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Stably weakly shadowing transitive sets and dominated splittingsMar 10 2010We prove that for any $C^1$-stably weakly shadowing transitive set $\Lambda$, either $\Lambda$ is a sink or a source, or $\Lambda$ admits a dominated splitting.

On the dimension of the Hilbert scheme of curvesAug 26 2008Consider a component of the Hilbert scheme whose general point corresponds to a degree d genus g smooth irreducible and nondegenerate curve in a projective variety X. We give lower bounds for the dimension of such a component when X is P^3, P^4 or a smooth ... More

Log Minimal Model Program for the Kontsevich Space of Stable Maps $\bar{\mathcal M}_{0,0}(\mathbb P^{3}, 3)$Sep 04 2007This work is inspired by conversations with Izzet Coskun and Joe Harris. We run the log minimal model program for the Kontsevich space of stable maps $\bar{\mathcal M}_{0,0}(\mathbb P^{3}, 3)$ and give modular interpretations to all the intermediate spaces ... More

Simply branched covers of an elliptic curve and the moduli space of curvesJun 04 2008Consider genus g curves that admit degree d covers to an elliptic curve simply branched at 2g-2 points. Vary a branch point and the locus of such covers forms a one-parameter family W. We investigate the geometry of W by using admissible covers to study ... More

Differential projective modules over algebras with radical square zeroMar 31 2018Let $Q$ be a finite quiver and $\Lambda$ be the radical square zero algebra of $Q$ over a field. We give a full and dense functor from the category of reduced differential projective modules over $\Lambda$ to the category of representations of the opposite ... More

Teichmüller dynamics in the eyes of an algebraic geometerFeb 06 2016This is an introduction to the algebraic aspect of Teichm\"uller dynamics, with a focus on its interplay with the geometry of moduli spaces of curves as well as recent advances in the field.

Stable Base Locus Decompositions of Kontsevich Moduli SpacesFeb 11 2009In this paper, we determine the stable base locus decomposition of the Kontsevich moduli spaces of degree two and three stable maps to Grassmannians. This gives new examples of the decomposition for varieties with Picard rank three. We also discuss the ... More

Reconciling Irrational Human Behavior with AI based Decision Making: A Quantum Probabilistic ApproachAug 14 2018There are many examples of human decision making which cannot be modeled by classical probabilistic and logic models, on which the current AI systems are based. Hence the need for a modeling framework which can enable intelligent systems to detect and ... More

Investigating Order Effects in Multidimensional Relevance Judgment using Query LogsJul 14 2018Mar 13 2019There is a growing body of research which has investigated relevance judgment in IR being influenced by multiple factors or dimensions. At the same time, the Order Effects in sequential decision making have been quantitatively detected and studied in ... More

Detaching embedded pointsNov 11 2009Aug 24 2010We show that if $D \subset \mathbb P^N$ is obtained from a codimension two local complete intersection $C$ by adding embedded points of multiplicity $\leq 3$, then $D$ is a flat limit of $C$ and isolated points. As applications, we determine the irreducible ... More

Homoclinic tangencies and singular hyperbolicity for three-dimensional vector fieldsFeb 20 2017Sep 13 2018We prove that any vector field on a three-dimensional compact manifold can be approximated in the C1-topology by one which is singular hyperbolic or by one which exhibits a homoclinic tangency associated to a regular hyperbolic periodic orbit. This answers ... More

Existence of nontrivial solutions for periodic Schrodinger equations with new nonlinearitiesApr 03 2014We study the Schr\"{o}dinger equation: \begin{eqnarray} - \Delta u+V(x)u+f(x,u)=0,\qquad u\in H^{1}(\mathbb{R}^{N}),\nonumber \end{eqnarray} where $V$ is periodic and $f$ is periodic in the $x$-variables, $0$ is in a gap of the spectrum of the operator ... More

