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Counting multi-quadratic number fields of bounded discriminantFeb 08 2019We prove an asymptotic formula for the number of multi-quadratic number fields of bounded discriminant with a power-saving error term. Furthermore, we explicitly calculate the leading coefficient and extend our result to totally real multi-quadratic number ... More

Measuring the knowledge base of regional innovation systems in Germany in terms of a Triple Helix dynamicsNov 17 2009The interaction among the three sub-dynamics of economic exchange, technological innovation, and institutional control can be captured with a generalized Triple Helix model. We propose to use the information contained in the configuration among the three ... More

Cohomology of a Quaternionic ComplexJul 18 1995We investigate the cohomology of a certain elliptic complex defined on a compact quaternionic-K\"{a}hler manifold with negative scalar curvature. We show that this particular complex is exact, with the possible exception of one term.

Birkhoff's theorem in Lovelock gravityMay 03 2005We show that the generic solutions of the Lovelock equations with spherical, planar or hyperbolic symmetry are locally isometric to the corresponding static Lovelock black hole. As a consequence, these solutions are locally static: they admit an additional ... More

A strong form of the quantitative Wulff inequalityMar 23 2015Mar 26 2016Quantitative isoperimetric inequalities for anisotropic surface energies are shown where the isoperimetric deficit controls both the Fraenkel asymmetry and a measure of the oscillation of the boundary with respect to the boundary of the corresponding ... More

Decay of currents for strong interactionsMar 25 2011Jul 26 2011The decay of current autocorrelation functions is investigated for quantum systems featuring strong 'interactions'. Here, the term interaction refers to that part of the Hamiltonian causing the (major) decay of the current. On the time scale before the ... More

Reassessment of the GZK cutoff in the spectrum of UHE cosmic rays in a universe with low photon-baryon ratioSep 29 2003A prediction of standard Big Bang cosmology is that the observed UHECR (ultra-high-energy cosmic rays) spectrum will exhibit a cutoff at the GKZ limit, resulting from interaction with the photons that constitute the cosmic microwave background. We show ... More

The Planetary Nebula Luminosity FunctionJul 14 2004The [O III] 5007 planetary nebula luminosity function (PNLF) occupies an important place on the extragalactic distance ladder: it is the only standard candle that can be applied to all the large galaxies of the Local Supercluster. We review the method's ... More

The Planetary Nebula Luminosity Function: Pieces of the PuzzleSep 24 2009Extragalactic surveys in the emission line of [O III] 5007 have provided us with the absolute line strengths of large, homogeneous sets of planetary nebulae. These data have been used to address a host of problems, from the measurement of the extragalactic ... More

Inhomogeneous Parabolic Neumann ProblemsAug 31 2011We study second order parabolic equations on Lipschitz domains subject to inhomogeneous Neumann (or, more generally, Robin) boundary conditions. We prove existence and uniqueness of weak solutions and their continuity up to the boundary of the parabolic ... More

QCD Sum Rule Studies of Heavy Quarkonium-like StatesJul 08 2014The research presented here uses QCD sum rules (QSR) to study exotic hadrons. There are several themes in this work. First is the use of QSR to predict the masses of exotic hadrons that may exist among the heavy quarkonium-like states. The second theme ... More

Geometry of arithmetically Gorenstein curves in ${\mathbb P}^4$Jan 15 2003We characterize the postulation character of arithmetically Gorenstein curves in ${\mathbb P}^4$. We give conditions under which the curve can be realized in the form $mH-K$ on some ACM surface. Finally, we strengthen a theorem of Watanabe by showing ... More

The Bernstein-Sato b-Function of the Space of Cyclic PairsMar 03 2014Jan 09 2015We compute the Bernstein-Sato polynomial of $f$, a function which given a pair $(M,v)$ in $X = M_n(\mathbf{C}) \times \mathbf{C}^n$ tests whether $v$ is a cyclic vector for $M$. The proof includes a description of shift operators corresponding to the ... More

Conference matrices and unimodular latticesJul 19 2000Conference matrices are used to define complex structures on real vector spaces. Certain lattices in these spaces become modules for rings of quadratic integers. Multiplication of these lattices by non-principal ideals yields simple constructions of further ... More

