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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

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

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

On the mathematical Structure of Quantum Measurement TheoryMay 10 2005Sep 01 2005We show that the key problems of quantum measurement theory, namely the reduction of the wave packet of a microsystem and the specification of its quantum state by a macroscopic measuring instrument, may be rigorously resolved within the traditional framework ... 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

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

On connective K-theory of elementary abelian 2-groups and local dualityDec 29 2011The connective ku-(co)homology of elementary abelian 2-groups is determined as a functor of the elementary abelian 2-group. The argument requires only the calculation of the rank one case and the Atiyah-Segal theorem for KU-cohomology together with an ... More

Symmetric powers, Steenrod operations and representation stabilitySep 24 2018Feb 13 2019Working over the prime field F_p, the structure of the indecomposables Q^* for the action of the algebra of Steenrod reduced powers A(p) on the symmetric power functors S^* is studied by exploiting the theory of strict polynomial functors. In particular, ... More

On the BP<n>-cohomology of elementary abelian p-groupsApr 03 2013Jan 13 2015The structure of the BP<n>-cohomology of elementary abelian p-groups is studied, obtaining a presentation expressed in terms of BP-cohomology and mod-p singular cohomology, using the Milnor derivations. The arguments are based on a result on multi-Koszul ... More

The Random-Cluster ModelMay 23 2002Jun 10 2003The class of random-cluster models is a unification of a variety of stochastic processes of significance for probability and statistical physics, including percolation, Ising, and Potts models; in addition, their study has impact on the theory of certain ... 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

Three Graphs and the Erdős-Gyárfás ConjectureMar 22 2014Three graphs related to the \EGC\, are presented. The graphs are derived from the Buckyball, the Petersen graph, and the Tutte-Coxeter graph. The first graph is a partial answer to a question posed by Heckman and Krakovski \cite{planar} in their recent ... More

On the Singer functor R_1 and the functor FixDec 04 2009Lannes' T-functor is used to give a construction of the Singer functor R_1 on the category U of unstable modules over the Steenrod algebra A. This leads to a direct proof that the composite functor Fix R_1 is naturally equivalent to the identity. Further ... More

Algebraic infinite delooping and derived destabilizationJan 23 2017May 11 2017Working over the prime field of characteristic two, consequences of the Koszul duality between the Steenrod algebra and the big Dyer-Lashof algebra are studied, with an emphasis on the interplay between instability for the Steenrod algebra action and ... More

Galactic Center Pulsars with the ngVLAOct 15 2018Pulsars in the Galactic Center (GC) are important probes of General Relativity, star formation, stellar dynamics, stellar evolution, and the interstellar medium. Despite years of searching, only a handful of pulsars in the central 0.5 deg are known. The ... More

The JCMT Transient Survey: Data Reduction and Calibration MethodsJun 06 2017Jul 28 2017Though there has been a significant amount of work investigating the early stages of low-mass star formation in recent years, the evolution of the mass assembly rate onto the central protostar remains largely unconstrained. Examining in depth the variation ... 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

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

Correlation inequalities for the Potts modelJan 12 2009Mar 28 2016Correlation inequalities are presented for ferromagnetic Potts models with external field, using the random-cluster representation of Fortuin and Kasteleyn, together with the FKG inequality. These results extend and simplify earlier inequalities of Ganikhodjaev ... 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

Classical static final state of collapse with supertranslation memoryFeb 16 2016Sep 05 2016The Kerr metric models the final classical black hole state after gravitational collapse of matter and radiation. Any stationary metric which is close to the Kerr metric has been proven to be diffeomorphic to it. Now, finite supertranslation diffeomorphisms ... 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.

