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A Note on "Quantum Algorithm for Linear Systems of Equations"Feb 20 2018Recently, an efficient quantum algorithm for linear systems of equations introduced by Harrow, Hassidim, and Lloyd, has received great concern from the academic community. However, the error and complexity analysis for this algorithm seems so complicated ... More

A Statistical Study of the Magnetic Imprints of X-Class Flares using SDO/HMI Vector MagnetogramsMar 22 2018Magnetic imprints, the rapid and irreversible evolution of photospheric magnetic fields as a feedback from flares in the corona, have been confirmed by many previous studies. These studies showed that the horizontal field will permanently increase near ... More

Wearable Communications in 5G: Challenges and Enabling TechnologiesAug 17 2017Jul 11 2018As wearable devices become more ingrained in our daily lives, traditional communication networks primarily designed for human being-oriented applications are facing tremendous challenges. The upcoming 5G wireless system aims to support unprecedented high ... More

Dispersion of velocity gradients: Mapping magnetization with the Velocity Gradient TechniqueFeb 08 2018Recent developments of the Velocity Gradient Technique (VGT) show that the velocity provides a robust measure of magnetic field direction. In this paper, we use velocity centroids as the measures of velocity and propose a new way of studying media magnetization. ... More

Distribution of velocity gradient orientations: Mapping magnetization with the Velocity Gradient TechniqueFeb 08 2018Aug 01 2018Recent developments of the Velocity Gradient Technique (VGT) show that the velocity gradients provide a reliable tracing of magnetic field direction in turbulent plasmas. In this paper, we explore the ability of velocity gradients to measure the magnetization ... More

Quantum Szilard engines with arbitrary spinFeb 02 2015The quantum Szilard engine (QSZE) is a conceptual quantum engine for understanding the fundamental physics of quantum thermodynamics and information physics. We generalize the QSZE to an arbitrary spin case, i.e., a spin QSZE (SQSZE), and we systematically ... More

Survey of Cognitive Radio Techniques in Wireless NetworkApr 29 2011In this report, I surveyed the cognitive radio technique in wireless networks. Researched several kinds of cognitive techniques about their advantages and disadvantages.

On the integrated squared error of the linear wavelet density estimatorOct 29 2012Linear wavelet density estimators are wavelet projections of the empirical measure based on independent, identically distributed observations. We study here the law of the iterated logarithm (LIL) and a Berry-Esseen type theorem. These results are proved ... More

Automatic Hyperparameter Tuning Method for Local Outlier Factor, with Applications to Anomaly DetectionFeb 01 2019In recent years, there have been many practical applications of anomaly detection such as in predictive maintenance, detection of credit fraud, network intrusion, and system failure. The goal of anomaly detection is to identify in the test data anomalous ... More

On-the-fly Uplink Training and Pilot Code Sequence Design for Cellular NetworksNov 06 2018Cellular networks of massive MIMO base-stations employing TDD/OFDM and relying on uplink training for both downlink and uplink transmission are viewed as an attractive candidate for 5G deployments, as they promise high area spectral and energy efficiencies ... More

Quantum speedup for twin support vector machineFeb 24 2019In this work, we investigate how to speed up machine learning tasks based on quantum computation. We show an important classifier in machine learning, the twin support vector machine, can be exponentially speeded up on quantum computers. Specifically, ... More

Diffusion leaky LMS algorithm: analysis and implementationFeb 13 2016Aug 08 2017The diffusion least-mean square (dLMS) algorithms have attracted much attention owing to its robustness for distributed estimation problems. However, the performance of such filters may change when they are implemented for suppressing noises from speech ... More

Subband adaptive filter trained by differential evolution for channel estimationJan 29 2017Mar 17 2017The normalized subband adaptive filter (NSAF) is widely accepted as a preeminent adaptive filtering algorithm because of its efficiency under the colored excitation. However, the convergence rate of NSAF is slow. To address this drawback, in this paper, ... More

Adaptive beamforming method based on recursive maximum correntropy in impulsive noise with alpha-stable processDec 12 2016Feb 23 2017As a well-established adaptation criterion, the maximum correntropy criterion (MCC) has been receiving increasing attention due to its robust against outliers. In this paper, a new complex recursive maximum correntropy (CRMC) algorithm without any priori ... More