Algebraic TopologyApr 30 2013Sep 10 2013The chapter provides an introduction to the basic concepts of Algebraic Topology with an emphasis on motivation from applications in the physical sciences. It finishes with a brief review of computational work in algebraic topology, including persistent ... More

QPEL: Quantum Program and Effect LanguageDec 30 2014We present the syntax and rules of deduction of QPEL (Quantum Program and Effect Language), a language for describing both quantum programs, and properties of quantum programs - effects on the appropriate Hilbert space. We show how semantics may be given ... More

Drift-Diffusion in Mangled Worlds Quantum MechanicsMar 18 2003Mar 18 2003In Everett's many worlds interpretation, where quantum measurements are seen as decoherence events, inexact decoherence may let large worlds mangle the memories of observers in small worlds, creating a cutoff in observable world size. I solve a growth-drift-diffusion-absorption ... More

Generalized Divisors and BiliaisonJan 15 2003Nov 29 2006We extend the theory of generalized divisors so as to work on any scheme $X$ satisfying the condition $S_2$ of Serre. We define a generalized notion of Gorenstein biliaison for schemes in projective space. With this we give a new proof in a stronger form ... More

Homotopy Bott-Taubes integrals and the Taylor tower for spaces of knots and linksFeb 11 2011Jun 02 2015This work continues the study of a homotopy-theoretic construction of the author inspired by the Bott-Taubes integrals. Bott and Taubes constructed knot invariants by integrating differential forms along the fiber of a bundle over the space of knots. ... More

A homotopy-theoretic view of Bott-Taubes integrals and knot spacesOct 10 2008We construct cohomology classes in the space of knots by considering a bundle over this space and "integrating along the fiber" classes coming from the cohomology of configuration spaces using a Pontrjagin-Thom construction. The bundle we consider is ... More

A Shuffle that Mixes Sets of any Fixed Size much Faster than it Mixes the Whole DeckApr 02 2004Consider an n by n array of cards shuffled in the following manner. An element x of the array is chosen uniformly at random; Then with probability 1/2 the rectangle of cards above and to the left of x is rotated 180 degrees, and with probability 1/2 the ... More

Atmospheric heat redistribution and collapse on tidally locked rocky planetsDec 17 2014Atmospheric collapse is likely to be of fundamental importance to tidally locked rocky exoplanets but remains understudied. Here, general results on the heat transport and stability of tidally locked terrestrial-type atmospheres are reported. First, the ... More

Anomalous photon noise levels predicted for CMB measurements made by the Planck satellite missionMay 21 2009A fundamental assumption inherent in the standard Lambda+CDM Hot Big Bang (HBB) model is that photons lose energy as they are redshifted due to the expansion of the universe. We show that for the Quasi-Static Universe (QSU) model, in which photon energy ... More

Scale invariant gravity and the quasi-static universeMar 19 2002Apr 13 2002We highlight the fact that the lack of scale invariance in the gravitational field equations of General Relativity results from the underlying assumption that the appropriate scale for the gravitational force should be linked to the atomic scale. We show ... More

Machian General Relativity: a possible solution to the Dark Energy problem, and a replacement for Big Bang cosmologyJun 04 2001Jun 17 2001Observations of an apparent acceleration in the expansion rate of the universe, derived from measurements of high-redshift supernovae, have been used to support the hypothesis that the universe is permeated by some form of dark energy. We show that an ... More

Planetary Nebulae as Probes of Stellar PopulationsMay 02 2006Planetary nebulae (PNe) have the potential to revolutionize our understanding of extragalactic stellar populations. Indeed, in many systems, bright PNe are the only individual objects identifiable from the ground, and, even more often, they are the only ... More

Quantum and classical dynamics of methane scatteringJun 05 2001The dissociation of methane on transition metals is an important reaction in catalysis. It is the rate limiting step in steam reforming to produce syngas. Molecular beam experiments have shown that the energy in the internal vibrations are about as effective ... More

Liaison with Cohen-Macaulay ModulesDec 05 2005We describe some recent work concerning Gorenstein liaison of codimension two subschemes of a projective variety. Applications make use of the algebraic theory of maximal Cohen-Macaulay modules, which we review in an Appendix.