Rigidity of the interface for percolation and random-cluster modelsSep 17 2001We study conditioned random-cluster measures with edge-parameter p and cluster-weighting factor q satisfying q \ge 1. The conditioning corresponds to mixed boundary conditions for a spin model. Interfaces may be defined in the sense of Dobrushin, and ... More

$\mathbb ZS_n$-modules and polynomial identities with integer coefficientsJul 02 2013Aug 30 2014We show that, like in the case of algebras over fields, the study of multilinear polynomial identities of unitary rings can be reduced to the study of proper polynomial identities. In particular, the factors of series of $\mathbb ZS_n$-submodules in the ... More

Brill-Noether theory of curves on toric surfacesMar 10 2014Mar 30 2014A Laurent polynomial $f$ in two variables naturally describes a projective curve $C(f)$ on a toric surface. We show that if $C(f)$ is a smooth curve of genus at least 7, then $C(f)$ is not Brill-Noether general. To accomplish this, we classify all Newton ... More

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

X-ray follow-up of extragalactic transientsMar 13 2019Most violent and energetic processes in our universe, including mergers of compact objects, explosions of massive stars and extreme accretion events, produce copious amounts of X-rays. X-ray follow-up is an efficient tool for identifying transients because ... 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

Learning the Alpha-bits of Black HolesJul 16 2018Aug 01 2018When the bulk geometry in AdS/CFT contains a black hole, the boundary reconstruction of a given bulk operator will often necessarily depend on the choice of black hole microstate, an example of state dependence. As a result, whether a given bulk operator ... More

Bounds for the smallest $k$-chromatic graphs of given girthMay 17 2018Feb 13 2019Let $n_g(k)$ denote the smallest order of a $k$-chromatic graph of girth at least $g$. We consider the problem of determining $n_g(k)$ for small values of $k$ and $g$. After giving an overview of what is known about $n_g(k)$, we provide some new lower ... More

John Michael Hammersley (1920-2004)Oct 27 2006In writing this biographical memoir of John Hammersley, we have tried to communicate something of the character of the person, and of the impact of his scientific achievements across lattice models (for example, percolation, self-avoiding walks, first-passage ... 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

Jacobi trace functions in the theory of vertex operator algebrasSep 23 2013Aug 26 2015We describe a type of n-point function associated to strongly regular vertex operator algebras V and their irreducible modules. Transformation laws with respect to the Jacobi group are developed for 1-point functions. For certain elements in V, the finite-dimensional ... More

Random Electrical Networks on Complete Graphs II: ProofsJul 10 2001This paper contains the proofs of Theorems 2 and 3 of the article entitled Random Electrical Networks on Complete Graphs, written by the same authors and published in the Journal of the London Mathematical Society, vol. 30 (1984), pp. 171-192. The current ... More

Setting the boundary free in AdS/CFTMay 13 2008Jun 04 2008We describe a new class of boundary conditions for AdS_{d+1} under which the boundary metric becomes a dynamical field. The key technical point is to show that contributions from boundary counter-terms in the bulk gravitational action render such fluctuations ... 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

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

A Characterization of Closure Operations That Induce Big Cohen-Macaulay ModulesNov 02 2009Nov 03 2010The intent of this paper is to present a set of axioms that are sufficient for a closure operation to generate a balanced big Cohen-Macaulay module B over a complete local domain R. Conversely, we show that if such a B exists over R, then there exists ... More

Structure of the module of vector-valued modular formsJan 27 2009Let $V$ be a representation of the modular group $\Gamma$ of dimension $p$. We show that the $\mathbb{Z}$-graded space $\mathcal{H}(V)$ of holomorphic vector-valued modular forms associated to $V$ is a free module of rank $p$ over the algebra $\mathcal{M}$ ... More

Vertex operator algebras and weak Jacobi formsMar 04 2011Let $V$ be a strongly regular vertex operator algebra. For a state $h \in V_1$ satisfying appropriate integrality conditions, we prove that the space spanned by the trace functions Tr$_Mq^{L(0)-c/24}\zeta^{h(0)} ($M$ a $V$-module) is a vector-valued weak ... More

C-Graded Vertex Algebras and Conformal FlowAug 02 2013We consider C-graded vertex algebras, which are vertex algebras V with a C-grading such that V is an admissible V-module generated by 'lowest weight vectors'. We show that such vertex algebras have a 'good' representation theory in the sense that there ... 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

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

On integer solutions to x^5 - (x+1)^5 -(x+2)^5 +(x+3)^5 = 5^m + 5^nFeb 29 2016We give an infinite number of integer solutions to the Diophantine equation x^5 - (x+1)^5 -(x+2)^5 +(x+3)^5 = 5^m + 5^n, and some solutions to some similar equations.

