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Laue three dimensional neutron diffractionFeb 08 2019This article presents a measurement technique and data analysis tool to perform 3D grain distribution mapping and indexing of oligocrystalline samples using neutrons: Laue three-dimensional neutron diffraction (Laue3DND). The approach builds on forward ... More

On hitting times of the winding processes of planar Brownian motion and of Ornstein-Uhlenbeck processes, via Bougerol's identityJul 27 2010May 31 2011Some identities in law in terms of planar complex valued Ornstein-Uhlenbeck processes $(Z_{t}=X_{t}+iY_{t},t\geq0)$ including planar Brownian motion are established and shown to be equivalent to the well known Bougerol identity for linear Brownian motion:$(\beta_{t},t\geq0)$: ... More

Chern-Simons theory, analytic continuation and arithmeticNov 12 2007Oct 27 2008The purpose of the paper is to introduce some conjectures regarding the analytic continuation and the arithmetic properties of quantum invariants of knotted objects. More precisely, we package the perturbative and nonperturbative invariants of knots and ... More

Windings of planar processes and applications to the pricing of Asian optionsOct 22 2016Motivated by a common Mathematical Finance topic, this paper surveys several results concerning windings of 2-dimensional processes, including planar Brownian motion, complex-valued Ornstein-Uhlenbeck processes and planar stable processes. In particular, ... More

Applications of the lantern identityAug 19 1997The purpose of this note is to unify the role of the lantern identity in the proof of several finiteness theorems. In particular, we show that for every nonnegative integer m, the vector space (over the rationals) of type m (resp. T-type m) invariants ... More

On the windings of complex-valued Ornstein-Uhlenbeck processes driven by a Brownian motion and by a Stable processSep 18 2012Dec 23 2014We deal with a complex-valued Ornstein-Uhlenbeck (OU) process with parameter $\lambda\in\mathbb{R}$starting from a point different from 0 and the way that it winds around the origin.The starting point of this paper is the skew product representation for ... More

Bulk Fermions in Multi-Brane WorldsMar 22 2001Apr 01 2001We study bulk fermion fields in various multi-brane models with localized gravity. The chiral zero mode that these models support can be identified as a right-handed sterile neutrino. In this case small neutrino Dirac masses can naturally appear due to ... More

Frequency generation by a magnetic vortex-antivortex dipole in spin-polarized currentMar 05 2012A vortex-antivortex (VA) dipole may be generated due to a spin-polarized current flowing through a nano-aperture in a magnetic element. We study the vortex dipole dynamics using the Landau-Lifshitz equation in the presence of an in-plane applied magnetic ... More

Periodicity of Goussarov-Vassiliev knot invariantsJan 08 2002Sep 30 2002The paper is a survey of known periodicity properties of finite type invariants of knots, and their applications.

Whitehead doubling persistsMar 28 2000Oct 29 2004The operation of (untwisted) Whitehead doubling trivializes the Alexander module of a knot (and consequently, all known abelian invariants), and converts knots to topologically slice ones. In this note we show that Whitehead doubling does not trivialize ... More

Dynamical systems on the Liouville plane and the related strictly contact systemsJun 30 2016We study vector fields of the plane preserving the form of Liouville. We present their local models up to the natural equivalence relation, and describe local bifurcations of low codimension. To achieve that, a classification of univariate functions is ... More

Value-at-Risk and backtesting with the APARCH model and the standardized Pearson type IV distributionFeb 18 2016We examine the efficiency of the Asymmetric Power ARCH (APARCH) model in the case where the residuals follow the standardized Pearson type IV distribution. The model is tested with a variety of loss functions and the efficiency is examined via application ... More

Kustin-Miller unprojection with complexesNov 19 2001A main ingredient for Kustin-Miller unprojection, as developed in (S. Papadakis and M. Reid, Kustin-Miller unprojection without complexes, math.AG/0011094), is the module Hom_R(I, \om_R), where R is a local Gorenstein ring and I a codimension one ideal ... More

