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Learning Sparse Wavelet RepresentationsFeb 08 2018In this work we propose a method for learning wavelet filters directly from data. We accomplish this by framing the discrete wavelet transform as a modified convolutional neural network. We introduce an autoencoder wavelet transform network that is trained ... More

Charm bracelets and their application to the construction of periodic Golay pairsMay 28 2014Apr 06 2015A $k$-ary charm bracelet is an equivalence class of length $n$ strings with the action on the indices by the additive group of the ring of integers modulo $n$ extended by the group of units. By applying an $O(n^3)$ amortized time algorithm to generate ... More

Long-Range Correlations in Self-Gravitating N-Body SystemsJan 29 2002Observed self-gravitating systems reveal often fragmented non-equilibrium structures that feature characteristic long-range correlations. However, models accounting for non-linear structure growth are not always consistent with observations and a better ... More

Lumpy Structures in Self-Gravitating DisksMay 29 2001Following Toomre & Kalnajs (1991), local models of slightly dissipative self-gravitating disks show how inhomogeneous structures can be maintained over several galaxy rotations. Their basic physical ingredients are self-gravity, dissipation and differential ... More

Natural symmetric tensor normsFeb 22 2010Dec 14 2010In the spirit of the work of Grothendieck, we introduce and study natural symmetric n-fold tensor norms. We prove that there are exactly six natural symmetric tensor norms for $n\ge 3$, a noteworthy difference with the 2-fold case in which there are four. ... More

Equilateral Non-Gaussianity and New Physics on the HorizonFeb 25 2011Mar 23 2011We examine the effective theory of single-field inflation in the limit where the scalar perturbations propagate with a small speed of sound. In this case the non-linearly realized time-translation symmetry of the Lagrangian implies large interactions, ... More

Formalizing and Checking Thread Refinement for Data-Race-Free Execution Models (Extended Version)Oct 24 2015When optimizing a thread in a concurrent program (either done manually or by the compiler), it must be guaranteed that the resulting thread is a refinement of the original thread. Most theories of valid optimizations are formulated in terms of valid syntactic ... More

The symmetric Radon-Nikodým property for tensor normsMay 15 2010We introduce the symmetric-Radon-Nikod\'ym property (sRN property) for finitely generated s-tensor norms $\beta$ of order $n$ and prove a Lewis type theorem for s-tensor norms with this property. As a consequence, if $\beta$ is a projective s-tensor norm ... More

Signatures of Supersymmetry from the Early UniverseSep 01 2011Oct 11 2011Supersymmetry plays a fundamental role in the radiative stability of many inflationary models. Spontaneous breaking of the symmetry inevitably leads to fields with masses of order the Hubble scale during inflation. When these fields couple to the inflaton ... More

Desensitizing Inflation from the Planck ScaleApr 21 2010A new mechanism to control Planck-scale corrections to the inflationary eta parameter is proposed. A common approach to the eta problem is to impose a shift symmetry on the inflaton field. However, this symmetry has to remain unbroken by Planck-scale ... More

Inflating with BaryonsSep 15 2010We present a field theory solution to the eta problem. By making the inflaton field the phase of a baryon of SU(N_c) supersymmetric Yang-Mills theory we show that all operators that usually spoil the flatness of the inflationary potential are absent. ... More

Supergravity for Effective TheoriesSep 01 2011Higher-derivative operators are central elements of any effective field theory. In supersymmetric theories, these operators include terms with derivatives in the K\"ahler potential. We develop a toolkit for coupling such supersymmetric effective field ... More

Scaling Laws in Self-Gravitating DisksApr 16 1999The interstellar medium (ISM) reveals strongly inhomogeneous structures at every scale. These structures do not seem completely random since they obey certain power laws. Larson's law (\citeyear{Larson81}) $\sigma \propto R^{\delta}$ and the plausible ... More

Casimir force in O(n) lattice models with a diffuse interfaceJun 23 2008On the example of the spherical model we study, as a function of the temperature $T$, the behavior of the Casimir force in O(n) systems with a diffuse interface and slab geometry $\infty^{d-1}\times L$, where $2<d<4$ is the dimensionality of the system. ... More

Fragmentation in Kinematically Cold DisksJan 16 2001Gravity is scale free. Thus gravity may form similar structures in self-gravitating systems on different scales. Indeed, observations of the interstellar medium, spiral disks and cosmic structures, reveal similar characteristics. The structures in these ... More

