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A generic tool to generate a lexicon for NLP from Lexicon-Grammar tablesMay 31 2010Lexicon-Grammar tables constitute a large-coverage syntactic lexicon but they cannot be directly used in Natural Language Processing (NLP) applications because they sometimes rely on implicit information. In this paper, we introduce LGExtract, a generic ... More

ReQA: An Evaluation for End-to-End Answer Retrieval ModelsJul 10 2019Popular QA benchmarks like SQuAD have driven progress on the task of identifying answer spans within a specific passage, with models now surpassing human performance. However, retrieving relevant answers from a huge corpus of documents is still a challenging ... More

Character-Level Language Modeling with Deeper Self-AttentionAug 09 2018Dec 10 2018LSTMs and other RNN variants have shown strong performance on character-level language modeling. These models are typically trained using truncated backpropagation through time, and it is common to assume that their success stems from their ability to ... More

UV sky surveysJul 26 1998I review the development of UV and EUV astronomy, covering the spectral range from 5 to 300 nm, with emphasis on sky surveys for discrete sources. I discuss studies which resulted in lists of sources observed by imaging and deliberately omit most spectroscopic ... More

Modeling and Particle Tracking through Longitudinal Gradient Bending MagnetsOct 26 2015This report documents the development of a versatile model for longitudinal gradient bending magnets (LGB's) and its implementation in particle tracking simulations. The model presented below may be used to represent an arbitrary magnetic field profile, ... More

Intentional Design for EmpowermentAug 27 2013I argue for empowering education, adapting Marx's idea of ownership of the means of production, and discuss interactive simulations as one example of a tool in which intentional design can support student ownership of learning. I propose a model that ... More

Acyclic Colorings of Directed GraphsSep 26 2014The acyclic chromatic number of a directed graph $D$, denoted $\chi_A(D)$, is the minimum positive integer $k$ such that there exists a decomposition of the vertices of $D$ into $k$ disjoint sets, each of which induces an acyclic subgraph. For any $m ... More

The monodromy of real Bethe vectors for the Gaudin modelNov 15 2015The Bethe algebras for the Gaudin model act on the multiplicity space of tensor products of irreducible $ \mathfrak{gl}_r $-modules and have simple spectrum over real points. This fact is proved by Mukhin, Tarasov and Varchenko who also develop a relationship ... More

Mass-structure of weighted real treesJan 08 2018Rooted, weighted continuum random trees are used to describe limits of sequences of random discrete trees. Formally, they are random quadruples $(\mathcal{T},d,r,p)$, where $(\mathcal{T},d)$ is a tree-like metric space, $r\in\mathcal{T}$ is a distinguished ... More

K-theoretic Donaldson-Thomas theory and the Hilbert scheme of points on a surfaceMay 11 2019Integrals of characteristic classes of tautological sheaves on the Hilbert scheme of points on a surface frequently arise in enumerative problems. We use the K-theoretic Donaldson-Thomas theory of certain toric Calabi-Yau threefolds to study K-theoretic ... More

Conformal blocks and rational normal curvesDec 21 2010Jan 11 2015We prove that the Chow quotient parametrizing configurations of n points in $\mathbb{P}^d$ which generically lie on a rational normal curve is isomorphic to $\overline{M}_{0,n}$, generalizing the well-known $d = 1$ result of Kapranov. In particular, $\overline{M}_{0,n}$ ... More

The dwarf galaxy population of the Virgo ClusterJun 13 2002Jul 07 2002I review the status of knowledge about the dwarf galaxies in the Virgo Cluster (VC) concentrating on work published after 1995. I explain the present ideas about the nature and history of the dwarf elliptical galaxies and emphasize the major increments ... More

Groups with a Character of Large DegreeMar 10 2006Aug 28 2008Let G be a finite group of order n and V an irreducible representation over the complex numbers of dimension d. For some nonnegative number e, we have n=d(d+e). If e is small, then the character of V has unusually large degree. We fix e and attempt to ... More

Transfinite Recursion in Higher Reverse MathematicsOct 22 2013In this paper we investigate the reverse mathematics of higher-order analogues of the theory \ATRz{} within the framework of higher order reverse mathematics developed by Kohlenbach \cite{Koh01}. We define a theory \RCAzthr, a close higher-type analogue ... More