Asymptotics of generalized Galois numbers via affine Kac-Moody algebrasSep 12 2011Sep 21 2011Generalized Galois numbers count the number of flags in vector spaces over finite fields. Asymptotically, as the dimension of the vector space becomes large, we give their exponential growth and determine their initial values. The initial values are expressed ... More

Windings of planar processes and applications to the pricing of Asian optionsOct 22 2016Nov 16 2016Motivated by a common Mathematical Finance topic, this paper surveys several results concerning windings of 2-dimensional processes, including planar Brownian motion, complex-valued Ornstein-Uhlenbeck processes and planar stable processes. In particular, ... More

On the characteristic and deformation varieties of a knotJun 15 2003Sep 20 2004The colored Jones function of a knot is a sequence of Laurent polynomials in one variable, whose n-th term is the Jones polynomial of the knot colored with the n-dimensional irreducible representation of SL(2). It was recently shown by TTQ Le and the ... More

G-functions and multisum versus holonomic sequencesAug 31 2007Nov 12 2008The purpose of the paper is three-fold: (a) we prove that every sequence which is a multidimensional sum of a balanced hypergeometric term has an asymptotic expansion of Gevrey type-1 with rational exponents, (b) we construct a class of $G$-functions ... More

Magnetization oscillations by vortex-antivortex dipolesAug 22 2013A vortex-antivortex dipole can be generated due to current with in-plane spin-polarization, flowing into a magnetic element, which then behaves as a spin transfer oscillator. Its dynamics is analyzed using the Landau-Lifshitz equation including a Slonczewski ... More

Bougerol's identity in law and extensionsJan 27 2012Oct 16 2012We present a list of equivalent expressions and extensions of Bougerol's celebrated identity in law, obtained by several authors. We recall well-known results and the latest progress of the research associated with this celebrated identity in many directions, ... More

A closed character formula for symmetric powers of irreducible representationsDec 09 2009Sep 21 2010We prove a closed character formula for the symmetric powers $S^N V(\lambda)$ of a fixed irreducible representation $V(\lambda)$ of a complex semi-simple Lie algebra $\mathfrak{g}$ by means of partial fraction decomposition. The formula involves rational ... More

The Jones slopes of a knotNov 18 2009May 25 2010The paper introduces Slope Conjecture which relates the degree of the Jones polynomial of a knot and its parallels with the slopes of incompressible surfaces in the knot complement. More precisely, we introduce two knot invariants, the Jones slopes (a ... More

Canonical forms of Order-$k$ ($k = 2, 3, 4$) Symmetric Tensors of Format $3 \times \dots \times 3$ Over Prime FieldsFeb 20 2013Sep 12 2013We consider symmetric tensors of format: $3 \times 3$ over $\mathbb{F}_p$ for $p = 2, 3, 5$; $3 \times 3 \times 3$ over $\mathbb{F}_p$ for $p = 2, 3$; and $3 \times 3 \times 3 \times 3$ over $\mathbb{F}_p$ for $p = 2, 3$. In each case we compute their ... More

Magnetic Field Inversion in Vortices in MultilayersDec 17 1997We present a description of very dense vortex lattices in highly anisotropic multilayers, for high fields parallel to the layers. We show that a magnetic field inversion can occur away from the center of a vortex, provided the layers are sufficiently ... More

Three dimensional four-fermion models - A Monte Carlo studyDec 29 2006Jun 11 2007We present results from numerical simulations of three different 3d four-fermion models that exhibit Z_2, U(1), and SU(2) x SU(2) chiral symmetries, respectively. We performed the simulations by using the hybrid Monte Carlo algorithm. We employed finite ... More

Skyrmion dynamics in chiral ferromagnets under spin-transfer torqueAug 19 2015We study the dynamics of skyrmions under spin-transfer torque in Dzyaloshinskii-Moriya materials with easy-axis anisotropy. In particular, we study the motion of a topological skyrmion with skyrmion number $Q=1$ and a non-topological skyrmionium with ... More

