total 849took 0.15s

Low-lying Eigenvalues of the improved Wilson-Dirac Operator in QCDJan 20 1998The spectral flow of the low-lying eigenvalues of the improved and unimproved Wilson-Dirac operator is studied on instanton-like configurations and on thermalized quenched configurations at various $\beta$-values and lattice sizes. We also investigate ... More

An FPGA-based Torus Communication NetworkFeb 11 2011We describe the design and FPGA implementation of a 3D torus network (TNW) to provide nearest-neighbor communications between commodity multi-core processors. The aim of this project is to build up tightly interconnected and scalable parallel systems ... More

B-meson spectroscopy in HQET at order 1/mMay 13 2015Sep 02 2015We present a study of the B spectrum performed in the framework of Heavy Quark Effective Theory expanded to next-to-leading order in 1/m and non-perturbative in the strong coupling. Our analyses have been performed on Nf=2 lattice gauge field ensembles ... More

HQET form factors for $B_s\to K\ellν$ decays beyond leading orderNov 03 2017Nov 25 2017We compute semi-leptonic $B_s$ decay form factors using Heavy Quark Effective Theory on the lattice. To obtain good control of the $1/m_b$ expansion, one has to take into account not only the leading static order but also the terms arising at $O(1/m_b)$: ... More

The Schroedinger functional coupling in quenched QCD at low energiesOct 25 2001Existing non-perturbative computations of the running coupling of quenched QCD in the Schroedinger functional scheme are extended to scales mu lying much deeper in the low-energy regime. We are able to reach 1/mu ~ 0.9 fm, where a significant deviation ... More

Non-perturbative Heavy Quark Effective Theory: An application to semi-leptonic B-decaysJan 14 2015We review a lattice strategy how to non-perturbatively determine the coefficients in the HQET expansion of all components of the heavy-light axial and vector currents, including 1/m_h-corrections. We also discuss recent preliminary results on the form ... More

HQET at order $1/m$: II. Spectroscopy in the quenched approximationApr 15 2010Jul 12 2010Using Heavy Quark Effective Theory with non-perturbatively determined parameters in a quenched lattice calculation, we evaluate the splittings between the ground state and the first two radially excited states of the $B_s$ system at static order. We also ... More

Continuum limit of the leading order HQET form factor in $B_s \to K\ellν$ decaysJan 17 2016Jun 02 2016We discuss the computation of form factors for semi-leptonic decays of $\rm B$-, $\rm B_s$- mesons in lattice QCD. Considering in particular the example of the static $\rm B_s$ form factors we demonstrate that after non-perturbative renormalization the ... More

Exploring the HMC trajectory-length dependence of autocorrelation times in lattice QCDJun 02 2006We study autocorrelation times of physical observables in lattice QCD as a function of the molecular dynamics trajectory length in the hybrid Monte-Carlo algorithm. In an interval of trajectory lengths where energy and reversibility violations can be ... More

B $\to$ $π$ form factor with 2 flavours of $O(a)$ improved Wilson quarksOct 12 2012The determinations of $|V_{\rm ub}|$ from the exclusive branching ratios of $B\to \tau \nu$ and $B \to \pi l \nu$ tend to show a tension at the level of $3\sigma$ \cite{Beringer:1900zz}. On the theoretical side they depend on the lattice computation of ... More

Towards a non-perturbative matching of HQET and QCD with dynamical light quarksOct 05 2007Oct 17 2007We explain how the strategy of solving renormalization problems in HQET non-perturbatively by a matching to QCD in finite volume can be implemented to include dynamical fermions. As a primary application, some elements of an HQET computation of the mass ... More

Non-perturbative renormalization of lattice QCD at all scalesDec 05 1995A general strategy to solve the non-perturbative renormalization problem in lattice QCD, using finite-size techniques and numerical simulations, is described. As an illustration we discuss the computation of the axial current normalization constant, the ... More

Form factors for $\mathrm B_\mathrm s \to \mathrm K \ell ν$ decays in Lattice QCDNov 14 2014We present the current status of the computation of the form factor $f_+ (q^2)$ for the semi-leptonic decay $\mathrm B_\mathrm s \to \mathrm K \ell \nu$ by the ALPHA collaboration. We use gauge configurations which were generated as part of the Coordinated ... More