Noisy Feedback and Loss Unlimited Private CommunicationJan 11 2018Alice is transmitting a private message to Bob across a bosonic wiretap channel with the help of a public feedback channel to which all parties, including the fully-quantum equipped Eve, have completely noiseless access. We find that by altering the model ... More

Learning Non-Uniform Hypergraph for Multi-Object TrackingDec 10 2018The majority of Multi-Object Tracking (MOT) algorithms based on the tracking-by-detection scheme do not use higher order dependencies among objects or tracklets, which makes them less effective in handling complex scenarios. In this work, we present a ... More

Strong converse exponents for the feedback-assisted classical capacity of entanglement-breaking channelsJun 07 2015Aug 03 2016Quantum entanglement can be used in a communication scheme to establish a correlation between successive channel inputs that is impossible by classical means. It is known that the classical capacity of quantum channels can be enhanced by such entangled ... More

A search for evidence of solar rotation in Super-Kamiokande solar neutrino datasetApr 22 2016Jun 06 2016We apply the generalized Lomb-Scargle (LS) periodogram, proposed by Zechmeister and Kurster, to the solar neutrino data from Super-Kamiokande (Super-K) using data from its first five years. For each peak in the LS periodogram, we evaluate the statistical ... More

Neural Filters for Jet AnalysisMay 09 1993We study the efficiency of a neural-net filter and deconvolution method for estimating jet energies and spectra in high-background reactions such as nuclear collisions at the relativistic heavy-ion collider and the large hadron collider. The optimal network ... More

Strong converse exponents for the feedback-assisted classical capacity of entanglement-breaking channelsJun 07 2015Nov 03 2017Quantum entanglement can be used in a communication scheme to establish a correlation between successive channel inputs that is impossible by classical means. It is known that the classical capacity of quantum channels can be enhanced by such entangled ... More

Geometric Hypergraph Learning for Visual TrackingMar 18 2016Graph based representation is widely used in visual tracking field by finding correct correspondences between target parts in consecutive frames. However, most graph based trackers consider pairwise geometric relations between local parts. They do not ... More

Multi-view Deep Subspace Clustering NetworksAug 06 2019Multi-view subspace clustering aims to discover the inherent structure by fusing multi-view complementary information. Most existing methods first extract multiple types of hand-crafted features and then learn a joint affinity matrix for clustering. The ... More

Quantum Factorization of 143 on a Dipolar-Coupling NMR systemNov 16 2011Quantum algorithms could be much faster than classical ones in solving the factoring problem. Adiabatic quantum computation for this is an alternative approach other than Shor's algorithm. Here we report an improved adiabatic factoring algorithm and its ... More

Scale Invariant Fully Convolutional Network: Detecting Hands EfficientlyJun 11 2019Existing hand detection methods usually follow the pipeline of multiple stages with high computation cost, i.e., feature extraction, region proposal, bounding box regression, and additional layers for rotated region detection. In this paper, we propose ... More

Data Priming Network for Automatic Check-OutApr 10 2019Aug 01 2019Automatic Check-Out (ACO) receives increased interests in recent years. An important component of the ACO system is the visual item counting, which recognizes the categories and counts of the items chosen by the customers. However, the training of such ... More

Implementation of a Quantum-simulation Algorithm of Calculating Molecular Ground-state Energy on an NMR Quantum ComputerJul 21 2009Jul 22 2009It is exponentially hard to simulate quantum systems by classical algorithms, while quantum computer could in principle solve this problem polynomially. We demonstrate such an quantum-simulation algorithm on our NMR system to simulate an hydrogen molecule ... More

NMR Experimental Demonstration of Probabilistic Quantum CloningApr 19 2011The method of quantum cloning is divided into two main categories: approximate and probabilistic quantum cloning. The former method is used to approximate an unknown quantum state deterministically, and the latter can be used to faithfully copy the state ... More

