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Deep Reinforcement Learning for Mention-Ranking Coreference ModelsSep 27 2016Coreference resolution systems are typically trained with heuristic loss functions that require careful tuning. In this paper we instead apply reinforcement learning to directly optimize a neural mention-ranking model for coreference evaluation metrics. ... More

Fixing the functoriality of Khovanov homologyJan 12 2007Jan 21 2008We describe a modification of Khovanov homology (math.QA/9908171), in the spirit of Bar-Natan (math.GT/0410495), which makes the theory properly functorial with respect to link cobordisms. This requires introducing `disorientations' in the category of ... More

The baker's map with a convex holeMay 01 2017Jan 30 2018We consider the baker's map $B$ on the unit square $X$ and an open convex set $H\subset X$ which we regard as a hole. The survivor set $\mathcal J(H)$ is defined as the set of all points in $X$ whose $B$-trajectories are disjoint from $H$. The main purpose ... More

Sample Efficient Text Summarization Using a Single Pre-Trained TransformerMay 21 2019Language model (LM) pre-training has resulted in impressive performance and sample efficiency on a variety of language understanding tasks. However, it remains unclear how to best use pre-trained LMs for generation tasks such as abstractive summarization, ... More

Characteristic Direction Approach to Identify Differentially Expressed GenesJul 31 2013Genome-wide gene expression profiles, as measured with microarrays or RNA-Seq experiments, have revolutionized biological and biomedical research by providing a quantitative measure of the entire mRNA transcriptome. Typically, researchers set up experiments ... More

On the Highly Connected Dyadic, Near-Regular, and Sixth-Root-of-Unity MatroidsMar 09 2019Subject to announced results by Geelen, Gerards, and Whittle, we completely characterize the highly connected members of the classes of dyadic, near-regular, and sixth-root-of-unity matroids.

BAM! Born-Again Multi-Task Networks for Natural Language UnderstandingJul 10 2019It can be challenging to train multi-task neural networks that outperform or even match their single-task counterparts. To help address this, we propose using knowledge distillation where single-task models teach a multi-task model. We enhance this training ... More

Improving Coreference Resolution by Learning Entity-Level Distributed RepresentationsJun 04 2016Jun 08 2016A long-standing challenge in coreference resolution has been the incorporation of entity-level information - features defined over clusters of mentions instead of mention pairs. We present a neural network based coreference system that produces high-dimensional ... More

One-Time Programs made PracticalJul 01 2019A one-time program (OTP) works as follows: Alice provides Bob with the implementation of some function. Bob can have the function evaluated exclusively on a single input of his choosing. Once executed, the program will fail to evaluate on any other input. ... More

Deep Reinforcement Learning for Mention-Ranking Coreference ModelsSep 27 2016Oct 31 2016Coreference resolution systems are typically trained with heuristic loss functions that require careful tuning. In this paper we instead apply reinforcement learning to directly optimize a neural mention-ranking model for coreference evaluation metrics. ... More

Large-scale Analysis of Counseling Conversations: An Application of Natural Language Processing to Mental HealthMay 14 2016Aug 14 2016Mental illness is one of the most pressing public health issues of our time. While counseling and psychotherapy can be effective treatments, our knowledge about how to conduct successful counseling conversations has been limited due to lack of large-scale ... More

Benchmarking Obfuscators of FunctionalityJan 13 2015We propose a set of benchmarks for evaluating the practicality of software obfuscators which rely on provably-secure methods for functional obfuscation.

Rigidity of equality of Lyapunov exponents for geodesic flowsJan 24 2015Oct 28 2015We study the relationship between the Lyapunov exponents of the geodesic flow of a closed negatively curved manifold and the geometry of the manifold. We show that if each periodic orbit of the geodesic flow has exactly one Lyapunov exponent on the unstable ... More

The Rotation Class of a FlowOct 31 2000Generalizing a construction of A. Weil, we introduce a topological invariant for flows on compact, connected, finite dimensional, abelian, topological groups. We calculate this invariant for some examples and compare the invariant with other flow invariants. ... More

Flows on solenoids are generically not almost periodicJun 22 1999The space of non-singular flows on any given solenoid is shown to contain a generic subset consisting of flows that are not almost periodic. Whether this result carries over to Hamiltonian flows remains an open question.

