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Charge pair hopping and Bose-Einstein condensation in underdoped Mott insulatorsDec 06 2010Recently, we have solved the long-standing problem of connecting the physics of the Mott insulator to the underdoped regime of the t-J model [PRB 82, 014504, 2010]. We have derived a renormalized Hamiltonian valid for small doping (x) which is characterized ... More

A Consistent Theory of Underdoped Cuprates: Evolution of the RVB State From Half FillingOct 12 2009Oct 18 2009We have been able to resolve two long-standing issues that are central to the theory of high Tc superconductivity: (1) How is the physics of the doped region connected to that of the Mott insulator? (2) What is the origin of the two-dimensionality of ... More

Tunable $Γ- K$ Valley Populations in Hole-Doped Trilayer WSe$_2$Jan 10 2018We present a combined experimental and theoretical study of valley populations in the valence bands of trilayer WSe$_2$. Shubnikov$-$de Haas oscillations show that trilayer holes populate two distinct subbands associated with the $K$ and $\Gamma$ valleys, ... More

Emergence of Topologically Protected Helical States in Minimally Twisted Bilayer GrapheneFeb 08 2018Bilayer graphene samples in which inversion symmetry is broken have quantum valley Hall ground states that support counterpropogating topologically protected helical (TPH) edge states localized along domain walls between AB and BA stacking regions. Moreover, ... More

Topological Exciton Bands in Moiré HeterojunctionsOct 12 2016Moir\'e patterns are common in Van der Waals heterostructures and can be used to apply periodic potentials to elementary excitations. We show that the optical absorption spectrum of transition metal dichalcogenide bilayers is profoundly altered by long ... More

Ionic Binding in a Susy BackgroundNov 01 2006Jun 08 2007From string theory and the observation of a positive vacuum energy in our universe it seems inevitable that there will eventually be a phase transition to an exactly supersymmetric (susy) universe. In this phase there will be an effective weakening of ... More

Quantum Soliton Mass Corrections in SL(N) Affine Toda TheorySep 08 1992The first quantum mass corrections for the solitons of complex $sl(n)$ affine Toda field theory are calculated. The corrections are real and preserve the classical mass ratios. The formalism also proves that the solitons are classically stable.

Finiteness and Paradoxical Decompostions in C*-Dynamical SystemsFeb 21 2015We discuss the interplay between K-theoretical dynamics and the structure theory for certain C*-algebras arising from crossed products. For noncommutative C*-systems we present notions of minimality and topological transitivity in the K-theoretic framework ... More

On Milgram's construction and the Duke embedding conjecturesMar 10 2013Apr 18 2013Milgram constructed a 28-vertex cubic graph of genus 4 that disproved Duke's conjecture relating Betti number to minimum genus. We apply Milgram's method to construct to find graphs of higher genus violating Duke's conjecture, which gives a sharper bound ... More

On primes of the form $n_1^u + n_2^v + k$, on averageFeb 07 2012Oct 03 2012We use the Hardy-Littlewood circle method to study primes of the form $n_1^u + n_2^v + k$, on average.

The Bouniakowsky conjecture and the density of polynomial roots to prime moduliJun 06 2009We establish a result linking the Bouniakowsky conjecture and the density of polynomial roots to prime moduli.

From abstract alpha-Ramsey theory to abstract ultra-Ramsey theoryJan 15 2016We work within the framework of the Alpha-Theory introduced by Benci and Di Nasso. The Alpha-Theory postulates a few natural properties for an infinite "ideal" number $\alpha$. The formulation provides an elementary axiomatics for the methods of abstract ... More

Quantum Yang-Mills Theory in Two Dimensions: Exact versus PerturbativeAug 25 2015Sep 07 2016The standard Feynman diagrammatic approach to quantum field theories assumes that perturbation theory approximates the full quantum theory at small coupling even when a mathematically rigorous construction of the latter is absent. On the other hand, two-dimensional ... More

Families of G-constellations over resolutions of quotient singularitiesMay 14 2003Let G be a finite subgroup of GL_n(C). A study is made of the ways in which resolutions of the quotient space C^n / G can parametrise G-constellations, that is, G-regular finite length sheaves. These generalise G-clusters, which are used in the McKay ... More

Dissecting Equilateral Triangles into Non-Congruent Equilateral Triangles: A Novel Proof of Tutte's ResultDec 15 2014In this paper, we show that an equilateral triangle cannot be dissected into finitely many smaller equilateral triangles, no two of which share two vertices. We do this without the use of Electrical Networks.