Data Priming Network for Automatic Check-OutApr 10 2019Automatic Check-Out (ACO) receives increased interests in recent years. An important component of the ACO system is the visual item counting, which recognize the categories and counts of the items chosen by the customers. However, the training of such ... More

Boundary-sensitive Network for Portrait SegmentationDec 22 2017Apr 09 2018Compared to the general semantic segmentation problem, portrait segmentation has higher precision requirement on boundary area. However, this problem has not been well studied in previous works. In this paper, we propose a boundary-sensitive deep neural ... More

Approximation of Reachable Set for Coherently Controlled Open Quantum Systems: Application to Quantum State EngineeringDec 11 2014Aug 04 2015Precisely characterizing and controlling realistic open quantum systems is one of the most challenging and exciting frontiers in quantum sciences and technologies. In this Letter, we present methods of approximately computing reachable sets for coherently ... More

Data Priming Network for Automatic Check-OutApr 10 2019Aug 07 2019Automatic Check-Out (ACO) receives increased interests in recent years. An important component of the ACO system is the visual item counting, which recognizes the categories and counts of the items chosen by the customers. However, the training of such ... More

Simulation of chemical reaction dynamics on an NMR quantum computerMay 21 2011Quantum simulation can beat current classical computers with minimally a few tens of qubits and will likely become the first practical use of a quantum computer. One promising application of quantum simulation is to attack challenging quantum chemistry ... More

A Quantum Observation Scheme Can Universally Identify Causalities from CorrelationsMar 08 2019It has long been recognized as a difficult problem to determine whether the observed statistical correlation between two classical variables arise from causality or from common causes. Recent research has shown that in quantum theoretical framework, the ... More

Investigating Bell Inequalities for Multidimensional Relevance Judgments in Information RetrievalNov 16 2018Mar 13 2019Relevance judgment in Information Retrieval is influenced by multiple factors. These include not only the topicality of the documents but also other user oriented factors like trust, user interest, etc. Recent works have identified these various factors ... More

Quasimodularity and large genus limits of Siegel-Veech constantsJun 13 2016Quasimodular forms were first studied in the context of counting torus coverings. Here we show that a weighted version of these coverings with Siegel-Veech weights also provides quasimodular forms. We apply this to prove conjectures of Eskin and Zorich ... More

A Practical Bandit Method with Advantages in Neural Network TuningJan 26 2019Feb 21 2019Stochastic bandit algorithms can be used for challenging non-convex optimization problems. Hyperparameter tuning of neural networks is particularly challenging, necessitating new approaches. To this end, we present a method that adaptively partitions ... More

There is at least one pair of double primes for any even numberOct 16 2005We proved that any even number not less than 6 can be expressed as the sum of two old primes, $2n=p_i+p_j$

Towards Mori's program for the moduli space of stable mapsMay 18 2009We introduce and compute the class of a number of effective divisors on the moduli space of stable maps $\bar M_{0,0}(P^{r},d)$, which, for small d, provide a good understanding of the extremal rays and the stable base locus decomposition for the effective ... More

A numerical mode matching method for wave scattering in a layered medium with a stratified inhomogeneityApr 23 2018Numerical mode matching (NMM) methods are widely used for analyzing wave propagation and scattering in structures that are piece-wise uniform along one spatial direction. For open structures that are unbounded in transverse directions (perpendicular to ... More

Robust Mechanisms Under Common ValuationMar 20 2016Aug 29 2016We study robust mechanisms to sell a common-value good. We assume that the mechanism designer knows the prior distribution of the buyers' common value but is unsure of the buyers' information structure about the common value. We use linear programming ... More

On Level persistence (Relevant level persistence numbers)Apr 16 2014Apr 20 2014The purpose of this note is to describe of a new set of numerical invariants, the relevant level persistence numbers, and make explicit their relationship with the four types of bar codes, a more familiar set of complete invariants for level persistence. ... More