A Class of Diffusion Algorithms with Logarithmic Cost over Adaptive Sparse Volterra NetworkJun 28 2016May 02 2017In this Letter, we present a novel class of diffusion algorithms that can be used to estimate the coefficients of sparse Volterra network (SVN). The development of the algorithms is based on the logarithmic cost and l0-norm constraint. Simulations for ... More

An exact algorithm with the time complexity of $O^*(1.299^m)$ for the weighed mutually exclusive set cover problemFeb 23 2013In this paper, we will introduce an exact algorithm with a time complexity of $O^*(1.299^m)$ for the {\sc weighted mutually exclusive set cover} problem, where $m$ is the number of subsets in the problem. This problem has important applications in recognizing ... More

A Class of Diffusion Algorithms with Logarithmic Cost over Adaptive Sparse Volterra NetworkJun 28 2016Jun 29 2016In this Letter, we present a novel class of diffusion algorithms that can be used to estimate the coefficients of sparse Volterra network. The development of the algorithms is based on the logarithmic cost and l0-norm constraint. To further overcome the ... More

Diffusion leaky LMS algorithm: analysis and implementationFeb 13 2016Jul 30 2016The diffusion least-mean square (dLMS) algorithms have attracted much attention owing to its robustness for distributed estimation problems. However, the performance of such filters may change when they are implemented for suppressing noises from speech ... More

Hierarchical Continuous Time Hidden Markov Model, with Application in Zero-Inflated Accelerometer DataDec 04 2018Dec 25 2018Wearable devices including accelerometers are increasingly being used to collect high-frequency human activity data in situ. There is tremendous potential to use such data to inform medical decision making and public health policies. However, modeling ... More

Fast and interpretable classification of small X-ray diffraction datasets using data augmentation and deep neural networksNov 20 2018Apr 23 2019X-ray diffraction (XRD) data acquisition and analysis is among the most time-consuming steps in the development cycle of novel thin-film materials. We propose a machine-learning-enabled approach to predict crystallographic dimensionality and space group ... More

An exact algorithm for the weighed mutually exclusive maximum set cover problemJan 24 2014In this paper, we introduce an exact algorithm with a time complexity of $O^*(1.325^m)$ for the {\sc weighted mutually exclusive maximum set cover} problem, where $m$ is the number of subsets in the problem. This is an NP-hard motivated and abstracted ... More

Dressing as a Whole: Outfit Compatibility Learning Based on Node-wise Graph Neural NetworksFeb 21 2019With the rapid development of fashion market, the customers' demands of customers for fashion recommendation are rising. In this paper, we aim to investigate a practical problem of fashion recommendation by answering the question "which item should we ... More

PReS: Power Peak Reduction by Real-time Scheduling for Urban Railway TransitFeb 21 2019Railway transportation is one of the most popular options for Urban Massive Transportation Systems (UMTS) because of many attractive features. A robust electric power supply is essential to enable normal operation. However, the power peaks appearing at ... More

Sampling with Walsh TransformsFeb 22 2015Jul 26 2015With the advent of massive data outputs at a regular rate, admittedly, signal processing technology plays an increasingly key role. Nowadays, signals are not merely restricted to physical sources, they have been extended to digital sources as well. Under ... More

Uniform estimates for Stokes equations in domains with small holes and applications in homogenization problemsOct 06 2015Oct 24 2016We consider the Dirichlet problem for the Stokes equations in a domain with a shrinking hole in $\mathbb{R}^d$. An almost complete description concerning the uniform $W^{1,p}$ estimates as the size of the hole goes to zero is shown : for any $d'<p<d$, ... More

Practical Tera-scale Walsh-Hadamard TransformJun 28 2016In the mid-second decade of new millennium, the development of IT has reached unprecedented new heights. As one derivative of Moore's law, the operating system evolves from the initial 16 bits, 32 bits, to the ultimate 64 bits. Most modern computing platforms ... More

Small Generalized Breathers with Exponentially Small Tails for Klein-Gordon EquationsJul 24 2013We consider a class of nonlinear Klein-Gordon equation $u_{tt}=u_{xx}-u+f(u)$ and show that generically there exist small breathers with exponentially small tails.

