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The Geometry of b^k ManifoldsApr 13 2013Jul 30 2013Let $Z$ be a hypersurface of a manifold $M$. The $b$-tangent bundle of $(M, Z)$, whose sections are vector fields tangent to $Z$, is used to study pseudodifferential operators and stable Poisson structures on $M$. In this paper we introduce the $b^k$-tangent ... More

Torus Invariant CurvesApr 13 2013Jul 30 2013Using the language of T-varieties, we study torus invariant curves on a complete normal variety $X$ with an effective codimension-one torus action. In the same way that the $T$-invariant Weil divisors on $X$ are sums of "vertical" divisors and "horizontal" ... More

The geometry of E-manifoldsFeb 08 2018Motivated by the study of symplectic Lie algebroids, we study a describe a type of algebroid (called an $E$-tangent bundle) which is particularly well-suited to study of singular differential forms and their cohomology. This setting generalizes the study ... More

Graphs with Equal Chromatic Symmetric FunctionsAug 27 2013Stanley [9] introduced the chromatic symmetric function ${\bf X}_G$ associated to a simple graph $G$ as a generalization of the chromatic polynomial of $G$. In this paper we present a novel technique to write ${\bf X}_G$ as a linear combination of chromatic ... More

Action-angle variables and a KAM theorem for b-Poisson manifoldsFeb 11 2015Mar 02 2015In this article we prove an action-angle theorem for b-integrable systems on b-Poisson manifolds improving the action-angle theorem contained in [LMV11] for general Poisson manifolds in this setting. As an application, we prove a KAM-type theorem for ... More

Convexity for Hamiltonian torus actions on $b$-symplectic manifoldsDec 08 2014May 11 2016In [GMPS] we proved that the moment map image of a $b$-symplectic toric manifold is a convex $b$-polytope. In this paper we obtain convexity results for the more general case of non-toric hamiltonian torus actions on $b$-symplectic manifolds. The modular ... More

The Non-homogeneous Poisson Process for Fast Radio Burst RatesNov 02 2016This paper presents the non-homogeneous Poisson process (NHPP) for modeling the rate of fast radio bursts (FRBs) and other infrequently observed astronomical events. The NHPP, well-known in statistics, can model changes in the rate as a function of both ... More

Rare Event Statistics Applied to Fast Radio BurstsDec 02 2016Statistical interpretation of sparsely sampled event rates has become vital for new transient surveys, particularly those aimed at detecting fast radio bursts (FRBs). We provide an accessible reference for a number of simple, but critical, statistical ... More

Comparison of RFI Mitigation Strategies for Dispersed Pulse DetectionJan 07 2012Impulsive radio-frequency signals from astronomical sources are dispersed by the frequency dependent index of refraction of the interstellar media and so appear as chirped signals when they reach earth. Searches for dispersed impulses have been limited ... More

The Classification of Two Dimensional topological Field TheoriesMar 29 2014The goal of this paper is to introduce some of the major ideas behind extended topological quantum field theories with an emphasis on explicit examples and calculations. The statement of the Cobordism Hypothesis is explained and immediately used to classify ... More

The Riemann-Roch Theorem and Zero Energy Solutions of the Dirac Equation on the Riemann SphereSep 01 2009Sep 06 2009In this paper, we revisit the connection between the Riemann-Roch theorem and the zero energy solutions of the two-dimensional Dirac equation in the presence of a delta-function like magnetic field. Our main result is the resolution of a paradox - the ... More

Uniqueness and multiplicity of infinite clustersApr 14 2005Aug 16 2006The Burton--Keane theorem for the almost-sure uniqueness of infinite clusters is a landmark of stochastic geometry. Let $\mu$ be a translation-invariant probability measure with the finite-energy property on the edge-set of a $d$-dimensional lattice. ... More

On connective KO-theory of elementary abelian 2-groupsJul 30 2012Feb 10 2014A general notion of detection is introduced and used in the study of the cohomology of elementary abelian 2-groups with respect to the spectra in the Postnikov tower of orthogonal K-theory. This recovers and extends results of Bruner and Greenlees and ... More

Embedding the flag representation in divided powersSep 18 2009A generalization of a theorem of Crabb and Hubbuck concerning the embedding of flag representations in divided powers is given, working over an arbitrary finite field F, using the category of functors from finite-dimensional F-vector spaces to F-vector ... More

