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Effects of high vs moderate-intensity training on neuroplasticity and functional recovery after focal ischemiaFeb 08 2018Background and Purpose: This study was designed to compare the effects of high-intensity interval training (HIT) and moderate-intensity continuous training (MOD) on functional recovery and cerebral plasticity during the first 2 weeks following cerebral ... More

Retrieving information from a noisy "knowledge network"Apr 30 2007Jul 05 2007We address the problem of retrieving information from a noisy version of the ``knowledge networks'' introduced by Maslov and Zhang. We map this problem onto a disordered statistical mechanics model, which opens the door to many analytical and numerical ... More

On Hawking's Local Rigidity Theorems for Charged Black HolesMar 27 2009We show the existence of a Hawking vector field in a full neighborhood of a local, regular, bifurcate, non-expanding horizon embedded in a smooth Einstein-Maxwell space-time without assuming the underlying space-time is analytic. It extends one result ... More

Classification of phase transitions and ensemble inequivalence, in systems with long range interactionsMar 17 2003Oct 20 2004Systems with long range interactions in general are not additive, which can lead to an inequivalence of the microcanonical and canonical ensembles. The microcanonical ensemble may show richer behavior than the canonical one, including negative specific ... More

Ensemble inequivalence in random graphsMay 16 2007We present a complete analytical solution of a system of Potts spins on a random k-regular graph in both the canonical and microcanonical ensembles, using the Large Deviation Cavity Method (LDCM). The solution is shown to be composed of three different ... More

An exotic group with the Haagerup propertyMay 05 2012Nov 11 2012We prove the Haagerup property for an infinite discrete group constructed using surgery on a Euclidean Tits building of type $\tilde A_2$.

Surgery on discrete groupsNov 25 2016We study constructions of groups, in particular of groups of intermediate rank, which are accessible to surgery techniques.

Removing chambers in Bruhat-Tits buildingsMar 24 2010Nov 11 2012We introduce and study a family of countable groups constructed from Euclidean buildings by "removing" suitably chosen subsets of chambers.

Results from H.E.S.S. Observations of Relativistic SourcesJun 24 2010The High Energy Stereoscopic System (H.E.S.S.) is a southern hemisphere array of four Imaging Atmospheric Cherenkov Telescopes observing the sky in the very high energy gamma-ray range (E $>$ 100 GeV). VHE observations are an invaluable tool to study ... More

La propriete de decroissance rapide pour le groupe de WiseNov 11 2012We show that the group of presentation $< a,b,c,s,t\mid c=ab=ba,\, c^2=sas^{-1}=tbt^{-1}>$ (introduced by D. Wise) has the property of rapid decay.

Dynamical formation of black holes due to the condensation of matter fieldMay 30 2011The purpose of the paper is to understand a mechanism of evolutionary formation of trapped surfaces when there is an electromagnetic field coupled to the background space-time. Based on the short pulse ansatz, on a given finite outgoing null hypersurface ... More

Energy Estimates and Gravitational CollapseMay 13 2011We study the cancelations in the energy estimates for Einstein vacuum equations in order to prove the formation of black holes along evolutions. The novelty of the paper is that, we completely avoid using rotation vector fields to establish the global ... More

Lyapunov exponents as a dynamical indicator of a phase transitionFeb 19 2001We study analytically the behavior of the largest Lyapunov exponent $\lambda_1$ for a one-dimensional chain of coupled nonlinear oscillators, by combining the transfer integral method and a Riemannian geometry approach. We apply the results to a simple ... More

Spectral Galerkin methods for transfer operators in uniformly expanding dynamicsMay 12 2017Mar 06 2018Markov expanding maps, a class of simple chaotic systems, are commonly used as models for chaotic dynamics, but existing numerical methods to study long-time statistical properties such as invariant measures have a poor trade-off between computational ... More

The Maskit embedding of the twice punctured torusAug 15 2008The Maskit embedding M of a surface \Sigma is the space of geometrically finite groups on the boundary of quasifuchsian space for which the `top' end is homeomorphic to \Sigma, while the `bottom' end consists of two triply punctured spheres, the remains ... More

Gaussian Graphical Models: An Algebraic and Geometric PerspectiveJul 13 2017Gaussian graphical models are used throughout the natural sciences, social sciences, and economics to model the statistical relationships between variables of interest in the form of a graph. We here provide a pedagogic introduction to Gaussian graphical ... More

Quantum Measurements Cannot be Proved to be RandomAug 30 2010We show that it is impossible to prove that the outcome of a quantum measurement is random.

