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Latent Normalizing Flows for Discrete SequencesJan 29 2019Feb 13 2019Normalizing flows have been shown to be a powerful class of generative models for continuous random variables, giving both strong performance and the potential for non-autoregressive generation. These benefits are also desired when modeling discrete random ... More

Entity Tracking Improves Cloze-style Reading ComprehensionOct 05 2018Reading comprehension tasks test the ability of models to process long-term context and remember salient information. Recent work has shown that relatively simple neural methods such as the Attention Sum-Reader can perform well on these tasks; however, ... More

Semi-Amortized Variational AutoencodersFeb 07 2018Amortized variational inference (AVI) replaces instance-specific local inference with a global inference network. While AVI has enabled efficient training of deep generative models such as variational autoencoders (VAE), recent empirical work suggests ... More

Sequence-Level Knowledge DistillationJun 25 2016Sep 22 2016Neural machine translation (NMT) offers a novel alternative formulation of translation that is potentially simpler than statistical approaches. However to reach competitive performance, NMT models need to be exceedingly large. In this paper we consider ... More

Sequence-to-Sequence Learning as Beam-Search OptimizationJun 09 2016Nov 10 2016Sequence-to-Sequence (seq2seq) modeling has rapidly become an important general-purpose NLP tool that has proven effective for many text-generation and sequence-labeling tasks. Seq2seq builds on deep neural language modeling and inherits its remarkable ... More

A Tutorial on Dual Decomposition and Lagrangian Relaxation for Inference in Natural Language ProcessingJan 23 2014Dual decomposition, and more generally Lagrangian relaxation, is a classical method for combinatorial optimization; it has recently been applied to several inference problems in natural language processing (NLP). This tutorial gives an overview of the ... More

Lie-Access Neural Turing MachinesNov 09 2016Recent work has demonstrated the effectiveness of employing explicit external memory structures in conjunction with deep neural models for algorithmic learning (Graves et al. 2014; Weston et al. 2014). These models utilize differentiable versions of traditional ... More

Sequence-to-Sequence Learning as Beam-Search OptimizationJun 09 2016Sequence-to-Sequence (seq2seq) modeling has rapidly become an important general-purpose NLP tool that has proven effective for many text-generation and sequence-labeling tasks. Seq2seq builds on deep neural language modeling and inherits its remarkable ... More

Cyclic Sieving and Plethysm CoefficientsAug 27 2014Apr 05 2017A combinatorial expression for the coefficient of the Schur function $s_{\lambda}$ in the expansion of the plethysm $p_{n/d}^d \circ s_{\mu}$ is given for all $d$ dividing $n$ for the cases in which $n=2$ or $\lambda$ is rectangular. In these cases, the ... More

Latent Normalizing Flows for Discrete SequencesJan 29 2019Normalizing flows have been shown to be a powerful class of generative models for continuous random variables, giving both strong performance and the potential for non-autoregressive generation. These benefits are also desired when modeling discrete random ... More

Bottom-Up Abstractive SummarizationAug 31 2018Oct 09 2018Neural network-based methods for abstractive summarization produce outputs that are more fluent than other techniques, but which can be poor at content selection. This work proposes a simple technique for addressing this issue: use a data-efficient content ... More

What You Get Is What You See: A Visual Markup DecompilerSep 16 2016Building on recent advances in image caption generation and optical character recognition (OCR), we present a general-purpose, deep learning-based system to decompile an image into presentational markup. While this task is a well-studied problem in OCR, ... More

Semiclassical quantisation for a bosonic atom-molecule conversion systemMay 13 2015Jul 27 2015We consider a simple quantum model of atom-molecule conversion where bosonic atoms can combine into diatomic molecules and vice versa. The many-particle system can be expressed in terms of the generators a deformed $SU(2)$ algebra, and the mean-field ... More

Propagation of Gaussian beams in the presence of gain and lossJan 28 2016We consider the propagation of Gaussian beams in a waveguide with gain and loss in the paraxial approximation governed by the Schr\"odinger equation. We derive equations of motion for the beam in the semiclassical limit that are valid when the waveguide ... More

A Neural Attention Model for Abstractive Sentence SummarizationSep 02 2015Sep 03 2015Summarization based on text extraction is inherently limited, but generation-style abstractive methods have proven challenging to build. In this work, we propose a fully data-driven approach to abstractive sentence summarization. Our method utilizes a ... More