Gram's Law Fails a Positive Proportion of the TimeNov 06 2008This paper extends the work done by Titchmarsh on Gram's Law (an attempt to locate the zeroes of the zeta-function on the critical line). Herewith it is shown that a positive proportion of Gram intervals violate Gram's Law; and also that a weaker notion ... More

Exposing the Hidden Web: An Analysis of Third-Party HTTP Requests on 1 Million WebsitesNov 02 2015This article provides a quantitative analysis of privacy-compromising mechanisms on 1 million popular websites. Findings indicate that nearly 9 in 10 websites leak user data to parties of which the user is likely unaware; more than 6 in 10 websites spawn ... More

Lagrangian correspondences and Donaldson's TQFT construction of the Seiberg-Witten invariants of 3-manifoldsNov 15 2011Sep 08 2013Using Morse-Bott techniques adapted to the gauge-theoretic setting, we show that the limiting boundary values of the space of finite energy monopoles on a connected 3-manifold with at least two cylindrical ends provides an immersed Lagrangian submanifold ... More

Selective but not RamseyDec 19 2013We give a partial answer to the following question of Dobrinen: For a given topological Ramsey space $\mathcal{R}$, are the notions of selective for $\mathcal{R}$ and Ramsey for $\mathcal{R}$ equivalent? Every topological Ramsey space $\mathcal{R}$ has ... More

Bounds on Integral Means of Bergman Projections and their DerivativesMar 13 2015Sep 29 2016We bound integral means of the Bergman projection of a function in terms of integral means of the original function. As an application of these results, we bound certain weighted Bergman space norms of derivatives of Bergman projections in terms of weighted ... More

Computing area in group presentationsJun 28 2016Jul 23 2016The width of a word $w$ representing an element in a free group $F(a,b)$ was defined by Jiang to be the minimal $N$ such that $w$ freely equals a product of $N$ conjugates of powers of $a$ and $b$. In 1991 Grigorchuk and Kurchanov gave an algorithm computing ... More

Nonparametric Stochastic Discount Factor DecompositionDec 15 2014Aug 19 2016Stochastic discount factor (SDF) processes in dynamic economies admit a permanent-transitory decomposition in which the permanent component characterizes pricing over long investment horizons. This paper introduces econometric methods to extract the permanent ... More

Quantum Solitons in Affine Toda Field TheoriesOct 03 1991The spectra of $A_r$ affine Toda field theories with imaginary coupling constant, are investigated. Soliton solutions are found, which, despite the non-unitary form of the Lagrangian, have real classical masses and are stable to small perturbations. The ... More

The Perturbative Approach to Path Integrals: A Succinct Mathematical TreatmentMay 18 2015Sep 29 2016We study finite-dimensional integrals in a way that elucidates the mathematical meaning behind the formal manipulations of path integrals occurring in quantum field theory. This involves a proper understanding of how Wick's theorem allows one to evaluate ... More

Wilson Loop Area Law for 2D Yang-Mills in Generalized Axial GaugeJan 18 2016Jul 25 2016We prove that Wilson loop expectation values for arbitrary simple closed contours obey an area law up to second order in perturbative two-dimensional Yang-Mills theory. Our analysis occurs within a general family of axial-like gauges, which include and ... More

