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Probing Unseen Planet Populations with Resolved Debris Disk StructuresMar 25 2019Thousands of exoplanets have been found with many widely different from the ones in our own system. Despite the success, systems with planets in wide orbits analogous to those of Jupiter and Saturn, in the critical first several hundred million years ... More

The MICA Experiment: Astrophysics in Virtual WorldsJan 29 2013We describe the work of the Meta-Institute for Computational Astrophysics (MICA), the first professional scientific organization based in virtual worlds. MICA was an experiment in the use of this technology for science and scholarship, lasting from the ... More

Electrowetting of a soap bubbleApr 25 2013A proof-of-concept demonstration of the electrowetting-on-dielectric of a sessile soap bubble is reported here. The bubbles are generated using a commercial soap bubble mixture - the surfaces are composed of highly doped, commercial silicon wafers covered ... More

Measure of nodal sets of analytic Steklov eigenfunctionsMar 04 2014Let $(\Omega, g)$ be a real analytic Riemannian manifold with real analytic boundary $\partial \Omega$. Let $\psi_{\lambda}$ be an eigenfunction of the Dirichlet-to-Neumann operator $\Lambda$ of $(\Omega, g, \partial \Omega)$ of eigenvalue $\lambda$. ... More

Science Potential of a Deep Ocean Antineutrino ObservatoryNov 22 2006Dec 15 2006This paper presents science potential of a deep ocean antineutrino observatory under development at Hawaii. The observatory design allows for relocation from one site to another. Positioning the observatory some 60 km distant from a nuclear reactor complex ... More

Reactor Antineutrino Signals at Morton and BoulbyNov 05 2016Increasing the distance from which an antineutrino detector is capable of monitoring the operation of a registered reactor, or discovering a clandestine reactor, strengthens the Non-Proliferation of Nuclear Weapons Treaty. This report presents calculations ... More

Type theory and homotopyOct 09 2010The purpose of this survey article is to introduce the reader to a connection between Logic, Geometry, and Algebra which has recently come to light in the form of an interpretation of the constructive type theory of Martin-L\"of into homotopy theory, ... More

Neutrino Factory and Muon Collider R&DNov 05 2001European, Japanese, and US Neutrino Factory designs are presented. The main R&D issues and associated R&D programs, future prospects, and the additional issues that must be addressed to produce a viable Muon Collider design, are discussed.

Dirac phase leptogenesisOct 02 2007I present here a concise summary of the preprint arXiv:0707.3024, written in collaboration with A. Anisimov and P. Di Bari. There we discuss leptogenesis when {\em CP} violation stems exlusively from the Dirac phase in the PMNS mixing matrix. Under this ... More

Nontangential and probabilistic boundary behavior of pluriharmonic functionsNov 15 2005Sep 25 2006Let $u$ be a pluriharmonic function on the unit ball in $\mathbb{C}^n$. I consider the relationship between the set of points $L_u$ on the boundary of the ball at which $u$ converges nontangentially and the set of points $\mathcal{L}_u$ at which $u$ converges ... More

Predominance of entanglement of formation over quantum discord under quantum channelsJul 27 2012Mar 11 2013We present a study of the behavior of two different figures of merit for quantum correlations, entanglement of formation and quantum discord, under quantum channels showing how the former can, counterintuitively, be more resilient to such environments ... More

Criticality revealed through quench dynamics the Lipkin-Meshkov-Glick modelAug 18 2016Oct 19 2016We examine the dynamics after a sudden quench in the magnetic field of the Lipkin-Meshkov-Glick model. Starting from the groundstate and by employing the time-dependent fidelity, we see manifestly different dynamics are present if the system is quenched ... More

Short Homotopically independent loops on surfacesOct 04 2013In this paper, we are interested in short homologically and homotopically independent loops based at the same point on Riemannian surfaces and metric graphs. First, we show that for every closed Riemannian surface of genus $g \geq 2$ and area normalized ... More

Moving liquids with light: Photoelectrowetting on semiconductorsAug 24 2011Liquid transport in microchip-based systems is important in many areas such as Laboratory-on-a-chip, Microfluidics and Optofluidics. Actuation of liquids in such systems is usually achieved using either mechanical displacement11 or via energy conversion ... More