HQET at order 1/m: III. Decay constants in the quenched approximationJun 30 2010Oct 25 2010We report on the computation of the $B_s$ meson decay constant in Heavy Quark Effective Theory on the lattice. The next to leading order corrections in the HQET expansion are included non-perturbatively. We estimate higher order contributions to be very ... More

Spectroscopy and Decay Constants from Nonperturbative HQET at Order 1/mNov 08 2009Nov 09 2009We carry out a thorough analysis with the GEVP method to obtain ground-state and first-excited-state masses and decay constants of bottom-strange (pseudo-scalar and vector) mesons. This computation is done for quenched, nonperturbatively renormalized ... More

Matching of heavy-light flavour currents between HQET at order 1/m and QCD: I. Strategy and tree-level studyDec 05 2013Apr 25 2014We present a strategy how to match the full set of components of the heavy-light axial and vector currents in Heavy Quark Effective Theory (HQET), up to and including 1/m-corrections, to QCD. While the ultimate goal is to apply these matching conditions ... More

Topological structure of the SU(3) vacuum and exceptional eigenmodes of the improved Wilson-Dirac operatorSep 26 1997We present a study of the instanton size and spatial distributions in pure SU(3) gauge theory using under-relaxed cooling. We also investigate the low-lying eigenmodes of the (improved) Wilson-Dirac operator, in particular, the appearance of zero-modes ... More

Extraction of bare Form Factors for $\mathrm B_\mathrm s \to \mathrm K \ell ν$ Decays in non-perturbative HQETMar 14 2019We discuss the extraction of the ground state $\langle \mathrm{K} ({\bf p})|V_\mu(0)|\mathrm{B} ({\bf 0})\rangle$ matrix elements from Euclidean lattice correlation functions. The emphasis is on the elimination of excited state contributions. Two typical ... More

CP Violation and Strong Phases from Penguins in $\bf B^{\pm}\rightarrow PP$ and $\bf B^{\pm}\rightarrow VP$ DecaysOct 30 1994Oct 31 1994We calculate direct CP-violating rate asymmetries in charged $B\to PP$ and $B\to VP$ decays arising from the interference of amplitudes with different strong and CKM phases. The perturbative strong phases develop at order $\alpha_s$ from absorptive parts ... More

On the Stability of Empirical Risk Minimization in the Presence of Multiple Risk MinimizersFeb 10 2010Recently Kutin and Niyogi investigated several notions of algorithmic stability--a property of a learning map conceptually similar to continuity--showing that training-stability is sufficient for consistency of Empirical Risk Minimization while distribution-free ... More

CP Violation and Strong Phases from Penguins in $\bf B^{\pm}\rightarrow VV$ DecaysFeb 04 1994We calculate direct CP-violating observables in charged $B\to VV$ decays arising from the interference of amplitudes with different strong and CKM phases. The perturbative strong phases develop at order $\alpha_s$ from absorptive parts of one-loop matrix ... More

Klein's "Erlanger Programm": do traces of it exist in physical theories?Oct 28 2015A possible influence of Klein's Erlangen program on physical theories is investigated. While some connections are found, it is concluded that Lie's theory of transformation groups and Lie algebras have had a much larger impact. In this context, an extension ... More

Some rekarks on the early history of the Albert Einstein InstituteDec 05 2016The genesis of the Max Planck Institute for Gravitational Physics (Albert Einstein Institute) after German re-unification as described here, shows that the history of the founding of the institute is not as simplistic as claimed e.g., in the presentation ... More

Marginal relevance for the $γ$-stable pinning modelDec 07 2016We investigate disorder relevance for the pinning of a renewal when the law of the random environment is in the domain of attraction of a stable law with parameter $\gamma \in (1,2)$. Assuming that the renewal jumps have power-law decay, we determine ... More

