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Generalized Equivariant Cohomology and StratificationsOct 15 2014Dec 20 2014For $T$ a compact torus and $E_T^*$ a generalized $T$-equivariant cohomology theory, we provide a systematic framework for computing $E_T^*$ in the context of equivariantly stratified smooth complex projective varieties. This allows us to explicitly compute ... More

Human Y-chromosome gene classification using Fractal Dimension & Shannon EntropyApr 09 2014All genes on the human Y-chromosome were studied using fractal dimension and Shannon entropy. Clear outlier clusters were identified. Among these were 6 sequences that have since been withdrawn as CDSs and 1 additional sequence that is not in the current ... More

On the Braess Paradox with Nonlinear Dynamics and Control TheoryMar 27 2017We show the existence of the Braess paradox for a traffic network with nonlinear dynamics described by the Lighthill-Whitham-Richards model for traffic flow. Furthermore, we show how one can employ control theory to avoid the paradox. The paper offers ... More

Addendum to "The Kolmogorov--Riesz compactness theorem" (Expo. Math. 28:385--394 (2010))Aug 31 2015Oct 07 2015We show how to improve on Theorem 10 in [arXiv:0906.4883], describing when subsets in $W^{1,p}(\mathbb{R}^n)$ are totally bounded subsets of $L^q(\mathbb{R}^n)$ for $p<n$ and $p\le q<p^*$. This improvement was first shown by Dosso, Fofana, and Sanogo ... More

The Kolmogorov-Riesz compactness theoremJun 26 2009Jan 04 2010We show that the Arzela-Ascoli theorem and Kolmogorov compactness theorem both are consequences of a simple lemma on compactness in metric spaces. Their relation to Helly's theorem is discussed. The paper contains a detailed discussion on the historical ... More

Follow-the-Leader models can be viewed as a numerical approximation to the Lighthill-Whitham-Richards model for traffic flowFeb 06 2017Sep 21 2017We show how to view the standard Follow-the-Leader (FtL) model as a numerical method to compute numerically the solution of the Lighthill--Whitham--Richards (LWR) model for traffic flow. As a result we offer a simple proof that FtL models converge to ... More

Measuring the Orbital Parameters of Radial Velocity Systems in Mean Motion Resonance---a Case Study of HD 200964Aug 13 2019The presence of mean motion resonances (MMRs) complicates analysis and fitting of planetary systems observed through the radial velocity (RV) technique. MMR can allow planets to remain stable in regions of phase space where strong planet-planet interactions ... More

Lipschitz metric for the two-component Camassa--Holm systemJun 28 2013We construct a Lipschitz metric for conservative solutions of the Cauchy problem on the line for the two-component Camassa--Holm system $u_t-u_{txx}+3uu_x-2u_xu_{xx}-uu_{xxx}+\rho\rho_x=0$, and $\rho_t+(u\rho)_x=0$ with given initial data $(u_0, \rho_0)$. ... More

Global dissipative solutions of the two-component Camassa-Holm system for initial data with nonvanishing asymptoticsJan 08 2013We show existence of a global weak dissipative solution of the Cauchy problem for the two-component Camassa-Holm (2CH) system on the line with nonvanishing and distinct spatial asymptotics. The influence from the second component in the 2CH system on ... More

On the equivalence of Eulerian and Lagrangian variables for the two-component Camassa-Holm systemApr 18 2017The Camassa-Holm equation and its two-component Camassa-Holm system generalization both experience wave breaking in finite time. To analyze this, and to obtain solutions past wave breaking, it is common to reformulate the original equation given in Eulerian ... More

Algebro-Geometric Solutions of a Discrete System Related to the Trigonometric Moment ProblemAug 04 2004We derive theta function representations of algebro-geometric solutions of a discrete system governed by a transfer matrix associated with (an extension of) the trigonometric moment problem studied by Szego and Baxter. We also derive a new hierarchy of ... 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

Operator splitting for partial differential equations with Burgers nonlinearityFeb 21 2011We provide a new analytical approach to operator splitting for equations of the type $u_t=Au+u u_x$ where $A$ is a linear differential operator such that the equation is well-posed. Particular examples include the viscous Burgers' equation, the Korteweg-de ... More

An improvement of the Kolmogorov-Riesz compactness theoremMay 03 2017Mar 21 2019The purpose of this short note is to provide a new and very short proof of a result by Sudakov, offering an important improvement of the classical result by Kolmogorov-Riesz on compact subsets of Lebesgue spaces.