Ergodicity and intersections of nodal sets and geodesics on real analytic surfacesOct 02 2012We consider the the intersections of the complex nodal set of the analytic continuation of an eigenfunction of the Laplacian on a real analytic surface with the complexification of a geodesic. We prove that if the geodesic flow is ergodic and if the geodesic ... More

Strategies for observing extreme mass ratio inspiralsApr 27 2006Aug 26 2006I review the status of research, conducted by a variety of independent groups, aimed at the eventual observation of Extreme Mass Ratio Inspirals (EMRIs) with gravitational wave detectors. EMRIs are binary systems in which one of the objects is much more ... More

On the density of primes with a set of quadratic residues or non-residues in given arithmetic progressionApr 08 2013Jul 25 2013Let $\mathcal{A}$ denote a finite set of arithmetic progressions of positive integers and let $s \geq 2$ be an integer. If the cardinality of $\mathcal{A}$ is at least 2 and $U$ is the union formed by taking certain arithmetic progressions of length $s$ ... More

Criticality revealed through quench dynamics in a many-body systemAug 18 2016We examine the dynamics after a sudden quench in the magnetic field of the Lipkin-Meshkov-Glick model. Starting from the groundstate and by employing the Loschmidt echo, we see manifestly different dynamics are present if the system is quenched through ... More

Muon Cooling R&DAug 15 2001International efforts are under way to design and test a muon ionization cooling channel. The present R&D program is described, and future plans outlined.

Neutrino Factories: PhysicsAug 15 2000The recent evidence for neutrino oscillations opens a new and exciting era in neutrino physics. The next generation of accelerator based neutrino oscillation experiments are expected to confirm the nature of the oscillations, and begin to measure some ... More

A New Era of LeptogenesisJul 09 2008This thesis is devoted to some forefront issues in the field of leptogenesis. After reviewing the simplest picture where flavor effects are neglected and only the lightest right-handed neutrino contributes to the generation of asymmetry, we discuss in ... More

Scientific goals of the UKIRT Infrared Deep Sky SurveyOct 10 2002UKIDSS is the next generation near-infrared sky survey. The survey will commence in early 2004, and over 7 years will collect 100 times as many photons as 2MASS. UKIDSS will use the UKIRT Wide Field Camera to survey 7500 square degrees of the northern ... More

Ordered community structure in networksApr 05 2011Feb 13 2012Community structure in networks is often a consequence of homophily, or assortative mixing, based on some attribute of the vertices. For example, researchers may be grouped into communities corresponding to their research topic. This is possible if vertex ... More

Finding overlapping communities in networks by label propagationOct 28 2009Oct 14 2010We propose an algorithm for finding overlapping community structure in very large networks. The algorithm is based on the label propagation technique of Raghavan, Albert, and Kumara, but is able to detect communities that overlap. Like the original algorithm, ... More

On some abelian varieties of type IVMar 15 2018Aug 15 2018We study a certain class of simple abelian varieties of type $\mathrm{IV}$ (in Albert's classification) over number fields with Mumford-Tate groups of type $A$. In particular, we show that such abelian varieties have ordinary reduction away from a set ... More

Quantum Ergodicity and MixingMar 10 2005This is an expository article for the Encyclopedia of Mathematical Physics on the subject in the title.

An introduction to upper half plane polynomialsNov 26 2007This is a straightforward introduction to the properties of polynomials in many variables that do not vanish in the open upper half plane. Such polynomials generalize many of the well-known properties of polynomials with all real roots.