Fast rate of convergence in high dimensional linear discriminant analysisSep 11 2009Feb 19 2010This paper gives a theoretical analysis of high dimensional linear discrimination of Gaussian data. We study the excess risk of linear discriminant rules. We emphasis on the poor performances of standard procedures in the case when dimension p is larger ... More

Lambda DeterminantsApr 27 2013In this paper we prove a homogenous generalization of the lambda determinant formula of Mills, Robbins and Rumsey. In our formula the parameters depends on two indices. Our result also extends a recent formula of Di Francesco.

Linear Logic without UnitsMay 09 2013We study categorical models for the unitless fragment of multiplicative linear logic. We find that the appropriate notion of model is a special kind of promonoidal category. Since the theory of promonoidal categories has not been developed very thoroughly, ... More

Quantum Multiple ScatteringMar 12 2010The quest for Anderson localization of light is at the center of many experimental and the- oretical activities. Atomic vapors play a particular role in this research field, as they show a number of specific properties which makes them quite different ... More

Distances from Planetary NebulaeJan 15 2003The [O III] 5007 planetary nebula luminosity function (PNLF) occupies an important place on the extragalactic distance ladder. Since it is the only method that is applicable to all the large galaxies of the Local Supercluster, it is uniquely useful for ... More

Approximation of the Semigroup generated by the Robin Laplacian in terms of the Gaussian SemigroupJul 09 2008For smooth bounded open sets in euclidean space, we construct corresponding contractive linear extension operators for the space of continuous functions which preserve regularity of functions in the domain of the Robin Laplacian. We also prove a Trotter-like ... More

Causal Models for Estimating the Effects of Weight Gain on MortalityFeb 04 2008Suppose, contrary to fact, in 1950, we had put the cohort of 18 year old non-smoking American men on a stringent mandatory diet that guaranteed that no one would ever weigh more than their baseline weight established at age 18. How would the counter-factual ... More

A note on the implicit function theorem for quasi-linear eigenvalue problemsSep 23 2011We consider the quasi-linear eigenvalue problem $-\Delta_p u = \lambda g(u)$ subject to Dirichlet boundary conditions on a bounded open set $\Omega$, where $g$ is a locally Lipschitz continuous functions. Imposing no further conditions on $\Omega$ or ... More

The International Epsilon Aurigae Campaign 2009-2011. A description of the campaign and early results to May 2010Jan 07 2011In early 2009, immediately following the end of the WR140 periastron campaign (see these proceedings), I turned my telescope back to epsilon Aurigae in time for the start of the eclipse. As well as being an interesting object in its own right, the Pro-Am ... More

Some Comments on Multiple Discovery in MathematicsDec 11 2014Among perhaps many things common to Kuratowski's Theorem in graph theory, Reidemeister's Theorem in topology, and Cook's Theorem in theoretical computer science is this: all belong to the phenomenon of simultaneous discovery in mathematics. We are interested ... More

N-Gram Cluster Identification During Empirical Knowledge Representation GenerationDec 05 1994This paper presents an overview of current research concerning knowledge extraction from technical texts. In particular, the use of empirical techniques during the identification and generation of a semantic representation is considered. A key step is ... More

Combinatorial proofs of q-series identitiesSep 03 2001We provide combinatorial proofs of some of the q-series identities considered by Andrews, Jimenez-Urroz and Ono [q-series identities and values of certain $L$-functions. Duke Math. J. 108 (2001), no. 3, 395--419].

PL3: Structure FunctionsJan 14 1998Recent measurements of unpolarised and polarised nucleon structure functions and F_2(gamma) are reviewed. The implications for QCD and the gluon momentum distribution are discussed. The status of the understanding of the total virtual-photon proton total ... More

Risk bounds for purely uniformly random forestsJun 15 2010Random forests, introduced by Leo Breiman in 2001, are a very effective statistical method. The complex mechanism of the method makes theoretical analysis difficult. Therefore, a simplified version of random forests, called purely random forests, which ... More

Experiments with Gorenstein LiaisonJun 28 2001We give some experimental data of Gorenstein liaison, working with points in ${\mathbb P}^3$ and curves in ${\mathbb P}^4$, to see how far the familiar situation of liaison, biliaison, and Rao modules of curves in ${\mathbb P}^3$ will extend to subvarieties ... More

