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A rationality result for the exterior and the symmetric square $L$-functionDec 27 2014Let $G={\rm GL}_{2n}$ over a totally real number field $F$ and $n\geq 2$. Let $\Pi$ be a cuspidal automorphic representation of $G(\mathbb A)$, which is cohomological and a functorial lift from SO$(2n+1)$. The latter condition can be equivalently reformulated ... More

Automorphic Forms, Cohomology and CAP Representations. The Case $GL_2$ over a definite quaternion algebraMar 11 2010Sep 27 2011In this paper we fully describe the cuspidal and the Eisenstein cohomology of the group $G=GL_2$ over a definite quaternion algebra $D/\Q$. Functoriality is used to show the existence of residual and cuspidal automorphic forms, having cohomology in degree ... More

Whittaker periods, motivic periods, and special values of tensor product L-functionsAug 23 2013Aug 28 2014Let $\mathcal K$ be an imaginary quadratic field. Let $\Pi$ and $\Pi'$ be irreducible generic cohomological automorphic representation of $GL(n)/{\mathcal K}$ and $GL(n-1)/{\mathcal K}$, respectively. Each of them can be given two natural rational structures ... More

Special values of $L$-functions and the refined Gan-Gross-Prasad conjectureMay 22 2017We prove explicit rationality-results for Asai- $L$-functions, $L^S(s,\Pi',{\rm As}^\pm)$, and Rankin-Selberg $L$-functions, $L^S(s,\Pi\times\Pi')$, over arbitrary CM-fields $F$, relating critical values to explicit powers of $(2\pi i)$. Besides determining ... More

On the arithmetic of Shalika models and the critical values of L-functions for GL(2n)Jun 21 2011Apr 23 2013Let \Pi be a cohomological cuspidal automorphic representation of GL_2n(A) over a totally real number field F. Suppose that \Pi has a Shalika model. We define a rational structure on the Shalika model of \Pi_f. Comparing it with a rational structure on ... More

On the arithmetic of Shalika models and the critical values of $L$-functions for ${\rm GL}(2n)$Jun 21 2011Mar 07 2019Let $\Pi$ be a cohomological cuspidal automorphic representation of ${\rm GL}_{2n}(\mathbb A)$ over a totally real number field $F$. Suppose that $\Pi$ has a Shalika model. We define a rational structure on the Shalika model of $\Pi_f$. Comparing it with ... More

Whittaker rational structures and special values of the Asai $L$-functionAug 08 2014Nov 27 2014Let $F$ be a totally real number field and $E/F$ a totally imaginary quadratic extension of $F$. Let $\Pi$ be a cohomological, conjugate self-dual cuspidal automorphic representation of $GL_n(\mathbb A_E)$. Under a certain non-vanishing condition we relate ... More

Deligne's conjecture for automorphic motives over CM-fields, Part I: factorizationFeb 08 2018This is the first of two papers devoted to the relations between Deligne's conjecture on critical values of motivic $L$-functions and the multiplicative relations between periods of arithmetically normalized automorphic forms on unitary groups. The present ... More

On some arithmetic properties of automorphic forms of GL(m) over a division algebraFeb 09 2011Dec 26 2013In this paper we investigate arithmetic properties of automorphic forms on the group G' = GL_m/D, for a central division-algebra D over an arbitrary number field F. The results of this article are generalizations of results in the split case, i.e., D=F, ... More

On the Eisenstein cohomology of odd orthogonal groupsApr 16 2009Jun 06 2011The paper investigates a significant part of the automorphic, in fact of the so-called Eisenstein cohomology of split odd orthogonal groups over Q. The main result provides a description of residual and regular Eisenstein cohomology classes for maximal ... More

Quark Mass Hierarchies, Flavor Mixing and Maximal CP-ViolationJun 16 1998Flavor mixing and the quark mass spectrum are intimately related. In view of the observed strong hierarchy of the quark and lepton masses and of the flavor mixing angles it is argued that the description of flavor mixing must take this into account. One ... More

Flavor Mixing and the Masses of Quarks and LeptonsJun 04 1997A simple breaking of the subnuclear democracy of the quarks leads to a mixing between the second and the third family, in agrement with observation. Introducing the mixing between the first and the second family, one finds an interesting pattern of maximal ... More

