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Discovery of new stable and high-temperature Ti-Ta-X shape memory alloys from first principles calculationsMay 14 2019In conventional Ti-Ta shape memory alloys (SMAs), high (>100{\deg}C) transformation temperatures cannot be achieved without compromising the stability of the shape memory effect. A solution to this problem is the addition of other elements to form Ti-Ta-X ... More

Discovery of new stable and high-temperature Ti-Ta-X shape memory alloys from first principles calculationsMay 14 2019Jul 24 2019In conventional Ti-Ta shape memory alloys (SMAs), high (>100{\deg}C) transformation temperatures cannot be achieved without compromising the stability of the shape memory effect. A solution to this problem is the addition of other elements to form Ti-Ta-X ... More

Discovery of $ω$-free high-temperature Ti-Ta-X shape memory alloys from first principles calculationsMay 14 2019Aug 01 2019The rapid degradation of the functional properties of many Ti-based alloys is due to the precipitation of the $\omega$ phase. In the conventional high-temperature shape memory alloy Ti-Ta the formation of this phase compromises completely the shape memory ... More

Stable Leader Election in Population Protocols Requires Linear TimeFeb 14 2015Aug 20 2016A population protocol *stably elects a leader* if, for all $n$, starting from an initial configuration with $n$ agents each in an identical state, with probability 1 it reaches a configuration $\mathbf{y}$ that is correct (exactly one agent is in a special ... More

Integrals derived from the doubling methodOct 21 2018In this note, we use a basic identity, derived from the generalized doubling integrals of \cite{C-F-G-K1}, in order to explain the existence of various global Rankin-Selberg integrals for certain $L$-functions. To derive these global integrals, we use ... More

Binary Survival in the Outer Solar SystemMay 06 2019As indicated by their special characteristics, the cold classical Kuiper belt objects (KBOs) formed and survived at 42-47 au. Notably, they show a large fraction of equal-size binaries whose formation is probably related to the accretion of KBOs themselves. ... More

The RASNIK Real-Time Relative Alignment Monitor for the CDF Inner Tracking DetectorsDec 10 2002We describe the design and operation of the RASNIK optical relative alignment system designed for and installed on the CDF inner tracking detectors. The system provides low-cost minute-by-minute alignment monitoring with submicron precision. To reduce ... More

Results for the LISA Phase Measurement System ProjectNov 01 2004Jan 11 2005This article presents some of the more topical results of a study into the LISA phase measurement system. This system is responsible for measuring the phase of the heterodyne signal caused by the interference of the laser beams between the local and far ... More

Site Disordered Spin Systems in the Gaussian Variational ApproximationJun 06 1996Dec 16 1996We define a replica field theory describing finite dimensional site disordered spin systems by introducing the notion of grand canonical disorder, where the number of spins in the system is random but quenched. A general analysis of this field theory ... More

Splitting cycles in graphsApr 26 2012The goal of this paper is to describe a sufficient condition on cycles in graphs for which the edge ideal is splittable. We give an explicit splitting function for such ideals.

The transverse proximity effect in the z ~ 2 Lyman-alpha forest suggests QSO episodic lifetimes of ~1 MyrSep 12 2008We look for signs of the H~I transverse proximity effect in the spectra of 130 QSO pairs, most with transverse separations in the plane of the sky of 0.1 -- 3 Mpc at z ~ 2.2. We expected to see a decrease in Lyman-alpha forest HI absorption in the spectrum ... More

Comet Encounters and Carbon 14Nov 26 2012The $^{14}$C production of shock-accelerated particles is calculated in terms of the total energy released in energetic particles. The recently reported 1.2% jump in the $^{14}$C content of the atmosphere in the year C.E. 775, it is found, would require ... More

The Detection of Two Distinct High Ionization States in a QSO Lyman Limit Absorption System: Evidence for Hierarchical Galaxy Formation at z ~ 3?Jan 19 1999We have detected two high ionization phases of gas in the z ~ 2.77 partial Lyman limit system (LLS) towards QSO 1157-3143. We detect the first phase by CIV and SiIV absorption, and the second phase -- which is either warmer or undergoing larger random ... More