Evolution in the Color-Magnitude Relation of Early-Type Galaxies in Clusters of Galaxies at z~=1Mar 16 2005Mar 17 2005We present a study of the color evolution of elliptical and S0 galaxies in six clusters of galaxies inside the redshift range 0.78 < z < 1.27. For each cluster, we used imaging from the Hubble Space Telescope to determine morphological types by both an ... More

Distribution of Values of Real Quadratic Zeta FunctionsOct 29 2000The author has previously extended the theory of regular and irregular primes to the setting of arbitrary totally real number fields. It has been conjectured that the Bernoulli numbers, or alternatively the values of the Riemann zeta function at odd negative ... More

Local Conservation Laws and the Hamiltonian Formalism for the Ablowitz-Ladik HierarchyNov 11 2007We derive a systematic and recursive approach to local conservation laws and the Hamiltonian formalism for the Ablowitz-Ladik (AL) hierarchy. Our methods rely on a recursive approach to the AL hierarchy using Laurent polynomials and on asymptotic expansions ... More

Liouville dynamical percolationMay 16 2019May 20 2019We construct and analyze a continuum dynamical percolation process which evolves in a random environment given by a $\gamma$-Liouville measure. The homogeneous counterpart of this process describes the scaling limit of discrete dynamical percolation on ... More

A Note on Unconditional Subexponential-time Pseudo-deterministic Algorithms for BPP Search ProblemsJul 18 2017We show the first unconditional pseudo-determinism result for all of search-BPP. Specifically, we show that every BPP search problem can be computed pseudo-deterministically on average for infinitely many input lengths. In other words, for infinitely ... More

Operator splitting for well-posed active scalar equationsJan 30 2012Feb 01 2012We analyze operator splitting methods applied to scalar equations with a nonlinear advection operator, and a linear (local or nonlocal) diffusion operator or a linear dispersion operator. The advection velocity is determined from the scalar unknown itself ... More

Comparison of algorithms to calculate quadratic irregularity of prime numbersOct 29 2000In previous work, the author has extended the concept of regular and irregular primes to the setting of arbitrary totally real number fields k_{0}, using the values of the zeta function \zeta_{k_{0}} at negative integers as our ``higher Bernoulli numbers''. ... More

Addenda/Corrigenda: Fixed Points and Two-cycles of the Discrete LogarithmAug 04 2002Nov 18 2002The abstract of the original paper was as follows: We explore some questions related to one of Brizolis: does every prime p have a pair (g,h) such that h is a fixed point for the discrete logarithm with base g? We extend this question to ask about not ... More

Distribution of the Error in Estimated Numbers of Fixed Points of the Discrete LogarithmJan 03 2004Dec 19 2004Brizolis asked the question: does every prime p have a pair (g,h) such that h is a fixed point for the discrete logarithm with base g? The author and Pieter Moree, building on work of Zhang, Cobeli, and Zaharescu, gave heuristics for estimating the number ... More

The two subset recurrent property of Markov chainsFeb 23 2016This paper proposes a new type of recurrence where we divide the Markov chains into intervals that start when the chain enters into a subset A, then sample another subset B far away from A and end when the chain again return to A. The length of these ... More

Operator splitting for the KdV equationJun 26 2009We provide a new analytical approach to operator splitting for equations of the type $u_t=Au+B(u)$ where $A$ is a linear operator and $B$ is quadratic. A particular example is the Korteweg-de Vries (KdV) equation $u_t-u u_x+u_{xxx}=0$. We show that the ... More

A Comparison of Cryptography CoursesJan 03 2004The author taught two courses on cryptography, one at Duke University aimed at non-mathematics majors and one at Rose-Hulman Institute of Technology aimed at mathematics and computer science majors. Both tried to incorporate technical and societal aspects ... More

