained as possible, taking into account time and space. ... More

A numerical algorithm for $L_2$ semi-discrete optimal transport in 3DSep 03 2014This paper introduces a numerical algorithm to compute the $L_2$ optimal transport map between two measures $\mu$ and $\nu$, where $\mu$ derives from a density $\rho$ defined as a piecewise linear function (supported by a tetrahedral mesh), and where ... More

Discrete Morse Theory Is At Least As Perfect As Morse TheoryOct 04 2010Jul 09 2014In bounding the homology of a manifold, Forman's Discrete Morse theory recovers the full precision of classical Morse theory: Given a PL triangulation of a manifold that admits a Morse function with c_i critical points of index i, we show that some subdivision ... More

Deviation probability bounds for fractional martingales and related remarksApr 19 2012In this paper we prove exponential inequalities (also called Bernstein's inequality) for fractional martingales. As an immediate corollary, we will discuss weak law of large numbers for fractional martingales under divergence assumption on the $\beta-$variation ... More

A measurable stability theorem for holomorphic foliations transverse to fibrationsMar 22 2012We prove that a transversely holomorphic foliation which is transverse to the fibers of a fibration, is a Seifert fibration if the set of compact leaves is not of zero measure. Similarly, we prove that a finitely generated subgroup of holomorphic diffeomorphisms ... More

Graded multiplications on iterated bar constructionsFeb 09 2017Sep 20 2017We define a bar construction endofunctor on the category of commutative augmented monoids $A$ of a symmetric monoidal category $\mathcal{V}$ endowed with a left adjoint monoidal functor $F:s\mathbf{Set}\to \mathcal{V}$. To do this, we need to carefully ... More

Motifs et adjointsJun 28 2015Mar 23 2017We 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