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A complete characterization on the robust isolated calmness of the nuclear norm regularized convex optimization problemsFeb 20 2017In this paper, we provide a complete characterization on the robust isolated calmness of the Karush-Kuhn-Tucker (KKT) solution mapping for convex constrained optimization problems regularized by the nuclear norm function. This study is motivated by the ... More

On the efficient computation of a generalized Jacobian of the projector over the Birkhoff polytopeFeb 20 2017Sep 01 2018We derive an explicit formula, as well as an efficient procedure, for constructing a generalized Jacobian for the projector of a given square matrix onto the Birkhoff polytope, i.e., the set of doubly stochastic matrices. To guarantee the high efficiency ... More

A highly efficient semismooth Newton augmented Lagrangian method for solving Lasso problemsJul 19 2016May 03 2017We develop a fast and robust algorithm for solving large scale convex composite optimization models with an emphasis on the $\ell_1$-regularized least squares regression (Lasso) problems. Despite the fact that there exist a large number of solvers in ... More

A block symmetric Gauss-Seidel decomposition theorem for convex composite quadratic programming and its applicationsMar 20 2017May 23 2017For a symmetric positive semidefinite linear system of equations $\mathcal{Q} {\bf x} = {\bf b}$, where ${\bf x} = (x_1,\ldots,x_s)$ is partitioned into $s$ blocks, with $s \geq 2$, we show that each cycle of the classical block symmetric Gauss-Seidel ... More

A Convergent 3-Block Semi-Proximal Alternating Direction Method of Multipliers for Conic Programming with $4$-Type of ConstraintsApr 22 2014Dec 01 2014The objective of this paper is to design an efficient and convergent alternating direction method of multipliers (ADMM) for finding a solution of medium accuracy to conic programming problems whose constraints consist of linear equalities, linear inequalities, ... More

QSDPNAL: A two-phase augmented Lagrangian method for convex quadratic semidefinite programmingDec 30 2015Dec 30 2016In this paper, we present a two-phase augmented Lagrangian method, called QSDPNAL, for solving convex quadratic semidefinite programming (QSDP) problems with constraints consisting of a large number of linear equality, inequality constraints, a simple ... More

Characterization of the Robust Isolated Calmness for a Class of Conic Programming ProblemsJan 27 2016Oct 01 2016This paper is devoted to studying the robust isolated calmness of the Karush-Kuhn-Tucker (KKT) solution mapping for a large class of interesting conic programming problems (including most commonly known ones arising from applications) at a locally optimal ... More

A multi-stage convex relaxation approach to noisy structured low-rank matrix recoveryMar 11 2017This paper concerns with a noisy structured low-rank matrix recovery problem which can be modeled as a structured rank minimization problem. We reformulate this problem as a mathematical program with a generalized complementarity constraint (MPGCC), and ... More

A Rank-Corrected Procedure for Matrix Completion with Fixed Basis CoefficientsOct 13 2012Jun 22 2015For the problems of low-rank matrix completion, the efficiency of the widely-used nuclear norm technique may be challenged under many circumstances, especially when certain basis coefficients are fixed, for example, the low-rank correlation matrix completion ... More

A highly efficient semismooth Newton augmented Lagrangian method for solving Lasso problemsJul 19 2016Oct 07 2016We develop a fast and robust algorithm for solving large scale convex composite optimization models with an emphasis on the $\ell_1$-regularized least squares regression (Lasso) problems. Despite the fact that there exist a large number of solvers in ... More

An Efficient Semismooth Newton Based Algorithm for Convex ClusteringFeb 20 2018Clustering may be the most fundamental problem in unsupervised learning which is still active in machine learning research because its importance in many applications. Popular methods like K-means, may suffer from instability as they are prone to get ... More