Ultraviolet Sky SurveysSep 29 1996Sep 30 1996I review the development of UV and EUV astronomy, covering the spectral range from 5 to 300 nm, with emphasis on sky surveys for discrete sources. I discuss studies which resulted in lists of sources observed by imaging. The missions are compared in terms ... More

A Fibonacci summation formula from the Verlinde formulaApr 22 2019There is a family of vector bundles over the moduli space of stable curves that, while first appearing in theoretical physics, has been an active topic of study for algebraic geometers since the 1990s. By computing the rank of the exceptional group $G_2$ ... More

A rotational approach to triple point obstructionsJul 21 2012Subfactors where the initial branching point of the principal graph is 3-valent are subject to strong constraints called triple point obstructions. Since more complicated initial branches increase the index of the subfactor, triple point obstructions ... More

The Liouville phenomenon in the deformation problem of coisotropicsMay 16 2008The work of Oh and Park ([OP]) on the deformation problem of coisotropic submanifolds opened the possibility of studying a large and interesting class of foliations with some explicit geometric tools. These tools assemble into the structure of an L-infinity ... More

Thinking about ArcheoastronomyMar 29 2011I discuss various aspects of archeoastronomy concentrating on physical artifacts (i.e., not including ethno-archeoastronomy) focusing on the period that ended about 2000 years ago. I present examples of artifacts interpreted as showing the interest of ... More

Quest for truly isolated galaxiesJun 23 2009I describe attempts to identify and understand the most isolated galaxies starting from my 1983 Leiden PhD thesis, continuing through a string of graduate theses on various aspects of this topic, and concluding with an up-to-date account of the difficulty ... More

The TAUVEX UV ImagerSep 30 1996I present an up-to-date description of the TAUVEX UV imager, constructed to operate on the Spectrum X-Gamma international space observatory. The projected performance and the expected scientific yield of TAUVEX are described.

Casimir Energies of Periodic Dielectric GratingsJul 17 2014Sep 23 2014Reflection of electromagnetic waves from a periodic grating can be described in terms of a discrete coupled multichannel scattering problem. By modeling the grating as a space- and frequency-dependent dielectric, it is possible to use a variable phase ... More

Resolving a Conjecture on Degree of Regularity of Linear Homogeneous EquationsApr 13 2014A linear equation is $r$-regular, if, for every $r$-coloring of the positive integers, there exist positive integers of the same color which satisfy the equation. In 2005, Fox and Radoicic conjectured that the equation $x_1 + 2x_2 + \cdots + 2^{n-2}x_{n-1} ... More

Mednykh's Formula via Lattice Topological Quantum Field TheoriesMar 05 2007Aug 28 2008Mednykh proved that for any finite group G and any orientable surface S, there is a formula for #Hom(pi_1(S), G) in terms of the Euler characteristic of S and the dimensions of the irreducible representations of G. A similar formula in the nonorientable ... More

Brownian bricklayer: a random space-filling curveAug 23 2017Let $(B(t),\,t\ge0)$ denote the standard, one-dimensional Wiener process and $(\ell(y,t);\, y\in\mathbb{R},\, t\ge0)$ its local time at level $y$ up to time $t$. Then $\big( (B(t),\, \ell(B(t),t)),\; t\ge0 \big)$ is a random path that fills the upper ... More

The dual complex of $\bar{M}_{0,n}$ via phylogeneticsDec 01 2015May 09 2016The moduli space $\bar{M}_{0,n}$ of stable rational n-pointed curves has divisorial boundary with simple normal crossings. In this brief note I observe that the dual complex is a flag complex; that is, a collection of irreducible boundary divisors has ... More

Fibonacci, golden ratio, and vector bundlesApr 22 2019Apr 27 2019There is a family of vector bundles over the moduli space of stable curves that, while first appearing in theoretical physics, has been an active topic of study for algebraic geometers since the 1990s. By computing the rank of the exceptional group $G_2$ ... More

Galaxy interactions in the Hickson Compact Group 88Sep 21 2015I present observations of the Hickson Compact Group 88 (HCG88) obtained during the commissioning of a new 28-inch telescope at the Wise Observatory. This galaxy group was advertised to be non-interacting, or to be in a very early interaction stage, but ... More

Dwarf Irregular Galaxies and the Intergalactic MediumOct 20 1998Dwarf galaxies (DGs) are more numerous than large galaxies. Most dwarfs in clusters are dEs, but in the field they belong mostly to late types. The importance of late-type DGs in the context of the intergalactic medium (IGM) lies in the fact that (at ... More