The $β$-transformation with a holeDec 19 2014Sep 18 2015This paper extends those of Glendinning and Sidorov [3] and of Hare and Sidorov [6] from the case of the doubling map to the more general $\beta$-transformation. Let $\beta \in (1,2)$ and consider the $\beta$-transformation $T_{\beta}(x)=\beta x \pmod ... More

Unsupervised Language Acquisition: Theory and PracticeDec 10 2002In this thesis I present various algorithms for the unsupervised machine learning of aspects of natural languages using a variety of statistical models. The scientific object of the work is to examine the validity of the so-called Argument from the Poverty ... More

A generalization of Hagopian's theorem and exponentsMar 29 2000We generalize Hagopian's theorem characterizing solenoids to higher dimensions by showing that any homogeneous continuum admitting a fiber bundle projection onto a torus with totally disconnected fibers admits a compatible abelian topological group structure. ... More

Functoriality for the su(3) Khovanov homologyJun 03 2008We prove that Morrison and Nieh's categorification of the su(3) quantum knot invariant is functorial with respect to tangle cobordisms. This is in contrast to the categorified su(2) theory, which was not functorial as originally defined. We use methods ... More

The reduced effect of a single scattering with a low-mass particle via a point interactionJul 31 2008Jan 15 2009In this article, we study a second-order expansion for the effect induced on a large quantum particle which undergoes a single scattering with a low-mass particle via a repulsive point interaction. We give an approximation with third-order error in $\lambda$ ... More

On (Enriched) Left Bousfield Localization of Model CategoriesAug 15 2007Nov 29 2007I verify the existence of left Bousfield localizations and of enriched left Bousfield localizations, and I prove a collection of useful technical results characterizing certain fibrations of (enriched) left Bousfield localizations. I also use such Bousfield ... More

On the Dreaded Right Bousfield LocalizationAug 25 2007Nov 29 2007I verify the existence of right Bousfield localizations of right semimodel categories, and I apply this to construct a model of the homotopy limit of a left Quillen presheaf as a right semimodel category.

A limit theorem to a time-fractional diffusionOct 04 2011Feb 12 2013We prove a limit theorem for an integral functional of a Markov process. The Markovian dynamics is characterized by a linear Boltzmann equation modeling a one-dimensional test particle of mass $\lambda^{-1}\gg 1$ in an external periodic potential and ... More

Canonical bases for the quantum enveloping algebra of gl(m|1) and its modulesMay 13 2016We construct a crystal basis for the negative half of the quantum group U associated to the standard super Cartan datum of gl(m|1), which is compatible with known crystals on Kac modules and simple modules. We show that these crystals admit globalization ... More

Quantum osp(1|2n) knot invariants are the same as quantum so(2n+1) knot invariantsSep 11 2015We show that the quantum covering group associated to osp(1|2n) has an associated colored quantum knot invariant \`a la Reshetikhin-Turaev, which specializes to a quantum knot invariant for osp(1|2n), and to the usual quantum knot invariant for so(1+2n). ... More

Global circulation as the main source of cloud activity on TitanJul 03 2009Clouds on Titan result from the condensation of methane and ethane and, as on other planets, are primarily structured by circulation of the atmosphere. At present, cloud activity mainly occurs in the southern (summer) hemisphere, arising near the pole ... More

What Does BERT Look At? An Analysis of BERT's AttentionJun 11 2019Large pre-trained neural networks such as BERT have had great recent success in NLP, motivating a growing body of research investigating what aspects of language they are able to learn from unlabeled data. Most recent analysis has focused on model outputs ... More

Evidence of Titan's Climate History from Evaporite DistributionAug 13 2014Water-ice-poor, 5-$\mu$m-bright material on Saturn's moon Titan has previously been geomorphologically identified as evaporitic. Here we present a global distribution of the occurrences of the 5-$\mu$m-bright spectral unit, identified with Cassini's Visual ... More

Inducing Domain-Specific Sentiment Lexicons from Unlabeled CorporaJun 09 2016Sep 24 2016A word's sentiment depends on the domain in which it is used. Computational social science research thus requires sentiment lexicons that are specific to the domains being studied. We combine domain-specific word embeddings with a label propagation framework ... More

Integration of fluorescence collection optics with a microfabricated surface electrode ion trapAug 17 2010Sep 23 2010We have successfully demonstrated an integrated optical system for collecting the fluorescence from a trapped ion. The system, consisting of an array of transmissive, dielectric micro-optics and an optical fiber array, has been intimately incorporated ... More