Minimal graded Lie algebras and representations of quadratic algebrasSep 30 2014Jan 18 2017Let $({\go g}\_{0},B\_{0})$ be a quadratic Lie algebra (i.e. a Lie algebra $\go{g}\_{0}$ with a non degenerate symmetric invariant bilinear form $B\_{0}$) and let $(\rho,V)$ be a finite dimensional representation of ${\go g}\_{0}$. We define on $ \Gamma(\go{g}\_{0}, ... More

Decomposition of reductive regular prehomogeneous vector spacesMar 26 2010Jun 02 2010Let (G,V) be a regular prehomogeneous vector space (abbreviated to PV), where G is a connected reductive algebraic group over C. If $V= \oplus_{i=0}^{n}V_{i}$ is a decomposition of V into irreducible representations, then, in general, the PV's $(G,V_{i})$ ... More

Approximate Lifshitz law for the zero-temperature stochastic Ising model in any dimensionFeb 17 2011Oct 02 2012We study the Glauber dynamics for the zero-temperature Ising model in dimension d=4 with "plus" boundary condition.Let T+ be the time needed for an hypercube of size L entirely filled with "minus" spins to become entirely "plus". We prove that T+ is O(L^2(log ... More

Non-coincidence of Quenched and Annealed Connective Constants on the supercritical planar percolation clusterMar 27 2012Jul 21 2013In this paper, we study the abundance of self-avoiding paths of a given length on a supercritical percolation cluster on $\bbZ^d$. More precisely, we count $Z_N$ the number of self-avoiding paths of length $N$ on the infinite cluster, starting from the ... More

New bounds for the free energy of directed polymers in dimension 1+1 and 1+2Jan 06 2009Nov 19 2009We study the free energy of the directed polymer in random environment in dimension 1+1 and 1+2. For dimension 1, we improve the statement of Comets and Vargas concerning very strong disorder by giving sharp estimates on the free energy at high temperature. ... More

Influence of spatial correlation for directed polymersDec 18 2009Dec 09 2010In this paper, we study a model of a Brownian polymer in $\mathbb {R}_+\times \mathbb {R}^d$, introduced by Rovira and Tindel [J. Funct. Anal. 222 (2005) 178--201]. Our investigation focuses mainly on the effect of strong spatial correlation in the environment ... More

Desordre et phenomenes de localisationNov 19 2009Cette these est consacree a l' etude de differents modeles aleatoires de polymeres. On s'interesse en particulier a l'influence du desordre sur la localisation des trajectoires pour les modeles d'accrochage et pour les polymeres diriges en milieu aleatoire. ... More

Cayley Integers (long version)Jun 17 2005Jun 18 2005We present here some results of applying the Cayley-Dickson process to certain alternative algebras (notably built upon Galois fields and congruence rings), in a manner which might yield new building blocks for cryptographic systems. We focus on enumeration ... More

Quasi-compactness and absolutely continuous kernels, applications to Markov chainsJun 27 2006We show how the essential spectral radius of a bounded positive kernel, acting on bounded functions, is linked to its lower approximation by certain absolutely continuous kernels. The standart Doeblin's condition can be interpreted in this context, and, ... More

Pinning and disorder relevance for the lattice Gaussian Free Field II: the two dimensional caseDec 16 2015Feb 16 2016This paper continues a study initiated in [34], on the localization transition of a lattice free field on $\mathbb Z^d$ interacting with a quenched disordered substrate that acts on the interface when its height is close to zero. The substrate has the ... More

Superdiffusivity for Brownian motion in a Poissonian potential with long range correlation II: upper bound on the volume exponentJul 06 2011Dec 13 2011This paper continues a study on trajectories of Brownian Motion in a field of soft trap whose radius distribution is unbounded. We show here for both point-to-point and point-to-plane model the volume exponent (the exponent associated to transversal fluctuation ... More

Hierarchical pinning model with site disorder: Disorder is marginally relevantJul 30 2008May 14 2009We study a hierarchical disordered pinning model with site disorder for which, like in the bond disordered case [6, 9], there exists a value of a parameter b (enters in the definition of the hierarchical lattice) that separates an irrelevant disorder ... More