Semi-supervised learning of local structured output predictorsApr 11 2016In this paper, we study the problem of semi-supervised structured output prediction, which aims to learn predictors for structured outputs, such as sequences, tree nodes, vectors, etc., from a set of data points of both input-output pairs and single inputs ... More

Staggered chiral perturbation theory in the two-flavor caseNov 13 2009Nov 08 2010I study two-flavor staggered chiral perturbation theory in the light pseudoscalar sector. The pion mass and decay constant are calculated through NLO in the partially-quenched case. In the limit where the strange quark mass is large compared to the light ... More

Lagrange Multipliers and Rayleigh Quotient Iteration in Constrained Type EquationsAug 01 2019We generalize the Rayleigh quotient iteration to a class of functions called vector Lagrangians. The Rayleigh quotient is an expression used in literature as an estimate of the Lagrange multiplier in constrained optimization. We discuss two methods of ... More

An Overview of Mobile Capacitive Touch Technologies TrendsDec 25 2016Touch sensing, as a major human/machine interface, is widely used in various commercial products such as smart watches, mobile phones, tablets and TVs. State-of-the-art touch detections are mainly based on mutual capacitive sensing, which requires necessary ... More

Improving LSTM Neural Networks for Better Short-Term Wind Power PredictionsJun 30 2019Aug 03 2019This paper improves wind power prediction via weather forecast-contextualized Long Short-Term Memory Neural Network (LSTM) models. Initially, only wind power data was fed to a generic LSTM, but this model performed poorly, with erratic and naive behavior ... More

Higher order Poisson Kernels and $L^p$ polyharmonic boundary value problems in Lipschitz domainsMar 04 2015Mar 21 2015In this article, we introduce higher order conjugate Poisson and Poisson kernels, which are higher order analogues of the classical conjugate Poisson and Poisson kernels, as well as the polyharmonic fundamental solutions, and define multi-layer potentials ... More

A Polynomial time Algorithm for Hamilton Cycle and Its detailed proofApr 12 2010Nov 10 2016Popular algorithms to find a Hamilton circle in an undirected graph are generally based on the Rotation-Extension method developed by Posa. However, due to the deficiencies of Posa's method, such algorithms are only efficient for graphs that are either ... More

Preconditioning fractional spectral collocationOct 20 2015Fractional spectral collocation (FSC) method based on fractional Lagrange interpolation has recently been proposed to solve fractional differential equations. Numerical experiments show that the linear systems in FSC become extremely ill-conditioned as ... More

Improving LSTM Neural Networks for Better Short-Term Wind Power PredictionsJun 30 2019This paper introduces an improved method of wind power prediction via weather forecast-contextualized Long Short- Term Memory Neural Network (LSTM) models. Wind power and weather forecast data were acquired from open-source databases and combined. However, ... More

Trilateration-based Multi-hop for the Long Range Wide Area NetworkNov 15 2018Nov 20 2018Long Range Wide Area Network (LoRaWAN) has an open specification that defines the Medium Access Control (MAC) protocol for LoRa networks, mainly based on pure-Aloha with beacon option. The LoRaWAN has a star of star topology where end-devices are directly ... More

Long Range Wide Area Network: A Simulation Module for ns-3Nov 14 2018Nov 20 2018Long Range (LoRa) is a wireless communication technology for the Internet of Things (IoT), able to provide wide coverage networking to devices with low power consumption and low data-rate. This paper~proposes and describes a simulation module of LoRa ... More

Serious Game for Human Environmental Consciousness Education in Residents Daily LifeMar 20 2015Oct 24 2016It has been challenging to find ways to educate people to have better environmental consciousness. In some cases, people do not know what the right behaviors are to protect the environment. Game engine has been used in the AEC industry for visualization. ... More

On the power-law q-distribution function based on the probabilistically independent postulate in nonextensive statisticsDec 13 2010Dec 25 2010We deal with the power-law q-distribution functions, so-called q-exponentials in nonextensive statistics. The system considered is a many-body Hamiltonian system with arbitrary interacting potentials. We find that the usual form of power-law q-distribution ... More