Asymptotics of polynomials and eigenfunctionsAug 13 2002Jun 20 2003We review some recent results on asymptotic properties of polynomials of large degree, of general holomorphic sections of high powers of positive line bundles over Kahler manifolds, and of Laplace eigenfunctions of large eigenvalue on compact Riemannian ... More

Languages for Mobile AgentsJul 07 2015Mobile agents represent a new model for network computing. Many different languages have been used to implement mobile agents. The characteristics that make a language useful for writing mobile agents are: (1) their support of agent migration, (2) their ... More

Quadratic Residues and Non-Residues: Selected TopicsAug 01 2014Oct 21 2016Number theory as a coherent mathematical subject started with the work of Fermat in the decade from 1630 to 1640, but modern number theory, that is, the systematic and mathematically rigorous development of the subject from fundamental properties of the ... More

Survey of the inverse spectral problem for the Notices of the ICCMApr 08 2015This is an updated survey on the inverse spectral problem written for the Notices of the ICCM. It rapidly reviews some of the material in the previous survey of the same title (arXiv:math/0402356) and then discusses some relatively new results (rigidity ... More

A cubical model of homotopy type theoryJul 21 2016We construct an algebraic weak factorization system $(L, R)$ on the cartesian cubical sets, in which the canonical path object factorization $A \to A^I \to A\times A$ induced by the 1-cube $I$ is an $L$-$R$ factorization for any $R$-object $A$.

How Many Muons Do We Need to Store in a Ring For Neutrino Cross-Section Measurements?Apr 26 2012Analytical estimate of the number of muons that must decay in the straight section of a storage ring to produce a neutrino & anti-neutrino beam of sufficient intensity to facilitate cross-section measurements with a statistical precision of 1%.

Cosmology with the Square Kilometre ArrayMay 31 2011We review how the Square Kilometre Array (SKA) will address fundamental questions in cosmology, focussing on its use for neutral Hydrogen (HI) surveys. A key enabler of its unique capabilities will be large (but smart) receptors in the form of aperture ... More

Pluri-potential theory on Grauert tubes of real analytic Riemannian manifolds, IJul 03 2011We develop analogues for Grauert tubes of real analytic Riemannian manifolds (M,g) of some basic notions of pluri-potential theory, such as the Siciak extremal function. The basic idea is to use analytic continuations of eigenfunctions in place of polynomials ... More

Rates of convergence in active learningMar 09 2011We study the rates of convergence in generalization error achievable by active learning under various types of label noise. Additionally, we study the general problem of model selection for active learning with a nested hierarchy of hypothesis classes ... More

Reductions of abelian varieties of generalized Mumford typeNov 19 2016Oct 31 2017We study the special fibers of a certain class of absolutely simple abelian varieties over number fields with endomorphism rings $\bz$ and possessing $l$-adic monodromy groups of the least possible rank. We also study the Dirichlet density of the places ... More

Fast multipole networksApr 09 2019Two fundamental prerequisites for robotic multiagent systems are mobility and communication. We propose \emph{fast multipole networks} (FMNs) to achieve both ends within a unified framework. FMNs can be organized very efficiently in a distributed way ... More

On the Quadratic Formula Modulo NJul 27 2015Let $a, b, c,$ and $n$ be integers, with $a$ nonzero and $n$ at least two. Necessary and sufficient conditions on these parameters are derived which guarantee that all solutions of the congruence \[ ax^2+bx+c \equiv 0\ \textrm{mod}\ n \] are given precisely ... More

Quadratic Residues and Non-residues in Arithmetic ProgressionNov 09 2011Apr 17 2012Let S be an infinite set of non-empty, finite subsets of the nonnegative integers. If p is an odd prime, let c(p) denote the cardinality of the set {T {\in} S : T {\subseteq} {1,...,p-1} and T is a set of quadratic residues (respectively, non-residues) ... More

Aspects of stable polynomialsMar 03 2008This note is an introduction to the properties of stable polynomials in several variables with real or complex coefficients. These polynomials are defined in terms of where the polynomial is non-vanishing. We do not cover well-known topics in one variable ... More

A Greedy Approach to Adapting the Trace Parameter for Temporal Difference LearningJul 02 2016One of the main obstacles to broad application of reinforcement learning methods is the parameter sensitivity of our core learning algorithms. In many large-scale applications, online computation and function approximation represent key strategies in ... More

Progress in the Development of Plasma Panel Radiation DetectorsDec 30 2010Plasma Display Panels (PDP), the underlying engine of panel plasma television displays, are being investigated for their utility as radiation detectors called Plasma Panel Sensors (PPS). The PPS a novel variant of a micropattern radiation detector, is ... More

