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Fourier Domain Rotational Anisotropy Second Harmonic GenerationOct 04 2018We describe a novel scheme of detecting rotational anisotropy second harmonic generation (RA-SHG) signals using a lock-in amplifier referenced to a fast scanning RA-SHG apparatus. The method directly measures the $n^{th}$ harmonics of the scanning frequency ... More

Fast Reflective Optic-Based Rotational Anisotropy Nonlinear Harmonic Generation SpectrometerOct 31 2018We present a novel Rotational Anisotropy Nonlinear Harmonic Generation (RA-NHG) apparatus based primarily upon reflective optics. The data acquisition scheme used here allows for fast accumulation of RA-NHG traces, mitigating low frequency noise from ... More

Resonance-enhanced optical nonlinearity in the Weyl semimetal TaAsApr 19 2018Apr 20 2018While all media can exhibit first-order conductivity describing current linearly proportional to electric field, $E$, the second-order conductivity, $\sigma^{(2)}$ , relating current to $E^2$, is nonzero only when inversion symmetry is broken. Second ... More

Quantized Photocurrents in the Chiral Multifold Fermion System RhSiFeb 08 2019The rapid pace of discovery of new classes of Weyl semimetals is driving a search for properties that derive from their unique bandstructure topology. One of the most striking of the predicted properties is the quantized circular photogalvanic effect ... 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

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

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

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

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

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 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

An invariance principle for stochastic heat equations with periodic coefficientsMay 13 2015In this paper we investigate the asymptotic behaviors of solution $u(t, \cdot)$ of a stochastic heat equation with a periodic nonlinear term. Such equation appears related to the dynamical sine-Gordon model. We consider the reversible case and extend ... More

On finite-population Bayesian inferences for $2^K$ factorial designs with binary outcomesMar 12 2018Jan 24 2019Inspired by the pioneering work of Rubin (1978), we employ the potential outcomes framework to develop a finite-population Bayesian causal inference framework for randomized controlled $2^K$ factorial designs with binary outcomes, which are common in ... More

A Proof of Vivo-Pato-Oshanin's Conjecture on the Fluctuation of von Neumann EntropyJun 26 2017Jul 11 2017It was recently conjectured by Vivo, Pato, and Oshanin [Phys. Rev. E 93, 052106 (2016)] that for a quantum system of Hilbert dimension $mn$ in a pure state, the variance of the von Neumann entropy of a subsystem of dimension $m\leq n$ is given by \begin{equation*} ... More

Diagnostics for Regression Models with Discrete Outcomes Using Surrogate Empirical Residual Distribution FunctionsJan 14 2019Feb 20 2019Making informed decisions about model adequacy has been an outstanding issue for regression models with discrete outcomes. Standard residuals for such outcomes show a large discrepancy from the hypothesized pattern even under the true model and are often ... More

Morse theory methods for a class of quasi-linear elliptic systems of higher orderSep 07 2017Dec 04 2017We develop the local Morse theory for a class of non-twice continuously differentiable functionals on Hilbert spaces, including a new generalization of the Gromoll-Meyer's splitting theorem and a weaker Marino-Prodi perturbation type result. They are ... More

"Relative-Continuity" for Non-Lipschitz Non-Smooth Convex Optimization using Stochastic (or Deterministic) Mirror DescentOct 12 2017Aug 14 2018The usual approach to developing and analyzing first-order methods for non-smooth (stochastic or deterministic) convex optimization assumes that the objective function is uniformly Lipschitz continuous with parameter $M_f$. However, in many settings the ... More

The Complexity of All $(g,f)$-Factor ProblemFeb 20 2017May 31 2018Let $G$ be a graph with vertex set $V$ and let $g, f : V\rightarrow \mathbb{Z}^+$ be two functions such that $g\le f$. We say that $G$ has all $(g, f )$-factors if $G$ has an $h$-factor for every $h: V\rightarrow \mathbb{Z}^+$ such that $g(v)\le h(v)\le ... More