Continuum Percolation for Quermass ModelJan 11 2012The continuum percolation for Markov (or Gibbs) germ-grain models is investigated. The grains are assumed circular with random radii on a compact support. The morphological interaction is the so-called Quermass interaction defined by a linear combination ... More

Randomized greedy algorithms for independent sets and matchings in regular graphs: Exact results and finite girth correctionsJul 08 2008We derive new results for the performance of a simple greedy algorithm for finding large independent sets and matchings in constant degree regular graphs. We show that for $r$-regular graphs with $n$ nodes and girth at least $g$, the algorithm finds an ... More

Two Identities relating Eisenstein series on classical groupsAug 05 2018In this paper we introduce two general identities relating Eisenstein series on split classical groups, as well as double covers of symplectic groups. The first identity can be viewed as an extension of the doubling construction introduced in [CFGK17]. ... More

Linear Corotation Torques in Non-Barotropic DisksOct 31 2013Jan 13 2014I derive a fully analytic expression for the linear corotation torque to first order in eccentricity for planets in non-barotropic protoplanetary disks, taking into account the effect of disk entropy gradients. This torque formula is applicable to both ... More

Protoplanetary Disk Resonances and Type I MigrationJul 20 2011Oct 03 2011Waves reflected by the inner edge of a protoplanetary disk are shown to significantly modify Type I migration, even allowing the trapping of planets near the inner disk edge for small planets in a range of disk parameters. This may inform the distribution ... More

Bounds for the Lang-Trotter conjecturesAug 31 2015For a non-CM elliptic curve $E$ defined over the rationals, Lang and Trotter made very deep conjectures concerning the number of primes $p\leq x$ for which $a_p(E)$ is a fixed integer (and for which the Frobenius field at $p$ is a fixed imaginary quadratic ... More

Efficient arithmetic on elliptic curves in characteristic 2Jan 14 2016We present normal forms for elliptic curves over a field of characteristic $2$ analogous to Edwards normal form, and determine bases of addition laws, which provide strikingly simple expressions for the group law. We deduce efficient algorithms for point ... More

Addition law structure of elliptic curvesMay 20 2010Jan 13 2011The study of alternative models for elliptic curves has found recent interest from cryptographic applications, once it was recognized that such models provide more efficiently computable algorithms for the group law than the standard Weierstrass model. ... More

Universal coefficients for overconvergent cohomology and the geometry of eigenvarietiesSep 04 2012Oct 01 2012We prove a universal coefficients theorem for the overconvergent cohomology modules introduced by Ash and Stevens, and give several applications. In particular, we sketch a very simple construction of eigenvarieties using overconvergent cohomology and ... More

The Petersson norm of the Jacobi theta functionOct 03 2011We compute the Petersson norm of the Jacobi theta function, by a simple application of the Rankin-Selberg method and a little trick.

A note on star-like configurations in finite settingsSep 05 2013Given $E \subset \mathbb{F}_q^d$, we show that certain configurations occur frequently when $E$ is of sufficiently large cardinality. Specifically, we show that we achieve the statistically number of $k$-stars $\displaystyle\left|\left\{(x, x^1, \dots, ... More

Vesicles in magnetic fieldsAug 19 2016Liposome vesicles tend to align with an applied magnetic field. This is due to the directional magnetic susceptibility difference of the lipids which form the membrane of these vesicles. In this work a model of liposome vesicles exposed to magnetic field ... More

Reconstructing Pompeian HouseholdsFeb 14 2012A database of objects discovered in houses in the Roman city of Pompeii provides a unique view of ordinary life in an ancient city. Experts have used this collection to study the structure of Roman households, exploring the distribution and variability ... More

An Axiomatic Framework for Belief UpdatesMar 27 2013In the 1940's, a physicist named Cox provided the first formal justification for the axioms of probability based on the subjective or Bayesian interpretation. He showed that if a measure of belief satisfies several fundamental properties, then the measure ... More

A Bayesian Approach to Learning Causal NetworksFeb 20 2013May 16 2015Whereas acausal Bayesian networks represent probabilistic independence, causal Bayesian networks represent causal relationships. In this paper, we examine Bayesian methods for learning both types of networks. Bayesian methods for learning acausal networks ... More

Causal Independence for Knowledge Acquisition and InferenceMar 06 2013May 16 2015I introduce a temporal belief-network representation of causal independence that a knowledge engineer can use to elicit probabilistic models. Like the current, atemporal belief-network representation of causal independence, the new representation makes ... More