Scaling test of two-flavor O(a)-improved lattice QCDApr 21 2008Apr 30 2008We report on a scaling test of several mesonic observables in the non-perturbatively O(a) improved Wilson theory with two flavors of dynamical quarks. The observables are constructed in a fixed volume of 2.4fm x (1.8fm)^3 with Schroedinger functional ... More

Geometrical Lattice models for N=2 supersymmetric theories in two dimensionsNov 04 1991We introduce in this paper two dimensional lattice models whose continuum limit belongs to the $N=2$ series. The first kind of model is integrable and obtained through a geometrical reformulation, generalizing results known in the $k=1$ case, of the $\Gamma_{k}$ ... More

Mixing time and cutoff for the adjacent transposition shuffle and the simple exclusionSep 16 2013Mar 30 2016In this paper, we investigate the mixing time of the adjacent transposition shuffle for a deck of $N$ cards. We prove that around time $N^2\log N/(2\pi^2)$, the total variation distance to equilibrium of the deck distribution drops abruptly from $1$ to ... More

Existence of a non-averaging regime for the self-avoiding walk on a high-dimensional infinite percolation clusterDec 19 2012Jun 26 2013Let Z_N be the number of self-avoiding paths of length N starting from the origin on the infinite cluster obtained after performing Bernoulli percolation on Z^d with parameter p>p_c(Z^d). The object of this paper is to study the connective constant of ... More

The scaling limit for zero temperature planar Ising droplets: with and without magnetic fieldsOct 09 2012We consider the continuous time, zero-temperature heat-bath dynamics for the nearest-neighbor Ising model on $Z^2$ with positive magnetic field. For a system of size $L\in N$, we start with initial condition $\sigma$ such that $\sigma_x=-1$ if $x\in[-L,L]^2$ ... More

The Simple Exclusion Process on the Circle has a diffusive Cutoff WindowJan 28 2014Jan 04 2016In this paper, we investigate the mixing time of the simple exclusion process on the circle with $N$ sites, with a number of particle $k(N)$ tending to infinity, both from the worst initial condition and from a typical initial condition. We show that ... More

Invariant differential operators on a class of multiplicity free spacesMar 09 2011Feb 13 2014If $(G,V)$ is a multiplity free space with a one dimensional quotient we give generators and relations for the non-commutative algebra $D(V)^{G'}$ of invariant differential operators under the semi-simple part $G'$ of the reductive group $G$. More precisely ... More

FINMHD: an adaptive finite element code for magnetic reconnection and plasmoid chains formation in MagnetohydrodynamicsApr 25 2019Solving the problem of fast eruptive events in magnetically dominated astrophysical plasmas requires the use of particularly well adapted numerical tools. Indeed, the central mechanism based on magnetic reconnection is determined by a complex behavior ... More

Multiplicity free spaces with a one dimensional quotientMay 03 2012The multiplicity free spaces with a one dimensional quotient were introduced by Thierry Levasseur in [11]. Recently, the author has shown that the algebra of differential operators on such spaces which are invariant under the semi-simple part of the group ... More

Superdiffusivity for Brownian Motion in a Poissonian Potential with Long Range Correlation I: Lower Bound on the Volume ExponentApr 11 2011Dec 13 2011We study trajectories of d-dimensional Brownian Motion in Poissonian potential up to the hitting time of a distant hyper-plane. Our Poissonian potential V can be associated to a field of traps whose centers location is given by a Poisson Point process ... More

The scaling limit of polymer pinning dynamics and a one dimensional Stefan freezing problemApr 05 2012Apr 26 2013We consider the stochastic evolution of a 1+1-dimensional interface (or polymer) in presence of a substrate. This stochastic process is a dynamical version of the homogeneous pinning model. We start from a configuration far from equilibrium: a polymer ... More

The N-representability problem, the pseudo-spectral decomposition of antisymmetric 1-body operators, and collective behaviourApr 15 1995The pseudo--spectral decomposition of an $N$--particle antisymmetric 1--body positive--semidefinite operator that corresponds to the canonical convex decomposition into the extreme elements of the dual cone of the set of fermion $N$--representable $1$--density ... More

Polymers and percolation in two dimensions and twisted N=2 supersymmetryNov 04 1991It is shown how twisted N=2 (k=1) provides for the first time a complete conformal field theory description of the usual geometrical phase transitions in two dimensions, like polymers, percolation or brownian motion. In particular, four point functions ... More

