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Putting in All the Stops: Execution Control for JavaScriptFeb 08 2018Scores of compilers produce JavaScript, enabling programmers to use many languages on the Web, reuse existing code, and even use Web IDEs. Unfortunately, most compilers expose the browser's compromised execution model, so long-running programs freeze ... More

Preconditioned Conjugate Gradients, Radial Basis Functions and Toeplitz MatricesJun 12 2010Radial basis functions provide highly useful and flexible interpolants to multivariate functions. Further, they are beginning to be used in the numerical solution of partial differential equations. Unfortunately, their construction requires the solution ... More

The Interpolation Theory of Radial Basis FunctionsJun 12 2010In this dissertation, it is first shown that, when the radial basis function is a $p$-norm and $1 < p < 2$, interpolation is always possible when the points are all different and there are at least two of them. We then show that interpolation is not always ... More

A Model of Inductive Bias LearningJun 01 2011A major problem in machine learning is that of inductive bias: how to choose a learner's hypothesis space so that it is large enough to contain a solution to the problem being learnt, yet small enough to ensure reliable generalization from reasonably-sized ... More

On the existence of topological hairy black holes in $\mathfrak{su}(N)$ EYM theory with a negative cosmological constantMar 02 2014Jul 09 2015We investigate the existence of black hole solutions of four dimensional $\mathfrak{su}(N)$ EYM theory with a negative cosmological constant. Our analysis differs from previous works in that we generalise the field equations to certain non-spherically ... More

On the global existence of spherically symmetric hairy black holes and solitons in anti-de Sitter Einstein-Yang-Mills theories with compact semisimple gauge groupsApr 18 2016We investigate the existence of black hole and soliton solutions to four dimensional, anti-de Sitter (adS), Einstein-Yang-Mills theories with general semisimple connected and simply connected gauge groups, concentrating on the so-called "regular" case. ... More

The Riemann surface of the chiral Potts model free energy functionDec 03 2002In a recent paper we derived the free energy or partition function of the $N$-state chiral Potts model by using the infinite lattice ``inversion relation'' method, together with a non-obvious extra symmetry. This gave us three recursion relations for ... More

Onsager and Kaufman's calculation of the spontaneous magnetization of the Ising modelMar 17 2011Apr 18 2011Lars Onsager announced in 1949 that he and Bruria Kaufman had proved a simple formula for the spontaneous magnetization of the square-lattice Ising model, but did not publish their derivation. It was three years later when C. N. Yang published a derivation ... More

Spontaneous magnetization of the superintegrable chiral Potts model: calculation of the determinant D_PQDec 23 2009Jan 11 2010For the Ising model, the calculation of the spontaneous magnetization leads to the problem of evaluating a determinant. Yang did this by calculating the eigenvalues in the large-lattice limit. Montroll, Potts and Ward expressed it as a Toeplitz determinant ... More

A conjecture for the superintegrable chiral Potts modelMar 28 2008Jul 12 2008We adapt our previous results for the ``partition function'' of the superintegrable chiral Potts model with open boundaries to obtain the corresponding matrix elements of e^{-\alpha H}, where H is the associated hamiltonian. The spontaneous magnetization ... More

The "inversion relation" method for obtaining the free energy of the chiral Potts modelDec 03 2002We derive the free energy of the chiral Potts model by the infinite lattice ``inversion relation'' method. This method is non-rigorous in that it always needs appropriate analyticity assumptions. Guided by previous calculations based on exact finite-lattice ... More

Surface and corner free energies of the self-dual Potts modelJun 06 2016Jun 08 2016We calculate the surface free energies $f_s, f_s'$ of the anisotropic self-dual $Q$-state Potts model for $Q > 4$ and find agreement with the conjectures made by Vernier and Jacobsen (VJ) for the isotropic case. Each of $f_s, f_s'$ satisifies (as $f_b$ ... More

Algebraic reduction of the Ising modelMar 28 2008Jul 12 2008We consider the Ising model on a cylindrical lattice of L columns, with fixed-spin boundary conditions on the top and bottom rows. The spontaneous magnetization can be written in terms of partition functions on this lattice. We show how we can use the ... More

Hard Squares for z = -1Sep 27 2007Nov 21 2007The hard square model in statistical mechanics has been investigated for the case when the activity z is -1. For cyclic boundary conditions, the characteristic polynomial of the transfer matrix has an intriguingly simple structure, all the eigenvalues ... More

