Results for "Jason Eisner"

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Efficient Normal-Form Parsing for Combinatory Categorial GrammarJun 02 1996Under categorial grammars that have powerful rules like composition, a simple n-word sentence can have exponentially many parses. Generating all parses is inefficient and obscures whatever true semantic ambiguities are in the input. This paper addresses ... More
Three New Probabilistic Models for Dependency Parsing: An ExplorationJun 06 1997Jun 07 1997After presenting a novel O(n^3) parsing algorithm for dependency grammar, we develop three contrasting ways to stochasticize it. We propose (a) a lexical affinity model where words struggle to modify each other, (b) a sense tagging model where words fluctuate ... More
An Empirical Comparison of Probability Models for Dependency GrammarJun 06 1997This technical report is an appendix to Eisner (1996): it gives superior experimental results that were reported only in the talk version of that paper. Eisner (1996) trained three probability models on a small set of about 4,000 conjunction-free, dependency-grammar ... More
Easy and Hard Constraint Ranking in OT: Algorithms and ComplexityFeb 22 2001We consider the problem of ranking a set of OT constraints in a manner consistent with data. We speed up Tesar and Smolensky's RCD algorithm to be linear on the number of constraints. This finds a ranking so each attested form x_i beats or ties a particular ... 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
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
Fine-Grained Prediction of Syntactic Typology: Discovering Latent Structure with Supervised LearningOct 11 2017We show how to predict the basic word-order facts of a novel language given only a corpus of part-of-speech (POS) sequences. We predict how often direct objects follow their verbs, how often adjectives follow their nouns, and in general the directionalities ... More
The Galactic Dependencies Treebanks: Getting More Data by Synthesizing New LanguagesOct 10 2017We release Galactic Dependencies 1.0---a large set of synthetic languages not found on Earth, but annotated in Universal Dependencies format. This new resource aims to provide training and development data for NLP methods that aim to adapt to unfamiliar ... 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
The Neural Hawkes Process: A Neurally Self-Modulating Multivariate Point ProcessDec 29 2016Nov 21 2017Many events occur in the world. Some event types are stochastically excited or inhibited---in the sense of having their probabilities elevated or decreased---by patterns in the sequence of previous events. Discovering such patterns can help us predict ... More
Exotic cluster structures on $SL_{5}$Dec 10 2013Mar 30 2014A conjecture by Gekhtman, Shapiro and Vainshtein suggests a correspondence between the Belavin - Drinfeld classification of solutions of the classical Yang - Baxter equation and cluster structures on simple Lie groups. This paper confirms the conjecture ... More
Spell Once, Summon Anywhere: A Two-Level Open-Vocabulary Language ModelApr 23 2018Nov 23 2018We show how the spellings of known words can help us deal with unknown words in open-vocabulary NLP tasks. The method we propose can be used to extend any closed-vocabulary generative model, but in this paper we specifically consider the case of neural ... More
Neural Particle Smoothing for Sampling from Conditional Sequence ModelsApr 28 2018We introduce neural particle smoothing, a sequential Monte Carlo method for sampling annotations of an input string from a given probability model. In contrast to conventional particle filtering algorithms, we train a proposal distribution that looks ... More
Exotic Cluster Structures on $SL_n$ with Belavin-Drinfeld Data of Minimal Size, I. The StructureDec 17 2014Oct 05 2016Using the notion of compatibility between Poisson brackets and cluster structures in the coordinate rings of simple Lie groups, Gekhtman Shapiro and Vainshtein conjectured a correspondence between the two. Poisson Lie groups are classified by the Belavin-Drinfeld ... More
A Generative Model for Punctuation in Dependency TreesJun 26 2019Treebanks traditionally treat punctuation marks as ordinary words, but linguists have suggested that a tree's "true" punctuation marks are not observed (Nunberg, 1990). These latent "underlying" marks serve to delimit or separate constituents in the syntax ... More
Approximation-Aware Dependency Parsing by Belief PropagationAug 10 2015We show how to train the fast dependency parser of Smith and Eisner (2008) for improved accuracy. This parser can consider higher-order interactions among edges while retaining O(n^3) runtime. It outputs the parse with maximum expected recall -- but for ... More
Finite-State Phonology: Proceedings of the 5th Workshop of the ACL Special Interest Group in Computational Phonology (SIGPHON)Feb 22 2001Feb 23 2001Home page of the workshop proceedings, with pointers to the individually archived papers. Includes front matter from the printed version of the proceedings.