Synthesis of Self-assembled Iron Silicon Oxide Nanowires onto Single-crystalline Si(100)Jul 30 2013Iron silicon oxide nanowire has been synthesized by putting single crystalline Si(100) wafer into ammonium iron sulfate, hydrogen peroxide, and triethylamine solution heated to from 70 to 100 degree in the air. The prepared iron silicon oxide nanowires ... More

On the degenerated Arnold-Givental conjectureJun 01 2008Aug 06 2018We present another view dealing with the Arnold-Givental conjecture on a real symplectic manifold $(M, \omega, \tau)$ with nonempty and compact real part $L={\rm Fix}(\tau)$. For given $\Lambda\in (0, +\infty]$ and $m\in\N\cup\{0\}$ we show the equivalence ... More

Symplectic fixed points and Lagrangian intersections on weighted projective spacesJan 12 2006In this note we observe that Arnold conjecture for the Hamiltonian maps still holds on weighted projective spaces $\CP^n({\bf q})$, and that Arnold conjecture for the Lagrange intersections for $(\CP^n({\bf q}), \RP^n({\bf q}))$ is also true if each weight ... More

Periodic motion of a charge on a manifold in the magnetic fieldsMay 24 1999May 25 2000In this paper we prove the existence of a periodic motion of a charge on a large class of manifolds under the action of the magnetic fields. Our methods also give a class of closed manifolds whose cotangent bundle contain no the closed exact Lagrangian ... More

Attacking Hardware AES with DFAFeb 22 2019We present the first practical attack on a hardware AES accelerator with 256 bit embedded keys using DFA. We identify the challenges of adapting well-known theoretical AES DFA models to hardware under attack from voltage fault injection and present solutions ... More

Injecting Software Vulnerabilities with Voltage GlitchingFeb 14 2019We show how voltage glitching can cause timing violations in CMOS behavior. Then we attack a real, security hardened, consumer device to gain code execution and dump the secure boot ROM.

Heuristic Policies for Stochastic Knapsack Problem with Time-Varying Random DemandJul 18 2018In this paper, we consider the classic stochastic (dynamic) knapsack problem, a fundamental mathematical model in revenue management, with general time-varying random demand. Our main goal is to study the optimal policies, which can be obtained by solving ... More

No-reference Image Denoising Quality AssessmentOct 13 2018A wide variety of image denoising methods are available now. However, the performance of a denoising algorithm often depends on individual input noisy images as well as its parameter setting. In this paper, we present a no-reference image denoising quality ... More

PRADA Applicability in Industrial PracticeJul 21 2017The proliferation of Android devices brings the fragmentation problem. Selecting and prioritizing major device models are critical for mobile app developers to select testbeds and optimize various issues such as quality-assurance, release planning, revenues, ... More

Semantic Information Measure with Two Types of Probability for Falsification and ConfirmationSep 26 2016Logical Probability (LP) is strictly distinguished from Statistical Probability (SP). To measure semantic information or confirm hypotheses, we need to use sampling distribution (conditional SP function) to test or confirm fuzzy truth function (conditional ... More

Two-Monopole Systems and the Formation of Non-Abelian CloudsJun 29 1998Nov 20 1998We study the energy density of two distinct fundamental monopoles in SU(3) and Sp(4) theories with an arbitrary mass ratio. Several special limits of the general result are checked and verified. Based on the analytic expression of energy density the coefficient ... More

Iterative Reweighted Minimization Methods for $l_p$ Regularized Unconstrained Nonlinear ProgrammingSep 29 2012In this paper we study general $l_p$ regularized unconstrained minimization problems. In particular, we derive lower bounds for nonzero entries of first- and second-order stationary points, and hence also of local minimizers of the $l_p$ minimization ... More

Smooth Optimization Approach for Sparse Covariance SelectionApr 04 2009In this paper we first study a smooth optimization approach for solving a class of nonsmooth strictly concave maximization problems whose objective functions admit smooth convex minimization reformulations. In particular, we apply Nesterov's smooth optimization ... More

On the DDVV Conjecture and the Comass in Calibrated Geometry (II)Aug 21 2007In this paper, we proved P(n,3), which is an important part of the DDVV conjecture. The general case will be treated in the next version of the paper.