A product chain without cutoffJul 07 2014Nov 27 2014In this note, we construct an example of a sequence of $n$-fold product chains which does not display cutoff for total-variation distance neither for separation distance. In addition we show that this type of product chains necessarily displays pre-cutoff. ... More

The rounding of the phase transition for disordered pinning with stretched exponential tailsMay 27 2014Nov 13 2014The presence of frozen-in or quenched disorder in a system can often modify the nature of its phase transition. A particular instance of this phenomenon is the so-called rounding effect: it has been shown in many cases that the free-energy curve of the ... More

The cutoff profile for the simple exclusion process on the circleFeb 03 2015Sep 22 2016In this paper, we give a very accurate description of the way the simple exclusion process relaxes to equilibrium. Let $P_t$ denote the semi-group associated the exclusion on the circle with $2N$ sites and $N$ particles. For any initial condition $\chi$, ... More

Algebras of invariant differential operators on a class of multiplicity free spacesOct 29 2009Let G be a connected reductive algebraic group and let G'=[G,G] be its derived subgroup. Let (G,V) be a multiplicity free representation with a one dimensional quotient (see definition below). We prove that the algebra D(V)^{G'} of G'-invariant differential ... More

Explicit measures for the homogeneous transformOct 03 2016The homogeneous transform has many practical applications outside the realm of mathematics, for instance to represent the proportions of several chemical substances. We aim here to present results about the transformation of measures, which could be used ... More

Invariant differential operators and an infinite dimensional Howe-type correspondence. Part I: Structure of the associated algebras of differential operatorsFeb 04 2008If $Q$ is a non degenerate quadratic form on ${\bb C}^n$, it is well known that the differential operators $X=Q(x)$, $Y=Q(\partial)$, and $H=E+\frac{n}{2}$, where $E$ is the Euler operator, generate a Lie algebra isomorphic to ${\go sl}_{2}$. Therefore ... More

Existence of an intermediate phase for oriented percolationJan 22 2012Feb 07 2012We consider the following oriented percolation model of $\mathbb {N} \times \mathbb{Z}^d$: we equip $\mathbb {N}\times \mathbb{Z}^d$ with the edge set $\{[(n,x),(n+1,y)] | n\in \mathbb {N}, x,y\in \mathbb{Z}^d\}$, and we say that each edge is open with ... More

The martingale approach to disorder irrelevance for pinning modelsFeb 25 2010Mar 14 2011This paper presents a very simple and self-contained proof of disorder irrelevance for inhomogeneous pinning models with return exponent alpha in the Interval (0,1/2). We also give a new upper bound for the contact fraction of the disordered model at ... More

Parameters of Heavy Quark Effective Theory from Nf=2 lattice QCDMar 29 2012We report on a non-perturbative determination of the parameters of the lattice Heavy Quark Effective Theory (HQET) Lagrangian and of the time component of the heavy-light axial-vector current with Nf=2 flavors of massless dynamical quarks. The effective ... More

The determination of $α_s$ by the ALPHA collaborationNov 17 2016We review the ALPHA collaboration strategy for obtaining the QCD coupling at high scale. In the three-flavor effective theory it avoids the use of perturbation theory at $\alpha > 0.2$ and at the same time has the physical scales small compared to the ... More

B meson spectrum and decay constant from Nf=2 simulationsDec 06 2010Dec 10 2010We report on the status of an ALPHA Collaboration project to extract quantities for B physics phenomenology from Nf=2 lattice simulations. The framework is Heavy Quark Effective Theory (HQET) expanded up to the first order of the inverse b-quark mass. ... More

M_b and f_B from non-perturbatively renormalized HQET with Nf=2 light quarksDec 28 2011We present an updated analysis of the non-perturbatively renormalized b-quark mass and B meson decay constant based on CLS lattices with two dynamical non-perturbatively improved Wilson quarks. This update incorporates additional light quark masses and ... More

