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Selfie: Self-supervised Pretraining for Image EmbeddingJun 07 2019We introduce a pretraining technique called Selfie, which stands for SELF-supervised Image Embedding. Selfie generalizes the concept of masked language modeling to continuous data, such as images. Given masked-out patches in an input image, our method ... More

Findings of the Second Workshop on Neural Machine Translation and GenerationJun 08 2018Jun 18 2018This document describes the findings of the Second Workshop on Neural Machine Translation and Generation, held in concert with the annual conference of the Association for Computational Linguistics (ACL 2018). First, we summarize the research trends of ... More

Achieving Open Vocabulary Neural Machine Translation with Hybrid Word-Character ModelsApr 04 2016Jun 23 2016Nearly all previous work on neural machine translation (NMT) has used quite restricted vocabularies, perhaps with a subsequent method to patch in unknown words. This paper presents a novel word-character solution to achieving open vocabulary NMT. We build ... More

Latent Topic Conversational ModelsSep 19 2018Latent variable models have been a preferred choice in conversational modeling compared to sequence-to-sequence (seq2seq) models which tend to generate generic and repetitive responses. Despite so, training latent variable models remains to be difficult. ... More

On the Effective Use of Pretraining for Natural Language InferenceOct 05 2017Neural networks have excelled at many NLP tasks, but there remain open questions about the performance of pretrained distributed word representations and their interaction with weight initialization and other hyperparameters. We address these questions ... More

A Hierarchical Neural Autoencoder for Paragraphs and DocumentsJun 02 2015Jun 06 2015Natural language generation of coherent long texts like paragraphs or longer documents is a challenging problem for recurrent networks models. In this paper, we explore an important step toward this generation task: training an LSTM (Long-short term memory) ... More

Efficient Attention using a Fixed-Size Memory RepresentationJul 01 2017The standard content-based attention mechanism typically used in sequence-to-sequence models is computationally expensive as it requires the comparison of large encoder and decoder states at each time step. In this work, we propose an alternative attention ... More

Compression of Neural Machine Translation Models via PruningJun 29 2016Neural Machine Translation (NMT), like many other deep learning domains, typically suffers from over-parameterization, resulting in large storage sizes. This paper examines three simple magnitude-based pruning schemes to compress NMT models, namely class-blind, ... More

When Are Tree Structures Necessary for Deep Learning of Representations?Feb 28 2015Aug 18 2015Recursive neural models, which use syntactic parse trees to recursively generate representations bottom-up, are a popular architecture. But there have not been rigorous evaluations showing for exactly which tasks this syntax-based method is appropriate. ... More

Effective Approaches to Attention-based Neural Machine TranslationAug 17 2015Sep 20 2015An attentional mechanism has lately been used to improve neural machine translation (NMT) by selectively focusing on parts of the source sentence during translation. However, there has been little work exploring useful architectures for attention-based ... More

Massive Exploration of Neural Machine Translation ArchitecturesMar 11 2017Mar 21 2017Neural Machine Translation (NMT) has shown remarkable progress over the past few years with production systems now being deployed to end-users. One major drawback of current architectures is that they are expensive to train, typically requiring days to ... More

Semi-Supervised Sequence Modeling with Cross-View TrainingSep 22 2018Unsupervised representation learning algorithms such as word2vec and ELMo improve the accuracy of many supervised NLP models, mainly because they can take advantage of large amounts of unlabeled text. However, the supervised models only learn from task-specific ... More

Learning Longer-term Dependencies in RNNs with Auxiliary LossesMar 01 2018Jun 13 2018Despite recent advances in training recurrent neural networks (RNNs), capturing long-term dependencies in sequences remains a fundamental challenge. Most approaches use backpropagation through time (BPTT), which is difficult to scale to very long sequences. ... More

BAM! Born-Again Multi-Task Networks for Natural Language UnderstandingJul 10 2019It can be challenging to train multi-task neural networks that outperform or even match their single-task counterparts. To help address this, we propose using knowledge distillation where single-task models teach a multi-task model. We enhance this training ... More

Addressing the Rare Word Problem in Neural Machine TranslationOct 30 2014May 30 2015Neural Machine Translation (NMT) is a new approach to machine translation that has shown promising results that are comparable to traditional approaches. A significant weakness in conventional NMT systems is their inability to correctly translate very ... More

