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k-Means for Streaming and Distributed Big Sparse DataNov 29 2015Feb 07 2016We provide the first streaming algorithm for computing a provable approximation to the $k$-means of sparse Big data. Here, sparse Big Data is a set of $n$ vectors in $\mathbb{R}^d$, where each vector has $O(1)$ non-zeroes entries, and $d\geq n$. E.g., ... More

A Unified Framework for Approximating and Clustering DataJun 07 2011May 28 2016Given a set $F$ of $n$ positive functions over a ground set $X$, we consider the problem of computing $x^*$ that minimizes the expression $\sum_{f\in F}f(x)$, over $x\in X$. A typical application is \emph{shape fitting}, where we wish to approximate a ... More

k-Means Clustering of Lines for Big DataMar 16 2019Mar 19 2019The k-means for lines is a set of k centers (points) that minimizes the sum of squared distances to a given set of n lines in R^d. This is a straightforward generalization of the k-means problem where the input is a set of n points. Related problems minimize ... More

Generic Coreset for Scalable Learning of Monotonic Kernels: Logistic Regression, Sigmoid and moreFeb 21 2018Jun 10 2018Coreset (or core-set) in this paper is a small weighted \emph{subset} $Q$ of the input set $P$ with respect to a given \emph{monotonic} function $\phi:\REAL\to\REAL$ that \emph{provably} approximates its fitting loss $\sum_{p\in P}f(p\cdot x)$ to \emph{any} ... More

Aligning Points to Lines: Provable ApproximationsJul 23 2018Sep 09 2019We suggest a new optimization technique for minimizing the sum $\sum_{i=1}^n f_i(x)$ of $n$ non-convex real functions that satisfy a property that we call piecewise log-Lipschitz. This is by forging links between techniques in computational geometry, ... More

k-Means Clustering of Lines for Big DataMar 16 2019The k-means for lines is a set of k centers (points) that minimizes the sum of squared distances to a given set of n lines in R^d. This is a straightforward generalization of the k-means problem where the input is a set of n points. Related problems minimize ... More

Minimizing Sum of Non-Convex but Piecewise log-Lipschitz Functions using CoresetsJul 23 2018Oct 16 2018We suggest a new optimization technique for minimizing the sum $\sum_{i=1}^n f_i(x)$ of $n$ non-convex real functions that satisfy a property that we call piecewise log-Lipschitz. This is by forging links between techniques in computational geometry, ... More

Cylindric algebras of De Morgan-valued logicAug 31 2014We construct a De Morgan algebra-valued logic with quantifiers, where the truth values are in a finite De Morgan algebra, We show that there is a representation theorem of the cylindric algebra of this logic from which a completeness theorem for De Morgan ... More

Characterization theorems for $Q$-independent random variables with values in a locally compact Abelian groupMar 19 2017Let $X$ be a locally compact Abelian group, $Y$ be its character group. Following A. Kagan and G. Sz\'ekely we introduce a notion of $Q$-independence for random variables with values in $X$. We prove group analogues of the Cram\'er, Kac-Bernstein, Skitovich-Darmois ... More

On a generalisation of the Skitovich--Darmois theorem for several linear forms on Abelian groupsJul 30 2019Aug 02 2019A.M. Kagan introduced a class of distributions $\mathcal{D}_{m, k}$ in $\mathbb{R}^m$ and proved that if the joint distribution of $m$ linear forms of $n$ independent random variables belongs to the class $\mathcal{D}_{m, m-1}$, then the random variables ... More

Low-cost and Faster Tracking Systems Using Core-sets for Pose-EstimationNov 30 2015Jul 22 2016In the pose-estimation problem we need to align a set of $n$ markers (points in 3D space) and choose one of their n! permutations, so that the sum of squared corresponding distances to another ordered set of $n$ markers is minimized. We prove that every ... More