$\mathcal{S}$-categories, $\mathcal{S}$-groupoids, Segal categories and quasicategoriesJan 21 2004The notes were prepared for a series of talks that I gave in Hagen in late June and early July 2003, and, with some changes, in the University of La Lagu\~{n}a, the Canary Islands, in September, 2003. They aim (i) to revisit some oldish material on abstract ... More

What `shape' is space-time?Oct 22 2002Some examples from the mathematics of shape are presented that question some of the almost hidden assumptions behind results on limiting behaviour of finitary approximations to space-time. These are presented so as to focus attention on the observational ... More

Bootstrapping Deep Lexical Resources: Resources for CoursesSep 15 2007We propose a range of deep lexical acquisition methods which make use of morphological, syntactic and ontological language resources to model word similarity and bootstrap from a seed lexicon. The different methods are deployed in learning lexical items ... More

Derived McKay correspondence via pure-sheaf transformsJun 30 2006Feb 04 2008In most cases where it had been shown to exist the derived McKay correspondence D(Y) --> D^G(C^n) can be written as a Fourier-Mukai transform which sends point sheaves of the crepant resolution Y to pure sheaves in D^G(C^n). We give a sufficient condition ... More

A Class of Profinite Hopf-Galois Extensions Over QOct 14 2016Nov 18 2016For $p$ a prime and $a\in\mathbb{Q}$, where $a$ is not a $p^n$-th power of any rational number, the extension $\mathbb{Q}(w_n)/\mathbb{Q}$ where $w_n=\root p^n \of a$ is separable but non-normal. The Hopf-Galois theory for separable extensions was determined ... More

Reid's recipe and derived categoriesDec 24 2008May 15 2012We prove two existing conjectures which describe the geometrical McKay correspondence for a finite abelian G in SL3(C) such that C^3/G has a single isolated singularity. We do it by studying the relation between the derived category mechanics of computing ... More

The Seiberg-Witten Equations on Manifolds with Boundary II: Lagrangian Boundary Conditions for a Floer TheoryAug 11 2010Jun 01 2016In this paper, we study the Seiberg-Witten equations on the product R x Y, where Y is a compact 3-manifold with boundary. Following the approach of Salamon and Wehrheim in the instanton case, we impose Lagrangian boundary conditions for the Seiberg- Witten ... More

Regularity of Extremal Functions in Weighted Bergman and Fock Type SpacesNov 07 2014We discuss the regularity of extremal functions in certain weighted Bergman and Fock type spaces. Given an appropriate analytic function $k$, the corresponding extremal function is the function with unit norm maximizing $\text{Re} \int_\Omega f(z) \overline{k(z)}\, ... More

Death and extended persistence in computational algebraic topologySep 04 2016The main aim of this paper is to explore the ideas of persistent homology and extended persistent homology, and their stability theorems, using ideas from [Bubenik and Scott, 2014; Cohen-Steiner, Edelsbrunner, and Harer, 2007; and Cohen-Steiner, Edelsbrunner, ... More

An introduction to varieties in weighted projective spaceApr 08 2016Apr 17 2016Weighted projective space arises when we consider the usual geometric definition for projective space and allow for non-trivial weights. On its own, this extra freedom gives rise to more than enough interesting phenomena, but it is the fact that weighted ... More

Structural Properties of ${\cal R}_2$ Part IMar 07 2016This is the first of two papers establishing structural properties of ${\cal R}_2$.

On the sum of integers from some multiplicative sets and some powers of integersOct 17 2016We show that if there exists an integer subject to some congruence conditions that cannot be written as the sum of the norm of an ideal in $\mathbb{Z}[\exp(2\pi i/2^k)]$ and at most $k$ powers of $2$, $k\geq 3$, then there are infinitely many such integers. ... More

Adaptive testing on a regression function at a pointAug 15 2014Oct 14 2015We consider the problem of inference on a regression function at a point when the entire function satisfies a sign or shape restriction under the null. We propose a test that achieves the optimal minimax rate adaptively over a range of H\"{o}lder classes, ... More

