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A new determinantal formula for the classical discriminantDec 05 2008Jan 27 2009According to several classical results by Bezout, Sylvester, Cayley, and others, the classical discriminant D_n of degree n polynomials may be expressed as the determinant of a matrix whose entries are much simpler polynomials in the coefficients of f. ... More

Cool Core Bias in Sunyaev-Zel'dovich Galaxy Cluster SurveysJan 19 2015Sunyaev-Zeldovich (SZ) surveys find massive clusters of galaxies by measuring the inverse Compton scattering of cosmic microwave background off of intra-cluster gas. The cluster selection function from such surveys is expected to be nearly independent ... More

A Useful Approximation to the Cooling Coefficient of Trace ElementsMay 30 2001Radiative cooling is an important ingredient in hydrodynamical models involving evolution of high temperature plasmas. Unfortunately, calculating an accurate cooling coefficient generally requires the solution of over a hundred differential equations ... More

An Instability in the Radiative Ionization of Atomic Hydrogen/Helium GasApr 14 1996We show that the process of photoionizing a gas of atomic hydrogen and helium by line radiation whose energy is slightly above the helium single-ionization threshold is unstable if the helium fraction by number is less than approximately one half. However, ... More

A Geometric Consideration of the Erdős-Straus ConjectureNov 13 2014Dec 08 2014In this paper we will explore the solutions to the diophantine equation in the Erd\H{o}s-Straus conjecture. For a prime $p$ we are discussing the relationship between the values $x,y,z \in \mathbb{N}$ so that $$ \frac{4}{p} = \frac{1}{x} + \frac{1}{y} ... More

Stochastic Nonlinear Model Predictive Control with State Estimation by Incorporation of the Unscented Kalman FilterSep 05 2017Nonlinear model predictive control has become a popular approach to deal with highly nonlinear and unsteady state systems, the performance of which can however deteriorate due to unaccounted uncertainties. Model predictive control is commonly used with ... More

Short Laws for Finite Groups of Lie TypeNov 13 2018We produce new short laws in two variables valid in finite groups of Lie type. Our result improves upon results of Kozma and the second named author, and is sharp up to logarithmic factors, for all families except possibly the Suzuki groups. We also produce ... More

Matter and Gravity in Warped Extradimensional Models: Reinterpreting Randall-SundrumOct 16 2005Warped extra dimension claims remarkable success: solving the hierarchy problem; explaining hierarchies in particle phenomenology; yielding standard cosmology, plus interesting nonstandard scenarios. Yet it has marked shortcomings: we over-rely on a single ... More

Holographic Confinement/Deconfinement Transitions in Asymptotically Lifshitz SpacetimesJul 17 2012Aug 02 2012Under a Scherk-Schwarz compactification, the AdS soliton and black brane provide a dual description to a confinement/deconfinement phase transition. We extend this construction to asymptotically Lifshitz spacetimes. In particular, we show that there must ... More

Traffic distributions of random band matricesJan 10 2016May 20 2017We study random band matrices within the framework of traffic probability, an operadic non-commutative probability theory introduced by Male based on graph operations. As a starting point, we revisit the familiar case of the permutation invariant Wigner ... More

$CP$ violation in $B_s^0$ decays at LHCbAug 30 2014Latest LHCb measurements of $CP$ violation in the interference between mixing and decay are presented based on $pp$ collision data collected during LHC Run I, corresponding to an integrated luminosity of $3.0\, {\rm fb}^{-1}$. Approximately $27\, 000$ ... More

Dickson invariants, regularity and computation in group cohomologyMar 15 2003In this paper, we investigate the commutative algebra of the cohomology ring $H^*(G,k)$ of a finite group $G$ over a field $k$. We relate the concept of quasi-regular sequence, introduced by Benson and Carlson, to the local cohomology of the cohomology ... More

On Hierarchy, Charge Universality, and 4D Effective Theory in Randall-Sundrum ModelsJul 30 2004We present a variant formulation of the Randall-Sundrum model which solves both the hierarchy and charge universality problems. We first critique the rationale for hierarchy solution and 4D effective interactions in the Randall-Sundrum model. We note ... More

Unit Fractions in Norm-Euclidean Rings of IntegersMay 15 2014May 25 2014In this paper we make a Gaussian integer version of the Erd\H{o}s-Straus conjecture and we solve the Erd\H{o}s-Straus diophantine equation over the rings of integers of norm-Euclidean quadratic fields.

