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Singular values of large non-central random matricesFeb 08 2018We study largest singular values of large random matrices, each with mean of a fixed rank $K$. Our main result is a limit theorem as the number of rows and columns approach infinity, while their ratio approaches a positive constant. It provides a decomposition ... More

Robust Estimates of Covariance Matrices in the Large Dimensional RegimeApr 24 2012Apr 14 2014This article studies the limiting behavior of a class of robust population covariance matrix estimators, originally due to Maronna in 1976, in the regime where both the number of available samples and the population size grow large. Using tools from random ... More

A CLT for Information-theoretic statistics of Non-centered Gram random matricesJul 01 2011In this article, we study the fluctuations of the random variable: $$ {\mathcal I}_n(\rho) = \frac 1N \log\det(\Sigma_n \Sigma_n^* + \rho I_N),\quad (\rho>0) $$ where $\Sigma_n= n^{-1/2} D_n^{1/2} X_n\tilde D_n^{1/2} +A_n$, as the dimensions of the matrices ... More

Eigen-Inference for Energy Estimation of Multiple SourcesJan 22 2010Oct 24 2010In this paper, a new method is introduced to blindly estimate the transmit power of multiple signal sources in multi-antenna fading channels, when the number of sensing devices and the number of available samples are sufficiently large compared to the ... More

Eigenvalues of Large Sample Covariance Matrices of Spiked Population ModelsAug 12 2004We consider a spiked population model, proposed by Johnstone, whose population eigenvalues are all unit except for a few fixed eigenvalues. The question is to determine how the sample eigenvalues depend on the non-unit population ones when both sample ... More

Gaussian fluctuations for non-Hermitian random matrix ensemblesFeb 18 2005Feb 28 2007Consider an ensemble of $N\times N$ non-Hermitian matrices in which all entries are independent identically distributed complex random variables of mean zero and absolute mean-square one. If the entry distributions also possess bounded densities and finite ... More

An invariant of link cobordisms from symplectic Khovanov homologyDec 27 2009Feb 12 2012Symplectic Khovanov homology is an invariant of oriented links defined by Seidel and Smith and conjectured to be isomorphic to Khovanov homology. I define morphisms (up to a global sign ambiguity) between symplectic Khovanov homology groups, corresponding ... More

Fundamental limit of sample generalized eigenvalue based detection of signals in noise using relatively few signal-bearing and noise-only samplesFeb 25 2009The detection problem in statistical signal processing can be succinctly formulated: Given m (possibly) signal bearing, n-dimensional signal-plus-noise snapshot vectors (samples) and N statistically independent n-dimensional noise-only snapshot vectors, ... More

A Deterministic Equivalent for the Analysis of Correlated MIMO Multiple Access ChannelsJun 19 2009Oct 24 2010In this article, novel deterministic equivalents for the Stieltjes transform and the Shannon transform of a class of large dimensional random matrices are provided. These results are used to characterise the ergodic rate region of multiple antenna multiple ... More

The Random Matrix Regime of Maronna's M-estimator with elliptically distributed samplesNov 27 2013This article demonstrates that the robust scatter matrix estimator $\hat{C}_N\in {\mathbb C}^{N\times N}$ of a multivariate elliptical population $x_1,\ldots,x_n\in {\mathbb C}^N$ originally proposed by Maronna in 1976, and defined as the solution (when ... More

On the signal-to-interference ratio of CDMA systems in wireless communicationsFeb 28 2007Let $\{s_{ij}:i,j=1,2,...\}$ consist of i.i.d. random variables in $\mathbb{C}$ with $\mathsf{E}s_{11}=0$, $\mathsf{E}|s_{11}|^2=1$. For each positive integer $N$, let $\mathbf{s}_k={\mathbf{s}}_k(N)=(s_{1k},s_{2k},...,s_{Nk})^T$, $1\leq k\leq K$, with ... More