A Class of Profinite Hopf-Galois Extensions Over QOct 14 2016For $p$ a prime and $a\in\mathbb{Q}$, where $a$ is not a $p^n$-th power of any rational number, the extension $\mathbb{Q}(w_n)/\mathbb{Q}$ where $w_n=\root p^n \of a$ is separable but non-normal. The Hopf-Galois theory for separable extensions was determined ... More

On the Discrepancy of the Roots of $x^2+1$ and $x^2+2$ to Prime ModuliMar 07 2011Oct 03 2012In this paper, we make a conjecture (conjecture 1) related to the Bateman-Horn conjecture and proceed to study the roots of $x^2+1$ and $x^2+2$ to prime moduli, assuming the truth of the Bateman-Horn conjecture and conjecture 1 and using the Erd\H{o}s-Turan-Koksma ... More

A note on the lattice Dirac-Kaehler equationJul 18 1995A lattice version of the Dirac-Kaehler equation (DKE) describing fermions was discussed in articles by Becher and Joos. The decomposition of lattice Dirac-Kaehler fields (inhomogeneous cochains) to lattice Dirac fields remained as an open problem. I show ... More

On the parity of the multiplicative order of certain products of integers related to Gauss factorialsMar 08 2016Mar 15 2016In this note, we prove that under some conditions, certain products of integers related to Gauss factorials are always quadratic residues.

On the sum of integers from some multiplicative sets and some powers of integersOct 17 2016Oct 18 2016We show that if there exists an integer subject to some congruence conditions that cannot be written as the sum of the norm of an ideal in $\mathbb{Z}[\exp(2\pi i/2^k)]$ and at most $k$ powers of $2$, $k\geq 3$, then there are infinitely many such integers. ... More

A symplectic Gysin sequenceJul 11 2008We use the theory of pseudo-holomorphic quilts to establish a counterpart, in symplectic Floer homology, to the Gysin sequence for the homology of a sphere-bundle. In a motivating class of examples, this "symplectic Gysin sequence" is precisely analogous ... More

Tropical Vertex-Disjoint Cycles of a Vertex-Colored Digraph (TROPICAL EXCHANGE) is NP-CompleteOct 14 2016Given a directed graph, it is known that the problem of finnding a set of vertex-disjoint cycles with the maximum total number of vertices (MAX SIZE EXCHANGE) can be solved in polynomial time. Given a vertex-colored graph, if a set of vertices contains ... More

Natural G-Constellation FamiliesDec 31 2005Dec 25 2008Let G be a finite subgroup of GL_n(C). G-constellations are a scheme-theoretic generalization of orbits of G in C^n. We study flat families of G-constellations parametrised by an arbitrary resolution of the quotient space C^n/G. We develop a geometrical ... More

Improvements to Turing's MethodMar 11 2009Aug 05 2010This paper refines the argument of Lehman by reducing the size of the constants in Turing's method. This improvement is given in Theorem 1 and scope for further improvements is also given. Analogous improvements to Dirichlet L-functions and Dedekind zeta-functions ... More

Ramsey for $\mathcal{R}_{1}$ ultrafilter mappings and their Dedekind cutsJan 13 2014Associated to each ultrafilter $\mathcal{U}$ on $\omega$ and each map $p:\omega\rightarrow \omega$ is a Dedekind cut in the ultrapower $\omega^{\omega}/p( \mathcal{U})$. Blass has characterized, under CH, the cuts obtainable when $\mathcal{U}$ is taken ... More

Bergman-Hölder Functions, Area Integral Means and Extremal ProblemsAug 02 2016We study certain weighted area integral means of analytic functions in the unit disc. We relate the growth of these means to the property of being mean H\"older continuous with respect to the Bergman space norm. In contrast with earlier work, we use the ... More

Extremal Problems in Bergman Spaces and an Extension of Ryabykh's $H^p$ Regularity Theorem For $1<p<\infty$Feb 05 2015We study linear extremal problems in the Bergman space $A^p$ of the unit disc, where $1 < p < \infty$. Given a functional on the dual space of $A^p$ with representing kernel $k \in A^q$, where $1/p + 1/q = 1$, we show that if $q \le q_1 < \infty$ and ... More