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
Imputing Missing Events in Continuous-Time Event StreamsMay 14 2019Events in the world may be caused by other, unobserved events. We consider sequences of events in continuous time. Given a probability model of complete sequences, we propose particle smoothing---a form of sequential importance sampling---to impute the ... More
Continuous Schauder frames for Banach spacesDec 20 2018We introduce the notion of a continuous Schauder frame for a Banach space. This is both a generalization of continuous frames and coherent states for Hilbert spaces and a generalization of unconditional Schauder frames for Banach spaces. As a natural ... More
Divergence of weighted square averages in $L^1$Jul 25 2019We study convergence of ergodic averages along squares with polynomial weights. For a given polynomial $P\in \mathbb{Z}[\cdot]$, consider the set of all $\theta\in[0,1)$ such that for every aperiodic system $(X,\mu, T)$ there is a function $f\in L^1(X,\mu)$ ... 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
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
The Wide Integral Field Infrared Spectrograph: Commissioning Results and On-sky PerformanceSep 10 2018We have recently commissioned a novel infrared ($0.9-1.7$ $\mu$m) integral field spectrograph (IFS) called the Wide Integral Field Infrared Spectrograph (WIFIS). WIFIS is a unique instrument that offers a very large field-of-view (50$^{\prime\prime}$ ... 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 pointwise entangled ergodic theoremSep 18 2015May 06 2016We present some twisted compactness conditions for almost everywhere convergence of one-parameter entangled ergodic averages of the form $$\frac{1}{N}\sum_{n=1}^N T_k^n A_{k-1}T_{k-1}^nA_{k-1}\cdot \ldots \cdot A_0 T_0^nf$$ for $f\in L^p(X,\mu)$, $p\geq ... 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
Nilsystems and ergodic averages along primesJan 04 2016Mar 02 2019A celebrated result by Bourgain and Wierdl states that ergodic averages along primes converge almost everywhere for $L^p$-functions, $p>1$, with a polynomial version by Wierdl and Nair. Using an anti-correlation result for the von Mangoldt function due ... More
Linear sequences and weighted ergodic theoremsFeb 04 2013Feb 07 2013We present a simple way to produce good weights for several types of ergodic theorem including the Wiener-Wintner type multiple return time theorem and the multiple polynomial ergodic theorem. These weights are deterministic and come from orbits of certain ... More
Rigidity of contractions on Hilbert spacesSep 25 2009Apr 30 2014We study the asymptotic behaviour of contractive operators and strongly continuous semigroups on separable Hilbert spaces using the notion of rigidity. In particular, we show that a "typical" contraction $T$ contains the unit circle times the identity ... More
A "typical" contraction is unitaryJul 12 2008We show that (for the weak operator topology) the set of unitary operators on a separable infinite-dimensional Hilbert space is residual in the set of all contractions. The analogous result holds for isometries and the strong operator topology as well. ... More
Embedding operators into strongly continuous semigroupsAug 18 2008We study linear operators $T$ on Banach spaces for which there exists a $C_0$-semigroup $(T(t))_{t\geq 0}$ such that $T=T(1)$. We present a necessary condition in terms of the spectral value 0 and give classes of examples where this can or cannot be achieved. ... More
A new cohomological formula for helicity in $\R^{2k+1}$ reveals the effect of a diffeomorphism on helicityMar 08 2009Oct 26 2012The helicity of a vector field is a measure of the average linking of pairs of integral curves of the field. Computed by a six-dimensional integral, it is widely useful in the physics of fluids. For a divergence-free field tangent to the boundary of a ... More
Exotic cluster structures on $SL_n$ with Belavin-Drinfeld data of minimal size: II. Correspondence between cluster structures an BD triplesNov 25 2015Using the notion of compatibility between Poisson brackets and cluster structures in the coordinate rings of simple Lie groups, Gekhtman Shapiro and Vainshtein conjectured a correspondence between the two. Poisson Lie groups are classified by the Belavin--Drinfeld ... More
Nilsystems and ergodic averages along primesJan 04 2016Jul 28 2016A celebrated result by Bourgain and Wierdl states that ergodic averages along primes converge almost everywhere for $L^p$-functions, $p>1$, with a polynomial version by Wierdl and Nair. Using an anti-correlation result for the von Mangoldt function due ... More
On the Wiener-Wintner theorem for nilsequencesApr 22 2012Aug 22 2012We give a Fourier analytic proof of the generalisation due to Host and Kra of the classical Wiener-Wintner theorem and give some explicit bounds on the limit of the weighted ergodic averages.