Provable Approximations for Constrained $\ell_p$ RegressionFeb 27 2019The $\ell_p$ linear regression problem is to minimize $f(x)=||Ax-b||_p$ over $x\in\mathbb{R}^d$, where $A\in\mathbb{R}^{n\times d}$, $b\in \mathbb{R}^n$, and $p>0$. To avoid overfitting and bound $||x||_2$, the constrained $\ell_p$ regression minimizes ... More

Real-Time EEG Classification via Coresets for BCI ApplicationsJan 02 2019A brain-computer interface (BCI) based on the motor imagery (MI) paradigm translates one's motor intention into a control signal by classifying the Electroencephalogram (EEG) signal of different tasks. However, most existing systems either (i) use a high-quality ... More

Turning Big data into tiny data: Constant-size coresets for k-means, PCA and projective clusteringJul 12 2018We develop and analyze a method to reduce the size of a very large set of data points in a high dimensional Euclidean space R d to a small set of weighted points such that the result of a predetermined data analysis task on the reduced set is approximately ... More

Coresets for Kinematic Data: From Theorems to Real-Time SystemsNov 30 2015Dec 18 2017A coreset (or core-set) of a dataset is its semantic compression with respect to a set of queries, such that querying the (small) coreset provably yields an approximate answer to querying the original (full) dataset. In the last decade, coresets provided ... More

Tight Sensitivity Bounds For Smaller CoresetsJul 02 2019An $\varepsilon$-coreset for Least-Mean-Squares (LMS) of a matrix $A\in{\mathbb{R}}^{n\times d}$ is a small weighted subset of its rows that approximates the sum of squared distances from its rows to every affine $k$-dimensional subspace of ${\mathbb{R}}^d$, ... More

Coresets for Gaussian Mixture Models of Any ShapeJun 12 2019An $\varepsilon$-coreset for a given set $D$ of $n$ points, is usually a small weighted set, such that querying the coreset \emph{provably} yields a $(1+\varepsilon)$-factor approximation to the original (full) dataset, for a given family of queries. ... More

New Frameworks for Offline and Streaming Coreset ConstructionsDec 02 2016Let $P$ be a set (called points), $Q$ be a set (called queries) and a function $ f:P\times Q\to [0,\infty)$ (called cost). For an error parameter $\epsilon>0$, a set $S\subseteq P$ with a \emph{weight function} $w:P \rightarrow [0,\infty)$ is an $\epsilon$-coreset ... More

Coresets for Vector Summarization with Applications to Network GraphsJun 17 2017We provide a deterministic data summarization algorithm that approximates the mean $\bar{p}=\frac{1}{n}\sum_{p\in P} p$ of a set $P$ of $n$ vectors in $\REAL^d$, by a weighted mean $\tilde{p}$ of a \emph{subset} of $O(1/\eps)$ vectors, i.e., independent ... More

Fast and Accurate Least-Mean-Squares SolversJun 11 2019Least-mean squares (LMS) solvers such as Linear / Ridge / Lasso-Regression, SVD and Elastic-Net not only solve fundamental machine learning problems, but are also the building blocks in a variety of other methods, such as decision trees and matrix factorizations. ... More

Secure Search on the Cloud via Coresets and SketchesAug 19 2017\emph{Secure Search} is the problem of retrieving from a database table (or any unsorted array) the records matching specified attributes, as in SQL SELECT queries, but where the database and the query are encrypted. Secure search has been the leading ... More

Dimensionality Reduction of Massive Sparse Datasets Using CoresetsMar 05 2015In this paper we present a practical solution with performance guarantees to the problem of dimensionality reduction for very large scale sparse matrices. We show applications of our approach to computing the low rank approximation (reduced SVD) of such ... More

Secure $k$-ish Nearest Neighbors ClassifierJan 22 2018Apr 30 2019In machine learning, classifiers are used to predict a class of a given query based on an existing (classified) database. Given a database S of n d-dimensional points and a d-dimensional query q, the k-nearest neighbors (kNN) classifier assigns q with ... More