A Convergent $3$-Block Semi-Proximal ADMM for Convex Minimization Problems with One Strongly Convex BlockOct 29 2014In this paper, we present a semi-proximal alternating direction method of multipliers (ADMM) for solving $3$-block separable convex minimization problems with the second block in the objective being a strongly convex function and one coupled linear equation ... More

On the R-superlinear convergence of the KKT residues generated by the augmented Lagrangian method for convex composite conic programmingJun 27 2017Due to the possible lack of primal-dual-type error bounds, the superlinear convergence for the Karush-Kuhn-Tucker (KKT) residues of the sequence generated by augmented Lagrangian method (ALM) for solving convex composite conic programming (CCCP) has long ... More

A Majorized ADMM with Indefinite Proximal Terms for Linearly Constrained Convex Composite OptimizationDec 05 2014Jun 23 2015This paper presents a majorized alternating direction method of multipliers (ADMM) with indefinite proximal terms for solving linearly constrained $2$-block convex composite optimization problems with each block in the objective being the sum of a non-smooth ... More

On the Asymptotic Superlinear Convergence of the Augmented Lagrangian Method for Semidefinite Programming with Multiple SolutionsOct 04 2016Solving large scale convex semidefinite programming (SDP) problems has long been a challenging task numerically. Fortunately, several powerful solvers including SDPNAL, SDPNAL+ and QSDPNAL have recently been developed to solve linear and convex quadratic ... More

SDPNAL$+$: A Majorized Semismooth Newton-CG Augmented Lagrangian Method for Semidefinite Programming with Nonnegative ConstraintsJun 04 2014In this paper, we present a majorized semismooth Newton-CG augmented Lagrangian method, called SDPNAL$+$, for semidefinite programming (SDP) with partial or full nonnegative constraints on the matrix variable. SDPNAL$+$ is a much enhanced version of SDPNAL ... More

A Schur Complement Based Semi-Proximal ADMM for Convex Quadratic Conic Programming and ExtensionsSep 09 2014This paper is devoted to the design of an efficient and convergent {semi-proximal} alternating direction method of multipliers (ADMM) for finding a solution of low to medium accuracy to convex quadratic conic programming and related problems. For this ... More

An Efficient Inexact ABCD Method for Least Squares Semidefinite ProgrammingMay 16 2015May 25 2015We consider least squares semidefinite programming (LSSDP) where the primal matrix variable must satisfy given linear equality and inequality constraints, and must also lie in the intersection of the cone of symmetric positive semidefinite matrices and ... More

Best Nonnegative Rank-One Approximations of TensorsOct 31 2018In this paper, we study the polynomial optimization problem of multi-forms over the intersection of the multi-spheres and the nonnegative orthants. This class of problems is NP-hard in general, and includes the problem of finding the best nonnegative ... More

An asymptotically superlinearly convergent semismooth Newton augmented Lagrangian method for Linear ProgrammingMar 22 2019Powerful interior-point methods (IPM) based commercial solvers such as Gurobi and Mosek have been hugely successful in solving large-scale linear programming (LP) problems. The high efficiency of these solvers depends critically on the sparsity of the ... More

QSDPNAL: A two-phase proximal augmented Lagrangian method for convex quadratic semidefinite programmingDec 30 2015In this paper, we present a two-phase proximal augmented Lagrangian method, called QSDPNAL, for solving convex quadratic semidefinite programming (QSDP) problems with constraints consisting of a large number of linear equality, inequality constraints, ... More

Convex Clustering: Model, Theoretical Guarantee and Efficient AlgorithmOct 04 2018Clustering is a fundamental problem in unsupervised learning. Popular methods like K-means, may suffer from poor performance as they are prone to get stuck in its local minima. Recently, the sum-of-norms (SON) model (also known as the clustering path) ... More

On efficiently solving the subproblems of a level-set method for fused lasso problemsJun 27 2017In applying the level-set method developed in [Van den Berg and Friedlander, SIAM J. on Scientific Computing, 31 (2008), pp.~890--912 and SIAM J. on Optimization, 21 (2011), pp.~1201--1229] to solve the fused lasso problems, one needs to solve a sequence ... More