Enumeration of Cylindric Plane Partitions - part IApr 20 2012Cylindric plane partitions may be thought of as a natural generalization of reverse plane partitions. A generating series for the enumeration of cylindric plane partitions was recently given by Borodin. The first result of this paper is a $(q,t)$-analog ... More

Super-KMS functionals for graded-local conformal netsApr 23 2012Jul 16 2014Motivated by a few preceding papers and a question of R. Longo, we introduce super-KMS functionals for graded translation-covariant nets over R with superderivations, roughly speaking as a certain supersymmetric modification of classical KMS states on ... More

Periodic points of quadratic polynomials in Galois extensionsOct 04 2016Oct 13 2016For quadratic polynomials with coefficients in a field $k$ of characteristic zero, we seek to understand the periodic points under the actions of its iteration and the absolute Galois group $\mathrm{Gal}(\bar{k}/k)$. Supported by previous numerical work, ... More

A-infinity resolutions and the Golod property for monomial ringsDec 08 2016Let R=S/I be a monomial ring whose minimal free resolution F is rooted. We describe an A-infinity algebra structure on F. Using this structure, we show that R is Golod if and only if the product on Tor^S(R,k) vanishes. Furthermore, we give a necessary ... More

Rational Shi tableaux and the skew length statisticDec 14 2015Sep 15 2016We define two refinements of the skew length statistic on simultaneous core partitions. The first one relies on hook lengths and is used to prove a refined version of the theorem stating that the skew length is invariant under conjugation of the core. ... More

Tree-indexed processesApr 05 2004This article examines a recent body of work on stochastic processes indexed by a tree. Emphasis is on the application of this new framework to existing probability models. Proofs are largely omitted, with references provided.

Tackling the Minimal Superpermutation ProblemAug 21 2014A superpermutation on $n$ symbols is a string that contains each of the $n!$ permutations of the $n$ symbols as a contiguous substring. The shortest superpermutation on $n$ symbols was conjectured to have length $\sum_{i=1}^n i!$. The conjecture had been ... More

The Planetary Nebula Luminosity Function at the Dawn of GaiaMar 25 2012The [O III] 5007 Planetary Nebula Luminosity Function (PNLF) is an excellent extragalactic standard candle. In theory, the PNLF method should not work at all, since the luminosities of the brightest planetary nebulae (PNe) should be highly sensitive to ... More

On the Banach-Mazur Type for Normed SpacesDec 11 2008Jan 05 2009In order to measure qualitative properties we introduce a notion of a type for arbitrary normed spaces which measures the worst possible growth of partial sums of sequences weakly converging to zero. The ideas can be traced back to Banach and Mazur who ... More

Semantic Enhancement of Lecture MaterialDec 09 2014Today's lectures are often talks following a straight line of slides. In many lectures the process of content teaching is not as efficient as it could be. Technologies, such as smart-phones and wireless communication, enable a new level of interaction ... More

Clifford Index of ACM Curves in ${\mathbb P}^3$Apr 27 2001In this paper we review the notions of gonality and Clifford index of an abstract curve. For a curve embedded in a projective space, we investigate the connection between the \ci of the curve and the \gc al properties of its \emb. In particular if $C$ ... More

Local-entire cyclic cocycles for graded quantum field netsJun 26 2013Feb 17 2014In a recent paper we studied general properties of super-KMS functionals on graded quantum dynamical systems coming from graded translation-covariant quantum field nets over R, and we carried out a detailed analysis of these objects on certain models ... More

Spin-flipping with Holmium: Case study of proximity effect in superconductor/ferromagnet/superconductor heterostructuresApr 03 2015Superconductor/ferromagnet/superconductor heterostructures exhibit a so-called long-range proximity effect provided some layers of conical magnet Holmium are included in the respective interface regions. The Ho layers lead to a spin-flip process at the ... More

Proximity effect in superconductor/conical magnet/ferromagnet heterostructuresNov 13 2013At the interface between a superconductor and a ferromagnetic metal spin-singlet Cooper pairs can penetrate into the ferromagnetic part of the heterostructure with an oscillating and decaying spin-singlet Cooper pair density. However, if the interface ... More

Spin transport in the XXZ model at high temperatures: Classical dynamics versus quantum S=1/2 autocorrelationsOct 30 2011Feb 14 2012The transport of magnetization is analyzed for the classical Heisenberg chain at and especially above the isotropic point. To this end, the Hamiltonian equations of motion are solved numerically for initial states realizing harmonic-like magnetization ... More