On Orbits of Order Ideals of Minuscule PosetsAug 26 2011Jun 27 2012An action on order ideals of posets considered by Fon-Der-Flaass is analyzed in the case of posets arising from minuscule representations of complex simple Lie algebras. For these minuscule posets, it is shown that the Fon-Der-Flaass action exhibits the ... More

Classical-quantum correspondence in bosonic two-mode conversion systems: polynomial algebras and Kummer shapesOct 06 2015Feb 04 2016Bosonic quantum conversion systems can be modeled by many-particle single-mode Hamiltonians describing a conversion of $n$ molecules of type A into $m$ molecules of type B and vice versa. These Hamiltonians are analyzed in terms of generators of a polynomially ... More

End-to-End Content and Plan Selection for Data-to-Text GenerationOct 10 2018Learning to generate fluent natural language from structured data with neural networks has become an common approach for NLG. This problem can be challenging when the form of the structured data varies between examples. This paper presents a survey of ... More

Structured Attention NetworksFeb 03 2017Feb 16 2017Attention networks have proven to be an effective approach for embedding categorical inference within a deep neural network. However, for many tasks we may want to model richer structural dependencies without abandoning end-to-end training. In this work, ... More

Word Ordering Without SyntaxApr 28 2016Sep 24 2016Recent work on word ordering has argued that syntactic structure is important, or even required, for effectively recovering the order of a sentence. We find that, in fact, an n-gram language model with a simple heuristic gives strong results on this task. ... More

Sentence-Level Grammatical Error Identification as Sequence-to-Sequence CorrectionApr 16 2016We demonstrate that an attention-based encoder-decoder model can be used for sentence-level grammatical error identification for the Automated Evaluation of Scientific Writing (AESW) Shared Task 2016. The attention-based encoder-decoder models can be ... More

Classical and quantum dynamics in the (non-Hermitian) Swanson oscillatorSep 23 2014Dec 21 2014The non-Hermitian quadratic oscillator studied by Swanson is one of the popular $PT$-symmetric model systems. Here a full classical description of its dynamics is derived using recently developed metriplectic flow equations, which combine the classical ... More

Learning Global Features for Coreference ResolutionApr 11 2016There is compelling evidence that coreference prediction would benefit from modeling global information about entity-clusters. Yet, state-of-the-art performance can be achieved with systems treating each mention prediction independently, which we attribute ... More

Character-Aware Neural Language ModelsAug 26 2015Dec 01 2015We describe a simple neural language model that relies only on character-level inputs. Predictions are still made at the word-level. Our model employs a convolutional neural network (CNN) and a highway network over characters, whose output is given to ... More

Latent Alignment and Variational AttentionJul 10 2018Nov 07 2018Neural attention has become central to many state-of-the-art models in natural language processing and related domains. Attention networks are an easy-to-train and effective method for softly simulating alignment; however, the approach does not marginalize ... More

Towards AI-Complete Question Answering: A Set of Prerequisite Toy TasksFeb 19 2015Dec 31 2015One long-term goal of machine learning research is to produce methods that are applicable to reasoning and natural language, in particular building an intelligent dialogue agent. To measure progress towards that goal, we argue for the usefulness of a ... More

Visual Analysis of Hidden State Dynamics in Recurrent Neural NetworksJun 23 2016Recurrent neural networks, and in particular long short-term memory networks (LSTMs), are a remarkably effective tool for sequence modeling that learn a dense black-box hidden representation of their sequential input. Researchers interested in better ... More

Seq2Seq-Vis: A Visual Debugging Tool for Sequence-to-Sequence ModelsApr 25 2018Oct 16 2018Neural Sequence-to-Sequence models have proven to be accurate and robust for many sequence prediction tasks, and have become the standard approach for automatic translation of text. The models work in a five stage blackbox process that involves encoding ... More

Tensor Variable Elimination for Plated Factor GraphsFeb 08 2019A wide class of machine learning algorithms can be reduced to variable elimination on factor graphs. While factor graphs provide a unifying notation for these algorithms, they do not provide a compact way to express repeated structure when compared to ... More

OpenNMT: Open-source Toolkit for Neural Machine TranslationSep 12 2017We introduce an open-source toolkit for neural machine translation (NMT) to support research into model architectures, feature representations, and source modalities, while maintaining competitive performance, modularity and reasonable training requirements. ... More