Abelian varieties over finite fields with a specified characteristic polynomial modulo lOct 29 2000May 26 2001We estimate the fraction of isogeny classes of abelian varieties over a finite field which have a given characteristic polynomial P(T) modulo l. As an application we find the proportion of isogeny classes of abelian varieties with a rational point of ... More

Quadratic polynomials of small modulus cannot represent ORSep 29 2015Nov 12 2015An open problem in complexity theory is to find the minimal degree of a polynomial representing the $n$-bit OR function modulo composite $m$. This problem is related to understanding the power of circuits with $\text{MOD}_m$ gates where $m$ is composite. ... More

Non-abelian convexity of based loop groupsSep 17 2015If $K$ is a compact, connected, simply connected Lie group, its based loop group $\Omega K$ is endowed with a Hamiltonian $S^1 \times T$ action, where $T$ is a maximal torus of $K$. Atiyah and Pressley examined the image of $\Omega K$ under the moment ... More

First-hit analysis of algorithms for computing quadratic irregularityNov 08 2000Nov 10 2000The author has previously extended the theory of regular and irregular primes to the setting of arbitrary totally real number fields. It has been conjectured that the Bernoulli numbers, or alternatively the values of the Riemann zeta function at odd negative ... More

Quantifying the AGN-driven outflows in ULIRGs (QUADROS) IV: HST/STIS spectroscopy of the sub-kpc warm outflow in F14394+5332Aug 08 2019Considerable uncertainties remain about the nature of warm, AGN-driven outflows and their impact on the evolution of galaxies. This is because the outflows are often unresolved in ground-based observations. As part of a project to study the AGN outflows ... More

The rest-frame $K$-band luminosity function of galaxies in clusters to $z=1.3$Feb 02 2007We derive the rest-frame $K$-band luminosity function for galaxies in 32 clusters at $0.6 < z < 1.3$ using deep $3.6\mu$m and $4.5\mu$m imaging from the Spitzer Space Telescope InfraRed Array Camera (IRAC). The luminosity functions approximate the stellar ... More

The Intracluster Medium in z > 1 Galaxy ClustersDec 12 2000The Chandra X-ray Observatory was used to obtain a 190 ks image of three high redshift galaxy clusters in one observation. The results of our analysis of these data are reported for the two z > 1 clusters in this Lynx field, including the most distant ... More

Dynamical and content evolution of a sample of clusters from z~0 to z~0.5Sep 05 2000In this paper, we present an analysis of the dynamics and segregation of galaxies in rich clusters from z~0.32 to z~0.48 taken from the CFHT Optical PDCS (COP) survey and from the CNOC survey (Carlberg et al. 1997). Our results from the COP survey are ... More

A Deep Probing of the Coma clusterAug 22 1997We present here results from a deep spectroscopic survey of the Coma cluster of galaxies (29 galaxies between 18.98<m_R<21.5). Only 1 of these galaxies is within Coma compared to an expected 6.7 galaxies computed from nearby control fields. This discrepancy ... More

X-ray Observations of Distant Optically Selected ClusterAug 05 1997We have measured fluxes or flux limits for 31 of the 79 cluster candidates in the Palomar Distant Cluster Survey (PDCS) using archival ROSAT/PSPC pointed observations. Our X-ray survey reaches a flux limit of $\simeq 3 \times 10^{-14}$ erg s$^{-1}$ cm$^{-2}$ ... More

Deep probing of the Coma clusterFeb 27 1998As a continuation of our study of the faint galaxy luminosity function in the Coma cluster of galaxies, we report here on the first spectroscopic observations of very faint galaxies (R $\le$ 21.5) in the direction of the core of this cluster. Out of these ... More

The CFH Optical PDCS Survey (COP): First resultsJul 26 1999We present the first results of the COP survey about the reality of the PDCS clusters, about their velocity dispersions and dynamic and about the periodicity of the structures along the line of sight.