An HST/WFC3-UVIS View of the Starburst in the Cool Core of the Phoenix ClusterNov 29 2012Feb 10 2013We present Hubble Space Telescope Wide Field Camera 3 observations of the core of the Phoenix Cluster SPT-CLJ2344-4243 in five broadband filters spanning rest-frame 1000--5500A. These observations reveal complex, filamentary blue emission, extending for ... More

The Mid-Infrared Luminosities of Normal Galaxies over Cosmic TimeMar 06 2010Modern population synthesis models estimate that 50% of the restframe K-band light is produced by TP-AGB stars during the first Gyr of a stellar population, with a substantial fraction continuing to be produced by the TP-AGB over a Hubble time. Between ... More

Improving the use of equational constraints in cylindrical algebraic decompositionJan 19 2015May 07 2015When building a cylindrical algebraic decomposition (CAD) savings can be made in the presence of an equational constraint (EC): an equation logically implied by a formula. The present paper is concerned with how to use multiple ECs, propagating those ... More

On the linear stability of expanding Ricci solitonsSep 10 2014In previous work, the authors studied the linear stability of algebraic Ricci solitons on simply connected solvable Lie groups (solvsolitons), which are stationary solutions of a certain normalization of Ricci flow. Many examples were shown to be linearly ... More

Linear stability of algebraic Ricci solitonsSep 24 2013Sep 10 2014We consider a modified Ricci flow equation whose stationary solutions include Einstein and Ricci soliton metrics, and we study the linear stability of those solutions relative to the flow. After deriving various criteria that imply linear stability, we ... More

On the Stability of Electrostatic OrbitsAug 28 2008Jun 30 2009We analyze the stability of two charged conducting spheres orbiting each other. Due to charge polarization, the electrostatic force between the two spheres deviates significantly from $1/r^2$ as they come close to each other. As a consequence, there exists ... More

Galacticus: A Semi-Analytic Model of Galaxy FormationAug 10 2010We describe a new, free and open source semi-analytic model of galaxy formation, Galacticus. The Galacticus model was designed to be highly modular to facilitate expansion and the exploration of alternative descriptions of key physical ingredients. We ... More

The intrinsic asymmetry and inhomogeneity of Teichmuller spaceApr 28 2008Jan 18 2010Royden proved that any isometry of Teichmuller space in the Teichmuller metric must be an element of the extended mapping class group M(S). He also proved that the Teichmuller metric is not symmetric at any point. In this paper we give extensions of Royden's ... More

Étale homological stability and arithmetic statisticsDec 01 2015Dec 16 2015We contribute to the arithmetic/topology dictionary by relating asymptotic point counts and arithmetic statistics over finite fields to homological stability and representation stability over $\Cb$ in the example of configuration spaces of $n$ points ... More

Topology and arithmetic of resultants, II: the resultant $=1$ hypersurface (with an appendix by C. Cazanave)Jul 05 2015Nov 13 2015We consider the moduli space $\mathcal{R}_n$ of pairs of monic, degree $n$ polynomials whose resultant equals $1$. We relate the topology of these algebraic varieties to their geometry and arithmetic. In particular, we compute their \'{e}tale cohomology, ... More

Twisted Alice Loops as MonopolesApr 17 2003Dec 05 2003Symmetry breaking can produce ``Alice'' strings, which alter scattered charges and carry monopole number and charge when twisted into loops. We apply recent topological results, fixing Alice strings' stability and prescribing their twisting into loops ... More

Finite covers of graphs, their primitive homology, and representation theoryOct 27 2016Consider a finite, regular cover $Y\to X$ of finite graphs, with associated deck group $G$. We relate the topology of the cover to the structure of $H_1(Y;\mathbb{C})$ as a $G$-representation. A central object in this study is the {\em primitive homology} ... More

Moving homology classes in finite covers of graphsSep 30 2015Let $Y\to X$ be a finite normal cover of a wedge of $n\geq 3$ circles. We prove that for any $v\neq 0\in H_1(Y;\mathbb{Q})$ there exists a lift $\widetilde{F}$ to $Y$ of a homotopy equivalence $F:X\to X$ so that the set of iterates $\{\widetilde{F}^d(v): ... More

