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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

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

Morphological Word EmbeddingsJul 04 2019Linguistic similarity is multi-faceted. For instance, two words may be similar with respect to semantics, syntax, or morphology inter alia. Continuous word-embeddings have been shown to capture most of these shades of similarity to some degree. This work ... 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

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

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

Exact Hard Monotonic Attention for Character-Level TransductionMay 15 2019Jun 27 2019Many common character-level, string-to-string transduction tasks, e.g. graphemeto-phoneme conversion and morphological inflection, consist almost exclusively of monotonic transduction. Neural sequence-to-sequence models with soft attention, which are ... 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

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

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

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

It's All in the Name: Mitigating Gender Bias with Name-Based Counterfactual Data SubstitutionSep 02 2019This paper treats gender bias latent in word embeddings. Previous mitigation attempts rely on the operationalisation of gender bias as a projection over a linear subspace. An alternative approach is Counterfactual Data Augmentation (CDA), in which a corpus ... 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

Don't Forget the Long Tail! A Comprehensive Analysis of Morphological Generalization in Bilingual Lexicon InductionSep 06 2019Human translators routinely have to translate rare inflections of words - due to the Zipfian distribution of words in a language. When translating from Spanish, a good translator would have no problem identifying the proper translation of a statistically ... More

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 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

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

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

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

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

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

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

Morphological Irregularity Correlates with FrequencyJun 27 2019We present a study of morphological irregularity. Following recent work, we define an information-theoretic measure of irregularity based on the predictability of forms in a language. Using a neural transduction model, we estimate this quantity for the ... 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

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

On the Idiosyncrasies of the Mandarin Chinese Classifier SystemFeb 26 2019Apr 05 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

Uncovering Probabilistic Implications in Typological Knowledge BasesJun 18 2019The study of linguistic typology is rooted in the implications we find between linguistic features, such as the fact that languages with object-verb word ordering tend to have post-positions. Uncovering such implications typically amounts to time-consuming ... 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

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

Examining Gender Bias in Languages with Grammatical GenderSep 05 2019Sep 09 2019Recent studies have shown that word embeddings exhibit gender bias inherited from the training corpora. However, most studies to date have focused on quantifying and mitigating such bias only in English. These analyses cannot be directly extended to languages ... 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

Meaning to Form: Measuring Systematicity as InformationJun 13 2019Jul 26 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

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

Examining Gender Bias in Languages with Grammatical GenderSep 05 2019Recent studies have shown that word embeddings exhibit gender bias inherited from the training corpora. However, most studies to date have focused on quantifying and mitigating such bias only in English. These analyses cannot be directly extended to languages ... 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

New algorithms and lower bounds for circuits with linear threshold gatesJan 10 2014Let $ACC \circ THR$ be the class of constant-depth circuits comprised of AND, OR, and MOD$m$ gates (for some constant $m > 1$), with a bottom layer of gates computing arbitrary linear threshold functions. This class of circuits can be seen as a "midpoint" ... More

Coherent LQG Control, Free-Carrier Oscillations, Optical Ising Machines and Pulsed OPO DynamicsAug 26 2016Broadly speaking, this thesis is about nonlinear optics, quantum mechanics, and computing. More specifically, it covers four main topics: Coherent LQG Control, Free-Carrier Oscillations, Optical Ising Machines and Pulsed OPO Dynamics. Tying them all together ... More

Trapezoid Order ClassificationDec 11 1996We show the nonequivalence of combinations of several natural geometric restrictions on trapezoid representations of trapezoid orders. Each of the properties unit parallelogram, unit trapezoid and proper parallelogram, unit trapezoid and parallelogram, ... More

Random sets and exact confidence regionsFeb 08 2013Oct 15 2013An important problem in statistics is the construction of confidence regions for unknown parameters. In most cases, asymptotic distribution theory is used to construct confidence regions, so any coverage probability claims only hold approximately, for ... More

Analysis of Hamilton-Jacobi-Bellman equations arising in stochastic singular controlFeb 05 2011Sep 03 2011We study the partial differential equation max{Lu - f, H(Du)}=0 where u is the unknown function, L is a second-order elliptic operator, f is a given smooth function and H is a convex function. This is a model equation for Hamilton-Jacobi-Bellman equations ... More