Extending polynomials in maximal and minimal idealsOct 20 2009Feb 08 2010Given an homogeneous polynomial on a Banach space $E$ belonging to some maximal or minimal polynomial ideal, we consider its iterated extension to an ultrapower of $E$ and prove that this extension remains in the ideal and has the same ideal norm. As ... More

Unconditionality in tensor products and ideals of polynomials, multilinear forms and operatorsJun 17 2009Feb 08 2010We study tensor norms that destroy unconditionality in the following sense: for every Banach space $E$ with unconditional basis, the $n$-fold tensor product of $E$ (with the corresponding tensor norm) does not have unconditional basis. We establish an ... More

A Field Range Bound for General Single-Field InflationNov 13 2011We explore the consequences of a detection of primordial tensor fluctuations for general single-field models of inflation. Using the effective theory of inflation, we propose a generalization of the Lyth bound. Our bound applies to all single-field models ... More

Five basic lemmas for symmetric tensor products of normed spacesMay 18 2011We give the symmetric version of five lemmas which are essential for the theory of tensor products (and norms). These are: the approximation, extension, embedding, density and local technique lemmas. Some application of these tools to the metric theory ... More

A note on some fiber-integralsDec 22 2015We remark that the study of a fiber-integral of the type F (s) := f =s ($\omega$/df) $\land$ ($\omega$/df) either in the local case where $\rho$ $\not\equiv$ 1 around 0 is C $\infty$ and compactly supported near the origin which is a singular point of ... More

Quasi-proper meromorphic equivalence relationsJun 02 2010The aim of this article is to complete results of [M.00] and [B.08] and to show that they imply a rather general existence theorem for meromorphic quotient of strongly quasi-proper meromorphic equivalence relations. In this context, generic equivalence ... More

A finiteness theorem for \ $S-$relative formal Brieskorn modulesJul 17 2012Mar 01 2014We give a general result of finiteness for holomorphic families of Brieskorn modules constructed from a holomorphic family of one parameter degeneration of compact complex manifolds acquiring (general) singularities.

Asymptotics of a vanishing period : the quotient themes of a given frescoJan 20 2011In this paper we introduce the word "fresco" to denote a $[\lambda]-$primitive monogenic geometric (a,b)-module. The study of this "basic object" (generalized Brieskorn module with one generator) which corresponds to the minimal filtered (regular) differential ... More

Sur certaines singularites non isolees d'hypersurfaces IMay 19 2005Jan 09 2006The aim of this fisrt part is to introduce, for a rather large class of hypersurface singularities with 1 dimensionnal locus, the analog of the Brieskorn lattice at the origin (the singular point of the singular locus). The main results are the finitness ... More

Design, Evaluation and Analysis of Combinatorial Optimization Heuristic AlgorithmsJul 07 2012Combinatorial optimization is widely applied in a number of areas nowadays. Unfortunately, many combinatorial optimization problems are NP-hard which usually means that they are unsolvable in practice. However, it is often unnecessary to have an exact ... More

Quantifying Residual Finiteness of Linear GroupsFeb 15 2016Feb 27 2016Normal residual finiteness growth measures how well a finitely generated group is approximated by its finite quotients. We show that any linear group $\Gamma \leq \mathrm{GL}_d(K)$ has normal residual finiteness growth asymptotically bounded above by ... More

The matrix Lie algebra on a one-step ladder is zero product determinedOct 17 2015Dec 03 2015The class of matrix algebras on a ladder $\mathcal{L}$ generalizes the class of block upper triangular matrix algebras. It was previously shown that the matrix algebra on a ladder $\mathcal{L}$ is zero product determined under matrix multiplication. In ... More

$\mathfrak{sl}_n$-webs, categorification and Khovanov-Rozansky homologiesApr 23 2014Jul 21 2014In this paper we define an explicit basis for the $\mathfrak{sl}_n$-web algebra $H_n(\vec{k})$, the $\mathfrak{sl}_n$ generalization of Khovanov's arc algebra $H_{2}(m)$, using categorified $q$-skew Howe duality. Our construction is a $\mathfrak{sl}_n$-web ... More