AstroGrid-D: Grid Technology for Astronomical ScienceJul 23 2010We present status and results of AstroGrid-D, a joint effort of astrophysicists and computer scientists to employ grid technology for scientific applications. AstroGrid-D provides access to a network of distributed machines with a set of commands as well ... More

Stable, predictable operation of racetrack coils made of high-temperature superconducting Bi-2212 Rutherford cable at the very high wire current density of more than 1000 A/mm2Aug 08 2018Oct 25 2018Uncertain performance and long training with many unpredictable quenches and slowly increasing quench currents are characteristic of the accelerator magnets needed for high energy particle accelerators, particularly the Nb3Sn magnets planned for future ... More

Herschel-ATLAS/GAMA: What determines the far-infrared properties of radio-galaxies?Mar 25 2013We perform a stacking analysis of H-ATLAS data in order to obtain isothermal dust temperatures and rest-frame luminosities at 250um (L250), for 1599 radio sources over the H-ATLAS P1 GAMA area. The radio sample is generated using a combination of NVSS ... More

Pricing Credit Default Swap Subject to Counterparty Risk and CollateralizationMar 21 2018This article presents a new model for valuing a credit default swap (CDS) contract that is affected by multiple credit risks of the buyer, seller and reference entity. We show that default dependency has a significant impact on asset pricing. In fact, ... More

On the Compactness Theorem for Embedded Minimal Surfaces in 3-manifolds with Locally Bounded Area and GenusMar 07 2015Given a sequence of properly embedded minimal surfaces in a $3$-manifold with local bounds on area and genus, we prove subsequential convergence, smooth away from a discrete set, to a smooth embedded limit surface, possibly with multiplicity, and we analyze ... More

Counting Free Abelian ActionsApr 10 2013We consider the problem of counting commuting r-tuples of elements of the symmetric group S_n, i.e. computing |Hom(Z^r,S_n)|. The cases r=1,2 are well-known; a product formula for the case r=3 was conjectured by Adams-Watters and later proved by Britnell. ... More

Controlling Area Blow-up in Minimal or Bounded Mean Curvature VarietiesJul 14 2012Jun 26 2015Consider a sequence of minimal varieties M_i in a Riemannian manifold N such that the boundary measures are uniformly bounded on compact sets. Let Z be the set of points at which the areas of the M_i blow up. We prove that Z behaves in some ways like ... More

On Tverberg partitionsAug 28 2015May 15 2017A theorem of Tverberg from 1966 asserts that every set $X\subset\mathbb{R}^d$ of $n=T(d,r)=(d+1)(r-1)+1$ points can be partitioned into $r$ pairwise disjoint subsets, whose convex hulls have a point in common. Thus every such partition induces an integer ... More

The G-Ball, a New Icon for Codon Symmetry and the Genetic CodeFeb 26 2007A codon table is a useful tool for mapping codons to amino acids as they have been assigned by nature. It has become a scientific icon because of the way it embodies our understanding of this natural process and the way it immediately communicates this ... More

Cosmology with the Ly-a forestMay 23 2003The Lya forest has emerged as one of the few systems capable of probing small-scale structure at high-z with high precision. In this talk I highlight two areas in which the Lya forest is shedding light on fundamental questions in cosmology, one speculative ... More

Which Ambient Spaces Admit Isoperimetric Inequalities for Submanifolds?Apr 24 2008Dec 16 2008We give simple conditions on an ambient manifold that are necessary and sufficient for isoperimetric inequalities (for submanifolds) to hold.

Processes with inert driftApr 03 2006Apr 03 2006We construct a stochastic process whose drift is a function of the process's local time at a reflecting barrier. The process arose as a model of the interactions of a Brownian particle and an inert particle in (Knight, 2001). Interesting asymptotic results ... More

Digitized Waveform Processing for Fast TimingDec 04 2018The prospect of pileup induced backgrounds at the High Luminosity LHC (HL-LHC) has stimulated intense interest in technology for charged particle timing at high rates\cite{challenge}. In this paper I report on a framework for fast timing sensor and related ... More

Lower Bounds in the Preprocessing and Query Phases of Routing AlgorithmsJan 18 2015Sep 07 2015In the last decade, there has been a substantial amount of research in finding routing algorithms designed specifically to run on real-world graphs. In 2010, Abraham et al. showed upper bounds on the query time in terms of a graph's highway dimension ... More

