total 2352took 0.13s

Understanding The Impact of Partner Choice on Cooperation and Social Norms by means of Multi-agent Reinforcement LearningFeb 08 2019Feb 13 2019The human ability to coordinate and cooperate has been vital to the development of societies for thousands of years. While it is not fully clear how this behavior arises, social norms are thought to be a key factor in this development. In contrast to ... More

Understanding The Impact of Partner Choice on Cooperation and Social Norms by means of Multi-agent Reinforcement LearningFeb 08 2019The human ability to coordinate and cooperate has been vital to the development of societies for thousands of years. While it is not fully clear how this behavior arises, social norms are thought to be a key factor in this development. In contrast to ... More

Robust Extended Kalman Filtering for Systems with Measurement OutliersMar 31 2019Outliers can contaminate the measurement process of many nonlinear systems, which can be caused by sensor errors, model uncertainties, change in ambient environment, data loss or malicious cyber attacks. When the extended Kalman filter (EKF) is applied ... More

Division algebras graded by a finite groupApr 24 2019Let $k$ be a field containing an algebraically closed field of characteristic zero. If $G$ is a finite group and $D$ is a division algebra over $k$, finite dimensional over its center, we can associate to a faithful $G$-grading on $D$ a normal abelian ... More

A graph theoretic approach to graded identities for matricesJun 01 2011Nov 08 2011We consider the algebra M_k(C) of k-by-k matrices over the complex numbers and view it as a crossed product with a group G of order k by embedding G in the symmetric group S_k via the regular representation and embedding S_k in M_k(C) in the usual way. ... More

Simple G-graded algebras and their polynomial identitiesJul 23 2011Nov 15 2011Let G be any group and F an algebraically closed field of characteristic zero. We show that any G-graded finite dimensional associative G-simple algebra over F is determined up to a G-graded isomorphism by its G-graded polynomial identities. This result ... 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

Robust Geo-neutrino ResultsNov 11 2016Geo-neutrino observations probe the quantities and distributions of terrestrial heat-producing elements uranium and thorium. The quantities of these elements gauge global radiogenic power, offering insights into the origin and thermal history of the Earth. ... 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

Using twins and scaling to construct cospectral graphs for the normalized LaplacianSep 29 2014Oct 23 2014The spectrum of the normalized Laplacian matrix cannot determine the number of edges in a graph, however finding constructions of cospectral graphs with differing number of edges has been elusive. In this paper we use basic properties of twins and scaling ... 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

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.

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

Topological mixture estimationDec 12 2017May 31 2018Density functions that represent sample data are often multimodal, i.e. they exhibit more than one maximum. Typically this behavior is taken to indicate that the underlying data deserves a more detailed representation as a mixture of densities with individually ... More

Quantum simulated annealingDec 20 2000Dec 09 2002The question of whether or not quantum computers can efficiently solve NP-complete problems is open, although indications are that BQP does not contain NP. Still, many of these problems are natural candidates for solution on quantum computers. We outline ... More

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

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

Neutrino Experiments: Status, Recent Progress, and ProspectsNov 19 2007Nov 28 2007Neutrino physics has seen an explosion of activity and new results in the last decade. In this report the current state of the field is summarized, with a particular focus on progress in the last two years. Prospects for the near term (roughly 5 years) ... More

Geometry and curvature of diffeomorphism groups with $H^1$ metric and mean hydrodynamicsJul 15 1998Recently, Holm, Marsden, and Ratiu [1998] have derived a new model for the mean motion of an ideal fluid in Euclidean space given by the equation $\dot{V}(t) + \nabla_{U(t)} V(t) - \alpha^2 [\nabla U(t)]^t \cdot \triangle U(t) = -\text{grad} p(t)$ where ... 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

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

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

Effective temperature for finite systemsApr 24 2009Under the Ansatz that the occupation times of a system with finitely many states are given by the Gibbs distribution, an effective temperature is uniquely determined (up to a choice of scale), and may be computed de novo, without any reference to a Hamiltonian ... 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

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

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

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

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

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

Polynomials, roots, and interlacingDec 28 2006Mar 11 2008This work is divided into three parts. The first part concerns polynomials in one variable with all real roots. We consider linear transformations that preserve real rootedness, as well as matrices that preserve interlacing. The second part covers polynomials ... More

The Laguerre polynomials preserve real-rootednessAug 19 2008The linear transformation that sends $x^n$ to the n'th Laguerre polynomial preserves real-rootedness.

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

Topological density estimationJan 31 2017We introduce \emph{topological density estimation} (TDE), in which the multimodal structure of a probability density function is topologically inferred and subsequently used to perform bandwidth selection for kernel density estimation. We show that TDE ... More

Billiards and boundary traces of eigenfunctionsAug 23 2003This is a report for the 2003 Forges Les Eaux PDE conference on recent results with A. Hassell on quantum ergodicity of boundary traces of eigenfunctions on domains with ergodic billiards, and of work in progress with Hassell and Sogge on norms of boundary ... More

Quantum unique ergodicityJan 27 2003Jul 31 2003This short note proves that a Laplacian cannot be quantum uniquely ergodic if it possesses a quasimode of order zero which (i) has a singular limit, and (ii) is a linear combination of a uniformly bounded number of eigenfunctions (modulo an o(1) error). ... More

Towards Linearization Machine Learning AlgorithmsAug 14 2019This paper is about a machine learning approach based on the multilinear projection of an unknown function (or probability distribution) to be estimated towards a linear (or multilinear) dimensional space E'. The proposal transforms the problem of predicting ... More

Online Collective Animal Movement Activity RecognitionNov 22 2018Learning the activities of animals is important for the purpose of monitoring their welfare vis a vis their behaviour with respect to their environment and conspecifics. While previous works have largely focused on activity recognition in a single animal, ... More

Martingale-like sequences in Banach latticesFeb 04 2019Martingale-like sequences in vector lattice and Banach lattice frameworks are defined in the same way as martingales are defined in [Positivity 9 (2005), 437--456]. In these frameworks, a collection of bounded $X$-martingales is shown to be a Banach space ... More

Graded polynomial identities for matrices with the transpose involutionJun 02 2015Let $G$ be a group of order $k$. We consider the algebra $M_k(\mathbb{C})$ of $k$ by $k$ matrices over the complex numbers and view it as a crossed product with respect to $G$ by embedding $G$ in the symmetric group $S_k$ via the regular representation ... 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

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

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

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

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

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

Path abstractionJan 25 2017Given the set of paths through a digraph, the result of uniformly deleting some vertices and identifying others along each path is coherent in such a way as to yield the set of paths through another digraph, called a \emph{path abstraction} of the original ... 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

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

Functionally independent conservations laws in a quantum integrable modelMar 14 2013We study a recently proposed quantum integrable model defined on a lattice with N sites, with Fermions or Bosons populating each site, as a close relative of the well known spin-1/2 Gaudin model. This model has 2N arbitrary parameters, a linear dependence ... 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