ABC for climate: dealing with expensive simulatorsNov 11 2015This paper is due to appear as a chapter of the forthcoming Handbook of Approximate Bayesian Computation (ABC) by S. Sisson, L. Fan, and M. Beaumont. We describe the challenge of calibrating climate simulators, and discuss the differences in emphasis ... More

Simulations Applied to the Bright SHARC XCLF: Results and ImplicationsOct 06 1999We have performed simulations of the effectiveness of the Serendipitous High-redshift Archival ROSAT Cluster (SHARC) survey for various model universes. We find, in agreement with work based on a preliminary set of simulations no statistically significant ... More

Optical and Near-Infrared Photometry of Distant Galaxy ClustersMar 27 2002Apr 10 2002We present optical and near-infrared photometry of 45 clusters of galaxies at 0.1 < z < 1.3. Galaxy catalogs in each cluster were defined at the longest wavelenth available, generally the K-band, down to approximately two magnitudes below M*. We include ... More

X-ray temperature and morphology of z>0.8 clusters of galaxiesOct 01 2001We discuss our current progress in studying a sample of z>0.8 clusters of galaxies from the ROSAT Distant Cluster Survey. To date, we have Chandra observations for four of the ten clusters. We find that the morphology of two of these four are quite regular, ... More

A simplified multiphase multiscale model for tissue growthJun 25 2018In this paper, we derive an effective macroscale description suitable to describe the growth of biological tissue within a porous tissue-engineering scaffold. As in our recent work (Holden \textit{et al.} "A multiphase multiscale model for nutrient limited ... More

Monte Carlo simulations of the kagome lattice with magnetic dipolar interactionsApr 29 2015The results of extensive Monte Carlo simulations of classical spins on the two-dimensional kagome lattice with only dipolar interactions are presented. In addition to revealing the six-fold degenerate ground state, the nature of the finite-temperature ... More

Adaptive independent Metropolis--HastingsMar 03 2009We propose an adaptive independent Metropolis--Hastings algorithm with the ability to learn from all previous proposals in the chain except the current location. It is an extension of the independent Metropolis--Hastings algorithm. Convergence is proved ... More

Complexity, economic science and possible economic benefits of climate change mitigation policyOct 16 2013Jan 28 2015Conventional economic analysis of stringent climate change mitigation policy generally concludes various levels of economic slowdown as a result of substantial spending on low carbon technology. Equilibrium economics however could not explain or predict ... More

The dynamics of technology diffusion and the impacts of climate policy instruments in the decarbonisation of the global electricity sectorSep 29 2013Jun 22 2014This paper presents an analysis of climate policy instruments for the decarbonisation of the global electricity sector in a non-equilibrium economic and technology diffusion perspective. Energy markets are driven by innovation, path-dependent technology ... More

The CFH Optical PDCS survey (COP) I: The DataMar 09 2000This paper presents and gives the COP (COP: CFHT Optical PDCS; CFHT: Canada-France-Hawaii Telescope; PDCS: Palomar Distant Cluster Survey) survey data. We describe our photometric and spectroscopic observations with the MOS multi-slit spectrograph at ... More

The Bright SHARC Survey: The Selection Function and its Impact on the Cluster X-ray Luminosity FunctionJul 19 2000We present the results of a set of simulations designed to quantify the selection function of the Bright SHARC survey for distant clusters. The statistical significance of the simulations relied on the creation of thousands of artificial clusters with ... More

A Turn-over in the Galaxy Luminosity Function of the Coma Cluster Core?Oct 12 1999Dec 09 1999Our previous study of the faint end (R$\leq$21.5) of the galaxy luminosity function (GLF) was based on spectroscopic data in a small region near the Coma cluster center. In this previous study Adami et al. (1998) suggested, with moderate statistical significance, ... More

Spectroscopic Observations of Optically Selected Clusters of Galaxies from the Palomar Distant Cluster SurveyJul 29 1999We have conducted a redshift survey of sixteen cluster candidates from the Palomar Distant Cluster Survey (PDCS) to determine both the density of PDCS clusters and the accuracy of the estimated redshifts presented in the PDCS catalog (Postman et. al. ... More