A polynomial version of Sarnak's conjectureJan 18 2015Mar 26 2015Motivated by the variations of Sarnak's conjecture due to El Abdalaoui, Kulaga-Przymus, Lemanczyk, De La Rue and by the observation that the Mobius function is a good weight (with limit zero) for the polynomial pointwise ergodic theorem, we introduce ... More
A polynomial version of Sarnak's conjectureJan 18 2015Dec 01 2018Motivated by the variations of Sarnak's conjecture due to El Abdalaoui, Kulaga-Przymus, Lemanczyk, De La Rue and by the observation that the Mobius function is a good weight (with limit zero) for the polynomial pointwise ergodic theorem in $L^q$, q>1, ... More
A Minimal Subsystem of the Kari-Culik TilingsOct 06 2014Sep 29 2015The Kari-Culik tilings are formed from a set of 13 Wang tiles that tile the plane only aperiodically. They are the smallest known set of Wang tiles to do so and are not as well understood as other examples of aperiodic Wang tiles. We show that the $\mathbb{Z}^2$ ... More
The combinatorics of biased riffle shufflesDec 09 1997This paper studies biased riffle shuffles, first defined by Diaconis, Fill, and Pitman. These shuffles generalize the well-studied Gilbert-Shannon-Reeds shuffle and convolve nicely. An upper bound is given for the time for these shuffles to converge to ... More
Purification and characterization of a novel archaeo-eukaryotic primase from MimivirusAug 29 2016DNA replication is a process which is common to all domains of life yet different replication mechanisms are seen among different organisms. The mechanism by which Acanthamoeba polyphaga mimivirus (APMV) undergoes replication is not characterized. Presence ... More
Dialog-based Language LearningApr 20 2016Sep 28 2016A long-term goal of machine learning research is to build an intelligent dialog agent. Most research in natural language understanding has focused on learning from fixed training sets of labeled data, with supervision either at the word level (tagging, ... More
Explicit rank bounds for cyclic coversOct 29 2013Oct 19 2015Let $M$ be a closed, orientable hyperbolic 3-manifold and $\phi$ a homomorphism of its fundamental group onto $\mathbb{Z}$ that is not induced by a fibration over the circle. For each natural number $n$ we give an explicit lower bound, linear in $n$, ... More
Hall-Littlewood polynomials and Cohen-Lenstra heuristics for Jacobians of random graphsMar 03 2014Cohen-Lenstra heuristics for Jacobians of random graphs give rise to random partitions. We connect these random partitions to the Hall-Littlewood polynomials of symmetric function theory, and use this connection to give combinatorial proofs of properties ... More
Stein's Method and Random Character RatiosAug 16 2005Stein's method is used to prove limit theorems for random character ratios. Tools are developed for four types of structures: finite groups, Gelfand pairs, twisted Gelfand pairs, and association schemes. As one example an error term is obtained for a ... More
A Card Shuffling Analysis of Deformations of the Plancherel Measure of the Symmetric GroupFeb 25 2003We study deformations of the Plancherel measure of the symmetric group by lifting them to the symmetric group and using combinatorics of card shuffling. The existing methods for analyzing deformations of Plancherel measure are not obviously applicable ... More
A Probabilistic Approach to Conjugacy Classes in the Finite Symplectic and Orthogonal GroupsMar 02 2000Nov 06 2000Markov chains are used to give a purely probabilistic way of understanding the conjugacy classes of the finite symplectic and orthogonal groups in odd characteristic. As a corollary of these methods one obtains a probabilistic proof of Steinberg's count ... More
The eigenvalue spacing of a random unipotent matrix in its action on linesMay 24 1999The eigenvalue spacing of a uniformly chosen random finite unipotent matrix in its permutation action on lines is studied. We obtain bounds for the mean number of eigenvalues lying in a fixed arc of the unit circle and offer an approach toward other asymptotics. ... More
