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Are All Languages Equally Hard to Language-Model?Jun 10 2018For general modeling methods applied to diverse languages, a natural question is: how well should we expect our models to work on languages with differing typological profiles? In this work, we develop an evaluation framework for fair cross-linguistic ... More

A Structured Variational Autoencoder for Contextual Morphological InflectionJun 10 2018Statistical morphological inflectors are typically trained on fully supervised, type-level data. One remaining open research question is the following: How can we effectively exploit raw, token-level data to improve their performance? To this end, we ... More

Unsupervised Disambiguation of Syncretism in Inflected LexiconsJun 10 2018Lexical ambiguity makes it difficult to compute various useful statistics of a corpus. A given word form might represent any of several morphological feature bundles. One can, however, use unsupervised learning (as in EM) to fit a model that probabilistically ... More

Counterfactual Data Augmentation for Mitigating Gender Stereotypes in Languages with Rich MorphologyJun 11 2019Gender stereotypes are manifest in most of the world's languages and are consequently propagated or amplified by NLP systems. Although research has focused on mitigating gender stereotypes in English, the approaches that are commonly employed produce ... More

A Deep Generative Model of Vowel Formant TypologyJul 08 2018What makes some types of languages more probable than others? For instance, we know that almost all spoken languages contain the vowel phoneme /i/; why should that be? The field of linguistic typology seeks to answer these questions and, thereby, divine ... More

What Kind of Language Is Hard to Language-Model?Jun 11 2019How language-agnostic are current state-of-the-art NLP tools? Are there some types of language that are easier to model with current methods? In prior work (Cotterell et al., 2018) we attempted to address this question for language modeling, and observed ... More

Probabilistic Typology: Deep Generative Models of Vowel InventoriesMay 04 2017Linguistic typology studies the range of structures present in human language. The main goal of the field is to discover which sets of possible phenomena are universal, and which are merely frequent. For example, all languages have vowels, while most---but ... More

Explaining and Generalizing Back-Translation through Wake-SleepJun 12 2018Back-translation has become a commonly employed heuristic for semi-supervised neural machine translation. The technique is both straightforward to apply and has led to state-of-the-art results. In this work, we offer a principled interpretation of back-translation ... More

Cross-lingual, Character-Level Neural Morphological TaggingAug 30 2017Even for common NLP tasks, sufficient supervision is not available in many languages -- morphological tagging is no exception. In the work presented here, we explore a transfer learning scheme, whereby we train character-level recurrent neural taggers ... More

Exact Hard Monotonic Attention for Character-Level TransductionMay 15 2019Many common character-level, string-to-string transduction tasks, e.g., grapheme-to-phoneme conversion and morphological inflection, consist almost exclusively of monotonic transduction. Neural sequence-to-sequence models with soft attention, non-monotonic ... More

Analysis of Morphology in Topic ModelingAug 13 2016Topic models make strong assumptions about their data. In particular, different words are implicitly assumed to have different meanings: topic models are often used as human-interpretable dimensionality reductions and a proliferation of words with identical ... More

A Simple Joint Model for Improved Contextual Neural LemmatizationApr 04 2019English verbs have multiple forms. For instance, talk may also appear as talks, talked or talking, depending on the context. The NLP task of lemmatization seeks to map these diverse forms back to a canonical one, known as the lemma. We present a simple ... More

A Simple Joint Model for Improved Contextual Neural LemmatizationApr 04 2019Apr 05 2019English verbs have multiple forms. For instance, talk may also appear as talks, talked or talking, depending on the context. The NLP task of lemmatization seeks to map these diverse forms back to a canonical one, known as the lemma. We present a simple ... More

CoNLL-SIGMORPHON 2017 Shared Task: Universal Morphological Reinflection in 52 LanguagesJun 27 2017Jul 04 2017The CoNLL-SIGMORPHON 2017 shared task on supervised morphological generation required systems to be trained and tested in each of 52 typologically diverse languages. In sub-task 1, submitted systems were asked to predict a specific inflected form of a ... More

UniMorph 2.0: Universal MorphologyOct 25 2018The Universal Morphology UniMorph project is a collaborative effort to improve how NLP handles complex morphology across the world's languages. The project releases annotated morphological data using a universal tagset, the UniMorph schema. Each inflected ... More