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

Cubic graphs and the golden meanOct 01 2016May 25 2018The 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

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

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

Generalised Paley graphs with a product structureDec 20 2016A graph is Cartesian decomposable if it is isomorphic to a Cartesian product of (more than one) strictly smaller graphs, each of which has more than one vertex and admits no such decomposition. These smaller graphs are called the Cartesian-prime factors ... 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

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

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 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

The Scientific Context of WFIRST Microlensing in the 2020sMar 19 2019[abridged] WFIRST is uniquely capable of finding planets with masses as small as Mars at separations comparable to Jupiter, i.e., beyond the current ice lines of their stars. These planets fall between the close-in planets found by Kepler and the wide ... More

A few of Michel Henon's contributions to dynamical astronomyNov 17 2014Nov 19 2014This article reviews Michel Henon's contributions to a diverse set of problems in astrophysical dynamics, including violent relaxation, Saturn's rings, roundoff error in orbit integrations, and planet formation.

Splitting the Curvature of the Determinant Line BundleDec 21 1998It is shown that the determinant line bundle associated to a family of Dirac operators over a closed partitioned manifold has a canonical Hermitian metric with compatible connection whose curvature satisfies an additivity formula with contributions from ... More

The Hilbert Schemes of Degree Three Curves are ConnectedMar 14 1996In this paper we show that the Hilbert scheme $H(3,g)$ of locally Cohen-Macaulay curves in $\Pthree$ of degree three and genus $g$ is connected. In contrast to $H(2,g)$, which is irreducible, $H(3,g)$ generally has many irreducible components (roughly ... More

Oracles Are Subtle But Not MaliciousApr 12 2005Theoretical computer scientists have been debating the role of oracles since the 1970's. This paper illustrates both that oracles can give us nontrivial insights about the barrier problems in circuit complexity, and that they need not prevent us from ... More

Quantum Lower Bound for Recursive Fourier SamplingSep 09 2002Dec 18 2004One of the earliest quantum algorithms was discovered by Bernstein and Vazirani, for a problem called Recursive Fourier Sampling. This paper shows that the Bernstein-Vazirani algorithm is not far from optimal. The moral is that the need to "uncompute" ... More

Particle absorption by black holes and the generalized second law of thermodynamicsJul 11 2008Apr 08 2010The change in entropy, /DeltaS, associated with the quasi-static absorption of a particle of energy u by a Schwarzschild black hole (ScBH) is approximately (u/T)-s, where T is the Hawking temperature of the black hole and s is the entropy of the particle. ... More

A New Large-Number Coincidence and a Scaling Law for the Cosmological ConstantNov 12 2006Mar 16 2008An ensemble of pure numbers of order near 10^122 is produced naturally from the fundamental parameters of modern cosmology. This new large-number coincidence problem is resolved by demonstrating implicit physical connections that follow from the standard ... More

The Planck Length Scale and Einstein Mass-Energy Obtained from the Sciama-Mach Large Number RelationshipSep 22 2003Sep 25 2003If a physical significance should be attributed to the cosmological large number relationship obtained from Sciama's formulation of Mach's Principle, then a number of interesting physical conclusions may be drawn. The Planck length is naturally obtained ... More

SU(3) Ghosts with SpinJun 15 2007A new Lorentz-covariant gauge is presented for SU(3). In this gauge, both the ghosts and the gauge fields in the (4, 5, 6, 7) gauge directions acquire half-integral spin. As a result, the ghosts in these directions have the correct relationship between ... More