Mapping polar atmospheric features on Titan with VIMS: from the dissipation of the northern cloud to the onset of a southern polar vortexMay 02 2018We have analyzed the complete archive of the Visual and Infrared Mapping Spectrometer (VIMS) data in order to monitor and analyze the evolution of the clouds and haze coverage at both poles of Titan during the entire Cassini mission. Our objective is ... More

The Cassini VIMS archive of Titan: from browse products to global infrared color mapsSep 18 2018We have analyzed the complete Visual and Infrared Mapping Spectrometer (VIMS) data archive of Titan. Our objective is to build global surface cartographic products, by combining all the data gathered during the 127 targeted flybys of Titan into synthetic ... More

Diffusive behavior for randomly kicked Newtonian particles in a spatially periodic mediumOct 06 2009Oct 07 2011We prove a central limit theorem for the momentum distribution of a particle undergoing an unbiased spatially periodic random forcing at exponentially distributed times without friction. The start is a linear Boltzmann equation for the phase space density, ... More

Bounds for the state-modulated resolvent of a linear Boltzmann generatorOct 04 2011We study a generalized resolvent for the generator of a Markovian semigroup. The Markovian generator appears in a linear Boltzmann equation modeling a one-dimensional test particle in a periodic potential and colliding elastically with particles from ... More

Fibrations in $\infty$-category theoryJul 14 2016Aug 12 2016In this short expository note, we discuss, with plenty of examples, the bestiary of fibrations in quasicategory theory. We underscore the simplicity and clarity of the constructions these fibrations make available to end-users of higher category theory. ... More

On Weyl-Titchmarsh Theory for Singular Finite Difference Hamiltonian SystemsDec 09 2003We develop the basic theory of matrix-valued Weyl-Titchmarsh M-functions and the associated Green's matrices for whole-line and half-line self-adjoint Hamiltonian finite difference systems with separated boundary conditions.

Energy Positivity, Non-Renormalization, and Holomorphy in Lorentz-Violating Supersymmetric TheoriesMar 02 2013Aug 07 2013This paper shows that the positive-energy and non-renormalization theorems of traditional supersymmetry survive the addition of Lorentz violating interactions. The Lorentz-violating coupling constants in theories using the construction of Berger and Kostelecky ... More

Using MOEAs To Outperform Stock Benchmarks In The Presence of Typical Investment ConstraintsSep 15 2011Jan 02 2012Portfolio managers are typically constrained by turnover limits, minimum and maximum stock positions, cardinality, a target market capitalization and sometimes the need to hew to a style (such as growth or value). In addition, portfolio managers often ... More

Tiling Spaces, Codimension One Attractors and ShapeMay 04 2011May 24 2012We show that any codimension one hyperbolic attractor of a diffeomorphism of a (d+1)-dimensional closed manifold is shape equivalent to a (d+1)-dimensional torus with a finite number of points removed, or, in the non-orientable case, to a space with a ... More

Bihomogeneity of solenoidsJan 29 2002Solenoids are inverse limit spaces over regular covering maps of closed manifolds. M.C. McCord has shown that solenoids are topologically homogeneous and that they are principal bundles with a profinite structure group. We show that if a solenoid is bihomogeneous, ... More

Embedding solenoids in foliationsDec 05 2008Apr 27 2011In this paper we find smooth embeddings of solenoids in smooth foliations. We show that if a smooth foliation F of a manifold M contains a compact leaf L with H^1(L;R)= 0 and if the foliation is a product foliation in some saturated open neighbourhood ... More

Diffusion along transition chains of invariant tori and Aubry-Mather setsApr 06 2012We describe a topological mechanism for the existence of diffusing orbits in a dynamical system satisfying the following assumptions: (i) the phase space contains a normally hyperbolic invariant manifold diffeomorphic to a two-dimensional annulus, (ii) ... More

Small cocycles, fine torus fibrations, and a ${\mathbb Z}^2$ subshift with neitherJun 05 2015Feb 17 2017Following an earlier similar conjecture of Kellendonk and Putnam, Giordano, Putnam and Skau conjectured that all minimal, free ${\mathbb Z}^d$ actions on Cantor sets admit "small cocycles." These represent classes in $H^1$ that are mapped to small vectors ... More