Corner transfer matrices in statistical mechanicsNov 07 2006Corner transfer matrices are a useful tool in the statistical mechanics of simple two-dimensinal models. They can be very effective way of obtaining series expansions of unsolved models, and of calculating the order parameters of solved ones. Here we ... More

Equivalence of the two results for the free energy of the chiral Potts modelMay 13 1999May 14 1999The free energy of the chiral Potts model has been obtained in two ways. The first used only the star-triangle relation, symmetries and invariances, and led to a system of equations that implicitly define the free energy, and from which the critical behaviour ... More

Derivation of the order parameter of the chiral Potts modelJan 11 2005Feb 21 2005We derive the order parameter of the chiral Potts model, using the method of Jimbo et al. The result agrees with previous conjectures.

Completeness of the Bethe ansatz for the six and eight-vertex modelsNov 10 2001Feb 07 2002We discuss some of the difficulties that have been mentioned in the literature in connection with the Bethe ansatz for the six-vertex model and XXZ chain, and for the eight-vertex model. In particular we discuss the ``beyond the equator'', infinite momenta ... More

Dichromatic polynomials and Potts models summed over rooted mapsNov 23 2000Jan 12 2001We consider the sum of dichromatic polynomials over non-separable rooted planar maps, an interesting special case of which is the enumeration of such maps. We present some known results and derive new ones. The general problem is equivalent to the $q$-state ... More

A direct proof of Kim's identitiesJan 15 1998As a by-product of a finite-size Bethe Ansatz calculation in statistical mechanics, Doochul Kim has established, by an indirect route, three mathematical identities rather similar to the conjugate modulus relations satisfied by the elliptic theta constants. ... More

Refining enumeration schemes to count according to permutation statisticsJan 01 2014We consider the question of computing the distribution of a permutation statistics over restricted permutations via enumeration schemes. The restricted permutations are those avoiding sets of vincular patterns (which include both classical and consecutive ... More

A Maximum Likelihood Approach to Estimating Correlation FunctionsMay 20 2013Nov 26 2013We define a Maximum Likelihood (ML for short) estimator for the correlation function, {\xi}, that uses the same pair counting observables (D, R, DD, DR, RR) as the standard Landy and Szalay (1993, LS for short) estimator. The ML estimator outperforms ... More

Infinite-Horizon Policy-Gradient EstimationJun 03 2011Gradient-based approaches to direct policy search in reinforcement learning have received much recent attention as a means to solve problems of partial observability and to avoid some of the problems associated with policy degradation in value-function ... More

Star-Triangle Relation for a Three Dimensional ModelDec 10 1992The solvable $sl(n)$-chiral Potts model can be interpreted as a three-dimensional lattice model with local interactions. To within a minor modification of the boundary conditions it is an Ising type model on the body centered cubic lattice with two- and ... More

Abundant stable gauge field hair for black holes in anti-de Sitter spaceAug 17 2007Jan 08 2008We present new hairy black hole solutions of su(N) Einstein-Yang-Mills theory (EYM) in asymptotically anti-de Sitter (adS) space. These black holes are described by N+1 independent parameters, and have N-1 independent gauge field degrees of freedom. Solutions ... More

Every positive integer is a sum of three palindromesFeb 19 2016Jun 17 2017For integer $g\ge 5$, we prove that any positive integer can be written as a sum of three palindromes in base $g$.

A special case of the $Γ_{00}$ conjectureApr 03 2008Sep 02 2010In this paper we prove the $\Gamma_{00}$ conjecture of van Geemen and van der Geer, under the additional assumption that the matrix of coefficients of the tangent has rank at most 2. This assumption is satisfied by Jacobians, and thus our result gives ... More

Simple fixed-brane gauges in $S_1/Z_2$ braneworldsApr 07 2006For five-dimensional braneworlds with an $S_1/\mathbb{Z}_2$ orbifold topology for the extra dimension $x^5$, we discuss the validity of recent claims that a gauge exists where the two boundary branes lie at fixed positions and the metric satisfies $g_{\mu ... More