Cyclic Sieving and Plethysm CoefficientsAug 27 2014A combinatorial expression for the coefficient of the Schur function $s_{\lambda}$ in the expansion of the plethysm $p_{n/d}^d \circ s_{\mu}$ is given for all $d$ dividing $n$ for the cases in which $n=2$ or $\lambda$ is rectangular. In these cases, the ... More

Computing the Lusztig--Vogan BijectionNov 01 2017Let $G$ be a connected complex reductive algebraic group with Lie algebra $\mathfrak{g}$. The Lusztig--Vogan bijection relates two bases for the bounded derived category of $G$-equivariant coherent sheaves on the nilpotent cone $\mathcal{N}$ of $\mathfrak{g}$. ... More

Finite Sample Analysis of Approximate Message PassingJun 06 2016This paper analyzes the performance of Approximate Message Passing (AMP) in the regime where the problem dimension is large but finite. We consider the setting of high-dimensional regression, where the goal is to estimate a high-dimensional vector $\beta_0$ ... More

Orthogonal polynomials on the circle for the weight w satisfying conditions: w,1/w in BMO(T)Jan 13 2016Nov 02 2016In the case when the weight and its inverse belong to BMO(T), we prove the asymptotics of the monic orthogonal polynomials in L^p, 2<p<p_0. Immediate applications include the estimates on the uniform norm and asymptotics for the polynomial entropy.

On Schur parameters in Steklov's problemJun 14 2016We study the recursion (aka Schur) parameters for monic polynomials orthogonal on the unit circle with respect to a weight which provides negative answer to the conjecture of Steklov.

On Order Ideals of Minuscule Posets III: The CDE PropertyJul 27 2016Recent work of Hopkins establishes that the lattice of order ideals of a minuscule poset satisfies the coincidental down-degree expectations property of Reiner, Tenner, and Yong. His approach appeals to the classification of minuscule posets. A uniform ... More

On Orbits of Order Ideals of Minuscule Posets II: HomomesySep 27 2015The Fon-Der-Flaass action partitions the order ideals of a poset into disjoint orbits. For a product of two chains, Propp and Roby observed --- across orbits --- the mean cardinality of the order ideals within an orbit to be invariant. That this phenomenon, ... More

The Soft-X-Ray Spectral Shape of X-Ray-Weak SeyfertsJul 27 1995(I) We observed eight Seyfert~2s and two X--ray--weak Seyfert~1/QSOs with the ROSAT PSPC, and one Seyfert~2 with the ROSAT HRI. These targets were selected from the Extended 12\um\ Galaxy Sample. (II) Both Seyfert~1/QSOs vary by factors of 1.5---2. The ... More

Capacity-achieving Sparse Superposition Codes via Approximate Message Passing DecodingJan 23 2015Aug 02 2016Sparse superposition codes were recently introduced by Barron and Joseph for reliable communication over the AWGN channel at rates approaching the channel capacity. The codebook is defined in terms of a Gaussian design matrix, and codewords are sparse ... More

The Extended 12 Micron Galaxy SampleJun 17 1993We have selected an all--sky sample of 893 galaxies from the IRAS FSC--2, defined by a total (ADDSCAN) 12um flux limit of 0.22~Jy. Completeness is verified to 0.30~Jy, below which we have quantified the incompleteness down to 0.22~Jy for our statistical ... More

Scattering theory and Banach space valued singular integralsNov 28 2012We give a new sufficient condition for existence and completeness of wave operators in abstract scattering theory. This condition generalises both trace class and smooth approaches to scattering theory. Our construction is based on estimates for the Cauchy ... More

$L^2-$interpolation with error and size of spectraJun 18 2008Given a compact set $S$ and a uniformly discrete sequence $\La$, we show that "approximate interpolation" of delta--functions on $\La$ by a bounded sequence of $L^2-$functions with spectra in $S$ implies an estimate on measure of $S$ through the density ... More

Kazhdan-Laumon representations of finite Chevalley groups, character sheaves and some generalization of the Lefschetz-Verdeier trace formulaOct 01 1998In this paper we investigate the representations of reductive groups over a finite field, introduced in 1987 by D.Kazhdan and G.Laumon. We show that generically these representations are irreducible and that their character is equal to the function obtained ... More