Stability of Serrin's Problem and Dynamic Stability of a Model for Contact Angle MotionJul 21 2017Aug 24 2017We study the quantitative stability of Serrin's symmetry problem and it's connection with a dynamic model for contact angle motion of quasi-static capillary drops. We prove a new stability result which is both linear and depends only on a weak norm \[ ... More

Double-Sided Markets with Strategic Multi-dimensional PlayersMar 29 2016Nov 14 2016We consider mechanisms for markets that are double-sided and have players with multi-dimensional strategic spaces on at least one side. The players of the market are strategic, and act to optimize their own utilities. The mechanism designer, on the other ... More

Data-Dependent Coresets for Compressing Neural Networks with Applications to Generalization BoundsApr 15 2018Feb 20 2019We present an efficient coresets-based neural network compression algorithm that sparsifies the parameters of a trained fully-connected neural network in a manner that provably approximates the network's output. Our approach is based on an importance ... More

Training Gaussian Mixture Models at Scale via CoresetsMar 23 2017Jan 15 2018How can we train a statistical mixture model on a massive data set? In this work we show how to construct coresets for mixtures of Gaussians. A coreset is a weighted subset of the data, which guarantees that models fitting the coreset also provide a good ... More

On Activation Function Coresets for Network PruningJul 09 2019Model compression provides a means to efficiently deploy deep neural networks (DNNs) on devices that limited computation resources and tight power budgets, such as mobile and IoT (Internet of Things) devices. Consequently, model compression is one of ... More

Data-Dependent Coresets for Compressing Neural Networks with Applications to Generalization BoundsApr 15 2018May 18 2019We present an efficient coresets-based neural network compression algorithm that sparsifies the parameters of a trained fully-connected neural network in a manner that provably approximates the network's output. Our approach is based on an importance ... More

Double-Sided Markets with Strategic Multi-dimensional PlayersMar 29 2016Nov 10 2016We consider mechanisms for markets that are double-sided and have players with multi-dimensional strategic spaces on at least one side. The players of the market are strategic, and act to optimize their own utilities. The mechanism designer, on the other ... More

What could re-infection tell us about R0? a modeling case-study of syphilis transmissionMar 14 2019Many infectious diseases can lead to re-infection. We examined the relationship between the prevalence of repeat infection and the basic reproductive number (R0). First we solved a generic, deterministic compartmental model of re-infection to derive an ... More

Making a Sieve Random: Improved Semi-Streaming Algorithm for Submodular Maximization under a Cardinality ConstraintJun 26 2019In this paper we consider the problem of maximizing a non-negative submodular function subject to a cardinality constraint in the data stream model. Previously, the best known algorithm for this problem was a $5.828$-approximation semi-streaming algorithm ... More

On the Skitovich-Darmois theorem for some locally compact Abelian groupsMay 23 2018Let $X$ be a locally compact Abelian group, $\alpha_{j}, \beta_j$ be topological automorphisms of $X$. Let $\xi_1, \xi_2$ be independent random variables with values in $X$ and distributions $\mu_j$ with non-vanishing characteristic functions. It is known ... More

On a characterisation theorem for probability distributions on discrete Abelian groupsApr 11 2018Let $X$ be a countable discrete Abelian group containing no elements of order 2, $\alpha$ be an automorphism of $X$, $\xi_1$ and $\xi_2$ be independent random variables with values in the group $X$ and distributions $\mu_1$ and $\mu_2$. The main result ... More

Almost Optimal Semi-streaming Maximization for k-Extendible SystemsJun 11 2019In this paper we consider the problem of finding a maximum weight set subject to a $k$-extendible constraint in the data stream model. The only non-trivial algorithm known for this problem to date---to the best of our knowledge---is a semi-streaming $k^2(1 ... More

Constrained Submodular Maximization via a Non-symmetric TechniqueNov 10 2016The study of combinatorial optimization problems with a submodular objective has attracted much attention in recent years. Such problems are important in both theory and practice because their objective functions are very general. Obtaining further improvements ... More

Whittaker unitary dual of affine graded Hecke algebras of type EAug 29 2007Sep 22 2008This paper gives the classification of the Whittaker unitary dual for affine graded Hecke algebras of type E. By the Iwahori-Matsumoto involution, this is equivalent also to the classification of the spherical unitary dual for type E. This work completes ... More

Hermitian forms for affine Hecke algebrasDec 11 2013Mar 18 2015We study star operations for Iwahori-Hecke algebras and invariant hermitian forms for finite dimensional modules over (graded) affine Hecke algebras with a view towards a unitarity algorithm.