Separation of the largest eigenvalues in eigenanalysis of genotype data from discrete subpopulationsJan 18 2013We present a mathematical model, and the corresponding mathematical analysis, that justifies and quantifies the use of principal component analysis of biallelic genetic marker data for a set of individuals to detect the number of subpopulations represented ... More

A note on the CLT of the LSS for sample covariance matrix from a spiked population modelApr 23 2013Jul 05 2013In this note, we establish an asymptotic expansion for the centering parameter appearing in the central limit theorems for linear spectral statistic of large-dimensional sample covariance matrices when the population has a spiked covariance structure. ... More

Quasars in the 4D Eigenvector 1 Context: A stroll down memory laneJun 03 2015Recently some pessimism has been expressed about our lack of progress in understanding quasars over the 50+ year since their discovery. It is worthwhile to look back at some of the progress that has been made - but still lies under the radar - perhaps ... More

Quasars and their emission lines as cosmological probesOct 11 2013Quasars are the most luminous sources in the Universe. They are currently observed out to redshift z ~ 7 when the Universe was less than one tenth of its present age. Since their discovery 50 years ago astronomers have dreamed of using them as standard ... More

Quasar Outflows in the 4D Eigenvector 1 ContextOct 07 2012Gas outflows appear to be a phenomenon shared by the vast majority of quasars. Observations indicate that there is wide range in outflow prominence. In this paper we review how the 4D eigenvector 1 scheme helps to organize observed properties and lead ... More

Influence of Nanoparticle Additives on the Fragility of Polymer Glass Formation and the Buchenau RelationJun 29 2009We investigate the impact of the addition of nanoparticles (NP) on the fragility of a model glass-forming polymer melt by molecular dynamics simulations. We find significant changes in fragility for nanoparticle volume fractions $\phi$ exceeding $\approx$ ... More

String-theoretic breakdown of effective field theory near black hole horizonsApr 21 2015We investigate the validity of the equivalence principle near horizons in string theory, analyzing the breakdown of effective field theory caused by longitudinal string spreading effects. An experiment is set up where a detector is thrown into a black ... More

Modifying Fragility and Collective Motion in Polymer Melts with NanoparticlesJan 28 2011We investigate the impact of nanoparticles (NP) on the fragility and cooperative string-like motion in a model glass-forming polymer melt by molecular dynamics simulation. The NP cause significant changes to both the fragility and the average length of ... More

Edge-regular graphs with regular cliquesAug 20 2017Apr 02 2018We exhibit infinitely many examples of edge-regular graphs that have regular cliques and that are not strongly regular. This answers a question of Neumaier from 1981.

Neural Classification of Malicious Scripts: A study with JavaScript and VBScriptMay 15 2018Malicious scripts are an important computer infection threat vector. Our analysis reveals that the two most prevalent types of malicious scripts include JavaScript and VBScript. The percentage of detected JavaScript attacks are on the rise. To address ... More

4d Conformal Field Theories and Strings on OrbifoldsFeb 25 1998Mar 16 1998We propose correspondences between 4d quantum field theories with N=2,1,0 (super)conformal invariance and Type IIB string theory on various orbifolds. We argue using the spacetime string theory, and check using the beta functions (exactly for N=2,1 and ... More

On Vanishing Two Loop Cosmological Constants in Nonsupersymmetric StringsOct 16 1998It has recently been suggested that in certain special nonsupersymmetric type II string compactifications, at least the first two perturbative contributions to the cosmological constant $\Lambda$ vanish. Support for perturbative vanishing beyond 1-loop ... More

Singularities, Gauge Dynamics, and Nonperturbative Superpotentials in String TheoryAug 29 1996Aug 30 1996We describe a class of 4d N=1 compactifications of the $SO(32)$ heterotic/type I string theory which are destabilized by nonperturbatively generated superpotentials. In the type I description, the destabilizing superpotential is generated by a one instanton ... More