Compressible Euler equation with damping on Torus in arbitrary dimensionsSep 19 2013Oct 19 2014We study the exponential stability of constant steady state of isentropic compressible Euler equation with damping on $\mathbb T^n$. The local existence of solutions is based on semigroup theory and some commutator estimates. We propose a new method instead ... More

A central limit theorem for stochastic heat equations in random environmentNov 05 2015In this paper, we investigate the asymptotic behaviors of solution to a 1-dimensional stochastic heat equation with random non-linear terms which is generated by a stationary, ergodic random field. We prove the central limit theorem in L^1 sense with ... More

On the asymptotic linearity of reduction numberAug 20 2016Sep 17 2016Let $R$ be a standard graded Noetherian algebra over an infinite field $K$ and $M$ a finitely generated $\mathbb{Z}$-graded $R$-module. Then for any graded ideal $I\subseteq R_+$ of $R$, we show that there exist integers $e_1\geq e_2$ such that $r(I^nM)=\rho_I(M)n+e_1$ ... More

Food Image Recognition by Using Convolutional Neural Networks (CNNs)Dec 03 2016Food image recognition is one of the promising applications of visual object recognition in computer vision. In this study, a small-scale dataset consisting of 5822 images of ten categories and a five-layer CNN was constructed to recognize these images. ... More

A New Proof to the Period Problems of GL(2)Nov 11 2016We use the relations between the base change representations, theta lifts and Whittaker model, to give a new proof to the period problems of $GL(2)$ over a quadratic local field extension $E/F.$ And we classify both local and global $D^\times(F)-$distinguished ... More

Evolutionary system, global attractor, trajectory attractor and applications to the nonautonomous reaction-diffusion systemsFeb 17 2015Jul 19 2015In [Adv. Math., 267(2014), 277-306], Cheskidov and Lu develop a new framework of the evolutionary system that deals directly with the notion of a uniform global attractor due to Haraux, and by which a trajectory attractor is able to be defined for the ... More

Safe and Efficient Intersection Control of Connected and Autonomous Intersection TrafficJan 29 2018In this dissertation, we address a problem of safe and efficient intersection crossing traffic management of autonomous and connected ground traffic. Toward this objective, an algorithm that is called the Discrete-time occupancies trajectory based Intersection ... More

Geometric regularity of powers of two-dimensional squarefree monomial idealsAug 22 2018Aug 29 2018Let $I$ be a two-dimensional squarefree monomial ideal of a polynomial ring $S$. We evaluate the geometric regularity, $a_i$-invariants for $i\geq 1$ of the power $I^n$. It turns out they are all linear functions in $n$ from $n=2$. Moreover, it is proved ... More

A Bernstein Type Theorem For Self-similar ShrinkersDec 09 2009In this note, we prove that smooth self-shrinkers in $\Real^{n+1}$, that are entire graphs, are hyperplanes. Previously Ecker and Huisken showed that smooth self-shrinkers, that are entire graphs and have at most polynomial growth, are hyperplanes. The ... More

Special Lagrangian Tori on a Borcea-Voisin ThreefoldFeb 09 1999We show the existence of special Lagrangian tori on one family of Borcea-Voisin threefolds. We also construct a family of special Lagrangian submanifolds on the total space of the canonical line bundle of projective spaces.

Local curvature bound in Ricci flowJun 20 2009Aug 24 2010Some modification of the old version.In this note we give a proof of a result which is related to Perelman's theorem in Section 10.3 of the paper "The entropy formula for the Ricci flow and its geometric applications".