Electromagnetic Casimir Forces in Elliptic Cylinder GeometriesMar 26 2013The scattering theory approach makes it possible to carry out exact calculations of Casimir energies in any geometry for which the scattering T-matrix and a partial wave expansion of the free Green's function are available. We implement this program for ... More

Schwarzschild Quantum Fluctuations from Regge-Wheeler ScatteringOct 17 2018Jan 08 2019We apply a multichannel variable phase method to scattering from Regge-Wheeler potentials. Using a reduced version of the WKB subtraction developed by Candelas and Howard, this approach allows for efficient numerical calculations of scattering data for ... More

The largest $(k, \ell)$-sum-free sets in compact abelian groupsJan 10 2019Jan 15 2019A subset $A$ of a finite abelian group is called $(k,\ell)$-sum-free if $kA \cap \ell A=\emptyset.$ In this paper, we extend this concept to compact abelian groups and study the question of how large a measurable $(k,\ell)$-sum-free set can be. For integers ... More

Cloudifying the 3GPP IP Multimedia Subsystem for 4G and Beyond: A SurveyDec 01 20154G systems have been continuously evolving to cope with the emerging challenges of human-centric and machine-to- machine (M2M) applications. Research has also now started on 5G systems. Scenarios have been proposed and initial requirements derived. 4G ... More

A Fluid Approach for Poisson Wireless NetworksJan 24 2014Among the different models of networks usually considered, the hexagonal network model is the most popular. However, it requires extensive numerical computations. The Poisson network model, for which the base stations (BS) locations form a spatial Poisson ... More

Analytical Performance Model for Poisson Wireless Networks with Pathloss and Shadowing PropagationNov 19 2014The SINR (signal to interference plus noise ratio) is a key factor for wireless networks analysis. Indeed, the SINR distribution allows the derivation of performance and quality of service (QoS) evaluation. Moreover, it also enables the analysis of radio ... More

Multilingual Universal Sentence Encoder for Semantic RetrievalJul 09 2019We introduce two pre-trained retrieval focused multilingual sentence encoding models, respectively based on the Transformer and CNN model architectures. The models embed text from 16 languages into a single semantic space using a multi-task trained dual-encoder ... More

A Simple Isolation Criterion based on 3D Redshift Space MappingSep 22 2009We selected a sample of galaxies, extremely isolated in 3D redshift space, based on data from NED and the ongoing ALFALFA HI (21cm) survey. A simple selection criterion was employed: having no neighbors closer than 300 km/s in 3D redshift space. The environments ... More

Comment on "Detecting Novel Associations In Large Data Sets" by Reshef Et Al, Science Dec 16, 2011Jan 29 2014The proposal of Reshef et al. (2011) is an interesting new approach for discovering non-linear dependencies among pairs of measurements in exploratory data mining. However, it has a potentially serious drawback. The authors laud the fact that MIC has ... More

Adversarial Evaluation for Models of Natural LanguageJul 01 2012Jul 15 2012We now have a rich and growing set of modeling tools and algorithms for inducing linguistic structure from text that is less than fully annotated. In this paper, we discuss some of the weaknesses of our current methodology. We present a new abstract framework ... More

A Permutation Approach to Testing Interactions in Many DimensionsJun 27 2012To date, testing interactions in high dimensions has been a challenging task. Existing methods often have issues with sensitivity to modeling assumptions and heavily asymptotic nominal p-values. To help alleviate these issues, we propose a permutation-based ... More

Good dynamics versus bad kinematics. Is entanglement needed for quantum computation?Jun 01 1999Jun 03 1999We consider quantum computing with pseudo-pure states. This framework arises in certain implementations of quantum computing using NMR. We analyze quantum computational protocols which aim to solve exponential classical problems with polynomial resources ... More

On the role of entanglement in quantum computational speed-upJan 30 2002Mar 08 2002For any quantum algorithm operating on pure states we prove that the presence of multi-partite entanglement, with a number of parties that increases unboundedly with input size, is necessary if the quantum algorithm is to offer an exponential speed-up ... More

The Halting Problem for Quantum ComputersJun 16 1998Jun 29 1998We argue that the halting problem for quantum computers which was first raised by Myers, is by no means solved, as has been claimed recently. We explicitly demonstrate the difficulties that arise in a quantum computer when different branches of the computation ... More