N=1 Dual String Pairs and Gaugino CondensationDec 01 1995Dec 12 1995We study a class of four-dimensional N=1 heterotic string theories which have nontrivial quantum dynamics arising from asymptotically free gauge groups. These models are obtained by orbifolding 4d N=2 heterotic/type II dual pairs by symmetries which leave ... More

Collective Motion in the Interfacial and Interior Regions of Supported Polymer Films and its Relation to RelaxationFeb 12 2019To understand the role of collective motion in the often large changes in interfacial molecular mobility observed in polymer films, we investigate the extent of collective motion in the interfacial regions of a thin supported polymer film and within the ... More

The Effect of Nanoparticle Shape on Polymer-Nanocomposite Rheology and Tensile StrengthJan 24 2007Nanoparticles can influence the properties of polymer materials by a variety of mechanisms. With fullerene, carbon nanotube, and clay or graphene sheet nanocomposites in mind, we investigate how particle shape influences the melt shear viscosity $\eta$ ... More

Discovery learning in an interdisciplinary course on finite fields and applicationsOct 24 2018Math 148 at the University of California Davis covers finite fields and combinatorial applications including block designs and error-correcting codes. Teaching this course presents some unique challenges, as much of the content typically appears in a ... More

The Relationship of Dynamical Heterogeneity to the Adam-Gibbs and Random First-Order Transition Theories of Glass FormationFeb 20 2013We carefully examine common measures of dynamical heterogeneity for a model polymer melt and test how these scales compare with those hypothesized by the Adam and Gibbs (AG) and random first-order transition (RFOT) theories of relaxation in glass-forming ... More

Obliquity Evolution of the Potentially Habitable Exoplanet Kepler-62fOct 23 2017Variations in the axial tilt, or obliquity, of terrestrial planets can affect their climates and therefore their habitability. Kepler-62f is a 1.4 R$_\oplus$ planet orbiting within the habitable zone of its K2 dwarf host star (Borucki et al. 2013). We ... More

Energy conservation in the 3D Euler equations on $\mathbb{T}^2\times \mathbb{R}_+$Nov 01 2016Jun 30 2017The aim of this paper is to prove energy conservation for the incompressible Euler equations in a domain with boundary. We work in the domain $\mathbb{T}^2\times\mathbb{R}_+$, where the boundary is both flat and has finite measure. However, first we study ... More

Energy conservation for the Euler equations on $\mathbb{T}^2\times \mathbb{R}_+$ for weak solutions defined without reference to the pressureJun 01 2018We study weak solutions of the incompressible Euler equations on $\mathbb{T}^2\times \mathbb{R}_+$; we use test functions that are divergence free and have zero normal component, thereby obtaining a definition that does not involve the pressure. We prove ... More

Energy Conservation for the Compressible Euler and Navier-Stokes Equations with VacuumAug 15 2018We consider the compressible isentropic Euler equations on $\mathbb{T}^d\times [0,T]$ with a pressure law $p\in C^{1,\gamma-1}$, where $1\le \gamma <2$. This includes all physically relevant cases, e.g.\ the monoatomic gas. We investigate under what conditions ... More

Varying dilaton as a tracer of classical string interactionsApr 09 2017Apr 27 2017We analyze tree-level string amplitudes in a linear dilaton background, motivated by its use as a gauge-invariant tracer of string interactions in scattering experiments and its genericity among simple perturbative string theory limits. A simple case ... More

Vacuum Energy Cancellation in a Non-supersymmetric StringJul 10 1998Dec 21 1998We present a nonsupersymmetric orbifold of type II string theory and show that it has vanishing cosmological constant at the one and two loop level. We argue heuristically that the cancellation persists at higher loops.