Mass Hierarchies, Hidden Symmetry and Maximal CP-ViolationJul 30 1998In view of the observed strong hierarchy of the quark and lepton masses and of the flavor mixing angles it is argued that the description of flavor mixing must take this into account. One particular interesting way to describe the flavor mixing, which, ... More

Flavor Mixing, CP-Violation and the Masses ov the Light QuarksSep 10 1997Sep 15 1997The observed hierarchy of the quark masses is interpreted as a signal for an underlying ``subnuclear democracy'' as the relevant symmetry of the quark mass terms. A simple breaking of the symmetry leads to a mixing between the second and the third family, ... More

The Gluonic Decay of the $b$--Quark and tne $η'$--MesonAug 14 1997Sep 15 1997The observed inclusive decay of B-mesons into eta' + X is interpreted as the consequence of the gluonic decay of the b-quark into an s-quark. As a result of the QCD anomaly this decay proceeds partly as the decay b ---> s + eta', similar to b ---> s + ... More

The stellar populations of early-type galaxies in the Fornax clusterJan 12 2000We have measured central line strengths for a magnitude-limited sample of early-type galaxies in the Fornax cluster, comprising 11 elliptical (E) and 11 lenticular (S0) galaxies, more luminous than MB=-17. When compared with single-burst stellar population ... More

The Evolution of an Inhomogeneous UniverseJul 22 2014A refined version of a recently introduced method for analysing the dynamics of an inhomogeneous irrotational dust universe is presented. A fully non-perturbative numerical computation of the time dependence of volume in this framework leads to the following ... More

Technologies for Web and cloud service interaction: a surveyAug 12 2014Mar 09 2015The evolution of Web and service technologies has led to a wide landscape of standards and protocols for interaction between loosely coupled software components. Examples range from Web applications, mashups, apps, and mobile devices to enterprise-grade ... More

Composite Weak Bosons at the LHCMar 26 2012Mar 30 2012In a composite model of the weak bosons the p-wave bosons are studied. The state with the lowest mass is identified with the boson, which might have been detected recently at the LHC. Specific properties of these excited bosons are studied, in particular ... More

On the Use of Skeletons when Learning in Bayesian NetworksJan 16 2013In this paper, we present a heuristic operator which aims at simultaneously optimizing the orientations of all the edges in an intermediate Bayesian network structure during the search process. This is done by alternating between the space of directed ... More

Confluence by Decreasing Diagrams -- FormalizedOct 01 2012Apr 11 2013This paper presents a formalization of decreasing diagrams in the theorem prover Isabelle. It discusses mechanical proofs showing that any locally decreasing abstract rewrite system is confluent. The valley and the conversion version of decreasing diagrams ... More

Edge Effects on Local Statistics in Lattice Dimers: A Study of the Aztec Diamond (Finite Case)Jul 22 2000We compute the probability of any local pattern at an arbitrary position in a random dimer configuration in a square grid with an Aztec-diamond boundary.

On the square-free sieveSep 05 2003Oct 01 2004We improve on the best available bounds for the square-free sieve and provide a general framework for its applicability. The failure of the local-to-global principle allows us to obtain results better than those reached by a classical sieve-based approach. ... More

The Pattern of Quark Masses and Maximal CP-ViolationJan 17 1995A simple breaking of the subnuclear democracy of the quarks leads to a mixing between the secons and the third family, in agreement with observation. Introducing the mixing between the first and the second family, one finds an interesting pattern of maximal ... More

The Large Mixing of the Pseudoscalars in QCD and Large Flavor Mixing of NeutrinosOct 19 1998In analogy to the mixing pattern of the pseudoscalar mesons in QCD we discuss the mixing of massive neutrinos. Unlike the quarks flavor mixing angles the leptonic mixing angles are large, nearly maximal. The three massive neutrinos are nearly degenerate. ... More

The Symmetry and the Problem of Mass GenerationMar 05 1997The mass problem in particle physics and its impact for other fields is discussed. While the problem of the nuclear masses has been resolved within the QCD framework, many parameters of the ``Standard Model'' are related to the fermion sector. The origin ... More

Gauge invariant operators in field theories on non-commutative spacesJan 21 2002We review some selected aspects of the construction of gauge invariant operators in field theories on non-commutative spaces and their relation to the energy momentum tensor as well as to the non-commutative loop equations.