Generic unipotent standard modulesSep 29 2009Apr 19 2012Using Lusztig's geometric classification, we find the reducibility points of a standard module for the affine Hecke algebra, in the case when the inducing data is generic. This recovers the known result of Muic-Shahidi for representations of split p-adic ... More

Unitary equivalences for reductive p-adic groupsSep 28 2009Apr 07 2011We establish a transfer of unitarity for a Bernstein component of the category of smooth representations of a reductive p-adic group to the associated Hecke algebra, in the framework of the theory of types, whenever the Hecke algebra is an affine Hecke ... More

Global Solutions of Shock Reflection by Large-Angle Wedges for Potential FlowAug 19 2007When a plane shock hits a wedge head on, it experiences a reflection-diffraction process and then a self-similar reflected shock moves outward as the original shock moves forward in time. Experimental, computational, and asymptotic analysis has shown ... More

An empirical template library of stellar spectra for a wide range of spectral classes, luminosity classes, and metallicities using SDSS BOSS spectraFeb 22 2017Mar 22 2017We present a library of empirical stellar spectra created using spectra from the Sloan Digital Sky Survey's Baryon Oscillation Spectroscopic Survey (BOSS). The templates cover spectral types O5 through L3, are binned by metallicity from -2.0 dex through ... More

Compactifying normal algebraic spacesSep 18 2007Sep 20 2007The author wrote this note after being asked about the existence of compactifications of algebraic spaces. Subsequent to posting the article to the math arXiv, the author learned from Yutakaa Matsuura that the results of this paper had been proved by ... More

Supernova Rates in Galaxy ClustersJan 23 2005Measurements of SN rates in different environments and redshifts can shed light on the nature of SN-Ia progenitors, star formation history, and chemical enrichment history. I summarize some recent work by our group in this area, and discuss the implications. ... More

Limits on Dust in Rich Clusters of Galaxies from the Color of Background QuasarsAug 20 1995I measure the V-I color distribution of two samples of radio-selected quasars. Quasars from one sample are projected on the sky within 1 degree of a rich foreground Abell cluster of galaxies, while quasars from the other sample are more than 3 degrees ... More

On the fraction of intermediate-mass close binaries that explode as type-Ia supernovaeJul 31 2007Nov 09 2007Type-Ia supernovae (SNe-Ia) are thought to result from a thermonuclear runaway in white dwarfs (WDs) that approach the Chandrasekhar limit, either through accretion from a companion or a merger with another WD. I compile observational estimates of the ... More

Ultraviolet Imaging and Spectroscopy of LINERsDec 12 1995I review the UV properties of LINERs (low-ionization nuclear emission-line regions), based mostly on the recent {\it HST} UV imaging survey of nearby galaxies by Maoz et al. (1995). 25 of the galaxies in the northern subsample host a LINER nucleus. Six ... More

Factorization in color-suppressed B -> D(*)0 pi0 decays from the soft-collinear effective theoryNov 08 2004The soft-collinear effective theory has been recently applied to prove novel factorization theorems for many B decays. We describe here in some detail the factorization relation for color-supressed nonleptonic B -> D(*)0 pi0 decays and update the phenomenological ... More

Bound on $\cosα$ from exclusive weak radiative B decaysJun 28 2000We present a bound on the weak phase $\alpha$ from isospin-breaking effects in weak radiative decays, which requires the CP-averaged branching ratios for the weak radiative decays $B^\pm\to \rho^\pm \gamma$, $B^0\to \rho^0/\omega \gamma$, $B\to K^* \gamma$ ... More