Multi-task Sequence to Sequence LearningNov 19 2015Mar 01 2016Sequence to sequence learning has recently emerged as a new paradigm in supervised learning. To date, most of its applications focused on only one task and not much work explored this framework for multiple tasks. This paper examines three multi-task ... More

Online and Linear-Time Attention by Enforcing Monotonic AlignmentsApr 03 2017Jun 29 2017Recurrent neural network models with an attention mechanism have proven to be extremely effective on a wide variety of sequence-to-sequence problems. However, the fact that soft attention mechanisms perform a pass over the entire input sequence when producing ... More

Unsupervised Data AugmentationApr 29 2019Despite its success, deep learning still needs large labeled datasets to succeed. Data augmentation has shown much promise in alleviating the need for more labeled data, but it so far has mostly been applied in supervised settings and achieved limited ... More

Sumsets of the distance set in $\mathbb{F}_q^d$Nov 19 2016Let $\mathbb{F}_q$ be a finite field of order $q$, where $q$ is large odd prime power. In this paper, we improve some recent results on the additive energy of the distance set, and on sumsets of the distance set due to Shparlinski (2016). More precisely, ... More

QANet: Combining Local Convolution with Global Self-Attention for Reading ComprehensionApr 23 2018Current end-to-end machine reading and question answering (Q\&A) models are primarily based on recurrent neural networks (RNNs) with attention. Despite their success, these models are often slow for both training and inference due to the sequential nature ... More

Growth of homology torsion in finite coverings and hyperbolic volumeDec 24 2014May 22 2016We give an upper bound for the growth of homology torsions of finite coverings of irreducible 3-manifolds with tori boundary in terms of hyperbolic volume.

On positivity of Kauffman bracket skein algebras of surfacesMar 27 2016We show that the Chebyshev polynomials form a basic block of any positive basis of the Kauffman bracket skein algebras of surfaces.

Local well-posedness for the Zakharov system on the background of a line solitonMay 12 2016We prove that the Cauchy problem for the two-dimensional Zakharov system is locally well-posed for initial data which are localized perturbations of a line solitary wave. Furthermore, for this Zakharov system, we prove weak convergence to a nonlinear ... More

Product of sumsets over arbitrary finite fieldsNov 19 2018Nov 25 2018Let $\mathbb{F}_q$ be an arbitrary finite field of order $q$. For $A, B, C, D\subset \mathbb{F}_q$, we show that if $|A||B||C||D|\gg q^{5/2},$ then the set $(A-B)(C-D)$ covers a positive proportion of all elements in $\mathbb{F}_q.$ Our result significantly ... More

Weak approximation, Brauer and R-equivalence in algebraic groups over arithmetical fieldsNov 12 1997Dec 31 1997We prove some new relations between weak approximation and some rational equivalence relations (Brauer and R-equivalence) in algebraic groups over arithmetical fields. By using weak approximation and local - global approach, we compute completely the ... More

Weak approximation and Manin group of R-equivalencesMar 05 1996We extend an exact sequence of Colliot-Thelene and Sansuc which connects arithmetic and birational invariants of tori over a number field to one for arbitrary connected linear algebraic groups.

Quasi-isometric embeddings of non-uniform latticesDec 22 2015Let $G$ and $G'$ be simple Lie groups of equal real rank and real rank at least $2$. Let $\Gamma <G$ and $\Lambda < G'$ be non-uniform lattices. We prove a theorem that often implies that any quasi-isometric embedding of $\Gamma$ into $\Lambda$ is at ... More

Generalized Broughton polynomials and characteristic varietiesMay 04 2012Aug 31 2012We introduce a family of generalized Broughton polynomials and compute the characteristic varieties of complement of a curve arrangement defined by fibers of some generalized Broughton polynomials

Admissibility of local systems for some classes of line arrangementsJul 18 2012Apr 15 2013Let $\A$ be a line arrangement in the complex projective plane $\PP^2$. Denote by $M$ its complement and by $\M$ the set of points in $\A$ with multiplicity at least 3. A rank one local system $\mathcal{L}$ on $M$ is admissible if roughly speaking the ... More

A Critique of a Critique of Word Similarity Datasets: Sanity Check or Unnecessary Confusion?Jul 12 2017Critical evaluation of word similarity datasets is very important for computational lexical semantics. This short report concerns the sanity check proposed in Batchkarov et al. (2016) to evaluate several popular datasets such as MC, RG and MEN -- the ... More

Growth of regulators in finite abelian coveringsDec 30 2012We show that the regulator, which is the difference between the homology torsion and the combinatorial Ray-Singer torsion, of fnite abelian coverings of a fixed complex has sub-exponential growth rate.