A Note on the Convergence of ADMM for Linearly Constrained Convex Optimization ProblemsJul 08 2015Feb 22 2016This note serves two purposes. Firstly, we construct a counterexample to show that the statement on the convergence of the alternating direction method of multipliers (ADMM) for solving linearly constrained convex optimization problems in a highly influential ... More

An Efficient Inexact Symmetric Gauss-Seidel Based Majorized ADMM for High-Dimensional Convex Composite Conic ProgrammingJun 02 2015Mar 17 2016In this paper, we propose an inexact multi-block ADMM-type first-order method for solving a class of high-dimensional convex composite conic optimization problems to moderate accuracy. The design of this method combines an inexact 2-block majorized semi-proximal ... More

Computing the Best Approximation Over the Intersection of a Polyhedral Set and the Doubly Nonnegative ConeMar 17 2018This paper introduces an efficient algorithm for computing the best approximation of a given matrix onto the intersection of linear equalities, inequalities and the doubly nonnegative cone (the cone of all positive semidefinite matrices whose elements ... More

Linear Rate Convergence of the Alternating Direction Method of Multipliers for Convex Composite Quadratic and Semi-Definite ProgrammingAug 10 2015In this paper, we aim to provide a comprehensive analysis on the linear rate convergence of the alternating direction method of multipliers (ADMM) for solving linearly constrained convex composite optimization problems. Under a certain error bound condition, ... More

Spectral Operators of MatricesJan 10 2014The class of matrix optimization problems (MOPs) has been recognized in recent years to be a powerful tool by researchers far beyond the optimization community to model many important applications involving structured low rank matrices. This trend can ... More

Spectral operators of matrices: semismoothness and characterizations of the generalized JacobianOct 22 2018Spectral operators of matrices proposed recently in [C. Ding, D.F. Sun, J. Sun, and K.C. Toh, Math. Program. {\bf 168}, 509--531 (2018)] are a class of matrix valued functions, which map matrices to matrices by applying a vector-to-vector function to ... More

A semi-proximal augmented Lagrangian based decomposition method for primal block angular convex composite quadratic conic programming problemsDec 12 2018We propose a semi-proximal augmented Lagrangian based decomposition method for convex composite quadratic conic programming problems with primal block angular structures. Using our algorithmic framework, we are able to naturally derive several well known ... More

An Efficient Linearly Convergent Regularized Proximal Point Algorithm for Fused Multiple Graphical Lasso ProblemsFeb 19 2019Nowadays, analysing data from different classes or over a temporal grid has attracted a great deal of interest. As a result, various multiple graphical models for learning a collection of graphical models simultaneously have been derived by introducing ... More

An efficient Hessian based algorithm for solving large-scale sparse group Lasso problemsDec 16 2017The sparse group Lasso is a widely used statistical model which encourages the sparsity both on a group and within the group level. In this paper, we develop an efficient augmented Lagrangian method for large-scale non-overlapping sparse group Lasso problems ... More

A Fast Globally Linearly Convergent Algorithm for the Computation of Wasserstein BarycentersSep 12 2018In this paper, we consider the problem of computing a Wasserstein barycenter for a set of discrete probability distributions with finite supports, which finds many applications in different areas such as statistics, machine learning and image processing. ... More

Efficient sparse semismooth Newton methods for the clustered lasso problemAug 22 2018May 01 2019We focus on solving the clustered lasso problem, which is a least squares problem with the $\ell_1$-type penalties imposed on both the coefficients and their pairwise differences to learn the group structure of the regression parameters. Here we first ... More

On the Closed-form Proximal Mapping and Efficient Algorithms for Exclusive Lasso ModelsFeb 01 2019The exclusive lasso regularization based on the $\ell_{1,2}$ norm has become popular recently due to its superior performance over the group lasso regularization. Comparing to the group lasso regularization which enforces the competition on variables ... More