New N=1 Superconformal Field Theories in Four Dimensions from D-brane ProbesOct 27 1996We present several new examples of nontrivial 4d N=1 superconformal field theories. Some of these theories exhibit exotic global symmetries, including non-simply laced groups (such as $F_4$). They are obtained by studying threebrane probes in F-theory ... More

dS/dS and $T\bar T$Nov 19 2018The $T\bar T$ deformation of a conformal field theory has a dual description as a cutoff $AdS_3$ spacetime, at least at the level of pure 3d gravity. We generalize this deformation in such a way that it builds up a patch of bulk $dS_3$ spacetime instead. ... More

New Dimensions for Wound Strings: The Modular Transformation of Geometry to TopologyDec 13 2006Jan 03 2007We show, using a theorem of Milnor and Margulis, that string theory on compact negatively curved spaces grows new effective dimensions as the space shrinks, generalizing and contextualizing the results in hep-th/0510044. Milnor's theorem relates negative ... More

Retrofitting O'Raifeartaigh Models with Dynamical ScalesAug 23 2006Sep 05 2006We provide a method for obtaining simple models of supersymmetry breaking, with all small mass scales generated dynamically, and illustrate it with explicit examples. We start from models of perturbative supersymmetry breaking, such as O'Raifeartaigh ... More

Mapping IR Enhancements in Closely Interacting Spiral-Spiral Pairs. I. ISO~CAM and ISO~SWS ObservationsMay 01 2000Mid-infrared (MIR) imaging and spectroscopic observations are presented for a well defined sample of eight closely interacting (CLO) pairs of spiral galaxies that have overlapping disks and show enhanced far-infrared (FIR) emission. The goal is to study ... More

Tate cohomology of circle actions as a Heisenberg groupFeb 16 2001Sep 13 2001We study the Madsen-Tillman spectrum \CP^\infty_{-1} as a quotient of the Mahowald pro-object \CP^\infty_{-\infty}, which is closely related to the Tate cohomology of circle actions. That theory has an associated symplectic structure, whose symmetries ... More

Transcendental Julia Sets with Fractional Packing DimensionMay 19 2019We construct a family of transcendental entire functions whose Julia sets have packing dimension in $(1,2)$. These are the first examples where the computed packing dimension is not $1$ or $2$. Our construction will allow us further show that the set ... More

Cohomology and base change for algebraic stacksJun 19 2012Mar 15 2013We prove that cohomology and base change holds for algebraic stacks, generalizing work of Brochard in the tame case. We also show that Hom-spaces on algebraic stacks are represented by abelian cones, generalizing results of Grothendieck, Brochard, Olsson, ... More

Moduli of Singular CurvesNov 28 2010The purpose of this note is to prove that there is an algebraic stack U parameterizing all curves. The curves that appear in the algebraic stack U are allowed to be arbitrarily singular, non-reduced, disconnected, and reducible. We also prove the boundedness ... More

Techniques for Profile Binning and Analysis of Eigenvector Composite Spectra: Comparing Hbeta and MgII 2800 as Virial EstimatorsOct 16 2013We review the basic techniques for extracting information about quasar structure and kinematics from the broad emission lines in quasars. We consider which lines can most effectively serve as virial estimators of black hole mass. At low redshift the Balmer ... More

The Markov approximation for the atomic output couplerOct 30 1998The regions of validity of the Markov approximation for the coupling of atoms out of an atomic trap are determined. We consider radio-frequency output coupling in the presence of gravity and collisional repulsion, and Raman output coupling. The Markov ... More

CIV 1549 as an Eigenvector 1 Parameter for Active Galactic NucleiMay 14 2007[Abridged] We have been exploring a spectroscopic unification for all known types of broad line emitting AGN. The 4D Eigenvector 1 (4DE1) parameter space shows promise as a unification capable of organizing quasar diversity on a sequence primarily governed ... More

Complex orientations for THH of some perfectoid fieldsAug 16 2016Oct 02 2016This sketch argues that work of Hesselholt [8] on the topological Hochschild homology of $\Cp$ extends, using work of Scholze [15, 23] on flat descent, to define complex orientations for a version of topological Hochschild homology for rings of integers ... More

A theory of base motivesAug 21 2009A category of correspondences based on Waldhausen A-theory has interesting analogies, in the context of differential topology, to categories of mixed Tate motives studied in arithmetic geometry. In particular, the Hopf object S \wedge_A S (regarding A(*) ... More

Complex cobordism and algebraic topologyJul 21 2007This is a historical survey, beginning where Atiyah and Sullivan leave off...