Moments of random sums and Robbins' problem of optimal stoppingJul 17 2011Robbins' problem of optimal stopping asks one to minimise the expected {\it rank} of observation chosen by some nonanticipating stopping rule. We settle a conjecture regarding the {\it value} of the stopped variable under the rule optimal in the sense ... More

Subtle Characteristic ClassesJan 26 2014We construct new subtle Stiefel--Whitney classes of quadratic forms. These classes are much more informative than the ones introduced by Milnor. In particular, they see all the powers of the fundamental ideal of the Witt ring, contain the Arason invariant ... More

Discrete Translates in $L^2(R)$Dec 02 2016A set $\Lambda\subset R$ is called $p$-spectral, if there is a function $\varphi\in L^p(R)$ whose $\Lambda$-translates $\{\varphi(t-\lambda),\lambda\in\Lambda\}$ span $L^p(R)$. We prove that exponentially small non-zero perturbations of the integers are ... More

Governing Singularities of Schubert VarietiesMar 12 2006Jun 29 2006We present a combinatorial and computational commutative algebra methodology for studying singularities of Schubert varieties of flag manifolds. We define the combinatorial notion of *interval pattern avoidance*. For "reasonable" invariants P of singularities, ... More

Diagonalization of the Finite Hilbert Transform on two adjacent intervalsNov 06 2015We study the interior problem of tomography. The starting point is the Gelfand-Graev formula, which converts the tomographic data into the finite Hilbert transform (FHT) of an unknown function $f$ along a collection of lines. Pick one such line, call ... More

On multi-dimensional sampling and interpolationApr 02 2013The paper discusses sharp sufficient conditions for interpolation and sampling for functions of n variables with convex spectrum. When n=1, the classical theorems of Ingham and Beurling state that the critical values in the estimates from above (from ... More

Cauchy independent measures and super-additivity of analytic capacityNov 12 2012We show that, given a family of discs centered at a nice curve, the analytic capacities of arbitrary subsets of these discs add up. However we need that the discs in question would be slightly separated, and it is not clear whether the separation condition ... More

Random "dyadic" lattice in geometrically doubling metric space and $A_2$ conjectureMar 27 2011Apr 21 2011Recently three proofs of the $A_2$-conjecture were obtained. All of them are "glued" to euclidian space and a special choice of one random dyadic lattice. We build a random "dyadic" lattice in any doubling metric space which have properties that are enough ... More

Reachability in Higher-Order-CountersJun 05 2013Higher-order counter automata (\HOCS) can be either seen as a restriction of higher-order pushdown automata (\HOPS) to a unary stack alphabet, or as an extension of counter automata to higher levels. We distinguish two principal kinds of \HOCS: those ... More

Exceptional collections on isotropic GrassmanniansOct 25 2011Sep 13 2015We introduce a new construction of exceptional objects in the derived category of coherent sheaves on a compact homogeneous space of a semisimple algebraic group and show that it produces exceptional collections of the length equal to the rank of the ... More

Full exceptional collections on the Lagrangian Grassmannians LG(4,8) and LG(5,10)Oct 13 2009We construct full exceptional collections of vector bundles on the Lagrangian Grassmannians LG(4,8) and LG(5,10).

Projectively full ideals in Noetherian rings, a surveyDec 07 2007We discuss projective equivalence of ideals in Noetherian rings and the existence or failure of existence of projectively full ideals. We describe connections with the Rees valuations and Rees integers of an ideal, and consider the question of whether ... More

The Radio Properties of Seyfert Galaxies in the 12--Micron and CfA SamplesJun 28 1996We report the results of 20, 6, and 2 cm VLA and 1.5 cm OVRO observations of the optically-selected CfA Seyfert galaxies and the bolometric-flux-limited 12-Micron active galaxy sample. Every object observed was detected at 6 cm. Only 6-8% of the 12um ... More

String center of mass operator and its effect on BRST cohomologyNov 15 1995We consider the theory of bosonic closed strings on the flat background R(25,1). We show how the BRST complex can be extended to a complex where the string center of mass operator, x^mu_0, is well defined. We investigate the cohomology of the extended ... More

An ICT-Based Real-Time Surveillance System for Controlling Dengue in Sri LankaMay 16 2014Dengue is a notifiable communicable disease in Sri Lanka since 1996. Dengue fever spread rapidly among people living in most of the districts of Sri Lanka. The present notification system of dengue communicable diseases which is enforced by law is a passive ... More