A sparse semismooth Newton based proximal majorization-minimization algorithm for nonconvex square-root-loss regression problemsMar 27 2019In this paper, we consider high-dimensional nonconvex square-root-loss regression problems and introduce a proximal majorization-minimization (PMM) algorithm for these problems. Our key idea for making the proposed PMM to be efficient is to develop a ... More

SDPNAL+: A Matlab software for semidefinite programming with bound constraints (version 1.0)Oct 29 2017SDPNALP is a {\sc Matlab} software package that implements an augmented Lagrangian based method to solve large scale semidefinite programming problems with bound constraints. The implementation was initially based on a majorized semismooth Newton-CG augmented ... More

Solving the OSCAR and SLOPE Models Using a Semismooth Newton-Based Augmented Lagrangian MethodMar 28 2018The octagonal shrinkage and clustering algorithm for regression (OSCAR), equipped with the $\ell_1$-norm and a pair-wise $\ell_{\infty}$-norm regularizer, is a useful tool for feature selection and grouping in high-dimensional data analysis. The computational ... More

A Proximal Point Dual Newton Algorithm for Solving Group Graphical Lasso ProblemsJun 11 2019Undirected graphical models have been especially popular for learning the conditional independence structure among a large number of variables where the observations are drawn independently and identically from the same distribution. However, many modern ... More

On the convergence properties of a majorized ADMM for linearly constrained convex optimization problems with coupled objective functionsJan 31 2015In this paper, we establish the convergence properties for a majorized alternating direction method of multipliers (ADMM) for linearly constrained convex optimization problems whose objectives contain coupled functions. Our convergence analysis relies ... More

A Unified Algorithmic Framework of Symmetric Gauss-Seidel Decomposition based Proximal ADMMs for Convex Composite ProgrammingDec 17 2018This paper aims to present a fairly accessible generalization of several symmetric Gauss-Seidel decomposition based multi-block proximal alternating direction methods of multipliers (ADMMs) for convex composite optimization problems. The proposed method ... More

On the Equivalence of Inexact Proximal ALM and ADMM for a Class of Convex Composite ProgrammingMar 28 2018Jan 28 2019In this paper, we show that for a class of linearly constrained convex composite optimization problems, an (inexact) symmetric Gauss-Seidel based majorized multi-block proximal alternating direction method of multipliers (ADMM) is equivalent to an {\em ... More

A Unified Algorithmic Framework of Symmetric Gauss-Seidel Decomposition based Proximal ADMMs for Convex Composite ProgrammingDec 17 2018Apr 04 2019This paper aims to present a fairly accessible generalization of several symmetric Gauss-Seidel decomposition based multi-block proximal alternating direction methods of multipliers (ADMMs) for convex composite optimization problems. The proposed method ... More

Efficient sparse Hessian based algorithms for the clustered lasso problemAug 22 2018Aug 23 2018We focus on solving the clustered lasso problem, which is a least squares problem with the $\ell_1$-type penalties imposed on both the coefficients and their pairwise differences to learn the group structure of the regression parameters. Here we first ... More

A sparse semismooth Newton based proximal majorization-minimization algorithm for nonconvex square-root-loss regression problemsMar 27 2019Apr 02 2019In this paper, we consider high-dimensional nonconvex square-root-loss regression problems and introduce a proximal majorization-minimization (PMM) algorithm for these problems. Our key idea for making the proposed PMM to be efficient is to develop a ... More

A Fast Globally Linearly Convergent Algorithm for the Computation of Wasserstein BarycentersSep 12 2018May 02 2019In this paper, we consider the problem of computing a Wasserstein barycenter for a set of discrete probability distributions with finite supports, which finds many applications in different areas such as statistics, machine learning and image processing. ... More