The Usefulness of Type Ia Supernovae for Cosmology - a Personal ReviewMay 30 2012We review some results of the past 12 years derived from optical and infrared photometry of Type Ia supernovae. A combination of optical and infrared photometry allows us to determine accurately the extinction along the line of sight. The resulting distance ... More

Existence, Smoothness and Decay Properties of Density Functions for Distributions Characterized by Stochastic Fixed-Point EquationsApr 20 2016We consider systems of stochastic fixed-point equations that arise in the asymptotic analysis of random recursive structures and algorithms such as Quicksort, generalized Polya urn processes and path lengths of random recursive trees and split trees. ... More

Supersymmetry without Grassmann VariablesFeb 12 2001Supersymmetry transformations may be represented by unitary operators in a formulation of supersymmetry without numbers that anti-commute. The physical relevance of this formulation hinges on whether or not one may add states of even and odd fermion number, ... More

Theories with Finite Green's FunctionsDec 03 2012Jan 21 2013The addition of certain nonrenormalizable terms to the usual action density of a free scalar field leads to nonrenormalizable theories whose exact euclidian and minkowskian Green's functions are less singular than those of the free theory. In some cases, ... More

Helices in BiomoleculesFeb 27 2005Oct 15 2005Identical objects, regularly assembled, form a helix, which is the principal motif of nucleic acids, proteins, and viral capsids.

Instantaneous shock location and one-dimensional nonlinear stability of viscous shock waveSep 13 2009We illustrate in a simple setting the instantaneous shock tracking approach to stability of viscous conservation laws introduced by Howard, Mascia, and Zumbrun. This involves a choice of the definition of instanteous location of a viscous shock-- we show ... More

$2$-modified characteristic Fredholm determinants, Hill's method, and the periodic Evans function of GardneNov 26 2010Using the relation established by Johnson--Zumbrun between Hill's method of aproximating spectra of periodic-coefficient ordinary differential operators and a generalized periodic Evans function given by the $2$-modified characteristic Fredholm determinant ... More

Planar stability critera for viscous shock waves of systems with real viscosityJan 06 2004We present a streamlined account of recent developments in the stability theory for planar viscous shock waves, with an emphasis on applications to physical models with ``real,'' or partial viscosity. The main result is the establishment of necessary, ... More

Some superconcentration inequalities for extrema of stationary Gaussian ProcessesMar 23 2015This note is concerned with concentration inequalities for extrema of stationary Gaussian processes. It provides non-asymptotic tail inequalities which fully reflect the fluctuation rate, and as such improve upon standard Gaussian concentration. The arguments ... More

Path integrals for actions that are not quadratic in their time derivativesJan 02 2015Mar 25 2015The standard way to construct a path integral is to use a Legendre transformation to find the hamiltonian, to repeatedly insert complete sets of states into the time-evolution operator, and then to integrate over the momenta. This procedure is simple ... More

M-theory in the Omega-background and 5-dimensional non-commutative gauge theoryOct 13 2016The $\Omega$-background is defined for supergravity, and a very general class of such backgrounds is constructed for 11-dimensional supergravity. 11-dimensional supergravity in a certain $\Omega$-background is shown to be equivalent to a 5-dimensional ... More

Optimal Tree Hash Modes: the Case of Trees Having their Leaves at All the LevelsJul 01 2016Oct 16 2016A recent work shows how we can optimize a tree based mode of operation for a hash function where the sizes of input message blocks and digest are the same, subject to the constraint that the involved tree structure has all its leaves at the same depth. ... More

Tracking an Object with Unknown Accelerations using a Shadowing FilterJan 21 2015A commonly encountered problem is the tracking of a physical object, like a maneuvering ship, aircraft, land vehicle, spacecraft or animate creature carrying a wireless device. The sensor data is often limited and inaccurate observations of range or bearing. ... More

Clôture intégrale et opérations de tores algébriques de complexité un dans les variétés affinesFeb 06 2012Nov 07 2013We describe explicitly the normalization of affine varieties with an algebraic torus action of complexity one in terms of polyhedral divisors. We also provide a description of homogeneous integrally closed ideals of affine T-varieties of complexity one. ... More

