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From tokamaks to stellarators: understanding the role of 3D shapingMay 01 2017Jul 11 2017In this work, the role which three-dimensional shaping plays in the generation of rotational transform in toroidal magnetically confinement devices is explored. The susceptance matrix as defined by Strand & Houlberg (2001) is presented and compared to ... More

Verification of the global gyrokinetic stellarator code XGC-S for linear ion temperature gradient driven modesMay 14 2019XGC (X-point Gyrokinetic Code) is a whole-volume, total-f gyrokinetic particle-in-cell code developed for modelling tokamaks. In recent work, XGC has been extended to model more general 3D toroidal magnetic configurations, such as stellarators. These ... 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

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

A Flexible Thread Scheduler for Hierarchical Multiprocessor MachinesJun 27 2005With the current trend of multiprocessor machines towards more and more hierarchical architectures, exploiting the full computational power requires careful distribution of execution threads and data so as to limit expensive remote memory accesses. Existing ... More

On the rate of equidistribution of expanding horospheres in finite-volume quotients of $\mathrm{SL}(2,\mathbb{C})$Dec 08 2015Let $\Gamma$ be a lattice in $G=\mathrm{SL}(2,\mathbb{C})$. We give an effective equidistribution result with precise error terms for expanding translates of pieces of horospherical orbits in $\Gamma\backslash G$. Our method of proof relies on the theory ... More

Hamiltonian anomalies from extended field theoriesOct 27 2014Apr 22 2015We develop a proposal by Freed to see anomalous field theories as relative field theories, namely field theories taking value in a field theory in one dimension higher, the anomaly field theory. We show that when the anomaly field theory is extended down ... More

Optimal designs for treatment comparisons represented by graphsDec 20 2016Consider an experiment consisting of a set of independent trials for comparing a set of treatments. In each trial, one treatment is chosen and the mean response of the trial is equal to the effect of the chosen treatment. We examine the optimal approximate ... 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

On the McKay correspondences for the Hilbert scheme of points on the affine planeOct 11 2004The quotient of a finite-dimensional vector space by the action of a finite subgroup of automorphisms is usually a singular variety. Under appropriate assumptions, the McKay correspondence relates the geometry of nice resolutions of singularities and ... More

Towards the multiplicative behavior of the K-theoretical McKay correspondenceJan 24 2005May 01 2005When the quotient of a symplectic vector space by the action of a finite subgroup of symplectic automorphisms admits as a crepant projective resolution of singularities the Hilbert scheme of regular orbits of Nakamura, then there is a natural isomorphism ... 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

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

Asymptotically faster algorithm for counting self-avoiding walks and self-avoiding polygonsMar 10 2019We give an algorithm for counting self-avoiding walks or self-avoiding polygons that runs in time $\exp(C\sqrt{n\log n})$ on 2-dimensional lattices and time $\exp(C_dn^{(d-1)/d}\log n)$ on $d$-dimensional lattices for $d>2$.

A Modern Point of View on AnomaliesMar 07 2019We review the concept of anomaly field theory, namely the fact that the anomalies of a $d$-dimensional field theory can be encoded in a $d+1$-dimensional field theory functor. We give numerous examples of anomaly field theories, explain how classical ... More

Monte Carlo simulation of 192Ir radioactive source in a phantom designed for brachytherapy dosimetry and source position evaluationNov 25 2018In this report simulations of 192Ir source located inside a phantom designed for measuring the absorbed dose and radioactive source position are presented. Monte Carlo simulations were performed and results were compared with a theoretical model that ... More

Homogeneous 3-dimensional permutation structuresOct 14 2017We provide a classification of the homogeneous 3-dimensional permutation structures, i.e. homogeneous structures in a language of 3 linear orders, partially answering a question of Cameron. We also arrive at a natural description of all known homogeneous ... More

Upper Bounds for Non-Congruent Sphere PackingsSep 28 2015We prove upper bounds on the average kissing number $k(\mathcal{P})$ and contact number $C(\mathcal{P})$ of an arbitrary finite non-congruent sphere packing $\mathcal{P}$, and prove an upper bound on the packing density $\delta(\mathcal{P})$ of an arbitrary ... More

Multiplication matrices and ideals of projective dimension zeroMar 11 2009Mar 12 2009We introduce the concept of multiplication matrices for ideals of projective dimension zero. We discuss various applications and in particular, we give a new algorithm to compute the variety of an ideal of projective dimension zero.