$\mathfrak{sl}_3$-web bases, intermediate crystal bases and categorificationOct 10 2013Mar 05 2014We give an explicit graded cellular basis of the $\mathfrak{sl}_3$-web algebra $K_S$. In order to do this, we identify Kuperberg's basis for the $\mathfrak{sl}_3$-web space $W_S$ with a version of Leclerc-Toffin's intermediate crystal basis and we identify ... More

Virtual Khovanov homology using cobordismsNov 02 2011Sep 02 2014We extend Bar-Natan's cobordism based categorification of the Jones polynomial to virtual links. Our topological complex allows a direct extension of the classical Khovanov complex ($h=t=0$), the variant of Lee ($h=0,t=1$) and other classical link homologies. ... More

Categorification and applications in topology and representation theoryJul 03 2013This thesis splits into two major parts. The connection between the two parts is the notion of "categorification" which we shortly explain/recall in the introduction. In the first part of this thesis we extend Bar-Natan's cobordism based categorification ... More

Asteroseismology of Cool StarsNov 04 2014The measurement of oscillations excited by surface convection is a powerful method to study the structure and evolution of cool stars. CoRoT and Kepler have initiated a revolution in asteroseismology by detecting oscillations in thousands of stars from ... More

Fault-Tolerant Quantum ComputationJan 16 2007Aug 30 2007I give a brief overview of fault-tolerant quantum computation, with an emphasis on recent work and open questions.

Overconvergent F-isocrystals and differential overcoherenceNov 03 2006Let $\mathcal{V}$ be a mixed characteristic complete discrete valuation ring, $k$ its residual field, $\mathcal{P}$ a proper smooth formal scheme over $\mathcal{V}$, $P$ its special fiber, $T$ a divisor of $P$, $U:=P\setminus T$, $Y$ a smooth closed subscheme ... More

On the stability of the overconvergence under the direct image by a proper smooth morphismNov 28 2008Oct 05 2012Up to a translation in the language of arithmetic $\D$-modules, we prove a conjecture of Berthelot on the preservation of the overconvergence under the direct image by a smooth proper morphism of varieties over a perfect field of characteristic $p>0$. ... More

Sur la compatibilité à Frobenius de l'isomorphisme de dualité relativeSep 20 2005Jan 26 2009Let $\V$ be a mixed characteristic complete discrete valuation ring, let $\X$ and $\Y$ be two smooth formal $\V$-schemes, let $f_0$ : $X \to Y$ be a projective morphism between their special fibers, let $T$ be a divisor of $Y$ such that $T_X := f_0 ^{-1} ... More

Universal 2-local Hamiltonian Quantum ComputingFeb 02 2010Nov 21 2011We present a Hamiltonian quantum computation scheme universal for quantum computation (BQP). Our Hamiltonian is a sum of a polynomial number (in the number of gates L in the quantum circuit) of time-independent, constant-norm, 2-local qubit-qubit interaction ... More

Complex bounds for multimodal maps: bounded combinatoricsSep 19 2000Sep 19 2000We proved the so called complex bounds for multimodal, infinitely renormalizable analytic maps with bounded combinatorics: deep renormalizations have polynomial-like extensions with definite modulus. The complex bounds is the first step to extend the ... More

Overview of TMD evolutionFeb 03 2015Transverse momentum dependent parton distributions (TMDs) appear in many scattering processes at high energy, from the semi-inclusive DIS experiments at a few GeV to the Higgs transverse momentum distribution at the LHC. Predictions for TMD observables ... More

TMD evolution of the Sivers asymmetryApr 19 2013The energy scale dependence of the Sivers asymmetry in semi-inclusive deep inelastic scattering is studied numerically within the framework of TMD factorization that was put forward in 2011. The comparison to previous results in the literature shows that ... More

Transversity AsymmetriesAug 21 2008Ways to access transversity through asymmetry measurements are reviewed. The recent first extraction and possible near future extractions are discussed.