First results on the running coupling in QCD with two massless flavoursMay 03 2001May 28 2001We report on the non-perturbative computation of the running coupling of two-flavour QCD in the Schr"odinger functional scheme. The corresponding Lambda-parameter, which describes the coupling strength at high energy, is related to a low energy scale ... More

B-physics from non-perturbatively renormalized HQET in two-flavour lattice QCDOct 24 2012We report on the ALPHA Collaboration's lattice B-physics programme based on N_f=2 O(a) improved Wilson fermions and HQET, including all NLO effects in the inverse heavy quark mass, as well as non-perturbative renormalization and matching, to fix the parameters ... More

A lattice approach to the conformal $\OSp(2S+2|2S)$ supercoset sigma model. Part II: The boundary spectrumJan 02 2008We consider the partition function of the boundary $OSp(2S+2|2S)$ coset sigma model on an annulus, based on the lattice regularization introduced in the companion paper. Using results for the action of $OSp(2S+2|2S)$ and $B_L(2)$ on the corresponding ... More

Dust diffusion in protoplanetary discs by magnetorotational turbulenceJan 28 2005Aug 17 2005We measure the turbulent diffusion coefficient of dust grains embedded in magnetorotational turbulence in a protoplanetary disc directly from numerical simulations and compare it to the turbulent viscosity of the flow. The simulations are done in a local ... More

Maxwell's Demon, Szilard's Engine and Quantum MeasurementsJan 15 2003We propose and analyze a quantum version of Szilard's ``one-molecule engine.'' In particular, we recover, in the quantum context, Szilard's conclusion concerning the free energy ``cost'' of measurements: $\Delta F \geq k_B T\ln2$ per bit of information. ... More

BPS kinks in the Gross-Neveu modelMay 15 2001We find the exact spectrum and degeneracies for the Gross-Neveu model in two dimensions. This model describes N interacting Majorana fermions; it is asymptotically free, and has dynamical mass generation and spontaneous chiral symmetry breaking. We show ... More

Soundly Handling Static Fields: Issues, Semantics and AnalysisJul 19 2010Jul 20 2010Although in most cases class initialization works as expected, some static fields may be read before being initialized, despite being initialized in their corresponding class initializer. We propose an analysis which compute, for each program point, the ... More

On the SU(2|1) WZW model and its statistical mechanics applicationsNov 14 2006Motivated by a careful analysis of the Laplacian on the supergroup $SU(2|1)$ we formulate a proposal for the state space of the $SU(2|1)$ WZNW model. We then use properties of $\hat{sl}(2|1)$ characters to compute the partition function of the theory. ... More

First hard X-ray observations of the blazar S5 0716+714 with NuSTAR during a multiwavelength campaignMay 02 2016We report the results of a multifrequency campaign targeting S5 0716+714 in the flaring state of the source observed in 2015 January and February. The observations have been performed using the following instruments: Fermi/Large Area Telescope (LAT), ... More

Lagrangian Curves in Affine Symplectic 4-spaceMay 14 2013Dec 22 2013Lagrangian curves in 4-space entertain intriguing relationships with second order deformation of plane curves under the special affine group and null curves in a 3-dimensional Lorentzian space form. We provide a natural affine symplectic frame for Lagrangian ... More

A mathematical perspective on metastable wettingDec 30 2013In this paper we investigate the dynamical behavior of an interface or polymer, in interaction with a distant attractive substrate. The interface is modeled by the graph of a nearest neighbor path with non-negative integer coordinates, and the equilibrium ... More

Log-canonical forms and log canonical singularitiesDec 15 2000For a normal subvariety $V$ of ${\bf C}^n$ with a good ${\bf C}^*$-action we give a simple characterization for when it has only log canonical, log terminal or rational singularities. Moreover we are able to give formulas for the plurigenera of isolated ... More

On Wave Dark Matter, Shells in Elliptical Galaxies, and the Axioms of General RelativityDec 23 2012This paper is a sequel to the author's paper entitled "On Dark Matter, Spiral Galaxies, and the Axioms of General Relativity" [arXiv:1004.4016] which explored a geometrically natural axiomatic definition for dark matter modeled by a scalar field satisfying ... More

