Results for "Geoffrey Scott"

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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
On the Fourier coefficients of 2-dimensional vector-valued modular formsSep 03 2010Let $\rho: SL(2,\mathbb{Z})\to GL(2,\mathbb{C})$ be an irreducible representation of the modular group such that $\rho(T)$ has finite order $N$. We study holomorphic vector-valued modular forms $F(\tau)$ of integral weight associated to $\rho$ which have ... 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
On quadratic coalgebras, duality and the universal Steenrod algebraDec 31 2010The notion of quadratic self-duality for coalgebras is developed with applications to algebraic structures which arise naturally in algebraic topology, related to the universal Steenrod algebra via an appropriate form of duality. This explains and unifies ... 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
A brief history of the positivity conjecture in tensor category theoryMar 27 2017We show the existence of a finite group $G$ having an irreducible character $\chi$ with Frobenius-Schur indicator $\nu_2(\chi){=}{+}1$ such that $\chi^2$ has an irreducible constituent $\varphi$ with $\nu_2(\varphi){=}{-}1$. This provides counterexamples ... 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
An Analysis of Chandra Deep Follow-up GRBs: Implications for Off-Axis JetsMay 19 2014Apr 05 2015We present a sample of 27 GRBs with detailed Swift light curves supplemented by late time Chandra observations. To answer the missing jet-break problem in general, we develop a numerical simulation based model which can be directly fit to the data using ... More
Five not-so-easy pieces:open problems about vertex ringsDec 15 2018We present five open problems in the theory of vertex rings. They cover a variety of different areas of research where vertex rings have been, or are threatening to be, relevant. They have also been chosen because I personally find them interesting, and ... More
On double Poisson structures on commutative algebrasMar 24 2016Jul 08 2016Double Poisson structures (a la Van den Bergh) on commutative algebras are studied; the main result shows that there are no non-trivial such structures on polynomial algebras of Krull dimension greater than one. For a general commutative algebra A, this ... More
Lorentz spacetimes of constant curvatureJun 11 2007This paper was first written in 1990, but was never published. In it, the author presents a novel approach to the study of constant curvature spacetimes in 2+1 dimensions. A parameterization of flat 2+1-dimensional domains of dependence is given in terms ... More
Role of Dynamical Research in the Detection and Characterization of ExoplanetsMay 18 2007(Abridged) The discovery of extrasolar planetary systems revealed an unexpected diversity of planetary systems that has revolutionized planet formation theory. A strong program of theoretical research is essential to maximize both the discovery potential ... 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
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
Tight Closure of Finite Length Modules in Graded RingsAug 18 2005Jan 11 2007We look at how the equivalence of tight closure and plus closure (or Frobenius closure) in the homogeneous m-coprimary case implies the same closure equivalence in the non-homogeneous m-coprimary case in standard graded rings. Although our result does ... 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
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
On Toeplitz matrices over GF(2)Apr 03 2018For each positive integer $n$ let $\mathcal{A}_n$ be a Toeplitz matrix over $GF(2)$ and suppose for each $n$ that $\mathcal{A}_n$ is the upper left corner of $\mathcal{A}_{n+1}$. We study the structure of the sequence $\nu = \{\nu_n :n \in \mathbb{N}\}$, ... 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
Carter Subgroups, Amalgams, Simple Groups, and the Zp*-theoremJan 30 2015We consider an amalgam of groups constructed from fusion systems for different odd primes p and q. This amalgam contains a self-normalizing cyclic subgroup of order pq and isolated elements of order p and q.
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
Most vertex superalgebras associated to an odd unimodular lattice of rank 24 have an N=4 superconformal structureSep 29 2018Odd, positive-definite, integral, unimodular lattices N of rank 24 were classified by Borcherds. There are 273 isometry classes of such lattices. Associated to them are vertex superalgebras $V_N$ of central charge c=24. We show that at least 267 of these ... 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
Subrings of singular cohomology associated to spectraApr 17 2009This paper extends the relation established for group cohomology by Green, Hunton and Schuster between chromatic phenomena in stable homotopy theory and certain natural subrings of singular cohomology. This exploits the theory due to Henn, Lannes and ... More
On influence and compromise in two-tier voting systemsApr 03 2018May 14 2019We examine two aspects of the mathematical basis for two-tier voting systems, such as that of the Council of the European Union. These aspects concern the use of square-root weights and the choice of quota. Square-root weights originate in the Penrose ... More
Higher Hochschild homology and exponential functorsFeb 21 2018Jun 14 2018We study higher Hochschild homology evaluated on wedges of circles, viewed as a functor on the category of free groups. The principal results use coefficients arising from square-zero extensions; this is motivated in part by work of Turchin and Willwacher ... 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 $n = 6, 7, 10, 11, 12, 13 \mbox{ and } 14$.