Quantum generalized cohomologyJul 11 1998We construct a ring structure on complex cobordism tensored with the rationals, which is related to the usual ring structure as quantum cohomology is related to ordinary cohomology. The resulting object defines a generalized two- dimensional topological ... More

Toward a fundamental groupoid for the stable homotopy categoryAug 31 2005Mar 27 2009This very speculative sketch suggests that a theory of fundamental groupoids for tensor triangulated categories could be used to describe the ring of integers as the singular fiber in a family of ring-spectra parametrized by a structure space for the ... More

On gauge theories of massJan 06 2010May 22 2010Mass as broken conformal symmetry: the graviton makes better sense as a Goldstone boson associated to the dilaton, than vice versa. The discussion of the Yamabe problem for the interior Schwarzschild solution [\S 4.2.4] has been sharpened in this revision. ... More

Techniques for classifying nonnegatively curved left-invariant metrics on compact Lie groupsAug 14 2006We provide techniques for studying the nonnegatively curved left-invariant metrics on a compact Lie group. For "straight" paths of left-invariant metrics starting at bi-invariant metrics and ending at nonnegatively curved metrics, we deduce a nonnegativity ... More

A catalogue of spectroscopic binary candidate stars derived from a comparison of Gaia DR2 with other radial velocity cataloguesJan 25 2019Using the recently published Gaia second data release which includes measurements of the mean radial velocity of about 7.2 million stars, we performed a systematic comparison with other existing radial velocity catalogues in order to search for variations ... More

On the automorphy of $l$-adic Galois representations with small residual imageJul 29 2011We prove new automorphy lifting theorems for essentially conjugate self-dual Galois representations into $GL_n$. Existing theorems require that the residual representation have 'big' image, in a certain technical sense. Our theorems are based on a strengthening ... More

Largeness of LERF and 1-relator groupsMar 26 2008We consider largeness of groups given by a presentation of deficiency 1, where the group is respectively free-by-cyclic, LERF or 1-relator. We give the first examples of (finitely generated free)-by-(infinite cyclic) word hyperbolic groups which are large, ... More

All Fuchsian Schottky groups are classical Schottky groupsOct 25 1998Not all Schottky groups of Moebius transformations are classical Schottky groups. In this paper we show that all Fuchsian Schottky groups are classical Schottky groups, but not necessarily on the same set of generators.

Forecasting the Progression of Alzheimer's Disease Using Neural Networks and a Novel Pre-Processing AlgorithmMar 18 2019Alzheimer's disease (AD) is the most common neurodegenerative disease in older people. Despite considerable efforts to find a cure for AD, there is a 99.6% failure rate of clinical trials for AD drugs, likely because AD patients cannot easily be identified ... More

Local deformation rings and a Breuil-Mézard conjecture when l\neq pSep 06 2013Aug 04 2016We compute the deformation rings of two dimensional mod l representations of Gal(Fbar/F) with fixed inertial type, for l an odd prime, p a prime distinct from p and F/Q_p a finite extension. We show that in this setting (when p is also odd) an analogue ... More

Construction of a Prototype Spark ChamberOct 19 2010A small demonstration spark chamber is to be built at the Cavendish laboratory. A prototype chamber consisting of five 20x22.5cm plates has been built and descriptions of its properties and construction are given, while a second chamber with a somewhat ... More

Topological gravity in Minkowski spaceJul 07 2004May 22 2006The two-category with three-manifolds as objects, h-cobordisms as morphisms, and diffeomorphisms of these as two-morphisms, is extremely rich; from the point of view of classical physics it defines a nontrivial topological model for general relativity. ... More