The Southern SHARC Survey: the z = 0.3 - 0.7 Cluster XLFAug 15 1997We present the z = 0.3 - 0.7 cluster X-ray luminosity function (XLF) determined from the Southern SHARC (Serendipitous High-redshift Archival ROSAT Cluster) survey. Over the luminosity range L ~ (0.3 - 3) x 10^44 erg/s (0.5 - 2.0 keV) the XLF is in close ... More

Evolution in the X-ray Cluster Luminosity Function RevisitedNov 22 1996(Shortened Abstract) We present new X-ray data taken from the ROSAT PSPC pointing archive for 21 clusters in the Einstein Extended Medium Sensitivity Survey (EMSS). We have supplemented these data with new optical follow-up observations found in the literature ... More

SLE as a mating of trees in Euclidean geometryOct 17 2016Let $\eta$ be a whole-plane Schramm-Loewner evolution with parameter $\kappa>4$, parameterized by Lebesgue measure. We introduce a two-dimensional continuous process $(L_t,R_t)_{t\in \mathbb R}$ which describes the Minkowski content of the left and right, ... More

Local Conservation Laws and the Hamiltonian Formalism for the Toda Hierarchy RevisitedAug 16 2006We revisit an elementary recursive approach to local conservation laws and the Hamiltonian formalism for the Toda hierarchy.

Algebro-Geometric Solutions of the Camassa--Holm hierarchyMay 08 2001May 21 2001We provide a detailed treatment of the Camassa--Holm (CH) hierarchy with special emphasis on its algebro-geometric solutions. In analogy to other completely integrable hierarchies of soliton equations such as the KdV or AKNS hierarchies, the CH hierarchy ... More

The Cole-Hopf and Miura transformations revisitedDec 21 1998An elementary yet remarkable similarity between the Cole-Hopf transformation relating the Burgers and heat equation and Miura's transformation connecting the KdV and mKdV equations is studied in detail.

A Search For Large-Scale Structure at High RedshiftFeb 03 1997We present new and exciting results on our search for large-scale structure at high redshift. Specifically, we have just completed a detailed analysis of the area surrounding the cluster CL0016+16 (z=0.546) and have the most compelling evidence yet that ... More

The Environmental Dependence of Properties of Galaxies around the RDCSJ0910+54 Cluster at z=1.1Aug 14 2008(Abridged) We report on the environmental dependence of properties of galaxies around the RDCSJ0910+54 cluster at z=1.1. We have obtained multi-band wide-field images of the cluster with Suprime-Cam and MOIRCS on Subaru and WFCAM on UKIRT. Also, an intensive ... More

Weak-Lensing Detection at z~1.3: Measurement of the Two Lynx Clusters with Advanced Camera for SurveysJan 16 2006(Abridged) We present a HST/ACS weak-lensing study of RX J0849+4452 and RX J0848+4453, the two most distant (at z=1.26 and z=1.27, respectively) clusters yet measured with weak-lensing. The two clusters are separated by ~4' from each other and appear ... More

An X-ray Selected Galaxy Cluster at z=1.11 in the Rosat Deep Cluster SurveyOct 31 2001We report the discovery of an X-ray luminous galaxy cluster at z =1.11. RDCS J0910+5422 was selected as an X-ray cluster candidate in the ROSAT Deep Cluster Survey on the basis of its spatial extent in a Rosat PSPC image. Deep optical and near-IR imaging ... More

Moderate Temperature Clusters of Galaxies from the RDCS and the High Redshift Luminosity-Temperature RelationMar 27 2002Aug 23 2002We present our discovery observations and analysis of RDCS1317+2911, z = 0.805, and RDCS1350+6007, z= 0.804, two clusters of galaxies identified through X-ray emission in the ROSAT Deep Cluster Survey (RDCS). We find a temperature of 3.7 +1.5 -0.9 keV ... More

In-Plane Spectral Weight Shift of Charge Carriers in $YBa_2Cu_3O_{6.9}$May 04 2004The temperature dependent redistribution of the spectral weight of the $CuO_2$ plane derived conduction band of the $YBa_2Cu_3O_{6.9}$ high temperature superconductor (T_c = 92.7 K) was studied with wide-band (from 0.01 to 5.6 eV) spectroscopic ellipsometry. ... More