Indices of inseparability in towers of field extensionsFeb 21 2014Jan 08 2015Let $K$ be a local field whose residue field has characteristic $p$ and let $L/K$ be a finite separable totally ramified extension of degree $n=ap^{\nu}$. The indices of inseparability $i_0,i_1,...,i_{\nu}$ of $L/K$ were defined by Fried in the case char$(K)=p$ ... More

A refined Bloch group and the third homology of SL_2 of a fieldJan 17 2011Jan 18 2013We use the properties of the refined Bloch group of a field to prove that H_3 of SL_2 of a global field is never finitely generated, and to calculate - up to some 2-torsion - H_3 of SL_2 of local fields with finite residue field of odd characteristic. ... More

On Rotation Curve AnalysisFeb 14 2018An analysis of analytical methods used for computing galactic masses on the basis of rotation curves (Saari 2015) is shown to be flawed.

The Inferential Design of Entropy and its Application to Quantum MeasurementsApr 24 2018This thesis synthesizes probability and entropic inference with Quantum Mechanics (QM) and quantum measurement [1-6]. It is shown that the standard and quantum relative entropies are tools designed for the purpose of updating probability distributions ... More

Examples of infinite direct sums of spectral triplesFeb 24 2016May 25 2016We study two ways of summing an infinite family of noncommutative spectral triples. First, we propose a definition of the integration of spectral triples and give an example using algebras of Toeplitz operators acting on weighted Bergman spaces over the ... More

Integers with a divisor in (y,2y]Jul 19 2006Mar 17 2013We give a relatively short proof of one of the central cases of the main theorem from the paper "The distribution of integers with a divisor in a given interval", math.NT/0401223. Namely, we determine the order of magnitude of the number of integers <=x ... More

Rigidity of tilting modules in category OSep 27 2017Oct 09 2017In this note we give an overview of rigidity properties and Loewy lengths of tilting modules in the BGG category O associated to a reductive Lie algebra. These results are well-known by several specialists, but seem difficult to find in the existing literature. ... More

The orthosymplectic superalgebra in harmonic analysisAug 19 2012We introduce the orthosymplectic superalgebra osp(m|2n) as the algebra of Killing vector fields on Riemannian superspace R^{m|2n} which stabilize the origin. The Laplace operator and norm squared on R^{m|2n}, which generate sl(2), are orthosymplectically ... More

The orthosymplectic supergroup in harmonic analysisFeb 03 2012The orthosymplectic supergroup OSp(m|2n) is introduced as the supergroup of isometries of flat Riemannian superspace R^{m|2n} which stabilize the origin. It also corresponds to the supergroup of isometries of the supersphere S^{m-1|2n}. The Laplace operator ... More

Predicting the Voltage Dependence of Interfacial Electrochemical Processes at Lithium-Intercalated Graphite Edge PlanesFeb 01 2015The applied potential governs lithium-intercalation and electrode passivation reactions in lithium ion batteries, but are challenging to calibrate in condensed phase DFT calculations. In this work, the "anode potential" of charge-neutral lithium-intercalated ... More

First Principles Modeling of the Initial Stages of Organic Solvent Decomposition on Li(x)Mn(2)O(4) (100) SurfacesSep 15 2012Density functional theory and ab initio molecular dynamics simulations are applied to investigate the initial steps of ethylene carbonate (EC) decomposition on spinel Li(0.6)Mn(2)O(4) (100) surfaces. EC is a key component of the electrolyte used in lithium ... More

The periplectic Brauer algebraSep 21 2016Mar 15 2018We study the periplectic Brauer algebra introduced by Moon in the study of invariant theory for periplectic Lie superalgebras. We determine when the algebra is quasi-hereditary and, for fields of characteristic zero, describe the block decomposition. ... More

Equisingularity of families of hypersurfaces and applications to mappingsMar 12 2008Jul 02 2008In the study of equisingularity of isolated singularities we have the classical theorem of Briancon, Speder and Teissier which states that a family of isolated hypersurface singularities is Whitney equisingular if and only if the mu^*-sequence for a hypersurface ... More

Equisingularity and The Euler Characteristic of a Milnor FibreJul 03 2008We study the Euler characteristic of the Milnor fibre of a hypersurface singularity. This invariant is given in terms of the Euler characteristic of a fibre in between the original singularity and its Milnor fibre and in terms of the Euler characteristics ... More

The Strong Atiyah conjecture for virtually cocompact special groupsMay 06 2013Oct 07 2013We provide new conditions for the Strong Atiyah conjecture to lift to finite group extensions. In particular, we show cocompact special groups satisfy these conditions, so the Strong Atiyah conjecture holds for virtually cocompact special groups.

