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Superconvergence of a discontinuous Galerkin method for fractional diffusion and wave equationsJun 12 2012We consider an initial-boundary value problem for $\partial_tu-\partial_t^{-\alpha}\nabla^2u=f(t)$, that is, for a fractional diffusion ($-1<\alpha<0$) or wave ($0<\alpha<1$) equation. A numerical solution is found by applying a piecewise-linear, discontinuous ... More

Numerical solution of the time-fractional Fokker-Planck equation with general forcingJul 21 2015We study two schemes for a time-fractional Fokker-Planck equation with space- and time-dependent forcing in one space dimension. The first scheme is continuous in time and is discretized in space using a piecewise-linear Galerkin finite element method. ... More

FEM for time-fractional diffusion equations, novel optimal error analysesOct 18 2016A semidiscrete Galerkin finite element method applied to time-fractional diffusion equations with time-space dependent diffusivity on bounded convex spatial domains will be studied. The main focus is on achieving optimal error results with respect to ... More

Time-stepping discontinuous Galerkin methods for fractional diffusion problemsSep 24 2014Time-stepping $hp$-versions discontinuous Galerkin (DG) methods for the numerical solution of fractional subdiffusion problems of order $-\alpha$ with $-1<\alpha<0$ will be proposed and analyzed. Generic $hp$-version error estimates are derived after ... More

Well-posedness of time-fractional, advection-diffusion-reaction equationsOct 11 2018Feb 05 2019We establish the well-posedness of an initial-boundary value problem for a general class of time-fractional, advection-diffusion-reaction equations, allowing space- and time-dependent coefficients as well as initial data that may have low regularity. ... More

A Superconvergent discontinuous Galerkin method for Volterra integro-differential equations, smooth and non-smooth kernelsJan 28 2013We study the numerical solution for Volerra integro-differential equations with smooth and non-smooth kernels. We use a $h$-version discontinuous Galerkin (DG) method and derive nodal error bounds that are explicit in the parameters of interest. In the ... More

Regularity theory for time-fractional advection-diffusion-reaction equationsFeb 03 2019We investigate the behavior of the time derivatives of the solution to a linear time-fractional, advection-diffusion-reaction equation, allowing space- and time-dependent coefficients as well as initial data that may have low regularity. Our focus is ... More

A hybridizable discontinuous Galerkin method for fractional diffusion problemsSep 25 2014We study the use of the hybridizable discontinuous Galerkin (HDG) method for numerically solving fractional diffusion equations of order $-\alpha$ with $-1<\alpha<0$. For exact time-marching, we derive optimal algebraic error estimates {assuming} that ... More

Time-stepping error bounds for fractional diffusion problems with non-smooth initial dataMay 09 2014We apply the piecewise constant, discontinuous Galerkin method to discretize a fractional diffusion equation with respect to time. Using Laplace transform techniques, we show that the method is first order accurate at the \$n\$th time level \$t_n\$, but ... More

A discontinuous Petrov-Galerkin method for time-fractional diffusion equationsSep 05 2014We propose and analyze a time-stepping discontinuous Petrov-Galerkin method combined with the continuous conforming finite element method in space for the numerical solution of time-fractional subdiffusion problems. We prove the existence, uniqueness ... More

Convergence and superconvergence analyses of HDG methods for time fractional diffusion problemsDec 05 2014We study the hybridizable discontinuous Galerkin (HDG) method for the spatial discretization of time fractional diffusion models with Caputo derivative of order $0<\alpha<1$. For each time $t \in [0,T]$, the HDG approximations are taken to be piecewise ... More

A priori estimates of a finite element method for fractional diffusion problems by energy argumentsMay 30 2016In this article, the Galerkin piecewise-linear finite element (FE) method is applied to approximate the solution of time-fractional diffusion equations with variable diffusivity on bounded convex domains. Standard energy arguments do not provide satisfactory ... More