The Prouhet-Tarry-Escott problem for Gaussian integersNov 04 2010Feb 13 2011Given natural numbers $n$ and $k$, with $n>k$, the Prouhet-Tarry-Escott (PTE) problem asks for distinct subsets of $\Z$, say $X=\{x_1,...,x_n\}$ and $Y=\{y_1,...,y_n\}$, such that \[x_1^i+...+x_n^i=y_1^i+...+y_n^i\] for $i=1,...,k$. Many partial solutions ... More

The Prescribed Ricci Curvature Problem on Three-Dimensional Unimodular Lie GroupsJul 12 2016Let G be a three-dimensional unimodular Lie group, and let T be a left-invariant symmetric (0, 2)-tensor field on G. We provide the necessary and sufficient conditions on T for the existence of a pair (g, c) consisting of a left-invariant Riemannian metric ... More

Tidal Tails of Interacting GalaxiesOct 25 2012Oct 30 2012This paper has been withdrawn by the author. A computer simulation of two galaxies, passing in parabolic orbits, was made to show their interaction and the tidal patterns formed. The galaxies were modelled as a point masses surrounded by 5 densely packed, ... More

Hamiltonian handleslides for Heegaard Floer homologyJan 03 2008Feb 27 2008A $g$-tuple of disjoint, linearly independent circles in a Riemann surface of genus $g$ determines a `Heegaard torus' in its $g$-fold symmetric product. Changing the circles by a handleslide produces a new torus. It is proved that, for symplectic forms ... More

Stochastic Feynman Rules for Yang-Mills Theory on the PlaneJul 25 2016Oct 13 2016We analyze quantum Yang-Mills theory on $\mathbb{R}^2$ using a novel discretization method based on an algebraic analogue of stochastic calculus. Such an analogue involves working with "Gaussian" free fields whose covariance matrix is indefinite rather ... More

Quantization of the Nonlinear Sigma Model RevisitedAug 19 2014Sep 06 2016We revisit the subject of perturbatively quantizing the nonlinear sigma model in two dimensions from a rigorous, mathematical point of view. Our main contribution is to make precise the cohomological problem of eliminating potential anomalies that may ... More

Geometric Aspects of Multiagent SystemsOct 25 2002Recent advances in Multiagent Systems (MAS) and Epistemic Logic within Distributed Systems Theory, have used various combinatorial structures that model both the geometry of the systems and the Kripke model structure of models for the logic. Examining ... More

A new upper bound for $|ζ(1+ it)|$Oct 25 2012It is known that $|\zeta(1+ it)|\ll (\log t)^{2/3}$. This paper provides a new explicit estimate, viz.\ $|\zeta(1+ it)|\leq 3/4 \log t$, for $t\geq 3$. This gives the best upper bound on $|\zeta(1+ it)|$ for $t\leq 10^{2\cdot 10^{5}}$.

Computing area in presentations of the trivial groupJun 28 2016Nov 01 2016We give polynomial-time dynamic-programming algorithms finding the areas of words in the presentations $\langle a, b \mid a, b \rangle$ and $\langle a, b \mid a^k, b^k; \ k \in \mathbb{N} \rangle$ of the trivial group. In the first of these two cases, ... More

Stable Commutator Length in Amalgamated Free ProductsOct 08 2013May 12 2014We show that stable commutator length is rational on free products of free Abelian groups amalgamated over $\mathbb{Z}^k$, a class of groups containing the fundamental groups of all torus knot complements. We consider a geometric model for these groups ... More

MF Actions and K-theoretic DynamicsApr 16 2014We study the interplay of C*-dynamics and K-theory. Notions of chain recurrence for transformations groups (X,G) and MF actions for non-commutative C*-dynamical systems (A,G) are translated into K-theoretical language, where purely algebraic conditions ... More