Quantum Electronic Circuit Simulation of Generalized sine-Gordon ModelsFeb 24 2019Investigation of strongly interacting, nonlinear quantum field theories (QFT-s) remains one of the outstanding challenges of modern physics. Here, we describe analog quantum simulators for nonlinear QFT-s using mesoscopic superconducting circuit lattices. ... More

A Note on Generic ProjectionsOct 10 2002Let $X \subseteq {\bf P}^N ={\bf P}^{2n}_K$ be a subvariety of dimension $n$ and $P \in {\bf P}^N$ a generic point. If the tangent variety Tan$ X$ is equal to ${\bf P}^N$ then for generic points $x$, $y$ of $X$ the projective tangent spaces $t_xX$ and ... More

Zero-Energy Fields on Complex Projective SpaceAug 08 2011We consider complex projective space with its Fubini-Study metric and the X-ray transform defined by integration over its geodesics. We identify the kernel of this transform acting on symmetric tensor fields.

Short-Term Memory Through Persistent Activity: Evolution of Self-Stopping and Self-Sustaining Activity in Spiking Neural NetworksNov 25 2014Memories in the brain are separated in two categories: short-term and long-term memories. Long-term memories remain for a lifetime, while short-term ones exist from a few milliseconds to a few minutes. Within short-term memory studies, there is debate ... More

Algebras in Higher Dimensional Statistical Mechanics - the Exceptional Partition (MEAN Field) AlgebrasFeb 19 1993We determine the structure of the partition algebra $P_n(Q)$ (a generalized Temperley-Lieb algebra) for specific values of $Q \in \C$, focusing on the quotient which gives rise to the partition function of $n$ site $Q$-state Potts models (in the continuous ... More

Non-commutativity of exponential spectrumOct 27 2015Nov 24 2015In a Banach algebra, the spectrum satisfies $\sigma(ab)\setminus\{0\} = \sigma(ba)\setminus\{0\}$ for each pair of elements $a,b$. We show that this is no longer true for the exponential spectrum, thereby solving a problem open since 1992. Our proof depends ... More

Cosmological Experiments in Condensed Matter SystemsJul 18 1996Topological defects are thought to be left behind by the cosmological phase transitions which occur as the universe expands and cools. Similar processes can be studied in the phase transitions which take place in the laboratory: ``Cosmological'' experiments ... More

Circle averages and disjointness in typical flat surfaces on every Teichmueller discOct 20 2015We prove that on the typical flat surface the flow in almost every pair of directions are not isomorphic to each other and are in fact disjoint. We provide an application to the convergence of 'circle averages' for the flow (away from a sequence of radii ... More

Loci in strata of meromorphic differentials with fully degenerate Lyapunov spectrumJul 12 2013We construct explicit closed GL(2, R)-invariant loci in strata of meromorphic differentials of arbitrary large dimension with fully degenerate Lyapunov spectrum. This answers a question of Forni-Matheus-Zorich.

Applying Supervised Learning Algorithms and a New Feature Selection Method to Predict Coronary Artery DiseaseFeb 03 2014From a fresh data science perspective, this thesis discusses the prediction of coronary artery disease based on genetic variations at the DNA base pair level, called Single-Nucleotide Polymorphisms (SNPs), collected from the Ontario Heart Genomics Study ... More

Quantum Theory of the Classical: Quantum Jumps, Born's Rule, and Objective Classical Reality via Quantum DarwinismJul 05 2018Emergence of the classical world from the quantum substrate of our Universe is a long-standing conundrum. I describe three insights into the transition from quantum to classical that are based on the recognition of the role of the environment. I begin ... More

The Penrose inequality in general relativity and volume comparison theorems involving scalar curvature (thesis)Feb 18 2009In this thesis we describe how minimal surface techniques can be used to prove the Penrose inequality in general relativity for two classes of 3-manifolds. We also describe how a new volume comparison theorem involving scalar curvature for 3-manifolds ... More

Central Limit Theorem for probability measures defined by sum-of-digits function in base 2May 20 2016Dec 11 2017In this paper we prove a central limit theorem for some probability measures defined as asymtotic densities of integer sets defined via sum-of-digit-function. To any integer a we can associate a measure on Z called $\mu$a such that, for any d, $\mu$a(d) ... More