Blow-up Continuity for Type-I, Mean-Convex Mean Curvature FlowMar 07 2017Under mean curvature flow, a closed, embedded hypersurface $M(t)$ becomes singular in finite time. For certain classes of mean-convex mean curvature flows, we show the continuity of the first singular time $T$ and the limit set "$M(T)$", with respect ... More

Models of Membrane ElectrostaticsJan 22 2011May 15 2012I derive formulas for the electrostatic potential of a charge in or near a membrane modeled as one or more dielectric slabs lying between two semi-infinite dielectrics. One can use these formulas in Monte Carlo codes to compute the distribution of ions ... More

Simple Model of the Transduction of Cell-Penetrating PeptidesSep 19 2010Cell-penetrating peptides (CPPs) such as HIV's trans-activating transcriptional activator (TAT) and polyarginine rapidly pass through the plasma membranes of mammalian cells by an unknown mechanism called transduction. They may be medically useful when ... More

Molecular Electroporation and the Transduction of OligoargininesOct 14 2008Oct 30 2009Certain short polycations, such as TAT and polyarginine, rapidly pass through the plasma membranes of mammalian cells by an unknown mechanism called transduction as well as by endocytosis and macropinocytosis. These cell-penetrating peptides (CPPs) promise ... More

Alternative Splicing and Genomic StabilityMar 27 2004Jul 01 2004Alternative splicing allows an organism to make different proteins in different cells at different times, all from the same gene. In a cell that uses alternative splicing, the total length of all the exons is much shorter than in a cell that encodes the ... More

A More Effective PotentialOct 29 1992In theories with spontaneous symmetry breaking, the conventional effective potential possesses a defective loop expansion. For such theories, the exact effective potential $V(\phi_c,T)$ is real and convex, but its perturbative series is complex and concave ... More

Inflation in a Symmetric VacuumMay 23 2007If in a finite universe, the tree-level vacuum is a symmetric superposition of coherent states, in each of which the inflaton field assumes a different, energy-minimizing mean value (vev), then the resulting energy is positive and decreases exponentially ... More

Parametrization of the Hybrid Potential for Pairs of Neutral AtomsJun 20 2006Jun 22 2007The hybrid form is a combination of the Rydberg potential and the London inverse-sixth-power energy. It is accurate at all relevant distance scales and simple enough for use in all-atom simulations of biomolecules. One may compute the parameters of the ... More

Gauge Invariance and Confinement in Noncompact Simulations of SU(2)Dec 20 1993Wilson loops have been measured at strong coupling, $\beta=0.5$, on a $12^4$ lattice in a noncompact simulation of pure SU(2) in which random compact gauge transformations impose a kind of lattice gauge invariance. The Wilson loops suggest a confining ... More

A More-Effective PotentialFeb 01 1993May 20 1994In theories with spontaneous symmetry breaking, the loop expansion of the effective potential is awkward. In such theories, the exact effective potential $V(\phi_c,T)$ is real and convex (as a function of the classical field $\phi_c$), but its perturbative ... More

On arithmetic progressions in A + B + CNov 21 2012Oct 09 2013Our main result states that when A, B, C are subsets of Z/NZ of respective densities \alpha,\beta,\gamma, the sumset A + B + C contains an arithmetic progression of length at least e^{c(\log N)^c} for densities \alpha > (\log N)^{-2 + \epsilon} and \beta,\gamma ... More

The Study of Climate on Alien WorldsJun 16 2012Characterizing atmospheres beyond the Solar System is an endeavor no longer confined to the realm of science fiction.