High dimensional gaussian classificationJun 04 2008Jul 10 2008High dimensional data analysis is known to be as a challenging problem. In this article, we give a theoretical analysis of high dimensional classification of Gaussian data which relies on a geometrical analysis of the error measure. It links a problem ... More

Self-gravitating branes of codimension 4 in Lovelock gravityJan 15 2008We construct a familly of exact solutions of Lovelock equations describing codimension four branes with discrete symmetry in the transverse space. Unlike what is known from pure Einstein gravity, where such brane solutions of higher codimension are singular, ... More

The Climate of Early MarsJun 09 2016The nature of the early Martian climate is one of the major unanswered questions of planetary science. Key challenges remain, but a new wave of orbital and in situ observations and improvements in climate modeling have led to significant advances over ... More

Nearly optimal separations between communication (or query) complexity and partitionsDec 03 2015We show a nearly quadratic separation between deterministic communication complexity and the logarithm of the partition number, which is essentially optimal. This improves upon a recent power 1.5 separation of G\"o\"os, Pitassi, and Watson (FOCS 2015). ... More

An optimal quantum algorithm for the oracle identification problemNov 29 2013Jan 06 2014In the oracle identification problem, we are given oracle access to an unknown N-bit string x promised to belong to a known set C of size M and our task is to identify x. We present a quantum algorithm for the problem that is optimal in its dependence ... More

Finite Products are Biproducts in a Compact Closed CategoryApr 25 2006May 02 2007If a compact closed category has finite products or finite coproducts then it in fact has finite biproducts, and so is semi-additive.

Some Examples of Gorenstein Liaison in Codimension ThreeMar 22 2001Oct 02 2001Gorenstein liaison seems to be the natural notion to generalize to higher codimension the well-known results about liaison of varieties of codimension~2 in projective space. In this paper we study points in ${\mathbb P}^3$ and curves in ${\mathbb P}^4$ ... More

Towards a theory of negative dependenceApr 05 2004The FKG theorem says that the POSITIVE LATTICE CONDITION, an easily checkable hypothesis which holds for many natural families of events, implies POSITIVE ASSOCIATION, a very useful property. Thus there is a natural and useful theory of positively dependent ... More

Symmetric Graphs and their QuotientsJun 20 2013In this expository paper we describe a group theoretic characterization of arc-transitive graphs and their quotients. When passing from a symmetric graph to its quotient, much information is lost, but some of this information may be recovered from a certain ... More

Betti number signatures of homogeneous Poisson point processesSep 22 2006The Betti numbers are fundamental topological quantities that describe the k-dimensional connectivity of an object: B_0 is the number of connected components and B_k effectively counts the number of k-dimensional holes. Although they are appealing natural ... More

The Milnor triple-linking number of string links by cut-and-paste topologySep 27 2012Oct 29 2013Bott and Taubes constructed knot invariants by integrating differential forms along the fiber of a bundle over the space of knots, generalizing the Gauss linking integral. Their techniques were later used to construct real cohomology classes in spaces ... More

Bott-Taubes/Vassiliev cohomology classes by cut-and-paste topologyDec 21 2015Jun 26 2016Bott and Taubes used integrals over configuration spaces to produce finite-type (a.k.a. Vassiliev) knot invariants. Their techniques were then used to construct "Vassiliev classes" in the real cohomology spaces of knots and links in higher-dimensional ... More

Symmetry properties of the Novelli-Pak-Stoyanovskii algorithmMar 20 2014The number of standard Young tableaux of a fixed shape is famously given by the hook-length formula due to Frame, Robinson and Thrall. A bijective proof of Novelli, Pak and Stoyanovskii relies on a sorting algorithm akin to jeu-de-taquin which transforms ... More

Structural phase transitions in Pr$_{1-x}$La$_{x}$AlO$_{3}$: Heat capacity and x-ray scattering studiesMay 16 2014Structural phase transitions in Pr$_{1-x}$La$_x$AlO$_3$ (0 $\leq x\leq$ 1) single crystals have been studied through heat capacity and high-resolution x-ray scattering measurements. For PrAlO$_3$, the heat capacity shows a sharp first-order peak at the ... More