A semidiscrete finite element approximation of a time-fractional Fokker-Planck equation with nonsmooth initial dataFeb 08 2019We present a new stability and convergence analysis for the spatial discretization of a time-fractional Fokker--Planck equation in a convex polyhedral domain, using continuous, piecewise-linear, finite elements. The forcing may depend on time as well ... More

Finite volume element method for two-dimensional fractional subdiffusion problemsOct 26 2015In this paper, a semi-discrete spatial finite volume (FV) method is proposed and analyzed for approximating solutions of anomalous subdiffusion equations involving a temporal fractional derivative of order $\alpha \in (0,1)$ in a two-dimensional convex ... More

Next-to-next-to-leading order Skyrme interaction in nuclear matter: Nuclear bulk quantities at second order in perturbation theoryJul 20 2016We present the explicit form of the next-to-next-to-leading order (N$^2$LO) Skyrme interaction in momentum space by including the fourth-order gradient potentials to the standard Skyrme interaction. With the N$^2$LO Skyrme interaction, we evaluate the ... More

An inverse source problem for a two-parameter anomalous diffusion with local time datumApr 23 2016We determine the space-dependent source term for a two-parameter fractional diffusion problem subject to nonlocal non-self-adjoint boundary conditions and two local time-distinct datum. A bi-orthogonal pair of bases is used to construct a series representation ... More

Les interprétations de la mécanique quantique : une vue d'ensemble introductiveSep 07 2015La m\'ecanique quantique est une th\'eorie physique contemporaine r\'eput\'ee pour ses d\'efis au sens commun et ses paradoxes. Depuis bient\^ot un si\`ecle, plusieurs interpr\'etations de la th\'eorie ont \'et\'e propos\'ees par les physiciens et les ... More

Notes sur la notion d'invariant caractéristiqueJul 05 2007Let $G$ be a Lie group acting on a vector space $V$. Given a set of $G$-invariants, one can ask the question : does this set of invariants characterize the group $G$ ? We recall here some known results, ask questions and state some conjectures for different ... More

Remarks on the formulation of the cosmological constant/dark energy problemsApr 19 2005Sep 25 2007Associated with the cosmic acceleration are the old and new cosmological constant problems, recently put into the more general context of the dark energy problem. In broad terms, the old problem is related to an unexpected order of magnitude of this component ... More

Dimensional regularization applied to nuclear matter with a zero--range interactionFeb 15 2012Jul 07 2012We apply the dimensional regularization procedure to treat an ultraviolet divergence occurring in the framework of the nuclear many-body problem. We consider the second--order correction (beyond the mean-field approximation) to the equation of state of ... More

Les invariants polynômes de la représentation coadjointe de groupes inhomogènesMar 30 2009Explicit generators are given for the ring of invariant polynomials under the coadjoint representation of certain inhomogeneous groups.

On perfect fluid models in non-comoving observational spherical coordinatesMay 18 2004We use null spherical (observational) coordinates to describe a class of inhomogeneous cosmological models. The proposed cosmological construction is based on the observer past null cone. A known difficulty in using inhomogeneous models is that the null ... More

Gaussian estimates for spatially inhomogeneous random walks on ${\mathbf{Z}}^d$Feb 27 2006It is shown in this paper that the transition kernel corresponding to a spatially inhomogeneous random walk on ${\mathbf{Z}}^d$ admits upper and lower Gaussian estimates.

Quantum-like models cannot account for the conjunction fallacyOct 12 2015Jun 14 2016Human agents happen to judge that a conjunction of two terms is more probable than one of the terms, in contradiction with the rules of classical probabilities---this is the conjunction fallacy. One of the most discussed accounts of this fallacy is currently ... More

Testing quantum-like models of judgment for question order effectJan 19 2015Mar 07 2016Lately, so-called "quantum" models, based on parts of the mathematics of quantum mechanics, have been developed in decision theory and cognitive sciences to account for seemingly irrational or paradoxical human judgments. We consider here some such quantum-like ... More