Extremal Problems in Bergman Spaces and an Extension of Ryabykh's TheoremJan 31 2013We study linear extremal problems in the Bergman space $A^p$ of the unit disc for $p$ an even integer. Given a functional on the dual space of $A^p$ with representing kernel $k \in A^q$, where $1/p + 1/q = 1$, we show that if the Taylor coefficients of ... More

The Prescribed Ricci Curvature Problem on Three-Dimensional Unimodular Lie GroupsJul 12 2016Oct 05 2016Let G be a three-dimensional unimodular Lie group, and let T be a left-invariant symmetric (0, 2)-tensor field on G. We provide the necessary and sufficient conditions on T for the existence of a pair (g, c) consisting of a left-invariant Riemannian metric ... More

Stochastic Feynman Rules for Yang-Mills Theory on the PlaneJul 25 2016We analyze quantum Yang-Mills theory on $\mathbb{R}^2$ using a novel discretization method based on an algebraic analogue of stochastic calculus. Such an analogue involves working with "Gaussian" free fields whose covariance matrix is indefinite rather ... More

Structural Properties of ${\cal R}_2$ Part IIMar 07 2016This is the second of two papers establishing structural properties of ${\cal R}_2$.

Anisotropic Function Spaces and Elliptic Boundary Value ProblemsOct 19 2010Mar 01 2011In this paper, we study anisotropic Bessel potential and Besov spaces, where the anisotropy measures the extra amount of regularity in certain directions. Some basic properties of these spaces are established along with applications to elliptic boundary ... More

The Analytic Structure of Trigonometric S MatricesMay 11 1993May 17 1993$S$-matrices associated to the vector representations of the quantum groups for the classical Lie algebras are constructed. For the $a_{m-1}$ and $c_m$ algebras the complete $S$-matrix is found by an application of the bootstrap equations. It is shown ... More

A Pohozaev Identity on Warped Product SolitonsFeb 02 2016Mar 10 2016Warped product metrics are a class of Riemannian metrics on cross products $B \times F$ which have been well studied and provide a rich set of examples. In this paper we consider shrinking gradient Ricci solitons which are warped product metrics. We prove ... More

Ricci Flow Emerging from Rotationally Symmetric Degenerate NeckpinchesNov 13 2014Feb 05 2015In previous work, Angenent, Isenberg, and Knopf created type-II Ricci flow neckpinch singularities. In this paper we construct solutions to Ricci flow whose initial data is the singular metric resulting from these singularities. We show in particular ... More

Towards in-situ cleaning of a trapped ion quantum computerJul 08 2012Sep 08 2012A plasma glow discharge system was created using a conventional microwave oven to ignite and maintain the plasma. The system was used for plasma cleaning and its properties were analysed to assess its viability for removing surface contaminants, which ... More

Hopf-Galois Structures Arising From Groups with Unique Subgroup of Order pMay 19 2014Aug 07 2014For $\Gamma$ a group of order $mp$ for $p$ prime where $gcd(p,m)=1$, we consider those regular subgroups $N\leq Perm(\Gamma)$ normalized by $\lambda(\Gamma)$, the left regular representation of $\Gamma$. These subgroups are in one-to-one correspondence ... More

Analysis of a Double Kruskal TheoremMar 07 2016The strength of an extension of Kruskal's Theorem to certain pairs of cohabitation trees is calibrated.

Formal Homotopy Quantum Field Theories, II : Simplicial Formal MapsDec 01 2005Simplicial formal maps were introduced in the first paper, (math.QA/0512032), of this series as a tool for studying Homotopy Quantum Field Theories with background a general homotopy 2-type. Here we continue their study, showing how a natural generalisation ... More

Continuity of the asymptotics of expected zeros of fewnomialsNov 27 2013In "Random complex fewnomials, I," B. Shiffman and S. Zelditch determine the limiting formula as N goes to infinity of the (normalized) expected distribution of complex zeros of a system of k random n-nomials in m variables where the coefficients are ... More

A modest improvement on the function $S(T)$Oct 21 2010This paper contains a small improvement to the explicit bounds on the growth of the function $S(T)$. It is shown how more substantial improvements are possible if one has better explicit bounds on the growth of $|\zeta(\frac{1}{2}+it)|$.