Free Bosonic Vertex Operator Algebras on Genus Two Riemann Surfaces IINov 09 2011We continue our program to define and study $n$-point correlation functions for a vertex operator algebra $V$ on a higher genus compact Riemann surface obtained by sewing surfaces of lower genus. Here we consider Riemann surfaces of genus 2 obtained by ... More
Central Invariants and Frobenius-Schur Indicators for Semisimple Quasi-Hopf AlgebrasMar 18 2003Apr 29 2003In this paper, we obtain a canonical central element $\nu_H$ for each semi-simple quasi-Hopf algebra $H$ over any field $k$ and prove that $\nu_H$ is invariant under gauge transformations. We show that if $k$ is algebraically closed of characteristic ... More
Bounds on connective constants of regular graphsOct 23 2012May 01 2013Bounds are proved for the connective constant \mu\ of an infinite, connected, \Delta-regular graph G. The main result is that \mu\ \ge \sqrt{\Delta-1} if G is vertex-transitive and simple. This inequality is proved subject to weaker conditions under which ... More
Non-coupling from the pastJul 12 2019The method of 'coupling from the past' permits exact sampling from the invariant distribution of a Markov chain on a finite state space. The coupling is successful whenever the stochastic dynamics are such that there is coalescence of all trajectories. ... 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
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
Quantum Smart MatterNov 13 1996The development of small-scale sensors and actuators enables the construction of smart matter in which physical properties of materials are controlled in a distributed manner. In this paper, we describe how quantum computers could provide an additional ... More
Degressive representation of Member States in the European Parliament 2019-2024Feb 21 2018Primary law of the European Union demands that the allocation of the seats of the European Parliament between the Member States must obey the principle of degressive proportionality. The principle embodies the political aim that the more populous states ... More
Probability calculations under the IAC hypothesisFeb 16 2012We show how powerful algorithms recently developed for counting lattice points and computing volumes of convex polyhedra can be used to compute probabilities of a wide variety of events of interest in social choice theory. Several illustrative examples ... More
Strong Consistency of Prototype Based Clustering in Probabilistic SpaceApr 19 2010In this paper we formulate in general terms an approach to prove strong consistency of the Empirical Risk Minimisation inductive principle applied to the prototype or distance based clustering. This approach was motivated by the Divisive Information-Theoretic ... More
Inherent Tradeoffs in Learning Fair RepresentationJun 19 2019With the prevalence of machine learning in high-stakes applications, especially the ones regulated by anti-discrimination laws or societal norms, it is crucial to ensure that the predictive models do not propagate any existing bias or discrimination. ... More
Weighted self-avoiding walksApr 15 2018Jun 05 2019We study the connective constants of weighted self-avoiding walks (SAWs) on infinite graphs and groups. The main focus is upon weighted SAWs on finitely generated, virtually indicable groups. Such groups possess so-called 'height functions', and this ... 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
Identifying the magnetospheric driver of STEVEJun 20 2019For the first time, we identify the magnetospheric driver of STEVE, east-west aligned narrow emissions in the subauroral region. In the ionosphere, STEVE is associated with subauroral ion drift (SAID) features of high electron temperature peak, density ... 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
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.