Symmetry Breaking in BRST Quantization of SU(3)Jan 21 2007New BRST-invariant states for SU(3) gauge field theory are presented. The states have finite norms and unlike the states that are usually used to derive path integrals, they break SU(3) symmetry by choosing preferred gauge directions. This symmetry breaking ... More

New Ghost States in SU(3) Gauge Field TheoryDec 26 2006The ghost sector of SU(3) gauge field theory is studied, and new BRST-invariant states are presented that do not have any analog in other SU(N) field theories. The new states come in either ghost doublets or triplets, and they appear exclusively in SU(3) ... More

PT-Invariance and Indefinite MetricOct 27 2009A new proof is given for why the non-Hermitian, PT-Invariant cubic oscillator with imaginary coupling has real eigenvalues. The proof consists of two steps. In the first step, it is shown that for many PT-Invariant Hamiltonians, one can define corresponding ... More

The Whitney Extension Theorem for $C^1$, horizontal curves in the Heisenberg groupJul 08 2015Nov 04 2016For 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

Computing and Sampling Restricted Vertex Degree Subgraphs and Hamiltonian CyclesAug 31 2000Feb 27 2001Let $G=(V,E)$ be a bipartite graph embedded in a plane (or $n$-holed torus). Two subgraphs of $G$ differ by a {\it $Z$-transformation} if their symmetric difference consists of the boundary edges of a single face---and if each subgraph contains an alternating ... More

A Cohomology Theory for Planar Trivalent Graphs with Perfect MatchingsOct 16 2018Dec 28 2018In this paper, we prove a new cohomology theory that is an invariant of a planar trivalent graph with a given perfect matching. This bigraded cohomology theory appears to be very powerful: the graded Euler characteristic of the cohomology is a one variable ... More

The odd couple: quasars and black holesJul 23 2014Quasars emit more energy than any other objects in the universe, yet are not much bigger than the solar system. We are almost certain that quasars are powered by giant black holes of up to $10^{10}$ times the mass of the Sun, and that black holes of between ... More

On the origin of irregular structure in Saturn's ringsNov 07 2002We suggest that the irregular structure in Saturn's B ring arises from the formation of shear-free ring-particle assemblies of up to ~100 km in radial extent. The characteristic scale of the irregular structure is set by the competition between tidal ... More

Three Discrete Models of Planar Lie Group Equivariant PresheavesAug 25 2016We utilise the theory of crossed simplicial groups to introduce a collection of Quillen model structures on the category of simplicial presheaves with a compact planar Lie group action on a small Grothendieck site.

Action in a fractal universe and the holographic upper boundFeb 28 2008Aug 13 2008The basic scaling laws for structures in a fractal universe require that the characteristic quantity of action associated with astronomical bodies should be of order near the maximum possible action allowed by the holographic upper bound. That conclusion ... More

A fundamental scale of mass for black holes from the cosmological constantJan 24 2007Dec 22 2008The existence of a positive cosmological constant leads naturally to two fundamental scales of length, being the De Sitter horizon and the radius of the cell associated with a holographic degree of freedom. Associated with each of those scales of length ... More

Scaling Law for the Cosmological Constant from Quantum Cosmology with Seven Extra DimensionsOct 09 2006Mar 16 2008According to a model of quantum cosmology the maximum number of degrees of freedom allowed in our three dimensions was determined by the size of seven extra dimensions in an initial excited state before inflation. The size of the extra dimensions can ... More

The fundamental scales of structures from first principlesApr 15 2008May 29 2008Five fundamental scales of mass follow from holographic limitations, a self-similar law for angular momentum and the basic scaling laws for a fractal universe with dimension 2. The five scales correspond to the observable universe, clusters, galaxies, ... More

Coherent Phase Argument for InflationSep 05 2003Cosmologists have developed a phenomenally successful picture of structure in the universe based on the idea that the universe expanded exponentially in its earliest moments. There are three pieces of evidence for this exponential expansion -- {\it inflation} ... More