Review of QCD spin physicsMay 27 2003A short review is given of QCD spin physics and its major aims: obtaining the polarized gluon density, the transversity distribution and understanding single spin asymmetries. The importance of the Drell-Yan process, the role of electron-positron colliders ... More

Average transverse momentum quantities approaching the lightfrontSep 29 2014In this contribution to Light Cone 2014, three average transverse momentum quantities are discussed: the Sivers shift, the dijet imbalance, and the $p_T$ broadening. The definitions of these quantities involve integrals over all transverse momenta that ... More

Anomalous Drell-Yan asymmetry from hadronic or QCD vacuum effectsNov 03 2005The anomalously large cos(2 phi) asymmetry measured in the Drell-Yan process is discussed. Possible origins of this large deviation from the Lam-Tung relation are considered with emphasis on the comparison of two particular proposals: one that suggests ... More

Mapping the Transverse Nucleon SpinJun 24 2002Jul 23 2002The transverse nucleon spin can be transferred to the quarks and gluons in several ways. In the factorizing, hard scattering processes to be considered, these are parameterized at leading twist by the transversity distribution function and at next-to-leading ... More

Double transverse spin asymmetries in vector boson productionApr 24 2000Sep 09 2000We investigate a helicity non-flip double transverse spin asymmetry in vector boson production in hadron-hadron scattering, which was first considered by Ralston and Soper at the tree level. It does not involve transversity functions and in principle ... More

Intrinsic transverse momentum and transverse spin asymmetriesMay 13 1999We investigate leading twist transverse momentum dependent origins of transverse spin asymmetries in hadron-hadron collisions. The chiral-odd T-odd distribution function with intrinsic transverse momentum dependence, which would signal an intrinsic handedness ... More

On a theorem of Bombieri, Friedlander and IwaniecAug 01 2011In this article, we show to which extent one can improve a theorem of Bombieri, Friedlander and Iwaniec by using Hooley's variant of the divisor switching technique. We also give an application of the theorem in question, which is a Bombieri-Vinogradov ... More

Composition of Kinetic Momenta: The U_q(sl(2)) caseDec 10 1992Mar 29 1993The tensor products of (restricted and unrestricted) finite dimensional irreducible representations of $\uq$ are considered for $q$ a root of unity. They are decomposed into direct sums of irreducible and/or indecomposable representations.

Nonlinear wave equationsApr 24 2003The analysis of nonlinear wave equations has experienced a dramatic growth in the last ten years or so. The key factor in this has been the transition from linear analysis, first to the study of bilinear and multilinear wave interactions, useful in the ... More

Differentiability of Mather's beta function in low dimensionsSep 18 2009Nov 29 2012Let L be a time-periodic Lagrangian on a two-torus. Then the beta-function of L is differentiable at least in k directions at any k-irrational homology class, for k= 0, 1, 2.

Vertices of Mather's Beta function, IIDec 01 2006If the $\beta$-function of a time-periodic Lagrangian on a manifold $M$ has a vertex at a $k$-irrational homology class $h$, then $2k \leq \dim M$. Furthermore if $\dim M =2$ $h$ is rational.

Analyticity in Hubbard modelsOct 23 1998Feb 11 1999The Hubbard model describes a lattice system of quantum particles with local (on-site) interactions. Its free energy is analytic when \beta t is small, or \beta t^2/U is small; here, \beta is the inverse temperature, U the on-site repulsion and t the ... More

The relation between Feynman cycles and off-diagonal long-range orderMar 31 2006Aug 23 2006The usual order parameter for the Bose-Einstein condensation involves the off-diagonal correlation function of Penrose and Onsager, but an alternative is Feynman's notion of infinite cycles. We present a formula that relates both order parameters. We ... More

A Hsu-Robbins-Erdős strong law in first-passage percolationMay 27 2013Sep 09 2015Large deviations in the context of first-passage percolation was first studied in the early 1980s by Grimmett and Kesten, and has since been revisited in a variety of studies. However, none of these studies provides a precise relation between the existence ... More

Erratum to the paper: Compact hyperkaehler manifolds: basic resultsJun 03 2001This is an Erratum to the paper: Compact hyperkaehler manifolds: basic results. (alg-geom/9705025, Inv. math. 135). We give a correct proof of the projectivity criterion for hyperkaehler manifolds. We use a recent result of Demailly and Paun math.AG/0105176. ... More

A note on the Bloch-Beilinson conjecture for K3 surfaces and spherical objectsSep 22 2010For a projective K3 surface X we introduce the dense triangulated subcategory S^* of the bounded derived category D^b(Coh(X)) of coherent sheaves on X that is generated by spherical objects. For a K3 surface X over \bar Q it is shown that S^* admits a ... More

Chow groups and derived categories of K3 surfacesDec 29 2009This survey is based on my talk at the conference `Classical algebraic geometry today' at the MSRI. Some new results on the action of symplectomorphisms on the Chow group are added.