The hydrostatic equilibrium and Tsallis equilibrium for self-gravitating systemsJun 10 2004Mar 25 2005Self-gravitating systems are generally thought to behavior non-extensively due to the long-range nature of gravitational forces. We obtain a relation between the nonextensive parameter q of Tsallis statistics, the temperature gradient and the gravitational ... More

A new form of Tsallis distribution based on the probabilistically independent postulateJun 08 2009Apr 01 2010The current form of Tsallis distribution for a Hamiltonian system with an arbitrary potential is found to represent a simple isothermal situation. In this letter, the q-exponential of a sum can be applied as the product of the q-exponential based on the ... More

The Chandrasekhar condition of the equilibrium and stability for a star in the nonextensive kinetic theoryFeb 05 2006Jul 26 2006The idea of Chandrasekhar condition of the equilibrium and stability for a star is revisited in the nonextensive kinetic theory based on Tsallis entropy. A new analytical formula generalizing the Chandrasekhar condition is derived by assuming that the ... More

Asymptotic behavior of positive solutions to a degenerate elliptic equation in the upper half space with a nonlinear boundary conditionApr 16 2015We consider positive solutions of the problem \begin{equation} \left\{\begin{array}{l}-\mbox{div}(x_{n}^{a}\nabla u)=0\qquad \mbox{in}\;\;\mathbb{R}_+^n,\\ \frac{\partial u}{\partial \nu^a}=u^{q} \qquad \mbox{on}\;\;\partial \mathbb{R}_+^n,\\ \end{array} ... More

A Polynomial time Algorithm for Hamilton Cycle and Its detailed proofApr 12 2010Aug 29 2016Popular algorithms to find a Hamilton circle in an undirected graph are generally based on the Rotation-Extension method developed by Posa. However, due to the deficiencies of Posa's method, such algorithms are only efficient for graphs that are either ... More

Higher Groupoid Actions, Bibundles, and DifferentiationDec 14 2015In this thesis, we employ simplicial methods to study actions, principal bundles, and bibundles of higher groupoids. Roughly, we use Kan fibrations to model actions of higher groupoids, we use pairs of a Kan fibration and a special acyclic fibration to ... More

Random Walks on Dicyclic GroupMar 16 2009This paper works out the rate of convergence of two "natural" random walks on the dicyclic group.

Quantum-State Purity of Heralded Single Photons Produced from Frequency-Anti-Correlated BiphotonsJul 13 2015Sep 15 2015We analyze the quantum-state purity of heralded single photons produced from frequency-anti-correlated biphotons. We find that the quantum-state purity in time-frequency domain depends strongly on the response time uncertainty of the trigger-photon detector ... More

A Polynomial time Algorithm for Hamilton Cycle and its detailed proofApr 12 2010Mar 21 2019Based on the famous Rotation-Extension technique, by creating the new concepts and methods: broad cycle, main segment, useful cut and insert, destroying edges for a main segment, main goal Hamilton cycle, depth-first search tree, we develop a polynomial ... More

Application of Autoencoder-Assisted Recurrent Neural Networks to Prevent Cases of Sudden Infant Death SyndromeApr 28 2019This project develops and trains a Recurrent Neural Network (RNN) that monitors sleeping infants from an auxiliary microphone for cases of Sudden Infant Death Syndrome (SIDS), manifested in sudden or gradual respiratory arrest. To minimize invasiveness ... More

Two spectral methods for 2D quasi-periodic scattering problemsJul 06 2015Jul 12 2015We consider the 2D quasi-periodic scattering problem in optics, which has been modelled by a boundary value problem governed by Helmholtz equation with transparent boundary conditions. A spectral collocation method and a tensor product spectral method ... More