SDPNAL+: A Matlab software for semidefinite programming with bound constraints (version 1.0)Oct 29 2017May 16 2019SDPNAL+ is a {\sc Matlab} software package that implements an augmented Lagrangian based method to solve large scale semidefinite programming problems with bound constraints. The implementation was initially based on a majorized semismooth Newton-CG augmented ... More

Fast algorithms for large scale generalized distance weighted discriminationApr 19 2016High dimension low sample size statistical analysis is important in a wide range of applications. In such situations, the highly appealing discrimination method, support vector machine, can be improved to alleviate data piling at the margin. This leads ... More

Fast algorithms for large scale generalized distance weighted discriminationApr 19 2016Aug 17 2017High dimension low sample size statistical analysis is important in a wide range of applications. In such situations, the highly appealing discrimination method, support vector machine, can be improved to alleviate data piling at the margin. This leads ... More

Approximate Message Passing with Nearest Neighbor Sparsity Pattern LearningJan 04 2016We consider the problem of recovering clustered sparse signals with no prior knowledge of the sparsity pattern. Beyond simple sparsity, signals of interest often exhibits an underlying sparsity pattern which, if leveraged, can improve the reconstruction ... More

Multi-Scale Fully Convolutional Network for Cardiac Left Ventricle SegmentationSep 19 2018The morphological structure of left ventricle segmented from cardiac magnetic resonance images can be used to calculate key clinical parameters, and it is of great significance to the accurate and efficient diagnosis of cardiovascular diseases. Compared ... More

Projective embedding of log Riemann surfaces and K-stabilityMay 03 2016Aug 16 2016Given a smooth polarized Riemann surface (X, L) endowed with a hyperbolic metric $\omega$ with cusp singularities along a divisor D, we show the L^2 projective embedding of (X, D) defined by L^k is asymptotically almost balanced in a weighted sense. The ... More

Projective embedding of log Riemann surfaces and K-stabilityMay 03 2016Sep 25 2017Given a smooth polarized Riemann surface (X, L) endowed with a hyperbolic metric $\omega$ with cusp singularities along a divisor D, we show the L^2 projective embedding of (X, D) defined by L^k is asymptotically almost balanced in a weighted sense. The ... More

Sphere theorems for submanifolds in Kähler ManifoldOct 17 2018In this paper, we prove some differentiable sphere theorems and topological sphere theorems for submanifolds in K\"ahler manifold, especially in complex space forms.

SPLZ: An Efficient Algorithm for Single Source Shortest Path Problem Using Compression MethodAug 11 2014Jan 11 2015Efficient solution of the single source shortest path (SSSP) problem on road networks is an important requirement for numerous real-world applications. This paper introduces an algorithm for the SSSP problem using compression method. Owning to precomputing ... More

Sphere theorems for Lagrangian and Legendrian submanifoldsOct 22 2018In this paper, we prove some differentiable sphere theorems and topological sphere theorems for Lagrangian submanifolds in K\"ahler manifold and Legendrian submanifolds in Sasaki space form.

Different Particle Sizes Obtained from Static and Dynamic Laser Light ScatteringMay 31 2004Dec 08 2004Detailed investigation of static and dynamic laser light scattering has been attempted in this work both theoretically and experimentally based on dilute water dispersions of two different homogenous spherical particles, polystyrene latexes and poly($N$-isopropylacrylamide) ... More

Note on K-stability of pairsAug 23 2011Nov 23 2012We prove that a pair (X, D) with X Fano and D a smooth anti-canonical divisor is K-unstable for negative angles, and K-semistable for zero angle.