Numerical solutions to the cosmological 3-fluid problemFeb 27 2013Sep 24 2013We show that, for the scalar field cosmology with exponential potential, the set of values of the coupling parameter for which the solutions undergo a transient period of acceleration is much larger than the set discussed in the literature. The gradual ... More

Quadratic superconducting cosmic strings revisitedFeb 22 2008It has been shown that 5-dimensional general relativity action extended by appropriate quadratic terms admits a singular superconducting cosmic string solution. We search for cosmic strings endowed with similar and extended physical properties by directly ... More

Stability of Transparent Spherically Symmetric Thin Shells and WormholesAug 24 2001Dec 11 2001The stability of transparent spherically symmetric thin shells (and wormholes) to linearized spherically symmetric perturbations about static equilibrium is examined. This work generalizes and systematizes previous studies and explores the consequences ... More

Black hole thermodynamics: No inconsistency via the inclusion of the missing P-V termsNov 10 2014Mar 23 2015The early literature on black hole thermodynamics ignored the $P$-$V$ term associated with the existence of a fundamental physical constant in the black hole solution. The inclusion of this constant in the first law becomes inconsistent with the Smarr ... More

Geometrothermodynamics: Comments, critics, and supportsNov 27 2013Jun 02 2014We write explicitly the Euler identity and the Gibbs-Duhem relation for thermodynamic potentials that are not homogeneous first-order functions of their natural extensive variables. We apply the rules to the theory of geometrothermodynamics and show how ... More

A minimal set of invariants as a systematic approach to higher order gravity modelsAug 07 2008Dec 28 2008Higher-order gravity models have been recently the subject of much attention in the context of cosmic acceleration. These models are derived by adding various curvature invariants to the Einstein-Hilbert action. Several studies showed that these models ... More

Evolution of Gaussian Wave Packet and Nonadiabatic Geometrical Phase for the time-dependent Singular OscillatorApr 22 2002The geometrical phase of a time-dependent singular oscillator is obtained in the framework of Gaussian wave packet. It is shown by a simple geometrical approach that the geometrical phase is connected to the classical nonadiabatic Hannay angle of the ... More

Instability of two-dimensional heterotic stringy black holesFeb 01 1999We solve the eigenvalue problem of general relativity for the case of charged black holes in two-dimensional heterotic string theory, derived by McGuigan et al. For the case of $m^{2}>q^{2}$, we find a physically acceptable time-dependent growing mode; ... More

Solutions Stationnaires en Théorie de Kaluza-KleinNov 06 1995Dec 21 1995Kaluza-Klein theory is a 5-dimensional Einstein general relativity; it has the interest of describing on an equal footing the laws of gravitation and electromagnetism in a geometrically unified way. We present it in Chapter 1, and we generalize it by ... More

Data Stream Clustering: Challenges and IssuesJun 28 2010Very large databases are required to store massive amounts of data that are continuously inserted and queried. Analyzing huge data sets and extracting valuable pattern in many applications are interesting for researchers. We can identify two main groups ... More

Errors, chaos and the collisionless limitApr 18 2018Jan 02 2019We simultaneously study the dynamics of the growth of errors and the question of the faithfulness of simulations of $N$-body systems. The errors are quantified through the numerical reversibility of small-$N$ spherical systems, and by comparing fixed-timestep ... More

Ultra faint dwarf galaxies: an arena for testing dark matter versus modified gravityApr 04 2016The scenario consistent with a wealth of observations for the missing mass problem is that of weakly interacting dark matter particles. However, arguments or proposals for a Newtonian or relativistic modified gravity scenario continue to be made. A distinguishing ... More

Nordhaus-Gaddum and other bounds for the sum of squares of the positive eigenvalues of a graphJul 27 2016Terpai [22] proved the Nordhaus-Gaddum bound that $\mu(G) + \mu(\overline{G}) \le 4n/3 - 1$, where $\mu(G)$ is the spectral radius of a graph $G$ with $n$ vertices. Let $s^+$ denote the sum of the squares of the positive eigenvalues of $G$. We prove that ... More