Collisions of solitons and vortex rings in cylindrical Bose-Einstein condensatesApr 04 2005Jun 27 2005Interactions of solitary waves in a cylindrically confined Bose-Einstein condensate are investigated by simulating their head-on collisions. Slow vortex rings and fast solitons are found to collide elastically contrary to the situation in the three-dimensional ... More

Finite type 3-manifold invariants and the structure of the Torelli group IMar 14 1996May 09 1997Using the recently developed theory of finite type invariants of integral homology 3-spheres we study the structure of the Torelli group of a closed surface. Explicitly, we construct (a) natural cocycles of the Torelli group (with coefficients in a space ... More

On Finite Type 3-Manifold Invariants IIJun 12 1995This paper continues the study of finite-type invariants of homology spheres studied by Ohtsuki and Garoufalidis. We apply the surgery classification of links to give a diagrammatic description, using ideas of Ohtsuki. This uses a computation of the surgery ... More

Some IHX type relations on trivalent graphs and symplectic representation theoryMay 05 1997May 18 1998We consider several algebras that arise in the study of the mapping class group (by means of topology and Hodge theory) and describe their symplectic-invariant parts in terms of algebras on trivalent graphs.

A rational noncommutative invariant of boundary linksMay 03 2001Feb 20 2004In 1999, Rozansky conjectured the existence of a rational presentation of the Kontsevich integral of a knot. Roughly speaking, this rational presentation of the Kontsevich integral would sum formal power series into rational functions with prescribed ... More

Concordance and 1-loop cloversFeb 13 2001Nov 20 2001We show that surgery on a connected clover (or clasper) with at least one loop preserves the concordance class of a knot. Surgery on a slightly more special class of clovers preserves invertible concordance. We also show that the converse is false. Similar ... More

Homology surgery and invariants of 3-manifoldsMay 30 2000Jun 24 2001We introduce a homology surgery problem in dimension 3 which has the property that the vanishing of its algebraic obstruction leads to a canonical class of \pi-algebraically-split links in 3-manifolds with fundamental group \pi . Using this class of links, ... More

The non-commutative $A$-polynomial of twist knotsFeb 27 2008Jul 09 2009The purpose of the paper is two-fold: to introduce a multivariable creative telescoping method, and to apply it in a problem of Quantum Topology: namely the computation of the non-commutative $A$-polynomial of twist knots. Our multivariable creative telescoping ... More

A non-commutative formula for the colored Jones functionNov 23 2004Mar 07 2005The colored Jones function of a knot is a sequence of Laurent polynomials that encodes the Jones polynomial of a knot and its parallels. It has been understood in terms of representations of quantum groups and Witten gave an intrinsic quantum field theory ... More

Speed Selection Mechanism for Propagating Fronts in Reaction-Diffusion Systems with Multiple FieldsNov 15 2001We introduce a speed selection mechanism for front propagation in reaction-diffusion systems with multiple fields. This mechanism applies to pulled and pushed fronts alike, and operates by restricting the fields to large "finite" intervals in the comoving ... More

The loop expansion of the Kontsevich integral, the null move and S-equivalenceMar 28 2000Oct 14 2003This is a substantially revised version. The Kontsevich integral of a knot is a graph-valued invariant which (when graded by the Vassiliev degree of graphs) is characterized by a universal property; namely it is a universal Vassiliev invariant of knots. ... More

Holographic polymer-dispersed liquid crystal Bragg grating integrated inside a solid core photonic crystal fiberNov 04 2013A polymer/liquid crystal-based fiber Bragg grating (PLC-FBG) is fabricated with visible two-beam holography by photo-induced modulation of a pre-polymer/LC solution infiltrated into the hollow channels of a solid core photonic crystal fiber (PCF). The ... More