About the dynamics and thermodynamics of trapped ionsFeb 16 2009May 14 2009This tutorial introduces the dynamics of charged particles in a radiofrequency trap in a very general manner to point out the differences between the dynamics in a quadrupole and in a multipole trap. When dense samples are trapped, the dynamics is modified ... More

On algebraic damping close to inhomogeneous Vlasov equilibria in multi-dimensional spacesOct 30 2012We investigate the asymptotic damping of a perturbation around inhomogeneous stable stationary states of the Vlasov equation in spatially multi-dimensional systems. We show that branch singularities of the Fourier-Laplace transform of the perturbation ... More

Twisted gamma filtration and algebras with orthogonal involutionNov 14 2012For the Grothendieck group of a split simple linear algebraic group, the twisted gamma-filtration provides a useful tool for constructing torsion elements in gamma-rings of twisted flag varieties. In this paper, we construct a non-trivial torsion element ... More

On the neighborhood of an inhomogeneous stable stationary solution of the Vlasov equation - Case of the Hamiltonian mean-field modelNov 13 2013We consider the one-dimensional Vlasov equation with an attractive cosine potential, and its non homogeneous stationary states that are decreasing functions of the energy. We show that in the Sobolev space $W^{1,p}$ ($p>2$) neighborhood of such a state, ... More

Laplacian Controllability of Threshold GraphsNov 29 2017Jun 13 2018This paper is concerned with the controllability problem of a connected threshold graph following the Laplacian dynamics. An algorithm is proposed to generate a spanning set of orthogonal Laplacian eigenvectors of the graph from a straightforward computation ... More

Construction of Cauchy Data of Vacuum Einstein field equations Evolving to Black HolesJul 13 2012We show the existence of complete, asymptotically flat Cauchy initial data for the vacuum Einstein field equations, free of trapped surfaces, whose future development must admit a trapped surface. Moreover, the datum is exactly a constant time slice in ... More

Network Robustness: Detecting Topological Quantum PhasesAug 06 2014Can the topology of a network that consists of many particles interacting with each other change in complexity when a phase transition occurs? The answer to this question is particularly interesting to understand the nature of phase transitions if the ... More

Edgeworth trading on networksMar 23 2018Jan 08 2019We define a class of pure exchange Edgeworth trading processes that under minimal assumptions converge to a stable set in the space of allocations, and characterise the Pareto set of these processes. Choosing a specific process belonging to this class, ... More

Momentum dissipation and holographic transport without self-dualitySep 15 2016Oct 13 2016We implement the momentum dissipation introduced by spatial linear axionic fields in a holographic model without self-duality, broke by Weyl tensor coupling to Maxwell field, and study its response. It is found that for the positive Weyl coupling parameter ... More

Quantum Lefschetz Hyperplane TheoremMar 21 2000Dec 06 2000The mirror theorem is generalized to any smooth projective variety X. That is, a fundamental relation between the Gromov-Witten invariants of X and Gromov-Witten invariants of complete intersections Y in X is established.

On high order accurate schemes for space fractional diffusion equations with variable coefficientsAug 29 2016Sep 29 2016We study high order schemes for spatial fractional differential equations with variable coefficients. Approximations of fractional derivatives basing on the weighted and shifted Gr\"unwald-Letnikov formulas and weighted and shifted Lubich formulas are ... More

Foundations of anisotropic relativistic mechanicsDec 06 2008Jun 30 2009We lay down the foundations of particle dynamics in mechanical theories that satisfy the relativity principle and whose kinematics can be formulated employing reference frames of the type usually adopted in special relativity. Such mechanics allow for ... More

Low-lying quasiparticle excitations in strongly-correlated superconductors: An ansatz from BCS quasiparticle excitations?Mar 28 2013The question about the existence of Bogoliubov's quasiparticles in the BCS wave functions underneath Gutzwiller's projection is of importance to strongly correlated systems. We develop a method to examine the two-particle excitations of Gutzwiller-projected ... More