Isospin Mass Differences of Heavy BaryonsNov 04 2008We discuss the mass differences for isospin multiplets of the charmed and b-flavored baryons. The mass of the neutral b-flavored sigma baryon, which is not measured, is calculated. We point out, that the measurements of the mass differences between the ... More

The Spin Structure of the Constituent Quarks and of the NucleonMar 31 2005We define a constituent quark within QCD. It is shown that the spin of such a quark and hence also the spin of the nucleon reduced due to $\bar{q}q$-pairs, in agreement with experiment. A solution to the spin problem is given.

The Physics of Flavor - Challenge for the FutureJul 06 2004This is the summary talk for the theoretical part of ICFP03. The contents of the talk are reviewed and a general outlook is given.

Excited Weak Bosons and Dark MatterJul 10 2016The weak bosons are bound states of new constituents, the haplons. The p-wave excitations are studied. The state with the lowest mass is identified with the boson, which has been discovered at the LHC. Specific properties of the excited bosons are discussed, ... More

Does the QCD Scale vary in time?Jul 06 2004Last year I talked at this meeting about a possible time dependence of the QCD coupling constant $\alpha_s$. This year I shall look into the problem once more, without fully repeating the arguments given last year. Astrophysical indications that the fine ... More

More on Wilson loops for two touching circlesMay 03 2019We calculate both at leading weak and strong coupling the renormalised Maldacena-Wilson loop for contours formed by consecutive passage of two touching circles. At the touching point both circles should have the same normal direction but form cusps of ... More

More on Wilson loops for two touching circlesMay 03 2019May 15 2019We calculate both at leading weak and strong coupling the renormalised Maldacena-Wilson loop for contours formed by consecutive passage of two touching circles. At the touching point both circles should have the same normal direction but form cusps of ... More

Root numbers and the parity problemMay 30 2003Let E be a one-parameter family of elliptic curves over a number field. It is natural to expect the average root number of the curves in the family to be zero. All known counterexamples to this folk conjecture occur for families obeying a certain degeneracy ... More

Stationary Point Sets: Convex Quadratic Optimization is Universal in Nonlinear OptimizationOct 25 2012Nov 04 2013We investigate the local topological structure, stationary point sets in parametric optimization genericly may have. Our main result states that, up to stratified isomorphism, any such structure is already present in the small subclass of parametric problems ... More

CP Violation and the Light Quark SectorSep 09 1999In view of the observed strong hierarchy of quark masses, we discuss a new description of flavor mixing which is particularly suited for models of quark mass matrices based on flavor symmetries. The necessary and sufficient conditions for CP violation ... More

Flavour Mixing and Fermion Mass Generation as a Result of Symmetry BreakingMay 30 1994It is shown that a simple breaking of the subnuclear democracy leads to a successful description of the mixing between the second and third family. In the lepton channel the $\nu _{\mu } - \nu_{\tau }$ oscillations are expected to be described by a mixing ... More

On the logarithmic divergent part of entanglement entropy, smooth versus singular regionsAug 17 2016Aug 23 2016The entanglement entropy for smooth regions $\cal A$ has a logarithmic divergent contribution with a shape dependent coefficient and that for regions with conical singularities an additional $\log ^2$ term. Comparing the coefficient of this extra term, ... More

Towards finiteness without supersymmetryMar 26 1993Some aspects of finite quantum field theories in 3+1 dimensions are discussed. A model with non--supersymmetric particle content and vanishing one-- and two--loop beta functions for the gauge coupling and one--loop beta functions for Yukawa--couplings ... More

A comment on ``On Non-Abelian Duality'' by Enrique Álvarez, Luis Álvarez-Gaumé and Yolanda LozanoSep 14 1994The paper commented upon gives the impression that whether the gauged version of a sigma model gives rise to the original or the dual model depends on the choice of gauge fixing. It is demonstrated here that this is not so.

SAT Techniques for Lexicographic Path OrdersMay 05 2006This seminar report is concerned with expressing LPO-termination of term rewrite systems as a satisfiability problem in propositional logic. After relevant algorithms are explained, experimental results are reported.