Renormalized waves and thermalization of the Klein-Gordon equation: What sound does a nonlinear string make?Nov 04 2010Jun 30 2011We study the thermalization of the classical Klein-Gordon equation under a u^4 interaction. We numerically show that even in the presence of strong nonlinearities, the local thermodynamic equilibrium state exhibits a weakly nonlinear behavior in a renormalized ... More

A note on insufficiency and the preservation of Fisher informationJul 19 2011Apr 20 2012Kagan and Shepp (2005, Amer. Statist.) presented an elegant example of a mixture model for which an insufficient statistic preserves Fisher information. This note uses the regularity property of differentiability in quadratic mean to provide another explanation ... More

Multiple Landen values and the tribonacci numbersApr 21 2015Apr 24 2015Multiple Landen values (MLVs) are defined as iterated integrals on the interval $x\in[0,1]$ of the differential forms $A=d\log(x)$, $B=-d\log(1-x)$, $F=-d\log(1-\rho^2x)$ and $G=-d\log(1-\rho x)$, where $\rho=(\sqrt{5}-1)/2$ is the golden section. I conjecture ... More

On the growth of permutation classesJun 22 2015We study aspects of the enumeration of permutation classes, sets of permutations closed downwards under the subpermutation order. First, we consider monotone grid classes of permutations. We present procedures for calculating the generating function of ... More

$w=-1$ as an AttractorFeb 05 2016May 02 2016It has recently been shown, in flat Robertson-Walker geometries, that the dynamics of gravitational actions which are minimally coupled to matter fields leads to the appearance of "attractors" - sets of physical observables on which phase space measures ... More

Minimal Coupling and AttractorsJul 15 2014The effects of minimally coupling a gravity to matter on a flat Robertson-Walker geometry are explored. Particular attention is paid to the evolution of the symplectic structure and the Liouville measure it defines. We show that the rescaling freedom ... More

Evolution of cosmological perturbations in a brane-universeOct 10 2000The present article analyses the impact on cosmology, in particular on the evolution of cosmological perturbations, of the existence of extra-dimensions. The model considered here is that of a five-dimensional Anti-de Sitter spacetime where ordinary matter ... More

Glimpses into the early UniverseOct 02 2009This contribution gives a brief overview of the theoretical ideas underlying our current understanding of the early Universe. Confronting the predictions of the early Universe models with cosmological observations, in particular of the cosmic microwave ... More

Superfluid neutron starsFeb 02 2001Neutron stars are believed to contain (neutron and proton) superfluids. I will give a summary of a macroscopic description of the interior of neutron stars, in a formulation which is general relativistic. I will also present recent results on the oscillations ... More

Cosmological CMBR dipole in open universes ?Jun 10 1997The observed CMBR dipole is generally interpreted as a Doppler effect arising from the motion of the Earth relative to the CMBR frame. An alternative interpretation, proposed in the last years, is that the dipole results from ultra-large scale isocurvature ... More

Control of pseudodifferential operators by maximal functions via weighted inequalitiesAug 23 2016We establish general weighted $L^2$ inequalities for pseudodifferential operators associated to the H\"ormander symbol classes $S^m_{\rho,\delta}$. Such inequalities provide optimal control of these operators by geometrically-defined maximal functions, ... More

Velocity Effects on the Deflection of Light by Gravitational MicrolensesOct 07 2004We study the influence of general lens and source velocities on the gravitational deflection of light by single and two-point-mass microlenses with general axis orientation. We demonstrate that in all cases the lens equation preserves its form exactly. ... More

Run II Searches for SupersymmetrySep 30 2004In these proceedings, we present all of the Run II results in the search for Supersymmetry from the Tevatron. At the time of presentation ~200 pb-1 of Run II data had been analyzed for the presence of new physics. We summarize searches for CHAMPS, Squarks ... More

Conformal Tensors via Lovelock GravityJun 19 2013Jun 24 2013Constructs from conformal geometry are important in low dimensional gravity models, while in higher dimensions the higher curvature interactions of Lovelock gravity are similarly prominent. Considering conformal invariance in the context of Lovelock gravity ... More