On the Automorphism Group of a GraphJul 02 2016An automorphism of a graph $G$ with $n$ vertices is a bijective map $\phi$ from $V(G)$ to itself such that $\phi(v_i)\phi(v_j)\in E(G)$ $\Leftrightarrow$ $v_i v_j\in E(G)$ for any two vertices $v_i$ and $v_j$ of $G$. Denote by $\mathfrak{G}$ the group ... More

On Graph Isomorphism ProblemOct 26 2017Let $G$ and $H$ be two simple graphs. A bijection $\phi:V(G)\rightarrow V(H)$ is called an isomorphism between $G$ and $H$ if $(\phi v_i)(\phi v_j)\in E(H)$ $\Leftrightarrow$ $v_i v_j\in E(G)$, $\forall v_i,v_j \in V(G)$. In the case that $G = H$, we ... More

The Unmanned Aerial Vehicle Benchmark: Object Detection and TrackingMar 26 2018With the advantage of high mobility, Unmanned Aerial Vehicles (UAVs) are used to fuel numerous important applications in computer vision, delivering more efficiency and convenience than surveillance cameras with fixed camera angle, scale and view. However, ... More

Solving Quantum Ground-State Problems with Nuclear Magnetic ResonanceJun 02 2011Quantum ground-state problems are computationally hard problems; for general many-body Hamiltonians, there is no classical or quantum algorithm known to be able to solve them efficiently. Nevertheless, if a trial wavefunction approximating the ground ... More

UA-DETRAC: A New Benchmark and Protocol for Multi-Object Detection and TrackingNov 13 2015Sep 04 2016In recent years, numerous effective multi-object tracking (MOT) methods are developed because of the wide range of applications. Existing performance evaluations of MOT methods usually separate the object tracking step from the object detection step by ... More

Serious Game for Human Environmental Consciousness Education in Residents Daily LifeMar 20 2015It has been challenging to find ways to educate people to have better environmental consciousness. In some cases, people do not know what the right behaviors are to protect the environment. Game engine has been used in the AEC industry for visualization. ... More

Enhanced Spin-Orbit Torques and Magnetization Switching through Interface EngineeringJun 13 2018The origin of spin-orbit torques generated from the conversion of charge-to-spin currents is of considerable debate. Solid understanding of the physics behind is key to the development of current and voltage controlled switching dynamics in ultrathin ... More

The Discrete Sell or Hold Problem with Constraints on Asset ValuesJul 23 2014The discrete sell or hold problem (DSHP), which is introduced in \cite{H12}, is studied under the constraint that each asset can only take a constant number of different values. We show that if each asset can take only two values, the problem becomes ... More

Ranking via Arrow-Debreu EquilibriumOct 03 2009In this paper, we establish a connection between ranking theory and general equilibrium theory. First of all, we show that the ranking vector of PageRank or Invariant method is precisely the equilibrium of a special Cobb-Douglas market. This gives a natural ... More

Upper bounds for Fourier decay rates of fractal measuresAug 15 2019For spherical and parabolic averages of the Fourier transform of fractal measures, we obtain new upper bounds on rates of decay by an "intermediate dimension" trick.

The Torsion Generating Set Of The Dehn Twist Subgroups Of Non-orientable SurfacesNov 12 2018Nov 19 2018Let $N_g$ be the non-orientable surface with genus $g$, $\text{MCG}(N_g)$ be the mapping class group of $N_g$, $\mathcal{T}(N_g)$ be the index 2 subgroup generated by all Dehn twists of $\text{MCG}(N_g)$. We prove that for odd genus, $\mathcal{T}(N_g)$ ... More

Transition state theory: a generalization to nonequilibrium systems with power-law distributionsFeb 17 2011Feb 18 2011Transition state theory (TST) is generalized for the nonequilibrium system with power-law distributions. The stochastic dynamics that gives rise to the power-law distributions for the reaction coordinate and momentum is modeled by the Langevin equations ... More