The CoNLL--SIGMORPHON 2018 Shared Task: Universal Morphological ReinflectionOct 16 2018Oct 18 2018The CoNLL--SIGMORPHON 2018 shared task on supervised learning of morphological generation featured data sets from 103 typologically diverse languages. Apart from extending the number of languages involved in earlier supervised tasks of generating inflected ... More

Hard Non-Monotonic Attention for Character-Level TransductionAug 29 2018Character-level string-to-string transduction is an important component of various NLP tasks. The goal is to map an input string to an output string, where the strings may be of different lengths and have characters taken from different alphabets. Recent ... More

Paradigm Completion for Derivational MorphologyAug 30 2017The generation of complex derived word forms has been an overlooked problem in NLP; we fill this gap by applying neural sequence-to-sequence models to the task. We overview the theoretical motivation for a paradigmatic treatment of derivational morphology, ... More

Generalizing Procrustes Analysis for Better Bilingual Dictionary InductionAug 31 2018Sep 14 2018Most recent approaches to bilingual dictionary induction find a linear alignment between the word vector spaces of two languages. We show that projecting the two languages onto a third, latent space, rather than directly onto each other, while equivalent ... More

A Discriminative Latent-Variable Model for Bilingual Lexicon InductionAug 28 2018Oct 25 2018We introduce a novel discriminative latent-variable model for the task of bilingual lexicon induction. Our model combines the bipartite matching dictionary prior of Haghighi et al. (2008) with a state-of-the-art embedding-based approach. To train the ... More

A Probabilistic Generative Model of Linguistic TypologyMar 26 2019May 15 2019In the principles-and-parameters framework, the structural features of languages depend on parameters that may be toggled on or off, with a single parameter often dictating the status of multiple features. The implied covariance between features inspires ... More

A Markov Model for Ontology AlignmentApr 20 2013The explosion of available data along with the need to integrate and utilize that data has led to a pressing interest in data integration techniques. In terms of Semantic Web technologies, Ontology Alignment is a key step in the process of integrating ... More

On the Diachronic Stability of Irregularity in Inflectional MorphologyApr 23 2018Many languages' inflectional morphological systems are replete with irregulars, i.e., words that do not seem to follow standard inflectional rules. In this work, we quantitatively investigate the conditions under which irregulars can survive in a language ... More

On the Complexity and Typology of Inflectional Morphological SystemsJul 08 2018We quantify the linguistic complexity of different languages' morphological systems. We verify that there is an empirical trade-off between paradigm size and irregularity: a language's inflectional paradigms may be either large in size or highly irregular, ... More

Contextualization of Morphological InflectionMay 04 2019Critical to natural language generation is the production of correctly inflected text. In this paper, we isolate the task of predicting a fully inflected sentence from its partially lemmatized version. Unlike traditional morphological inflection or surface ... More

A Probabilistic Generative Model of Linguistic TypologyMar 26 2019In the Principles and Parameters framework, the structural features of languages depend on parameters that may be toggled on or off, with a single parameter often dictating the status of multiple features. The implied covariance between features inspires ... More

On the Idiosyncrasies of the Mandarin Chinese Classifier SystemFeb 26 2019While idiosyncrasies of the Chinese classifier system have been a richly studied topic among linguists (Adams and Conklin, 1973; Erbaugh, 1986; Lakoff, 1986), not much work has been done to quantify them with statistical methods. In this paper, we introduce ... More

Unsupervised Discovery of Gendered Language through Latent-Variable ModelingJun 11 2019Studying the ways in which language is gendered has long been an area of interest in sociolinguistics. Studies have explored, for example, the speech of male and female characters in film and the language used to describe male and female politicians. ... More

Frame-Based Continuous Lexical Semantics through Exponential Family Tensor Factorization and Semantic Proto-RolesJun 29 2017We study how different frame annotations complement one another when learning continuous lexical semantics. We learn the representations from a tensorized skip-gram model that consistently encodes syntactic-semantic content better, with multiple 10% gains ... More