A Large Data Regime for non-linear Wave EquationsOct 07 2012For semi-linear wave equations with null form non-linearities on $\mathbb{R}^{3+1}$, we exhibit an open set of initial data which are allowed to be large in energy spaces, yet we can still obtain global solutions in the future. We also exhibit a set of ... More

Some properties of the holographic fermions in an extremal charged dilatonic black holeAug 31 2011We study the properties of the Green's functions of the fermions in the extremal charged dilatonic black hole proposed by Gubser and Rocha [Phys. Rev. D \textbf{81}, 046001 (2010)]. We find that many properties seem to be in agreement with that of Fermi ... More

Almost-Prime Polynomials with Prime ArgumentsJun 11 2016We improve Irving's method of the double-sieve by using the DHR sieve. By extending the upper and lower sieve functions into their respective non-elementary ranges, we are able to make improvements on the previous records on the number of prime factors ... More

Long time solutions for wave maps with large dataJul 24 2012For 2 + 1 dimensional wave maps with $\mathbb{S}^2$ as the target, we show that for all positive numbers $T_0 > 0$ and $E_0 > 0$, there exist Cauchy initial data with energy at least $E_0$, so that the solution's life-span is at least $[0,T_0]$. We assume ... More

A Uniqueness Theorem for Free Waves on $\mathbb{R}^{n+1}$Jul 20 2010In this short note, based on Carleman estimates and Holmgren's type theorems, we provide a converse theorem of the classical Huygens principle for free wave equations. Possible generalizations to other underlying space-times or other wave type equations ... More

On global dynamics of the Maxwell-Klein-Gordon equationsMar 30 2018Sep 12 2018On the three dimensional Euclidean space, for data with finite energy, it is well-known that the Maxwell-Klein-Gordon equations admit global solutions. However, the asymptotic behaviours of the solutions for the data with non-vanishing charge and arbitrary ... More

On the formation of shocks for quasilinear wave equationsDec 09 2014Oct 12 2016The paper is devoted to the study of shock formation of the 3-dimensional quasilinear wave equation \begin{equation}\label{Main Equation} - \big(1+3G^{\prime\prime}(0) (\partial_t\phi)^2\big)\partial^2_t \phi +\Delta\phi=0,\tag{\textbf{$\star$}} \end{equation} ... More

Deriving relativistic momentum and energyFeb 05 2004Sep 15 2004We present a new derivation of the expressions for momentum and energy of a relativistic particle. In contrast to the procedures commonly adopted in textbooks, the one suggested here requires only the knowledge of the composition law for velocities along ... More

On high order accurate schemes for space fractional diffusion equations with variable coefficientsAug 29 2016Oct 14 2016We study high order schemes for spatial fractional differential equations with variable coefficients. Approximations of fractional derivatives basing on the weighted and shifted Gr\"unwald-Letnikov formulas and weighted and shifted Lubich formulas are ... More

On the Average Value of the Canonical Height in Higher Dimensional Families of Elliptic curvesMay 30 2013Feb 08 2015Given an elliptic curve E over a function field K=Q(T_1,...,T_n), we study the behavior of the canonical height ^h_(E_w) of the specialized elliptic curve E_w with respect to the height of w in Q^n. In this paper, we prove that there exists a uniform ... More

Variational Monte Carlo simulation in hole-doped cuprate superconductors: Competition between antiferromagnetism and superconductivityJun 16 2015We present variational Monte Carlo (VMC) results for the Gutzwiller-projected coexisting state including both antiferromagnetic (AFM) order and superconducting (SC) order in the two-dimensional t-t'-t"-J model. By further considering off-site spin correlation ... More

Holographic fermionic spectrum from Born-Infeld AdS black holeMay 18 2017In this letter, we systematically explore the holographic (non-)relativistic fermionic spectrum without/with dipole coupling dual to Born-Infeld anti-de Sitter (BI-AdS) black hole. For the relativistic fermionic fixed point, this holographic fermionic ... More

Heights and the Specialization Map for Families of Elliptic Curves over P^nSep 10 2014Jun 22 2015For $n\geq 2$, let $K=\overline{\mathbb{Q}}(\mathbb{P}^n)=\overline{\mathbb{Q}}(T_1, \ldots, T_n)$. Let $E/K$ be the elliptic curve defined by a minimal Weiestrass equation $y^2=x^3+Ax+B$, with $A,B \in \overline{\mathbb{Q}}[T_1, \ldots, T_n]$. There's ... More