Charged String-like Solutions of Low-energy Heterotic String TheoryOct 06 1992Two string-like solutions to the equations of motion of the low-energy effective action for the heterotic string are found, each a source of electric and magnetic fields. The first carries an electric current equal to the electric charge per unit length ... More

Vertical flows and a general currential homotopy formulaMay 05 2014We generalize some of the results of Harvey, Lawson and Latschev about transgression formulas. The focus here is on flowing forms via vertical vector fields, especially Morse-Bott-Smale vector fields. We prove a very general transgression formula including ... More

On the hyperbolicity of the Feigenbaum fixed pointJan 11 2003We show the hyperbolicity of the Feigenbaum fixed point using the inflexibility of the Feigenbaum tower, the Man\~e-Sad-Sullivan $\lambda$-Lemma and the existence of parabolic domains (petals) for semi-attractive fixed points.

Parity Types, Cycle Structures and Autotopisms of Latin SquaresMar 01 2012Oct 03 2012The parity type of a Latin square is defined in terms of the numbers of even and odd rows and columns. It is related to an Alon-Tarsi-like conjecture that applies to Latin squares of odd order. Parity types are used to derive upper bounds for the size ... More

Dynamics of warped flux compactifications with backreacting anti-branesFeb 19 2014May 06 2014We revisit the effective low-energy dynamics of the volume modulus in warped flux compactifications with anti-D3-branes in order to analyze the prospects for meta-stable de Sitter vacua and brane inflation along the lines of KKLT/KKLMMT. At the level ... More

Ueber Eigenwerte, Integrale und pi^2/6: Die Idee der Spurformel (On eigenvalues, integrals and pi^2/6: The idea of the trace formula)Nov 02 2007This is an expository article that results from a talk given to second year students at Oldenburg university. The aim of the talk was to show what beautiful and unexpected results may be obtained if one plays with daring analogies in a way that is usually ... More

Iwasawa decompositions of some infinite-dimensional Lie groupsJan 15 2007We set up an abstract framework that allows the investigation of Iwasawa decompositions for involutive infinite-dimensional Lie groups modeled on Banach spaces. As an application, we construct Iwasawa decompositions for classical real or complex Banach-Lie ... More

Factorizations of Elements in Noncommutative Rings: A SurveyJul 27 2015May 30 2016We survey results on factorizations of non zero-divisors into atoms (irreducible elements) in noncommutative rings. The point of view in this survey is motivated by the commutative theory of non-unique factorizations. Topics covered include unique factorization ... More

Acyclic Jacobi DiagramsJul 18 2005Sep 24 2006We propose a simple new combinatorial model to study spaces of acyclic Jacobi diagrams, in which they are identified with algebras of words modulo operations. This provides a starting point for a word-problem type combinatorial investigation of such spaces, ... More

Coherence and decoherence in photon spin-qubit entanglementJan 14 2013Mar 18 2013We study the dynamics of spontaneous generation of coherence and photon spin-qubit entanglement or "flying qubits" in a $\Lambda$ system with non-degenerate lower levels. The cases of entanglement in frequency only and frequency and polarization are compared ... More

Quantum Spinodal DecompositionJan 22 1993We study the process of spinodal decomposition in a scalar quantum field theory that is quenched from an equilibrium disordered initial state at $T_i > T_f$ to a final state at $T_f \approx 0$. The process of formation and growth of correlated domains ... More

Nearly degenerate heavy sterile neutrinos in cascade decay: mixing and oscillationsSep 15 2014Nov 20 2014Some extensions beyond the Standard Model propose the existence of nearly degenerate heavy sterile neutrinos. If kinematically allowed these can be resonantly produced and decay in a cascade to common final states. The common decay channels lead to mixing ... More

On the strength of connectedness of a random hypergraphSep 04 2014Mar 09 2015Bollob\'{a}s and Thomason (1985) proved that for each $k=k(n) \in [1, n-1]$, with high probability, the random graph process, where edges are added to vertex set $V=[n]$ uniformly at random one after another, is such that the stopping time of having minimal ... More

TASI Lectures on InflationJul 30 2009Nov 30 2012In a series of five lectures I review inflationary cosmology. I begin with a description of the initial conditions problems of the Friedmann-Robertson-Walker (FRW) cosmology and then explain how inflation, an early period of accelerated expansion, solves ... More

On the Quantum Origin of Structure in the Inflationary UniverseOct 16 2007In this lecture I give a pedagogical introduction to inflationary cosmology with a special focus on the quantum generation of cosmological perturbations.