Representations and cohomology of a family of finite supergroup schemesMay 08 2019We examine the cohomology and representation theory of a family of finite supergroup schemes of the form $(\mathbb G_a^-\times \mathbb G_a^-)\rtimes (\mathbb G_{a(r)}\times (\mathbb Z/p)^s)$. In particular, we show that a certain relation holds in the ... More

Stable Adiabatic Times for Markov ChainsJul 19 2012Oct 19 2012In this paper we continue our work on adiabatic time of time-inhomogeneous Markov chains first introduced in Kovchegov (2010) and Bradford and Kovchegov (2011). Our study is an analog to the well-known Quantum Adiabatic (QA) theorem which characterizes ... More

Groups of diffeomorphisms of one-manifolds, III: Nilpotent subgroupsAug 13 2001Plante-Thurston proved that every nilpotent subgroup of $\Diff^2(S^1)$ is abelian. One of our main results is a sharp converse: $\Diff^1(S^1)$ contains every finitely-generated, torsion-free nilpotent group.

Group actions on one-manifolds, II: Extensions of Hölder's TheoremFeb 03 2001May 03 2001We study groups of homeomorphisms of R, each of whose elements have at most one fixed point. In particular we prove that any such group of C^2 diffeomorphisms is topologically conjugate to an affine group.

Galaxy Formation TheoryJun 28 2010Jul 12 2010We review the current theory of how galaxies form within the cosmological framework provided by the cold dark matter paradigm for structure formation. Beginning with the pre-galactic evolution of baryonic material we describe the analytical and numerical ... More

Measuring the Distribution of Galaxies Between HalosJan 17 2001We develop a method to measure the probability, P(N;M), of finding N galaxies in a dark-matter halo of mass M from the theoretically determined clustering properties of dark-matter halos and the observationally measured clustering properties of galaxies. ... More

Representation theory and homological stabilityAug 07 2010Jun 10 2013We introduce the idea of *representation stability* (and several variations) for a sequence of representations V_n of groups G_n. A central application of the new viewpoint we introduce here is the importation of representation theory into the study of ... More

Parametrized Abel-Jacobi maps and abelian cycles in the Torelli groupJan 07 2010Aug 05 2011Let I_g,* denote the (pointed) Torelli group. This is the group of homotopy classes of homeomorphisms of the genus g >= 2 surface S_g with a marked point, acting trivially on H := H_1(S_g). In 1983 Johnson constructed a beautiful family of invariants ... More

Infinite generation of the kernels of the Magnus and Burau representationsSep 26 2009Consider the kernel Mag_g of the Magnus representation of the Torelli group and the kernel Bur_n of the Burau representation of the braid group. We prove that for g >= 2 and for n >= 6 the groups Mag_g and Bur_n have infinite rank first homology. As a ... More

The Degree Theorem in higher rankJan 05 2001Let M be any closed, locally symmetric n-manifold (n>1) of nonpositive curvature. Assume that M has no locally Euclidean factors and no factors locally isometric to SL(3,R). Then for any closed Riemannian manifold N and any continuous map f:N -> M, we ... More

A universe in a global monopoleApr 06 2001We investigate brane physics in a universe with an extra dimensional global monopole and negative bulk cosmological constant. The graviton zero mode is naturally divergent; we thus invoke a physical cut-off to induce four dimensional gravity on a brane ... More

A compendium of extinction curves for simple galactic geometriesOct 02 2018We calculate the net extinction of galactic light as a function of wavelength, inclination, central optical depth, and morphology for simple galactic geometries using the Hyperion radiative transfer code. Compared to previous, similar works we tabulate ... More

A generalization of the Grid TheoremSep 28 2016A graph has tree-width at most $k$ if it can be obtained from a set of graphs each with at most $k+1$ vertices by a sequence of clique sums. We refine this definition by, for each non-negative integer $\theta$, defining the $\theta$-tree-width of a graph ... More

The Structure of a Bernoulli Process Variation of the Fibonacci SequenceNov 30 2007We consider the structure of a variation of the Fibonacci sequence which is determined by a Bernoulli process. The associated structure of all Bernoulli variations of the Fibonacci sequence can be represented by a directed binary tree, which we denote ... More

The secondary flow in a short aspect ratio circular lid driven cavity at small but finite Reynolds numberOct 21 2003Regular perturbation solutions are obtained for the Stokes flow field, the first order effects of inertia on the flow field, and the primary and secondary pressure fields in the circular lid driven cavity. The physical mechanism that causes vortex breakdown ... More

Groups of homeomorphisms of one-manifolds, I: actions of nonlinear groupsJul 11 2001Jul 12 2001This self-contained paper is part of a series \cite{FF2,FF3} on actions by diffeomorphisms of infinite groups on compact manifolds. The two main results presented here are: 1) Any homomorphism of (almost any) mapping class group or automorphism group ... More

Groups of homeomorphisms of one-manifolds, III: Nilpotent subgroupsFeb 03 2001Feb 19 2001This paper has been withdrawn by the authors; it will be incorporated into part I of the series (in preparation).