Probing New Physics with b -> sγDecaysJul 08 2002In the Standard Model, the photon emitted in b->s\gamma decays is predicted to be left-handed polarized. We discuss the types of New Physics which can produce a deviation from this prediction, focusing on the Minimal Supersymmetric Standard Model. A new ... More

Bifurcation scenario to Nikolaevskii turbulence in small systemsApr 14 2005We show that the chaos in Kuramoto-Sivashinsky equation occurs through period-doubling cascade (Feigenbaum scenario), in contrast, the chaos in Nikolaevskii equation occurs through torus-doubling bifurcation (Ruelle-Takens-Newhouse scenario).

Formation of Li I lines in photospheric granulationAug 21 1997Aug 27 1997The possibility of significant systematic errors due to the use of 1D homogeneous atmospheres in lithium-abundance determinations of cool stars motivates a study of non-local-thermodynamic-equilibrium (NLTE) effects on Li I line formation in a 3D solar-granulation ... More

A NLTE study of neutral boron in solar-type starsJan 12 1994The formation of the resonance lines of neutral boron in solar-type stellar atmospheres is investigated taking into account effects of departures from local thermodynamic equilibrium (NLTE effects). The latter are due to a combination of overionisation ... More

Thompson's Group F and Uniformly Finite HomologyJun 17 2008Mar 11 2009This paper demonstrates the uniformly finite homology developed by Block and Weinberger and its relationship to amenable spaces via applications to the Cayley graph of Thompson's Group F. In particular, a certain class of subgraph of F is shown to be ... More

Semiconductor ThermistorsMar 10 2005Semiconductor thermistors operating in the variable range hopping conduction regime have been used in thermal detectors of all kinds for more than fifty years. Their use in sensitive bolometers for infrared astronomy was a highly developed empirical art ... More

New invariants for a real valued and angle valued map (an Alternative to Morse- Novikov theory)May 24 2016This paper but section 6 is essentially my lecture at The Eighth Congress of Romanian Mathematicians, June 26 - July 1, 2015, Iasi, Romania. The paper summarizes the definitions and the properties of the invariants associated to a real or an angle valued ... More

Renormalization group flow, Entropy and EigenvaluesApr 07 2016The irreversibility of the renormalization group flow is conjectured to be closely related to the concept of entropy. In this paper, the variation of eigenvalues under the renormalization group flow will be studied. Based on the one-loop approximation ... More

On representations attached to generic level p Harder congruencesMay 11 2016We investigate the interplay between Galois and automorphic representations coming from generic Harder type congruences for degree 2 Siegel modular forms. Using Local Langlands results for GSp4 we see conditions that guarantee the existence of a level ... More

Deriving Z[J] from the time evolution operatorMay 30 2014An important quantity in quantum field theory is the vacuum-to-vacuum transition amplitude in the presence of an external source. This quantity is often designated by Z[J] and is the generator for the n-point Greens functions. In textbooks Z[J] is often ... More

Quantum source-channel coding and non-commutative graph theoryMay 20 2014Oct 18 2015Alice and Bob receive a bipartite state (possibly entangled) from some finite collection or from some subspace. Alice sends a message to Bob through a noisy quantum channel such that Bob may determine the initial state, with zero chance of error. This ... More

An uncountable set of tiling spaces with distinct cohomologyNov 18 2014We generalise the notion of a Barge-Diamond complex, in the one-dimensional case, to a mixed system of tiling substitutions. This gives a way of describing the associated tiling space as an inverse limit of Barge-Diamond complexes. We give an effective ... More

Gödel for Goldilocks: A Rigorous, Streamlined Proof of (a variant of) Gödel's First Incompleteness TheoremSep 21 2014Nov 19 2014Most discussions of G\"odel's theorems fall into one of two types: either they emphasize perceived philosophical, cultural "meanings" of the theorems, and perhaps sketch some of the ideas of the proofs, usually relating G\"odel's proofs to riddles and ... More