A scaling proof for Walsh's Brownian motion extended arc-sine lawJun 16 2012Dec 29 2012We present a new proof of the extended arc-sine law related to Walsh's Brownian motion, known also as Brownian spider. The main argument mimics the scaling property used previously, in particular by D. Williams in the 1-dimensional Brownian case, which ... More

A Central Limit Theorem for a sequence of Brownian motions in the unit sphere in RnJul 16 2011Nov 29 2011We use a Stochastic Differential Equation satisfied by Brownian motion taking values in the unit sphere $S_{n-1}subsetmathbb{R}^{n}$ and we obtain a Central Limit Theorem for a sequence of such Brownian motions. We also generalize the results to the case ... More

Transmutation of momentum into position in magnetic vorticesMar 19 2008We show that transmutation of linear momentum into position may occur in a system of three magnetic vortices thanks to a direct link between topology and dynamics in a ferromagnet. This happens via exchange between the linear momentum of a vortex-antivortex ... More

A new algorithm for the recursion of multisums with improved universal denominatorSep 26 2008Jul 09 2009The purpose of the paper is to introduce two new algorithms. The first one computes a linear recursion for proper hypergeometric multisums, by treating one summation variable at a time, and provides rational certificates along the way. A key part in the ... More

Constraints of Flat Spectrum Radio Quasars in the hadronic model: the case of 3C 273Jun 18 2015We present a method of constraining the properties of the $\gamma$-ray emitting region in flat spectrum radio quasars (FSRQs) in the one-zone proton synchrotron model, where the $\gamma$-rays are produced by synchrotron radiation of relativistic protons. ... More

From state integrals to q-seriesApr 09 2013It is well-known to the experts that multi-dimensional state integrals of products of Faddeev's quantum dilogarithm which arise in Quantum Topology can be written as finite sums of products of basic hypergeometric series in q=e^{2\pi i\tau} and \tilde{q}=e^{-2\pi ... More

A diagrammatic approach to the AJ ConjectureMar 05 2019The AJ Conjecture relates a quantum invariant, a minimal order recursion for the colored Jones polynomial of a knot (known as the $\hat{A}$ polynomial), with a classical invariant, namely the defining polynomial $A$ of the $\psl$ character variety of ... More

Resurgence of the Euler-MacLaurin summation formulaMar 21 2007Aug 27 2007The Euler-MacLaurin summation formula relates a sum of a function to a corresponding integral, with a remainder term. The remainder term has an asymptotic expansion, and for a typical analytic function, it is a divergent (Gevrey-1) series. Under some ... More

A principal component analysis approach to the morphology of Planetary NebulaeOct 22 2007Principal Component Analysis (PCA) is a well-known technique used to decorrelate a set of vectors. It has been applied to explore the star formation history of galaxies or to determine distances of mass-lossing stars. Here we apply PCA to the optical ... More

Darboux polynomials and global phase portraits for the D_2 vector fieldApr 05 2018Aug 12 2018We study a vector field of R^3 equivariant under the D_2 symmetry group, called "the D_2 field" in the literature. We construct the complete list of Darboux polynomials for it, solving the partial differential equation defining them. We also use these ... More

Alternating knots, planar graphs and q-seriesApr 03 2013Dec 13 2013Recent advances in Quantum Topology assign $q$-series to knots in at least three different ways. The $q$-series are given by generalized Nahm sums (i.e., special $q$-hypergeometric sums) and have unknown modular and asymptotic properties. We give an efficient ... More

Rationality of the SL(2,C)-Reidemeister torsion in dimension 3Aug 12 2009Aug 31 2011If $M$ is a finite volume complete hyperbolic 3-manifold with one cusp and no 2-torsion, the geometric component $X_M$ of its $\SL(2,\BC)$-character variety is an affine complex curve, which is smooth at the discrete faithful representation $\rho_0$. ... More