A Time Dependence of QCDNov 30 2004From astrophysics there are indications that the finestructure constant $\alpha $ has changed during the past 10 billion years. Within grand unification one can deduce that also the QCD scale has changed. Tests for a time variation of this scale are described. ... More

Quantum cohomology of Grassmannians modulo symmetriesNov 04 2002The quantum cohomology of Grassmannians exhibits two symmetries related to the quantum product, namely a \Bbb {Z}/n action and an involution related to complex conjugation. We construct a new ring by dividing out these symmetries in an ideal theoretic ... More

An Involution on the Quantum Cohomology Ring of the GrassmannianMay 24 2002For a Fano manifold M, complex conjugation defines a real involution on the quantum cohomology ring. For the Grassmannian we identify this involution with an explicit transformation on Schubert classes defined over the integers. It is a composition of ... More

The Quark Mass Problem and CP-ViolationMay 24 1996A simple breaking of the subnuclear democracy among the quarks leads to a mixing between the second and the third family, in agreement with observation. Introducing the mixing between the first and the second family, one finds an interesting pattern of ... More

Quark Mass Hierarchy and Flavor MixingFeb 27 1998In view of the observed strong hierarchy of the quark and lepton masses and of the flavor mixing angles it is argued that the description of flavor mixing must take this into account. One particular interesting way to describe the flavor mixing, which, ... More

The Kinematics and Dynamics of Flavor MixingOct 20 1997In view of the observed strong hierarchy of the quark and lepton masses and of the flavor mixing angles, it is argued that the description of flavor mixing must take this into account. One particularly interesting way to describe the flavor mixing, which, ... More

Improved approximations of Poissonian errors for high confidence levelsJan 15 2003We present improved numerical approximations to the exact Poissonian confidence limits for small numbers n of observed events following the approach of Gehrels (1986). Analytic descriptions of all parameters used in the approximations are provided to ... More

Weight systems for toric Calabi-Yau varieties and reflexivity of Newton polyhedraMar 07 1996According to a recently proposed scheme for the classification of reflexive polyhedra, weight systems of a certain type play a prominent role. These weight systems are classified for the cases $n=3$ and $n=4$, corresponding to toric varieties with K3 ... More

Renormalization Group Flow in a General Gauge TheoryJul 15 1994The renormalization group flow in a general renormalizable gauge theory with a simple gauge group in 3+1 dimensions is analyzed. The flow of the ratios of the Yukawa couplings and the gauge coupling is described in terms of a bounded potential, which ... More

Reflexive Polyhedra and their Applications in String and F-theoryFeb 29 2000This is an informal introduction to the concept of reflexive polyhedra and some of their most important applications in perturbative and non-perturbative string physics. Following the historical development, topics like mirror symmetry, gauged linear ... More

String Dualities and Toric Geometry: An IntroductionJun 07 1998This note is supposed to be an introduction to those concepts of toric geometry that are necessary to understand applications in the context of string and F-theory dualities. The presentation is based on the definition of a toric variety in terms of homogeneous ... More

Line-of-sight velocity distribution corrections for Lick/IDS indices of early-type galaxiesJul 12 2004We investigate line-of-sight velocity distribution (LOSVD) corrections for absorption line-strength indices of early-type galaxies in the Lick/IDS system. This system is often used to estimate basic stellar population parameters such as luminosity weighted ... More

Order conditions for exponential integratorsFeb 28 2019This paper provides an algebraic framework for the generation of order conditions for the construction of exponential integrators like splitting and Magnus-type methods for the numerical solution of evolution equations. The generation of order conditions ... More

Flavor Mixing and Neutrino MassesMar 26 2015Jul 28 2015We discuss mass matrices with four texture zeros for the quarks and leptons. The three mixing angles for the quarks and leptons are functions of the fermion masses. The results agree with the experimental data. The ratio of the masses of the first two ... More

Cosmic Acceleration as an Optical IllusionAug 06 2015Sep 29 2016We consider light propagation in an inhomogeneous irrotational dust universe with vanishing cosmological constant, with initial conditions as in standard linear perturbation theory. A non-perturbative approach to the dynamics of such a universe is combined ... More

Inhomogeneity implies Accelerated ExpansionOct 03 2013Jan 27 2014The Einstein equations for an inhomogeneous irrotational dust universe are analysed. A set of mild assumptions, all of which are shared by the standard FLRW type scenarios, results in a model that depends only on the distribution of scalar spatial curvature. ... More