Ideals in the Goldman AlgebraDec 12 2017The goal of this work is to study the ideals of the Goldman Lie algebra $S$. To do so, we construct an algebra homomorphism from $S$ to a simpler algebraic structure, and focus on finding ideals of this new structure instead. The structure $S$ can be ... More

Irredundant generating sets and dimension-like invariants of the finite groupDec 11 2017Dec 13 2017Whiston proved that the maximum size of an irredundant generating set in the symmetric group $S_n$ is $n-1$, and Cameron and Cara characterized all irredundant generating sets of $S_n$ that achieve this size. Our goal is to extend their results. Using ... More

Variational Analysis for the Bilateral Minimal Time FunctionMay 09 2017In this paper, we derive formulas for the Fr\'echet (singular) subdiferentials of the bilateral minimal time function $T:\mathbb{R}^n \times \mathbb{R}^n \to [0,+\infty]$ associated with a system governed by differential inclusions. As a consequence, ... More

Fast estimation of posterior probabilities in change-point models through a constrained hidden Markov modelMar 20 2012Jan 22 2013The detection of change-points in heterogeneous sequences is a statistical challenge with applications across a wide variety of fields. In bioinformatics, a vast amount of methodology exists to identify an ideal set of change-points for detecting Copy ... More

Occurrence of distances in vector spaces over prime fieldsMay 16 2019Let $\mathbb{F}_q$ be an arbitrary finite field, and $\mathcal{E}$ be a set of points in $\mathbb{F}_q^d$. Let $\Delta(\mathcal{E})$ be the set of distances determined by pairs of points in $\mathcal{E}$. By using the Kloosterman sums, Iosevich and Rudnev ... More

Hidden Markov Model Applications in Change-Point AnalysisDec 08 2012The detection of change-points in heterogeneous sequences is a statistical challenge with many applications in fields such as finance, signal analysis and biology. A wide variety of literature exists for finding an ideal set of change-points for characterizing ... More

Almost periodic solutions of periodic linear partial functional differential equationsJul 10 2018We study conditions for the abstract periodic linear functional differential equation $\dot{x}=Ax+F(t)x_t+f(t)$ to have almost periodic with the same structure of frequencies as $f$. The main conditions are stated in terms of the spectrum of the monodromy ... More

Optimal Portfolio Problem Using Entropic Value at Risk: When the Underlying Distribution is Non-EllipticalJun 26 2014This paper is devoted to study the optimal portfolio problem. Harry Markowitz's Ph.D. thesis prepared the ground for the mathematical theory of finance. In modern portfolio theory, we typically find asset returns that are modeled by a random variable ... More

Stabilization of Cooperative Information Agents in Unpredictable Environment: A Logic Programming ApproachMar 14 2005Mar 24 2005An information agent is viewed as a deductive database consisting of 3 parts: an observation database containing the facts the agent has observed or sensed from its surrounding environment, an input database containing the information the agent has obtained ... More

Occurrence of distances in vector spaces over prime fieldsMay 16 2019May 23 2019Let $\mathbb{F}_q$ be an arbitrary finite field, and $\mathcal{E}$ be a set of points in $\mathbb{F}_q^d$. Let $\Delta(\mathcal{E})$ be the set of distances determined by pairs of points in $\mathcal{E}$. By using the Kloosterman sums, Iosevich and Rudnev ... More

Nash equilibria in Voronoi games on graphsFeb 09 2007Apr 13 2007In this paper we study a game where every player is to choose a vertex (facility) in a given undirected graph. All vertices (customers) are then assigned to closest facilities and a player's payoff is the number of customers assigned to it. We show that ... More

Mining Hierarchical Temporal Roles with Multiple MetricsMar 08 2016Jul 30 2016Temporal role-based access control (TRBAC) extends role-based access control to limit the times at which roles are enabled. This paper presents a new algorithm for mining high-quality TRBAC policies from timed ACLs (i.e., ACLs with time limits in the ... More

Operator-Valued Bochner Theorem, Fourier Feature Maps for Operator-Valued Kernels, and Vector-Valued LearningAug 19 2016This paper presents a framework for computing random operator-valued feature maps for operator-valued positive definite kernels. This is a generalization of the random Fourier features for scalar-valued kernels to the operator-valued case. Our general ... More