A Probabilistic Generative Model of Linguistic TypologyMar 26 2019Apr 09 2019In the principles-and-parameters framework, the structural features of languages depend on parameters that may be toggled on or off, with a single parameter often dictating the status of multiple features. The implied covariance between features inspires ... More

System Synthesis for Networks of Programmable BlocksOct 25 2007The advent of sensor networks presents untapped opportunities for synthesis. We examine the problem of synthesis of behavioral specifications into networks of programmable sensor blocks. The particular behavioral specification we consider is an intuitive ... More

Combining Sentiment Lexica with a Multi-View Variational AutoencoderApr 05 2019When assigning quantitative labels to a dataset, different methodologies may rely on different scales. In particular, when assigning polarities to words in a sentiment lexicon, annotators may use binary, categorical, or continuous labels. Naturally, it ... More

Marrying Universal Dependencies and Universal MorphologyOct 15 2018The Universal Dependencies (UD) and Universal Morphology (UniMorph) projects each present schemata for annotating the morphosyntactic details of language. Each project also provides corpora of annotated text in many languages - UD at the token level and ... More

Meaning to Form: Measuring Systematicity as InformationJun 13 2019A longstanding debate in semiotics centers on the relationship between linguistic signs and their corresponding semantics: is there an arbitrary relationship between a word form and its meaning, or does some systematic phenomenon pervade? For instance, ... More

Gender Bias in Contextualized Word EmbeddingsApr 05 2019In this paper, we quantify, analyze and mitigate gender bias exhibited in ELMo's contextualized word vectors. First, we conduct several intrinsic analyses and find that (1) training data for ELMo contains significantly more male than female entities, ... More

A decomposition theorem for higher rank Coxeter groupsJul 21 2010In this paper, we show that any Coxeter graph which defines a higher rank Coxeter group must have disjoint induced subgraphs each of which defines a hyperbolic or higher rank Coxeter group. We then use this result to demonstrate several classes of Coxeter ... More

Option pricing in the large risk aversion, small transaction cost limitFeb 17 2011May 27 2014We characterize the price of a European option on several assets for a very risk averse seller, in a market with small transaction costs as a solution of a nonlinear diffusion equation. This problem turns out to be one of asymptotic analysis of parabolic ... More

A statistical inference course based on p-valuesJun 07 2016Introductory statistical inference texts and courses treat the point estimation, hypothesis testing, and interval estimation problems separately, with primary emphasis on large-sample approximations. Here I present an alternative approach to teaching ... More

Concerning the Szlenk indexJan 27 2015We discuss pruning and coloring lemmas on regular families. We discuss several applications of these lemmas to computing the Szlenk index of certain $w^*$ compact subsets of the dual of a separable Banach space. Applications include estimates of the Szlenk ... More

Pick interpolation in several variablesOct 03 2011Oct 05 2011We investigate the Pick problem for the polydisk and unit ball using dual algebra techniques. Some factorization results for Bergman spaces are used to describe a Pick theorem for any bounded region in $\mathbb{C}^d$.

Asymptotic results on Klazar set partition avoidanceAug 07 2016We establish asymptotic bounds for the number of partitions of $[n]$ avoiding a given partition in Klazar's sense, obtaining the correct answer to within an exponential for the block case. This technique also enables us to establish a general lower bound. ... More

The Decrits Consensus Algorithm: Decentralized Agreement without Proof of WorkNov 04 2014Decrits is a cryptocurrency in development that makes use of a novel consensus algorithm that does not require proof-of-work. This paper describes how the Decrits Consensus Algorithm (DCA) is as trustless as a proof-of-work algorithm while offering superior ... More

Combinatorial spin structures on triangulated manifoldsJun 20 2013Oct 11 2014This paper gives a combinatorial description of spin and spin^c-structures on triangulated PL-manifolds of arbitrary dimension. These formulations of spin and spin^c-structures are established primarily for the purpose of aiding in computations. The novelty ... More

A trajectory map for the pressureless Euler equationsFeb 12 2019We consider the dynamics of a collection of particles that interact pairwise and are restricted to move along the real line. Moreover, we focus on the situation in which particles undergo perfectly inelastic collisions when they collide. The equations ... More