$G$-equivariant embedding theorems for CR manifolds of high codimensionOct 23 2018Let $(X,T^{1,0}X)$ be a $(2n+1+d)$-dimensional compact CR manifold with codimension $d+1$, $d\geq1$, and let $G$ be a $d$-dimensional compact Lie group with CR action on $X$ and $T$ be a globally defined vector field on $X$ such that $\mathbb C TX=T^{1,0}X\oplus ... More

Nuclear mean field from chiral pion-nucleon dynamicsAug 06 2001Using the two-loop approximation of chiral perturbation theory, we calculate the momentum and density dependent single particle potential of nucleons in isospin-symmetric nuclear matter. The contributions from one- and two-pion exchange diagrams give ... More

Matter wave speckle observed in an out-of-equilibrium quantum fluidJun 06 2016Jan 23 2019We report the results of a direct comparison of a freely expanding turbulent Bose-Einstein condensate and the propagation of an optical speckle pattern. We found remarkably similar statistical properties underlying the spatial propagation of both phenomena. ... More

Random Walk in a Random Environment and First-Passage Percolation on TreesApr 02 2004We show that the transience or recurrence of a random walk in certain random environments on an arbitrary infinite locally finite tree is determined by the branching number of the tree, which is a measure of the average number of branches per vertex. ... More

On which graphs are all random walks in random environments transient?Apr 05 2004An infinite graph G has the property that a random walk in random environment on G defined by i.i.d. resistances with any common distribution is almost surely transient, if and only if for some p<1, simple random walk is transient on a percolation cluster ... More

Proof equivalence in MLL is PSPACE-completeOct 21 2015Mar 01 2016MLL proof equivalence is the problem of deciding whether two proofs in multiplicative linear logic are related by a series of inference permutations. It is also known as the word problem for star-autonomous categories. Previous work has shown the problem ... More

Gradient stability for the Sobolev inequality: the case $p\geq 2$Oct 07 2015Oct 02 2016We prove a strong form of the quantitative Sobolev inequality in $\mathbb{R}^n$ for $p\geq 2$, where the deficit of a function $u\in \dot W^{1,p} $ controls $\| \nabla u -\nabla v\|_{L^p}$ for an extremal function $v$ in the Sobolev inequality.

Abiotic oxygen-dominated atmospheres on terrestrial habitable zone planetsMar 11 2014Mar 20 2014Detection of life on other planets requires identification of biosignatures, i.e., observable planetary properties that robustly indicate the presence of a biosphere. One of the most widely accepted biosignatures for an Earth-like planet is an atmosphere ... More

A Protocol for Generating Random Elements with their ProbabilitiesDec 09 2013Mar 24 2014We give an AM protocol that allows the verifier to sample elements x from a probability distribution P, which is held by the prover. If the prover is honest, the verifier outputs (x, P(x)) with probability close to P(x). In case the prover is dishonest, ... More

Water loss from terrestrial planets with CO2-rich atmospheresJun 13 2013Oct 12 2013Water photolysis and hydrogen loss from the upper atmospheres of terrestrial planets is of fundamental importance to climate evolution but remains poorly understood in general. Here we present a range of calculations we performed to study the dependence ... More

Projection operator approach to spin diffusion in the anisotropic Heisenberg chain at high temperaturesJun 23 2010We investigate spin transport in the anisotropic Heisenberg chain in the limit of high temperatures ({\beta} \to 0). We particularly focus on diffusion and the quantitative evaluation of diffusion constants from current autocorrelations as a function ... More

Hedged maximum likelihood estimationJan 12 2010This paper proposes and analyzes a new method for quantum state estimation, called hedged maximum likelihood (HMLE). HMLE is a quantum version of Lidstone's Law, also known as the "add beta" rule. A straightforward modification of maximum likelihood estimation ... More

A bridge between Sobolev and Escobar inequalities and beyondSep 08 2016Nov 06 2016The classical Sobolev and Escobar inequalities are embedded into the same one-parameter family of sharp trace-Sobolev inequalities on half-spaces. Equality cases are characterized for each inequality in this family by tweaking a well-known mass transportation ... More

Higher Regularity of the Free Boundary in the Obstacle Problem for the Fractional LaplacianJun 03 2016Jun 27 2016We prove a higher regularity result for the free boundary in the obstacle problem for the fractional Laplacian via a higher order boundary Harnack inequality.