Three theorems in discrete random geometryOct 11 2011Jan 27 2012These notes are focused on three recent results in discrete random geometry, namely: the proof by Duminil-Copin and Smirnov that the connective constant of the hexagonal lattice is \sqrt{2+\sqrt 2}; the proof by the author and Manolescu of the universality ... More

David George Kendall, a biographical accountOct 07 2008This biographical account of the life and work of David Kendall includes details of his personal and professional activities. Kendall is probably best known for his work in applied probability, especially queueing theory, and in stochastic analysis and ... More

Space-time percolationMay 03 2007The contact model for the spread of disease may be viewed as a directed percolation model on $\ZZ \times \RR$ in which the continuum axis is oriented in the direction of increasing time. Techniques from percolation have enabled a fairly complete analysis ... More

Search for $W'\rightarrow t\bar{b}$ in the lepton plus jets final states with the ATLAS detector at the LHCNov 28 2014This document presents a search for a $W'$ boson, decaying to a top quark and a $b$ quark in an effective coupling approach, using a multivariate method based on boosted decision trees. It reports exclusion limits on the $W'\rightarrow tb$ cross-section ... More

Seeable matter; unseeable antimatterJul 16 2014The universe we see gives every sign of being composed of matter. This is considered a major unsolved problem in theoretical physics. Using the mathematical modeling based on the algebra ${\bf{T}} := {\bf{C}}\otimes{\bf{H}}\otimes{\bf{O}}$, an interpretation ... More

A Millisecond Interferometric Search for Fast Radio Bursts with the Very Large ArrayDec 23 2014We report on the first millisecond timescale radio interferometric search for the new class of transient known as fast radio bursts (FRBs). We used the Very Large Array (VLA) for a 166-hour, millisecond imaging campaign to detect and precisely localize ... More

Toric actions on b-symplectic manifoldsSep 07 2013Mar 05 2014We study Hamiltonian actions on $b$-symplectic manifolds with a focus on the effective case of half the dimension of the manifold. In particular, we prove a Delzant-type theorem that classifies these manifolds using polytopes that reside in a certain ... More

Galerkin Methods for Complementarity Problems and Variational InequalitiesJun 20 2013Complementarity problems and variational inequalities arise in a wide variety of areas, including machine learning, planning, game theory, and physical simulation. In all of these areas, to handle large-scale problem instances, we need fast approximate ... More

Reversible Communicating ProcessesFeb 11 2016Reversible distributed programs have the ability to abort unproductive computation paths and backtrack, while unwinding communication that occurred in the aborted paths. While it is natural to assume that reversibility implies full state recovery (as ... More

Constraining the Rate of Relativistic Jets from Tidal Disruptions Using Radio SurveysMar 22 2011Tidal disruption of stars by massive black holes produce transient accretion flows that flare at optical, UV, and X-ray wavelengths. At late times, these accretion flows may launch relativistic jets that can be detected through the interaction of the ... More

Criticality, universality, and isoradialityApr 10 2014Critical points and singularities are encountered in the study of critical phenomena in probability and physics. We present recent results concerning the values of such critical points and the nature of the singularities for two prominent probabilistic ... More

Logarithmic vector-valued modular formsOct 20 2009We consider logarithmic vector- and matrix-valued modular forms of integral weight $k$ associated with a $p$-dimensional representation $\rho: SL_2(\mathbb{Z}) \to GL_p(\mathbb{C})$ of the modular group, subject only to the condition that $\rho(T)$ has ... More

How much information about a dynamical system do its recurrences contain?Jun 27 2007Jul 04 2007We show that, under suitable assumptions, Poincare recurrences of a dynamical system determine its topology in phase space. Therefore, dynamical systems with the same recurrences are topologically equivalent.