On the Rigidity of Horizontal SlicesMay 26 2005In this paper, we proved a rigidity theorem of the Hodge metric for concave horizontal slices and a local rigidity theorem for the monodromy representation.

On the Curvature Tensor of the Hodge Metric of Moduli Space of Polarized Calabi-Yau ThreefoldsMay 26 2005Jun 02 2005In this paper, we give an expression and some estimates of the curvature tensor of the Hodge metric over the moduli space of a polarized Calabi-Yau threefold. The symmetricity of the Yukawa coupling is also studied. In the last section of this paper, ... More

A note on the holomorphic invariants of Tian-ZhuMay 26 2005In this paper, we compute the Tian-Zhu invariant on hypersurfaces of complex projective spaces.

Gradient estimates of the Yukawa couplingMay 26 2005The paper is related to the classification of special manifolds and projective special manifolds. One of the result of this paper is that, if the Weil-Petersson metric on a projective special manifold is complete, then the Hodge metrc and the Weil-Petersson ... More

A Note on the Analytic Families of Compact Submanifolds of Complex ManifoldsMay 26 2005In this paper, we prove a result related to the deformation of complex submanifolds, modifying a result of Kodaira (Ann. Math, 75(1), 146-162, 1962).

GRBS: Standard Model & BeyondJan 03 2001There have been great and rapid progresses in the field of $\gamma$-ray bursts since BeppoSAX and other telescopes discovered their afterglows in 1997. In this talk, the main observational facts of $\gamma$-ray bursts and their afterglows, and the standard ... More

What do $γ$-ray bursts look like?Feb 08 2000There have been great and rapid progresses in the field of $\gamma$-ray bursts (denoted as GRBs) since BeppoSAX and other telescopes discovered their afterglows in 1997. Here, we will first give a brief review on the observational facts of GRBs and direct ... More

Toward Computation and Memory Efficient Neural Network Acoustic Models with Binary Weights and ActivationsJun 28 2017Jul 04 2017Neural network acoustic models have significantly advanced state of the art speech recognition over the past few years. However, they are usually computationally expensive due to the large number of matrix-vector multiplications and nonlinearity operations. ... More

Parametrizing Program Analysis by Lifting to Cardinal Power DomainsMay 25 2010A parametric analysis is an analysis whose input and output are parametrized with a number of parameters which can be instantiated to abstract properties after analysis is completed. This paper proposes to use Cousot and Cousot's Cardinal power domain ... More

Deriving Abstract Semantics for Forward Analysis of Normal Logic ProgramsNov 06 1998The problem of forward abstract interpretation of {\em normal} logic programs has not been formally addressed in the literature although negation as failure is dealt with through the built-in predicate ! in the way it is implemented in Prolog. This paper ... More

On the Lower Order Terms of the Asymptotic Expansion of ZelditchNov 21 1998Jan 31 1999In this paper, we computed the first three coefficients of the asymptotic expansion of Zelditch. We also proved that in general, the $k$-th coefficient is a polynomial of the curvature and its derivative of weight $k$.

Semantic Channel and Shannon's Channel Mutually Match for Multi-Label ClassificationMay 02 2018A group of transition probability functions form a Shannon's channel whereas a group of truth functions form a semantic channel. Label learning is to let semantic channels match Shannon's channels and label selection is to let Shannon's channels match ... More

Knowware: the third star after Hardware and SoftwareNov 27 2007This book proposes to separate knowledge from software and to make it a commodity that is called knowware. The architecture, representation and function of Knowware are discussed. The principles of knowware engineering and its three life cycle models: ... More

SCGDet: Malware Detection using Semantic Features Based on Reachability RelationJun 10 2019Recently, with the booming development of software industry, more and more malware variants are designed to perform malicious behaviors. The evolution of malware makes it difficult to detect using traditional signature-based methods. Moreover, malware ... More

Form factor description of the non-collinear Compton scattering tensorJul 10 1997Aug 08 1997We present a parameterization of the non-collinear (virtual) Compton scattering tensor in terms of form factors, in which the Lorentz tensor associated with each form factor possesses manifest electromagnetic gauge invariance. The main finding is that ... More