The Chen-Gibney-Krashen moduli space as a Chow quotientSep 11 2015The space of n distinct points and a disjoint parameterized hyperplane in projective d-space up to projectivity---equivalently, configurations of n distinct points in affine d-space up to translation and homothety---has a beautiful compactification introduced ... More

Nonnegative Tensor Factorization for Directional Blind Audio Source SeparationNov 18 2014We augment the nonnegative matrix factorization method for audio source separation with cues about directionality of sound propagation. This improves separation quality greatly and removes the need for training data, but doubles the computation.

Geometry in the CourtroomSep 17 2017There has been a recent media blitz on a cohort of mathematicians valiantly working to fix America's democratic system by combatting gerrymandering with geometry. While statistics commonly features in the courtroom (forensics, DNA analysis, etc.), the ... More

Exact Electromagnetic Casimir Energy of a Disk Opposite a PlaneJun 03 2016Sep 08 2016Building on work of Meixner [J. Meixner, Z. Naturforschung 3a, 506 (1948)], we show how to compute the exact scattering amplitude (or $T$-matrix) for electromagnetic scattering from a perfectly conducting disk. This calculation is a rare example of a ... More

Robust Constraint of Luminosity Function Evolution Through MCMC SamplingJul 03 2014Sep 30 2014We present a new galaxy survey simulation package, which combines the power of Markov Chain Monte Carlo (MCMC) sampling with a robust and adaptable model of galaxy evolution. The aim of this code is to aid in the characterization and study of new and ... More

Sparse-Input Neural Networks for High-dimensional Nonparametric Regression and ClassificationNov 21 2017Jun 21 2019Neural networks are usually not the tool of choice for nonparametric high-dimensional problems where the number of input features is much larger than the number of observations. Though neural networks can approximate complex multivariate functions, they ... More

New results on the lower central series quotients of a free associative algebraFeb 27 2009Feb 27 2009We continue the study of the lower central series and its associated graded components for a free associative algebra with n generators, as initiated by B. Feigin and B. Shoikhet. We establish a linear bound on the degree of tensor field modules appearing ... More

Subfactors of index less than 5, part 1: the principal graph odometerJul 10 2010Feb 23 2011In this series of papers we show that there are exactly ten subfactors, other than $A_\infty$ subfactors, of index between 4 and 5. Previously this classification was known up to index $3+\sqrt{3}$. In the first paper we give an analogue of Haagerup's ... More

Computational geometry and the U.S. Supreme CourtOct 27 2018We use the United States Supreme Court as an illuminative context in which to discuss three different spatial voting preference models: an instance of the widely used single-peaked preferences, and two models that are more novel in which vote outcomes ... More

Multimodal Generative Models for Scalable Weakly-Supervised LearningFeb 14 2018Nov 12 2018Multiple modalities often co-occur when describing natural phenomena. Learning a joint representation of these modalities should yield deeper and more useful representations. Previous generative approaches to multi-modal input either do not learn a joint ... More

A Grassmann algebra for matroidsOct 15 2015Sep 14 2017We introduce an idempotent analogue of the exterior algebra for which the theory of tropical linear spaces (and valuated matroids) can be seen in close analogy with the classical Grassmann algebra formalism for linear spaces. The top wedge power of a ... More

An Optical-UV-IR Survey of the North Celestial Cap: I. The CatalogueJun 16 2014We describe the final product of the North Celestial Cap Survey (NCC Survey, NCCS) - the optical-UV-IR merged catalogue for the region within 10 deg of the North Celestial Pole. The NCC region at DEC > 80 deg is poorly covered by modern CCD-based surveys. ... More

Scale-free interpersonal influences on opinions in complex systemsJan 12 2014An important side effect of the evolution of the human brain is an increased capacity to form opinions in a very large domain of issues, which become points of aggressive interpersonal disputes. Remarkably, such disputes are often no less vigorous on ... More

The half-twist for U_q(g) representationsOct 01 2008Oct 30 2009We introduce the notion of a half-ribbon Hopf algebra, which is a ribbon Hopf algebra along with a distinguished element $t$ corresponding to twisting a ribbon by 180 degrees (the half-twist). We show that U_q(g) is a (topological) half-ribbon Hopf algebra, ... More