The C-polynomial of a knotApr 14 2005Apr 30 2009In an earlier paper the first author defined a non-commutative A-polynomial for knots in 3-space, using the colored Jones function. The idea is that the colored Jones function of a knot satisfies a non-trivial linear q-difference equation. Said differently, ... More

AMAT: Medial Axis Transform for Natural ImagesMar 24 2017Aug 02 2017We introduce Appearance-MAT (AMAT), a generalization of the medial axis transform for natural images, that is framed as a weighted geometric set cover problem. We make the following contributions: i) we extend previous medial point detection methods for ... More

Embedding rationally independent languages into maximal onesJul 02 2015We consider the embedding problem in coding theory: given an independence (a code-related property) and an independent language $L$, find a maximal independent language containing $L$. We consider the case where the code-related property is defined via ... More

The Ricci flow approach to homogeneous Einstein metrics on flag manifoldsOct 17 2010We give the global picture of the normalized Ricci flow on generalized flag manifolds with two or three isotropy summands. The normalized Ricci flow for these spaces descents to a parameter depending system of two or three ordinary differential equations, ... More

Evaluation of state integrals at rational pointsNov 22 2014Apr 27 2015Multi-dimensional state-integrals of products of Faddeev's quantum dilogarithms arise frequently in Quantum Topology, quantum Teichm\"uller theory and complex Chern--Simons theory. Using the quasi-periodicity property of the quantum dilogarithm, we evaluate ... More

Towards Compositional Feedback in Non-Deterministic and Non-Input-Receptive SystemsOct 21 2015Apr 27 2016Feedback is an essential composition operator in many classes of reactive and other systems. This paper studies feedback in the context of compositional theories with refinement. Such theories allow to reason about systems on a component-by-component ... More

Twisting q-holonomic sequences by complex roots of unityJan 16 2012May 16 2012A sequence $f_n(q)$ is $q$-holonomic if it satisfies a nontrivial linear recurrence with coefficients polynomials in $q$ and $q^n$. Our main theorems state that $q$-holonomicity is preserved under twisting, i.e., replacing $q$ by $\omega q$ where $\omega$ ... More

The SL_3 Jones polynomial of the trefoil: a case study of $q$-holonomic sequencesNov 29 2010Mar 01 2011The SL_3 colored Jones polynomial of the trefoil knot is a $q$-holonomic sequence of two variables with natural origin, namely quantum topology. The paper presents an explicit set of generators for the annihilator ideal of this $q$-holonomic sequence ... More

Finite type invariants of cyclic branched coversJul 30 2001Oct 14 2003Updated rerefences and introduction. Given a knot in an integer homology sphere, one can construct a family of closed 3-manifolds (parametrized by the positive integers), namely the cyclic branched coverings of the knot. In this paper we give a formula ... More

Monte Carlo simulations of the NJL model near the nonzero temperature phase transitionJan 03 2005Feb 09 2005We present results from numerical simulations of the Nambu-Jona-Lasinio model with an SU(2)xSU(2) chiral symmetry and N_c=4,8, and 16 quark colors at nonzero temperature. We performed the simulations by utilizing the hybrid Monte Carlo and hybrid Molecular ... More

Integrability properties and limit theorems for the exit time from a cone of planar Brownian motionJan 13 2012Dec 11 2013We obtain some integrability properties and some limit theorems for the exit time from a cone of a planar Brownian motion, and we check that our computations are correct via Bougerol's identity.