Detecting highly cyclic structure with complex eigenpairsAug 24 2016Many large, real-world complex networks have rich community structure that a network scientist seeks to understand. These communities may overlap or have intricate internal structure. Extracting communities with particular topological structure, even ... More

Ramanujan and Eckford Cohen totients from Visible Point IdentitiesDec 12 2012We define an extension of the Ramanujan trigonometric function to arbitrary dimensions, and give the Dirichlet series generating function. The extension was first given by Eckford Cohen long ago. This links directly to visible point vector identities, ... More

Squeezing through: capsule or bubble?Oct 10 2013In this fluid dynamics video, we compare the deformation of two flexible particles as they propagate through a sudden constriction of a liquid filled channel under constant-flux flow: a gas bubble, and a capsule formed by encapsulating a liquid droplet ... More

Minidisks in Binary Black Hole AccretionNov 01 2016Newtonian simulations have demonstrated that accretion onto binary black holes produces accretion disks around each black hole ("minidisks"), fed by gas streams flowing through the circumbinary cavity from the surrounding circumbinary disk. We study the ... More

Linear and Circular Polarization from Sagittarius A* and M81*Feb 11 2003We describe recent results for Sgr A*, M81* and other low luminosity active galactic nuclei. We have conducted linear and circular polarimetry over a frequency range of 1.4 to 230 GHz and detected a variety of phenomena. The polarization properties of ... More

New Lower Bounds for 28 Classical Ramsey NumbersApr 09 2015Jul 19 2015We establish new lower bounds for $28$ classical two and three color Ramsey numbers, and describe the heuristic search procedures we used. Several of the new three color bounds are derived from the two color constructions; specifically, we were able to ... More

Tidal coupling of a Schwarzschild black hole and circularly orbiting moonMay 31 2005Nov 13 2005We describe the possibility of using LISA's gravitational-wave observations to study, with high precision, the response of a massive central body to the tidal gravitational pull of an orbiting, compact, small-mass object. Motivated by this application, ... More

Bond percolation on isoradial graphs: criticality and universalityApr 02 2012Mar 07 2013In an investigation of percolation on isoradial graphs, we prove the criticality of canonical bond percolation on isoradial embeddings of planar graphs, thus extending celebrated earlier results for homogeneous and inhomogeneous square, triangular, and ... More

The Potts and random-cluster modelsDec 08 2014This is a short account of connections between the Tutte polynomial and the Ising, Potts, and random-cluster models. The four principal elements are the Ising model of 1925, the Tutte polynomial of 1947, the Potts model of 1952, and the random-cluster ... More

Lifting a 5-dimensional representation of $M_{11}$ to a complex unitary representation of a certain amalgamFeb 02 2015Feb 08 2015We lift the $5$-dimensional characteristic $3$ representation of $M_{11}$ to a complex representation of the amalgam ${\rm GL}(2,3)*_{D_8}S_{4}$, and consider its reduction (mod $p$) for other odd primes.

On smallest trianglesAug 06 2002Pick n points independently at random in R^2, according to a prescribed probability measure mu, and let D^n_1 <= D^n_2 <= ... be the areas of the binomial n choose 3 triangles thus formed, in non-decreasing order. If mu is absolutely continuous with respect ... More

Branching Processes, and Random-Cluster Measures on TreesOct 13 2004Random-cluster measures on infinite regular trees are studied in conjunction with a general type of `boundary condition', namely an equivalence relation on the set of infinite paths of the tree. The uniqueness and non-uniqueness of random-cluster measures ... More

The work of Lucio Russo on percolationApr 17 2016May 20 2016The contributions of Lucio Russo to the mathematics of percolation and disordered systems are outlined. The context of his work is explained, and its ongoing impact on current work is described and amplified.

European Apportionment via the Cambridge CompromiseMay 21 2011Aug 22 2011Seven mathematicians and one political scientist met at the Cambridge Apportionment Meeting in January 2011. They agreed a unanimous recommendation to the European Parliament for its future apportionments between the EU Member States. This is a short ... More

Local and Semilocal Vertex Operator AlgebrasSep 21 2004We investigate a general structure theory for a vertex operator algebra. We discuss the center and blocks, the Jacobson radical and solvable radical and local vertex operator algebras. The main consequence of our structure theory is that if the vertex ... More

On the operator content of nilpotent orbifold modelsDec 12 1994Let $V$ be a simple vertex operator algebra and $G$ be a finite nilpotent group of automorphisms of $V.$ We prove the following in this paper: (1) There is a Galois correspondence between subgroups of $G$ and the vertex operator subalgebras of $V$ which ... More