Attractors of sequences of iterated function systemsNov 03 2016If $F$ and $G$ are iterated function systems, then any infinite word $W$ in the symbols $F$ and $G$ induces a limit set. It is natural to ask whether this Cantor set can also be realized as the limit set of a single $C^{1 + \alpha}$ iterated function ... More

Foundations of a pathwise volatility framework with explicit fast reversion limitsFeb 05 2019Our first main results are the existence and uniqueness of solutions to a `generalised CIR initial-value problem', which originates from the classical Cox-Ingersoll-Ross (CIR) stochastic differential equation after a time-change. These results hold on ... More

A new proposal for group field theory I: the 3d caseNov 14 2006In this series of papers, we propose a new rendition of 3d and 4d state sum models based upon the group field theory (GFT) approach to non-perturbative quantum gravity. We will see that the group field theories investigated in the literature to date are, ... More

Introductory Clifford AnalysisMar 26 2003This paper is an elaboration of an introductory talk given by the author at a workshop on Clifford algebras at Tennessee Technical University, in May 2002. We give an introduction to the basic concepts of Clifford analysis, including links to harmonic ... More

Offensive Language Analysis using Deep Learning ArchitectureMar 12 2019Mar 19 2019SemEval-2019 Task 6 (Zampieri et al., 2019b) requires us to identify and categorise offensive language in social media. In this paper we will describe the process we took to tackle this challenge. Our process is heavily inspired by Sosa (2017) where he ... More

The weighted Fourier inequality, polarity, and reverse Hölder inequalityJul 23 2016Nov 17 2017We examine the problem of the Fourier transform mapping one weighted Lebesgue space into another, by studying necessary conditions and sufficient conditions which expose an underlying geometry. In the necessary conditions, this geometry is connected to ... More

New inequalities for subspace arrangementsMay 11 2009Oct 26 2009For each positive integer $n \geq 4$, we give an inequality satisfied by rank functions of arrangements of $n$ subspaces. When $n=4$ we recover Ingleton's inequality; for higher $n$ the inequalities are all new. These inequalities can be thought of as ... More

Uniqueness of the measure of maximal entropy for the squarefree flowMay 13 2012Oct 07 2014The squarefree flow is a natural dynamical system whose topological and ergodic properties are closely linked to the behavior of squarefree numbers. We prove that the squarefree flow carries a unique measure of maximal entropy and express this measure ... More

Möbius disjointness for homogeneous dynamicsJun 25 2015Oct 16 2016We prove Sarnak's M\"obius disjointness conjecture for all unipotent translations on homogeneous spaces of real connected Lie groups. Namely, we show that if $G$ is any such group, $\Gamma\subset G$ a lattice, and $u\in G$ an Ad-unipotent element, then ... More

Distributed Memory Techniques for Classical Simulation of Quantum CircuitsJan 02 2018Jun 21 2018In this paper we describe, implement, and test the performance of distributed memory simulations of quantum circuits on the MSU Laconia Top500 supercomputer. Using OpenMP and MPI hybrid parallelization, we first use a distributed matrix-vector multiplication ... More

Little cubes and long knotsSep 26 2003Dec 18 2006This paper gives a partial description of the homotopy type of K, the space of long knots in 3-dimensional Euclidean space. The primary result is the construction of a homotopy equivalence between K and the free little 2-cubes object over the space of ... More

Rank functions on rooted tree quiversJul 28 2008Mar 09 2009The free abelian group R(Q) on the set of indecomposable representations of a quiver Q, over a field K, has a ring structure where the multiplication is given by the tensor product. We show that if Q is a rooted tree (an oriented tree with a unique sink), ... More

Natural Proofs Versus DerandomizationDec 09 2012Jul 21 2015We study connections between Natural Proofs, derandomization, and the problem of proving "weak" circuit lower bounds such as ${\sf NEXP} \not\subset {\sf TC^0}$. Natural Proofs have three properties: they are constructive (an efficient algorithm $A$ is ... More

A Casual Tour Around a Circuit Complexity BoundNov 04 2011I will discuss the recent proof that the complexity class NEXP (nondeterministic exponential time) lacks nonuniform ACC circuits of polynomial size. The proof will be described from the perspective of someone trying to discover it.