Approximation of discrete functions and size of spectrumApr 02 2013Let $\Lambda$ be a uniformly discrete set and $S$ be a compact set in $R$. We prove that if there exists a bounded sequence of functions in Paley--Wiener space $PW_S$, which approximates $\delta-$functions on $\Lambda$ with $l^2-$error $d$, then measure($S$)$\geq ... More

A Gröbner basis for Kazhdan-Lusztig idealsSep 03 2009Nov 11 2011Kazhdan-Lusztig ideals, a family of generalized determinantal ideals investigated in [Woo-Yong '08], provide an explicit choice of coordinates and equations encoding a neighbourhood of a torus-fixed point of a Schubert variety on a type A flag variety. ... More

Neutrino energy quantization in rotating mediumSep 30 2008Exact solution of the modified Dirac equation in rotating medium is found in polar coordinates in the limit of vanishing neutrino mass. The solution for the active left-handed particle exhibit properties similar to those peculiar for the charged particle ... More

General Conditions for Lepton Flavour Violation at Tree- and 1-Loop LevelSep 20 2007In this work, we compile the necessary and sufficient conditions a theory has to fulfill in order to ensure general lepton flavour conservation, in the spirit of the Glashow-Weinberg criteria for the absence of flavour-changing neutral currents. At tree-level, ... More

Spectral perturbation theory and the two weights problemJun 08 2013The famous two weights problem consists in characterising all possible pairs of weights such that the Hardy projection is bounded between the corresponding weighted $L^2$ spaces. Koosis' theorem of 1980 gives a way to construct a certain class of pairs ... More

Exponential-Uniform Identities Related to RecordsJun 05 2012We consider a rectangular grid induced by the south-west records from the planar Poisson point process in $R^2_+$. A random symmetry property of the matrix whose entries are the areas of tiles of the grid implies cute multivariate distributional identities ... More

Yet again on polynomial convergence for SDEs with a gradient-type driftJun 28 2017Jul 23 2017Bounds on convergence rate to the invariant distribution for a class of stochastic differential equations (SDEs) with a gradient-type drift are obtained.

Mild and viscosity solutions to semilinear parabolic path-dependent PDEsNov 24 2016Nov 14 2018We study and compare two concepts for weak solutions to semilinear parabolic path-dependent partial differential equations (PPDEs). The first is that of mild solutions as it appears, e.g., in the log-Laplace functionals of historical superprocesses. The ... More

Magnetic susceptibility of the quark condensate via holographyFeb 11 2009Jan 13 2010We discuss the holographic derivation of the magnetic susceptibility of the quark condensate. It is found that the susceptibility emerges upon the account of the Chern-Simons term in the holographic action. We demonstrate that Vainshtein's relation is ... More

On Beurling's sampling theorem in $\R^n$Jun 03 2011We present an elementary proof of the classical Beurling sampling theorem which gives a sufficient condition for sampling of multi-dimensional band-limited functions.

Derived categories of cyclic covers and their branch divisorsNov 07 2014Dec 17 2015Given a variety $Y$ with a rectangular Lefschetz decomposition of its derived category, we consider a degree $n$ cyclic cover $X \to Y$ ramified over a divisor $Z \subset Y$. We construct semiorthogonal decompositions of $\mathrm{D^b}(X)$ and $\mathrm{D^b}(Z)$ ... More

On the Duality between Sampling and InterpolationDec 04 2015We present a simple method based on the stability and duality of the properties of sampling and interpolation, which allows one to substantially simplify the proofs of some classical results.

Regenerative compositions in the case of slow variation: A renewal theory approachSep 27 2011Sep 01 2012A regenerative composition structure is a sequence of ordered partitions derived from the range of a subordinator by a natural sampling procedure. In this paper, we extend previous studies Barbour and Gnedin (2006), Gnedin, Iksanov and Marynych (2010) ... More

Mild and viscosity solutions to quasilinear parabolic path-dependent PDEsNov 24 2016We study and compare two different concepts for weak solutions to quasilinear parabolic path-dependent partial differential equations (PPDEs). The first concept is that of a mild solution as it appears, e.g., in the Laplace functionals of historical superprocesses. ... More

When is a Schubert variety Gorenstein?Sep 25 2004Nov 21 2005A (normal) variety is Gorenstein if it is Cohen-Macualay and its canonical sheaf is a line bundle. This property, which measures the ``pathology'' of the singularities of a variety, is thus stronger than Cohen-Macualayness, but is also weaker than smoothness. ... More