Finite higher spin transformations from exponentiationFeb 18 2014Mar 19 2015We study the exponentiation of elements of the gauge Lie algebras ${\rm hs}(\lambda)$ of three-dimensional higher spin theories. Exponentiable elements generate one-parameter groups of finite higher spin symmetries. We show that elements of ${\rm hs}(\lambda)$ ... More

Siegel-Veech constants in H(2)Mar 30 2005Mar 16 2009Abelian differentials on Riemann surfaces can be seen as translation surfaces, which are flat surfaces with cone-type singularities. Closed geodesics for the associated flat metrics form cylinders whose number under a given maximal length generically ... More

Biologically Unavoidable SequencesDec 02 2012Feb 05 2013A biologically unavoidable sequence is an infinite gender sequence which occurs in every gendered, infinite genealogical network satisfying certain tame conditions. We show that every eventually periodic sequence is biologically unavoidable (this generalizes ... More

Borel reductions of profinite actions of SL(n,Z)Sep 03 2009Sep 30 2010Greg Hjorth and Simon Thomas proved that the classification problem for torsion-free abelian groups of finite rank \emph{strictly increases} in complexity with the rank. Subsequently, Thomas proved that the complexity of the classification problems for ... 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

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.

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

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 quantum lower bound for the collision problemApr 24 2003We extend Shi's 2002 quantum lower bound for collision in $r$-to-one functions with $n$ inputs. Shi's bound of $\Omega((n/r)^{1/3})$ is tight, but his proof applies only in the case where the range has size at least $3n/2$. We give a modified version ... 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

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.

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

Algorithmic No-Cloning TheoremAug 09 2018We introduce the notions of algorithmic mutual information and rarity of quantum states. These definitions enjoy conservation inequalities over unitary transformations and partial traces. We show that a large majority of pure states have minute self algorithmic ... More

Stable solutions of semilinear elliptic equations in unbounded domainsOct 19 2018This paper establishes some properties for stable solutions of a semilin-ear elliptic equation with homogeneous Neumann boundary conditions in unbounded domains. A seminal result of Casten, Holland [16] and Matano [23] states that, in convex bounded domains, ... More

$Λ$-ultrametric spaces and lattices of equivalence relationsNov 27 2018For a finite lattice $\Lambda$, $\Lambda$-ultrametric spaces have, among other reasons, appeared as a means of constructing structures with lattices of equivalence relations embedding $\Lambda$. This makes use of an isomorphism of categories between $\Lambda$-ultrametric ... 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

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

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

Minimising Hausdorff Dimension under Hölder EquivalenceJan 18 2019We study the infimal value of the Hausdorff dimension of spaces that are H\"older equivalent to a given metric space; we call this bi-H\"older-invariant "H\"older dimension". This definition and some of our methods are analogous to those used in the study ... 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

Constant Slope Models for Finitely Generated MapsJul 14 2017We study countably monotone and Markov interval maps. We establish sufficient conditions for uniqueness of a conjugate map of constant slope. We explain how global window perturbation can be used to generate a large class of maps satisfying these conditions. ... More

Vector space bases associated to vanishing ideals of pointsAug 26 2008Apr 14 2009We discuss four different constructions of vector space bases associated to vanishing ideals of points. We show how to compute normal forms with respect to these bases and give new complexity bounds. As an application, we improve the computational algebra ... 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

The Maximum Number of Subset Divisors of a Given SizeJul 17 2014May 20 2015If $s$ is a positive integer and $A$ is a set of positive integers, we say that $B$ is an $s$-divisor of $A$ if $\sum_{b\in B} b\mid s\sum_{a\in A} a$. We study the maximal number of $k$-subsets of an $n$-element set that can be $s$-divisors. We provide ... 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