High-performance sampling of generic Determinantal Point ProcessesMay 01 2019Determinantal Point Processes (DPPs) were introduced by Macchi as a model for repulsive (fermionic) particle distributions. But their recent popularization is largely due to their usefulness for encouraging diversity in the final stage of a recommender ... More

An integral lift of the Gamma-genusJan 09 2011Jul 14 2012The Hirzebruch genus of complex-oriented manifolds associated to the Gamma-function lifts to a ring-homomorphism defined by a family of deformations of the Dirac operator, parametrized by the homogeneous space Sp/U.

Topological gravity in dimensions two and fourAug 01 1999Recent work by physicists on gravity in two dimensions has a natural generalization to four dimensions, formulated in terms of an analogue of Segal's category [defined for the study of conformal field theory].

The Spectral Kuznetsov Formula on SL(3)Nov 28 2014The $SL(3)$ Kuznetsov formula exists in several versions, and has been employed with some success to study automorphic forms on $SL(3)$. In each version, the weight functions on the geometric side are given by multiple integrals with complicated oscillating ... More

Birational geometry of moduli spaces of sheaves and Bridgeland stabilityJun 08 2016Jun 23 2016Moduli spaces of sheaves and Hilbert schemes of points have experienced a recent resurgence in interest in the past several years, due largely to new techniques arising from Bridgeland stability conditions and derived category methods. In particular, ... More

Representations of twisted tensor productsMay 06 2015We obtain a faithful representation of the twisted tensor product $B\otimes_{\chi} A$ of unital associative algebras, when $B$ is finite dimensional. This generalizes the representations of [C] where $B=K[X]/<X^2-X>$, [GGV] where $B=K[X]/<X^n>$ and [JLNS] ... More

Generalizing the GAGA PrincipleJan 26 2011Jan 27 2011This paper generalizes the fundamental GAGA results of Serre cite{MR0082175} in three ways---to the non-separated setting, to stacks, and to families. As an application of these results, we show that analytic compactifications of $\mathcal{M}_{g,n}$ possessing ... More

Abelian varieties and the Kervaire invariantMay 03 2011Notes from a talk at the April 2011 ICMS (Edinburgh) conference on the recent solution of the Kervaire invariant problem. This is an entirely expository account, emphasizing connections with the theory of topological automorphic forms.

Graph-Based Models for Kirchberg AlgebrasApr 14 2005We give a construction of Kirchberg algebras from graphs. By using product graphs in the construction we are able to provide models for general (UCT) Kirchberg algebras while maintaining the explicit generators and relations of the underlying graphs.

A topological group of extensions of $\Q$ by $\Z$Oct 13 2013The group of extensions (as in the title), endowed with something like a connection at Archimedean infinity, is isomorphic to the ad\'ele-class group of $\Q$: which is a topological group with interesting Haar measure.}

The arithmetic Kuznetsov formula on $GL(3)$, I: The Whittaker caseAug 31 2017Jun 02 2018The original formulae of Kuznetsov for $SL(2,\mathbb{Z})$ allowed one to study either a spectral average via Kloosterman sums or to study an average of Kloosterman sums via a spectral interpretation. In previous papers, we have developed the spectral ... More

Groupoids and C*-algebras for categories of pathsNov 29 2011May 20 2014In this paper we describe a new method of defining C*-algebras from oriented combinatorial data, thereby generalizing the constructions of algebras from directed graphs, higher-rank graphs, and ordered groups. We show that only the most elementary notions ... More

On formal groups and geometric quantizationMay 15 2019In the theory of geometric quantization, the (cobordism classes of) complex projective spaces, regarded as symplectic manifolds, are to the (cobordism classes of) complex projective spaces, regarded as almost complex manifolds, as elementary symmetric ... More