Testing gravity theories using tensor perturbationsMay 11 2016Primordial gravitational waves constitute a promising probe of the very-early universe and the laws of gravity. We study changes to tensor mode perturbations that can arise in various proposed modified gravity (MG) theories. These include additional friction ... More

Lattice gas model in random medium and open boundaries: hydrodynamic and relaxation to the steady stateNov 13 2008Dec 21 2008We consider a lattice gas interacting by the exclusion rule in the presence of a random field given by i.i.d. bounded random variables in a bounded domain in contact with particles reservoir at different densities. We show, in dimensions $d \ge 3$, that ... More

Clumps into VoidsJun 06 2000We consider a spherically symmetric distribution of dust and show that it is possible, under general physically reasonable conditions, for an overdensity to evolve to an underdensity (and vice versa). We find the conditions under which this occurs and ... More

Inverse approach to Einstein's equations for fluids with vanishing anisotropic stress tensorJul 10 2007Dec 30 2007We expand previous work on an inverse approach to Einstein Field Equations where we include fluids with energy flux and consider the vanishing of the anisotropic stress tensor. We consider the approach using warped product spacetimes of class $B_1$. Although ... More

Selection criteria for two-parameter solutions to scalar-tensor gravityDec 09 2009We make a systematic investigation of the generic properties of static, spherically symmetric, asymptotically flat solutions to the field equations describing gravity minimally coupled to a nonlinear self-gravitating real scalar field. Seven corollaries ... More

An inverse approach to Einstein's equations for non-conducting fluidsApr 17 2003Oct 06 2003We show that a flow (timelike congruence) in any type $B_{1}$ warped product spacetime is uniquely and algorithmically determined by the condition of zero flux. (Though restricted, these spaces include many cases of interest.) The flow is written out ... More

Vibration analysis of a pre-stressed graphene sheet embedded in a deformable matrixJul 24 2015The effect of the initial uniaxial stress and a surrounding elastic matrix on the transverse vibration response of a single-layered graphene sheet (SLGS) is investigated through a theoretical formulation that is based on the nonlocal Kirchhoff plate theory. ... More

Low-temperature data for carbon dioxideMar 18 2014We investigate the empirical data for the vapor pressure (154$ \leq$$T$$\leq$196 K) and heat capacity (15.52$ \leq$$T$$\leq$189.78 K) of the solid carbon dioxide. The approach is both theoretical and numerical, using a computer algebra system (CAS). From ... More

Phase-space analysis of the cosmological 3-fluid problem: Families of attractors and repellersApr 28 2013Sep 02 2013We perform a phase-space analysis of the cosmological 3-fluid problem consisting of a barotropic fluid with an equation-of-state parameter $\gamma-1$, a pressureless dark matter fluid, plus a scalar field $\phi$ (representing dark energy) coupled to exponential ... More

Vacuum and nonvacuum black holes in a uniform magnetic fieldMar 25 2016Jul 12 2016We modify and generalize the known solution for the electromagnetic field when a vacuum, stationary, axisymmetric black hole is immersed in a uniform magnetic field to the case of nonvacuum black holes (of modified gravity) and determine all linear terms ... More

Wormhole solutions sourced by fluids, II: Three-fluid two-charged sourcesSep 01 2015Dec 11 2015Lack of a consistent metric for generating rotating wormholes motivates us to present a new one endowed with interesting physical and geometrical properties. When combined with the generalized method of superposition of fields, which consists in attaching ... More

Rotation and twist regular modes for trapped ghostsJun 07 2012A parameter-independent notion of stationary slow motion is formulated then applied to the case of stationary rotation of massless trapped ghosts. The excitations correspond to a rotation mode with angular momentum $J\neq 0$ and twist modes. It is found ... More

Ultra faint dwarf galaxies: an arena for testing dark matter versus modified gravityApr 04 2016Nov 18 2016The scenario consistent with a wealth of observations for the missing mass problem is that of weakly interacting dark matter particles. However, arguments or proposals for a Newtonian or relativistic modified gravity scenario continue to be made. A distinguishing ... More