Remarks on profinite groups having few open subgroupsApr 14 2013May 06 2013Examples are given of profinite groups that are not strongly complete, and have other `bad' properties, yet have only finitely many open subgroups of each finite index. It is shown that a profinite group with the latter property must be finite if it has ... More

Noncommutative Chern-Simons theory on the quantum 3-sphere $S^3_θ$Oct 27 2013Oct 11 2016We consider the $\theta$-deformed quantum three sphere $S^3_\theta$ and study its Chern--Simons theory from a spectral point of view. We first construct a spectral triple on $S^3_\theta$ as a generalization of the Dirac geometry on $S^3 $. Since the choice ... More

No Unwanted Universally Baire MorphismsAug 26 2015We show that the usual proof that there are no morphisms (in the sense of cardinal characteristics), whose constituent maps are Borel, between certain challenge-response relations generalizes to show that there are no morphisms whose constituent maps ... More

Why do non-gauge invariant terms appear in the vacuum polarization tensor?Jul 21 2015It is will known that quantum field theory at the formal level is gauge invariant. However a calculation of the vacuum polarization tensor will include non-gauge invariant terms. These terms must be removed from the calculation in order to get a physically ... More

Disjoint Borel FunctionsAug 19 2014Mar 21 2016For each $a \in {^\omega \omega}$, we define a Baire class one function $f_a : {^\omega \omega} \to {^\omega \omega}$ which encodes $a$ in a certain sense. We show that for each Borel $g : {^\omega \omega} \to {^\omega \omega}$, $f_a \cap g = \emptyset$ ... More

Evenly Divisible Rational Approximations of Quadratic IrrationalitiesDec 01 2016In a recent paper of Blomer, Bourgain, Radziwi\l\l\ and Rudnick, the authors proved the existence of small gaps between eigenvalues of the Laplacian in a rectangular billiard with sides $\pi$ and $\pi/\sqrt\alpha$, i.e. numbers of the form $\alpha m^2+ ... More

TASI 2008 Lectures on Dark MatterJan 26 2009Based on lectures given at the 2008 Theoretical Advanced Study Institute (TASI), I review here some aspects of the phenomenology of particle dark matter, including the process of thermal freeze-out in the early universe, and the direct and indirect detection ... More

The Empirical Case For 10 GeV Dark MatterJan 05 2012In this article, I summarize and discuss the body of evidence which has accumulated in favor of dark matter in the form of approximately 10 GeV particles. This evidence includes the spectrum and angular distribution of gamma rays from the Galactic Center, ... More

Indirect Searches For Dark Matter: Signals, Hints and OtherwiseOct 10 2007For the SUSY 2007 conference, I was asked to review the topic of indirect searches for dark matter. As part of that talk, I summarized several observations which have been interpreted as the product of dark matter annihilations. In my contribution to ... More

A Formal Approach to Modeling the Memory of a Living OrganismMar 19 2010We consider a living organism as an observer of the evolution of its environment recording sensory information about the state space X of the environment in real time. Sensory information is sampled and then processed on two levels. On the biological ... More

Orthogonal polynomial expansions for the Riemann xi functionFeb 17 2019Mar 05 2019We study infinite series expansions for the Riemann xi function $\Xi(t)$ in three specific families of orthogonal polynomials: (1) the Hermite polynomials; (2) the symmetric Meixner-Pollaczek polynomials $P_n^{(3/4)}(x;\pi/2)$; and (3) the continuous ... More

Approximately Reachable Directions for Piecewise Linear Switched SystemsJul 06 2018Oct 26 2018This paper deals with some reachability issues for piecewise linear switched systems with time-dependent coefficients and multiplicative noise. Namely, it aims at characterizing data that are almost reachable at some fixed time T > 0 (belong to the closure ... More

Poloids from the Points of View of Partial Transformations and Category TheoryOct 12 2017Aug 03 2018Monoids and groupoids are examples of poloids. On the one hand, poloids can be regarded as one-sorted categories; on the other hand, poloids can be represented by partial magmas of partial transformations. In this article, poloids are considered from ... More

