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Search for gamma-ray emission from $p$-wave dark matter annihilation in the Galactic CenterApr 12 2019Indirect searches for dark matter through Standard Model products of its annihilation generally assume a cross-section which is dominated by a term independent of velocity ($s$-wave annihilation). However, in many DM models an $s$-wave annihilation cross-section ... 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

The Optimal Sample Complexity of PAC LearningJul 02 2015Feb 07 2016This work establishes a new upper bound on the number of samples sufficient for PAC learning in the realizable case. The bound matches known lower bounds up to numerical constant factors. This solves a long-standing open problem on the sample complexity ... More

Park City lectures on EigenfunctionsOct 29 2013This is an expository article based on my lectures on eigenfunctions of the Laplacian for the 2013 IAS/Park City Mathematics Institute (PCMI) summer school in geometric analysis. Many of the results are based on joint work with H. Christianson, J. Jung, ... More

Wetting of soap bubbles on hydrophilic, hydrophobic and superhydrophobic surfacesMar 26 2013Wetting of sessile bubbles on solid and liquid surfaces has been studied. A model is presented for the contact angle of a sessile bubble based on a modified Young equation - the experimental results agree with the model. A hydrophilic surface results ... More

Logarithmic lower bound on the number of nodal domainsOct 18 2015We prove that the number of nodal domains of a density one subsequence of eigenfunctions grows at least logarithmically with the eigenvalue on negatively curved `real Riemann surfaces'. The geometric model is the same as in prior joint work with Junehyuk ... More

Off-diagonal decay of toric Bergman kernelsMar 28 2016We study the off-diagonal decay of Bergman kernels $\Pi_{h^k}(z,w)$ and Berezin kernels $P_{h^k}(z,w)$ for ample invariant line bundles over compact toric projective \kahler manifolds of dimension $m$. When the metric is real analytic, $P_{h^k}(z,w) \simeq ... More

Verifying black hole orbits with gravitational spectroscopyNov 29 2007May 08 2009Gravitational waves from test masses bound to geodesic orbits of rotating black holes are simulated, using Teukolsky's black hole perturbation formalism, for about ten thousand generic orbital configurations. Each binary radiates power exclusively in ... More

Inverse Spectral Problem for Surfaces of RevolutionFeb 05 2000This paper concerns the inverse spectral problem for analytic simple surfaces of revolution. By `simple' is meant that there is precisely one critical distance from the axis of revolution. Such surfaces have completely integrable geodesic flows with global ... 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

Abelian varieties in pairing-based cryptographyDec 30 2018Mar 22 2019We study the problem of the embedding degree of an abelian variety over a finite field which is vital in pairing-based cryptography. In particular, we show that for a prescribed CM field $L$ of degree $\geq 4$, prescribed integers $m$, $n$ and any prime ... 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

Asphericity for certain groups of cohomological dimension 2Jan 27 2015Mar 16 2015A finite connected 2-complex K whose fundamental group is of cohomological dimension 2 is aspherical iff the subgroup \Sigma_K of H_2(K) consisting of spherical 2-cycles is zero. A finite connected subcomplex of an aspherical 2-complex is aspherical iff ... 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

Geo-neutrinos: recent developmentsDec 11 2014Radiogenic heating is a key component of the energy balance and thermal evolution of the Earth. It contributes to mantle convection, plate tectonics, volcanoes, and mountain building. Geo-neutrino observations estimate the present radiogenic power of ... More

Testing Geological Models with Terrestrial Antineutrino Flux MeasurementsDec 14 2009Uranium and thorium are the main heat producing elements in the earth. Their quantities and distributions, which specify the flux of detectable antineutrinos generated by the beta decay of their daughter isotopes, remain unmeasured. Geological models ... More

The art of juggling with two balls or A proof for a modular condition of Lucas numbersApr 24 2010Apr 28 2010In this short note we look at the problem of counting juggling patterns with one ball or two balls with a throw at every occurrence. We will do this for both traditional juggling and for spherical juggling. In the latter case we will show a connection ... 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

Simple estimators for network samplingApr 03 2018Apr 22 2019A new estimation method is presented for network sampling designs, including Respondent Driven Sampling (RDS) and Snowball (SB) sampling. These types of link-tracing designs are essential for studies of hidden populations, such as people at risk for HIV. ... 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

Szego kernels and a theorem of TianFeb 03 2000We give a simple proof of Tian's theorem that the Kodaira embeddings associated to a positive line bundle over a compact complex manifold are asymptotically isometric. The proof is based on the diagonal asymptotics of the Szego kernel (i.e. the orthogonal ... More