Optimal $γ$ and $C$ for $ε$-Support Vector Regression with RBF KernelsJun 12 2015The objective of this study is to investigate the efficient determination of $C$ and $\gamma$ for Support Vector Regression with RBF or mahalanobis kernel based on numerical and statistician considerations, which indicates the connection between $C$ and ... More

Modified Einstein-Cartan Gravity and its Implications for CosmologyJun 29 2014Jul 03 2014We propose a modification of Einstein-Cartan gravity equations. The modified cosmology departs from the standard model of cosmology for small Hubble parameter. A characteristic Hubble scale h0, which is intrinsically related to cosmological constant, ... More

Stability Conditions and Mirror Symmetry of K3 Surfaces in Attractor BackgroundsOct 28 2012We study the space of stability conditions on $K3$ surfaces from the perspective of mirror symmetry. It is done in the so called attractor backgrounds (moduli) which can be far from the conventional large complex limits and are selected by the attractor ... More

Introduction to Local and Global Euler Characteristic FormulasDec 19 2011Jan 11 2012This is a note of talks I gave at the number theory seminar at Tsinghua University in Fall 2011. We will introduce the local and global Euler characteristic formulas given by John Tate(1962) for Galois cohomology. We will give a detailed proof based on ... More

The second coefficient of the asymptotic expansion of the Bergman kernel of the Hodge-Dolbeault operatorDec 25 2012We calculate the second coefficient of the asymptotic expansion of the Bergman kernel of the Hodge-Dolbeault operator associated to high powers of a Hermitian line bundle with non-degenerate curvature, using the method of formal power series developed ... More

Yang-Mills Interactions and Gravity in Terms of Clifford AlgebraJul 31 2010A model of Yang-Mills interactions and gravity in terms of the Clifford algebra Cl(0,6) is presented. The gravity and Yang-Mills actions are formulated as different order terms in a generalized action. The feebleness of gravity as well as the smallness ... More

Novel Structure Function for Photon Fragmentation into a $Λ$ Hyperon and Transverse $Λ$ Polarization in Unpolarized Electron-Positron AnnihilationMay 23 1995Nov 16 1995The possibility is examined for the inclusive $\Lambda$ in unpolarized electron-positron annihilation to be transversely polarized. Due to final-state interactions, there exists a novel structure function $\hat F(z,Q^2)$ for the inclusive $\Lambda$ hyperon ... More

8-rank of the class group and isotropy indexDec 04 2013Apr 27 2014Suppose $F=\mathbb{Q}(\sqrt{-p_1\dotsm p_t})$ is an imaginary quadratic number field with distinct primes $p_1,\dots,p_{t}$, where $p_i\equiv 1\pmod{4}$ ($i=1,\dots,t-1$) and $p_t\equiv 3\pmod{4}$. We express the possible values of the 8-rank $r_8$ of ... More

The SL(1,D)-distinction problemMay 13 2018We use the local theta correspondences between the quaternionic Hermitian groups and the quaternionic skew-Hermitian groups to understand the distinction problem for the symmetric pair SL(2,E)/SL(1,D), where E is a quadratic field extension of a nonarchimedean ... More

Convergence of fundamental solutions of linear parabolic equations under Cheeger-Gromov convergenceMay 06 2010In this note we show the convergence of the fundamental solutions of the parabolic equations assuming the Cheeger-Gromov convergence of the underlying manifolds and the uniform $L^1$-bound of the solutions. We also prove a local integral estimate of fundamental ... More

The maximum $p$-Spectral Radius of Hypergraphs with $m$ EdgesMar 23 2018For $r\geq 2$ and $p\geq 1$, the $p$-spectral radius of an $r$-uniform hypergraph $H=(V,E)$ on $n$ vertices is defined to be $$\rho_p(H)=\max_{{\bf x}\in \mathbb{R}^n: \|{\bf x}\|_p=1}r \cdot \!\!\!\! \sum_{\{i_1,i_2,\ldots, i_r\}\in E(H)} x_{i_1}x_{i_2}\cdots ... More

Cone avoiding closed setsFeb 11 2016We prove that for an arbitrary subtree $T$ of $2^{<\omega}$ with each element extendable to a path, a given countable class $\mathcal{M}$ closed under disjoint union, and any set $A$, if none of the members of $\mathcal{M}$ strongly $k$-enumerate $T$ ... More

Uniqueness of Self-similar Shrinkers with Asymptotically Conical EndsOct 03 2011Let $C\subset\mathbb{R}^{n+1}$ be a regular cone with vertex at the origin. In this paper, we show the uniqueness for smooth properly embedded self-shrinking ends in $\mathbb{R}^{n+1}$ that are asymptotic to $C$. As an application, we prove that not every ... More