A generalization of the Zerilli master variable for a dynamical spherical spacetimeMay 20 2015The evolution of polar perturbations on a spherical background spacetime is analyzed. The matter content is assumed to be a massless scalar field.This provides a nontrivial dynamics to the background and the linearized equations of motion become much ... More

Classical and quantum behavior of the harmonic and the quartic oscillatorsNov 06 2014Dec 16 2014In a previous paper a formalism to analyze the dynamical evolution of classical and quantum probability distributions in terms of their moments was presented. Here the application of this formalism to the system of a particle moving on a potential is ... More

A Simple Spin Glass Perspective on Martensitic Shape-memory AlloysJan 15 2008Mar 04 2008A brief qualitative mapping is given between austenite, tweed and twinned phases of martensite alloys and corresponding paramagnetic, spin glass and periodic phases in spin glass alloys.

Understanding glassy phenomena in materialsJul 09 2010Oct 11 2010A basis for understanding and modelling glassy behaviour in martensitic alloys and relaxor ferroelectrics is discussed from the perspective of spin glasses.

The Minority Game: a statistical physics perspectiveDec 14 2005A brief review is given of the minority game, an idealized model stimulated by a market of speculative agents, and its complex many-body behaviour. Particular consideration is given to analytic results for the model rather than discussions of its relevance ... More

Strategies for The Determination of phi3 in B- -> D0 K-Mar 30 2001Direct CP violation in decays such as B- -> D0 K- is sensitive to the CKM angle phi_3 because these decays allow the interference of b-quark to c-quark with b-quark to u-quark transitions. Indeed, phi_3 may be determined if one can infer the strong phase ... More

A Direct Proof of BCFW Recursion for Twistor-StringsJul 01 2010This paper gives a direct proof that the leading trace part of the genus zero twistor-string path integral obeys the BCFW recursion relation. This is the first complete proof that the twistor-string correctly computes all tree amplitudes in maximally ... More

Encoding !-tensors as !-graphs with neighbourhood ordersNov 05 2015Diagrammatic reasoning using string diagrams provides an intuitive language for reasoning about morphisms in a symmetric monoidal category. To allow working with infinite families of string diagrams, !-graphs were introduced as a method to mark repeated ... More

Internally heated convection beneath a poor conductorJun 29 2016We consider convection in an internally heated layer of fluid that is bounded below by a perfect insulator and above by a poor conductor. The poorly conducting boundary is modelled by a fixed heat flux. Using solely analytical methods, we find linear ... More

A Quantum Hall Fluid of VorticesJun 26 2003Jul 03 2003In this note we demonstrate that vortices in a non-relativistic Chern-Simons theory form a quantum Hall fluid. We show that the vortex dynamics is controlled by the matrix mechanics previously proposed by Polychronakos as a description of the quantum ... More

The Moduli Space of BPS Domain WallsFeb 01 2002Apr 25 2002N=2 SQED with several flavors admits multiple, static BPS domain wall solutions. We determine the explicit two-kink metric and examine the dynamics of colliding domain walls. The multi-kink metric has a toric Kahler structure and we reduce the Kahler ... More

Superconformal Vortex StringsOct 19 2006Nov 27 2006We study the low-energy dynamics of semi-classical vortex strings living above Argyres-Douglas superconformal field theories. The worldsheet theory of the string is shown to be a deformation of the CP^N model which flows in the infra-red to a superconformal ... More

Classicality of quantum information processingAug 22 2001May 01 2002The ultimate goal of the classicality programme is to quantify the amount of quantumness of certain processes. Here, classicality is studied for a restricted type of process: quantum information processing (QIP). Under special conditions, one can force ... More

Constructing local L-packets for tame unitary groupsNov 29 2013We generalize the work of DeBacker and Reeder to the case of unitary groups split by a tame extension. The approach is broadly similar and the restrictions on the parameter the same, but many of the details of the arguments differ. Let $G$ be a unitary ... More

Developing and Analyzing Boundary Detection Operators Using Probabilistic ModelsMar 27 2013Most feature detectors such as edge detectors or circle finders are statistical, in the sense that they decide at each point in an image about the presence of a feature, this paper describes the use of Bayesian feature detectors.