A Sequent Calculus for Dynamic Topological LogicJul 25 2014Aug 03 2014We introduce a sequent calculus for the temporal-over-topological fragment $\textbf{DTL}_{0}^{\circ * \slash \Box}$ of dynamic topological logic $\textbf{DTL}$, prove soundness semantically, and prove completeness syntactically using the axiomatization ... More

On Improved Bounds on Bounded Degree Spanning Trees for Points in Arbitrary DimensionMay 13 2013Jan 05 2014Given points in Euclidean space of arbitrary dimension, we prove that there exists a spanning tree having no vertices of degree greater than 3 with weight at most 1.559 times the weight of the minimum spanning tree. We also prove that there is a set of ... More

Exploratory topic modeling with distributional semanticsJul 16 2015As we continue to collect and store textual data in a multitude of domains, we are regularly confronted with material whose largely unknown thematic structure we want to uncover. With unsupervised, exploratory analysis, no prior knowledge about the content ... More

On Quantum NoncompressionNov 16 2015This article presents a quantum transmission problem, in which Alice is trying to send a number of qbits to Bob. Alice has access to two channels, one that sends classical bits and another that sends quantum bits. We show that under certain error terms, ... More

Canonical Cartan connection for $4$-dimensional CR-manifolds belonging to general class ${\sf II}$May 05 2014We study the equivalence problem for $4$-dimensional CR-manifolds of CR-dimension $1$ and codimension $2$ which are referred to as Engel CR-manifolds. We construct a canonical Cartan connection on such CR-manifolds through Cartan equivalence's method. ... More

Towards 3-Dimensional Rewriting TheoryMar 17 2014Apr 02 2014String rewriting systems have proved very useful to study monoids. In good cases, they give finite presentations of monoids, allowing computations on those and their manipulation by a computer. Even better, when the presentation is confluent and terminating, ... More

A Dichotomy in Machine KnowledgeAug 04 2011We show that a machine, which knows basic logic and arithmetic and basic axioms of knowledge, and which is factive (knows nothing false), can either know that it is factive, or know its own Goedel number, but not both.

Highly lopsided information and the Borel hierarchyJun 01 2011In a game where both contestants have perfect information, there is a strict limit on how perfect that information can be. By contrast, when one player is deprived of all information, the limit on the other player's information disappears, admitting a ... More

Extraction of Cosmological Information from WiggleZApr 06 2016In this thesis, I analyse the 2D anisotropic Baryon Acoustic Oscillation (BAO) signal present in the final WiggleZ dataset. I utilise newly released covariance matrices from the WizCOLA simulations and follow well tested methodologies used in prior analyses ... More

The global gravitational anomaly of the self-dual field theoryOct 20 2011May 10 2013We derive a formula for the global gravitational anomaly of the self-dual field theory on an arbitrary compact oriented Riemannian manifold. Along the way, we uncover interesting links between the theory of determinant line bundles of Dirac operators, ... More

Escaping the Tragedy of the Commons through Targeted PunishmentJun 04 2015Failures of cooperation cause many of society's gravest problems. It is well known that cooperation among many players faced with a social dilemma can be maintained thanks to the possibility of punishment, but achieving the initial state of widespread ... More

Interplay between Network Topology and Dynamics in Neural SystemsFeb 16 2013This thesis is a compendium of research which brings together ideas from the fields of Complex Networks and Computational Neuroscience to address two questions regarding neural systems: 1) How the activity of neurons, via synaptic changes, can shape the ... More

Polar actions on Hermitian and quaternion-Kähler symmetric spacesDec 18 2006Jan 17 2007We analyze polar actions on Hermitian and quaternion-K\"ahler symmetric spaces of compact type. For complex integrable polar actions on Hermitian symmetric spaces of compact type we prove a reduction theorem and several corollaries concerning the geometry ... More

Chern classes of the tangent bundle on the Hilbert scheme of points on the affine planeOct 21 2004Mar 31 2005The cohomology of the Hilbert schemes of points on smooth projective surfaces can be approached both with vertex algebra tools and equivariant tools. Using the first tool, we study the existence and the structure of universal formulas for the Chern classes ... More

Infinitesimal thickenings of Morava K-theoriesJul 05 2006Mar 06 2008A. Baker has constructed certain sequences of cohomology theories which interpolate between the Johnson-Wilson and the Morava K-theories. We realize the representing sequences of spectra as sequences of MU-algebras. Starting with the fact that the spectra ... More