An Overview of the Square Kilometre ArrayNov 18 2013The Square Kilometre Array (SKA) will be the premier instrument to study radiation at centimetre and metre wavelengths from the cosmos, and in particular hydrogen, the most abundant element in the universe. The SKA will probe the dawn of galaxy formation ... More

Optimized replica gas estimation of absolute integrals and partition functionsFeb 03 2010In contrast with most Monte Carlo integration algorithms, which are used to estimate ratios, the replica gas identities recently introduced by Adib enable the estimation of absolute integrals and partition functions using multiple copies of a system and ... More

Density-Dependent Analysis of Nonequilibrium Paths Improves Free Energy EstimatesJan 21 2009Apr 29 2009When a system is driven out of equilibrium by a time-dependent protocol that modifies the Hamiltonian, it follows a nonequilibrium path. Samples of these paths can be used in nonequilibrium work theorems to estimate equilibrium quantities, such as free ... More

Convergence to Equilibrium of Some Kinetic ModelsAug 04 2012We introduce in this paper a new approach to the problem of the convergence to equilibrium for kinetic equations. The idea of the approach is to prove a 'weak' coercive estimate, which implies exponential or polynomial convergence rate. Our method works ... More

Katznelson-Tzafriri Type Theorems for Individual Solutions of Evolution EquationsMar 28 2007Aug 22 2007In this paper we present an extension of the Katznelson-Tzafriri Theorem to the asymptotic behavior of individual solutions of evolution equations $u'(t) =Au(t)+f(t)$. The obtained results do not require the uniform continuity of solutions as well as ... More

Weil-etale Cohomology and Special Values of L-functionsNov 06 2016We construct the Weil-\'etale cohomology and Euler characteristics for a subclass of the class of $\mathbb{Z}$-constructible sheaves on an open subscheme of the spectrum of the ring of integers of a number field. Then we show that the special value of ... More

Further properties of Gaussian Reproducing Kernel Hilbert SpacesOct 23 2012We generalize the orthonormal basis for the Gaussian RKHS described in \cite{MinhGaussian2010} to an infinite, continuously parametrized, family of orthonormal bases, along with some implications. The proofs are direct generalizations of those in \cite{MinhGaussian2010}. ... More

Two-party Models and the No-go TheoremsAug 22 2006Sep 24 2006In this paper, we reconsider the communication model used in the no-go theorems on the impossibility of quantum bit commitment and oblivious transfer. We state that a macroscopic classical channel may not be replaced with a quantum channel which is used ... More

Tackling Error Propagation through Reinforcement Learning: A Case of Greedy Dependency ParsingFeb 22 2017Error propagation is a common problem in NLP. Reinforcement learning explores erroneous states during training and can therefore be more robust when mistakes are made early in a process. In this paper, we apply reinforcement learning to greedy dependency ... More

A classification of quadratic and odd quadratic Lie superalgebras in low dimensionsFeb 19 2013Feb 21 2013In this paper, we give an expansion of two notions of double extension and $T^*$-extension for quadratic and odd quadratic Lie superalgebras. Also, we provide a classification of quadratic and odd quadratic Lie superalgebras up to dimension 6. This classification ... More

A Spectral Theory of Non-Uniformly Continuous Functions and the Loomis-Arendt-Batty-Vu Theory on the Asymptotic Behavior of Solutions of Evolution EquationsSep 22 2006Mar 30 2009In this paper we present a new approach to the spectral theory of {\it non-uniformly continuous} functions and a new framework for the Loomis-Arendt-Batty-Vu theory. Our approach is direct and free of $C_0$-semigroups, so the obtained results, that extend ... More

A Pfaffian formula for the monomer-dimer model on surface graphsMay 02 2017We consider the monomer-dimer model on weighted graphs embedded in surfaces with boundary, with the restriction that only monomers located on the boundary are allowed. We give a Pfaffian formula for the corresponding partition function, which generalises ... More

Some Properties of Large Excursions of a Stationary Gaussian ProcessMay 18 2012Mar 31 2014The present work investigates two properties of level crossings of a stationary Gaussian process $X(t)$ with autocorrelation function $R_X(\tau)$. We show firstly that if $R_X(\tau)$ admits finite second and fourth derivatives at the origin, the length ... More