Gorenstein projective dimension with respect to a semidualizing moduleNov 22 2006Jan 02 2009We introduce and investigate the notion of $\gc$-projective modules over (possibly non-noetherian) commutative rings, where $C$ is a semidualizing module. This extends Holm and J{\o}rgensen's notion of $C$-Gorenstein projective modules to the non-noetherian ... More

Subsequent Singularities in Mean-Convex Mean Curvature FlowMar 08 2011Apr 07 2013We use Ilmanen's elliptic regularization to prove that for an initially smooth mean convex hypersurface in Euclidean n-space moving by mean curvature flow, the surface is very nearly convex in a spacetime neighborhood of every singularity. Previously ... More

The Maximum Principle for Minimal Varieties of Arbitrary CodimensionMay 31 2009Nov 12 2010We prove that an m-dimensional minimal variety in a Riemannian manifold cannot touch the boundary at a point where the sum of the smallest m principal curvatures is greater than 0. We also prove an analogous result for varieties with bounded mean curvature. ... More

Unifying task specification in reinforcement learningSep 07 2016Reinforcement learning tasks are typically specified as Markov decision processes. This formalism has been highly successful, though specifications often couple the dynamics of the environment and the learning objective. This lack of modularity can complicate ... More

Automorphisms of geometric structures associated to Coxeter groupsFeb 29 2012In this paper, we consider the automorphism groups of the Cayley graph with respect to the Coxeter generators and the Davis complex of an arbitrary Coxeter group. We determine for which Coxeter groups these automorphism groups are discrete. In the case ... More

Model Structures on Commutative Monoids in General Model CategoriesMar 26 2014Jun 05 2016We provide conditions on a monoidal model category $\mathcal{M}$ so that the category of commutative monoids in $\mathcal{M}$ inherits a model structure from $\mathcal{M}$ in which a map is a weak equivalence or fibration if and only if it is so in $\mathcal{M}$. ... More

Experimental Challenges of the European Strategy for Particle PhysicsSep 30 2013Oct 07 2013In planning for the Phase II upgrades of CMS and ATLAS major considerations are: 1)being able to deal with degradation of tracking and calorimetry up to the radiation doses to be expected with an integrated luminosity of 3000 $fb^{-1}$ and 2)maintaining ... More

Neutron Production and Zero Degree Calorimeter Acceptance at LHCDec 22 2009May 10 2010We calculate cross sections for the far forward LHC detectors to be used for luminosity measurement. A simple model, based on a parametrization of available inclusive neutron data and the assumption that 2 arm rates in non-diffractive events are uncorrelated, ... More

Diffractive J/$ψ$ production in Ultraperipheral AuAu Collisions at RHICOct 31 2005We report on the first measurement of diffractive J/psi production in Ultraperipheral Au+Au collisions at \sqrt{s_{NN}}=200 GeV.

The cardinality of sets in Tverberg partitionsAug 28 2015A theorem of Tverberg from 1966 asserts that every set $X\subset\mathbb{R}^d$ of $n=T(d,r)=(d+1)(r-1)+1$ points can be partitioned into $r$ pairwise disjoint subsets, whose convex hulls have a point in common. Thus every such partition induces an integer ... More

Baryon oscillationsJul 12 2005Jul 28 2005The coupling of photons and baryons by Thomson scattering in the early universe imprints features in both the Cosmic Microwave Background (CMB) and matter power spectra. The former have been used to constrain a host of cosmological parameters, the latter ... More

Baryons and weak lensing power spectraMay 28 2004Jun 04 2004We provide a simple toy model to elucidate the effects of baryonic cooling on predictions of the convergence power spectrum in weak gravitational lensing. Our model suggests that the effects of baryonic cooling on dark matter halo profiles can alter the ... More

The mass of a haloNov 27 2000We discuss the different definitions of the mass of a halo in common use and how one may convert between them. Using N-body simulations we show that mass estimates based on spherical averages are much more tightly correlated with each other than with ... More

A Computational Approach to Aspectual CompositionJul 01 1995In this paper, I argue, contrary to the prevailing opinion in the linguistics and philosophy literature, that a sortal approach to aspectual composition can indeed be explanatory. In support of this view, I develop a synthesis of competing proposals by ... More

Reconstructing the CMB power spectrumFeb 15 1994We discuss a method for a model independent reconstruction of the CMB temperature fluctuation power spectrum on small and intermediate scales that is geared to individual experiments. The importance of off-diagonal correlations for determining the shape ... More

Evolution of curves and surfaces by mean curvatureDec 01 2002This article describes the mean curvature flow, some of the discoveries that have been made about it, and some unresolved questions.