I-adic towers in topologyNov 18 2004Nov 30 2005A large variety of cohomology theories is derived from complex cobordism MU^*(-) by localizing with respect to certain elements or by killing regular sequences in MU_*. We study the relationship between certain pairs of such theories which differ by a ... More

Infinite graphs in systematic biology, with an application to the species problemJan 13 2012Dec 13 2012We argue that C. Darwin and more recently W. Hennig worked at times under the simplifying assumption of an eternal biosphere. So motivated, we explicitly consider the consequences which follow mathematically from this assumption, and the infinite graphs ... More

Convergence of the Yang-Mills-Higgs flow on gauged holomorphic maps and applicationsOct 07 2016The symplectic vortex equations admit a variational description as global minimum of the Yang--Mills--Higgs functional. We study its negative gradient flow on holomorphic pairs $(A,u)$ where $A$ is a connection on a principal $G$-bundle $P$ over a closed ... More

On weighted optimality of experimental designsOct 20 2016When the experimental objective is expressed by a set of estimable functions, and any eigenvalue-based optimality criterion is selected, we prove the equivalence of the recently introduced weighted optimality and the 'standard' optimality criteria for ... More

Lazy Transformation-Based LearningJun 03 1998We introduce a significant improvement for a relatively new machine learning method called Transformation-Based Learning. By applying a Monte Carlo strategy to randomly sample from the space of rules, rather than exhaustively analyzing all possible rules, ... More

Noncommutativity inspired Black Holes as Dark Matter CandidateApr 17 2015May 30 2016We study a black hole with a blurred mass density instead of a singular one, which could be caused by the noncommutativity of 3-space. Depending on its mass, such object has either none, one or two event horizons. It possesses new properties, which become ... More

The degree of the Jacobian locus and the Schottky problemFeb 29 2004We show that the degree of the images of the moduli space of (principally polarized) abelian varieties A_g and of the moduli space of curves M_g in the projective space under the theta constant embedding are equal to the top self-intersection numbers ... More

Geometry of A_g and Its CompactificationsNov 01 2007Sep 02 2010In this survey we give a brief introduction to, and review the progress made in the last decade in understanding the geometry of the moduli spaces A_g of principally polarized abelian varieties and its compactifications. Topics surveyed include: compactifications; ... More

Explicit upper bound for the Weil-Petersson volumesMar 30 2000Jun 20 2001An explicit upper bound for the Weil-Petersson volumes of the moduli spaces of punctured Riemann surfaces is obtained, using Penner's combinatorial integration scheme with embedded trivalent graphs. It is shown that for a fixed number of punctures n and ... More

Measuring the primordial power spectrum: Principal component analysis of the cosmic microwave backgroundJun 16 2005Sep 19 2006We implement and investigate a method for measuring departures from scale-invariance, both scale-dependent as well as scale-free, in the primordial power spectrum of density perturbations using cosmic microwave background (CMB) C_l data and a principal ... More

A Cantor-Bendixson-like process which detects Delta_2^0Jun 13 2011Jan 23 2012For each subset of Baire space, we define, in away similar to a common proof of the Cantor-Bendixson Theorem, a sequence of decreasing subsets S_alpha of N^N, indexed by ordinals. We use this to obtain two new characterizations of the boldface Delta_2^0 ... More

The First-Order Syntax of Variadic FunctionsMay 20 2011Jan 23 2012We extend first-order logic to include variadic function symbols, and prove a substitution lemma. Two applications are given: one to bounded quantifier elimination and one to the definability of certain Borel sets.

Automatic Determination of Chord RootsJan 11 2016Even though chord roots constitute a fundamental concept in music theory, existing models do not explain and determine them to full satisfaction. We present a new method which takes sequential context into account to resolve ambiguities and detect nonharmonic ... More

Noncommutativity inspired Black Holes as Dark Matter CandidateApr 17 2015Oct 25 2016We study a black hole with a blurred mass density instead of a singular one, which could be caused by the noncommutativity of 3-space. Depending on its mass, such object has either none, one or two event horizons. It possesses new properties, which become ... More

Analysing Survey Propagation Guided Decimation on Random FormulasFeb 22 2016Let $\varPhi$ be a uniformly distributed random $k$-SAT formula with $n$ variables and $m$ clauses. For clauses/variables ratio $m/n \leq r_{k\text{-SAT}} \sim 2^k\ln2$ the formula $\varPhi$ is satisfiable with high probability. However, no efficient ... More