The Galaxy Population of Cluster RXJ0848+4453 at z=1.27Apr 16 2001We present a study of the galaxy population in the cluster RXJ0848+4453 at z=1.27, using deep HST NICMOS and WFPC2 images. We morphologically classify all galaxies to K_s=20.6 that are covered by the HST imaging, and determine photometric redshifts using ... More

Superclustering at Redshift Z=0.54Oct 07 1996We present strong evidence for the existence of a supercluster at a redshift of z=0.54 in the direction of Selected Area 68. From the distribution of galaxies with spectroscopic redshifts we find that there is a large over-density of galaxies (a factor ... More

A search for distant X-ray galaxy clustersDec 06 1995We report on the progress of our search for serendipitous distant X-ray galaxy clusters in the ROSAT PSPC pointed observations archive. The initial aim of our work is to measure the X-ray luminosity function of clusters down to 4 x 10^-14 erg cm^-2 s^-1 ... More

The Damped String Problem RevisitedSep 09 2010We revisit the damped string equation on a compact interval with a variety of boundary conditions and derive an infinite sequence of trace formulas associated with it, employing methods familiar from supersymmetric quantum mechanics. We also derive completeness ... More

Statistics for fixed points of the self-power mapMar 21 2014Jul 13 2015The map x -> x^x modulo p is related to a variation of the digital signature scheme in a similar way to the discrete exponentiation map, but it has received much less study. We explore the number of fixed points of this map by a statistical analysis of ... More

A comparison of the most massive quiescent galaxies from $z \sim 3$ to the present: slow evolution in size, and spheroid-dominatedApr 06 2017We use Hubble Space Telescope imaging to study the structural properties of ten of the most massive ($M \geq 10^{11.25}$ Msun) quiescent galaxies (QGs) in the UKIDSS UDS at $2.5<z<3.0$. The low spatial density of these galaxies required targeted WFC3 ... More

New Conjectures and Results for Small Cycles of the Discrete LogarithmMay 21 2003Jun 04 2003Brizolis asked the question: does every prime p have a pair (g,h) such that h is a fixed point for the discrete logarithm with base g? The first author previously extended this question to ask about not only fixed points but also two-cycles, and gave ... More

Dubrovin equations and integrable systems on hyperelliptic curvesJul 14 1998We introduce the most general version of Dubrovin-type equations for divisors on a hyperelliptic curve of arbitrary genus, and provide a new argument for linearizing the corresponding completely integrable flows. Detailed applications to completely integrable ... More

Lower bounds for trace reconstructionAug 04 2018In the trace reconstruction problem, an unknown bit string ${\bf x}\in\{0,1\}^n$ is sent through a deletion channel where each bit is deleted independently with some probability $q\in(0,1)$, yielding a contracted string $\widetilde{\bf x}$. How many i.i.d. ... More

Real-Valued Algebro-Geometric Solutions of the Camassa--Holm hierarchyAug 14 2002We provide a treatment of real-valued, smooth, and bounded algebro-geometric solutions of the Camassa--Holm (CH) hierarchy and describe the associated isospectral torus. We also discuss real-valued algebro-geometric solutions with a cusp behavior.

Darboux-type transformations and hyperelliptic curvesJan 23 1999We systematically study Darboux-type transformations for the KdV and AKNS hierarchies and provide a complete account of their effects on hyperelliptic curves associated with algebro-geometric solutions of these hierarchies.