Distributed Computing Concepts in D0Oct 16 2003The D0 experiment faces many challenges enabling access to large datasets for physicists on four continents. The new concepts for distributed large scale computing implemented in D0 aim for an optimal use of the available computing resources while minimising ... More

The geometric stability of Voronoi diagrams with respect to small changes of the sitesMar 21 2011Apr 06 2011Voronoi diagrams appear in many areas in science and technology and have numerous applications. They have been the subject of extensive investigation during the last decades. Roughly speaking, they are a certain decomposition of a given space into cells, ... More

On the computation of zone and double zone diagramsAug 14 2012Apr 29 2013Classical objects in computational geometry are defined by explicit relations. A few years ago an interesting family of geometric objects defined by implicit relations was introduced in the pioneering works of T. Asano, J. Matousek and T. Tokuyama. An ... More

QCD renormalization for the top-quark mass in a mass geometrical mean hierarchyApr 13 1992$QCD$ renormalization for the top-quark mass is calculated in a mass geometrical mean hierarchy, $m_d m_b = m_s^2$ and $m_u m_t = m_c^2$. The physical mass, $m_t(m_t) = 160 {\pm} 50 GeV$ is obtained, which agrees very well with electroweak precision measurement. ... More

New bounds on Simonyi's conjectureOct 26 2015We say that a pair $(\mathcal{A},\mathcal{B})$ is a recovering pair if $\mathcal{A}$ and $\mathcal{B}$ are set systems on an $n$ element ground set, such that for every $A,A' \in \mathcal{A}$ and $B,B' \in \mathcal{B}$ we have that ($A \setminus B = A' ... More

Sets of lengths in maximal orders in central simple algebrasJun 04 2013Aug 14 2013Let $\mathcal O$ be a holomorphy ring in a global field $K$, and $R$ a classical maximal $\mathcal O$-order in a central simple algebra over $K$. We study sets of lengths of factorizations of cancellative elements of $R$ into atoms (irreducibles). In ... More

Comments on the floating body and the hyperplane conjectureFeb 13 2011Feb 20 2011We provide a reformulation of the hyperplane conjecture (the slicing problem) in terms of the floating body and give upper and lower bounds on the logarithmic Hausdorff distance between an arbitrary convex body $K\subset \mathbb{R}^{d}$\ and the convex ... More

Sums of squares on reducible real curvesAug 04 2008Mar 08 2009We ask whether every polynomial function that is non-negative on a real algebraic curve can be expressed as a sum of squares in the coordinate ring. Scheiderer has classified all irreducible curves for which this is the case. For reducible curves, we ... More

An iterative algorithm for evaluating approximations to the optimal exercise boundary for a nonlinear Black-Scholes equationOct 28 2007The purpose of this paper is to analyze and compute the early exercise boundary for a class of nonlinear Black--Scholes equations with a nonlinear volatility which can be a function of the second derivative of the option price itself. A motivation for ... More

Modern hierarchical, agglomerative clustering algorithmsSep 12 2011This paper presents algorithms for hierarchical, agglomerative clustering which perform most efficiently in the general-purpose setup that is given in modern standard software. Requirements are: (1) the input data is given by pairwise dissimilarities ... More

Positivity of continuous piecewise polynomialsApr 19 2010Mar 04 2011Real algebraic geometry provides certificates for the positivity of polynomials on semi-algebraic sets by expressing them as a suitable combination of sums of squares and the defining inequalitites. We show how Putinar's theorem for strictly positive ... More

The Seiberg-Witten invariants of manifolds with wells of negative curvatureMay 22 2002We extend the vanishing theorem for the Seiberg-Witten invariants of a manifold with positive scalar curvature to the case when the curvature is allowed to be negative on a set of small volume. (The precise curvature bounds are described in the paper.) ... More