Spot deformation and replication in the two-dimensional Belousov-Zhabotinski reaction in water-in-oil microemulsionJul 20 2006Apr 03 2007In the limit of large diffusivity ratio, spot-like solutions in the two-dimensional Belousov-Zhabotinski reaction in water-in-oil microemulsion are studied. It is shown analytically that such spots undergo an instability as the diffusivity ratio is decreased. ... More

Boundary driven Kawasaki process with long range interaction: dynamical large deviations and steady statesOct 20 2011Sep 30 2012A particle system with a single locally-conserved field (density) in a bounded interval with different densities maintained at the two endpoints of the interval is under study here. The particles interact in the bulk through a long range potential parametrized ... More

New SU(1, 1) Position-Dependent Effective Mass Coherent States for the Generalized Shifted Harmonic OscillatorJun 02 2013A new SU(1, 1) position-dependent effective mass coherent states (PDEM CS) related to the shifted harmonic oscillator (SHO) are deduced. This is accomplished by applying a similarity transformation to the generally deformed oscillator algebra (GDOA) generators ... More

Boundary Asymptotic Analysis for an Incompressible Viscous Flow: Navier Wall LawsNov 25 2010We consider a new way of establishing Navier wall laws. Considering a bounded domain $\Omega$ of R N , N=2,3, surrounded by a thin layer $\Sigma \epsilon$, along a part $\Gamma$2 of its boundary $\partial \Omega$, we consider a Navier-Stokes flow in $\Omega ... More

Kaluza-Klein and Gauss-Bonnet cosmic stringsMar 29 1996We make a systematic investigation of stationary cylindrically symmetric solutions to the five-dimensional Einstein and Einstein-Gauss-Bonnet equations. Apart from the five-dimensional neutral cosmic string metric, we find two new exact solutions which ... More

Second-order equation of state with the full Skyrme interaction: toward new effective interactions for beyond mean-field modelsApr 06 2012In a quantum Fermi system the energy per particle calculated at the second order beyond the mean-field approximation diverges if a zero-range interaction is employed. We have previously analyzed this problem in symmetric nuclear matter by using a simplified ... More

A Game-Theoretic Framework for Optimum Decision Fusion in the Presence of ByzantinesJul 02 2015Optimum decision fusion in the presence of malicious nodes - often referred to as Byzantines - is hindered by the necessity of exactly knowing the statistical behavior of Byzantines. By focusing on a simple, yet widely studied, set-up in which a Fusion ... More

Sensorless position estimation of Permanent-Magnet Synchronous Motors using a saturation modelJul 24 2012Sensorless control of Permanent-Magnet Synchronous Motors (PMSM) at low velocity remains a challenging task. A now well-established method consists in injecting a high-frequency signal and use the rotor saliency, both geometric and magnetic-saturation ... More

SIR epidemics on evolving graphsJan 19 2019We consider evoSIR, a variant of the SIR model, on Erd\H os-Renyi random graphs in which susceptibles with an infected neighbor break that connection at rate $\rho$ and rewire to a randomly chosen individual. We compute the critical infection rate $\lambda_c$ ... More

Asymptotic behaviour of a cylindrical elastic structure periodically reinforced along identical fibersNov 19 2010We describe the asymptotic behaviour of a cylindrical elastic body, reinforced along identical $\epsilon$-periodically distributed fibers of size $r_{\epsilon}$, with $0 < r_{\epsilon} < \epsilon$, filled in with some different elastic material, when ... More

Optimum Fusion of Possibly Corrupted Reports for Distributed Detection in Multi-Sensor NetworksMar 19 2015The most common approach to mitigate the impact that the presence of malicious nodes has on the accuracy of decision fusion schemes consists in observing the behavior of the nodes over a time interval T and then removing the reports of suspect nodes from ... More

Signal injection and averaging for position estimation of Permanent-Magnet Synchronous MotorsMar 26 2012Sensorless control of Permanent-Magnet Synchronous Motors at low velocity remains a challenging task. A now well-established method consists in injecting a high-frequency signal and use the rotor saliency, both geometric and magnetic-saturation induced. ... More