Guessing, Mind-changing, and the Second Ambiguous ClassJan 09 2014In his dissertation, Wadge defined a notion of guessability on subsets of the Baire space and gave two characterizations of guessable sets. A set is guessable iff it is in the second ambiguous class (boldface Delta^0_2), iff it is eventually annihilated ... More

Multi-agent flocking under topological interactionsNov 23 2013In this paper, we consider a multi-agent system consisting of mobile agents with second-order dynamics. The communication network is determined by the so-called topological interaction rule: agents interact with a fixed number of their closest neighbors. ... More

Sub-Compton quantum non-equilibrium and Majorana systemsJun 05 2013We study the Majorana equation from the point of view of the de Broglie-Bohm pilot-wave theory (according to which a quantum ensemble of fermions is not only described by a spinor but also by a distribution of position configurations). Although the Majorana ... More

Accelerating Implicit Finite Difference Schemes Using a Hardware Optimized Tridiagonal Solver for FPGAsFeb 20 2014Oct 14 2015We present a design and implementation of the Thomas algorithm optimized for hardware acceleration on an FPGA, the Thomas Core. The hardware-based algorithm combined with the custom data flow and low level parallelism available in an FPGA reduces the ... More

Explicit absolute parallelism for $2$-nondegenerate real hypersurfaces $M^5 \subset \mathbb{C}^3$ of constant Levi rank $1$Dec 22 2013May 05 2014We study the local equivalence problem for five dimensional real hypersurfaces $M^5$ of $\mathbb{C}^3$ which are $2$-nondegenerate and of constant Levi rank $1$ under biholomorphisms. We find two invariants, $J$ and $W$, which are expressed explicitly ... More

On Non-Standard Models of Peano Arithmetic and Tennenbaum's TheoremNov 25 2013Throughout the course of mathematical history, generalizations of previously understood concepts and structures have led to the fruitful development of the hierarchy of number systems, non-euclidean geometry, and many other epochal phases in mathematical ... More

CP Violation and Mixing in Multi-body $D$ decaysNov 19 2013We present recent LHCb results and future prospects for CP violation and mixing measurements in multi-body charm decays. The complex amplitude structure of multi-body decays provides unique sensitivity to CP violation localised in certain phase space ... More

Quantifying the Ease of Scientific DiscoveryDec 08 2009May 14 2010It has long been known that scientific output proceeds on an exponential increase, or more properly, a logistic growth curve. The interplay between effort and discovery is clear, and the nature of the functional form has been thought to be due to many ... More

A survey of the GIT picture for the Yang-Mills equation over Riemann surfacesNov 25 2015Dec 11 2015The purpose of this paper is to give a self-contained exposition of the Atiyah-Bott picture for the Yang-Mills equation over Riemann surfaces with an emphasis on the analogy to finite dimensional geometric invariant theory. The main motivation is to provide ... More

Stratified Steady Periodic Water WavesJul 03 2008Feb 11 2009This paper considers two-dimensional stratified water waves propagating under the force of gravity over an impermeable flat bed and with a free surface. We prove the existence of a global continuum of classical solutions that are periodic and traveling. ... More

The global anomalies of (2,0) superconformal field theories in six dimensionsJun 17 2014Sep 02 2014We compute the global gauge and gravitational anomalies of the A-type (2,0) superconformal quantum field theories in six dimensions, and conjecture a formula valid for the D- and E-type theories. We show that the anomaly contains terms that do not contribute ... More

Curvature Free Rigidity for Higher Rank Three-ManifoldsAug 16 2016We prove two rigidity results for complete Riemannian three-manifolds of higher rank. Complete three-manifolds have higher spherical rank if an only if they are spherical space forms. Complete finite volume three-manifolds have higher hyperbolic rank ... More

f-Vectors of Triangulated BallsDec 10 2009We describe two methods for showing that a vector can not be the f-vector of a homology d-ball. As a consequence, we disprove a conjectured characterization of the f-vectors of balls of dimension five and higher due to Billera and Lee. We also provide ... More