Composite Weak Bosons at the Large Hadron ColliderJul 24 2013In a composite model of the weak bosons the excited bosons, in particular the p-wave bosons, are studied. The state with the lowest mass is identified with the boson, which has been discovered recently at the "Large Hadron Collider" at CERN. Specific ... More

On Wilson loops for two touching circles with opposite orientationNov 02 2018Jan 07 2019We study the Wilson loops for contours formed by a consecutive passage of two touching circles with a common tangent, but opposite orientation. The calculations are performed in lowest nontrivial order for ${\cal N}=4$ SYM at weak and strong coupling ... More

On the logarithmic divergent part of entanglement entropy, smooth versus singular regionsAug 17 2016Nov 01 2016The entanglement entropy for smooth regions $\cal A$ has a logarithmic divergent contribution with a shape dependent coefficient and that for regions with conical singularities an additional $\log ^2$ term. Comparing the coefficient of this extra term, ... More

Towards a Numerical Unitarity Approach for Two-loop Amplitudes in QCDJul 04 2016Mar 24 2017The numerical unitarity approach has been important for obtaining reliable QCD predictions for the LHC. Here I discuss the extension of the approach beyond the leading quantum corrections for computing multi-loop amplitudes. The numerical unitarity approach ... More

Holographic entanglement entropy for hollow cones and banana shaped regionsFeb 22 2016Jun 10 2016We consider banana shaped regions as examples of compact regions, whose boundary has two conical singularities. Their regularised holographic entropy is calculated with all divergent as well as finite terms. The coefficient of the squared logarithmic ... More

Lepton Mixing and the Neutrino Mixing Angle theta_13Mar 20 2012We discuss the neutrino oscillations, using texture zero mass matrices for the leptons, including radiative correction. The neutrino mixing angle theta_13 is calculated and agrees with the result of the new Daya Bay experiment.

Why is the Legendre Transformation Involutive?Sep 27 2012The question posed in the title is answered in terms of a simple pictorial argument that is manifestly symmetric between the two functions that are Legendre transform of each other.

Composite Weak BosonsOct 07 2010Nov 04 2010The weak bosons, leptons and quarks are considered as composite particles. The interaction of the constituents is a confining gauge interaction. The standard electroweak model is a low energy approximation. The mixing of the neutral weak boson with the ... More

Traffic Load Uniformity in Optical Packet Switched NetworksJun 23 2019A crucial issue in Optical Packet Switched (OPS) networks is packet loss due to contentions. In this paper we study how traffic load uniformity influences the packet loss in a single OPS node. Traffic load uniformity is a measure of the load asymmetry ... More

Collaborative Filtering via High-Dimensional RegressionApr 30 2019While the SLIM approach obtained high ranking-accuracy in many experiments in the literature, it is also known for its high computational cost of learning its parameters from data. For this reason, we focus in this paper on variants of high-dimensional ... More

The Fundamental Constants in Physics and their Time DependenceFeb 01 2008Oct 24 2016We discuss the fundamemtal constants in the Standard Model of particle physics, in particular possible changes of these constants on the cosmological time scale. The Grand Unification of the observed strong, electromagnetic and weak interactions implies ... More

The Problem of Mass and Mass GenerationMay 14 1996The mass problem in particle physics for other fields is discussed. While the problem of the nuclear masses has been resolved within the QCD framework, 3 parameters of the ``Standard Model'' are related to the fermion sector. The origin of the ferion ... More

The Fundamental Constants in Physics and their Time DependenceFeb 01 2008We discuss the fundamemtal constants in the Standard Model of particle physics, in particular possible changes of these constants on the cosmological time scale. The Grand Unification of the observed strong, electromagnetic and weak interactions implies ... More

Quark Mass Hierarchies and Maximal CP--ViolationJan 12 1999It is argued taking into account the observed mass spectra of the leptons and quarks that the phenomenon of flavor mixing is intimately related to the mass spectra. We discuss a particularly interesting way to describe the flavor mixing which is particularly ... More

Lepton-Quark Masses and Democratic SymmetryNov 29 1994It is shown that the simplest breaking of the subnuclear democracy leads to a successful description of the mixing between the second and third family. In the lepton channel the nu_mu - nu_tau -oscillations are expected to be described by a mixing angle ... More