Discrete and continuous symmetries in monotone Floer theoryMar 15 2017Apr 12 2019This paper studies the self-Floer theory of a monotone Lagrangian submanifold $L$ of a symplectic manifold $X$ in the presence of various kinds of symmetry. First we suppose $L$ is $K$-homogeneous and compute the image of low codimension $K$-invariant ... More

The Balmer spectrum of a tame stackNov 23 2014Let $X$ be a quasi-compact algebraic stack with quasi-finite and separated diagonal. We classify the thick $\otimes$-ideals of $\mathsf{D}_{\mathrm{qc}}(X)^c$. If $X$ is tame, then we also compute the Balmer spectrum of the $\otimes$-triangulated category ... More

GAGA theoremsApr 05 2018We prove a new and unified GAGA theorem for proper schemes and algebraic spaces. This recovers all analytic and formal GAGA results in the literature, and is also valid in the non-noetherian setting.

The Bagger-Lambert model and Type IIA string theoryMay 17 2014We conjecture the existence of a `compactified' version of Fukaya's homology for symplectic manifolds, which carries a canonical 2-Gerstenhaber algebra structure. This may help to understand the 2-Lie algebra structure involved in models for interacting ... More

Interpolation on surfaces in P^3Jun 24 2010Jan 04 2011Given a surface S in P^3 and a collection of general points on it, how many surfaces of a given degree intersect S in a curve with prescribed multiplicities at the points? We formulate two natural conjectures which would answer this question, and we show ... More

Restrictions of Steiner bundles and divisors on the Hilbert scheme of points in the planeFeb 28 2011Mar 01 2012The Hilbert scheme of n points in the projective plane parameterizes degree n zero-dimensional subschemes of the projective plane. We examine the dual cones of effective divisors and moving curves on the Hilbert scheme. By studying interpolation, restriction, ... More

Galaxy Cluster Radio Relics in Adaptive Mesh Refinement Cosmological Simulations: Relic Properties and Scaling RelationshipsJun 17 2010May 09 2011Cosmological shocks are a critical part of large-scale structure formation, and are responsible for heating the intracluster medium in galaxy clusters. In addition, they are also capable of accelerating non-thermal electrons and protons. In this work, ... More

On The Road To More Realistic Galaxy Cluster Simulations: The Effects of Radiative Cooling and Thermal Feedback Prescriptions on the Observational Properties of Simulated Galaxy ClustersNov 13 2012Flux limited X-ray surveys of galaxy clusters show that clusters come in two roughly equally proportioned varieties: "cool core" clusters (CCs) and non-"cool core" clusters (NCCs). In previous work, we have demonstrated using cosmological $N$-body + Eulerian ... More

A Multiwavelength Study of Stephan's QuintetNov 07 2001Stephan's Quintet (SQ) is a compact group that we find in an atypical moment when a high velocity intruder is passing through it. The intrusion is particularly interesting because a previous intruder had stripped most of the gas from the group members. ... More

Average Behavior of Minimal Free Resolutions of Monomial IdealsFeb 19 2018Oct 02 2018We describe the typical homological properties of monomial ideals defined by random generating sets. We show that, under mild assumptions, random monomial ideals (RMI's) will almost always have resolutions of maximal length; that is, the projective dimension ... More

Controlled non-Fermi liquids from spacetime dependent couplingsFeb 24 2014We construct perturbatively controlled non-Fermi liquids in 3+1 spacetime dimensions, using mild power-law translation breaking interactions. Our mechanism balances the leading tree level effects from such gradients against quantum effects from the interaction ... More

Micromanaging de Sitter holographyMay 28 2010We develop tools to engineer de Sitter vacua with semi-holographic duals, using elliptic fibrations and orientifolds to uplift Freund-Rubin compactifications with CFT duals. The dual brane construction is compact and constitutes a microscopic realization ... More

Low ionization lines in high luminosity quasars: The calcium tripletDec 16 2013In order to investigate where and how low ionization lines are emitted in quasars we are studying a new collection of spectra of the CaII triplet at $\lambda$8498, $\lambda$8542, $\lambda$8662 observed with the Very Large Telescope (VLT) using the Infrared ... More