SLE as a mating of trees in Euclidean geometryOct 17 2016Feb 27 2018The mating of trees approach to Schramm-Loewner evolution (SLE) in the random geometry of Liouville quantum gravity (LQG) has been recently developed by Duplantier-Miller-Sheffield (2014). In this paper we consider the mating of trees approach to SLE ... More

Conformal welding for critical Liouville quantum gravityDec 31 2018Consider two critical Liouville quantum gravity surfaces (i.e., $\gamma$-LQG for $\gamma=2$), each with the topology of $\mathbb{H}$ and with infinite boundary length. We prove that there a.s. exists a conformal welding of the two surfaces, when the boundaries ... More

Global semigroup of conservative solutions of the nonlinear variational wave equationOct 28 2009We prove the existence of a global semigroup for conservative solutions of the nonlinear variational wave equation $u_{tt}-c(u)(c(u)u_x)_x=0$. We allow for initial data $u|_{t=0}$ and $u_t|_{t=0}$ that contain measures. We assume that $0<\kappa^{-1}\le ... More

The general peakon-antipeakon solution for the Camassa-Holm equationFeb 26 2015We compute explicitly the peakon-antipeakon solution of the Camassa-Holm equation $u_t-u_{txx}+3uu_x-2u_xu_{xx}-uu_{xxx}=0$ in the non-symmetric and $\alpha$-dissipative case. The solution experiences wave breaking in finite time, and the explicit solution ... More

Robust guarantees for learning an autoregressive filterMay 23 2019The optimal predictor for a linear dynamical system (with hidden state and Gaussian noise) takes the form of an autoregressive linear filter, namely the Kalman filter. However, a fundamental problem in reinforcement learning and control theory is to make ... More

Convergence of uniform triangulations under the Cardy embeddingMay 30 2019We consider an embedding of planar maps into an equilateral triangle $\Delta$ which we call the Cardy embedding. The embedding is a discrete approximation of a conformal map based on percolation observables that are used in Smirnov's proof of Cardy's ... More

Human judgment vs. theoretical models for the management of ecological resourcesMar 15 2016Despite major advances in quantitative approaches to natural resource management, there has been resistance to using these tools in the actual practice of managing ecological populations. Given a managed system and a set of assumptions, translated into ... More

Multiple Model-Free KnockoffsDec 12 2018Dec 20 2018Model-free knockoffs is a recently proposed technique for identifying covariates that is likely to have an effect on a response variable. The method is an efficient method to control the false discovery rate in hypothesis tests for separate covariates. ... More

A mixture model for unsupervised tail estimationFeb 24 2009This paper proposes a new method to combine several densities such that each density dominates a separate part of a joint distribution. The method is fully unsupervised, i.e. the parameters in the densities and the thresholds are simultaneously estimated. ... More

A combined sine-Gordon and modified Korteweg-de Vries hierarchy and its algebro-geometric solutionsJul 20 1997Dec 11 1997We derive a zero-curvature formalism for a combined sine-Gordon (sG) and modified Korteweg-de Vries (mKdV) equation which yields a local sGmKdV hierarchy. In complete analogy to other completely integrable hierarchies of soliton equations, such as the ... More

The classical Boussinesq hierarchy revisitedDec 21 1998We develop a systematic approach to the classical Boussinesq (cBsq) hierarchy based on an elementary polynomial recursion formalism. Moreover, the gauge equivalence between the cBsq and AKNS hierarchies is studied in detail and used to provide an effortless ... More

Scaling limits of the Schelling modelFeb 09 2018The Schelling model, introduced by Schelling in 1969 as a model for residential segregation in cities, describes how populations of multiple types self-organize to form homogeneous clusters of one type. In this model, vertices in an $N$-dimensional lattice ... More

Some Heuristics and Results for Small Cycles of the Discrete LogarithmJan 03 2004Oct 16 2004Brizolis asked the question: does every prime p have a pair (g,h) such that h is a fixed point for the discrete logarithm with base g? The first author previously extended this question to ask about not only fixed points but also two-cycles, and gave ... More

Lower bounds for trace reconstructionAug 04 2018Jun 07 2019In the trace reconstruction problem, an unknown bit string ${\bf x}\in\{0,1 \}^n$ is sent through a deletion channel where each bit is deleted independently with some probability $q\in(0,1)$, yielding a contracted string $\widetilde{\bf x}$. How many ... More

Multiple Model-Free KnockoffsDec 12 2018Mar 28 2019Model-free knockoffs is a recently proposed technique for identifying covariates that is likely to have an effect on a response variable. The method is an efficient method to control the false discovery rate in hypothesis tests for separate covariates. ... More