Skyrmion dynamics in chiral ferromagnetsMay 17 2015Aug 10 2015We study the dynamics of skyrmions in Dzyaloshinskii-Moriya materials with easy-axis anisotropy. An important link between topology and dynamics is established through the construction of unambiguous conservation laws obtained earlier in connection with ... More

Finite type 3-manifold invariants and the structure of the TorelliSep 22 1996We apply the theory of finite-type invariants of homology 3-spheres to investigate the structure of the Torelli group. We construct natural cocycles in the Torelli group and show that the lower central series quotients of the Torelli group map onto a ... More

On Chern-Simons Matrix ModelsJan 16 2006Jan 17 2006The contribution of reducible connections to the U(N) Chern-Simons invariant of a Seifert manifold $M$ can be expressed in some cases in terms of matrix integrals. We show that the U(N) evaluation of the LMO invariant of any rational homology sphere admits ... More

The non-commutative A-polynomial of (-2,3,n) pretzel knotsJan 14 2011Sep 11 2012We study q-holonomic sequences that arise as the colored Jones polynomial of knots in 3-space. The minimal-order recurrence for such a sequence is called the (non-commutative) A-polynomial of a knot. Using the "method of guessing", we obtain this polynomial ... More

On the first fall degree of summation polynomialsJun 13 2019We improve on the first fall degree bound of polynomial systems that arise from a Weil descent along Semaev's summation polynomials relevant to the solution of the Elliptic Curve Discrete Logarithm Problem via Gr\"obner basis algorithms.

Learning Moore Machines from Input-Output TracesMay 25 2016Sep 02 2016The problem of learning automata from example traces (but no equivalence or membership queries) is fundamental in automata learning theory and practice. In this paper we study this problem for finite state machines with inputs and outputs, and in particular ... More

On the law of large numbers for Demazure modules of sl2hatSep 15 2010Oct 22 2011We determine the covariance of the weight distribution in level 1 Demazure modules of sl2hat. This allows us to prove a weak law of large numbers for these weight distributions, and leads to a conjecture about the asymptotic concentration of weights for ... More

Dynamics of vortex-antivortex pairs in ferromagnetsDec 21 2007We study the dynamics of vortex-antivortex (VA) pairs in an infinitely thin ferromagnetic film with easy-plane anisotropy. These are localized excitations with finite energy that are characterized by a topological (skyrmion) number N = 0,+1,-1. Topologically ... More

Finite type invariants III: manifold weight systemsMay 07 1997We introduce the notion of weight system for finite type invariants of integral homology 3-spheres, and we show that invariants of type m are determined, modulo invariants of type m-1, by their associated weight system.

Analytic invariants of boundary linksFeb 13 2001Using basic topology and linear algebra, we define a plethora of invariants of boundary links whose values are power series with noncommuting variables. These turn out to be useful and elementary reformulations of an invariant originally defined by M. ... More

Nonlocal interactions in collapsing condensates in a boxApr 17 2019The collapse of attractive Bose-Einstein condensates in a box with tunable interatomic interactions was studied experimentally recently. Not only were remarkably stable remnant condensates observed, but furthermore they often seem to involve two stable ... More

Values of zeta functions at negative integers, Dedekind sums and toric geometryMay 23 1997Sep 21 1998This is an expanded version. We study relations among special values of zeta functions, invariants of toric varieties, and generalized Dedekind sums. In particular, we use invariants arising in the Todd class of a toric variety to give a new explicit ... More

Algebraic G-functions associated to matrices over a group-ringAug 30 2007Oct 09 2007Given a square matrix with elements in the group-ring of a group, one can consider the sequence formed by the trace (in the sense of the group-ring) of its powers. We prove that the corresponding generating series is an algebraic $G$-function (in the ... More

Resurgence of the fractional polylogarithmsJan 25 2007Jul 16 2009The fractional polylogarithms, depending on a complex parameter $\a$, are defined by a series which is analytic inside the unit disk. After an elementary conversion of the series into an integral presentation, we show that the fractional polylogarithms ... More

Some infinite divisibility properties of the reciprocal of planar Brownian motion exit time from a coneJan 13 2012With the help of the Gauss-Laplace transform for the exit time from a cone of planar Brownian motion, we obtain some infinite divisibility properties for the reciprocal of this exit time.