Robustness of complex many-body networks: Novel perspective in 2D metal-insulator transitionFeb 10 2014May 27 2014We present a novel theoretical framework established by complex network analysis for understanding the phase transition beyond the Landau symmetry breaking paradigm. In this paper we take a two-dimensional metal-insulator transition driven by electron ... More

A Blowup Problem of Reaction Diffusion Equation Related to the Diffusion Induced Blowup PhenomenonJul 31 2003This work studies nonnegative solutions for the Cauchy, Neumann, and Dirichlet problems of a logistic type reaction-diffusion equation. The finite time blowup results for nonnegative solutions under various restrictions on the coefficients of this equation ... More

Deriving relativistic momentum and energy. II. Three-dimensional caseApr 14 2005Jun 14 2005We generalise a recent derivation of the relativistic expressions for momentum and kinetic energy from the one-dimensional to the three-dimensional case.

New Approaches to Honesty Theory and Applications in Quantum Dynamical SemigroupsJul 24 2015We prove some new characterisations of honesty of the perturbed semigroup in Kato's Perturbation Theorem on abstract state spaces via three approaches, namely mean ergodicity of operators, adjoint operators and uniqueness of the perturbed semigroup. We ... More

Transport phenomena and Weyl correction in effective holographic theory of momentum dissipationFeb 08 2019We construct a higher derivative theory involving an axionic field and the Weyl tensor in four dimensional spacetime. Up to the first order of the coupling parameters, the charged black brane solution with momentum dissipation in a perturbative manner ... More

Clustering in a model with repulsive long-range interactionsJan 26 2001A striking clustering phenomenon in the antiferromagnetic Hamiltonian Mean-Field model has been previously reported. The numerically observed bicluster formation and stabilization is here fully explained by a non linear analysis of the Vlasov equation. ... More

Links between nonlinear dynamics and statistical mechanics in a simple one-dimensional modelJul 26 2004We consider the links between nonlinear dynamics and thermodynamics in the framework of a simple nonlinear model for DNA. Two analyses of the phase transition, either with the transfer integral approach or by considering the instability of a nonlinear ... More

Ensemble Inequivalence in Mean-field Models of MagnetismSep 16 2002Mean-field models, while they can be cast into an {\it extensive} thermodynamic formalism, are inherently {\it non additive}. This is the basic feature which leads to {\it ensemble inequivalence} in these models. In this paper we study the global phase ... More

Variations on the theme of quantum LefschetzDec 04 2018Mar 24 2019In this companion piece to 1712.03573, some variations on the main results there are sketched. In particular, the recursions in 1712.03573, which we interpreted as the quantum Lefschetz, is reformulated in terms of Givental's quantization formalism, or ... More

Revisiting Spectral Graph Clustering with Generative Community ModelsSep 14 2017Oct 05 2017The methodology of community detection can be divided into two principles: imposing a network model on a given graph, or optimizing a designed objective function. The former provides guarantees on theoretical detectability but falls short when the graph ... More

Quasi-normal modes of holographic system with Weyl correction and momentum dissipationApr 29 2018We study the charge response in complex frequency plane and the quasi-normal modes (QNMs) of the boundary quantum field theory with momentum dissipation dual to a probe generalized Maxwell system with Weyl correction. When the strength of the momentum ... More

Polynomial overreproduction by Hermite subdivision operators, and $p$-Cauchy numbersApr 24 2019We study the case of Hermite subdivision operators satisfying a spectral condition of order greater than their size. We show that this can be characterized by operator factorizations involving Taylor operators and difference factorizations of a rank one ... More

Transient Thermal Behaviour in a Model of Linear Friction WeldingFeb 12 2016We derive a non-local model for the evolution of temperature in workpieces being joined by linear friction welding. The non-locality arises through the velocity being fixed by the temperature gradient at the weld. Short- and long-time behaviours are considered. ... More

Cohomology of generalized supergrassmannians and character formulae for basic classical Lie superalgebrasJun 04 2009Jun 22 2009In this paper, we use geometrical methods adapted from the Borel-Weil-Bott theory to compute the character of every finite dimensional simple module over a basic classical Lie superalgebra.