Evaluation of the Einstein's strength of difference schemes for some chemical reaction-diffusion equationsMar 10 2018In this paper we present a difference algebraic technique for the evaluation of the Einstein's strength of a system of partial difference equations and apply this technique to the comparative analysis of difference schemes for chemical reaction-diffusion ... More

Spherical structures on torus knots and linksAug 02 2010Jul 07 2011The present paper considers two infinite families of cone-manifolds endowed with spherical metric. The singular strata is either the torus knot ${\rm t}(2n+1, 2)$ or the torus link ${\rm t}(2n, 2)$. Domains of existence for a spherical metric are found ... More

Quasiclassical analysis of Bloch oscillations in non-Hermitian tight-binding latticesApr 07 2016Jun 06 2016Many features of Bloch oscillations in one-dimensional quantum lattices with a static force can be described by quasiclassical considerations for example by means of the acceleration theorem, at least for Hermitian systems. Here the quasiclassical approach ... More

Near-Contemporaneous Optical Spectroscopic and Infrared Photometric Observations of Candidate Herbig Ae/Be Stars in the Magellanic CloudsMay 27 2011We present near-IR (J,H,Ks) photometry for 27 of the 28 candidate Herbig Ae/Be stars in the Small and Large Magellanic Clouds identified via the EROS1 and EROS2 surveys as well as near-contemporaneous optical (H-alpha) spectroscopy for 21 of these 28 ... More

Soft X--Ray Properties of Seyfert Galaxies in the Rosat All--Sky SurveyMay 08 1996We present the results of ROSAT All-Sky Survey observations of Seyfert and IR-luminous galaxies from the Extended 12 Micron Galaxy Sample and the optically-selected CfA Sample. Roughly half of the Seyferts (mostly Seyfert 1s) have been fitted to an absorbed ... More

Electronic Raman scattering in Magnetite, Spin vs. Charge gapJul 09 2009We report Raman scattering data of single crystals of magnetite (Fe3O4) with Verwey transition temperatures (Tv) of 123 and 117K, respectively. Both single crystals reveal broad electronic background extending up to 900 wavenumbers (~110 meV). Redistribution ... More

Compositions of consistent systems of rank one discrete valuation ringsSep 26 2008Let V be a rank one discrete valuation ring (DVR) on a field F and let L/F be a finite separable algebraic field extension with [L:F] = m. The integral closure of V in L is a Dedekind domain that encodes the following invariants: (i) the number of extensions ... More

The Bernoulli sieve: an overviewMay 31 2010The Bernoulli sieve is a version of the classical balls-in-boxes occupancy scheme, in which random frequencies of infinitely many boxes are produced by a multiplicative random walk, also known as the residual allocation model or stick-breaking. We give ... More

Limit theorems for the number of occupied boxes in the Bernoulli sieveJan 27 2010The Bernoulli sieve is a version of the classical `balls-in-boxes' occupancy scheme, in which random frequencies of infinitely many boxes are produced by a multiplicative renewal process, also known as the residual allocation model or stick-breaking. ... More

A generalization of the Erdős-Turán law for the order of random permutationApr 26 2011May 03 2012We consider random permutations derived by sampling from stick-breaking partitions of the unit interval. The cycle structure of such a permutation can be associated with the path of a decreasing Markov chain on $n$ integers. Under certain assumptions ... More

Projective equivalence of ideals in Noetherian integral domainsDec 05 2007Let I be a nonzero proper ideal in a Noetherian integral domain R. In this paper we establish the existence of a finite separable integral extension domain A of R and a positive integer m such that all the Rees integers of IA are equal to m. Moreover, ... More

Lambda-coalescents with dust componentFeb 06 2011We consider the lambda-coalescent processes with positive frequency of singleton clusters. The class in focus covers, for instance, the beta$(a,b)$-coalescents with $a>1$. We show that some large-sample properties of these processes can be derived by ... More

A note on Itoh (e)-Valuation Rings of and IdealJul 18 2016Let $I$ be a regular proper ideal in a Noetherian ring $R$, let $e \ge 2$ be an integer, let $\mathbf T_e = R[u,tI,u^{\frac{1}{e}}]' \cap R[u^{\frac{1}{e}},t^{\frac{1}{e}}]$ (where $t$ is an indeterminate and $u =\frac{1}{t}$), and let $\mathbf r_e = ... More

Meromorphic Solutions to a Differential--Difference Equation Describing Certain Self-Similar PotentialsMar 23 2001In this paper we prove the existence of meromorphic solutions to a nonlinear differential difference equation that describe certain self-similar potentials for the Schroedinger operator.