Photons from axial-vector radiative decay in a hadron gasJun 21 1994Strange and non-strange axial-vector meson radiative decays contribute to photon production in hadron gas. One- and two-hadron radiative decay modes of $b_{1}(1235)$, $a_{1}(1260)$ and $K_{1}(1270)$ are studied. At 200 MeV temperature and for a narrow ... More

Finiteness properties of the Johnson subgroupsOct 02 2015Nov 16 2016The main goal of this note is to provide evidence that the first rational homology of the Johnson subgroup $K_{g,1}$ of the mapping class group of a genus g surface with one marked point is finite-dimensional. Building on work of Dimca-Papadima, we use ... More

Solvability of Matrix Riccati InequalitiesMay 19 2015We consider matrix Riccati inequality arising in the theory of absolute stability, $H_\infty$ control problem, $LQ$ problem, and optimal estimation problem. In the case of sign definite frequency domain function, the solvability of Riccati inequalities ... More

Note on Optimal Trees for Parallel Hash FunctionsApr 14 2016A recent work shows how we can optimize a tree based mode of operation for a rate 1 hash function. In particular, an algorithm and a theorem are presented for selecting a good tree topology in order to optimize both the running time and the number of ... More

Demonstrating the Elliptical Orbit of Mars using Naked Eye DataOct 18 2016Over the course of eleven months we determined the position of Mars on 45 occasions using a handheld cross staff and two to five bright reference stars of known right ascension and declination on each occasion. On average the observed positions are within ... More

Operators on Asymptotic $\ell_p$ Spaces which are not Compact Perturbations of a Multiple of the IdentityAug 08 2009We give sufficient conditions on an asymptotic $\ell_p$ (for $1 < p < \infty$) Banach space which ensure the space admits an operator which is not a compact perturbation of a multiple of the identity. These conditions imply the existence of strictly singular ... More

Loop quantum cosmology and the k = - 1 RW modelDec 12 2006Feb 07 2007The loop quantization of the negatively curved k=-1 RW model poses several technical challenges. We show that the issues can be overcome and a successful quantization is possible that extends the results of the k=0,+1 models in a natural fashion. We discuss ... More

On the Hamiltonian Constraint of Loop Quantum CosmologyFeb 20 2005In this paper we construct the Hamiltonian constraint operator of loop quantum cosmology using holonomies defined for arbitrary irreducible SU(2) representations labeled by spin J. We show that modifications to the effective semi-classical equations of ... More

Sparse graphs of high gonalityJun 21 2016Jul 11 2016By considering graphs as discrete analogues of Riemann surfaces, Baker and Norine (Adv. Math. 2007) developed a concept of linear systems of divisors for graphs. Building on this idea, a concept of gonality for graphs has been defined and has generated ... More

The third homology of SL_2 of fields with discrete valuationApr 25 2012May 23 2016For a field F with discrete valuation and residue field $k$ we relate the third homology of SL_2(F) with half-integral coefficients to the third homology of SL_2(k) and a certain refined scissors congruence group of k. As an application, we obtain explicit ... More

Generalized Smirnov statistics and the distribution of prime factorsApr 13 2007Jun 27 2007We apply recent bounds of the author (math.PR/0609224) for generalized Smirnov statistics to the distribution of integers whose prime factors satisfy certain systems of inequalities.

Quasi-isometries of rank one S-arithmetic latticesApr 11 2005Jan 08 2008We complete the quasi-isometric classification of irreducible lattices in semisimple Lie groups over nondiscrete locally compact fields of characteristic zero by showing that any quasi-isometry of a rank one S-arithmetic lattice in a semisimple Lie group ... More

Embedding Galilean and Carrollian geometries I. Gravitational wavesNov 30 2018The aim of this series of papers is to generalise the ambient approach of Duval et al. regarding the embedding of Galilean and Carrollian geometries inside gravitational waves with parallel rays. In this first part, we propose a generalisation of the ... More

Ringel duals of Brauer algebras via super groupsOct 06 2018Mar 31 2019We prove that the Brauer algebra, for all parameters for which it is quasi-hereditary, is Ringel dual to a category of representations of the orthosymplectic super group. As a consequence we obtain new and algebraic proofs for some results on the fundamental ... More

Automating Software Development for Mobile Computing Platforms (Doctoral Symposium)Jul 18 2018Mobile devices such as smartphones and tablets have become ubiquitous in today's modern computing landscape. The applications that run on these mobile devices (often referred to as "apps") have become a primary means of computing for millions of users ... More

What Does "Metallicity" Mean When Interpreting Spectra of Exoplanetary Atmospheres?Jul 16 2018One of the desired outcomes of studying exoplanetary atmospheres is to set decisive constraints on exoplanet formation theories. Astronomers often speak of the "metallicity" in broad terms. When modeling the bulk metallicity, workers refer to the elemental ... More