An explicit isomorphism between Floer homology and quantum homologyNov 21 2000May 21 2004We use Liu-Tian's virtual moduli cycle methods to construct detailedly the explicit isomorphism between Floer homology and quantum homology for any closed symplectic manifold that was first outlined by Piunikhin, Salamon and Schwarz for the case of the ... More

Randomized block proximal damped Newton method for composite self-concordant minimizationJul 01 2016In this paper we consider the composite self-concordant (CSC) minimization problem, which minimizes the sum of a self-concordant function $f$ and a (possibly nonsmooth) proper closed convex function $g$. The CSC minimization is the cornerstone of the ... More

The distinction problem for metaplectic caseMay 20 2019We use the theta lifts between Mp(2) and PD to study the distinction problems for the pair (Mp(2,E), SL(2,F )), where E is a quadratic field extension over a nonarchimedean local field F of characteristic zero and D is a quaternion algebra. With a similar ... More

On the asymptotic linearity of reduction numberAug 20 2016Sep 14 2017Let $R$ be a standard graded Noetherian algebra over an infinite field $K$ and $M$ a finitely generated $\mathbb{Z}$-graded $R$-module. Then for any graded ideal $I\subseteq R_+$ of $R$, we show that there exist integers $e_1\geq e_2$ such that $r(I^nM)=\rho_I(M)n+e_1$ ... More

The braided monoidal structure on the category of Hom-type Doi-Hopf modulesDec 29 2015Let $(H,\a_H)$ be a Hom-Hopf algebra, $(A,\a_A)$ a right $H$-comodule algebra and $(C,\a_C)$ a left $H$-module coalgebra. Then we have the category $_A\mathcal{M}(H)^C$ of Hom-type Doi-Hopf modules. The aim of this paper is to make the category $_A\mathcal{M}(H)^C$ ... More

Discrete Polymatroids satisfying a stronger symmetric exchange propertyDec 15 2014Mar 08 2017In this paper we introduce discrete polymatroids satisfying the one-sided strong exchange property and show that they are sortable (as a consequence their base rings are Koszul) and that they satisfy White's conjecture. Since any pruned lattice path polymatroid ... More

Methods of infinite dimensional Morse theory for geodesics on Finsler manifoldsDec 10 2012Nov 12 2014We prove the shifting theorems of the critical groups of critical points and critical orbits for the energy functionals of Finsler metrics on Hilbert manifolds of $H^1$-curves, and two splitting lemmas for the functionals on Banach manifolds of $C^1$-curves. ... More

Measurement of hadron composition in charged jets from pp collisions with the ALICE experimentJul 31 2014Aug 04 2014We report the first measurement of charged pion, kaon and (anti-)proton production in jets from hadron colliders. The measurement was carried out with the ALICE detector using $2\times10^8$ minimum bias pp collisions at a centre-of-mass energy of $\sqrt{s}=7$ ... More

Linked Ego Networks: Improving Estimate Reliability and Validity with Respondent-driven SamplingMay 09 2012Oct 16 2012Respondent-driven sampling (RDS) is currently widely used for the study of HIV/AIDS-related high risk populations. However, recent studies have shown that traditional RDS methods are likely to generate large variances and may be severely biased since ... More

Corrigendum: The Conley conjecture for Hamiltonian systems on the cotangent bundle and its analogue for Lagrangian systemsSep 03 2009Feb 10 2011In lines 8-11 of \cite[pp. 2977]{Lu} we wrote: "For integer $m\ge 3$, if $M$ is $C^m$-smooth and $C^{m-1}$-smooth $L:\R\times TM\to\R$ satisfies the assumptions (L1)-(L3), then the functional ${\cal L}_\tau$ is $C^2$-smooth, bounded below, satisfies the ... More

The Semantic Information Method for Maximum Mutual Information and Maximum Likelihood of Tests, Estimations, and Mixture ModelsJun 24 2017It is very difficult to solve the Maximum Mutual Information (MMI) or Maximum Likelihood (ML) for all possible Shannon Channels or uncertain rules of choosing hypotheses, so that we have to use iterative methods. According to the Semantic Mutual Information ... More