Causality PrincipleApr 16 2001We advance a famous principle - causality principle - but under a new view. This principle is a principium automatically leading to most fundamental laws of the nature. It is the inner origin of variation, rules evolutionary processes of things, and the ... More

Sliding invariants and classification of singular holomorphic foliations in the planeApr 17 2013Feb 26 2014By introducing a new invariant called the set of slidings, we give a complete strict classification of the class of germs of non-dicritical holomorphic foliations in the plan whose Camacho-Sad indices are not rational. Moreover, we will show that, in ... More

Wave Essence of ParticlesJan 17 2000Feb 22 2000We state several ideas based on the view-point of particle behaviour of matter to explain wave character of photon and elementary particles. By using Newton's suggestion of light ray, we clarify integrally the behaviour of light ``wave''. And ``wave'' ... More

Coin-Flipping-based Quantum Oblivious TransferMay 02 2006Sep 26 2006When submitting ``Coin-Flipping-based Quantum Oblivious Transfer'' (quant-ph/0605027v4) to Indocrypt-2006, I received valuable reviews. Due to the attacks in these reviews, my major protocols, for cheat-sensitive and coin-flipping-based 2-1 oblivious ... More

On 2-antiparallel encounters on factors of the hyperbolic planeMar 08 2017In this paper, we consider the geodesic flow on factors of the hyperbolic plane. We prove that a periodic orbit including a 2-antiparallel encounter has a partner orbit. We construct the partner orbit and give an estimate for the action different between ... More

Lorentz Transformation in Flat 5D Complex-Hyperbolic SpaceFeb 19 2010Feb 23 2010The Lorentz transfomation is derived in 5D flat pseudo-complex affine space or TT Space. The TT space or pseudo-Complex space accomodates one uncompactified time-like extra dimension. It is shown that the maximum allowable speed for particles living in ... More

Malliavin-Stein method for multi-dimensional U-statistics of Poisson point processesNov 09 2011In this paper, we give an upper bound for a probabilistic distance between a Gaussian vector and a vector of U-statistics of Poisson point processes by applying Malliavin-Stein inequality on the Poisson space.

Partner orbits and action differences on compact factors of the hyperbolic plane. II: Higher-order encountersJan 18 2015Feb 21 2016Physicists have argued that periodic orbit bunching leads to universal spectral fluctuations for chaotic quantum systems. To establish a more detailed mathematical understanding of this fact, it is first necessary to look more closely at the classical ... More

A Formula For the S-Class Number of an Algebraic TorusNov 06 2016We obtain a formula for the S-class number of an algebraic torus defined over a number field in terms of the etale and Galois cohomology groups of its character module. As applications, we give different proofs of some classical class number formulas ... More

Contact loci and motivic nearby cycles of nondegenerate polynomialsMar 18 2019We study polynomials with complex coefficients which are nondegenerate with respect to their Newton polyhedron through data on contact loci, motivic nearby cycles and motivic Milnor fiber. Introducing an explicit description of these quantities we can ... 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

Implicit Ligand Theory: Rigorous Binding Free Energies and Thermodynamic Expectations from Molecular DockingAug 24 2012A rigorous formalism for estimating noncovalent binding free energies and thermodynamic expectations from calculations in which receptor configurations are sampled independently from the ligand is derived. Due to this separation, receptor configurations ... More

Multiple Potentials of Mean Force from Biased Experiments Along a Single CoordinateJan 05 2007Mar 20 2007External biasing forces are often applied to enhance sampling in regions of phase space which would otherwise be rarely observed. While the typical goal of these experiments is to calculate the potential of mean force (PMF) along the biasing coordinate, ... More

Improving Human Action Recognition by Non-action ClassificationApr 21 2016Apr 22 2016In this paper we consider the task of recognizing human actions in realistic video where human actions are dominated by irrelevant factors. We first study the benefits of removing non-action video segments, which are the ones that do not portray any human ... More

Protein-Ligand Binding Potential of Mean Force Calculations with Hamiltonian Replica Exchange on Alchemical Interaction GridsJul 14 2015A binding potential of mean force (BPMF) is a free energy of noncovalent association in which one binding partner is flexible and the other is rigid. I have developed a method to calculate BPMFs for protein-ligand systems. The method is based on replica ... More

On Optimal Latency of CommunicationsSep 30 2016In this paper we investigate the optimal latency of communications. Focusing on fixed rate communication without any feedback channel, this paper encompasses low-latency strategies with which one hop and multi-hop communication issues are treated from ... More