Unimodality of Partitions in Near-Rectangular Ferrers DiagramsAug 18 2014May 20 2015We look at the rank generating function $G_\lambda$ of partitions inside the Ferrers diagram of some partition $\lambda$, investigated by Stanton in 1990, as well as a closely related problem investigated by Stanley and Zanello in 2013. We show that $G_\lambda$ ... More

Automorphismes naturels de l'espace de Douady de points sur une surfaceMay 27 2009We prove some general results concerning the size of the group of automorphisms of the Douady space of points on a surface. We then study some properties of the automorphisms coming from an automorphism of the surface, in particular their action on the ... More

Veech surfaces associated with rational billiardsMay 23 2002A nice trick for studying the billiard flow in a rational polygon is to unfold the polygon along the trajectories. This gives rise to a translation or half-translation surface tiled by the original polygon, or equivalently an Abelian or quadratic differential. ... More

Cubic equations for the hyperelliptic locusMar 02 2005We discuss the conjecture of Buchstaber and Krichever that their multi-dimensional vector addition formula for Baker-Akhiezer functions characterizes Jacobians among principally polarized abelian varieties, and prove that it is indeed a weak characterization, ... More

Multiplier ideals in algebraic geometryFeb 17 2005Mar 28 2005In this expository introductory text we discuss the multiplier ideals in algebraic geometry. We state Kawamata-Viehweg's and Nadel's vanishing theorems, give a proof (following Ein and Lazarsfeld) of Koll\'ar's bound on the maximal multiplicity of the ... More

The Schottky ProblemSep 02 2010Sep 30 2010In this survey we discuss some of the classical and modern methods in studying the (Riemann-)Schottky problem, the problem of characterizing Jacobians of curves among principally polarized abelian varieties. We present many of the recent results in this ... More

f-vectors of Simplicial Posets that are BallsSep 10 2010Results of R. Stanley and M. Masuda completely characterize the h-vectors of simplicial posets whose order complexes are spheres. In this paper we examine the corresponding question in the case where the order complex is a ball. Using the face rings of ... More

Separability of Lyapunov Functions for Contractive Monotone SystemsSep 20 2016We consider constructing Lyapunov functions for systems that are both monotone and contractive with respect to a weighted one norm or infinity norm. This class of systems admits separable Lyapunov functions that are either the sum or the maximum of a ... More

Duality and contravariant functors in the representation theory of artin algebrasMar 18 2016May 22 2016The model theory of modules leads to a way of obtaining definable categories of modules over a ring $R$ as the kernels of certain functors $(R\textbf{-Mod})^{\text{op}}\to\textbf{Ab}$ rather than of functors $R\textbf{-Mod}\to\textbf{Ab}$ which are given ... More

Geometric ergodicity of the Random Walk Metropolis with position-dependent proposal covarianceJul 21 2015Jul 29 2015We consider a Metropolis-Hastings method with proposal kernel $\mathcal{N}(x,hG^{-1}(x))$, where $x$ is the current state. After discussing specific cases from the literature, we analyse the ergodicity properties of the resulting Markov chains. In one ... More

Lie algebras of infinitesimal automorphisms for the model manifolds of general classes ${\sf II}$, ${\sf III_2}$ and ${\sf IV_2}$Apr 22 2014May 05 2014We determine the Lie algebras of infinitesimal automorphisms for the models of the CR-manifolds belonging to general classes ${\sf II}$, ${\sf III_2}$ and ${\sf IV_2}$ through Cartan's equivalence method.

A machine that knows its own codeMay 27 2013We construct a machine that knows its own code, at the price of not knowing its own factivity.

All Sampling Methods Produce OutliersApr 14 2013May 10 2013Given a computable probability measure P over natural numbers or infinite binary sequences, there is no method that can produce an arbitrarily large sample such that all its members are typical of P. This paper also contains upper bounds on the minimal ... More

On Ruby's solid angle formula and some of its generalizationsOct 15 2014Using the Mellin-Barnes representation, we show that Ruby's solid angle formula and some of its generalizations may be expressed in a compact way in terms of the Appell F4 and Lauricella Fc functions.