InfraNotes: Inconspicuous Handwritten Trajectory Tracking for Lecture Note Recording with Infrared SensorsOct 07 2016Lecture notes are important for students to review and understand the key points in the class. Unfortunately, the students often miss or lose part of the lecture notes. In this paper, we design and implement an infrared sensor based system, InfraNotes, ... 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

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

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

Heavy Ions Interpretation of Highest Energy Cosmic RaysDec 14 2001A brief review of the energy spectrum of primary cosmic rays above $10^{10}$ eV and the measurement techniques used to investigate the ultra high energy ones is given. This is followed by a discussion of the atmospheric shower profile of the highest energy ... 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

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

Discovering dynamic functional networks in the human neonatal brain with electric source imagingFeb 11 2019When the human brain manifests the birth of organised communication among local and large-scale neuronal populations activity remains undescribed. We report, in resting-state EEG source-estimates of 100 infants at term age, the existence of macro-scale ... More

Survey of the inverse spectral problemFeb 23 2004This is a survey of the inverse spectral problem on (mainly compact) Riemannian manifolds, with or without boundary. The emphasis is on wave invariants: on how wave invariants have been calculated and how they have been applied to concrete inverse spectral ... More

Topology of the Standard Model, I: FermionsJun 16 2013Dec 26 2015The Harari-Shupe model for fermions is extended to a topological model which contains an explanation for the observed fact that there are only three generations of fermions. Topological explanations are given for $\beta$-decay and for proton decay predicted ... 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

Fast Markov Chain Monte Carlo Algorithms via Lie GroupsJan 24 2019From basic considerations of the Lie group that preserves a target probability measure, we derive the Barker, Metropolis, and ensemble Markov chain Monte Carlo (MCMC) algorithms, as well as two new MCMC algorithms. The convergence properties of these ... More

Smooth global Lagrangian flow for the 2D Euler and second-grade fluid equationsJul 05 2000We present a very simple proof of the global existence of a $C^\infty$ Lagrangian flow map for the 2D Euler and second-grade fluid equations (on a compact Riemannian manifold with boundary) which has $C^\infty$ dependence on initial data $u_0$ in the ... 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

Precision and Casimir Force Measurements in Superfluid and Vacuum with Silicon Nitride MembranesAug 28 2008The recent discovery that silicon nitride membranes can be used as extremely high Q mechanical resonators makes possible a number of novel experiments, which include improved long range vacuum Casimir force measurements, and measurments of the properties ... More

Two-particle self-consistent approximation, pseudogap and superconductivity in the attractive Hubbard modelDec 15 2000In this thesis, I present a non-perturbative approach to the single-band attractive Hubard model which is an extension of previous work by Vilk and Tremblay on the repulsive model. Exact results are derived in the general context of functional derivative ... More

Integrating electricity markets: Impacts of increasing trade on prices and emissions in the western United StatesOct 10 2018Feb 14 2019This paper presents estimates of short-term relationships between regional electricity trade in the western United States (U.S.) and prices, emissions, and generation dispatch. Consistent with economic theory, I find a negative short term relationship ... More

A Markov model for inferring flows in directed contact networksOct 25 2018Directed contact networks (DCNs) are a particularly flexible and convenient class of temporal networks, useful for modeling and analyzing the transfer of discrete quantities in communications, transportation, epidemiology, etc. Transfers modeled by contacts ... More

Statistical Modeling in Continuous Speech Recognition (CSR)(Invited Talk)Jan 10 2013Automatic continuous speech recognition (CSR) is sufficiently mature that a variety of real world applications are now possible including large vocabulary transcription and interactive spoken dialogues. This paper reviews the evolution of the statistical ... More

Addendum: Level Spacings for Integrable Quantum Maps in Genus ZeroFeb 04 2000In this addendum we strengthen the results of math-ph/0002010 in the case of polynomial phases. We prove that Cesaro means of the pair correlation functions of certain integrable quantum maps on the 2-sphere at level N tend almost always to the Poisson ... More

Quantum ergodicity of C* dynamical systemsFeb 03 2000This paper contains a very simple and general proof that eigenfunctions of quantizations of classically ergodic systems become uniformly distributed in phase space. This ergodicity property of eigenfunctions f is shown to follow from a convexity inequality ... 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

Questions about determinants and polynomialsAug 13 2008We discuss several conjectures about the real-rootedness of polynomials whose coefficients are determinants of coefficients of a real-rooted polynomial. We also consider some questions about matrices generalizing totally positive matrices, namely totally ... More

Well-posedness and global attractors for liquid crystals on Riemannian manifoldsJan 24 2001We study the coupled Navier-Stokes Ginzburg-Landau model of nematic liquid crystals introduced by F.H. Lin, which is a simplified version of the Ericksen-Leslie system. We generalize the model to compact n-dimensional Riemannian manifolds, and show that ... More