Infinite Mixtures of Multivariate Gaussian ProcessesJul 26 2013This paper presents a new model called infinite mixtures of multivariate Gaussian processes, which can be used to learn vector-valued functions and applied to multitask learning. As an extension of the single multivariate Gaussian process, the mixture ... More

Independence of $\ell$ for the supports in the Decomposition TheoremDec 04 2015In this note, we prove a result on the independence of $\ell$ for the supports of irreducible perverse sheaves occurring in the Decomposition Theorem, as well as for the family of local systems on each support. It generalizes Gabber's result on the independence ... More

W-Operators and Permutation GroupsOct 20 2016W-operators are differential operators on the polynomial ring. A special example of W-operators is the cut-and-join operator. We study the relation between W-operators and permutation groups. We find the W-operator $W([d])$ can be written as the sum of ... More

Stability of sheaves of locally closed and exact formsMay 13 2009For any smooth projective variety $X$ of dimension $n$ over an algebraically closed field $k$ of characteristic $p>0$ with $\mu(\Omega^1_X)>0$. If ${\rm T}^{\ell}(\Omega^1_X)$ ($0<\ell<n(p-1)$) are semi-stable, then the sheaf $B^1_X$ of exact 1-forms ... More

Suspicion on Engrafting HBT From Astronomy to Heavy Ion CollisionDec 13 2004Aug 19 2005HBT method in astronomy and heavy ion collision is contrasted in present article.Some differences are found and validity of using HBT in heavy ion collision is suspected.

Factorization of generalized theta functions at reducible caseApr 17 2000We proved the factorization of generalized theta functions when the curve has two irreducible components meeting at one node.

Topological Phases of Fermionic Ladders with Periodic Magnetic FieldsDec 14 2015In recent experiments bosonic [Atala et al., Nat. Phys. 10, 588 (2014), B. K. Stuhl et al., Science 349, 1514 (2015)] as well as fermionic ladders [M. Mancini et al., Science 349, 1510 (2015)] with a uniform flux were studied and different interesting ... More

The Spatial Scaling Laws of Compressible TurbulenceFeb 10 2015Oct 17 2016The spatial scaling laws of velocity kinetic energy spectrum for compressible turbulence flow and its density-weighted counterpart have been formulated in terms of wavenumber, dissipation rate and Mach number by using dimensional analysis. We have applied ... More

Physarum-inspired Network Optimization: A ReviewDec 08 2017The popular Physarum-inspired Algorithms (PAs) have the potential to solve challenging network optimization problems. However, the existing researches on PAs are still immature and far from being fully recognized. A major reason is that these researches ... More

Topics in Quantum NetworkingMar 07 2019It is an era full of imaginations and lack of impossibilities. The knowledge boundaries have been being pushed back on and on. The quantum age is on the edge of transforming quantum theories into quantum technologies. We present a sketch of the advances ... More

A probabilistic approach to enumeration of Gessel walksMar 02 2009We consider Gessel walks in the plane starting at the origin $(0, 0)$ remaining in the first quadrant $i, j \geq 0$ and made of West, North-East, East and South-West steps. Let $F(m; n_1, n_2)$ denote the number of these walks with exact $m$ steps ending ... More

Cash sub-additive risk statistics with scenario analysisApr 16 2019Since the money is of time value, we will study a new class of risk statistics, named cash sub-additive risk statistics in this paper. This new class of risk statistics can be considered as a kind of risk extension of risk statistics introduced by Kou, ... More

Universal central extensions of twisted forms of split simple Lie algebras over ringsNov 17 2010Nov 19 2010We give sufficient conditions for the descent construction to be the universal central extension of a twisted form of a split simple Lie algebra over a ring. In particular, the universal central extensions of twisted multiloop Lie tori are obtained by ... More

Frobenius morphism and semi-stable bundlesApr 09 2009This article is the expanded version of a talk given at the conference: Algebraic geometry in East Asia 2008, Seoul. In this notes, I intend to give a brief survey of results on the behavior of semi-stable bundles under the Frobenius pullback and direct ... More

An exact axisymmetric spiral solution of incompressible 3D Euler equationsJan 29 2011Jul 31 2011Spiral structure is one of the most common structures in the nature flows. A general steady spiral solution of incompressible inviscid axisymmetric flow was obtained analytically by applying separation of variables to the 3D Euler equations. The solution, ... More

Zero-Entropy Dynamical Systems with Gluing Orbit PropertyOct 21 2018We show that a dynamical system with gluing orbit property and zero topological entropy is equicontinuous, hence it is topologically conjugate to a minimal rotation.