The Grothendieck-Katz Conjecture for certain locally symmetric varietiesJul 08 2008Using Margulis's results on lattices in semisimple Lie groups, we prove the Grothendieck-Katz $p$-Curvature Conjecture for certain locally symmetric varieties, including the moduli space of abelian varieties ${\cal A}_g$ when $g > 1.$

Topology and arithmetic of resultants, I: spaces of rational mapsJun 08 2015Jul 07 2015We consider the interplay of point counts, singular cohomology, \'etale cohomology, eigenvalues of the Frobenius and the Grothendieck ring of varieties for two families of varieties: spaces of rational maps and moduli spaces of marked, degree $d$ rational ... More

A Topological Criterion for Alice StringsApr 17 2003Dec 05 2003Symmetry breaking can produce ``Alice'' strings, which alter scattered charges and carry monopole number and charge when twisted into loops. Alice behavior arises algebraically, when a string's untraced Wilson loop obstructs unbroken symmetries -- a fragile ... More

An adaptive MCMC method for multiple changepoint analysis with applications to large datasetsJun 30 2016We consider the problem of Bayesian inference for changepoints where the number and position of the changepoints are both unknown. In particular, we consider product partition models where it is possible to integrate out model parameters for the regime ... More

Building a Predictive Model of Galaxy Formation - I: Phenomenological Model Constrained to the $z=0$ Stellar Mass FunctionMay 21 2014We constrain a highly simplified semi-analytic model of galaxy formation using the $z\approx 0$ stellar mass function of galaxies. Particular attention is paid to assessing the role of random and systematic errors in the determination of stellar masses, ... More

Erratum for "The degree theorem in higher rank"Nov 22 2014May 17 2015The purpose of this erratum is to correct a mistake in the proof of Theorem 4.1 of our paper \cite{CF}.

Curvature and rank of Teichmüller spaceSep 06 2001Let S be a surface with genus g and n boundary components and let d(S) = 3g-3+n denote the number of curves in any pants decomposition of S. We employ metric properties of the graph of pants decompositions CP(S) prove that the Weil-Petersson metric on ... More

Symmetric tensor categories in characteristic 2Jul 15 2018We construct and study a nested sequence of finite symmetric tensor categories ${\rm Vec}=\mathcal{C}_0\subset \mathcal{C}_1\subset\cdots\subset \mathcal{C}_n\subset\cdots$ over a field of characteristic $2$ such that $\mathcal{C}_{2n}$ are incompressible, ... More

On the asymptotic geometry of abelian-by-cyclic groupsMay 17 2000A finitely presented, torsion free, abelian-by-cyclic group can always be written as an ascending HNN extension Gamma_M of Z^n, determined by an n x n integer matrix M with det(M) \ne 0. The group Gamma_M is polycyclic if and only if |det(M)|=1. We give ... More

NNDrone: a toolkit for the mass application of machine learning in High Energy PhysicsDec 25 2017Feb 12 2019Machine learning has proven to be an indispensable tool in the selection of interesting events in high energy physics. Such technologies will become increasingly important as detector upgrades are introduced and data rates increase by orders of magnitude. ... More

Symmetric tensor categories in characteristic 2Jul 15 2018Apr 04 2019We construct and study a nested sequence of finite symmetric tensor categories ${\rm Vec}=\mathcal{C}_0\subset \mathcal{C}_1\subset\cdots\subset \mathcal{C}_n\subset\cdots$ over a field of characteristic $2$ such that $\mathcal{C}_{2n}$ are incompressible, ... More

Fields of definition for representations of associative algebrasFeb 21 2017We examine situations, where representations of a finite-dimensional $F$-algebra $A$ defined over a separable extension field $K/F$, have a unique minimal field of definition. Here the base field $F$ is assumed to be a $C_1$-field. In particular, $F$ ... More

Examples of support varieties for Hopf algebras with noncommutative tensor productsAug 23 2013The representations of some Hopf algebras have curious behavior: Nonprojective modules may have projective tensor powers, and the variety of a tensor product of modules may not be contained in the intersection of their varieties. We explain a family of ... More

Separating the complexity classes NL and NPApr 17 2000May 12 2000Withdrawn since -order- was overlooked. First order reductions without order are much too weak to separate.