Pseudo-radial solutions of semi-linear elliptic equations on symmetric domainsJun 07 2008In this paper we investigate existence and characterization of non-radial pseudo-radial (or separable) solutions of some semi-linear elliptic equations on symmetric 2-dimensional domains. The problem reduces to the phase plane analysis of a dynamical ... More

Spectral theory and time asymptotics of size-structured two-phase population modelsFeb 08 2019This work provides a general spectral analysis of size-structured two-phase population models. Systematic functional analytic results are given. We deal first with the case of finite maximal size. We characterize the irreducibility of the corresponding ... More

A hierarchy of LMI inner approximations of the set of stable polynomialsJun 30 2010Exploiting spectral properties of symmetric banded Toeplitz matrices, we describe simple sufficient conditions for positivity of a trigonometric polynomial formulated as linear matrix inequalities (LMI) in the coefficients. As an application of these ... More

Weak and strong expansions of the generalized q-deformed coherent states approximate eigenfunctions and its resolution of unityJun 03 2014Aug 30 2016The aim of this paper is to provide an explicit expressions for the generalized q-deformed harmonic oscillator coherent states obtained in terms of a weak and strong behavior expansions. We first use the weak (s --> 0) deformed version of q-boson annihilation ... More

Isospectral Hamiltonian for position-dependent mass for an arbitrary quantum system and coherent statesNov 16 2016By means of the unitary transformation, a new way for discussing the ordering prescription of Schrodinger equation with a position-dependent mass (PDM) for isospectral Hamiltonian operators is presented. We show that the ambiguity parameter choices in ... More

Averaged universe confronted to cosmological observations: a fully covariant approachApr 12 2016One of the outstanding problems in general relativistic cosmology is that of the averaging. That is, how the lumpy universe that we observe at small scales averages out to a smooth Friedmann-Lemaitre-Robertson-Walker (FLRW) model. The root of the problem ... More

Consumption Factor Optimization for Multihop Relaying over Nakagami-m Fading channelsNov 19 2014In this paper, the energy efficiency of multihop relaying over Nakagami-$m$ fading channels is investigated. The "consumption factor" is used as a metric to evaluate the energy efficiency, and it is derived in closed-form for both amplify-and-forward ... More

Optical phase extraction algorithm based on the continuous wavelet and the Hilbert transformsMay 21 2010In this paper we present an algorithm for optical phase evaluation based on the wavelet transform technique. The main advantage of this method is that it requires only one fringe pattern. This algorithm is based on the use of a second {\pi}/2 phase shifted ... More

Figures of merit and constraints from testing General Relativity using the latest cosmological data sets including refined COSMOS 3D weak lensingMar 07 2011Dec 27 2011We use cosmological constraints from current data sets and a figure of merit (FoM) approach to probe any deviations from general relativity (GR) at cosmological scales. The FoM approach is used to study the constraining power of various combinations of ... More

Growth factor parametrization in curved spaceMar 02 2009Jul 01 2009The growth rate of matter perturbation and the expansion rate of the Universe can be used to distinguish modified gravity and dark energy models in explaining cosmic acceleration. We explore here the inclusion of spatial curvature into the growth factor. ... More

Adaptation of TURN protocol to SIP protocolFeb 05 2010Today, SIP is a protocol par Excellence in the field of communication over Internet. But, the fact that it belongs to the application layer constitutes a weakness vis-a-vis the NAT traversal. This weakness is due to the way in which the server replies ... More

Metastable Markov chains: from the convergence of the trace to the convergence of the finite-dimensional distributionsMar 28 2017Mar 17 2018We consider continuous-time Markov chains which display a family of wells at the same depth. We provide sufficient conditions which entail the convergence of the finite-dimensional distributions of the order parameter to the ones of a finite state Markov ... More