Stein's Method and Characters of Compact Lie GroupsJun 13 2008Jun 24 2008Stein's method is used to study the trace of a random element from a compact Lie group or symmetric space. Central limit theorems are proved using very little information: character values on a single element and the decomposition of the square of the ... More
Separation cutoffs for random walk on irreducible representationsMar 10 2007Random walk on the irreducible representations of the symmetric and general linear groups is studied. A separation distance cutoff is proved and the exact separation distance asymptotics are determined. A key tool is a method for writing the multiplicities ... More
Card shuffling and the decomposition of tensor productsJul 03 2003Let H be a subgroup of a finite group G. We use Markov chains to quantify how large r should be so that the decomposition of the r tensor power of the representation of G on cosets on H behaves (after renormalization) like the regular representation of ... More
Descent identities, Hessenberg varieties, and the Weil conjecturesDec 09 1997The Weil Conjectures are applied to the Hessenberg Varieties to obtain interesting information about the combinatorics of descents in the symmetric group. Combining this with elementary linear algebra leads to elegant proofs of some identities from the ... More
On the close interaction between algorithmic randomness and constructive/computable measure theoryDec 08 2018This is a survey of constructive and computable measure theory with an emphasis on the close connections with algorithmic randomness. We give a brief history of constructive measure theory from Brouwer to the present, emphasizing how Schnorr randomness ... More
A $2$-compact group as a spetsJun 03 2019Jun 12 2019In 1998 Malle introduced spetses which are mysterious objects with non-real Weyl groups. In algebraic topology, a $p$-compact group $\mathbf{X}$ is a space which is a homotopy-theoretic $p$-local analogue of a compact Lie group. A connected $p$-compact ... More
When does randomness come from randomness?Aug 20 2015Mar 08 2016A result of Shen says that if $F\colon2^{\mathbb{N}}\rightarrow2^{\mathbb{N}}$ is an almost-everywhere computable, measure-preserving transformation, and $y\in2^{\mathbb{N}}$ is Martin-L\"of random, then there is a Martin-L\"of random $x\in2^{\mathbb{N}}$ ... More
The classification of compact simply connected biquotients in dimension 6 and 7Mar 24 2014Aug 23 2016We classify all compact simply connected biquotients of dimension 6 and 7. For each $6$-dimensional biquotient, all pairs of groups $(G,H)$ and homomorphisms $H\rightarrow G\times G$ giving rise to it are classified.
Rationally $4$-periodic biquotientsMay 25 2016Aug 22 2017An $n$-dimensional manifold $M$ is said to be rationally $4$-periodic if there is an element $e\in H^4(M;\mathbb{Q})$ with the property that cupping with $e$, $\cdot \cup e:H^\ast(M;\mathbb{Q})\rightarrow H^{\ast + 4}(M;\mathbb{Q})$ is injective for $0< ... More
Generalized equivariant homology on simplicial complexesMar 08 2011A careful account is given of generalized equivariant homology theories on the category of topological pairs acted on by a group. In particular, upon restriction to the category of equivariant simplicial complexes, the equivalence of equivariant simplicial ... More
Random data final-state problem for the mass-subcritical NLS in $L^2$Mar 29 2017Jul 16 2017We study the final-state problem for the mass-subcritical NLS above the Strauss exponent. For $u_+\in L^2$, we perform a physical-space randomization, yielding random final states $u_+^\omega\in L^2$. We show that for almost every $\omega$, there exists ... More
Totally geodesic surfaces and homologyJan 23 2006Apr 23 2009We construct examples of hyperbolic rational homology spheres and hyperbolic knot complements in rational homology spheres containing closed embedded totally geodesic surfaces.