To Motivate Social Grouping in Wireless NetworksNov 05 2015Jun 21 2016We consider a group of neighboring smartphone users who are roughly at the same time interested in the same network content, called common interests. However, ever-increasing data traffic challenges the limited capacity of base-stations (BSs) in wireless ... More

Complete system of analytic invariants for unfolded differential linear systems with an irregular singularity of Poincaré rank 1May 11 2011In this, paper, we give a complete system of analytic invariants for the unfoldings of nonresonant linear differential systems with an irregular singularity of Poincar\'e rank 1 at the origin over a fixed neighborhood $D_r$. The unfolding parameter $\epsilon ... More

Modernity of Halphen's variations on a theme of MongeFeb 14 2016We construct a Z_3-slice to the natural action of PGL(V) on the variety of smooth arcs in the projective space P(V).

Evolution of eccentricity and orbital inclination of migrating planets in 2:1 mean motion resonanceJun 09 2014We determine, analytically and numerically, the conditions needed for a system of two migrating planets trapped in a 2:1 mean motion resonance to enter an inclination-type resonance. We provide an expression for the asymptotic equilibrium value that the ... More

Quasiparticle-vibration coupling effects on nuclear transitions of astrophysical interestSep 11 2017The relativistic quasiparticle time-blocking approximation (RQTBA) is applied to the description of nuclear excitation modes of astrophysical interest. This method is based on the meson-nucleon Lagrangian and goes beyond the standard relativistic quasiparticle ... More

Direct reconstruction of dark energyFeb 26 2010May 04 2010An important issue in cosmology is reconstructing the effective dark energy equation of state directly from observations. With so few physically motivated models, future dark energy studies cannot only be based on constraining a dark energy parameter ... More

Coupling charge-exchange vibrations to nucleons in a relativistic framework: effect on Gamow-Teller transitions and beta-decay half-livesJun 04 2018Nov 22 2018The nuclear response theory for isospin-transfer modes in the relativistic particle-vibration coupling framework is extended to include coupling of single nucleons to isospin-flip (charge-exchange) phonons, in addition to the usual neutral vibrations. ... More

Nuclear response theory for spin-isospin excitations in a relativistic quasiparticle-phonon coupling frameworkMay 02 2016Jul 29 2016A new theoretical approach to spin-isospin excitations in open-shell nuclei is presented. The developed method is based on the relativistic meson-exchange nuclear Lagrangian of Quantum Hadrodynamics and extends the response theory for superfluid nuclear ... More

Loading Monotonicity of Weighted Premiums, and Total Positivity Properties of Weight FunctionsJun 10 2018Feb 21 2019We consider the construction of insurance premiums that are monotonically increasing with respect to a loading parameter. By introducing weight functions that are totally positive of higher order, we derive higher monotonicity properties of weighted transformed ... More

Weighted distribution of low-lying zeros of GL(2) L-functionsJun 15 2018Sep 12 2018We show that if the zeros of an automorphic $L$-function are weighted by the central value of the $L$-function or a quadratic imaginary base change, then for certain families of holomorphic GL(2) newforms, it has the effect of changing the distribution ... More

Limits of limit sets IJul 05 2011We show that for a strongly convergent sequence of geometrically finite Kleinian groups with geometrically finite limit, the Cannon-Thurston maps of limit sets converge uniformly. If however the algebraic and geometric limits differ, as in the well known ... More

An extremal graph problem with a transcendental solutionJul 26 2016Aug 04 2016We prove that the number of multigraphs with vertex set $\{1, \ldots, n\}$ such that every four vertices span at most nine edges is $a^{n^2 + o(n^2)}$ where $a$ is transcendental (assuming Schanuel's conjecture from number theory). This is an easy consequence ... More

Stabilization of nanobubbles under hydrophobic confinementSep 13 2018It has been recently shown that nanobubbles exhibit a remarkable and unexpected stability. The lifetime of nanobubbles, formed either within liquids or on hydrophobic surfaces, can exceed by more than 10 orders of magnitude the theoretical expectation, ... More

Recurrence on Affine GrassmanniansMar 31 2017We study the action of the affine group $G$ of $\mathbb{R}^d$ on the space $X_{k,\,d}$ of $k$-dimensional affine subspaces. Given a compactly-supported Zariski dense probability measure $\mu$ on $G$, we show that $X_{k,\,d}$ supports a $\mu$-stationary ... More

On Gromov-Witten theory of projective bundlesJul 04 2016Given two equivariant vector bundles over an algebraic GKM manifold with the same equivariant Chern classes, we show that the genus zero equivariant Gromov--Witten theory of their projective bundles are naturally isomorphic.