Evolutionary system, global attractor, trajectory attractor and applications to the nonautonomous reaction-diffusion systemsFeb 17 2015Nov 15 2018In [Adv. Math., 267(2014), 277-306], Cheskidov and Lu develop a new framework of the evolutionary system that deals directly with the notion of a uniform global attractor due to Haraux, and by which a trajectory attractor is able to be defined for the ... More

Strong Unique Continuation Property for Stochastic Parabolic EquationsJan 09 2017Jun 10 2017We establish a strong unique continuation property for stochastic parabolic equations. Our method is based on a suitable stochastic version of Carleman estimate. As far as we know, this is the first result for strong unique continuation property of stochastic ... More

Stochastic Well-posed Systems and Well-posedness of Some Stochastic Partial Differential Equations with Boundary Control and ObservationJan 08 2015Jul 06 2015We generalize the concept "well-posed linear system" to stochastic linear control systems and study some basic properties of such kind systems. Under our generalized definition, we show the well-posedness of the stochastic heat equation and the stochastic ... More

A Novel PMU Fog based Early Anomaly Detection for an Efficient Wide Area PMU NetworkMay 09 2018Based on phasor measurement units (PMUs), a synchronphasor system is widely recognized as a promising smart grid measurement system. It is able to provide high-frequency, high-accuracy phasor measurements sampling for Wide Area Monitoring and Control ... More

Sequential Convex Programming Methods for A Class of Structured Nonlinear ProgrammingOct 10 2012In this paper we study a broad class of structured nonlinear programming (SNLP) problems. In particular, we first establish the first-order optimality conditions for them. Then we propose sequential convex programming (SCP) methods for solving them in ... More

Reducts of the Generalized Random Bipartite GraphJul 20 2011Let \Gamma be the generalized random bipartite graph that has two sides Rl and Rr with edges for every pair of vertices between R1 and Rr but no edges within each side, where all the edges are randomly colored by three colors P1; P2; P3. In this paper, ... More

Unsupervised Learning on Neural Network Outputs: with Application in Zero-shot LearningJun 02 2015May 23 2016The outputs of a trained neural network contain much richer information than just an one-hot classifier. For example, a neural network might give an image of a dog the probability of one in a million of being a cat but it is still much larger than the ... More

Geometry of Two-dimensional Self-shrinkersMay 01 2015We prove a local graphical theorem for two-dimensional self-shrinkers away from the origin. As applications, we study the asymptotic behavior of noncompact self-shrinkers with finite genus. Also, we show uniform boundedness on the second fundamental form ... More

Small Amplitude Periodic Solutions of Klein-Gordon EquationsSep 19 2013Oct 14 2014We consider a class of nonlinear Klein-Gordon equations $u_{tt}=u_{xx}-u+f(u)$ and obtain a family of small amplitude periodic solutions, where the temporal and spatial period have different scales.

Covariate adjustment in randomization-based causal inference for 2K factorial designsJun 17 2016Jul 12 2016We develop finite-population asymptotic theory for covariate adjustment in randomization-based causal inference for 2K factorial designs. In particular, we confirm that both the unadjusted and covariate-adjusted estimators of the factorial effects are ... More

On Randomization-based and Regression-based Inferences for 2^K Factorial DesignsFeb 12 2016We extend the randomization-based causal inference framework in Dasgupta et al. (2015) for general 2^K factorial designs, and demonstrate the equivalence between regression-based and randomization-based inferences. Consequently, we justify the use of ... More

Discrete Polymatroids satisfying a stronger symmetric exchange propertyDec 15 2014Sep 22 2015In this paper we introduce discrete polymatroids satisfying the one-sided strong exchange property and show that they are sortable (as a consequence their base rings are Koszul) and that they satisfy White's conjecture. Since any pruned lattice path polymatroid ... More

On the Erasure Robustness Property of Random MatricesFeb 03 2017The study of the restricted isometry property (RIP) for corrupted random matrices is particularly important in the field of compressed sensing (CS) with corruptions. If a matrix still satisfy RIP after a certain portion of rows are erased, then we say ... More