C-axis lattice dynamics in Bi-based cuprate superconductorsJul 21 2003We present results of a systematic study of the c axis lattice dynamics in single layer Bi2Sr2CuO6 (Bi2201), bilayer Bi2Sr2CaCu2O8 (Bi2212) and trilayer Bi2Sr2Ca2Cu3O10 (Bi2223) cuprate superconductors. Our study is based on both experimental data obtained ... More

Josephson plasma resonance and phonon anomalies in trilayer Bi_2Sr_2Ca_2Cu_3O_10 superconductorMay 16 2002The far-infrared (FIR) c axis conductivity of a Bi2223 crystal has been measured by ellipsometry. Below T$_c$ a strong absorption band develops near 500 cm $^{-1}$, corresponding to a transverse Josephson-plasmon. The related increase in FIR spectral ... More

The SWELLS survey. II. Breaking the disk-halo degeneracy in the spiral galaxy gravitational lens SDSS J2141-0001Jan 08 2011Mar 14 2011The degeneracy among the disk, bulge and halo contributions to galaxy rotation curves prevents an understanding of the distribution of baryons and dark matter in disk galaxies. In an attempt to break this degeneracy, we present an analysis of the spiral ... More

Cl 1205+44, a fossil group at z = 0.59Jan 22 2005May 03 2005This is a report of Chandra, XMM-Newton, HST and ARC observations of an extended X-ray source at z = 0.59. The apparent member galaxies range from spiral to elliptical and are all relatively red (i'-Ks about 3). We interpret this object to be a fossil ... More

Notes on an analogue of the Fontaine-Mazur conjectureMay 10 2001Mar 27 2004We estimate the proportion of function fields satisfying certain conditions which imply a function-field analogue of the Fontaine-Mazur conjecture. As a byproduct, we compute the fraction of abelian varieties (or even Jacobians) over a finite field which ... More

The continuum limit of Follow-the-Leader models - a short proofSep 22 2017Sep 27 2017We offer a simple and self-contained proof that the Follow-the-Leader model converges to the Lighthill-Whitham-Richards model for traffic flow.

Mapping the Discrete LogarithmApr 30 2006The discrete logarithm is a problem that surfaces frequently in the field of cryptography as a result of using the transformation g^a mod n. This paper focuses on a prime modulus, p, for which it is shown that the basic structure of the functional graph ... More

The Evolution of the Field and Cluster Morphology-Density Relation for Mass-Selected Samples of GalaxiesJul 18 2007Nov 01 2007The Sloan Digital Sky Survey (SDSS) and photometric/spectroscopic surveys in the GOODS-South field (the Chandra Deep Field-South, CDFS) are used to construct volume-limited, stellar mass-selected samples of galaxies at redshifts 0<z<1. The CDFS sample ... More

RX J0848+4456: Disentangling a Moderate Redshift ClusterMay 01 2001Jun 10 2001We present a multi-wavelength study of RX J0848+4456, a cluster of galaxies discovered through X-ray emission in the ROSAT Deep Cluster Survey. Our observations consist of WFPC2 imaging, optical spectra, and X-ray data collected with the Chandra observatory. ... More

The Ellipticities of Cluster Early-type Galaxies from z~1 to z~0: No Evolution in the Overall Distribution of Bulge-to-Disk RatiosNov 12 2008Mar 05 2009We have compiled a sample of early-type cluster galaxies from 0 < z < 1.3 and measured the evolution of their ellipticity distributions. Our sample contains 487 galaxies in 17 z>0.3 clusters with high quality space-based imaging and a comparable sample ... More

Measuring $Ω_m$ with the ROSAT Deep Cluster SurveyJun 24 2001We analyze the ROSAT Deep Cluster Survey (RDCS) to derive cosmological constraints from the evolution of the cluster X-ray luminosity distribution. The sample contains 103 galaxy clusters out to z=0.85 and flux-limit Flim=3 10^{-14} cgs (RDCS-3) in the ... More