Bias-Variance Tradeoff of Graph Laplacian RegularizerJun 02 2017This paper presents a bias-variance tradeoff of graph Laplacian regularizer, which is widely used in graph signal processing and semi-supervised learning tasks. The scaling law of the optimal regularization parameter is specified in terms of the spectral ... More

Profit Incentive In A Secondary Spectrum Market: A Contract Design ApproachJul 27 2012In this paper we formulate a contract design problem where a primary license holder wishes to profit from its excess spectrum capacity by selling it to potential secondary users/buyers. It needs to determine how to optimally price the excess spectrum ... More

Quantum K-theory on flag manifolds, finite-difference Toda lattices and quantum groupsAug 15 2001We conjecture that appropriate K-theoretic Gromov-Witten invariants of complex flag manifolds G/B are governed by finite-difference versions of Toda systems constructed in terms of the Langlands-dual quantized universal enveloping algebras U_q(g'). The ... More

EM duality and Quasi-normal modes from higher derivatives with homogeneous disorderDec 30 2018We study the electromagnetic (EM) duality from $6$ derivative theory with homogeneous disorder. We find that with the change of the sign of the coupling parameter $\gamma_1$ of the $6$ derivative theory, the particle-vortex duality with homogeneous disorder ... More

Variations on the theme of quantum LefschetzDec 04 2018Apr 14 2019In this companion piece to 1712.03573, some variations on the main results there are sketched. In particular, the recursions in 1712.03573, which we interpreted as the quantum Lefschetz, is reformulated in terms of Givental's quantization formalism, or ... More

Towards a quantum Lefschetz hyperplane theorem in all generaDec 10 2017Apr 19 2018An effective algorithm of determining Gromov--Witten invariants of smooth hypersurfaces in any genus (subject to a degree bound) from Gromov--Witten invariants of the ambient space is proposed. The Appendix is joint with E. Schulte-Geers.

Thermal non-Gaussianity in Near-Milne universeAug 17 2009Jan 31 2010The thermal non-Gaussianity in Near-Milne universe is investigated in this letter. Through classifying thermal fluctuations into two types, one characterized by a phase transition and the other without phase transition, we show that for fluctuations undergoing ... More

A note on entropic force and brane cosmologyJan 29 2010Feb 05 2010Recently Verlinde proposed that gravity is an entropic force caused by information changes when a material body moves away from the holographic screen. In this note we apply this argument to brane cosmology, and show that the cosmological equation can ... More

Delta-33 medium mass modification and pion spectraJul 13 2005May 21 2007We study the pi+- spectra obtained in 2,4,6,8 A GeV Au-Au collisions within the thermal model. We find that the main features of the data can be well described after we include the pions from the decay of the Delta-resonance with medium mass modification. ... More

On the Supermodularity of Active Graph-based Semi-supervised Learning with Stieltjes Matrix RegularizationApr 09 2018Active graph-based semi-supervised learning (AG-SSL) aims to select a small set of labeled examples and utilize their graph-based relation to other unlabeled examples to aid in machine learning tasks. It is also closely related to the sampling theory ... More

Particle motion and chaosJul 02 2018In this note, we explicitly illuminate that the velocity bound in the gravity corresponds to the chaos bound in the quantum system by studying the particle free falling in hyperscaling violating (HV) black brane. We also study the particle falling in ... More

Deep Global-Connected Net With The Generalized Multi-Piecewise ReLU Activation in Deep LearningJun 19 2018Recent Progress has shown that exploitation of hidden layer neurons in convolution neural networks incorporating with a carefully designed activation function can yield better classification results in the field of computer vision. The paper firstly introduces ... More

The Stokes phenomenon in the confluence of the hypergeometric equation using Riccati equationJun 12 2007Nov 01 2007In this paper we study the confluence of two regular singular points of the hypergeometric equation into an irregular one. We study the consequence of the divergence of solutions at the irregular singular point for the unfolded system. Our study covers ... More