Integrability of C_2-cofinite vertex operator algebrasJan 23 2006The following integrability theorem for vertex operator algebras V satisfying some finiteness conditions(C_2-cofinite and CFT-type) is proved: the vertex operator subalgebra generated by a simple Lie subalgebra {\frak g} of the weight one subspace V_1 ... More

Shifted Vertex Operator AlgebrasNov 24 2004We study the properties of shifted vertex operator algebras, which are vertex algebras derived from a given theory by shifting the conformal vector. In this way, we are able to exhibit large numbers of vertex operator algebras which are regular(rational ... More

Evolving Aggregates of Quantum-Universe-Constituents Von-Neumann Big-Bang, Gelfand-Dirac Theory of Every 'Thing'Dec 11 2015Sep 30 2016'Quc' is shorthand here for 'quantum-universe constituent'. Self-adjoint 'Gelfand-Dirac' (GD) Hilbert-space angular-momentum and momentum operators generate quc rotations and spatial displacements, but no single-quc is a 'thing'. We propose, nevertheless, ... More

Congruence properties of Taylor coefficients of modular formsJun 11 2014In their work, Serre and Swinnerton-Dyer study the congruence properties of the Fourier coefficients of modular forms. We examine similar congruence properties, but for the coefficients of a modified Taylor expansion about a CM point $\tau$. These coefficients ... More

On the Chromatic Number of $\mathbb{R}^n$ for Small Values of $n$Aug 09 2014The lower bound for the chromatic number of $\mathbb{R}^n$ is improved for $n = 6, 7, 10, 11, 12, 13 \mbox{ and } 14$.

The millimeter VLBI Properties of EGRET BlazarsAug 13 1999We give a progress report on a snapshot 86 GHz-VLBI survey of the EGRET blazars with the observatories of the CMVA. A high fraction (17/18) of the EGRET blazars were detected on the Pico Veleta-Onsala baseline with a baseline length on the order of 500 ... More

Cocycle conjugacy classes of binary shiftsFeb 18 2016We show that every binary shift on the hyperfinite $II_1$ factor $R$ is cocycle conjugate to at least countably many non-conjugate binary shifts. This holds in particular for binary shifts of infinite commutant index.

Gaussian integer solutions for the fifth power taxicab number problemNov 21 2015The famous open problem of finding positive integer solutions to $a^5 + b^5 = c^5 + d^5$ is considered, and related solutions are found in two distinct settings: firstly, where $a$ and $b$ are both positive integers with $c$ and $d$ both Gaussian integers; ... More

Self-avoiding walks and amenabilityOct 29 2015Nov 24 2015The connective constant $\mu(G)$ of an infinite transitive graph $G$ is the exponential growth rate of the number of self-avoiding walks from a given origin. The relationship between connective constants and amenability is explored in the current work. ... More

Connective constants and height functions for Cayley graphsJan 02 2015Aug 22 2016The connective constant $\mu(G)$ of an infinite transitive graph $G$ is the exponential growth rate of the number of self-avoiding walks from a given origin. In earlier work of Grimmett and Li, a locality theorem was proved for connective constants, namely, ... More

End-to-end LSTM-based dialog control optimized with supervised and reinforcement learningJun 03 2016This paper presents a model for end-to-end learning of task-oriented dialog systems. The main component of the model is a recurrent neural network (an LSTM), which maps from raw dialog history directly to a distribution over system actions. The LSTM automatically ... More

On the number of simple modules in a block of a finite groupDec 18 2015Nov 07 2016We prove that if $B$ is a $p$-block with non-trivial defect group $D$ of a finite $p$-solvable group $G$, then $\ell(B) < p^r$, where $r$ is the sectional rank of $D$. We remark that there are infinitely many $p$-blocks $B$ with non-Abelian defect groups ... More

Locality of connective constantsNov 29 2014Aug 21 2016The connective constant $\mu(G)$ of a quasi-transitive graph $G$ is the exponential growth rate of the number of self-avoiding walks from a given origin. We prove a locality theorem for connective constants, namely, that the connective constants of two ... More

Critical surface of the hexagonal polygon modelAug 29 2015Mar 08 2016The hexagonal polygon model arises in a natural way via a transformation of the 1-2 model on the hexagonal lattice, and it is related to the high temperature expansion of the Ising model. There are three types of edge, and three corresponding parameters ... More

Torus Chiral n-Point Functions for Free Boson and Lattice Vertex Operator AlgebrasApr 26 2002We obtain explicit expressions for all genus one chiral n-point functions for free bosonic and lattice vertex operator algebras. We also consider the elliptic properties of these functions.