Euler-Mahonian polynomials for C_a \wr S_nDec 05 2004In a recent paper, Regev and Roichman introduced the <_L order and the L-descent number statistic, des_L, on the group of colored permutations, C_a \wr S_n. Here we define the L-reverse major index statistic, rmaj_L, on the same group and study the distribution ... More

The conservation of mass-moment parametersFeb 16 2007In this paper we study a concept of mass-moment parameter which is the generalization of the mass and the moments of inertia of a continuous media. We shall present some interesting kinematical results in the hypothesis that a set of mass-moment parameters ... More

The Angular Momentum-Energy SpaceFeb 09 2007In this paper we shall define and study the angular momentum-energy space for the classical problem of plane-motions of a particle situated in a potential field of a central force. We shall present the angular momentum-energy space for some important ... More

Hyperbolic tessellations associated to Bianchi groupsAug 12 2009Oct 20 2009Let F/Q be number field. The space of positive definite binary Hermitian forms over F form an open cone in a real vector space. There is a natural decomposition of this cone into subcones, which descend give rise to hyperbolic tessellations of 3-dimensional ... More

Alternative to Morse-Novikov Theory for closed 1-form (I)Mar 01 2019Aug 01 2019This paper extends the Alternative to Morse-Novikov Theory we have proposed in [1] from real- and angle-valued map to closed 1-forms. For a topological closed 1-form on a compact ANR, a concept generalizing closed differential 1-form on a compact manifold, ... More

A refinement of Betti numbers and homology in the presence of a continuous function II (the case of an angle valued map)Mar 06 2016Mar 24 2018For a continuous angle-valued map defined on a compact ANR, a fixed field and any degree one proposes a refinement of the Novikov-Betti number and of the Novikov homology of the pair consisting of the ANR and the degree one integral cohomology class represented ... More

Dirt, Gravity, and Lunar-Based Telescopes: The Value Proposition for AstronomyFeb 16 2007The lunar surface has historically been considered an optimal site for a broad range of astronomical telescopes. That assumption, which has come to be somewhat reflexive, is critically examined in this paper and found to be poorly substantiated. The value ... More

Polynomial maps with nilpotent Jacobians in dimension three IIOct 08 2017In the paper, we first classify all polynomial maps of the form $H=(u(x,y),v(x,y,z), h(x,y))$ in the case that $JH$ is nilpotent and $(\deg_yu,\deg_yh)\leq 3$, $H(0)=0$. Then we classify all polynomial maps of the form $H=(u(x,y,z),v(x,y,u), h(x,y))$ ... More

Spectral Flexibility of Symplectic Manifolds T^2 x MAug 07 2005Oct 11 2007We consider Riemannian metrics compatible with the natural symplectic structure on T^2 x M, where T^2 is a symplectic 2-Torus and M is a closed symplectic manifold. To each such metric we attach the corresponding Laplacian and consider its first positive ... More

On the existence of spines for Q-rank 1 groupsJan 04 2006Let X=Gamma\G/K be an arithmetic quotient of a symmetric space of non-compact type. In the case that G has Q-rank 1, we construct Gamma-equivariant deformation retractions of D=G/K onto a set D_0. We prove that D_0 is a spine, having dimension equal to ... More

Singularities of the Hilbert scheme of non-reduced curvesNov 09 2016Jun 19 2018In this article, we study the Hilbert scheme of generically non-reduced curves in $\mathbb{P}^3$. We prove the existence of generically non-reduced curves in $\mathbb{P}^3$ for which there exist infinitesimal deformations of the curve that do not induce ... More

Asymmetric anisotropic fractional Sobolev normsOct 22 2014Bourgain, Brezis & Mironescu showed that (with suitable scaling) the fractional Sobolev $s$-seminorm of a function $f\in W^{1,p}(\mathbb{R}^n)$ converges to the Sobolev seminorm of $f$ as $s\rightarrow1^-$. Ludwig introduced the anisotropic fractional ... More

