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Bees with attitude: the effect of gusts on flight dynamicsFeb 10 2018Flight is a complicated task at small scales in part due to the ubiquitous unsteady air which contains it. Flying organisms deal with these difficulties using active and passive control mechanisms to steer their body motion. Body attitudes of flapping ... More

Tiling Vertices and the Spacing Distribution of their Radial ProjectionJan 23 2014The Fourier-based diffraction approach is an established method to extract order and symmetry propertiesfrom a given point set. We want to investigate a different method for planar sets which works in direct spaceand relies on reduction of the point set ... More

Geographies of an online social networkMar 26 2015Aug 13 2015How is online social media activity structured in the geographical space? Recent studies have shown that in spite of earlier visions about the "death of distance", physical proximity is still a major factor in social tie formation and maintenance in virtual ... More

Comparing DNA sequence collections by direct comparison of compressed text indexesApr 19 2013Popular sequence alignment tools such as BWA convert a reference genome to an indexing data structure based on the Burrows-Wheeler Transform (BWT), from which matches to individual query sequences can be rapidly determined. However the utility of also ... More

More Structural Characterizations of Some Subregular Language Families by BiautomataMay 22 2014We study structural restrictions on biautomata such as, e.g., acyclicity, permutation-freeness, strongly permutation-freeness, and orderability, to mention a few. We compare the obtained language families with those induced by deterministic finite automata ... 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

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

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

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

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

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

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

The Magic Number Problem for Subregular Language FamiliesAug 10 2010We investigate the magic number problem, that is, the question whether there exists a minimal n-state nondeterministic finite automaton (NFA) whose equivalent minimal deterministic finite automaton (DFA) has alpha states, for all n and alpha satisfying ... More

Towards Communication-Efficient Quantum Oblivious Key DistributionAug 13 2012Oblivious Transfer, a fundamental problem in the field of secure multi-party computation is defined as follows: A database DB of N bits held by Bob is queried by a user Alice who is interested in the bit DB_b in such a way that (1) Alice learns DB_b and ... More

Orbital-selective Mott Transitions in a Doped Two-band Hubbard ModelJun 16 2009Sep 22 2009We extend previous studies on orbital-selective Mott transitions in the paramagnetic state of the half-filled degenerate two-band Hubbard model to the general doped case, using a high-precision quantum Monte Carlo dynamical mean-field theory solver. For ... More

Aggregation-fragmentation model of robust concentration gradient formationFeb 06 2015Concentration gradients of signaling molecules are essential for patterning during development and they have been observed in both unicellular and multicellular systems. In subcellular systems, clustering of the signaling molecule has been observed. We ... More

Classical Interaction of a Magnet and a Point Charge: The Classical Electromagnetic Forces Responsible for the Aharonov-Bohm Phase ShiftAug 16 2014Aug 26 2014A new classical electromagnetic analysis is presented suggesting that the Aharonov-Bohm phase shift is overwhelmingly likely to arise from a classical lag effect based upon classical electromagnetic forces. The analysis makes use of several aspects of ... More

Classical Zero-Point Radiation and Relativity: The Problem of Atomic Collapse RevisitedNov 06 2015The physicists of the early 20th century were unaware of two aspects which are vital to understanding some aspects of modern physics within classical theory. The two aspects are: 1) the presence of classical electromagnetic zero-point radiation, and 2) ... More

An exact integration of a φ^4 quantum field theoryJun 27 2013Most quantum field theories are not exactly solvable. In this paper show the statistical equivalence of the standard exponential path integral to products of Heaviside functions, i.e. a product of specially tuned uniform distributions. This allows exact ... More

Exact solution to the 1d one component Coulomb gas at fixed energyNov 02 2011Mar 07 2012The one dimensional one component plasma has applications to one dimensional particle systems with logarithmic interactions such as charges in a single channel wire or vortex filaments in a fluid convection stream. The exact integral of this plasma in ... More

Weighted KS Statistics for Inference on Conditional Moment InequalitiesDec 05 2011This paper proposes confidence regions for the identified set in conditional moment inequality models using Kolmogorov-Smirnov statistics with a truncated inverse variance weighting with increasing truncation points. The new weighting differs from those ... More

The Emergent Copenhagen Interpretation of Quantum MechanicsDec 12 2013We introduce a new and conceptually simple interpretation of quantum mechanics based on reduced density matrices of sub-systems from which the standard Copenhagen interpretation emerges as an effective description of macroscopically large systems. Wave ... More