Bound State Solutions of the Dirac Equation in the Extreme Kerr GeometryJul 26 2002Feb 19 2004In this paper we consider bound state solutions, i.e., normalizable time-periodic solutions of the Dirac equation in the exterior region of an extreme Kerr black hole with mass $M$ and angular momentum $J$. It is shown that for each azimuthal quantum ... More

About the Suitability of Clouds in High-Performance ComputingJan 08 2016Cloud computing has become the ubiquitous computing and storage paradigm. It is also attractive for scientists, because they do not have to care any more for their own IT infrastructure, but can outsource it to a Cloud Service Provider of their choice. ... More

A Grammatical Inference Approach to Language-Based Anomaly Detection in XMLJun 25 2013False-positives are a problem in anomaly-based intrusion detection systems. To counter this issue, we discuss anomaly detection for the eXtensible Markup Language (XML) in a language-theoretic view. We argue that many XML-based attacks target the syntactic ... More

An extension of the functional Ito formula under a family of non-dominated measuresDec 06 2012Motivated by questions arising in financial mathematics, Dupire introduced a notion of smoothness for functionals of paths (different from the usual Fr\'echet--Gat\'eaux derivatives) and arrived at a generalization of It\=o's formula applicable to functionals ... More

Strong Conservation Form and Grid Generation in Nonsteady Curvilinear Coordinates for Implicit Radiation Hydrodynamics in 2D and 3DOct 18 2012A generalization of implicit conservative numerics to multiple dimensions requires advanced concepts of tensor analysis and differential geometry and hence a more thorough dedication to mathematical fundamentals than maybe expected at first glance. Hence ... More

Embarrassingly Shallow Autoencoders for Sparse DataMay 08 2019Combining simple elements from the literature, we define a linear model that is geared toward sparse data, in particular implicit feedback data for recommender systems. We show that its training objective has a closed-form solution, and discuss the resulting ... More

On Type II Strings in Two DimensionsFeb 21 2005We consider type IIA/B strings in two-dimensions and their projection with respect to the nilpotent space-time supercharge. Based on the ground ring structure, we propose a duality between perturbed type II strings and the topological B-model on deformed ... More

Gravitational F-terms of N=1 Supersymmetric SU(N) Gauge TheoriesSep 03 2003Jan 16 2004We use the generalized Konishi anomaly equations and R-symmetry anomaly to compute the exact perturbative and non-perturbative gravitational F-terms of four-dimensional N=1 supersymmetric gauge theories. We formulate the general procedure for computation ... More

Perturbative Computation of Glueball Superpotentials for SO(N) and USp(N)Nov 27 2002We use the superspace method of hep-th/0211017 to prove the matrix model conjecture for N=1 USp(N) and SO(N) gauge theories in four dimensions. We derive the prescription to relate the matrix model to the field theory computations. We perform an explicit ... More

A pedestrian approach to the high energy limits of branes and other gravitational systemsJul 13 2000In this article we study limits of models that contain a dimensionful parameter such as the mass of the relativistic point-particle. The limits are analogous to the massless limit of the particle and may be thought of as high energy limits. We present ... More

An anchoring transition at surfaces with grafted liquid-crystalline chain moleculesMar 25 2002The anchoring of nematic liquid crystals on surfaces with grafted liquid crystalline chain molecules is studied by computer simulations and within a mean field approach. The computer simulations show that a swollen layer of collectively tilted chains ... More

Surface anchoring on layers of grafted liquid-crystalline chain molecules: A computer simulationMay 15 2002By Monte Carlo simulations of a soft ellipsoid model for liquid crystals, we study whether a layer of grafted liquid-crystalline chain molecules can induce tilt in a nematic fluid. The chains are fairly short (four monomers) and made of the same particles ... More

Conformal boundary and geodesics for $AdS_5\times S^5$ and the plane wave: Their approach in the Penrose limitFeb 19 2003Mar 05 2003Projecting on a suitable subset of coordinates, a picture is constructed in which the conformal boundary of $AdS_5\times S^5$ and that of the plane wave resulting in the Penrose limit are located at the same line. In a second line of arguments all $AdS_5\times ... More

Persistence of Kardar-Parisi-Zhang InterfacesSep 17 1998The probabilities $P_\pm(t_0,t)$ that a growing Kardar-Parisi-Zhang interface remains above or below the mean height in the time interval $(t_0, t)$ are shown numerically to decay as $P_\pm \sim (t_0/t)^{\theta_\pm}$ with $\theta_+ = 1.18 \pm 0.08$ and ... More