Weak Siegel-Weil formula for M_2(Q) and arithmetic on quaternionsApr 14 2018May 17 2018In this paper, we prove the weak Siegel-Weil formula for the space M_2(Q) . We study the Hecke correspondence and representation numbers associated to Eichler orders, and give the explicit formula for degree of Hecke correspondence and average representation ... More

An Explicit Formula for Likelihood Function for Gaussian Vector Autoregressive Moving-Average Model Conditioned on Initial Observables with Application to Model CalibrationApr 29 2016We derive an explicit formula for likelihood function for Gaussian VARMA model conditioned on initial observables where the moving-average (MA) coefficients are scalar. For fixed MA coefficients the likelihood function is optimized in the autoregressive ... More

Robust Mechanisms Under Common ValuationMar 20 2016Nov 19 2016We study robust mechanisms to sell a common-value good. We assume that the mechanism designer knows the prior distribution of the buyers' common value but is unsure of the buyers' information structure about the common value. We use linear programming ... More

The Extended Mapping Class Group Can Be Generated by Two TorsionsJul 14 2016Let $S_g$ be the closed oriented surface of genus g and let $\text{Mod}^{\pm}(S_g)$ be the extended mapping class group of $S_g$. When the genus is at least 5, we prove that $\text{Mod}^{\pm}(S_g)$ can be generated by two torsion elements. One of these ... More

Generating the mapping class groups with torsionsJun 14 2015Let $S_g$ be the closed oriented surface of genus g and let $\text{Mod}(S_g)$ be the mapping class group. When the genus is at least 3, $\text{Mod}(S_g)$ can be generated by torsion elements. We prove the follow results. For $g \geq 4$, $\text{Mod}(S_g)$ ... More

Negative frequency communicationDec 07 2010Sep 26 2011Spectrum is the most valuable resource in communication system, but unfortunately, so far, a half of the spectrum has been wasted. In this paper, we will see that the negative frequency not only has a physical meaning but also can be used in communication. ... More

On the canonical maps of nonsingular threefolds of general typeDec 21 2016Dec 28 2016Let $S$ be a nonsingular minimal complex projective surface of general type and the canonical map of $S$ is generically finite. Beauville showed that the geometric genus of the image of the canonical map is vanishing or equals the geometric genus of $S$ ... More

Smooth solution to higher dimensional complex Plateau problemDec 07 2017Dec 14 2017Let $X$ be a compact connected strongly pseudoconvex $CR$ manifold of real dimension $2n-1$ in $\mathbb{C}^{N}$. For $n\ge 3$, Yau solved the complex Plateau problem of hypersurface type by checking a bunch of Kohn-Rossi cohomology groups in 1981. In ... More

On well-conditioned spectral collocation and spectral methods by the integral reformulationNov 04 2015Well-conditioned spectral collocation and spectral methods have recently been proposed to solve differential equations. In this paper, we revisit the well-conditioned spectral collocation methods proposed in [T.~A. Driscoll, {\it J. Comput. Phys.}, 229 ... More

Preconditioning rectangular spectral collocationOct 01 2015Oct 21 2015Rectangular spectral collocation (RSC) methods have recently been proposed to solve linear and nonlinear differential equations with general boundary conditions and/or other constraints. The involved linear systems in RSC become extremely ill-conditioned ... More

Surface plasmon resonance under conditions of electromagnetically induced transparencyDec 18 2011A scheme for a surface plasmon resonance system under conditions of electromagnetically induced transparency (EIT) is proposed. The system is composed of three layers: a prism, a thin metal film, and a hybrid dielectric consisting of EIT atoms and a background ... More

On Self-mapping Degrees of $S^3$-geometry manifoldsNov 26 2008In this paper we determined all of the possible self mapping degrees of the manifolds with $S^3$-geometry, which are supposed to be all 3-manifolds with finite fundamental groups. This is a part of a project to determine all possible self mapping degrees ... More