Inhomogeneous Quantum WalksJun 19 2009We study a natural construction of a general class of inhomogeneous quantum walks (namely walks whose transition probabilities depend on position). Within the class we analyze walks that are periodic in position and show that, depending on the period, ... More

Measurement entropy in Generalized Non-Signalling Theory cannot detect bipartite non-localityJul 13 2012Nov 13 2012We consider entropy in Generalized Non-Signalling Theory (also known as box world) where the most common definition of entropy is the measurement entropy. In this setting, we completely characterize the set of allowed entropies for a bipartite state. ... More

Hypergraph VersalsFeb 04 2016Let H be a hypergraph on n vertices with the property that no edge contains another. We prove some results for a special case of the Isolation Lemma when the label set for the edges of H can only take two values. Given any set of vertices S and an edge ... More

A time-distance trade-off for GDD with preprocessing---Instantiating the DLW heuristicFeb 22 2019For $0 \leq \alpha \leq 1/2$, we show an algorithm that does the following. Given appropriate preprocessing $P(\mathcal{L})$ consisting of $N_\alpha := 2^{O(n^{1-2\alpha} + \log n)}$ vectors in some lattice $\mathcal{L} \subset \mathbb{R}^n$ and a target ... More

Contextual Word Representations: A Contextual IntroductionFeb 15 2019Feb 19 2019This introduction aims to tell the story of how we put words into computers. It is part of the story of the field of natural language processing (NLP), a branch of artificial intelligence. It targets a wide audience with a basic understanding of computer ... More

From Poland to "Petersburg": The Banach-Tarski Paradox in Bely's Modernist NovelOct 16 2017Andrei Bely's novel "Petersburg," first published in 1913, was declared by Vladimir Nabokov one of the four greatest masterpieces of 20th-century prose. The Banach-Tarski Paradox, published in 1924, is one of the most striking and well-known results in ... More

Robustness of Measurement, discrimination games and accessible informationSep 07 2018We introduce a way of quantifying how informative a quantum measurement is, starting from a resource-theoretic perspective. This quantifier, which we call the robustness of measurement, describes how much `noise' must be added to a measurement before ... More

Principal component analysis of IUE galaxy spectraFeb 12 2004We analyse the UV spectral energy distribution of a sample of normal galaxies listed in the IUE-INES Guide No. 2-Normal Galaxies (Formiggini & Brosch, 2000) using a Principal Component Analysis. The sample consists of the IUE-SW spectra of the central ... More

Using Propensity Scores to Develop and Evaluate Treatment Rules with Observational DataMay 29 2019In this paper, we outline a principled approach to estimate an individualized treatment rule that is appropriate for data from observational studies where, in addition to treatment assignment not being independent of individual characteristics, some characteristics ... More

Using Propensity Scores to Develop and Evaluate Treatment Rules with Observational DataMay 29 2019Jun 03 2019In this paper, we outline a principled approach to estimate an individualized treatment rule that is appropriate for data from observational studies where, in addition to treatment assignment not being independent of individual characteristics, some characteristics ... More

An analysis of the cost of hyper-parameter selection via split-sample validation, with applications to penalized regressionMar 28 2019In the regression setting, given a set of hyper-parameters, a model-estimation procedure constructs a model from training data. The optimal hyper-parameters that minimize generalization error of the model are usually unknown. In practice they are often ... More

Gradient-based Regularization Parameter Selection for Problems with Non-smooth Penalty FunctionsMar 28 2017In high-dimensional and/or non-parametric regression problems, regularization (or penalization) is used to control model complexity and induce desired structure. Each penalty has a weight parameter that indicates how strongly the structure corresponding ... More

Modular interpretation of a non-reductive Chow quotientSep 11 2015Sep 17 2017The space of n distinct points and a disjoint parameterized hyperplane in projective d-space up to projectivity---equivalently, configurations of n distinct points in affine d-space up to translation and homothety---has a beautiful compactification introduced ... More

Learning Semantic Textual Similarity from ConversationsApr 20 2018We present a novel approach to learn representations for sentence-level semantic similarity using conversational data. Our method trains an unsupervised model to predict conversational input-response pairs. The resulting sentence embeddings perform well ... More