Distributed delays stabilize negative feedback loopsOct 23 2009Linear scalar differential equations with distributed delays appear in the study of the local stability of nonlinear differential equations with feedback, which are common in biology and physics. Negative feedback loops tend to promote oscillation around ... More

Homology of I-adic towersNov 09 2004Nov 29 2005Let R be a commutative ring with unit and let I be an ideal generated by a regular sequence. Then it is known that the natural sequences 0-> Tor_*^R(R/I,I^s)-> Tor_*^R(R/I,I^s/I^{s+1})-> Tor_{*-1}^R(R/I,I^{s+1})-> 0 are short exact sequences of graded ... More

Quantum Deformations from Toric GeometryNov 03 2005Feb 23 2006We will demonstrate how calculations in toric geometry can be used to compute quantum corrections to the relations in the chiral ring for certain gauge theories. We focus on the gauge theory of the del Pezzo 2, and derive the chiral ring relations and ... More

Topological field theories on manifolds with Wu structuresJul 05 2016We construct invertible field theories generalizing abelian prequantum spin Chern-Simons theory to manifolds of dimension 4k+3 endowed with a Wu structure of degree 2k+2. After analysing the anomalies of a certain discrete symmetry, we gauge it, producing ... More

A Simple Proof of Vitali's Theorem for Signed MeasuresFeb 09 2012May 14 2012There are several theorems named after the Italian mathematician Vitali. In this note we provide a simple proof of an extension of Vitali's Theorem on the existence of non-measurable sets. Specifically, we show, without using any decomposition theorems, ... More

Analytic Combinatorics of Planar Lattice PathsApr 23 2013Lattice paths effectively model phenomena in chemistry, physics and probability theory. Asymptotic enumeration of lattice paths is linked with entropy in the physical systems being modeled. Lattice paths restricted to different regions of the plane are ... More

Counting nonsingular matrices with primitive row vectorsNov 12 2012May 02 2013We give an asymptotic expression for the number of nonsingular integer n-by-n-matrices with primitive row vectors, determinant k, and Euclidean matrix norm less than T, for large T. We also investigate the density of matrices with primitive rows in the ... More

A Discrete Inverse Scattering Transform for Q3$_δ$Oct 05 2012We derive a fully discrete Inverse Scattering Transform as a method for solving the initial-value problem for the Q3$_\delta$ lattice (difference-difference) equation for real-valued solutions. The initial condition is given on an infinite staircase within ... More

Homology of powers of regular idealsAug 27 2003For a commutative ring R with an ideal I, generated by a finite regular sequence, we construct differential graded algebras which provide R-free resolutions of I^s and of R/I^s for s>0 and which generalise the Koszul resolution. We derive these from a ... More

Rectifications of Convex PolyhedraApr 03 2016A convex polyhedron, that is, a compact convex subset of $\mathbb{R}^3$ which is the intersection of finitely many closed half-spaces, can be rectified by taking the convex hull of the midpoints of the edges of the polyhedron. We derive expressions for ... More

Canonical Cartan connection for $5$-dimensional CR-manifolds belonging to general class ${\sf III_2}$May 05 2014We study the equivalence problem for CR-manifolds belonging to general class III_2, i.e. the 5-dimensional CR-manifolds of CR-dimension 1 and codimension 3 whose CR-bundle satisfies a certain degeneracy condition. For such a CR-manifold M, we construct ... More

Fast-collapsing theoriesNov 13 2013Nov 14 2013Reinhardt's conjecture, a formalization of the statement that a truthful knowing machine can know its own truthfulness and mechanicalness, was proved by Carlson using sophisticated structural results about the ordinals and transfinite induction just beyond ... More

Properties of the thermal two-point functions in curved spacetimes for a self-interacting scalar fieldJan 21 2016We will present a method for building a consistent AQFT on Schwarzschild spacetime for a thermal system ruled by an interacting and massive scalar field, extending the methods and the results of K. Fredenhagen and F. Lindner valid for the flat case. In ... More

Wick Rotation in the Tangent SpaceOct 26 2015Wick rotation is usually performed by rotating the time coordinate to imaginary values. In a general curved spacetime, the notion of a time coordinate is ambiguous. We note here, that within the tetrad formalism of general relativity, it is possible to ... More

On Guessing Whether A Sequence Has A Certain PropertyNov 30 2010Jan 23 2012A concept of "guessability" is defined for sets of sequences of naturals. Eventually, these sets are thoroughly characterized. To do this, a nonstandard logic is developed, a logic containing symbols for the ellipsis as well as for functions without fixed ... More