The distribution of zeros of the derivative of a random polynomialSep 27 2011In this note we initiate the probabilistic study of the critical points of polynomials of large degree with a given distribution of roots. Namely, let f be a polynomial of degree n whose zeros are chosen IID from a probability measure mu on the complex ... More

Explicit Mumford isomorphism for hyperelliptic curvesAug 27 2004May 03 2012Using an explicit version of the Mumford isomorphism on the moduli space of hyperelliptic curves we derive a closed formula for the Arakelov-Green function of a hyperelliptic Riemann surface evaluated at its Weierstrass points.

Conducting sparse feature selection on arbitrarily long phrases in text corpora with a focus on interpretabilityNov 20 2015Jul 23 2016We propose a general framework for topic-specific summarization of large text corpora, and illustrate how it can be used for analysis in two quite different contexts: an OSHA database of fatality and catastrophe reports (to facilitate surveillance for ... More

Symmetric Pascal matrices modulo pDec 10 2002Jan 31 2003We study characteristic polynomials of symmetric matrices with entries ${i+j\choose i}$ the binomial coefficients, over finite fields.

The Bernstein-Sato $b$-function of the Vandermonde determinantMar 03 2015The Bernstein-Sato polynomial, or the $b$-function, is an important invariant of singularities of hypersurfaces that is difficult to compute in general. We describe a few different results towards computing the $b$-function of the Vandermonde determinant ... More

A leave-p-out based estimation of the proportion of null hypothesesApr 08 2008In the multiple testing context, a challenging problem is the estimation of the proportion $\pi_0$ of true-null hypotheses. A large number of estimators of this quantity rely on identifiability assumptions that either appear to be violated on real data, ... More

t factor: A metric for measuring impact on TwitterAug 10 2015Based on the definition of the well-known h index we propose a t factor for measuring the impact of publications (and other entities) on Twitter. The new index combines tweet and retweet data in a balanced way whereby retweets are seen as data reflecting ... More

Data Recombination for Neural Semantic ParsingJun 11 2016Modeling crisp logical regularities is crucial in semantic parsing, making it difficult for neural models with no task-specific prior knowledge to achieve good results. In this paper, we introduce data recombination, a novel framework for injecting such ... More

Realizing the analytic surgery group of Higson and Roe geometrically, Part II: Relative eta-invariantsMar 21 2014Jan 08 2016We apply the geometric analog of the analytic surgery group of Higson and Roe to the relative $\eta$-invariant. In particular, by solving a Baum-Douglas type index problem, we give a "geometric" proof of a result of Keswani regarding the homotopy invariance ... More

Continuous-time performance limitations for overshoot and resulted tracking measuresMar 22 2011A dual formulation for the problem of determining absolute performance limitations on overshoot, undershoot, maximum amplitude and fluctuation minimization for continuous-time feedback systems is constructed. Determining, for example, the minimum possible ... More

Local invariants attached to Weierstrass pointsOct 29 2007Apr 24 2012Let X/S be a hyperelliptic curve of genus g over the spectrum of a discrete valuation ring. Two fundamental numerical invariants are attached to X/S: the valuation of the hyperelliptic discriminant of X/S, and the valuation of the Mumford discriminant ... More

Asymptotic and exact results on the complexity of the Novelli-Pak-Stoyanovskii algorithmJun 24 2016May 24 2017The Novelli-Pak-Stoyanovskii algorithm is a sorting algorithm for Young tableaux of a fixed shape that was originally devised to give a bijective proof of the hook-length formula. We obtain new asymptotic results on the average case and worst case complexity ... More

What is the probability of intersecting the set of Brownian double points?Apr 05 2004Nov 20 2007We give potential theoretic estimates for the probability that a set $A$ contains a double point of planar Brownian motion run for unit time. Unlike the probability for $A$ to intersect the range of a Markov process, this cannot be estimated by a capacity ... More

An extension of the Frobenius coin-exchange problemApr 02 2002Given positive integers $a_1,...,a_n$ with $\gcd(a_1,...,a_n) = 1$, we call an integer t representable if there exist nonnegative integers $m_1,...,m_n$ such that $t = m_1 a_1 + ... + m_n a_n$. In this paper, we discuss the linear diophantine problem ... More