Alternation-Trading Proofs, Linear Programming, and Lower BoundsJan 05 2010Feb 03 2010A fertile area of recent research has demonstrated concrete polynomial time lower bounds for solving natural hard problems on restricted computational models. Among these problems are Satisfiability, Vertex Cover, Hamilton Path, Mod6-SAT, Majority-of-Majority-SAT, ... More

Applying Practice to TheoryNov 09 2008How can complexity theory and algorithms benefit from practical advances in computing? We give a short overview of some prior work using practical computing to attack problems in computational complexity and algorithms, informally describe how linear ... More

Strong ETH Breaks With Merlin and Arthur: Short Non-Interactive Proofs of Batch EvaluationJan 18 2016We present an efficient proof system for Multipoint Arithmetic Circuit Evaluation: for every arithmetic circuit $C(x_1,\ldots,x_n)$ of size $s$ and degree $d$ over a field ${\mathbb F}$, and any inputs $a_1,\ldots,a_K \in {\mathbb F}^n$, $\bullet$ the ... More

Heavy quark physics from lattice QCDNov 08 2001Apr 07 2002I review the current status of lattice calculations of heavy quark quantities. Particular emphasis is placed on leptonic and semileptonic decay matrix elements.

Lattice determinations of the strange quark massAug 17 1999Aug 18 1999Lattice calculations of the mass of the strange quark are reviewed. In particular, the reason for the spread in values is explained with emphasis on the effects that recently implemented improvements have had on the lattice determinations.

Finite orbits in random subshifts of finite typeJun 08 2015Nov 15 2016For each $n, d \in \mathbb{N}$ and $0 < \alpha < 1$, we define a random subset of $\mathcal{A}^{\{1, 2, \dots, n\}^d}$ by independently including each element with probability $\alpha$ and excluding it with probability $1-\alpha$, and consider the associated ... More

Galactic Disc Rotation: Analytic models and asymptotic resultsJan 22 2013Jul 22 2013This paper outlines an exact analytic model for self-gravitating thin disc galaxies with flat rotation curves. It is shown that thin discs of matter alone can support perfectly flat rotation curves under Newtonian gravity, without needing extended halos ... More

An eigenvalue problem for fully nonlinear elliptic equations with gradient constraintsDec 27 2014Aug 30 2015We consider the problem of finding $\lambda\in \mathbb{R}$ and a function $u:\mathbb{R}^n\rightarrow\mathbb{R}$ that satisfy the PDE $$ \max\left\{\lambda + F(D^2u) -f(x),H(Du)\right\}=0, \quad x\in \mathbb{R}^n. $$ Here $F$ is elliptic, positively homogeneous ... More

Compactness methods for doubly nonlinear parabolic systemsOct 29 2014Aug 23 2015We study solutions of the system of PDE $D\psi({\bf v}_t)=\text{div}DF(D{\bf v})$, where $\psi$ and $F$ are convex functions. This type of system arises in various physical models for phase transitions. We establish compactness properties of solutions ... More

A new Computer Friendly Notation for Musical Composition in Just Intonation allowing Easy Transposition by Multiplication of NotationsAug 31 2015Mar 11 2016Musical notation systems provide ways of recording which notes musicians should play at which times. One essential parameter described is the frequency. For twelve note tuning systems the frequency can be described using letters A to G with sharp or flat ... More

Proximity to $\ell_p$ and $c_0$ in Banach spacesFeb 20 2015We construct a class of minimal trees and use these trees to establish a number of coloring theorems on general trees. Among the applications of these trees and coloring theorems are quantification of the Bourgain $\ell_p$ and $c_0$ indices, dualization ... More

Estimation of the Szlenk index of reflexive Banach spaces using generalized Baernstein spacesAug 25 2013For each ordinal $\alpha< \omega_1$, we prove the existence of a separable, reflexive Banach space with a basis and Szlenk index $\omega^{\alpha+1}$ which is universal for the class of separable, reflexive Banach spaces $X$ such that the Szlenk indices ... More

On nonparametric estimation of a mixing density via the predictive recursion algorithmDec 05 2018Nonparametric estimation of a mixing density based on observations from the corresponding mixture is a challenging statistical problem. This paper surveys the literature on a fast, recursive estimator based on the predictive recursion algorithm. After ... More