Ramsey Numbers of Odd Cycles Versus Larger Even WheelsSep 13 2016Sep 14 2016The generalized Ramsey number $R(G_1, G_2)$ is the smallest positive integer $N$ such that any red-blue coloring of the edges of the complete graph $K_N$ either contains a red copy of $G_1$ or a blue copy of $G_2$. Let $C_m$ denote a cycle of length $m$ ... More

A New Look at Chern-Simons on Circle Bundles I: The Caloron CorrespondenceJul 06 2015We consider Chern-Simons theory on 3-manifold $M$ that is the total space of a circle bundle over a 2d base $\Sigma$. We show that this theory is equivalent to a new 2d TQFT on the base, which we call Caloron BF theory, that can be obtained by an appropriate ... More

Training Neural Networks with Stochastic Hessian-Free OptimizationJan 16 2013May 01 2013Hessian-free (HF) optimization has been successfully used for training deep autoencoders and recurrent networks. HF uses the conjugate gradient algorithm to construct update directions through curvature-vector products that can be computed on the same ... More

Source Coding Optimization for Distributed Average ConsensusOct 04 2017Consensus is a common method for computing a function of the data distributed among the nodes of a network. Of particular interest is distributed average consensus, whereby the nodes iteratively compute the sample average of the data stored at all the ... More

The independent discovery of planet candidates around low mass stars and astrophysical false positives from the first two TESS sectorsDec 19 2018Continuous data releases throughout the TESS primary mission will provide unique opportunities for the exoplanet community at large to contribute to maximizing TESS's scientific return via the discovery and validation of transiting planets. This paper ... More

JSJ-decompositions of knot and link complements in the 3-sphereJun 25 2005Oct 29 2007This paper is a survey of some of the most elementary consequences of the JSJ-decomposition and geometrization for knot and link complements in the 3-sphere. Formulated in the language of graphs, the result is the construction of a bijective correspondence ... More

Topology of spaces of knots in dimension 3Jun 25 2005Aug 11 2009This paper is a computation of the homotopy type of K, the space of long knots in R^3, the same space of knots studied by Vassiliev via singularity theory. Each component of K corresponds to an isotopy class of long knot, and we `enumerate' the components ... More

Families and moduli of covers with specified ramificationDec 26 2013We study branched covers of curves with specified ramification points, under a notion of equivalence derived from linear series. In characteristic 0, no non-constant families of covers with fixed ramification points exist. In positive characteristic we ... More

Chermak-Delgado Simple GroupsOct 14 2015This paper provides the first steps in classifying the finite solvable groups having Property A, which is a property involving abelian normal subgroups. We see that this classification is reduced to classifying the solvable Chermak-Delgado simple groups, ... More

Projection Method for Solving Stokes FlowDec 06 2017Dec 20 2017Various methods for numerically solving Stokes Flow, where a small Reynolds number is assumed to be zero, are investigated. If pressure, horizontal velocity, and vertical velocity can be decoupled into three different equations, the numerical solution ... More

A pathwise variation estimate for the sticky particle systemApr 25 2018Apr 30 2019We 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

An operad for splicingApr 22 2010Mar 31 2012A new topological operad is introduced, called the splicing operad. This operad acts on a broad class of spaces of self-embeddings N --> N where N is a manifold. The action of this operad on EC(j,M) (self embeddings R^j x M --> R^j x M with support in ... More

Estimation of the Szlenk index of Banach Spaces via Schreier spacesDec 21 2012Aug 25 2013For each ordinal $\alpha<\omega_1$, we prove the existence of a space with a basis and Szlenk index $\omega^{\alpha+1}$ which is universal for the class of spaces with Szlenk index not exceeding $\omega^\alpha$. Our proof involves developing a characterization ... More

Rank loci in representation spaces of quiversApr 12 2010Apr 19 2010Rank functors on a quiver $Q$ are certain additive functors from the category of representations of $Q$ to the category of finite-dimensional vector spaces. Composing with the dimension function on vector spaces gives a rank function on $Q$. These induce ... 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

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

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

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

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