Comments on "Maximum or minimum entropy production ? How to select a necessary criterion of stability for a dissipative fluid or plasma"Sep 03 2012In a recent paper, Phys. Rev E 81, 041137 (2010), the author attempts to derive ten necessary conditions for stability of dissipative fluids and plasmas. Assuming the validity of the local equilibrium principle, these criteria have been obtained solely ... More

Averaged universe confronted with cosmological observations: A fully covariant approachApr 12 2016Nov 18 2016One of the outstanding problems in general relativistic cosmology is that of the averaging. That is, how the lumpy universe that we observe at small scales averages out to a smooth Friedmann-Lemaitre-Robertson-Walker (FLRW) model. The root of the problem ... More

A Gamma-convergence argument for the blow-up of a non-local semilinear parabolic equation with Neumann boundary conditionsJan 26 2007In this paper we study a simple non-local semilinear parabolic equation with Neumann boundary condition. We give local existence result and prove global existence for small initial data. A natural non increasing in time energy is associated to this equation. ... More

Dynamical dark energy: Current constraints and forecastsNov 30 2004Mar 11 2005We consider how well the dark energy equation of state $w$ as a function of red shift $z$ will be measured using current and anticipated experiments. We use a procedure which takes fair account of the uncertainties in the functional dependence of $w$ ... More

Luminosity distance and redshift in the Szekeres inhomogeneous cosmological modelsMay 17 2010May 11 2011The Szekeres inhomogeneous models can be used to model the true lumpy universe that we observe. This family of exact solutions to Einstein's equations was originally derived with a general metric that has no symmetries. In this work, we develop and use ... More

A Framework For Intelligent Multi Agent System Based Neural Network Classification ModelOct 11 2009TIntelligent multi agent systems have great potentials to use in different purposes and research areas. One of the important issues to apply intelligent multi agent systems in real world and virtual environment is to develop a framework that support machine ... More

A new contraction family for porous medium and fast diffusion equationJun 25 2014Jul 12 2014In this paper, we present a surprising two-dimensional contraction family for porous medium and fast diffusion equations. This approach provides new a priori estimates on the solutions, even for the standard heat equation.

Helgason Gabor Fourier transform and uncertainty principlesDec 06 2018Windowing a Fourier transform is a useful tool, which gives us the similarity between the signal and time frequency signal, and it allows to get sense when/where ceratin frequencies occur in the input signal, this method is introduced by Dennis Gabor. ... More

Greatest least eigenvalue of the Laplacian on the Klein bottleJun 29 2005We prove the following conjecture recently formulated by Jakobson, Nadirashvili and Polterovich \cite{JNP}: For any Riemannian metric $g$ on the Klein bottle $\mathbb{K}$ one has $$\lambda\_1 (\mathbb{K}, g) A (\mathbb{K}, g)\le 12 \pi E(2\sqrt 2/3),$$ ... More

The effects of structure anisotropy on lensing observables in an exact general relativistic setting for precision cosmologyNov 23 2013Apr 09 2014The study of relativistic, higher order and nonlinear effects has become necessary in recent years in the pursuit of precision cosmology. We develop and apply here a framework to study gravitational lensing in exact models in general relativity that are ... More

Effects of anisotropy on gravitational infall in galaxy clusters using an exact general relativistic modelNov 22 2013Jan 27 2014We study the effects and implications of anisotropies at the scale of galaxy clusters by building an exact general relativistic model of a cluster using the inhomogeneous and anisotropic Szekeres metric. The model is built from a modified Navarro-Frenk-White ... More

Testing General Relativity at Cosmological Scales: Implementation and Parameter CorrelationsSep 21 2011Dec 23 2011The testing of general relativity at cosmological scales has become a possible and timely endeavor that is not only motivated by the pressing question of cosmic acceleration but also by the proposals of some extensions to general relativity that would ... More

Reduced measures associated to parabolic problemsMay 27 2008We study the existence and the properties of the reduced measures for the parabolic equations $\partial_tu-\Delta u+g(u)=0$ in $\Omega\times (0,\infty)$ subject to the conditions ($P$): $u=0$ on $\partial\Omega\times (0,\infty)$, $u(x,0)=\mu$ and ($P'$): ... More