Descent algebras, hyperplane arrangements, and shuffling cardsJan 20 1998Jul 15 1999Two notions of riffle shuffling on finite Coxeter groups are given: one using Solomon's descent algebra and another using random walk on chambers of hyperplane arrangements. These coincide for types $A$,$B$,$C$, $H_3$, and rank two groups. Both notions ... More
The Kodaira dimension of spaces of rational curves on low degree hypersurfacesMay 29 2003For a hypersurface in complex projective space $X\subset \PP^n$, we investigate the singularities and Kodaira dimension of the Kontsevich moduli spaces $\Kbm{0,0}{X,e}$ parametrizing rational curves of degree $e$ on $X$. If $d+e \leq n$ and $X$ is a general ... More
Bulk Comptonization by Turbulence in Black Hole Accretion DiscsMar 31 2018Apr 03 2018Radiation pressure dominated accretion discs may have turbulent velocities that exceed the electron thermal velocities. Bulk Comptonization by the turbulence may therefore dominate over thermal Comptonization in determining the emergent spectrum. We discuss ... More
Relations among conditional probabilitiesAug 08 2008We describe a Groebner basis of relations among conditional probabilities in a discrete probability space, with any set of conditioned-upon events. They may be specialized to the partially-observed random variable case, the purely conditional case, and ... More
Improving on bold play when the gambler is restrictedDec 18 2004Suppose a gambler starts with a fortune in (0,1) and wishes to attain a fortune of 1 by making a sequence of bets. Assume thay whenever the gambler stakes the amount s, the gambler's fortune increases by s with probability w and decreases by s with probability ... More
The Doorways Problem and Sturmian WordsMay 01 2017The doorways problem considers adjacent parallel hallways of unit width each with a single doorway (aligned with integer lattice points) of unit width. It then asks, what are the properties of lines that pass through each doorway? Configurations of doorways ... More
A note on the Brown--Erdős--Sós conjecture in groupsFeb 20 2019Apr 09 2019We show that a dense subset of a sufficiently large group multiplication table contains either a large part of the addition table of the integers modulo some $k$, or the entire multiplication table of a certain large abelian group, as a subgrid. As a ... More
Jørgensen Number and ArithmeticityMay 08 2009A J{\o}rgensen group is a non-elementary Kleinian group that can be generated by two elements for which equality holds in J{\o}rgensen's Inequality. This paper shows that the only torsion-free J{\o}rgensen group is the figure-eight knot group, identifies ... More
On some moduli of complexes on K3 surfacesMar 07 2012We consider moduli stacks of Bridgeland semistable objects that previously had only set-theoretic identifications with Uhlenbeck compactification spaces. On a K3 surface $X$, we give examples where such a moduli stack is isomorphic to a moduli stack of ... More
On the maximal graded shifts of ideals and modulesJan 24 2018We generalize a result of Eisenbud-Huneke-Ulrich on the maximal graded shifts of a module with prescribed annihilator and prove a linear regularity bound for ideals in a polynomial ring depending only on the first $p - c$ steps in the resolution, where ... More
The exponential of the spin representation of the Lorentz algebraJan 29 2012As discussed in a previous article, any (real) Lorentz algebra element possess a unique orthogonal decomposition as a sum of two mutually annihilating decomposable Lorentz algebra elements. In this article, this concept is extended to the spin representation ... More
Applications of Symmetric Functions to Cycle and Increasing Subsequence Structure after Shuffles (Part 2)Mar 31 2001Apr 16 2001Using the Berele/Remmel/Kerov/Vershik variation of the Robinson-Schensted-Knuth correspondence, we study the cycle and increasing subsequence structure after various methods of shuffling. One consequence is a cycle index for shuffles like: cut a deck ... More
New Examples of Potential Theory on Bratelli DiagramsDec 17 1999We consider potential theory on Bratteli diagrams arising from Macdonald polynomials. The case of Hall-Littlewood polynomials is particularly interesting; the elements of the diagram are partitions, the branching multiplicities are integers, the combinatorial ... More