$W^{2,p}$-solutions of parabolic SPDEs in general domainsMay 17 2018The Dirichlet problem for a class of stochastic partial differential equations is studied in Sobolev spaces. The existence and uniqueness result is proved under certain compatibility conditions that ensure the finiteness of $L^{p}(\Omega\times(0,T),W^{2,p}(G))$-norms ... More

Lagrange Multipliers and Rayleigh Quotient Iteration in Constrained Type EquationsAug 01 2019Sep 02 2019We generalize the Rayleigh quotient iteration to a class of functions called vector Lagrangians. The Rayleigh quotient is an expression used in literature as an estimate of the Lagrange multiplier in constrained optimization. We discuss two methods of ... More

Entropy Bound for the Classical Capacity of a Quantum Channel Assisted by Classical FeedbackFeb 07 2019We prove that the classical capacity of an arbitrary quantum channel assisted by a free classical feedback channel is bounded from above by the maximum average output entropy of the quantum channel. As a consequence of this bound, we conclude that a classical ... More

Tautological ring of strata of differentialsAug 01 2017Strata of $k$-differentials on smooth curves parameterize sections of the $k$-th power of the canonical bundle with prescribed orders of zeros and poles. Define the tautological ring of the projectivized strata using the $\kappa$ and $\psi$ classes of ... More

Square-tiled surfaces and rigid curves on moduli spacesMar 03 2010This work is motivated by two central questions in the birational geometry of moduli spaces of curves -- Fulton's conjecture and the effective cone of $\bar M_g$. We study the algebro-geometric aspect of Teichmuller curves parameterizing square-tiled ... More

A Quantum Many-body Wave Function Inspired Language Modeling ApproachAug 28 2018Sep 03 2018The recently proposed quantum language model (QLM) aimed at a principled approach to modeling term dependency by applying the quantum probability theory. The latest development for a more effective QLM has adopted word embeddings as a kind of global dependency ... More

Modelling Dynamic Interactions between Relevance DimensionsJul 25 2019Relevance is an underlying concept in the field of Information Science and Retrieval. It is a cognitive notion consisting of several different criteria or dimensions. Theoretical models of relevance allude to interdependence between these dimensions, ... More

Prediction of novel interface-driven spintronic effectsMay 28 2014The recently-proposed coupling between the angular momentum density and magnetic moment [A. Raeliarijaona et al, Phys. Rev. Lett. 110, 137205 (2013)] is shown here to result in the prediction of (i) novel spin currents generated by an electrical current ... More

On the capacity dimension of the boundary of CAT(0) spacesApr 02 2019In this paper, we study the capacity dimension of the boundary of $CAT(0)$ spaces. We first compare the two metrics on the boundary of a hyperbolic $CAT(0)$ space, i.e., the visual metric and Moran's metric, and prove that they give the same capacity ... More

Affine geometry of strata of differentialsJun 04 2017Affine varieties among all algebraic varieties have simple structures. For example, an affine variety does not contain any complete algebraic curve. In this paper we study affine related properties of strata of $k$-differentials on smooth curves which ... More

A Survey on Dialogue Systems: Recent Advances and New FrontiersNov 06 2017Jan 11 2018Dialogue systems have attracted more and more attention. Recent advances on dialogue systems are overwhelmingly contributed by deep learning techniques, which have been employed to enhance a wide range of big data applications such as computer vision, ... More

Structured Information Retrieval Strategies for Localising Software ChangesNov 30 2018Dec 12 2018During software maintenance and evolution, developers need to deal with a large number of change requests by modifying existing code or adding code into the system. An efficient tackling of change request calls for an accurate localising of software changes, ... More

A Confident Information First Principle for Parametric Reduction and Model Selection of Boltzmann MachinesFeb 05 2015Typical dimensionality reduction (DR) methods are often data-oriented, focusing on directly reducing the number of random variables (features) while retaining the maximal variations in the high-dimensional data. In unsupervised situations, one of the ... More