An hierarchical artificial neural network system for the classification of transmembrane proteinsFeb 18 2009May 09 2016This work presents a simple artificial neural network which classifies proteins into two classes from their sequences alone: the membrane protein class and the non-membrane protein class. This may be important in the functional assignment and analysis ... More

Expected degree of weights in Demazure modules of $\hat{sl}_2$May 18 2010We compute the expected degree of a randomly chosen element in a basis of weight vectors in the Demazure module $V_w(\Lambda)$ of $\hat{sl}_2$. We obtain en passant a new proof of Sanderson's dimension formula for these Demazure modules.

The number of flags in finite vector spaces: Asymptotic normality and Mahonian statisticsSep 21 2011Apr 09 2012We study the generalized Galois numbers which count flags of length r in N-dimensional vector spaces over finite fields. We prove that the coefficients of those polynomials are asymptotically Gaussian normally distributed as N becomes large. Furthermore, ... More

Emergence of Approximate Translation Invariance in Finite Intervals as a Speed Selection Mechanism for Propagating FrontsOct 20 2000We introduce a new velocity selection criterion for fronts propagating into unstable and metastable states. We restrict these fronts to large finite intervals in the comoving frame of reference and require their centers be insensitive to the locations ... More

The Alexander polynomial and finite type 3-manifold invariantsAug 02 1997Apr 02 1998This is a revised version (replacing an older one) with typos fixed and the introduction expanded.

A surgery view of boundary linksMay 31 2002Oct 31 2002A celebrated theorem of Kirby identifies the set of closed oriented connected 3-manifolds with the set of framed links in $S^3$ modulo two moves. We give a similar description for the set of knots (and more generally, boundary links) in homology 3-spheres. ... More

SUSYGEN 2.2 - A Monte Carlo Event Generator for MSSM Sparticle Production at e+ e- CollidersNov 21 1997SUSYGEN is a Monte Carlo program designed for computing distributions and generating events for MSSM sparticle production in e+ e- collisions. The Supersymmetric (SUSY) mass spectrum may either be supplied by the user, or can alternatively be calculated ... More

"+-+" Brane Model PhenomenologyMar 21 2000Dec 22 2000We explore the phenomenology of the recently proposed "+-+" brane model which has a characteristic anomalously light first Kaluza-Klein mode. We consider the processes e^+ e^- to mu^+ mu^- and the Kaluza-Klein production e^+ e^- to gamma KK giving missing ... More

Tree-level invariants of three-manifolds, Massey products and the Johnson homomorphismApr 20 1999Oct 14 2003Two references added and the introduction slightly expanded. We show that the tree-level part of a recent theory of invariants of 3-manifolds (due, independently, to Goussarov and Habiro) is essentially given by classical algebraic topology in terms of ... More

On Finite Type 3-manifold invariants IV: Comparison of DefinitionsSep 27 1995Sep 27 1995This paper compares the definitions of finite-type invariants due to Ohtsuki and to Garoufalidis, showing that, residually, type 3m of the former equals type m of the latter. It also shows that type 2m Ohtsuki invariants define knot invariants of type ... More

Universality and asymptotics of graph counting problems in nonorientable surfacesDec 05 2008Oct 21 2009Bender-Canfield showed that a plethora of graph counting problems in oriented/unoriented surfaces involve two constants $t_g$ and $p_g$ for the oriented and the unoriented case respectively. T.T.Q. Le and the authors recently discovered a hidden relation ... More

Analyticity of the planar limit of a matrix modelOct 05 2010Jun 14 2012Using Chebyshev polynomials combined with some mild combinatorics, we provide a new formula for the analytical planar limit of a random matrix model with a one-cut potential $V$. For potentials $V(x)=x^{2}/2-\sum_{n\ge1}a_{n}x^{n}/n$, as a power series ... More

Finite type invariants, the mapping class group and blinksDec 17 1997Dec 18 1997The goal of the present paper is to find higher genus surgery formulae for the set of finite-type invariants of homology spheres, and to develop a companion theory of finite-type invariants to be applied, in a subsequent publication, to the study of subgroups ... More