Lectures on Minimal Surface TheoryAug 15 2013Jan 17 2016An article based on a four-lecture introductory minicourse on minimal surface theory given at the 2013 summer program of the Institute for Advanced Study and the Park City Mathematics Institute.

Curvatures of embedded minimal disks blow up on subsets of C^1 curvesMar 29 2011Feb 19 2015Any sequence of properly embedded minimal disks in an open subset U of Euclidean 3-space has a subsequence such that the curvatures blow up on a relatively closed subset K of U and such that the disks converge in the complement of K to a minimal lamination ... More

On the Bumpy Metrics Theorem for Minimal SubmanifoldsMar 05 2015This paper proves several natural generalizations of the theorem that for a generic, $C^k$ Riemannian metric on a smooth manifold, there are no closed, embedded, minimal submanifolds with nontrivial jacobi fields.

Mean Curvature Flow with BoundaryJan 10 2019We develop a theory of surfaces with boundary moving by mean curvature flow. In particular, we prove a general existence theorem by elliptic regularization, and we prove boundary regularity at all positive times under rather mild hypotheses.

A marked correlation function for constraining modified gravity modelsSep 27 2016Future large scale structure surveys will provide increasingly tight constraints on our cosmological model. These surveys will report results on the distance scale and growth rate of perturbations through measurements of Baryon Acoustic Oscillations and ... More

A Fuzzy Clustering Algorithm for the Mode Seeking FrameworkJun 27 2014Jun 22 2016In this paper, we propose a new fuzzy clustering algorithm based on the mode-seeking framework. Given a dataset in $\mathbb{R}^d$, we define regions of high density that we call cluster cores. We then consider a random walk on a neighborhood graph built ... More

The Pitchfork BifurcationSep 20 2016We give development of a new theory of the Pitchfork bifurcation, which removes the perspective of the third derivative and a requirement of symmetry.

Mathematics of the GenomeOct 01 2015Apr 27 2016This work gives a mathematical foundation for bifurcation from a stable equilibrium in the genome. We construct idealized dynamics associated with the genome. For this dynamics we investigate the two main bifurcations from a stable equilibrium. Finally, ... More

Number variance of random zerosDec 30 2005Jan 06 2006The main results of this article are asymptotic formulas for the variance of the number of zeros of a Gaussian random polynomial of degree $N$ in an open set $U \subset C$ as the degree $N \to \infty$, and more generally for the zeros of random holomorphic ... More

A spectral optical flow method for determining velocities from digital imageryApr 17 2015We present a method for determining surface flows from solar images based upon optical flow techniques. We apply the method to sets of images obtained by a variety of solar imagers to assess its performance. The {\tt opflow3d} procedure is shown to extract ... More

Generating and Searching Families of FFT AlgorithmsMar 29 2011Aug 30 2011A fundamental question of longstanding theoretical interest is to prove the lowest exact count of real additions and multiplications required to compute a power-of-two discrete Fourier transform (DFT). For 35 years the split-radix algorithm held the record ... More

Two Theorems in List DecodingJan 12 2010We prove the following results concerning the list decoding of error-correcting codes: (i) We show that for \textit{any} code with a relative distance of $\delta$ (over a large enough alphabet), the following result holds for \textit{random errors}: With ... More

Web Application for Modeling Global AntineutrinosOct 19 2015Electron antineutrinos stream freely from rapidly decaying fission products within nuclear reactors and from long-lived radioactivity within Earth. Those with energy greater than 1.8 MeV are regularly observed by several kiloton-scale underground detectors. ... More

MSE-based analysis of optimal tuning functions predicts phenomena observed in sensory neuronsFeb 11 2010Biological systems display impressive capabilities in effectively responding to environmental signals in real time. There is increasing evidence that organisms may indeed be employing near optimal Bayesian calculations in their decision-making. An intriguing ... More

A database of Hilbert modular formsMay 09 2016We describe the computation of tables of Hilbert modular forms of parallel weight 2 over totally real fields.