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
Experimental Design : Optimizing Quantities of Interest to Reliably Reduce the Uncertainty in Model Input ParametersJan 25 2016As stakeholders and policy makers increasingly rely upon quantitative predictions from advanced computational models, a problem of fundamental importance is the quantification and reduction of uncertainties in both model inputs and output data. The typical ... 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
Viscosity at RHIC: Theory and PracticeSep 01 2008Hydrodynamic behavior and the associated discussions of viscosity at RHIC has inspired a r enaissance in modeling viscous hydrodynamics. An explanation of Israel-Stewart hydrodynamics is presented here, with an emphasis on the tangible benefits compared ... More
Formulating Viscous Hydrodynamics for Large Velocity GradientsNov 25 2007Viscous corrections to relativistic hydrodynamics, which are usually formulated for small velocity g radients, have recently been extended from Navier-Stokes formulations to a class of treatments based on Israel-Stewart equations. Israel-Stewart treatments, ... More
Alternative Contributions to the Angular Correlations Observed at RHIC Associated with Parity FluctuationsFeb 09 2010Recent measurements at RHIC of angular correlations of same-sign vs. opposite sign pairs have been interpreted as evidence for large-scale fluctuations of parity-odd fields. In this paper, we provide alternative explanations of the same phenomena based ... More
The Long Slow Death of the HBT PuzzleDec 26 2008Femtoscopic measurements at RHIC have been hailed as a source of insight into the bulk properties of QCD matter. However, hydrodynamic models, which have been successful in reproducing other observables have failed to satisfactorily explain femtoscopic ... More
Correlations and Fluctuations, A Summary of Quark Matter 2002Aug 06 2003Results for correlations and fluctuations presented at Quark Matter 2002 are summarized. These results include Hanbury-Brown Twiss interferometry of a wide variety of species, large scale fluctuations and correlations in $p_t$ and multiplicity, and charge ... More
Kergin Approximation in Banach SpacesOct 01 2008We explore the convergence of Kergin interpolation polynomials of holomorphic functions in Banach spaces, which need not be of bounded type. We also investigate a case where the Kergin series diverges.
A note on Cauchy integrabilitySep 23 2014We show that for any bounded function $f:[a,b]\rightarrow{\mathbb R}$ and $\epsilon>0$ there is a partition $P$ of $[a,b]$ with respect to which the Riemann sum of $f$ using right endpoints is within $\epsilon$ of the upper Darboux sum of $f$. This leads ... 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
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 braid group surjects onto $G_2$ tensor spaceJul 01 2009Let V be the 7-dimensional irreducible representation of the quantum group U_q(g_2). For each n, there is a map from the braid group B_n to the endomorphism algebra of the n-th tensor power of V, given by R-matrices. We can extend this linearly to a map ... 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
Convex Sets Associated to C*-AlgebrasSep 02 2015Dec 01 2015For A a separable unital C*-algebra and M a separable McDuff II_1-factor, we show that the space Hom_w(A,M) of weak approximate unitary equivalence classes of unital *-homomorphisms A \rightarrow M may be considered as a closed, bounded, convex subset ... More
Impossibility of Succinct Quantum Proofs for Collision-FreenessJan 02 2011We show that any quantum algorithm to decide whether a function f:[n]->[n] is a permutation or far from a permutation must make Omega(n^{1/3}/w) queries to f, even if the algorithm is given a w-qubit quantum witness in support of f being a permutation. ... More
The Learnability of Quantum StatesAug 18 2006Mar 04 2007Traditional quantum state tomography requires a number of measurements that grows exponentially with the number of qubits n. But using ideas from computational learning theory, we show that "for most practical purposes" one can learn a state using a number ... More
On Perfect Completeness for QMAJun 03 2008Aug 23 2008Whether the class QMA (Quantum Merlin Arthur) is equal to QMA1, or QMA with one-sided error, has been an open problem for years. This note helps to explain why the problem is difficult, by using ideas from real analysis to give a "quantum oracle" relative ... More
NP-complete Problems and Physical RealityFeb 12 2005Feb 21 2005Can NP-complete problems be solved efficiently in the physical universe? I survey proposals including soap bubbles, protein folding, quantum computing, quantum advice, quantum adiabatic algorithms, quantum-mechanical nonlinearities, hidden variables, ... More
Quantum Computing and Hidden Variables I: Mapping Unitary to Stochastic MatricesAug 05 2004This paper initiates the study of hidden variables from the discrete, abstract perspective of quantum computing. For us, a hidden-variable theory is simply a way to convert a unitary matrix that maps one quantum state to another, into a stochastic matrix ... More
Crossed Simplicial Group Categorical NervesMar 29 2016We will extend the notion of the nerve of a category for a small class of crossed simplicial groups, explicitly describing them using generators and relations. We do this by first considering a generalised bar construction of a group. We then go on to ... More