Moments Finiteness Problem and Center Problem for Ordinary Differential EquationsMay 18 2013We study the moments finiteness problem for the class of Lipschitz maps $F: [a,b]\rightarrow\mathbb R^n$ with images in a compact Lipschitz triangulable curve $\Gamma$. We apply the obtained results to the center problem for ODEs describing in some cases ... More

On Local Behavior of Holomorphic Functions Along Complex Submanifolds of C^NAug 25 2007Dec 28 2007In this paper we establish some general results on local behavior of holomorphic functions along complex submanifolds of $\Co^{N}$. As a corollary, we present multi-dimensional generalizations of an important result of Coman and Poletsky on Bernstein ... More

Note on Malmstèn's paper De Integralibus quibusdam definitis seriebusque infinitisJun 16 2013We present a proof of the functional equation of the Riemann zeta-function or more precisely the Dirichlet eta-function, which proof seems to be new but follows almost immediately from Malmst\`en's paper ``De integralibus quibusdam definitis seriebusque ... More

Quantization of geometry associated to the quantized Knizhnik-Zamolodchikov equationsJun 05 1996It is known that solutions of the Knizhnik-Zamolodchikov differential equations are given by integrals of closed differential forms over suitable cycles. In this paper a quantization of this geometric construction is described leading to solution of the ... More

Critical set of the master function and characteristic variety of the associated Gauss-Manin differential equationsOct 09 2014Aug 30 2016We consider a weighted family of $n$ parallelly transported hyperplanes in a $k$-dimensioinal affine space and describe the characteristic variety of the Gauss-Manin differential equations for associated hypergeometric integrals. The characteristic variety ... More

Special functions, KZ type equations and Representation theoryMay 29 2002May 29 2002This paper is a set of lecture notes of my course "Special functions, KZ type equations, and representation theory" given at MIT during the spring semester of 2002. The notes do not contain new results, and are an exposition (mostly without proofs) of ... More

A monotonicity formula for free boundary surfaces with respect to the unit ballFeb 19 2014We prove a monotonicity identity for compact surfaces with free boundaries inside the boundary of unit ball in $\mathbb R^n$ that have square integrable mean curvature. As one consequence we obtain a Li-Yau type inequality in this setting, thereby generalizing ... More

On the difference of partial theta functionsDec 26 2007Sums of the form add((-1)^n q^(n(n-1)/2) x^n, n>=0) are called partial theta functions. In his lost noteboook, Ramanujan recorded many identities for these functions. A few years ago Warnaar found an elegant formula for a sum of two partial theta series. ... More

The field of the Reals and the Random Graph are not Finite-Word Ordinal-AutomaticOct 20 2014Recently, Schlicht and Stephan lifted the notion of automatic-structures to the notion of (finite-word) ordinal-automatic structures. These are structures whose domain and relations can be represented by automata reading finite words whose shape is some ... More

Relative continuous K-theory and cyclic homologyDec 11 2013Oct 09 2014We show that for an associative algebra A and its ideal I such that the I-adic topology on A coincides with the p-adic topology, the relative continuous K-theory pro-spectrum "lim"K(A_i, IA_i), where A_i :=A/p^i A, is naturally isogenous to the cyclic ... More

Expanders from Markov basesMay 12 2015Diaconis and Sturmfels introduced an influential method to construct Markov chains using commutative algebra. One major point of their method is that infinite families of graphs are simultaneously proved to be connected by a single algebraic calculation. ... More

Analogue of Weil representation for abelian schemesDec 19 1997In this paper we construct a projective action of certain arithmetic group on the derived category of coherent sheaves on an abelian scheme $A$, which is analogous to Weil representation of the symplectic group. More precisely, the arithmetic group in ... More

On the Origin of the Charge-Asymmetric Matter. II. Localized Dirac WaveformsApr 07 2016May 19 2016This paper continues the author's work \cite{PartI}, where a new framework of the matter-induced physical geometry was built and an intrinsic nonlinearity of the Dirac equation discovered. Here, the nonlinear Dirac equation is solved and the localized ... More