Discrete Bayesian Networks: The Exact Posterior Marginal DistributionsNov 23 2014In a Bayesian network, we wish to evaluate the marginal probability of a query variable, which may be conditioned on the observed values of some evidence variables. Here we first present our "border algorithm," which converts a BN into a directed chain. ... More

Infinite-dimensional Log-Determinant divergences II: Alpha-Beta divergencesOct 13 2016This work presents a parametrized family of divergences, namely Alpha-Beta Log- Determinant (Log-Det) divergences, between positive definite unitized trace class operators on a Hilbert space. This is a generalization of the Alpha-Beta Log-Determinant ... More

Path Integral Quantization of Self Interacting Scalar Field with Higher DerivativesSep 28 2007Jan 17 2008Scalar field systems containing higher derivatives are studied and quantized by Hamiltonian path integral formalism. A new point to previous quantization methods is that field functions and their derivatives with time are considered as independent canonical ... More

Efficient texture retrieval using multiscale local extrema descriptors and covariance embeddingAug 03 2018This paper presents an efficient method for texture retrieval using multiscale feature extraction and embedding based on the local extrema keypoints. The idea is to first represent each texture image by its local maximum and local minimum pixels. The ... More

Mean Field Limit of the Learning Dynamics of Multilayer Neural NetworksFeb 07 2019Can multilayer neural networks -- typically constructed as highly complex structures with many nonlinearly activated neurons across layers -- behave in a non-trivial way that yet simplifies away a major part of their complexities? In this work, we uncover ... More

Asymptotic Behavior of Individual Orbits of Discrete SystemsNov 04 2008Dec 28 2008We consider the asymptotic behavior of bounded solutions of the difference equations of the form $x(n+1)=Bx(n) + y(n)$ in a Banach space $\X$, where $n=1,2,...$, $B$ is a linear continuous operator in $\X$, and $(y(n))$ is a sequence in $\X$ converging ... More

On the Asymptotic Behavior of Volterra Difference EquationsOct 26 2010Feb 27 2012We consider the asymptotic behavior of solutions of the difference equations of the form $x(n+1)=Ax(n) + \sum_{k=0}^n B(n-k)x(k) + y(n)$ in a Banach space $\X$, where $n=0,1,2,...$; $A,B(n)$ are linear bounded operator in $\X$. Our method of study is ... More

W-graph determining elements in type AMar 02 2015Mar 04 2015Let $(W,S)$ be a Coxeter system of type $A$, so that $W$ can be identified with the symmetric group $\mathrm{Sym}(n)$ for some positive integer $n$ and $S$ with the set of simple transpositions $\{\,(i,i+1)\mid 1\leqslant i\leqslant n-1\,\}$. Let $\leqslant_{\mathsf ... More

BV solutions constructed by epsilon-neighborhood methodSep 07 2012Feb 10 2016We study a certain class of weak solutions to rate-independent systems, which is constructed by using the local minimality in a small neighborhood of order $\varepsilon$ and then taking the limit $\varepsilon \to 0$. We show that the resulting solution ... More

Tame structures via multiplicative character sums on varieties over finite fieldsApr 12 2017Nov 16 2017We study the model theory of $(\mathbb{F};<_\chi)$ where the field $\mathbb{F}$ is an algebraic closure of a finite field and $<_\chi$ is an ordering on the multiplicative group $\mathbb{F}^\times$ induced by a group embedding $\chi: \mathbb{F}^\times ... More

A semi-implicit scheme based on Arrow-Hurwicz method for saddle point problemsDec 11 2017We search saddle points for a large class of convex-concave Lagrangian. A generalized explicit iterative scheme based on Arrow-Hurwicz method converges to a saddle point of the problem. We also propose in this work, a convergent semi-implicit scheme in ... More

Variations on Quantum Oblivious TransferJun 03 2005Sep 26 2006This paper has been withdrawn by the author, due to the insecurity against attacks received in quant-ph/0605027v5.