Ultraquantum DynamicsApr 03 2003Segal proposed ultraquantum commutation relations with two ultraquantum constants hbar' and hbar'' besides Planck's quantum constant hbar with a variable i. The Heisenberg quantum algebra is a contraction - in a more general sense than that of Inonu and ... More

On The Beta-Function in N=2 Supersymmetric Yang-Mills TheoryOct 14 1997Jun 09 1998The constraints of N=2 supersymmetry, in combination with several other quite general assumptions, have recently been used to show that N=2 supersymmetric Yang-Mills theory has a low energy quantum parameter space symmetry characterised by the discrete ... 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

Notes on the Theory of Algebraic NumbersJul 27 2015A series of lecture notes on the elementary theory of algebraic numbers, using only knowledge of a first-semester graduate course in algebra (primarily groups and rings). No prerequisite knowledge of fields is required. Based primarily on the texts of ... More

Refined Error Bounds for Several Learning AlgorithmsDec 22 2015Sep 10 2016This article studies the achievable guarantees on the error rates of certain learning algorithms, with particular focus on refining logarithmic factors. Many of the results are based on a general technique for obtaining bounds on the error rates of sample-consistent ... More

Virtual Reality: A Definition History - A Personal EssayDec 16 2013This essay, written in 1998 by an active participant in both virtual reality development and the virtual reality definition debate, discusses the definition of the phrase "Virtual Reality" (VR). I start with history from a personal perspective, concentrating ... More

Natural models of homotopy type theoryJun 12 2014Mar 19 2015The notion of a natural model of type theory is defined in terms of that of a representable natural transfomation of presheaves. It is shown that such models agree exactly with the concept of a category with families in the sense of Dybjer, which can ... More

Gaussian beams on Zoll manifolds and maximally degenerate LaplaciansApr 10 2014Gaussian beams exist along all closed geodesics of a Zoll surface, despite the fact that the algorithm for constructing them assumes that the closed geodesics are non-degenerate. Similarly, there exists a global Birkhoff normal for a Zoll Laplacian despite ... More

Random orthonormal bases of spaces of high dimensionOct 07 2012We consider a sequence H_N of Hilbert spaces of dimensions d_N tending to infinity. The motivating examples are eigenspaces or quasi-mode spaces of a Laplace or Schrodinger operator. We define a random ONB of H_N by fixing one ONB and changing it by a ... More

Matrix elements of Fourier Integral OperatorsAug 05 2013This article is concerned with the semi-classical limits of matrix elements $<F \phi_j, \phi_j>$ of eigenfunctions of the Laplacian $\Delta_g$ of a compact Riemannian manifold $(M, g)$ with respect to a Fourier integral operator $F$ on $L^2(M)$. Many ... More

Growth of balls in the universal cover of surfaces and graphsApr 12 2013Apr 16 2013In this paper, we prove uniform lower bounds on the volume growth of balls in the universal covers of Riemannian surfaces and graphs. More precisely, there exists a constant $\delta>0$ such that if $(M,hyp)$ is a closed hyperbolic surface and $h$ another ... More

Significance of Rapid Solutions Development to Business Process ManagementAug 19 2012Business process management (BPM) is moving from a niche market into the mainstream. One of the factors leading to this transformation is the emergence of very powerful rapid solutions development tools for creating BPM solutions (BPM RSD). It has been ... More

Activized Learning: Transforming Passive to Active with Improved Label ComplexityAug 08 2011We study the theoretical advantages of active learning over passive learning. Specifically, we prove that, in noise-free classifier learning for VC classes, any passive learning algorithm can be transformed into an active learning algorithm with asymptotically ... More

Temporal Reasoning About Uncertain WorldsMar 27 2013We present a program that manages a database of temporally scoped beliefs. The basic functionality of the system includes maintaining a network of constraints among time points, supporting a variety of fetches, mediating the application of causal rules, ... More

Coloring the 600 CellFeb 18 2008The 600 cell S has exactly 10 5-colorings. From these colorings we can construct the space of colorings $B(S)$. This complex has 1344 colorings, and is isomorphic to the space of 5 by 5 Latin Squares. These simplices split into 4 copies of a quotient ... 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

Geo-neutrinos and the Radioactive Power of the EarthNov 25 2011Sep 11 2012Chemical and physical Earth models agree little as to the radioactive power of the planet. Each predicts a range of radioactive powers, overlapping slightly with the other at about 24 TW, and together spanning 14-46 TW. Approximately 20 % of this radioactive ... More

Geo-neutrinos and Silicate Earth Enrichment of U and ThMay 25 2010Aug 30 2010The terrestrial distribution of U, Th, and K abundances governs the thermal evolution, traces the differentiation, and reflects the bulk composition of the earth. Comparing the bulk earth composition to chondritic meteorites estimates the net amounts ... More