Variations on Ramanujan's nested radicalsNov 21 2015We give new nested radical equations of similar kind to Ramanujan's questions to the Indian Mathematical Society 100 years ago. While many have since considered these from the perspectives of the Notebooks of Ramanujan and from the theory of Class numbers ... More

Counting self-avoiding walksApr 26 2013Mar 22 2015The connective constant $\mu(G)$ of a graph $G$ is the asymptotic growth rate of the number of self-avoiding walks on $G$ from a given starting vertex. We survey three aspects of the dependence of the connective constant on the underlying graph $G$. Firstly, ... More

The 1-2 modelJul 15 2015Sep 08 2015The current paper is a short review of rigorous results for the 1-2 model. The 1-2 model on the hexagonal lattice is a model of statistical mechanics in which each vertex is constrained to have degree either 1 or 2. It was proposed in a study by Schwartz ... More

Strict inequalities for connective constants of transitive graphsJan 14 2013Apr 24 2014The connective constant of a graph is the exponential growth rate of the number of self-avoiding walks starting at a given vertex. Strict inequalities are proved for connective constants of vertex-transitive graphs. Firstly, the connective constant decreases ... More

Group Cohomology and Gauge Equivalence of some Twisted Quantum DoublesFeb 29 2000Dijkgraaf, Pasquier and Roche introduced twisted quantum doubles of a finite group in the context of conformal field theory. We study equivalences that arise among the braided monoidal categories associated to these quantum doubles, especially in the ... More

An explicit approach to the Ahlgren-Ono conjectureJul 27 2014Let $p(n)$ be the partition function. Ahlgren and Ono conjectured that every arithmetic progression contains infinitely many integers $N$ for which $p(N)$ is not congruent to $0\pmod{3}$. Radu proved this conjecture in 2010 using work of Deligne and Rapoport. ... More

Percolation since Saint-FlourJul 02 2012This is a short survey of work on percolation and first-passage percolation since the publication (in 1996 and 1984, respectively) of the two authors' Saint-Flour notes on these topics.

On the number of simple modules in a block of a finite groupDec 18 2015We prove that if $B$ is a $p$-block with non-trivial defect group $D$ of a finite $p$-solvable group $G$, then $\ell(B) < p^r$, where $r$ is the sectional rank of $D$. We remark that there are infinitely many $p$-blocks $B$ with non-Abelian defect groups ... More

MHC Restriction of V-V Interactions in Serum IgGMar 04 2014According to Jerne's idiotypic network hypothesis, the adaptive immune system is regulated by interactions between the variable regions of antibodies, B cells, and T cells.1 The symmetrical immune network theory2,3 is based on Jerne's hypothesis, and ... More

Petroleum Refinery Multi-Antenna Propagation MeasurementsNov 01 2016This paper presents the results of the first multi- antenna propagation measurement campaign to be conducted at an operating petroleum refining facility. The measurement equipment transmits pseudo-random noise test signals from two antennas at a 2.47 ... More

The series that Ramanujan misunderstoodOct 12 2016We give a new appraisal of a famous oscillating power series considered by Hardy and Ramanujan related to the erroneous theory of distribution of primes by Ramanujan.

Cubic graphs and the golden meanOct 01 2016The connective constant $\mu(G)$ of a graph $G$ is the exponential growth rate of the number of self-avoiding walks starting at a given vertex. We investigate the validity of the inequality $\mu \ge \phi$ for infinite, transitive, simple, cubic graphs, ... More

Critical surface of the 1-2 modelJun 28 2015Jul 13 2016The 1-2 model on the hexagonal lattice is a model of statistical mechanics in which each vertex is constrained to have degree either $1$ or $2$. There are three types of edge, and three corresponding parameters $a$, $b$, $c$. It is proved that, when $a ... More

A Search for Radio Transients in VLA Archival Images of the 3C 286 FieldDec 30 2010We present a search for radio transients in the field of the bright radio source 3C 286 using archival observations from the Very Large Array. These observations span 23 years and include 1852 epochs at 1.4 GHz in the C and D configurations. We find no ... More