Effective Parallel Corpus Mining using Bilingual Sentence EmbeddingsJul 31 2018Aug 02 2018This paper presents an effective approach for parallel corpus mining using bilingual sentence embeddings. Our embedding models are trained to produce similar representations exclusively for bilingual sentence pairs that are translations of each other. ... More

Complex Objects in the Polytopes of the Linear State-Space ProcessJan 21 2014A simple object (one point in $m$-dimensional space) is the resultant of the evolving matrix polynomial of walks in the irreducible aperiodic network structure of the first order DeGroot (weighted averaging) state-space process. This paper draws on a ... More

Grey Milky Way Extinction from SDSS Stellar PhotometrySep 01 2009We report results concerning the distribution and properties of galactic extinction at high galactic latitudes derived from stellar statistics using the Sloan Digital Sky Survey (SDSS). We use the classical Wolf diagram method to identify regions with ... More

A presentation of the deformed W_{1+\infty} algebraSep 03 2012We provide a generators and relation description of the deformed W_{1+\infty}-algebra introduced in previous joint work of E. Vasserot and the second author. This gives a presentation of the (spherical) cohomological Hall algebra of the one-loop quiver, ... More

Discriminant Analysis with Adaptively Pooled CovarianceNov 07 2011Dec 06 2011Linear and Quadratic Discriminant analysis (LDA/QDA) are common tools for classification problems. For these methods we assume observations are normally distributed within group. We estimate a mean and covariance matrix for each group and classify using ... More

Bell nonlocality and Bayesian game theoryOct 03 2012We discuss a connection between Bell nonlocality and Bayesian games. This link offers interesting perspectives for Bayesian games, namely to allow the players to receive advice in the form of nonlocal correlations, for instance using entangled quantum ... More

Quantum communication beyond the localization length in disordered spin chainsJan 31 2008We study the effects of localization on quantum state transfer in spin chains. We show how to use quantum error correction and multiple parallel spin chains to send a qubit with high fidelity over arbitrary distances; in particular distances much greater ... More

Quantum temporal logic and decoherence functionals in the histories approach to generalised quantum theoryMay 11 1994We analyse and develop the recent suggestion that a temporal form of quantum logic provides the natural mathematical framework within which to discuss the proposal by Gell-Mann and Hartle for a generalised form of quantum theory based on the ideas of ... More

Preparing graduate students to be educatorsSep 01 2006We present two programs that address needs to better prepare graduate students for their roles as professional physicists, particularly in the areas of teaching and education research. The two programs, Preparing Future Physicists (PFP) and a course, ... More

Rank conditional coverage and confidence intervals in high dimensional problemsFeb 22 2017Confidence interval procedures used in low dimensional settings are often inappropriate for high dimensional applications. When a large number of parameters are estimated, marginal confidence intervals associated with the most significant estimates have ... More

Radiatively induced symmetry breaking and the conformally coupled magnetic monopole in AdS spaceOct 29 2013We implement quantum corrections for a magnetic monopole in a classically conformally invariant theory containing gravity. This yields the trace (conformal) anomaly and introduces a length scale in a natural fashion via the process of renormalization. ... More

Mathematical Symbolism in a Russian Literary MasterpieceSep 07 2017Andrei Bely's modernist novel "Petersburg," first published in 1913, is considered a pinnacle of the Symbolist movement. Nabokov famously ranked it as one of the four greatest masterpieces of 20th-century prose. The author's father, Bugaev, was an influential ... More

Normal Galaxies - INES Guide No. 2Feb 12 2004This guide presents, in a uniform manner, all the information collected by the IUE satellite on normal galaxies. It contains information on 274 galaxies and it supersedes the previous IUE guide to normal galaxies (Longo & Capaccioli 1992). The data shown ... More

Sparse-Input Neural Networks for High-dimensional Nonparametric Regression and ClassificationNov 21 2017Neural networks are usually not the tool of choice for nonparametric high-dimensional problems where the number of input features is much larger than the number of observations. Though neural networks can approximate complex multivariate functions, they ... More

Spatial analysis of U.S. Supreme Court 5-to-4 decisionsApr 22 2018While the U.S. Supreme Court is commonly viewed as comprising a liberal bloc and a conservative bloc, with a possible swing vote or median justice between them, surprisingly many case decisions are not explained by this simple model. We introduce a pair ... More