Martingales and character ratiosFeb 25 2004Some general connections between martingales and character ratios of finite groups are developed. As an application we sharpen the convergence rate in a central limit theorem for the character ratio of a random representation of the symmetric group on ... More
Stein's Method and Plancherel Measure of the Symmetric GroupMay 29 2003Nov 11 2003We initiate a Stein's method approach to the study of the Plancherel measure of the symmetric group. A new proof of Kerov's central limit theorem for character ratios of random representations of the symmetric group on transpositions is obtained; the ... More
Exact constraints on D$\leq 10$ Myers Perry black holes and the Wald ProblemSep 30 2010Jan 31 2011Exact relations on the existence of event horizons of Myers Perry black holes are obtained in $D\leq 10$ dimensions. It is further shown that naked singularities can not be produced by "spinning-up" these black holes by shooting particles into their $\lfloor\frac{D-1}{2}\rfloor$ ... More
The centered dual and the maximal injectivity radius of hyperbolic surfacesAug 27 2013Sep 05 2013We give sharp upper bounds on the maximal injectivity radius of finite-area hyperbolic surfaces and use them, for each g at least 2, to identify a constant r_{g-1,2} with the property that the set of closed genus-g hyperbolic surfaces with maximal injectivity ... More
Tessellations of hyperbolic surfacesMar 23 2011A finite subset S of a closed hyperbolic surface F canonically determines a "centered dual decomposition" of F: a cell structure with vertex set S, geodesic edges, and 2-cells that are unions of the corresponding Delaunay polygons. Unlike a Delaunay polygon, ... More
Altmetrics (Chapter from Beyond Bibliometrics: Harnessing Multidimensional Indicators of Scholarly Impact)Jul 06 2015This chapter discusses altmetrics (short for "alternative metrics"), an approach to uncovering previously-invisible traces of scholarly impact by observing activity in online tools and systems. I argue that citations, while useful, miss many important ... More
Contextuality from missing and versioned dataAug 10 2017Traditionally categorical data analysis (e.g. generalized linear models) works with simple, flat datasets akin to a single table in a database with no notion of missing data or conflicting versions. In contrast, modern data analysis must deal with distributed ... More
Rotations in three, four, and five dimensionsMar 08 2011The geometry of rotations in dimensions 3, 4, and 5 is discussed using the matrix exponential map. Explicit closed formulas for the exponential of an antisymmetric matrix, as well as the logarithm of a rotation, are given for these dimensions.
Denominators and Differences of Boundary Slopes for (1,1)-KnotsJan 26 2013Jul 23 2014We show that every nonzero integer occurs in the denominator of a boundary slope for infinitely many (1,1)-knots and that infinitely many (1,1)-knots have boundary slopes of arbitrarily small difference. Specifically, we prove that for any integers m, ... More
Desingularization of Coassociative 4-folds with Conical SingularitiesNov 07 2006Nov 27 2007Given a coassociative 4-fold N with a conical singularity in a varphi-closed 7-manifold M (a manifold endowed with a distinguished closed 3-form varphi), we construct a smooth family, {N'(t): t\in(0,tau)} for some tau>0, of (smooth, nonsingular,) compact ... More
Coassociative 4-folds with Conical SingularitiesJan 31 2006This paper is dedicated to the study of deformations of coassociative 4-folds in a G_2 manifold which have conical singularities. We stratify the types of deformations allowed into three problems. The main result for each problem states that the moduli ... More
The Rogers-Ramanujan Identities, the Finite General Linear Groups, and the Hall-Littlewood PolynomialsDec 09 1997The Rogers-Ramanujan identities have been studied from the viewpoints of combinatorics, number theory, affine Lie algebras, statistical mechanics, and quantum field theory. This note connects the Rogers-Ramanujan identities with the finite general linear ... More
The loop-erased random walk and the uniform spanning tree on the four-dimensional discrete torusFeb 23 2006Jul 29 2007Let x and y be points chosen uniformly at random from $\Z_n^4$, the four-dimensional discrete torus with side length n. We show that the length of the loop-erased random walk from x to y is of order $n^2 (\log n)^{1/6}$, resolving a conjecture of Benjamini ... More