Explicit phase diagram for a one-dimensional blister modelFeb 16 2014In this article, we consider a simple one-dimensional variational model, describing the delamination of thin films under cooling. We characterize the global minimizers, which correspond to films of three possible types: non delaminated, partially delaminated ... More

A priori gradient bounds for fully nonlinear parabolic equations and applications to porous medium modelsMar 04 2014We prove a priori gradient bounds for classical solutions of the fully nonlinear parabolic equation $$u_{t}=F(D^2u,D u,u,x,t).$$ The domain is the torus {\mathbb{T}}^{d} of dimension $d\ge1$. Up to the price of technicalities, our work can be extended ... More

Spontaneous motion of localized structures induced by parity symmetry transitionMar 27 2018We consider a paradigmatic nonvariational scalar Swift-Hohenberg equation that describes short wavenumber or large wavelength pattern forming systems. This work unveils evidence of the transition from stable stationary to moving localized structures in ... More

Polisis: Automated Analysis and Presentation of Privacy Policies Using Deep LearningFeb 07 2018Privacy policies are the primary channel through which companies inform users about their data collection and sharing practices. In their current form, policies remain long and difficult to comprehend, thus merely serving the goal of legally protecting ... More

Polisis: Automated Analysis and Presentation of Privacy Policies Using Deep LearningFeb 07 2018Jun 29 2018Privacy policies are the primary channel through which companies inform users about their data collection and sharing practices. These policies are often long and difficult to comprehend. Short notices based on information extracted from privacy policies ... More

A boundary driven generalised contact process with exchange of particles: Hydrodynamics in infinite volumeOct 02 2015We consider a two species process which evolves in an infinite domain in contact with particles reservoirs at different densities,according to the superposition of a generalised contact process and a rapid-stirring dynamics in the bulk of the domain, ... More

Probing Cosmic Acceleration Beyond the Equation of State: Distinguishing between Dark Energy and Modified Gravity ModelsJul 07 2005Aug 10 2006If general relativity is the correct theory of physics on large scales, then there is a differential equation that relates the Hubble expansion function, inferred from measurements of angular diameter distance and luminosity distance, to the growth rate ... More

Hydrostatics and dynamical large deviations of boundary driven gradient symmetric exclusionMar 31 2009We prove hydrostatics of boundary driven gradient exclusion processes, Fick's law and we present a simple proof of the dynamical large deviations principle which holds in any dimension

Thermodynamical, geometrical and Poincaré methods for charged black holes in presence of quintessenceNov 26 2012Sep 04 2013Properties pertaining to thermodynamical local stability of Reissner-Nordstr\"om black holes surrounded by quintessence as well as adiabatic invariance, adiabatic charging and a generalized Smarr formula are discussed. Limits for the entropy, temperature ... More

Time-dependent coupled oscillator model for charged particle motion in the presence of a time varyingmagnetic fieldOct 11 2010The dynamics of time-dependent coupled oscillator model for the charged particle motion subjected to a time-dependent external magnetic field is investigated. We used canonical transformation approach for the classical treatment of the system, whereas ... More

A unique extremal metric for the least eigenvalue of the Laplacian on the Klein bottleJan 26 2007We prove the following conjecture recently formulated by Jakobson, Nadirashvili and Polterovich \cite{JNP}: on the Klein bottle $\mathbb{K}$, the metric of revolution $$g_0= {9+ (1+8\cos ^2v)^2\over 1+8\cos ^2v} (du^2 + {dv^2\over 1+8\cos ^2v}),$$ $0\le ... More

Unification of the phonon mode behaviour in semiconductor alloys: Theory and ab initio calculationsSep 06 2007Feb 06 2008We demonstrate how to overcome serious problems in understanding and classification of vibration spectra in semiconductor alloys, following from traditional use of the virtual crystal approximation (VCA). We show that such different systems as InGaAs ... More