Splendid Morita equivalences for principal 2-blocks with dihedral defect groupsDec 26 2017Mar 07 2019Given a dihedral $2$-group $P$ of order at least~8, we classify the splendid Morita equivalence classes of principal $2$-blocks with defect groups isomorphic to $P$. To this end we construct explicit stable equivalences of Morita type induced by specific ... More

Fourier series windowed by a bump functionJan 14 2019We study the Fourier transform windowed by a bump function. We transfer Jackson's classical results on the convergence of the Fourier series of a periodic function to windowed series of a not necessarily periodic function. Numerical experiments illustrate ... More

Hagedorn wavepackets in time-frequency and phase spaceMar 21 2013Mar 12 2014The Hermite functions are an orthonormalbasis of the space of square integrable functions with favourable approximation properties. Allowing for a flexible localization in position and momentum, the Hagedorn wavepackets generalize the Hermite functions ... More

Multivariate Gaussians, Semidefinite Matrix Completion, and Convex Algebraic GeometryJun 18 2009We study multivariate normal models that are described by linear constraints on the inverse of the covariance matrix. Maximum likelihood estimation for such models leads to the problem of maximizing the determinant function over a spectrahedron, and to ... More

Second cohomology groups for algebraic groups and their Frobenius kernelsSep 17 2008Oct 23 2010Let $G$ be a simple simply connected algebraic group scheme defined over an algebraically closed field of characteristic $p > 0$. Let $T$ be a maximal split torus in $G$, $B \supset T$ be a Borel subgroup of $G$ and $U$ its unipotent radical. Let $F: ... More

Flow-firing processesFeb 06 2019We consider a discrete non-deterministic flow-firing process for rerouting flow on the edges of a planar complex. The process is an instance of higher-dimensional chip-firing. In the flow-firing process, flow on the edges of a complex is repeatedly diverted ... More

Discretising the Herman--Kluk PropagatorMay 02 2016The Herman--Kluk propagator is a popular semi-classical approximation of the unitary evolution operator in quantum molecular dynamics. In this paper we formulate the Herman--Kluk propagator as a phase space integral and discretise it by Monte Carlo and ... More

Large deviation techniques applied to systems with long-range interactionsJun 16 2004Feb 14 2005We discuss a method to solve models with long-range interactions in the microcanonical and canonical ensemble. The method closely follows the one introduced by Ellis, Physica D 133, 106 (1999), which uses large deviation techniques. We show how it can ... More

Out-of-equilibrium states as statistical equilibria of an effective dynamicsApr 18 2002Aug 29 2002We study the formation of coherent structures in a system with long-range interactions where particles moving on a circle interact through a repulsive cosine potential. Non equilibrium structures are shown to correspond to statistical equilibria of an ... More

Birth and long-time stabilization of out-of-equilibrium coherent structuresMar 01 2002We study an analytically tractable model with long-range interactions for which an out-of-equilibrium very long-lived coherent structure spontaneously appears. The dynamics of this model is indeed very peculiar: a bicluster forms at low energy and is ... More

Oscillating elastic defects: competition and frustrationAug 31 2005We consider a dynamical generalization of the Eshelby problem: the strain profile due to an inclusion or "defect" in an isotropic elastic medium. We show that the higher the oscillation frequency of the defect, the more localized is the strain field around ... More

On p-ary Bent Functions and Strongly Regular GraphsApr 19 2019Our main result is a generalized Dillon-type theorem, giving graph-theoretic conditions which guarantee that a $p$-ary function in an even number of variables is bent, for $p$ a prime number greater than 2. The key condition is that the component Cayley ... More

On adaptability and "intermediate phase" in randomly connected networksAug 17 2004We present a simple model that enables us to analytically characterize a floppy to rigid transition and an associated self-adaptive intermediate phase in a random bond network. In this intermediate phase, the network adapts itself to lower the stress ... More

Privacy Against Statistical InferenceOct 08 2012We propose a general statistical inference framework to capture the privacy threat incurred by a user that releases data to a passive but curious adversary, given utility constraints. We show that applying this general framework to the setting where the ... More

Network topology: detecting topological phase transitions in the Kitaev chain and the rotor planeAug 01 2013May 08 2014We propose a novel network measure of topological invariants, called small-worldness, for identifying topological phase transitions of quantum and classical spin models. Small-worldness is usually defined in the study of social networks based on the best ... More