Incorrigibility in the CIRL FrameworkSep 19 2017Jun 03 2018A value learning system has incentives to follow shutdown instructions, assuming the shutdown instruction provides information (in the technical sense) about which actions lead to valuable outcomes. However, this assumption is not robust to model mis-specification ... More

A pathwise variation estimate for the sticky particle systemApr 25 2018Aug 04 2018We study collections of finitely many point masses that move freely in space and stick together when they collide via perfectly inelastic collisions. We establish a uniform bound on the mass average of the total variation of the velocities of particle ... More

Cauchy kernels for some conformally flat manifoldsMar 26 2003Here we will consider examples of conformally flat manifolds that are conformally equivalent to open subsets of the n-dimensional sphere. For such manifolds we shall introduce a Cauchy kernel and Cauchy integral formula for sections tasking values in ... More

Edge-state instabilities of bosons in a topological bandAug 08 2013Feb 21 2014In this work, we consider the dynamics of bosons in bands with non-trivial topological structure. In particular, we focus on the case where bosons are prepared in a higher-energy band and allowed to evolve. The Bogoliubov theory about the initial state ... More

Security Landscape for RoboticsApr 05 2019In this paper, the current state of security in robotics is described to be in need of review. When we consider safety mechanisms implemented in an Internet-connected robot, the requirement of safety becomes a crucial security requirement. Upon review ... More

Notes on Beilinson's "How to glue perverse sheaves"Feb 08 2010Jul 11 2010The titular, foundational work of Beilinson not only gives a technique for gluing perverse sheaves but also implicitly contains constructions of the nearby and vanishing cycles functors of perverse sheaves. These constructions are completely elementary ... More

The rank of a quiver representationNov 07 2007Mar 09 2009We define a functor which gives the "global rank of a quiver representation" and prove that it has nice properties which make it a generalization of the rank of a linear map. We demonstrate how to construct other "rank functors" for a quiver Q, which ... More

Twisted Analytic Torsion and Adiabatic LimitsNov 26 2013We study an analogue of the analytic torsion for elliptic complexes that are graded by $\mathbb{Z}_2$, orignally constructed by Mathai and Wu. Motivated by topological T-duality, Bouwknegt an Mathai study the complex of forms on an odd-dimensional manifold ... More

Extremal Behavior in Exponential Random GraphsJun 03 2019Yin, Rinaldo, and Fadnavis classified the extremal behavior of the edge-triangle exponential random graph model by first taking the network size to infinity, then the parameters diverging to infinity along straight lines. Lubetzky and Zhao proposed an ... More

On the optimal stacking of noisy observationsApr 14 2010Observations where additive noise is present can for many models be grouped into a compound observation matrix, adhering to the same type of model. There are many ways the observations can be stacked, for instance vertically, horizontally, or quadratically. ... More

Big Bang Nucleosynthesis and the Helium Isotope RatioOct 09 2015The conventional approach to search for departures from the standard model of physics during Big Bang Nucleosynthesis involves a careful, and subtle measurement of the mass fraction of baryons consisting of helium. Recent measurements of this quantity ... More

A Conversation with Nan LairdDec 11 2015Nan McKenzie Laird is the Harvey V. Fineberg Professor of Biostatistics at the Harvard T. H. Chan School of Public Health. She has made fundamental contributions to statistical methods for longitudinal data analysis, missing data and meta-analysis. In ... More

The weighted Fourier inequality, polarity, and reverse Hölder inequalityJul 23 2016Oct 05 2016We examine the problem of the Fourier transform mapping one weighted Lebesgue space into another, by studying necessary conditions and sufficient conditions which expose an underlying geometry. In the necessary conditions, this geometry is connected to ... More

Dynamic Belief Fusion for Object DetectionFeb 26 2015Nov 12 2015A novel approach for the fusion of detection scores from disparate object detection methods is proposed. In order to effectively integrate the outputs of multiple detectors, the level of ambiguity in each individual detection score (called "uncertainty") ... More

Analogs of the Shapiro Shapiro Conjecture in Positive CharacteristicMay 19 2016Motivated by the Shapiro Shapiro conjecture, we consider the following: given a field $k$, under what conditions must a rational function with only $k$-rational ramification points be equivalent (after post-composition with a fractional linear transformation) ... More