Computing Hilbert modular forms over fields with nontrivial class groupNov 26 2007In previous work, the first author developed an algorithm for the computation of Hilbert modular forms. In this paper, we extend this to all totally real number fields of even degree and nontrivial class group. Using the algorithm over $\Q(\sqrt{10})$ ... More

Patterson-Sullivan distributions and quantum ergodicityJan 31 2006Feb 10 2006We relate two types of phase space distributions associated to eigenfunctions $\phi_{ir_j}$ of the Laplacian on a compact hyperbolic surface $X_{\Gamma}$: (1) Wigner distributions $\int_{S^*\X} a dW_{ir_j}=< Op(a)\phi_{ir_j}, \phi_{ir_j}>_{L^2(\X)}$, ... More

Quantum Ergodicity for Eisenstein functionsDec 21 2015A new proof is given of Quantum Ergodicity for Eisenstein Series for cusped hyperbolic surfaces. This result is also extended to higher dimensional examples, with variable curvature.

Connectedness of the dart digraph and the squared-dart digraphAug 29 2016In this note we revisit the dart graph and the squared dart digraph constructions and prove that they yield strongly connected digraphs when applied to connected graphs of minimum valence at least 3.

Second-order multisymplectic field theory: A variational approach to second-order multisymplectic field theorySep 17 1999This paper presents a geometric-variational approach to continuous and discrete {\it second-order} field theories following the methodology of \cite{MPS}. Staying entirely in the Lagrangian framework and letting $Y$ denote the configuration fiber bundle, ... More

On the sign patterns of the smallest signless Laplacian eigenvectorJul 29 2013Let $H$ be a connected bipartite graph, whose signless Laplacian matrix is $Q(H)$. Suppose that the bipartition of $H$ is $(S,T)$ and that $x$ is the eigenvector of the smallest eigenvalue of $Q(H)$. It is well-known that $x$ is positive and constant ... More

Trade-off between speed and cost in shortcuts to adiabaticitySep 15 2016Aug 07 2017Achieving effectively adiabatic dynamics is a ubiquitous goal in almost all areas of quantum physics. Here, we study the speed with which a quantum system can be driven when employing transitionless quantum driving. As a main result, we establish a rigorous ... More

What Are You Hiding? Algorithmic Transparency and User PerceptionsDec 07 2018Extensive recent media focus has been directed towards the dark side of intelligent systems, how algorithms can influence society negatively. Often, transparency is proposed as a solution or step in the right direction. Unfortunately, research is mixed ... More

"I had a solid theory before but it's falling apart": Polarizing Effects of Algorithmic TransparencyNov 06 2018The rise of machine learning has brought closer scrutiny to intelligent systems, leading to calls for greater transparency and explainable algorithms. We explore the effects of transparency on user perceptions of a working intelligent system for emotion ... More

Equilibrium distribution of zeros of random polynomialsJun 17 2002We consider ensembles of random polynomials of the form $p(z)=\sum_{j = 1}^N a_j P_j$ where $\{a_j\}$ are independent complex normal random variables and where $\{P_j\}$ are the orthonormal polynomials on the boundary of a bounded simply connected analytic ... More

Random polynomials with prescribed Newton polytopeNov 25 2002Jun 04 2003We show that the Newton polytope of a polynomial has a strong impact on the distribution of its mass and zeros. The basic theme is that Newton polytopes determine allowed and forbidden regions for these distributions. We equip the space of (holomorphic) ... More

Leptogenesis with an almost conserved lepton numberOct 17 2008Feb 15 2010Seesaw models with a slightly broken lepton number symmetry can explain small neutrino masses, and allow for low-scale leptogenesis. We make a thorough analysis of leptogenesis within the simplest model with two right-handed (RH) neutrinos (or with N_3 ... More