Graphs with few paths of prescribed length between any two verticesNov 04 2014We use a variant of Bukh's random algebraic method to show that for every natural number $k \geq 2$ there exists a natural number $\ell$ such that, for every $n$, there is a graph with $n$ vertices and $\Omega_k(n^{1 + 1/k})$ edges with at most $\ell$ ... More

Combinatorial theorems relative to a random setApr 12 2014May 22 2014We describe recent advances in the study of random analogues of combinatorial theorems.

Mapping R&D support infrastructures: A scientometric and webometric study of UK science parksJul 27 2014This thesis analyses UK SPs with an informetric approach to study (1) the role of public science and HEIs in research and development (R&D) networks associated with SPs, and (2) the web-based patterns that reflect the configuration of R&D support infrastructures ... More

Duality Invariance of Cosmological Perturbation SpectraSep 22 1998Apr 21 1999I show that cosmological perturbation spectra produced from quantum fluctuations in massless or self-interacting scalar fields during an inflationary era remain invariant under a two parameter family of transformations of the homogeneous background fields. ... More

Counting Rational Points on K3 SurfacesMar 02 1999Mar 04 1999For any algebraic variety $V$ defined over a number field $k$, and ample height function $H$ on $V$, one can define the counting function $N_V(B) = #{P\in V(k) \mid H(P)\leq B}$. In this paper, we calculate the counting function for Kummer surfaces $V$ ... More

Do parton cascade model results approach chemical equilibrium?Mar 03 1994Apr 05 1994This comment is withdrawn, as the figure on which it was based is inconsistent with other figures in the text and thus probably incorrect. Using the other figures, I find that the parton cascade model does approach chemical equilibrium correctly.

Edge Cover Colouring Versus Minimum Degree in MultigraphsJun 09 2009Jul 22 2010An edge colouring of a multigraph can be thought of as a partition of the edges into matchings (a matching meets each vertex at most once). Analogously, an edge cover colouring is a partition of the edges into edge covers (an edge cover meets each vertex ... More

An Optimal Distributed Edge-Biconnectivity AlgorithmFeb 05 2006We describe a synchronous distributed algorithm which identifies the edge-biconnected components of a connected network. It requires a leader, and uses messages of size O(log |V|). The main idea is to preorder a BFS spanning tree, and then to efficiently ... More

Estimating a bivariate linear relationshipFeb 05 2012Solutions of the bivariate, linear errors-in-variables estimation problem with unspecified errors are expected to be invariant under interchange and scaling of the coordinates. The appealing model of normally distributed true values and errors is unidentified ... More

Breaking the n^(log n) Barrier for Solvable-Group IsomorphismMay 03 2012Dec 11 2013We consider the group isomorphism problem: given two finite groups G and H specified by their multiplication tables, decide if G and H are isomorphic. The n^(log n) barrier for group isomorphism has withstood all attacks --- even for the special cases ... More

Orbifolds and SolitonsDec 19 1995May 09 1996We propose a conformal field theory description of a solitonic heterotic string in type $IIA$ superstring theory compactified on $K3$, generalizing previous work by J. Harvey, A. Strominger and A. Sen. In ten dimensions the construction gives a fivebrane ... More

Irreversibility of the Renormalization Group Flow in Two Dimensional Quantum GravityJul 20 1992We argue that the torus partition sum in $2d$ (super) gravity, which counts physical states in the theory, is a decreasing function of the renormalization group scale. As an application we chart the space of $(\hat c\leq1)$ $c\leq1$ models coupled to ... More

Studies toward a Candidate IDS Neutrino Factory Front-End ConfigurationJul 17 2012A front end scenario for the IDS neutrino factory is presented. The scenario is based on the Study 2A example for capture, bunching and phase-energy rotation of muons from a proton source for a neutrino factory, and the goal is the capture of a maximal ... More

Eight light flavors on large lattice volumesOct 25 2013Nov 10 2013I present first results from large-scale lattice investigations of SU(3) gauge theory with eight light flavors in the fundamental representation. Using leadership computing resources at Argonne, we are generating gauge configurations with lattice volumes ... More

Semantics, Representations and Grammars for Deep LearningSep 29 2015Deep learning is currently the subject of intensive study. However, fundamental concepts such as representations are not formally defined -- researchers "know them when they see them" -- and there is no common language for describing and analyzing algorithms. ... More

Pattern avoidance in "flattened" partitionsFeb 15 2008To flatten a set partition (with apologies to Mathematica) means to form a permutation by erasing the dividers between its blocks. Of course, the result depends on how the blocks are listed. For the usual listing--increasing entries in each block and ... More

A determinant of Stirling cycle numbers counts unlabeled acyclic single-source automataMar 31 2007We show that a determinant of Stirling cycle numbers counts unlabeled acyclic single-source automata. The proof involves a bijection from these automata to certain marked lattice paths and a sign-reversing involution to evaluate the determinant.