A $2$-compact group as a spetsJun 03 2019Jun 20 2019In 1998 Malle introduced spetses which are mysterious objects with non-real Weyl groups. In algebraic topology, a $p$-compact group $\mathbf{X}$ is a space which is a homotopy-theoretic $p$-local analogue of a compact Lie group. A connected $p$-compact ... More
T-structures on elliptic fibrationsSep 10 2015We consider t-structures that naturally arise on elliptic fibrations. By filtering the category of coherent sheaves on an elliptic fibration using the torsion pairs corresponding to these t-structures, we prove results describing equivalences of t-structures ... More
Weak Convergence of the Scaled Median of Independent Brownian MotionsJul 26 2005Aug 02 2006We consider the median of n independent Brownian motions, and show that this process, when properly scaled, converges weakly to a centered Gaussian process. The chief difficulty is establishing tightness, which is proved through direct estimates on the ... More
Fourier-Mukai transforms of slope stable torsion-free sheaves and stable 1-dimensional sheaves on Weierstrass elliptic threefoldsOct 10 2017We focus on a class of Weierstrass elliptic threefolds that allows the base of the fibration to be a Fano surface or a numerically $K$-trivial surface. In the first half of this article, we define the notion of limit tilt stability, which is closely related ... More
Moduli of PT-semistable objects IINov 29 2010May 04 2011We generalise the techniques of semistable reduction for flat families of sheaves to the setting of the derived category $D^b(X)$ of coherent sheaves on a smooth projective three-fold $X$. Then we construct the moduli of PT-semistable objects in $D^b(X)$ ... More
The minimum rank problem over finite fieldsJan 18 2008The structure of all graphs having minimum rank at most k over a finite field with q elements is characterized for any possible k and q. A strong connection between this characterization and polarities of projective geometries is explained. Using this ... More
Rigorous results for a population model with selection II: genealogy of the populationJul 01 2015We consider a model of a population of fixed size $N$ undergoing selection. Each individual acquires beneficial mutations at rate $\mu_N$, and each beneficial mutation increases the individual's fitness by $s_N$. Each individual dies at rate one, and ... More
Stillman's Question for Exterior Algebras and Herzog's Conjecture on Betti Numbers of Syzygy ModulesJul 30 2013Jan 24 2018Let K be a field of characteristic 0 and consider exterior algebras of finite dimensional K-vector spaces. In this short paper we exhibit principal quadric ideals in a family whose Castelnuovo-Mumford regularity is unbounded. This negatively answers the ... More
A Polynomial Bound on the Regularity of an Ideal in Terms of Half of the SyzygiesDec 01 2011Let K be a field and let S = K[x_1, ..., x_n] be a polynomial ring. Consider a homogenous ideal I in S. Let t_i denote reg(Tor_i (S/I, K)), the maximal degree of an ith syzygy of S/I. We prove bounds on the numbers t_i for i > n/2 purely in terms of the ... More
Learning Parameters for Weighted Matrix Completion via Empirical EstimationDec 31 2014Apr 02 2015Recently theoretical guarantees have been obtained for matrix completion in the non-uniform sampling regime. In particular, if the sampling distribution aligns with the underlying matrix's leverage scores, then with high probability nuclear norm minimization ... More
Iterative Hard Thresholding for Weighted Sparse ApproximationDec 12 2013Jan 07 2015Recent work by Rauhut and Ward developed a notion of weighted sparsity and a corresponding notion of Restricted Isometry Property for the space of weighted sparse signals. Using these notions, we pose a best weighted sparse approximation problem, i.e. ... More
Dialog-based Language LearningApr 20 2016Aug 23 2016A long-term goal of machine learning research is to build an intelligent dialog agent. Most research in natural language understanding has focused on learning from fixed training sets of labeled data, with supervision either at the word level (tagging, ... More
A sharp analysis of the mixing time for random walk on rooted treesAug 08 2009We define an analog of Plancherel measure for the set of rooted unlabeled trees on n vertices, and a Markov chain which has this measure as its stationary distribution. Using the combinatorics of commutation relations, we show that order n^2 steps are ... More