An online algorithm for generating fractal hash chains applied to digital chains of custodyMay 20 2007This paper gives an online algorithm for generating Jakobsson's fractal hash chains. Our new algorithm compliments Jakobsson's fractal hash chain algorithm for preimage traversal since his algorithm assumes the entire hash chain is precomputed and a particular ... More

Teichmuller geometry of moduli space, I: Distance minimizing rays and the Deligne-Mumford compactificationMar 02 2008Jun 18 2010Let $S$ be a closed, oriented surface with a finite (possibly empty) set of points removed. In this paper we relate two important but disparate topics in the study of the moduli space $\M(S)$ of Riemann surfaces: Teichm\"{u}ller geometry and the Deligne-Mumford ... More

Charge Violation and Alice Behavior in Global and Textured StringsMar 28 2001Spontaneous breaking of global symmetries can produce ``Alice'' strings: line defects which make unbroken symmetries multivalued, induce apparent charge violation via Aharonov-Bohm interactions, and form point defects when twisted into loops. We demonstrate ... More

Skyrmions and Semilocal Strings in CosmologyApr 05 1993It has been pointed out that cosmic string solutions can exist in gauge field theories with broken symmetry even when $\pi _1(G/H)$ is trivial. The stability of such semilocal defects is not guaranteed by topology and depends on dynamical considerations. ... More

Self-Consistent Theory of Halo Mergers - II: CDM Power SpectraFeb 25 2008We place additional constraints on the three parameters of the dark matter halo merger rate function recently proposed by Parkinson, Cole & Helly by utilizing Smoluchowski's coagulation equation, which must be obeyed by any binary merging process which ... More

Covariances of Galaxy Stellar Mass Functions and Correlation FunctionsJul 30 2018We compute covariance matrices for many observed estimates of the stellar mass function of galaxies from $z=0$ to $z\approx 4$, and for one estimate of the projected correlation function of galaxies split by stellar mass at $z\lesssim 0.5$. All covariance ... More

Gravitating Scalars and Critical Collapse in the Large $D$ LimitJul 26 2018We develop the large $D$ limit of general relativity for spherically symmetric scalar fields in both asymptotically flat and asymptotically anti-de Sitter spaces. The leading order equations in the $1/D$ expansion can be solved analytically, providing ... More

Bayesian inference, model selection and likelihood estimation using fast rejection sampling: the Conway-Maxwell-Poisson distributionSep 11 2017Bayesian inference for models with intractable likelihood functions represents a challenging suite of problems in modern statistics. In this work we analyse the Conway-Maxwell-Poisson (COM-Poisson) distribution, a two parameter generalisation of the Poisson ... More

Isometries, rigidity, and universal coversJun 27 2005Feb 05 2007We classify all closed, aspherical Riemannian manifolds M whose universal cover has indiscrete isometry group. One sample application is the theorem that any such M with word-hyperbolic fundamental group must be isometric to a negatively curved, locally ... More

Problems on the geometry of finitely generated solvable groupsMay 18 2000Feb 05 2001A survey of problems, conjectures, and theorems about quasi-isometric classification and rigidity for finitely generated solvable groups.

The variety of subadditive functions for finite group schemesApr 05 2016For a finite group scheme, the subadditive functions on finite dimensional representations are studied. It is shown that the projective variety of the cohomology ring can be recovered from the equivalence classes of subadditive functions. Using Crawley-Boevey's ... More

Schur-Weyl duality over finite fieldsMay 08 2008Jun 30 2009We prove a version of Schur--Weyl duality over finite fields. We prove that for any field $k$, if $k$ has at least $r+1$ elements, then Schur--Weyl duality holds for the $r$th tensor power of a finite dimensional vector space $V$. Moreover, if the dimension ... More

Constraining the Noise-Free Distribution of Halo Spin ParametersMay 04 2017Any measurement made using an N-body simulation is subject to noise due to the finite number of particles used to sample the dark matter distribution function, and the lack of structure below the simulation resolution. This noise can be particularly significant ... More