The geometry of ambiguity in one-dimensional phase retrievalNov 16 2018We consider the geometry associated to the ambiguities of the one-dimensional Fourier phase retrieval problem for vectors in ${\mathbb C}^{N+1}$. Our first result states that the space of signals has a finite covering (which we call the root covering) ... More

Asymptotics of orthogonal polynomials and the Painlevé transcendentsAug 16 2016Sep 14 2016In this survey, we review asymptotic results of some orthogonal polynomials which are relate to the Painlev\'e transcendents. They are obtained by applying Deift-Zhou's nonlinear steepest descent method for Riemann-Hilbert problems. In the last part of ... More

A Gauss-Kuzmin theorem for continued fractions associated with non-positive interger powers of an integer $m \geq 2$Sep 18 2013We consider a family $\{\tau_m:m\geq 2\}$ of interval maps introduced by Hei-Chi Chan [5] as generalizations of the Gauss transformation. For the continued fraction expansion arising from $\tau_m$, we solve its Gauss-Kuzmin-type problem by applying the ... More

A Remark on Recent Lower Bounds for Nodal SetsOct 21 2010Nov 01 2010Recently, Sogge-Zelditch and Colding-Minicozzi gave new power law lower bounds on the size of the nodal sets of eigenfunctions. The purpose of this short note is to point out a third method to obtain a power law lower bound on the volume of the nodal ... More

Connectivity patterns in loop percolation I: the rationality phenomenon and constant term identitiesMar 25 2013Oct 02 2013Loop percolation, also known as the dense O(1) loop model, is a variant of critical bond percolation in the square lattice Z^2 whose graph structure consists of a disjoint union of cycles. We study its connectivity pattern, which is a random noncrossing ... More

Multiplicity matrices for the affine graded Hecke algebraJan 09 2008In this paper, we look at the problem of determining the composition factors for the affine graded Hecke algebra via the computation of Kazhdan-Lusztig type polynomials. We review the algorithms of \cite{L1,L2}, and use them in particular to compute, ... More

Long-run growth rate in a random multiplicative modelMar 07 2015We consider the long-run growth rate of the average value of a random multiplicative process $x_{i+1} = a_i x_i$ where the multipliers $a_i=1+\rho\exp(\sigma W_i - \frac12 \sigma^2 t_i)$ have Markovian dependence given by the exponential of a standard ... More

The Ricci flow does not preserve the set of Zoll metricsSep 16 2008The question of whether or not the set of Zoll metrics on the 2-sphere is connected is still open. Here we show that a naive application of the Ricci flow is not sufficient to answer this problem.

The autocorrelation of the Möbius function and Chowla's conjecture for the rational function field in characteristic 2Sep 12 2014We prove a function field version of Chowla's conjecture on the autocorrelation of the M\"obius function in the limit of a large finite field of characteristic 2.

Quantum interference as a resource for quantum speedupMay 09 2013Aug 01 2014Quantum states can in a sense be thought of as generalizations of classical probability distributions, but are more powerful than probability distributions when used for computation or communication. Quantum speedup therefore requires some feature of ... More

Genus 2 paramodular Eisenstein congruencesMar 23 2016Sep 23 2016We investigate certain Eisenstein congruences, as predicted by Harder, for level p paramodular forms of genus 2. We use algebraic modular forms to generate new evidence for the conjecture. In doing this we see explicit computational algorithms that generate ... More

Persistent Phylogeny: A Galled-Tree and Integer Linear Programming ApproachJun 01 2015The Persistent-Phylogeny Model is an extension of the widely studied Perfect-Phylogeny Model, encompassing a broader range of evolutionary phenomena. Biological and algorithmic questions concerning persistent phylogeny have been intensely investigated ... More

The tautological ring of the space of pointed genus two curves of compact typeOct 28 2013Nov 25 2014We prove that the tautological ring of $M_{2,n}^{ct}$, the moduli space of n-pointed genus two curves of compact type, does not have Poincar\'e duality for any $n \geq 8$. This result is obtained via a more general study of the cohomology groups of $M_{2,n}^{ct}$. ... More