Permutations avoiding a nonconsecutive instance of a 2- or 3-letter patternOct 13 2006Nov 02 2006We count permutations avoiding a nonconsecutive instance of a two- or three-letter pattern, that is, the pattern may occur but only as consecutive entries in the permutation. Two-letter patterns give rise to the Fibonacci numbers. The counting sequences ... More

Top Quark Physics Results from CDF and D0Sep 18 1996I summarize recent top quark physics results from the Fermilab Tevatron experiments. Since the observation of the top quark by CDF and D0 in 1995, the experimental focus has shifted to a detailed study of the top quark's properties. This article describes ... More

A State-Transition Grammar for Data-Oriented ParsingFeb 27 1995This paper presents a grammar formalism designed for use in data-oriented approaches to language processing. The formalism is best described as a right-linear indexed grammar extended in linguistically interesting ways. The paper goes on to investigate ... More

Replicating and Applying a Neuro-Cognitive Experimental Technique in HCI ResearchJul 11 2013In cognitive neuroscience the sense of agency is defined as the as the experience of controlling ones own actions and, through this control, affecting the external world. At CHI 2012 I presented a paper entitled I did that! Measuring Users Experience ... More

Testing the Capital Asset Pricing Model (CAPM) on the Uganda Stock ExchangeDec 31 2010This paper examines the validity of the Capital Asset Pricing Model (CAPM) on the Ugandan stock market using monthly stock returns from 10 of the 11 companies listed on the Uganda Stock Exchange (USE), for the period 1st March 2007 to 10th November 2009. ... More

Charges in Gauge TheoriesFeb 28 2007Recent progress in the construction of both electric, coloured and magnetic charges in gauge theories will be presented. The topological properties of the charged sectors will be highlighted as well as the applications of this work to confinement and ... More

A Hausdorff measure version of the Jarník--Schmidt theorem in Diophantine approximationSep 13 2015Sep 02 2016We solve the problem of giving sharp asymptotic bounds on the Hausdorff dimensions of certain sets of badly approximable matrices, thus improving results of Broderick and Kleinbock (preprint 2013) as well as Weil (preprint 2013), and generalizing to higher ... More

Random Substitution-Insertion-Deletion (RSID) Model of Molecular Evolution with Alignment-free Parameter EstimationFeb 09 2011We present a comprehensive new framework for handling biologically accurate models of molecular evolution. This model provides a systematic framework for studying models of molecular evolution that implement heterogeneous rates, conservation of reading ... More

Topological Entropy of DNA SequencesJan 24 2011Topological entropy has been one of the most difficult to implement of all the entropy-theoretic notions. This is primarily due to finite sample effects and high-dimensionality problems. In particular, topological entropy has been implemented in previous ... More

Searching for Hydrogen in Type Ib Supernovae, and for Helium and Hydrogen in Type IcJul 09 2002Identifying the progenitors of Type Ib and Type Ic supernovae requires knowing, among other things, whether SNe Ib eject hydrogen, and whether SNe Ic eject helium, and perhaps even hydrogen. Recently it has become clear that some SNe Ib do eject hydrogen, ... More

On quasiconformal selfmappings of the unit disk and elliptic PDE in the planeSep 06 2010Feb 18 2012We prove the following theorem: if $w$ is a quasiconformal mapping of the unit disk onto itself satisfying elliptic partial differential inequality $|L[w]|\le \mathcal{B}|\nabla w|^2+\Gamma$, then $w$ is Lipschitz continuous. This {result} extends some ... More

A proof of Khavinson's conjecture in $\mathbf{R}^4$Jan 13 2016The paper deals with an extremal problem for bounded harmonic functions in the unit ball of $\mathbf{R}^4$. We solve the generalized Khavinson problem in $\mathbf{R}^4$. This precise problem was formulated by G. Kresin and V. Maz'ya for harmonic functions ... More