The non-projective part of the tensor powers of a moduleFeb 08 2019Let $M$ be a finite dimensional modular representation of a finite group $G$. We consider the generating function for the non-projective part of the tensor powers of $M$, and we write $\gamma_G(M)$ for the reciprocal of the radius of convergence of this ... More

Cylindrical Algebraic Decomposition with Equational ConstraintsMar 20 2019Cylindrical Algebraic Decomposition (CAD) has long been one of the most important algorithms within Symbolic Computation, as a tool to perform quantifier elimination in first order logic over the reals. More recently it is finding prominence in the Satisfiability ... More

Arrow ribbon graphsJul 16 2011Sep 13 2012We introduce an additional structure on ribbon graphs, arrow structure. We extend the Bollob\'as-Riordan polynomial to ribbon graph with this structure. The extended polynomial satisfies the contraction-deletion relations and naturally behaves with respect ... More

Orbital Parameters of Infalling Dark Matter SubstructuresJul 20 2004We present distributions of the orbital parameters of dark matter substructures at the time of merging into their host halo. Accurate knowledge of the orbits of dark matter substructures is a crucial input to studies which aim to assess the effects of ... More

Towards Fluid Instabilities of Stationary Non-Killing HorizonsJun 02 2016Flowing black holes are asymptotically locally AdS spacetimes that are stationary but have non-Killing horizons. Holographically, they are dual to a steady-state heat flow in the boundary field theory. We investigate the stability of these black holes ... More

Minimal entropy rigidity for lattices in products of rank one symmetric spacesJan 05 2001We prove minimal entropy rigidity for complete, finite volume manifolds locally isometric to a product of rank one symmetric spaces of dimension at least 3: the locally symmetric metric uniquely minimizes (normalized) entropy among all Riemannian metrics. ... More

Teichmuller geometry of moduli space, II: M(S) seen from far awayJul 11 2008Jun 29 2014We construct a metric simplicial complex which is an almost isometric model of the moduli space M(S) of Riemann surfaces. We then use this model to compute the "tangent cone at infinity" of M(S): it is the topological cone on the quotient of the complex ... More

Filling-invariants at infinity for manifolds of nonpositive curvatureApr 07 1995In this paper we construct and study isoperimetric functions at infinity for Hadamard manifolds. These quasi-isometry invariants give a measure of the spread of geodesics in such a manifold.

Real-analytic, volume-preserving actions of lattices on 4-manifoldsJan 17 2002We prove that any real-analytic, volume-preserving action of a lattice $\Gamma$ in a simple Lie group with $\Qrank(\Gamma)\geq 7$ on a closed 4-manifold of nonzero Euler characteristic factors through a finite group action.

Quasi-isometric rigidity for the solvable Baumslag-Solitar groups, IISep 02 1998Let BS(1,n)= < a,b: aba^{-1}=b^n >. We prove that any finitely-generated group quasi-isometric to BS(1,n) is (up to finite groups) isomorphic to BS(1,n). We also show that any uniform group of quasisimilarities of the real line is bilipschitz conjugate ... More

Hidden symmetry and arithmetic manifoldsMay 10 2004A "hidden symmetry" of a Riemannian manifold M is an isometry of a d-sheeted, 1<d<\infty, Riemannian cover of M which is not the lift of any isometry. In this paper we characterize the locally symmetric metric(s) on a closed, arithmetic manifold as the ... More

The Mass Function of Unprocessed Dark Matter Halos and Merger Tree Branching RatesOct 04 2016A common approach in semi-analytic modeling of galaxy formation is to construct Monte Carlo realizations of merger histories of dark matter halos whose masses are sampled from a halo mass function. Both the mass function itself, and the merger rates used ... More

Commensurations of Out(F_n)Jul 21 2006Jul 26 2007Let $\Out(F_n)$ denote the outer automorphism group of the free group $F_n$ with $n>3$. We prove that for any finite index subgroup $\Gamma<\Out(F_n)$, the group $\Aut(\Gamma)$ is isomorphic to the normalizer of $\Gamma$ in $\Out(F_n)$. We prove that ... More

Security Risks in Mechanical Engineering IndustriesNov 30 2015Inherent in any organization are security risks and barriers that must be understood, analyzed, and minimized in order to prepare for and perpetuate future growth and return on investment within the business. Likewise, company leaders must determine the ... More