A derivation of the beam equationDec 03 2015The Euler-Bernoulli equation describing the deflection of a beam is a vital tool in structural and mechanical engineering. However, its derivation usually entails a number of intermediate steps that may confuse engineering or science students at the beginnig ... More

Solution of the Dicke model for N=3Apr 09 2013The N=3 Dicke model couples three qubits to a single radiation mode via dipole interaction and constitutes the simplest quantum-optical system allowing for Greenberger-Horne-Zeilinger states. In contrast to the case N=1 (the Rabi model), it is non-integrable ... More

On an order based construction of a groupoid from an inverse semigroupApr 05 2006We present a construction, which assigns two groupoids, $\Gugamma$ and $\Gmgamma$, to an inverse semigroup $\Gamma$. By definition, $\Gmgamma$ is a subgroupoid (even a reduction) of $\Gugamma$. The construction unifies known constructions for groupoids. ... More

On Vaughan's approximation: The first momentAug 28 2015We investigate the first moment of the difference between $\psi(x;q,a)$ and Vaughan's approximation, in a certain range of $q$. We show that this last approximation is significantly more precise than the classical $x/\phi(q)$, and that it captures the ... More

On the non-vanishing of Dirichlet $L$-functions at the central pointMar 27 2014We investigate the consequences of natural conjectures of Montgomery type on the non-vanishing of Dirichlet $L$-functions at the central point. We first justify these conjectures using probabilistic arguments. We then show using a result of Bombieri, ... More

Highly biased prime number racesOct 25 2012Oct 28 2012Chebyshev observed in a letter to Fuss that there tends to be more primes of the form $4n+3$ than of the form $4n+1$. The general phenomenon, which is referred to as Chebyshev's bias, is that primes tend to be biased in their distribution among the different ... More

Tuner: a tool for designing and optimizing ion optical systemsSep 29 2011Designing and optimizing ion optical systems is often a complex and difficult task, which requires the use of computational tools to iterate and converge towards the desired characteristics and performances of the system. Very often these tools are not ... More

Recombination of H and He in Yang-Mills GravityOct 31 2014Jun 26 2015We investigate some aspects of the thermal history of the early universe according to Yang-Mills Gravity (YMG); a gauge theory of gravity set in flat spacetime. Specifically, equations for the ionization fractions of hydrogen and singly ionized helium ... More

Proof of the cases $p \leq 7$ of the Lieb-Seiringer formulation of the Bessis-Moussa-Villani conjectureFeb 08 2007Mar 13 2007It is shown that the polynomial $\lambda(t) = {\rm Tr}[(A + tB)^p]$ has nonnegative coefficients when $p \leq 7$ and A and B are any two complex positive semidefinite $n \times n$ matrices with arbitrary $n$. This proofs a general nontrivial case of the ... More

Uniformly hyperbolic attractor of the Smale-Williams type for a Poincaré map in the Kuznetsov systemJun 03 2010We propose a general algorithm for computer assisted verification of uniform hyperbolicity for maps which exhibit a robust attractor. The method has been successfully applied to a Poincare map for a system of coupled non-autonomous van der Pol oscillators. ... More

Generalized Qualitative Probability: Savage RevisitedAug 07 2014Preferences among acts are analyzed in the style of L. Savage, but as partially ordered. The rationality postulates considered are weaker than Savage's on three counts. The Sure Thing Principle is derived in this setting. The postulates are shown to lead ... More

Generalized Qualitative Probability: Savage revisitedFeb 20 2002Preferences among acts are analyzed in the style of L. Savage, but as partially ordered. The rationality postulates considered are weaker than Savage's on three counts. The Sure Thing Principle is derived in this setting. The postulates are shown to lead ... More

A note on Darwiche and PearlFeb 18 2002It is shown that Darwiche and Pearl's postulates imply an interesting property, not noticed by the authors.

Another perspective on Default ReasoningMar 01 2002The lexicographic closure of any given finite set D of normal defaults is defined. A conditional assertion "if a then b" is in this lexicographic closure if, given the defaults D and the fact a, one would conclude b. The lexicographic closure is essentially ... More

Two-spinor geometry and gauge freedomApr 20 2014Jul 01 2014Gauge freedom in quantum particle physics is shown to arise in a natural way from the geometry of two-spinors (Weyl spinors). Various related mathematical notions are reviewed, and a special ansatz of the kind "the system defines the geometry" is discussed ... More