Singularity categories of representations of quivers over local ringsFeb 05 2017Feb 20 2018Let $\Lambda$ be a finite-dimensional algebra with finite global dimension, $R_k=K[X]/(X^k)$ be the $\mathbb{Z}$-graded local ring with $k\geq1$, and $\Lambda_k=\Lambda\otimes_K R_k$. We consider the singularity category $D_{sg}(\mod^{\mathbb{Z}}(\Lambda_k))$ ... More

Carleman Estimate for Stochastic Parabolic Equations and Inverse Stochastic Parabolic ProblemsJul 28 2011May 03 2013In this paper, we establish a global Carleman estimate for stochastic parabolic equations. Based on this estimate, we solve two inverse problems for stochastic parabolic equations. One is concerned with a determination problem of the history of a stochastic ... More

Sharpening randomization-based causal inference for $2^2$ factorial designs with binary outcomesNov 13 2017In medical research, a scenario often entertained is randomized controlled $2^2$ factorial design with a binary outcome. By utilizing the concept of potential outcomes, Dasgupta et al. (2015) proposed a randomization-based causal inference framework, ... More

The Level Weighted Structural Similarity Loss: A Step Away from the MSEApr 30 2019The Mean Square Error (MSE) has shown its strength when applied in deep generative models such as Auto-Encoders to model reconstruction loss. However, in image domain especially, the limitation of MSE is obvious: it assumes pixel independence and ignores ... More

Improving Precision of Type Analysis Using Non-Discriminative UnionDec 12 2006This paper presents a new type analysis for logic programs. The analysis is performed with a priori type definitions; and type expressions are formed from a fixed alphabet of type constructors. Non-discriminative union is used to join type information ... More

Sequence Training and Adaptation of Highway Deep Neural NetworksJul 07 2016Mar 22 2017Highway deep neural network (HDNN) is a type of depth-gated feedforward neural network, which has shown to be easier to train with more hidden layers and also generalise better compared to conventional plain deep neural networks (DNNs). Previously, we ... More

Singularity categories of representations of algebras over local ringsFeb 05 2017Mar 27 2019Let $\Lambda$ be a finite-dimensional algebra with finite global dimension, $R_k=K[X]/(X^k)$ be the $\mathcal{Z}$-graded local ring with $k\geq1$, and $\Lambda_k=\Lambda\otimes_K R_k$. We consider the singularity category $\mathcal{D}_{sg}(\mathrm{mod}^\mathcal{Z}(\Lambda_k))$ ... More

Exotic Meson Decay to $ωπ^{0}π^{-}$May 17 2004A partial-wave analysis of the mesons from the reaction $\pi^{-}% p\to\pi^{+}\pi^{-}\pi^{-}\pi^{0}\pi^{0}p$ has been performed. The data show $b_{1}\pi$ decay of the spin-exotic states $\pi_{1}(1600)$ and \ $\pi_{1}(2000)$. Three isovector $2^{-+}$ states ... More

Observational Effects of Strange StarsJul 06 1998In this talk, after briefly reviewing some historical remarks concerning strange stars, the achievements in physics and dynamical behavior of strange stars are discussed. Especially, various observational effects in distinguishing strange stars from neutron ... More

New Approaches to Identify Gene-by-Gene Interactions in Genome Wide Association StudiesMay 07 2016Genetic variants identified to date by genome-wide association studies only explain a small fraction of total heritability. Gene-by-gene interaction is one important potential source of unexplained heritability. In the first part of this dissertation, ... More

GPS Information and Rate Tolerance - Clarifying Relationship between Rate Distortion and Complexity DistortionApr 17 2012I proposed rate tolerance and discussed its relation to rate distortion in my book "A Generalized Information Theory" published in 1993. Recently, I examined the structure function and the complexity distortion based on Kolmogorov's complexity theory. ... More

Practical Tera-scale Walsh-Hadamard TransformJun 28 2016Dec 24 2016In the mid-second decade of new millennium, the development of IT has reached unprecedented new heights. As one derivative of Moore's law, the operating system evolves from the initial 16 bits, 32 bits, to the ultimate 64 bits. Most modern computing platforms ... More