On Open String Sigma-Model and Noncommutative Gauge FieldsDec 08 1999Dec 14 1999We consider the ordinary and noncommutative Dirac-Born-Infeld theories within the open string sigma-model. First, we propose a renormalization scheme, hybrid point splitting regularization, that leads directly to the Seiberg-Witten description including ... More

String Field Theory and the Fuzzy SphereJun 20 2001Jul 16 2001We use boundary string field theory to study open string tachyon condensation on a three-sphere closed string background. We consider the closed string background described by $SU(2)_k$ WZW model in the limit of large $k$. We compute the exact tachyon ... More

Supergravity and D-branes Wrapping Supersymmetric 3-CyclesNov 30 2000Dec 13 2000We construct dual supergravity descriptions of D3-branes wrapping associative 3-cycles $L$. We analyse the conditions for having five-dimensional background solutions of the form $AdS_2 \times L$ and show that they require $L$ to be of constant negative ... More

An improved sieve of EratosthenesDec 25 2017Feb 28 2019We show how to carry out a sieve of Eratosthenes up to N in space O(N^{1/3} (log N)^{2/3}) and time O(N log N). These bounds constitute an improvement over the usual versions of the sieve, which take space about O(sqrt{N}) and time at least linear on ... More

Complete classification of reflexive polyhedra in four dimensionsFeb 28 2000Four dimensional reflexive polyhedra encode the data for smooth Calabi-Yau threefolds that are hypersurfaces in toric varieties, and have important applications both in perturbative and in non-perturbative string theory. We describe how we obtained all ... More

On the fixed point equation of a solvable 4D QFT modelMay 19 2015The regularisation of the $\lambda\phi^4_4$-model on noncommutative Moyal space gives rise to a solvable QFT model in which all correlation functions are expressed in terms of the solution of a fixed point problem. We prove that the non-linear operator ... More

Heavy-tailed random walks, buffered queues and hidden large deviationsJan 27 2017It is well-known that large deviations of random walks driven by independent and identically distributed heavy-tailed random variables are governed by the so-called principle of one large jump. We note that further subtleties hold for such random walks ... More

Fundamental constants and cosmic vacuum: the micro and macro connectionFeb 05 2015Mar 26 2015The idea that the vacuum energy density $\rho_{\Lambda}$ could be time dependent is a most reasonable one in the expanding Universe; in fact, much more reasonable than just a rigid cosmological constant for the entire cosmic history. Being $\rho_{\Lambda}=\rho_{\Lambda}(t)$ ... More

The ternary Goldbach problemApr 08 2014Apr 12 2014The ternary Goldbach conjecture, or three-primes problem, states that every odd number $n$ greater than $5$ can be written as the sum of three primes. The conjecture, posed in 1742, remained unsolved until now, in spite of great progress in the twentieth ... More

Growth in linear algebraic groups and permutation groups: towards a unified perspectiveApr 09 2018Nov 21 2018By now, we have a product theorem in every finite simple group $G$ of Lie type, with the strength of the bound depending only in the rank of $G$. Such theorems have numerous consequences: bounds on the diameters of Cayley graphs, spectral gaps, and so ... More

Proper Semirings and Proper Convex FunctorsFeb 21 2018Feb 24 2018Esik and Maletti introduced the notion of a proper semiring and proved that some important (classes of) semirings -- Noetherian semirings, natural numbers -- are proper. Properness matters as the equivalence problem for weighted automata over a semiring ... More

Quantum Haplodynamics, Dark Matter and Dark EnergyFeb 17 2014Aug 04 2014In quantum haplodynamics (QHD) the weak bosons, quarks and leptons are bound states of fundamental constituents, denoted as haplons. The confinement scale of the associated gauge group SU(2)_h is of the order of $\Lambda_h\simeq 0.3$ TeV. One scalar state ... More

Construction of the Φ^4_4-quantum field theory on noncommutative Moyal spaceFeb 05 2014We review our recent construction of the $\phi^4$-model on four-dimensional Moyal space. A milestone is the exact solution of the quartic matrix model $Z[E,J]=\int d\Phi \exp(tr(J\Phi- E\Phi^2 -(\lambda/4) \Phi^4))$ in terms of the solution of a non-linear ... More