Asymptotic results on Klazar set partition avoidanceAug 07 2016Mar 15 2018We establish asymptotic bounds for the number of partitions of $[n]$ avoiding a given partition in Klazar's sense, obtaining the correct answer to within an exponential for the block case. This technique also enables us to establish a general lower bound. ... More

The framed discs operad is cyclicJul 20 2006Mar 31 2007The operad of framed little discs is shown to be equivalent to a cyclic operad. This answers a conjecture of Salvatore in the affirmative, posed at the workshop `Knots and Operads in Roma,' at Universita di Roma ``La Sapienza'' in July of 2006.

A family of embedding spacesMay 02 2006Apr 02 2009Let Emb(S^j,S^n) denote the space of C^infty-smooth embeddings of the j-sphere in the n-sphere. This paper considers homotopy-theoretic properties of the family of spaces Emb(S^j,S^n) for n >= j > 0. There is a homotopy-equivalence of Emb(S^j,S^n) with ... More

Using the subspace theorem to bound unit distancesNov 21 2012Nov 29 2012We prove a special case of Erd\H{o}s' unit distance problem using a corollary of the subspace theorem bounding the number of solutions of linear equations from a multiplicative group. We restrict our attention to unit distances coming from a multiplicative ... More

Galois branched covers with fixed ramification locusOct 16 2013We examine conditions under which there exists a non-constant family of Galois branched covers of curves over an algebraically closed field $k$ of fixed degree and fixed ramification locus, under a notion of equivalence derived from considering linear ... More

A pointwise estimate for the Fourier transform and the number of maxima of a functionFeb 10 2009Nov 02 2009We show a pointwise estimate for the Fourier transform on the line involving the number of times the function changes monotonicity. The contrapositive of the theorem may be used to find a lower bound to the number of local maxima of a function. We also ... More

Partial regularity of weak solutions of the viscoelastic Navier-Stokes equations with dampingFeb 05 2011We prove an analog of the Caffarelli-Kohn-Nirenberg theorem for weak solutions of a system of PDE that model a viscoelastic fluid in the presence of an energy damping mechanism. The system was recently introduced as a possible method of establishing the ... More

The eigenvalue problem of singular ergodic controlFeb 05 2011Aug 30 2011We consider the problem of finding a real number lambda and a function u satisfying the PDE max{lambda -\Delta u -f,|Du|-1}=0, for all x in R^n. Here f is a convex, superlinear function. We prove that there is a unique lambda* such that the above PDE ... More

Induction and Analogy in a Problem of Finite SumsAug 13 2016What is a general expression for the sum of the first n integers, each raised to the mth power, where m is a positive integer? Answering this question will be the aim of the paper....We will take the unorthodox approach of presenting the material from ... More

ExoData: A python package to handle large exoplanet catalogue dataOct 09 2015May 29 2016Exoplanet science often involves using the system parameters of real exoplanets for tasks such as simulations, fitting routines, and target selection for proposals. Several exoplanet catalogues are already well established but often lack a version history ... More

Finding paths of length k in O*(2^k) timeJul 18 2008Nov 09 2008We give a randomized algorithm that determines if a given graph has a simple path of length at least k in O(2^k poly(n,k)) time.

Faster all-pairs shortest paths via circuit complexityDec 23 2013May 22 2014We present a new randomized method for computing the min-plus product (a.k.a., tropical product) of two $n \times n$ matrices, yielding a faster algorithm for solving the all-pairs shortest path problem (APSP) in dense $n$-node directed graphs with arbitrary ... More

Progress in leptonic and semileptonic decays in lattice QCDMay 04 1999The status of lattice calculations of heavy quark phenomenology is reviewed. Particular emphasis is placed on the understanding and control of the calculational uncertainties. The ensuing implications for constraining the CKM matrix elements are discussed. ... More

Automatically Segmenting Oral History TranscriptsSep 29 2015Dividing oral histories into topically coherent segments can make them more accessible online. People regularly make judgments about where coherent segments can be extracted from oral histories. But making these judgments can be taxing, so automated assistance ... More