Fault Diagnosis with Dynamic ObserversApr 16 2010In this paper, we review some recent results about the use of dynamic observers for fault diagnosis of discrete event systems. Fault diagnosis consists in synthesizing a diagnoser that observes a given plant and identifies faults in the plant as soon ... More

A stability conjecture for the colored Jones polynomialOct 26 2013We formulate a stability conjecture for the coefficients of the colored Jones polynomial of a knot, colored by irreducible representations in a fixed ray of a simple Lie algebra, and verify it for all torus knots and all simple Lie algebras of rank $2$. ... More

Constructing 1-cusped isospectral non-isometric hyperbolic 3-manifoldsSep 17 2015Aug 02 2016We construct infinitely many examples of pairs of isospectral but non-isometric $1$-cusped hyperbolic $3$-manifolds. These examples have infinite discrete spectrum and the same Eisenstein series. Our constructions are based on an application of Sunada's ... More

Resurgence of the Kontsevich-Zagier power seriesSep 21 2006Aug 09 2010The paper is concerned with the Kontsevich-Zagier formal power series $$ f(q)=\sum_{n=0}^\infty (1-q)... (1-q^n) $$ and its analytic properties. To begin with, we give an explicit formula for the Borel transform of the associated formal power series $F(x)=e^{-1/(24x)}f(e^{-1/x})$ ... More

Experimental evidence for the Volume Conjecture for the simplest hyperbolic non-2-bridge knotDec 16 2004May 28 2005Loosely speaking, the Volume Conjecture states that the limit of the n-th colored Jones polynomial of a hyperbolic knot, evaluated at the primitive complex n-th root of unity is a sequence of complex numbers that grows exponentially. Moreover, the exponential ... More

A construction of the graphic matroid from the lattice of integer flowsNov 19 2016The lattice of integer flows of a graph is known to determine the graph up to 2-isomorphism (work of Su--Wagner and Caporaso--Viviani). In this paper we give an algorithmic construction of the graphic matroid $\calM(G)$ of a graph $G$, given its lattice ... More

Graph Theoretic Analysis of Knowledge NetworksMay 08 2013Dec 26 2014Purpose of our work is to obtain a basic understanding and comparison of the performance and structure of real Knowledge Networks, to identify strengths and weaknesses and to highlight guidelines for improvements. We selected 18 Knowledge Networks from ... More

Irreducibility of q-difference operators and the knot 7_4Nov 26 2012Oct 21 2013Our goal is to compute the minimal-order recurrence of the colored Jones polynomial of the 7_4 knot, as well as for the first four double twist knots. As a corollary, we verify the AJ Conjecture for the simplest knot 7_4 with reducible non-abelian SL(2,C) ... More

Learning Best Response Strategies for Agents in Ad ExchangesFeb 10 2019Ad exchanges are widely used in platforms for online display advertising. Autonomous agents operating in these exchanges must learn policies for interacting profitably with a diverse, continually changing, but unknown market. We consider this problem ... More

The symplectic properties of the PGL(n,C)-gluing equationsOct 09 2013In a previous article we studied PGL(n,C)-representations of a 3-manifold via a generalization of Thurston's gluing equations. Neumann has proved some symplectic properties of Thurston's gluing equations that play an important role in recent developments ... More

Vortex lattices for ultracold bosonic atoms in a non-Abelian gauge potentialMar 15 2012The use of coherent optical dressing of atomic levels allows the coupling of ultracold atoms to effective gauge fields. These can be used to generate effective magnetic fields, and have the potential to generate non-Abelian gauge fields. We consider a ... More

Sum-integral interpolators and the Euler-Maclaurin formula for polytopesFeb 18 2010May 20 2010A local lattice point counting formula, and more generally a local Euler-Maclaurin formula follow by comparing two natural families of meromorphic functions on the dual of a rational vector space $V$, namely the family of exponential sums (S) and the ... More