On the easiest way to connect $k$ points in the Random Interlacements processJun 19 2012Jul 04 2012We consider the random interlacements process with intensity $u$ on ${\mathbb Z}^d$, $d\ge 5$ (call it $I^u$), built from a Poisson point process on the space of doubly infinite nearest neighbor trajectories on ${\mathbb Z}^d$. For $k\ge 3$ we want to ... More

Ergodicity for Infinite Periodic Translation SurfacesFeb 01 2012For a Z-cover of a translation surface, which is a lattice surface, and which admits infinite strips, we prove that almost every direction for the straightline flow is ergodic.

Circle averages and disjointness in typical flat surfaces on every Teichmueller discOct 20 2015May 23 2017We prove that on the typical translation surface the flow in almost every pair of directions are not isomorphic to each other and are in fact disjoint. It was not known if there were any translation surfaces other than torus covers with this property. ... More

Disorder relevance without Harris Criterion: the case of pinning model with $γ$-stable environmentOct 21 2016We investigate disorder relevance for the pinning of a renewal whose inter-arrival law has tail exponent $\alpha>0$ when the law of the random environment is in the domain of attraction of a stable law with parameter $\gamma \in (1,2)$. We prove that ... More

Superspecial Abelian Varieties and the Eichler Basis Problem for Hilbert Modular FormsNov 02 2007Jun 17 2008Let $p$ be an unramified prime in a totally real field $L$ such that $h^+(L)=1$. Our main result shows that Hilbert modular newforms of parallel weight two for $\Gamma_0(p)$ can be constructed naturally, via classical theta series, from modules of isogenies ... More

Normal affine surfaces with $\bf C^*$-actionsOct 10 2002A classification of normal affine surfaces admitting a $\bf C^*$-action was given in the work of Bia{\l}ynicki-Birula, Fieseler and L. Kaup, Orlik and Wagreich, Rynes and others. We provide a simple alternative description of such surfaces in terms of ... More

Rational curves and rational singularitiesSep 28 2001We study rational curves on algebraic varieties, especially on normal affine varieties endowed with a $\C^*$-action. For varieties with an isolated singularity, we show that the presence of sufficiently many rational curves outside the singular point ... More

Codimension and connectedness of degeneracy loci over local ringsJun 06 2005We deduce results on the dimension and connectedness of degeneracy loci of maps of finite modules $f:M\to N$ over a local noetherian ring $(A,{\mathfrak m})$. We show for instance that the expected determinantal bounds on the dimension of the t-$th$ degeneracy ... More

The effect of disorder on the free-energy for the Random Walk Pinning Model: smoothing of the phase transition and low temperature asymptoticsJul 29 2010We consider the continuous time version of the Random Walk Pinning Model (RWPM), studied in [5,6,7]. Given a fixed realization of a random walk Y$ on Z^d with jump rate rho (that plays the role of the random medium), we modify the law of a random walk ... More

Universal Entanglement Dynamics following a Local QuenchJan 30 2017Jun 17 2017We study the time dependence of the entanglement between two quantum wires after suddenly connecting them via tunneling through an impurity. The result at large times is given by the well known formula $S(t) \approx {1\over 3}\ln {t}$. We show that the ... More

"Convergent observations" with the stereoscopic HEGRA CT systemOct 26 1999Observations of air showers with the stereoscopic HEGRA IACT system are usually carried out in a mode where all telescopes point in the same direction. Alternatively, one could take into account the finite distance to the shower maximum and orient the ... More

Simplification of complexes for persistent homology computationsApr 30 2013In this paper we focus on preprocessing for persistent homology computations. We adapt some techniques which were successfully used for standard homology computations. The main idea is to reduce the complex prior to generating its boundary matrix, which ... More

The GL(1|1) WZW model: From Supergeometry to Logarithmic CFTOct 04 2005We present a complete solution of the WZW model on the supergroup GL(1|1). Our analysis begins with a careful study of its minisuperspace limit (``harmonic analysis on the supergroup''). Its spectrum is shown to contain indecomposable representations. ... More