The Donaldson hyperkähler metric on the almost-Fuchsian moduli spaceSep 04 2018Donaldon constructed a hyperk\"ahler moduli space $\mathcal{M}$ associated to a closed oriented surface $\Sigma$ with $\textrm{genus}(\Sigma) \geq 2$. This embeds naturally into the cotangent bundle $T^*\mathcal{T}(\Sigma)$ of Teichm\"uller space or can ... More

Boolean ideals and their varietiesNov 14 2012May 25 2015We consider ideals in the ring $\mathbb{Z}_2[x_1,\ldots, x_n]$ that contain the polynomials $x_i^2 - x_i$ for $i = 1, \ldots, n$ and give various results related to the one-to-one correspondence between these ideals and the subsets of $\mathbb{Z}_2^n$. ... More

The Square Sieve and a Lang-Trotter Question for Generic Abelian VarietiesFeb 09 2017Mar 02 2017Let $A$ be a $g$-dimensional abelian variety over $\mathbb{Q}$ whose adelic Galois representation has open image in $\text{GSp}_{2g} \widehat{\mathbb{Z}}$. We investigate the endomorphism algebras $\text{End}(A_p) \otimes \mathbb{Q} = \mathbb{Q}( \pi_p ... 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

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

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

Multidimensional Inverse Scattering of Integrable Lattice EquationsJan 23 2012Mar 21 2012We present a discrete inverse scattering transform for all ABS equations excluding Q4. The nonlinear partial difference equations presented in the ABS hierarchy represent a comprehensive class of scalar affine-linear lattice equations which possess the ... 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

The anomaly field theories of six-dimensional (2,0) superconformal theoriesJun 06 2017Jun 16 2017We construct 7-dimensional quantum field theories encoding the anomalies of conformal field theories with (2,0) supersymmetry in six dimensions. We explain how the conformal blocks of the (2,0) theories arise in this context. A result of independent interest ... 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.

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

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

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

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

Infinite Limits of Finite-Dimensional Permutation Structures, and their Automorphism Groups: Between Model Theory and CombinatoricsMay 11 2018In the course of classifying the homogeneous permutations, Cameron introduced the viewpoint of permutations as structures in a language of two linear orders, and this structural viewpoint is taken up here. The majority of this thesis is concerned with ... More

Ramsey expansions of $Λ$-ultrametric spacesOct 03 2017For a finite lattice $\Lambda$, $\Lambda$-ultrametric spaces are a convenient language for describing structures equipped with a family of equivalence relations. When $\Lambda$ is finite and distributive, there exists a generic $\Lambda$-ultrametric space, ... 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

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

Towards the undecidability of atomicity for permutation classes via the undecidability of joint embedding for hereditary graph classesMar 28 2019We work towards answering a question of Ru\v{s}kuc on the decidability of atomicity for permutation classes, which is equivalent to the decidability of the joint embedding property when permutations are viewed as structures in a language of two linear ... More

Non-vanishing forms in projective space over finite fieldsMay 04 2009May 25 2015We consider a subset of projective space over a finite field and give bounds on the minimal degree of a non-vanishing form with respect to this subset.

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

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

Unimodality of Partitions in Near-Rectangular Ferrers DiagramsAug 18 2014Oct 01 2017We 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

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 defect recollement, the MacPherson-Vilonen construction, and pp formulasAug 19 2018Apr 08 2019For any abelian category $\mathcal{A}$, Auslander constructed a localisation $w:\mathrm{fp}(\mathcal{A}^{\mathrm{op}},\mathrm{Ab})\to \mathcal{A}$ called the defect, which is the left adjoint to the Yoneda embedding $Y:\mathcal{A}\to\mathrm{fp}(\mathcal{A}^{\mathrm{op}},\mathrm{Ab})$. ... 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

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

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

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

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

On Certain Tilting Modules for SL2May 19 2017Sep 19 2017We give a complete picture of when the tensor product of an induced module and a Weyl module is a tilting module for the algebraic group $SL_2$ over an algebraically closed field of characteristic $p$. Whilst the result is recursive by nature, we give ... 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.

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