Effects of Data Resolution and Human Behavior on Large Scale Evacuation SimulationsDec 30 2014Traffic Analysis Zones (TAZ) based macroscopic simulation studies are mostly applied in evacuation planning and operation areas. The large size in TAZ and aggregated information of macroscopic simulation underestimate the real evacuation performance. ... More

The case for a natural composite boson and negative vacuum energyJan 03 2019Jan 22 2019We revisit a dynamical symmetry breaking model with 4-fermion interactions. A prescription is proposed to remove the momentum routing ambiguity associated with fermion-antifermion condensations. The dynamically generated composite boson mass and vacuum ... More

The Prasad conjectures for $\mathrm{GSp_4}$ and $\mathrm{PGSp_4}$Feb 28 2018May 08 2019In this paper, we use the theta correspondence between $\mathrm{GSp_4}$ and $\mathrm{GO(V)}$ to discuss the $\mathrm{GSp_4}$-distinction problems over a quadratic field extension $E/F.$ With a similar strategy, we study the period for the pair $(\mathrm{GSp_4(E)},\mathrm{GSp_{1,1}(F)}),$ ... More

Complex space-time and the classification of elementary particlesSep 07 2001It is shown that the Dirac theory implies complex space-time and complex space-time can lead to the Dirac equation. It is suggested that fermions are grouped into doublets, those doublets are then divided into color singlets (leptons) and color triplets ... More

On the possibility of a complex 4-dimensional space-time manifoldApr 15 1998The possibility of a complex 4-dimensional space-time manifold is suggested. This may imply the existence of a matter wave.

Generalized low solution of $\mathsf{RT}_k^1$ problemFeb 19 2016Feb 28 2016We study the "coding power" of an arbitrary $\mathsf{RT}_k^1$-instance. We prove that every $\mathsf{RT}_k^1$-instance admit non trivial generalized low solution. This is somewhat related to a problem proposed by Patey. We also answer a question proposed ... More

Reflected BSDE with stochastic Lipschitz coefficientDec 11 2009Dec 15 2009In this paper, we deal with a class of one-dimensional reflected backward stochastic differential equations with stochastic Lipschitz coefficient. We derive the existence and uniqueness of the solutions for those equations via Snell envelope and the fixed ... More

Parameterized splitting theorems and bifurcations for potential operatorsDec 10 2017We show that parameterized versions of splitting theorems in Morse theory can be effectively used to generalize some famous bifurcation theorems for potential operators. In particular, such generalizations based on the author's recent splitting theorems ... More

The splitting lemmas for nonsmooth functionals on Hilbert spaces INov 06 2012Jun 11 2014The Gromoll-Meyer's generalized Morse lemma (so called splitting lemma) near degenerate critical points on Hilbert spaces, which is one of key results in infinite dimensional Morse theory, is usually stated for at least $C^2$-smooth functionals. It obstructs ... More

Harmonic map heat flow with rough boundary dataOct 16 2010Let $B_1$ be the unit open disk in $\Real^2$ and $M$ be a closed Riemannian manifold. In this note, we first prove the uniqueness for weak solutions of the harmonic map heat flow in $H^1([0,T]\times B_1,M)$ whose energy is non-increasing in time, given ... More

An extension of Biran's Lagrangian barrier theoremNov 16 2001May 21 2004We use the Gromov-Witten invariants and a nonsqueezing theorem by the author to affirm a conjecture by P.Biran on the Lagrangian barriers.

Gromov-Witten invariants and rigidity of Hamiltonian loops with compact support on noncompact symplectic manifoldsMay 12 1999Jul 20 2003In this paper the Gromov-Witten invariants on a class of noncompact symplectic manifolds are defined by combining Ruan-Tian's method with that of McDuff-Salamon. The main point of the arguments is to introduce a method dealing with the transversality ... More

Symplectic capacities of toric manifolds and related resultsDec 29 2003May 03 2006In this paper we give concrete estimations for the pseudo symplectic capacities of toric manifolds in combinatorial data. Some examples are given to show that our estimates can compute their pseudo symplectic capacities. As applications we also estimate ... More