Normal forms of topologically quasi-homogeneous foliations on $(\C^2,0)$Sep 05 2013The aim of this paper is to construct formal normal forms for the class of topologically quasi-homogeneous foliations under generic conditions. Any such normal form is given as the sum of three terms: an initial generic quasi-homogeneous term, a hamiltonian ... More

The Equation of CausalityDec 03 1999Dec 07 1999We research the natural causality of the Universe. We find that the equation of causality provides very good results on physics. That is our first endeavour and success in describing a quantitative expression of the law of causality. Hence, our theoretical ... More

The Principle of Least Action for Fields Containing Higher Order DerivativesJul 28 2008When generalizing the principle of least action for fields containing higher order derivatives, in general, it is not possible not to take into account the surface integrated term since it gives direct contribution to the forms of the equations of motion,of ... More

On Optimal Latency of CommunicationsSep 30 2016Jan 04 2017In this paper we investigate the optimal latency of communications. Focusing on fixed rate communication without any feedback channel, this paper encompasses low-latency strategies with which one hop and multi-hop communication issues are treated from ... More

Evens norm, transfers and characteristic classes for extraspecial p-groupsMar 28 2009Let P be the extraspecial p-group of order p^{2n+1}, of p-rank n+1, and of exponent p if p>2. Let Z be the center of P and let kappa_{n,r} be the characteristic classes of degree 2^n - 2^r (resp. 2(p^n-p^r)) for p=2 (resp. p>2), 0 <= r <= n-1, of a degree ... More

Monitoring activities of satellite data processing services in real-time with SDDS Live MonitorDec 05 2018This work describes Live Monitor, the monitoring subsystem of SDDS - an automated system for space experiment data processing, storage, and distribution created at SINP MSU. Live Monitor allows operators and developers of satellite data centers to identify ... More

Extra-Dimensional Approach to Option Pricing and Stochastic VolatilityJan 24 2010Feb 05 2010The generalized 5D Black-Scholes differential equation with stochastic volatility is derived. The projections of the stochastic evolutions associated with the random variables from an enlarged space or superspace onto an ordinary space can be achieved ... More

Vector bundles, dualities, and classical geometry on a curve of genus twoFeb 24 2007Let $C$ be a curve of genus two. We denote by $SU_C(3)$ the moduli space of semi-stable vector bundles of rank 3 and trivial determinant over $C$, and by $J^d$ the variety of line bundles of degree $d$ on $C$. In particular, $J^1$ has a canonical theta ... More

Weil-etale cohomology and special values of L-functions at zeroAug 03 2016We construct the Weil-\'etale cohomology and Euler characteristics for a subclass of the class of $\mathbb{Z}$-constructible sheaves on the spectrum of the ring of integers of a totally imaginary number field. Then we show that the special value of an ... More

The Dirichlet problem for the minimal surface equation in $\rm Sol_3$, with possible infinite boundary dataDec 21 2013Jan 28 2014In this paper, we study the Dirichlet problem for the minimal surface equation in $\rm Sol_3$ with possible infinite boundary data, where $\rm Sol_3$ is the non-abelian solvable $3$-dimensional Lie group equipped with its usual left-invariant metric that ... More

Generating Realistic Sequences of Customer-level Transactions for Retail DatasetsJan 17 2019In order to better engage with customers, retailers rely on extensive customer and product databases which allows them to better understand customer behaviour and purchasing patterns. This has long been a challenging task as customer modelling is a multi-faceted, ... More

Unified quantum invariants for integral homology spheres associated with simple Lie algebrasMar 12 2015Nov 24 2015For each finite dimensional, simple, complex Lie algebra $\mathfrak g$ and each root of unity $\xi$ (with some mild restriction on the order) one can define the Witten-Reshetikhin-Turaev (WRT) quantum invariant $\tau_M^{\mathfrak g}(\xi)\in \mathbb C$ ... More

Unicity for Representations of the Kauffman bracket Skein AlgebraJul 28 2017Mar 21 2019This paper resolves the unicity conjecture of Bonahon and Wong for the Kauffman bracket skein algebras of all oriented finite type surfaces at all roots of unity. The proof is a consequence of a general unicity theorem that says that the irreducible representations ... More

Paraproducts and Products of functions in $BMO(\mathbb R^n)$ and $H^1(\mathbb R^n)$ through waveletsMar 09 2011In this paper, we prove that the product (in the distribution sense) of two functions, which are respectively in $ \BMO(\bR^n)$ and $\H^1(\bR^n)$, may be written as the sum of two continuous bilinear operators, one from $\H^1(\bR^n)\times \BMO(\bR^n) ... More

Document Searching System based on Natural Language Query Processing for Vietnam Open Courseware LibraryDec 09 2009The necessary of buiding the searching system being able to support users expressing their searching by natural language queries is very important and opens the researching direction with many potential. It combines the traditional methods of information ... More