Matrix Description of (1,0) Theories in Six DimensionsSep 16 1997We propose descriptions of interacting (1,0) supersymmetric theories without gravity in six dimensions in the infinite momentum frame. They are based on the large N limit of quantum mechanics or 1+1 dimensional field theories with SO(N) gauge group and ... More

Matrix Description of Interacting Theories in Six DimensionsJul 08 1997We propose descriptions of interacting (2,0) supersymmetric theories without gravity in six dimensions in the infinite momentum frame. They are based on the large $N$ limit of quantum mechanics or 1+1 dimensional field theories on the moduli space of ... More

A Neptune-Mass Planet Orbiting the Nearby M Dwarf GJ 436Aug 31 2004Sep 15 2004We report precise Doppler measurements of GJ 436 (M2.5V) obtained at Keck Observatory. The velocities reveal a planetary companion with orbital period of 2.644 d, eccentricity of 0.12 (consistent with zero) and velocity semi-amplitude of $K =18.1$ \ms. ... More

Approximating Shepp's constants for the Slepian processDec 28 2018Slepian process $S(t)$ is a stationary Gaussian process with zero mean and covariance $ E S(t)S(t')=\max\{0,1-|t-t'|\}\, . $ For any $T>0$ and $h>0$, define $F_T(h ) = {\rm Pr}\left\{\max_{t \in [0,T]} S(t) < h \right\} $ and the constants $\Lambda(h) ... More

The Frequent Paucity of Trivial StringsOct 23 2013May 07 2014A 1976 theorem of Chaitin can be used to show that arbitrarily dense sets of lengths n have a paucity of trivial strings (only a bounded number of strings of length n having trivially low plain Kolmogorov complexities). We use the probabilistic method ... More

Addendum: Étale dévissage, descent and pushouts of stacksDec 21 2017Using Nisnevich coverings and a Hilbert stack of stacky points, we prove \'etale d\'evissage results for non-representable \'etale and quasi-finite flat coverings. We give applications to absolute noetherian approximation of algebraic stacks and compact ... More

On the minimal ramification problem for $\ell$-groupsNov 18 2008Feb 13 2010Let p be a prime number. It is not known if every finite p-group of rank n>1 can be realized as a Galois group over Q with no more than n ramified primes. We prove that this can be done for the family of finite p-groups which contains all the cyclic groups ... More

Hermitian forms, trace equations and application to codesNov 16 2001Apr 21 2003We provide a systematic study of sesquilinear hermitian forms and a new proof of the calculus of some exponential sums defined with quadratic hermitian forms. The computation of the number of solutions of equations such as Tr(f(x)+v.x)=0 or Tr(f(x))=a ... More

Spin cobordism categories in low dimensionsAug 21 2009The Madsen-Tillmann spectra defined by categories of three- and four-dimensional Spin manifolds have a very rich algebraic structure, whose surface is scratched here.

Quantum Foam and Quantum Gravity PhenomenologyMay 14 2004Spacetime undergoes quantum fluctuations, giving rise to spacetime foam, a.k.a. quantum foam. We discuss some properties of spacetime foam, and point out the conceptual interconnections in the physics of quantum foam, black holes, and quantum computation. ... More

Clocks, computers, black holes, spacetime foam, and holographic principleOct 25 2000What do simple clocks, simple computers, black holes, space-time foam, and holographic principle have in common? I will show that the physics behind them is inter-related, linking together our concepts of information, gravity, and quantum uncertainty. ... More

From computation to black holes and space-time foamJun 29 2000Mar 30 2001We show that quantum mechanics and general relativity limit the speed $\tilde{\nu}$ of a simple computer (such as a black hole) and its memory space $I$ to $\tilde{\nu}^2 I^{-1} \lsim t_P^{-2}$, where $t_P$ is the Planck time. We also show that the life-time ... More