The Seiberg-Witten Equations on Manifolds with Boundary I: The Space of Monopoles and Their Boundary ValuesAug 11 2010Sep 08 2013In this paper, we study the Seiberg-Witten equations on a compact 3-manifold with boundary. Solutions to these equations are called monopoles. Under some simple topological assumptions, we show that the solution space of all monopoles is a Banach manifold ... More

Continuity of Extremal Elements in Uniformly Convex SpacesJan 30 2013In this paper, we study the problem of finding the extremal element for a linear functional over a uniformly convex Banach space. We show that a unique extremal element exists and depends continuously on the linear functional, and vice versa. Using this, ... More

Solution of Extremal Problems in Bergman Spaces Using the Bergman ProjectionNov 21 2013In this paper we discuss the explicit solution of certain extremal problems in Bergman spaces. In order to do this, we develop methods to calculate the Bergman projections of various functions. As a special case, we deal with canonical divisors for certain ... More

Lorentz Covariant Lattice Gauge TheoryOct 31 2012Lattice gauge theory's discretization of spacetime suffers from a drawback in that Lorentz covariance is lost because the axes of the lattice create preferred directions in spacetime. Smaller and smaller lattice spacings decrease the effect but fail to ... More

Interaction of a Magnet and a Point Charge: Unrecognized Internal Electromagnetic Momentum Eliminates the Myth of Hidden Mechanical MomentumAug 16 2014A model calculation using the Darwin Lagrangian is carried out for a magnet consisting of two current-carrying charges constrained by centripetal forces to move in a circular path in the presence of the electric field from a distant external point charge. ... More

Singular prior distributions in Bayesian D-optimal design for nonlinear modelsJun 09 2015Nov 17 2015For Bayesian D-optimal design, we define a singular prior distribution for the model parameters as a prior distribution such that the determinant of the Fisher information matrix has a prior geometric mean of zero for all designs. For such a prior distribution, ... More

A beginner's guide to forcingDec 09 2007May 08 2008This expository paper, aimed at the reader without much background in set theory or logic, gives an overview of Cohen's proof (via forcing) of the independence of the continuum hypothesis. It emphasizes the broad outlines and the intuitive motivation ... More

On the Asymptotic Distribution of Variance Weighted KS StatisticsFeb 01 2012This paper derives the asymptotic distribution of variance weighted Kolmogorov-Smirnov statistics for conditional moment inequality models for the case of a one dimensional covariate. The asymptotic distribution depends on the data generating process ... More

6 Lectures on QFT, RG and SUSYSep 04 2009An introduction to the theory of the renormalization group in the context of quantum field theories of relevance to particle physics is presented in the form of 6 lectures delivered to the British Universities Summer School in Theoretical Elementary Particle ... More

Five-Dimensional Gauge Theories and Quantum Mechanical Matrix ModelsFeb 20 2003Mar 05 2003We show how the Dijkgraaf-Vafa matrix model proposal can be extended to describe five-dimensional gauge theories compactified on a circle to four dimensions. This involves solving a certain quantum mechanical matrix model. We do this for the lift of the ... More

New Results from Glueball Superpotentials and Matrix Models: the Leigh-Strassler DeformationDec 05 2002Feb 27 2003Using the result of a matrix model computation of the exact glueball superpotential, we investigate the relevant mass perturbations of the Leigh-Strassler marginal ``q'' deformation of N=4 supersymmetric gauge theory. We recall a conjecture for the elliptic ... More

Calculating the Prepotential by Localization on the Moduli Space of InstantonsJan 14 2002Jan 24 2002We describe a new technique for calculating instanton effects in supersymmetric gauge theories applicable on the Higgs or Coulomb branches. In these situations the instantons are constrained and a potential is generated on the instanton moduli space. ... More