Empirical Limits on Radial Velocity Planet Detection for Young StarsAug 15 2014We report initial results from our long term search using precision radial velocities for planetary-mass companions located within a few AU of stars younger than the Sun. Based on a sample of >150 stars, we define a floor in the radial velocity scatter, ... More

Relative Zeta Determinants and the Quillen MetricOct 27 1999We compute the relative zeta-function metric on the determinant line bundle for a family of elliptic boundary value problems of Dirac-type. To do this we prove a general formula relating the zeta-determinant to a Fredholm determinant over the boundary ... More

The statistical mechanics of planet orbitsApr 05 2015Jun 10 2015The final "giant-impact" phase of terrestrial planet formation is believed to begin with a large number of planetary "embryos" on nearly circular, coplanar orbits. Mutual gravitational interactions gradually excite their eccentricities until their orbits ... More

Noisy 1-Bit Compressed Sensing Embeddings Enjoy a Restricted Isometry PropertyApr 12 2016We investigate the sign-linear embeddings of 1-bit compressed sensing given by Gaussian measurements. One can give short arguments concerning a Restricted Isometry Property of such maps using Vapnik-Chervonenkis dimension of sparse hemispheres. This approach ... More

The Whitney Extension Theorem for $C^1$, horizontal curves in $\mathbb{H}^n$Jul 08 2015Jul 16 2015For a real valued function defined on a compact set $K \subset \mathbb{R}^m$, the classical Whitney Extension Theorem from 1934 gives necessary and sufficient conditions for the existence of a $C^k$ extension to $\mathbb{R}^m$. In this paper, we prove ... More

The Complexity of AgreementJun 30 2004A celebrated 1976 theorem of Aumann asserts that honest, rational Bayesian agents with common priors will never "agree to disagree": if their opinions about any topic are common knowledge, then those opinions must be equal. Economists have written numerous ... More

Quantum Lower Bound for the Collision ProblemNov 20 2001The collision problem is to decide whether a function X:{1,..,n}->{1,..,n} is one-to-one or two-to-one, given that one of these is the case. We show a lower bound of Theta(n^{1/5}) on the number of queries needed by a quantum computer to solve this problem ... More

The Equivalence of Sampling and SearchingSep 26 2010In a sampling problem, we are given an input x, and asked to sample approximately from a probability distribution D_x. In a search problem, we are given an input x, and asked to find a member of a nonempty set A_x with high probability. (An example is ... More

Quantum Computing and Hidden Variables II: The Complexity of Sampling HistoriesAug 19 2004This paper shows that, if we could examine the entire history of a hidden variable, then we could efficiently solve problems that are believed to be intractable even for quantum computers. In particular, under any hidden-variable theory satisfying a reasonable ... More

Book Review: 'A New Kind of Science'Jun 13 2002Jul 30 2002This is a critical review of the book 'A New Kind of Science' by Stephen Wolfram. We do not attempt a chapter-by-chapter evaluation, but instead focus on two areas: computational complexity and fundamental physics. In complexity, we address some of the ... More

A Fundamental Scale for Acceleration from the Holographic PrincipleMay 25 2005Jun 26 2005From the Eddington-Weinberg relationship, which may be explained by the holographic principle and the cosmic coincidence in a flat Universe, it follows that the characteristic gravitational acceleration aN associated with the nucleon and its Compton wavelength ... More

The Large Number Coincidence, The Cosmic Coincidence and the Critical AccelerationFeb 09 2005May 19 2006The coincidence problem among the pure numbers of order near 10^{40} is resolved with the Raychaudhuri and Friedmann-Robertson-Lemaitre-Walker equations and a trivial relationship involving the fine structure constant. The fact that the large number coincidence ... More

An Inertial Reaction to Cosmological AccelerationsSep 01 2003May 17 2005Mach's "fixed stars" are actually not fixed at all. The distant clusters of galaxies are not only receding from each observer but they are also accelerating since the rate of cosmological expansion is not constant. If the distant cosmic masses in someway ... More

Stars and the holographic upper bound on gravitational actionApr 14 2007Dec 22 2008The holographic upper bound on entropy is applied to the gravitational action associated with the non-relativistic contraction of a nebula. A critical radius is identified, as a function of the initial radius and mass, for which the number of bits associated ... More