On J. C. C. Nitsche's type inequality for hyperbolic space $\mathbf{H}^3$Feb 20 2012Feb 21 2012Let $\mathbf H^3$ be the hyperbolic space identified with the unit ball $\mathbf{B}^3 = \{x\in \mathbf{R}^3: |x| < 1\}$ with the Poincar\'e metric $d_h$ and assume that ${\mathcal{A}}(x_0,p,q):=\{x: p<d_h(x,x_0)< q\}\subset \mathbf H^3$ is an hyperbolic ... More

Quasiconformal harmonic mappings between $\,\mathscr C^{1,μ}$ Euclidean surfacesMar 08 2011The conformal deformations are contained in two classes of mappings: quasiconformal and harmonic mappings. In this paper we consider the intersection of these classes. We show that, every $K$ quasiconformal harmonic mapping between $\,\mathscr C^{1,\mu}$ ... More

Cauchy transform and Poisson's equationMar 19 2010Let $u\in W^{2,p}_0$, $1\le p\le \infty$ be a solution of the Poisson equation $\Delta u = h$, $h\in L^p$, in the unit disk. It is proved that $\|\nabla u\|_{L^p} \le a_p\|h\|_{L^p}$ with sharp constant $a_p$ for $p=1$ and $p=\infty$ and that $\|\partial ... More

Elliptical Galaxy Dynamics: The Issues Pertaining to Galaxy FormationAug 31 1999How elliptical galaxy dynamics relate to galaxy structure, stellar populations, spiral galaxies and environment are reviewed. The evidence assembled shows that most, if not all, galaxies originally classified as gE contain disks within them. Taken together, ... More

Random road networks: the quadtree modelAug 29 2010Jan 27 2011What does a typical road network look like? Existing generative models tend to focus on one aspect to the exclusion of others. We introduce the general-purpose \emph{quadtree model} and analyze its shortest paths and maximum flow.

A bordism approach to string topologyJun 04 2003Jul 30 2003Using intersection theory in the context of Hilbert manifolds and geometric homology we show how to recover the main operations of string topology built by M. Chas and D. Sullivan. We also study and build an action of the homology of reduced Sullivan's ... More

Cuckoo Filter: Simplification and AnalysisApr 20 2016The cuckoo filter data structure of Fan, Andersen, Kaminsky, and Mitzenmacher (CoNEXT 2014) performs the same approximate set operations as a Bloom filter in less memory, with better locality of reference, and adds the ability to delete elements as well ... More

The Parametric Closure ProblemApr 16 2015We define the parametric closure problem, in which the input is a partially ordered set whose elements have linearly varying weights and the goal is to compute the sequence of minimum-weight lower sets of the partial order as the weights vary. We give ... More

Paired approximation problems and incompatible inapproximabilitiesSep 10 2009This paper considers pairs of optimization problems that are defined from a single input and for which it is desired to find a good approximation to either one of the problems. In many instances, it is possible to efficiently find an approximation of ... More

The Topology of Bendless Three-Dimensional Orthogonal Graph DrawingSep 26 2007Aug 22 2008We consider embeddings of 3-regular graphs into 3-dimensional Cartesian coordinates, in such a way that two vertices are adjacent if and only if two of their three coordinates are equal (that is, if they lie on an axis-parallel line) and such that no ... More

Dynamic Generators of Topologically Embedded GraphsJul 24 2002We provide a data structure for maintaining an embedding of a graph on a surface (represented combinatorially by a permutation of edges around each vertex) and computing generators of the fundamental group of the surface, in amortized time O(log n + log ... More

$k$-best enumerationDec 16 2014We survey $k$-best enumeration problems and the algorithms for solving them, including in particular the problems of finding the $k$ shortest paths, $k$ smallest spanning trees, and $k$ best matchings in weighted graphs.

Recognizing Partial Cubes in Quadratic TimeMay 08 2007Jul 19 2011We show how to test whether a graph with n vertices and m edges is a partial cube, and if so how to find a distance-preserving embedding of the graph into a hypercube, in the near-optimal time bound O(n^2), improving previous O(nm)-time solutions.