Transition To Order After Hilltop InflationJan 24 2014We investigate the rich nonlinear dynamics during the end of hilltop inflation by numerically solving the coupled Klein-Gordon-Friedmann equations in a expanding universe. In particular, we search for coherent, nonperturbative configurations that may ... More

Quantum subgroups of the Haagerup fusion categoriesFeb 13 2011Sep 01 2011We answer three related questions concerning the Haagerup subfactor and its even parts, the Haagerup fusion categories. Namely we find all simple module categories over each of the Haagerup fusion categories (in other words, we find the `"quantum subgroups" ... More

Linear extension numbers of $n$-element posetsJun 14 2019We address the following natural but hitherto unstudied question: what are the possible linear extension numbers of an $n$-element poset? Let $\mathbf{LE}(n)$ denote the set of all positive integers that arise as the number of linear extensions of some ... More

Neural Discourse Structure for Text CategorizationFeb 07 2017May 06 2017We show that discourse structure, as defined by Rhetorical Structure Theory and provided by an existing discourse parser, benefits text categorization. Our approach uses a recursive neural network and a newly proposed attention mechanism to compute a ... More

The cone of type A, level one conformal blocks divisorsMay 16 2011May 17 2011We prove that the type A, level one, conformal blocks divisors on $\bar{M}_{0,n}$ span a finitely generated, full-dimensional subcone of the nef cone. Each such divisor induces a morphism from $\bar{M}_{0,n}$, and we identify its image as a GIT quotient ... More

Projective linear configurations via non-reductive actionsJan 03 2014We study the iterated blow-up X of projective space along an arbitrary collection of linear subspaces. By replacing the universal torsor with an $\mathbb{A}^1$-homotopy equivalent model, built from $\mathbb{A}^1$-fiber bundles not just algebraic line ... More

UGC 4599: A Photometric Study of the Nearest Hoag-Type Ring GalaxyFeb 15 2011We present a photometric study of UGC 4599, a low-luminosity galaxy superficially resembling Hoag's Object in that on sky survey images it appears to be a complete ring surrounding a roundish core. The nature of the outer ring of Hoag-type galaxies is ... More

Discrete Gaussian Sampling Reduces to CVP and SVPJun 24 2015Apr 19 2016The discrete Gaussian $D_{L- t, s}$ is the distribution that assigns to each vector $x$ in a shifted lattice $L - t$ probability proportional to $e^{-\pi \|x\|^2/s^2}$. It has long been an important tool in the study of lattices. More recently, algorithms ... More

Acyclic Subgraphs of Planar DigraphsJul 30 2014An acyclic set in a digraph is a set of vertices that induces an acyclic subgraph. In 2011, Harutyunyan conjectured that every planar digraph on $n$ vertices without directed 2-cycles possesses an acyclic set of size at least $3n/5$. We prove this conjecture ... More

On a lower central series filtration of the Grothendieck-Teichmüller Lie algebra grt_1Jun 03 2014The Grothendieck-Teichm\"uller Lie algebra is a Lie subalgebra of a Lie algebra of derivations of the free Lie algebra in two generators. We show that the lower central series of the latter Lie algebra induces a decreasing filtration of the Grothendieck-Teichm\"uller ... More

Generalization of the PageRank ModelJan 19 2014This paper develops a generalization of the PageRank model of page centralities in the global webgraph of hyperlinks. The webgraph of adjacencies is generalized to a valued directed graph, and the scalar dampening coefficient for walks through the graph ... More

Factorization of point configurations, cyclic covers and conformal blocksAug 20 2012We describe a relation between the invariants of $n$ ordered points in $P^d$ and of points contained in a union of linear subspaces $P^{d1}\cup P^{d2} \subset P^d$. This yields an attaching map for GIT quotients parameterizing point configurations in ... More

An Optical-UV Survey of the North Celestial CapJan 08 2011We present preliminary results of an optical-UV survey of the North Celestial Cap (NCCS) based on ~5% areal coverage. The NCCS will provide good photometric and astrometric data for the North Celestial Cap region (80 < DEC < 90). This region, at galactic ... More

Late-Type Dwarf Galaxies in the Virgo Cluster: II. Star Formation PropertiesMar 25 1996Apr 22 1998We study star-formation-inducing mechanisms in galaxies through multi- wavelength measurements of a sample of dwarf galaxies in the Virgo cluster described in paper I. Our main goal is to test how star formation inducing mechanisms depend on several parameters ... More