Modified Spin-Wave Theory for Nanomagnets : Application to the Keplerate Molecule Mo(72)Fe(30)Dec 09 2004We adapt Takahashi's modified spin-wave theory to the context of nano-magnets, and apply it to the molecular compound based on the giant magnetic molecule Mo(72)Fe(30). This involves solving numerically the mean-field equations and then forcing the sublattice ... More

Setting the Stage: Ultraluminous Galaxies in a Cosmological ContextMar 02 1999Mar 03 1999I will try to put the ultraluminous galaxy phenomenon into a broad cosmological context. Viewed from this perspective, the significance of ultraluminous galaxies and the `starburst vs. monster' debate becomes clear. Ultraluminous galaxies are fascinating ... More

Matrix Units in the Symmetric Group Algebra, and Unitary IntegrationJul 17 2013In this paper, we establish an explicit isomorphism between the symmetric group algebra and the path algebra of the Young graph. Specifically, we construct a family of matrix units in the group algebra. As a main application of this construction, we obtain ... More

What is a closed-form number?May 08 1998If a student asks for an antiderivative of exp(x^2), there is a standard reply: the answer is not an elementary function. But if a student asks for a closed-form expression for the real root of x = cos(x), there is no standard reply. We propose a definition ... More

A Comparison of Tram Priority at Signalized IntersectionsNov 12 2013We study tram priority at signalized intersections using a stochastic cellular automaton model for multimodal traffic flow. We simulate realistic traffic signal systems, which include signal linking and adaptive cycle lengths and split plans, with different ... More

Basis States for Hamiltonian QCD with Dynamical QuarksOct 02 1992We discuss the construction of basis states for Hamiltonian QCD on the lattice, in particular states with dynamical quark pairs. We calculate the matrix elements of the operators in the QCD Hamiltonian between these states. Along with the ``harmonic oscillator'' ... More

The power of backtracking and the confinement of lengthJun 16 2011We show that there is a point on a computable arc that does not belong to any computable rectifiable curve. We also show that there is a point on a computable rectifiable curve with computable length that does not belong to any computable arc.

$\ell^2$-homology and planar graphsOct 05 2011In his 1930 paper, Kuratowksi categorized planar graphs, proving that a finite graph $\Gamma$ is planar if and only if it does not contain a subgraph that is homeomorphic to $K_5$, the complete graph on 5 vertices, or $K_{3,3}$, the complete bipartite ... More

On adjunctions for Fourier-Mukai transformsApr 18 2010Aug 16 2012We show that the adjunction counits of a Fourier-Mukai transform $\Phi$ from $D(X_1)$ to $D(X_2)$ arise from maps of the kernels of the corresponding Fourier-Mukai transforms. In a very general setting of proper separable schemes of finite type over a ... More

On Primes Represented by Cubic PolynomialsOct 06 2011Jul 31 2012In this paper, we prove a theorem on the distribution of primes in cubic progressions on average.

Model for vacancy-induced d$^0$ ferromagnetism in oxide compoundsMar 01 2006May 20 2006We propose a model with few parameters, for vacancy-induced ferromagnetism based on a correlated model for anions (oxygen orbitals) with random potentials that represent cation vacancies. There is a range of potential strength for which moments appear ... More

A Parameter Study of Type II Supernova Light Curves Using 6 M_odot He CoresSep 13 2004Results of numerical calculations of Type II supernova light curves are presented. The model progenitor stars have 6 $M{_\odot}$ cores and various envelopes, originating from a numerically evolved 20 $M{_\odot}$ star. Five parameters that affect the light ... More

On the absence of black hole event horizons: a test of De Sitter Yang-Mills TheoryApr 17 2014De Sitter Quantum Gravity is a Yang-Mills theory based on the de Sitter or SO(4,1) group and a promising candidate for a quantum theory of gravity. In this paper, an exact, static, spherically symmetric solution of the classical equations is derived. ... More