A search for the rare decay K+ -> pi+ nu nuJan 09 1997Recent results from the first phase of the E787 experiment and an update on the current status are presented. From the first phase the limit on the K+ -> pi+ nu nu (pnn) branching ratio is BR(pnn) < 2.4e-9 (90%CL). An observation of the decay K+ -> pi+ ... More

Integrating electricity markets: Impacts of increasing trade on prices and emissions in the western United StatesOct 10 2018This paper analyzes the market impacts of expanding California's centralized electricity market across the western United States and provides the first statistical assessment of this issue. Using market data from 2015-2018, I estimate the short-term effects ... More

Reductions of abelian varieties of generalized Mumford typeNov 19 2016We study the reductions of a class of absolutely simple abelian varieties over number fields with endomorphism rings $\mathbb{Z}$ and $l$-adic monodromy groups of low rank. We also study the densities of the places at which the possible reductions occur. ... 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

Level Spacings for Integrable Quantum Maps in Genus ZeroFeb 04 2000We consider the eigenvalue pair correlation problem for certain integrable quantum maps on the 2-sphere. The classical maps are time one maps of Hamiltonian flows of perfect Morse functions. The quantizations are unitary operators on spaces of homogeneous ... More

Families of Cyclic Cubic FieldsNov 15 2015We describe a procedure for generating families of cyclic cubic fields with explicit fundamental units. This method generates all known families and gives new ones.

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

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

Mass bias evolution in tSZ cluster cosmologyJan 10 2019Galaxy clusters observed through the thermal Sunyaev-Zeldovich (tSZ) effect are a recent cosmological probe. The precision on the cosmological constraints is mainly affected by the current knowledge of clusters physics, that enters the analysis through ... More

Superconformal R-charges and dyon multiplicities in N=2 gauge theoriesDec 11 2006N=(2,2) theories in 1+1D exhibit a direct correspondence between the R-charges of chiral operators at a conformal point and the multiplicities of BPS kinks in a massive deformation, as shown by Cecotti and Vafa. We obtain an analogous relation in 3+1D ... More

Central charges, S-duality and massive vacua of N=1* super Yang-MillsJun 07 2006Aug 02 2006We provide a simple derivation of the extremal values of the superpotential in massive vacua of N=1* SYM, making use of the required modular weight for the central charge of BPS walls interpolating between these vacua. This modular weight descends from ... More

A Note on Domain Walls and the Parameter Space of N=1 Gauge TheoriesAug 21 2003Sep 22 2003We study the spectrum of BPS domain walls within the parameter space of N=1 U(N) gauge theories with adjoint matter and a cubic superpotential. Using a low energy description obtained by compactifying the theory on R^3 x S^1, we examine the wall spectrum ... More

Cosmological Constraints on Very Dark PhotonsJul 03 2014Jul 10 2014We explore the cosmological consequences of kinetically mixed dark photons with a mass between 1 MeV and 10 GeV, and an effective electromagnetic fine structure constant as small as $10^{-38}$. We calculate the freeze-in abundance of these dark photons ... More

Directly Detecting MeV-scale Dark Matter via Solar ReflectionAug 11 2017Nov 16 2018If dark matter (DM) particles are lighter than a few MeV/$c^2$ and can scatter off electrons, their interaction within the solar interior results in a considerable hardening of the spectrum of galactic dark matter received on Earth. For a large range ... More

Direct detection prospects of dark vectors with xenon-based dark matter experimentsOct 15 2015Oct 16 2015Dark matter experiments primarily search for the scattering of WIMPs on target nuclei of well shielded underground detectors. The results from liquid scintillator experiments furthermore provide precise probes of very light and very weakly coupled particles ... More

Deep Neural Baselines for Computational ParalinguisticsJul 05 2019Detecting sleepiness from spoken language is an ambitious task, which is addressed by the Interspeech 2019 Computational Paralinguistics Challenge (ComParE). We propose an end-to-end deep learning approach to detect and classify patterns reflecting sleepiness ... More

A sample of 6C radio sources with virtually complete redshifts. II - optical spectroscopyOct 23 2000This is the second of two papers presenting basic observational data on the 6CE sample of extragalactic radio sources. It presents the results of optical spectroscopy which has yielded virtually complete redshift information for the 6CE sample: 56 of ... More

High-redshift clusters from NVSS: The TexOx Cluster (TOC) SurveyJan 16 2003The TexOx Cluster (TOC) Survey uses overdensities of radiosources in the NVSS to trace clusters of galaxies. The links between radiosources and rich environments make this a powerful way to find clusters which may potentially be overlooked by other selection ... More