Anisotropies in the Cosmic Microwave Background: TheoryFeb 14 1997Anisotropies in the Cosmic Microwave Background (CMB) contain a wealth of information about the past history of the universe and the present values of cosmological parameters. I ouline some of the theoretical advances of the last few years. In particular, ... More

Diversification Return, Portfolio Rebalancing, and the Commodity Return PuzzleSep 06 2011Diversification return is an incremental return earned by a rebalanced portfolio of assets. The diversification return of a rebalanced portfolio is often incorrectly ascribed to a reduction in variance. We argue that the underlying source of the diversification ... More

Symmetries of the Standard ModelOct 27 2004Feb 24 2005I present an overview of the standard model, concentrating on its global continuous symmetries, both exact and approximate. There are four lectures, dedicated to spacetime symmetry, flavor symmetry, custodial symmetry, and scale symmetry. Topics include ... More

Hadron Colliders, the Standard Model, and BeyondDec 02 2002I argue that the Fermilab Tevatron will contribute to our knowledge of the pieces of the standard model that we know the least about. I discuss five of the most important areas in which the Tevatron can confront the standard model: precision electroweak, ... More

A dynamical systems approach to actin-based motility in Listeria monocytogenesFeb 26 2010Nov 30 2010A simple kinematic model for the trajectories of Listeria monocytogenes is generalized to a dynamical system rich enough to exhibit the resonant Hopf bifurcation structure of excitable media and simple enough to be studied geometrically. It is shown how ... More

Viewing the Chemical Evolution of the Quark-Gluon Plasma with Charge Balance FunctionsApr 09 2013Correlations from charge conservation are affected by when charge/anticharge pairs are created during the course of a relativistic heavy ion collision. For charges created early, balancing charges are typically separated by the order of one unit of spatial ... More

Identifying the Charge Carriers of the Quark-Gluon PlasmaMar 20 2012Charge correlations in lattice gauge calculations suggest that up, down and strange charges move independently in the QGP (quark-gluon plasma), and that the density of such charges is similar to what is expected from simple thermal arguments. Here, we ... More

The Long Slow Death of the HBT Puzzle, Proceedings for QM 2009Jul 06 2009Oct 07 2009At the onset of the RHIC era femtoscopic source sizes inferred from two-particle correlations at RHIC defied description with hydrodynamic models. This failure, which became known as the HBT puzzle, now appears to be solved. The source of the discrepancy ... More

Extending the Reach of HydrodynamicsOct 30 2007Nov 13 2007Recent and ongoing improvements to hydrodynamic treatments at RHIC are extending the physics reach of hydrodynamics, and improving the phenomenology. Here, the links between technological improvements and the extension of physics are emphasized.

The theory of Hawking radiation in laboratory analoguesAug 11 2015Hawking radiation, despite being known to theoretical physics for nearly forty years, remains elusive and undetected. It also suffers, in its original context of gravitational black holes, from practical and conceptual difficulties. Of particular note ... More

On the concentration of the chromatic number of random graphsJun 02 2008Let 0<p<1 be fixed. Shamir and Spencer proved in the 1980s that the chromatic number of a random graph in G(n,p) is concentrated in an interval of length about n^{1/2}. We give an improvement on this, showing that the chromatic number is concentrated ... More

A Scalable Framework for NBA Player and Team Comparisons Using Player Tracking DataNov 13 2015Jan 10 2016The release of NBA player tracking data greatly enhances the granularity and dimensionality of basketball statistics used to evaluate and compare player performance. However, the high dimensionality of this new data source can be troublesome as it demands ... More

Harmonic Galois theory for finite graphsMar 08 2011Dec 07 2012This paper develops a harmonic Galois theory for finite graphs, thereby classifying harmonic branched $G$-covers of a fixed base $X$ in terms of homomorphisms from a suitable fundamental group of $X$ together with $G$-inertia structures on $X$. As applications, ... 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

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