Factorisation and Cohomology of Higher CategoriesJun 10 2014We construct an iterative method for factorising small strict n-categories into a unique (up to isomorphism) collection of small 1- categories. Following this we develop the theory to include a large class of $\infty$-categories. We use this factorisation ... More
Determining cosmic microwave background anisotropies in the presence of foregroundsDec 05 1995Separating foregrounds from the signal is one of the big challenges in cosmic microwave background (CMB) experiments. A simple way to estimate the CMB temperature in a given pixel is to fit for the amplitudes of the CMB and the various foreground components. ... More
CMB-Cluster LensingFeb 12 2004Clusters of galaxies are powerful cosmological probes, particularly if their masses can be determined. One possibility for mass determination is to study the cosmic microwave background (CMB) on small angular scales and observe deviations from a pure ... More
Cosmic Microwave Background: Past, Future, and PresentDec 22 1999I explain the origin and evolution of anisotropies in the Cosmic Microwave Background (CMB) and argue that upcoming experiments will measure cosmological and fundamental parameters very accurately. Most of the paper focuses on present data, which strongly ... More
Gauge Invariant States of QCDNov 18 2011Mar 02 2012None of the asymptotic states commonly used in perturbative QCD are gauge invariant. A similar statement could be made about QED, but in QED one can construct gauge invariant "dressed" states (with Dirac electrons) that are unitarily equivalent to the ... More
Pippi - painless parsing, post-processing and plotting of posterior and likelihood samplesJun 11 2012Nov 17 2016Interpreting samples from likelihood or posterior probability density functions is rarely as straightforward as it seems it should be. Producing publication-quality graphics of these distributions is often similarly painful. In this short note I describe ... More
Accounting for backflow in hydrodynamic-simulation interfacesJan 01 2014Methods for building a consistent interface between hydrodynamic and simulation modules is presented. These methods account for the backflow across the hydrodynamic/simulation hyper-surface. The algorithms are efficient, relatively straight-forward to ... More
Resolving the HBT Puzzle in Relativistic Heavy Ion CollisionNov 20 2008Two particle correlation data from the Relativistic Heavy Ion Collider have provided detailed femtoscopic information describing the space-time structure of the emission of pions. This data had avoided description with hydrodynamic-based approaches, in ... More
Interpreting scattering wave functions in the presence of energy-dependent interactionsOct 30 2007Nov 09 2007In scattering theory, the squared relative wave function $|\phi({\bf q},{\bf r})|^2$ is often interpreted as a weight, due to final-state interactions, describing the probability enhancement for emission with asymptotic relative momentum $q$. An equivalence ... More
Tsunamis, Viscosity and the HBT PuzzleOct 30 2007Nov 13 2007The equation of state and bulk and shear viscosities are shown to be able to affect the transverse dynamics of a central heavy ion collision. The net entropy, along with the femtoscopic radii are shown to be affected at the 10-20% level by both shear ... More
Shapes and Sizes from Non-Identical-Particle CorrelationsDec 02 2006I review the prospects for measuring source characteristics from correlations other than those involving identical pions. Correlations generated from Coulomb and strong interactions are shown to provide remarkable resolving power for determining three-dimensional ... More
Correlation Functions: Getting into ShapeNov 02 2005The ability to measure characteristics of source shapes using non-identical particle correlations is discussed. Both strong-interaction induced and Coulomb induced correlations are shown to provide sensitivity to source shapes. By decomposing correlation ... More
Refractive Distortions of Two-Particle Correlations from Classical Trajectory CalculationsAug 15 2005Calculations of two-particle correlations usually assume particles interact only pair-wise after their final collisions with third bodies. By considering classical trajectories, we show that interactions with the mean field can alter the spatial dimensions ... More
Recent Developments in Dynamical Supersymmetry BreakingJan 03 1998Some formal aspects of supersymmetry breaking are reviewed. The classic "requirements" for supersymmetry breaking include chiral matter, a dynamical superpotential, and a classical superpotential which completely lifts the moduli space. These "requirements" ... More
Calibrated Surrogate Losses for Classification with Label-Dependent CostsSep 14 2010We present surrogate regret bounds for arbitrary surrogate losses in the context of binary classification with label-dependent costs. Such bounds relate a classifier's risk, assessed with respect to a surrogate loss, to its cost-sensitive classification ... More
Generalized Inverse Limits Indexed by Totally Ordered SetsNov 01 2015Although inverse limits with factor spaces indexed by the positive integers are most commonly studied, Ingram and Mahavier have defined inverse limits with set-valued functions broadly enough for any directed index set to be used. In this paper, we investigate ... More
Seiberg-Witten vanishing theorem for $S^1$-manifolds with fixed pointsJan 07 2002Feb 10 2002In this paper we show that the Seiberg--Witten invariant is zero for all smooth 4--manifolds with $b_+{>}1$ which admit circle actions that have at least one fixed point. Furthermore, we show that all symplectic 4--manifolds which admit circle actions ... More