Symmetry analysis of the hadronic tensor for the semi-inclusive pseudoscalar meson leptoproduction from an unpolarized nucleon targetJun 16 1995Sep 09 1995By examining the symmetry constraints on the semi-inclusive pseudoscalar particle production in unpolarized inelastic lepton-hadron scattering, we present a complete, exact Lorentz decomposition for the corresponding hadronic tensor. As a result, we find ... More

Electroweak and Majorana Sector Higgs Bosons and Pseudo-Nambu-Goldstone BosonsMar 14 2016Jun 06 2016We propose a Clifford algebra based model, which treats both gravity and Yang-Mills interactions as gauge fields. There are two sectors of boson fields as electroweak and Majorana bosons. The electroweak boson sector induces fermion masses via spontaneous ... More

The splitting lemmas for nonsmooth functionals on Hilbert spacesFeb 10 2011Nov 07 2012The usual Gromoll-Meyer's generalized Morse lemma near degenerate critical points on Hilbert spaces, so called splitting lemma, is stated for at least $C^2$-smooth functionals. In this paper we establish a splitting theorem and a shifting theorem for ... More

Observability Estimate and State Observation Problems for Stochastic Hyperbolic EquationsMay 03 2013Jun 09 2013In this paper, we derive a boundary and an internal observability inequality for stochastic hyperbolic equations with nonsmooth lower order terms. The required inequalities are obtained by global Carleman estimate for stochastic hyperbolic equations. ... More

Exact Controllability for Stochastic Schrodinger EquationsApr 26 2013This paper is addressed to studying the exact controllability for stochastic Schr\"{o}dinger equations by two controls. One is a boundary control in the drift term and the other is an internal control in the diffusion term. By means of the standard duality ... More

Farrell cohomology of low genus pure mapping class groups with puncturesJul 22 2002In this paper, we calculate the p-torsion of the Farrell cohomology for low genus pure mapping class groups with punctures, where p is an odd prime. Here, `low genus' means g=1,2,3; and `pure mapping class groups with punctures' means the mapping class ... More

Magnon band topology in spin-orbital coupled magnets: classification and application to $α$-RuCl$_3$Jul 13 2018Jul 26 2018In spite of flourishing studies on the topology of spin waves, a generic framework to classify and compute magnon band topology in non-collinear magnets is still missing. In this work we provide such a theory framework, by mapping an arbitrary linear ... 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

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

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

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

Food Image Recognition by Using Convolutional Neural Networks (CNNs)Dec 03 2016Feb 25 2019Food 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

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

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

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

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

Illustrating Color Evolution and Color Blindness by the Decoding Model of Color VisionDec 12 2010A symmetrical model of color vision, the decoding model as a new version of zone model, was introduced. The model adopts new continuous-valued logic and works in a way very similar to the way a 3-8 decoder in a numerical circuit works. By the decoding ... 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

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".

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

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

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

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

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

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

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.

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

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

On the ground state of quantum layersAug 11 2007We provide some new results of the ground state of quantum layers.

On the Hodge Metric of the Universal Deformation Space of Calabi-Yau ThreefoldsMay 26 2005In this paper, we represent the Hodge metric in terms of the Weil-Petersson metric and its Ricci curvature on the moduli spaces of polarized Calabi-Yau threefolds.

Normal scalar curvature conjecture and its applicationsMar 04 2008May 09 2011In this paper, we proved the Normal Scalar Curvature Conjecture and the Bottcher-Wenzel Conjecture. We also established some new pinching theorems for minimal submanifolds in spheres.

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 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

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

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

Homogenization of Stokes equations in perforated domains: a unified approachAug 22 2019We consider the homogenization of the Stokes equations in a domain perorated with a large number of small holes which are periodically distributed. In [1,2], Allaire gave a systematic study on this problem. In this paper, we introduce a unified proof ... 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

Morse theory methods for a class of quasi-linear elliptic systems of higher orderSep 07 2017Jun 05 2019We develop the local Morse theory for a class of non-twice continuously differentiable functionals on Hilbert spaces, including a new generalization of the Gromoll-Meyer's splitting theorem and a weaker Marino-Prodi perturbation type result. They are ... 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