A Cosmological Modification to Energy from Mach-Hamilton ConsistencyMar 24 2004If Mach's Principle explains the Newtonian inertial reaction to acceleration then the role of the 'fixed stars' should also be manifest through Hamilton's formulation of mechanics. This consistency may be achieved if the expression for relativistic energy ... More

One-Loop QCD and Higgs to Partons Processes Using Six-Dimensional Helicity and Generalized UnitarityAug 01 2011Dec 06 2011We combine the six-dimensional helicity formalism of Cheung and O'Connell with D-dimensional generalized unitarity to obtain a new formalism for computing one-loop amplitudes in dimensionally regularized QCD. With this procedure, we simultaneously obtain ... More

Moduli Stabilization with the String Higgs EffectApr 23 2004May 02 2004We review the notion of the Higgs effect in the context of string theory. We find that by including this effect in time dependent backgrounds, one is led to a natural mechanism for stabilizing moduli at points of enhanced gauge symmetry. We consider this ... More

An Exposition on Inflationary CosmologyApr 29 2000May 27 2000This paper is intended to offer a pedagogical treatment of cosmological modeling and inflationary cosmology. In recent years, inflation has become accepted as a standard scenario making predictions that are testable by observations of the cosmic background. ... More

Reciprocity and rationality for the greedy normal form of a Coxeter groupSep 12 2008We show that the characteristic series for the greedy normal form of a Coxeter group is always a rational series, and prove a reciprocity formula for this series when the group is right-angled and the nerve is Eulerian. As corollaries we obtain many of ... More

Elementary treatment of $p^a \pm p^b + 1 = x^2$Aug 31 2006We give a shorter simpler proof of a result of Szalay on the equation $2^a + 2^b + 1 = x^2$. We give an elementary proof of a result of Luca on the equation of the title for prime $p > 2$. The elementary treatment is made possible by a lemma which is ... More

Szemerédi's Regularity Lemma for matrices and sparse graphsOct 04 2010Nov 08 2010Szemer\'edi's Regularity Lemma is an important tool for analyzing the structure of dense graphs. There are versions of the Regularity Lemma for sparse graphs, but these only apply when the graph satisfies some local density condition. In this paper, we ... More

Encoding Data for HTM SystemsFeb 18 2016Hierarchical Temporal Memory (HTM) is a biologically inspired machine intelligence technology that mimics the architecture and processes of the neocortex. In this white paper we describe how to encode data as Sparse Distributed Representations (SDRs) ... More

Pricing for Large Positions in Contingent ClaimsFeb 17 2012Dec 11 2013Approximations to utility indifference prices are provided for a contingent claim in the large position size limit. Results are valid for general utility functions on the real line and semi-martingale models. It is shown that as the position size approaches ... More

The evolution of galaxy formationDec 01 2011Our history of understanding galaxy formation could be traced through the development of individual ideas. A cynic might be tempted to suggest that new catchphrases are developed at a faster rate than genuine progress is made.

CMB ANISOTROPIES: AN OVERVIEWFeb 02 1995A brief outline of the current status of CMB anisotropies and what they might mean, heavily biased towards the perspective of Berkeley theorists. Based on a talk presented at the 17th Texas Symposium on Relativistic Astrophysics held in Munich, December ... More

Supercharacters of unipotent groups defined by involutionsNov 07 2013Dec 15 2014We construct supercharacter theories of finite unipotent groups in the orthogonal, symplectic and unitary types. Our method utilizes group actions in a manner analogous to that of Diaconis and Isaacs in their construction of supercharacters of algebra ... More

Supercharacter theories constructed by the method of little groupsMay 21 2014May 22 2014The method of little groups describes the irreducible characters of semidirect products with abelian normal subgroups in terms of the irreducible characters of the factor groups. We modify this method to construct supercharacter theories of semidirect ... More

Generalized Moonshine IV: Monstrous Lie algebrasAug 30 2012Aug 20 2016For each element of the Fischer-Griess Monster sporadic simple group, we construct an infinite dimensional Lie algebra equipped with a projective action of the centralizer of that element. Our construction is given by a string-theoretic "add a spacetime ... More