Strong Coupling N=2 Gauge Theory with Arbitrary Gauge GroupOct 08 1997A complete definition of the cycles, on the auxiliary Riemann surface defined by Martinec and Warner for describing pure N=2 gauge theories with arbitrary group, is provided. The strong coupling monodromies around the vanishing cycles are shown to arise ... More

Schrodinger's Cat and the FirewallMar 24 2014Apr 11 2014It has been argued that when black holes are treated as quantum systems there are implications at the horizon and not just the singularity. Infalling observers will meet a firewall of high energy quanta. We argue that the question of whether an observer ... More

New Modal Quantum MechanicsDec 17 2013We describe an interpretation of quantum mechanics based on reduced density matrices of sub-systems from which the standard Copenhagen interpretation emerges as an effective description for macro-systems. The interpretation is a modal one, but does not ... More

Constraints on MACHO Dark Matter from Compact Stellar Systems in Ultra-Faint Dwarf GalaxiesMay 12 2016Jun 09 2016I show that a recently discovered star cluster near the center of the ultra-faint dwarf galaxy Eridanus II provides strong constraints on massive compact halo objects (MACHOs) of >~5 M_sun as the main component of dark matter. MACHO dark matter will dynamically ... More

The Role of Starbursts in the Formation of Galaxies & Active Galactic NucleiDec 01 1999Starbursts are episodes of intense star-formation in the central regions of galaxies, and are the sites of roughly 25% of the high-mass star-formation in the local universe. In this contribution I review the role starbursts play in the formation and evolution ... More

The formation of bulges and black holes: lessons from a census of active galaxies in the SDSSJun 08 2004We examine the relationship between galaxies, supermassive black holes and AGN using a sample of 22,000 narrow-emission-line AGN drawn from a a sample of 122,000 galaxies from the Sloan Digital Sky Survey. We have studied how AGN host properties compare ... More

Galactic Superwinds Circa 2001Jul 23 2001In this contribution I summarize our current knowledge of the nature and significance of starburst-driven galactic winds (``superwinds''). Superwinds are complex multiphase outflows of cool, warm, and hot gas, dust, and magnetized relativistic plasma. ... More

Topological invariants of a fan associated to a toric varietyMay 24 1995Associated to a toric variety $X$ of dimension $r$ over a field $k$ is a fan $\Delta$ on $\Bbb R^r$. The fan $\Delta$ is a finite set of cones which are in one-to-one correspondence with the orbits of the torus action on $X$. The fan $\Delta$ inherits ... More

The Distinguishability of Interacting Dark Energy from Modified GravitySep 12 2012Jan 16 2013We study the observational viability of coupled quintessence models with their expansion and growth histories matched to modified gravity cosmologies. We find that for a Dvali-Gabadadze-Porrati model which has been fitted to observations, the matched ... More

Water wave transmission by an array of floating disksMar 15 2014An experimental validation of theoretical models of transmission of regular water waves by large arrays of floating disks is presented. The experiments are conducted in a wave basin. The models are based on combined potential-flow and thin-plate theories, ... More

The marginalization paradox and the formal Bayes' lawAug 10 2007It has recently been shown that the marginalization paradox (MP) can be resolved by interpreting improper inferences as probability limits. The key to the resolution is that probability limits need not satisfy the formal Bayes' law, which is used in the ... More

The $\ell^2$-homology of even Coxeter groupsJul 12 2007Jul 18 2007Given a Coxeter system (W,S), there is an associated CW-complex, Sigma, on which W acts properly and cocompactly. We prove that when the nerve L of (W,S) is a flag triangulation of the 3-sphere, then the reduced $\ell^2$-homology of Sigma vanishes in ... More

Quasar Radio-Loudness and the Elliptical Core ProblemJun 01 2010The dichotomy between radio-loud and radio-quiet QSOs is not simply one of host morphology. While spiral galaxies almost exclusively host radio-quiet QSOs, ellipticals can host either radio-louds or radio-quiets. We find that a combination of accretion ... More

Carathéodory's Theorem and moduli of local connectivityAug 17 2014Jan 07 2015We give a constructive proof of the Carath\'eodory Theorem by means of the concept of a modulus of local connectivity and the extremal distance of the separating curves of an annulus.

An operator-theoretic existence proof of solutions to planar Dirichlét problemsOct 25 2011By using some elementary techniques from operator theory, we prove constructively prove the existence of solutions to Dirichl\'et problems for planar Jordan domains with at least two boundary curves. An iterative method is thus obtained, and explicit ... More