Lifshitz SingularitiesNov 04 2011Nov 29 2011Lifshitz spacetimes are possible gravitational duals to strongly coupled field theories with an anisotropic scaling symmetry. These spacetimes however, have a null curvature singularity. We find that higher dimensional embeddings of Lifshitz also have ... More

A Framework for Practical Parallel Fast Matrix MultiplicationSep 09 2014Matrix multiplication is a fundamental computation in many scientific disciplines. In this paper, we show that novel fast matrix multiplication algorithms can significantly outperform vendor implementations of the classical algorithm and Strassen's fast ... More

Entropy Injection as a Global Feedback MechanismDec 13 2002Both preheating of the intergalactic medium and radiative cooling of low entropy gas have been proposed to explain the deviation from self-similarity in the cluster L_x-T_x relation and the observed entropy floor in these systems. However, severe overcooling ... More

X-rays and hard UV radiation From the First Galaxies: Ionization Bubbles and 21 cm ObservationsJul 15 2011The first stars and quasars are known sources of hard ionizing radiation in the first billion years of the Universe. We examine the joint effects of X-rays and hard UV radiation from such first-light sources on the hydrogen and helium reionization of ... More

Black DropletsMay 08 2014Black droplets and black funnels are gravitational duals to states of a large N, strongly coupled CFT on a fixed black hole background. We numerically construct black droplets corresponding to a CFT on a Schwarzchild background with finite asymptotic ... More

The Birman-Craggs-Johnson homomorphism and abelian cycles in the Torelli groupJan 09 2006In the 1970s, Birman-Craggs-Johnson used Rochlin's invariant for homology 3-spheres to construct a remarkable surjective homomorphism sigma:I_{g,1}->B_3, where I_{g,1} is the Torelli group and B_3 is a certain F_2-vector space of Boolean (square-free) ... More

Complete Phase Diagrams for a Holographic Superconductor/Insulator SystemJul 21 2010Aug 05 2010The gravitational dual of an insulator/superconductor transition driven by increasing the chemical potential has recently been constructed. However, the system was studied in a probe limit and only a part of the phase diagram was obtained. We include ... More

Black FunnelsAug 30 2012Dec 18 2012The Hartle-Hawking state of $\mathcal{N}=4$ SYM at strong coupling and large $N$ on a fixed black hole background has two proposed gravitational duals: a black funnel or a black droplet. We construct the black funnel solutions that are dual to the Hartle-Hawking ... More

A Counterexample for Lightning Flash Modules over E(e1,e2)Jul 03 2015Jul 07 2015We give a counterexample to Theorem 5 in Section 18.2 of Margolis' book, "Spectra and the Steenrod Algebra", and make remarks about the proofs of some later theorems in the book that depend on it. The counterexample is a module which does not split as ... More

A realization theorem for modules of constant Jordan type and vector bundlesJul 22 2010Let E be an elementary abelian p-group of rank r and let k be a field of characteristic p. We introduce functors F_i from finitely generated kE-modules of constant Jordan type to vector bundles over projective space of dimension r-1. The fibers of these ... More

Tidal Mass Loss from Collisionless SystemsJul 03 2006Nov 30 2006We examine the problem tidally-induced mass loss from collisionless systems such as dark matter haloes. We develop a model for tidal mass loss, based upon the phase space distribution of particles, which accounts for how both tidal and Coriolis torques ... More

Torelli buildings and their automorphismsOct 23 2014In this paper we introduce, for each closed orientable surface, an analogue of Tits buildings adjusted to investigation of the Torelli group of this surface. It is a simplicial complex with some additional structure. We call this complex with its additional ... More

The Future Landscape of High-Redshift Galaxy Cluster ScienceMar 13 2019Modern galaxy cluster science is a multi-wavelength endeavor with cornerstones provided by X-ray, optical/IR, mm, and radio measurements. In combination, these observations enable the construction of large, clean, complete cluster catalogs, and provide ... More

The Origin of the Hubble Sequence in Lambda-CDM CosmologyNov 23 2009Dec 02 2009The Galform semi-analytic model of galaxy formation is used to explore the mechanisms primarily responsible for the three types of galaxies seen in the local universe: bulge, bulge+disk and disk, identified with the visual morphological types E, S0/a-Sbc, ... More

The Torelli geometry and its applicationsNov 10 2003For each closed orientable surface we introduce a simplical complex with some additional structure which is a version of the complex of curves of this surface adjusted to investigation of its Torelli group. We call this complex the Torelli geometry of ... More