Long time behavior of the NLS-Szeg{ö} equationApr 19 2019Apr 24 2019We are interested in the influence of filtering the positive Fourier modes to the integrable non linear Schr{\"o}dinger equation. Equivalently, we want to study the effect of dispersion added to the cubic Szeg{\"o} equation, leading to the NLS-Szeg{\"o} ... More

Direct images of bundles under Frobenius morphismsNov 13 2006Mar 31 2008Let $X$ be a smooth projective variety of dimension $n$ over an algebraically closed field $k$ with ${\rm char}(k)=p>0$ and $F:X\to X_1$ be the relative Frobenius morphism. For any vector bundle $W$ on $X$, we prove that instability of $F_*W$ is bounded ... More

Ordinary p-adic automorphic formsSep 18 2017Generalizing the completed cohomology groups introduced by Matthew Emerton, we define certain spaces of "ordinary $p$-adic automorphic forms along a parabolic subgroup" and show that they interpret all classical ordinary automorphic forms.

Measures of Intermediate Entropies for Skew Product DiffeomorphismsJun 10 2009Jan 18 2010In this paper we study a skew product map $F$ with a measure $\mu$ of positive entropy. We show that if on the fibers the map are $C^{1+\alpha}$ diffeomorphisms with nonzero Lyapunov exponents, then $F$ has ergodic measures of intermediate entropies. ... More

W-Operator and Differential Equation for 3-Hurwitz NumberDec 09 2016We consider a new type of Hurwitz number, the number of ordered transitive factorizations of an arbitrary permutation into d-cycles. In this paper, we focus on the special case d = 3. The minimal number of transitive factorizations of any permutation ... More

Private Information DeliveryJun 14 2018Mar 25 2019We introduce the problem of private information delivery (PID), comprised of $K$ messages, a user, and $N$ servers (each holds $M\leq K$ messages) that wish to deliver one out of $K$ messages to the user privately, i.e., without revealing the delivered ... More

Overview of top quark physics at the ep collidersOct 17 2017In this talk we present a short overview of top physics at the electron-proton (ep) colliders. Currently, the proposed ep collider is the Large Hadron Electron Collider (LHeC), which is a combination of 60 GeV electron beam and 7 TeV proton beam of the ... More

Dark Matter Searches in Jet plus Missing Energy in $\rm γp$ collision at CERN LHCJul 21 2014Aug 01 2014In this paper, we investigate the $\rm \gamma p$ photoproduction of jet plus missing energy signal to set limits on the couplings of the fermionic dark matter to the quarks at the LHC via the main reaction $\rm pp\rightarrow p\gamma p\rightarrow p \chi\chi ... More

On the Clifford theorem for surfacesMar 04 2012We give two generalizations of the Clifford theorem to algebraic surfaces. As an application, we obtain some bounds for the number of moduli of surfaces of general type.

Strichartz-type Estimates for Wave Equation for Normally Hyperbolic Trapped DomainsJul 20 2015We establish a mixed-norm Strichartz type estimate for the wave equation on Riemannian manifolds $(\Omega,g)$, for the case that $\Omega$ is the exterior of a smooth, normally hyperbolic trapped obstacle in $n$ dimensional Euclidean space, and $n$ is ... More

Counting Hypergraphs in Data StreamsApr 28 2013We present the first streaming algorithm for counting an arbitrary hypergraph $H$ of constant size in a massive hypergraph $G$. Our algorithm can handle both edge-insertions and edge-deletions, and is applicable for the distributed setting. Moreover, ... More

Pluricanonical maps of varieties of Albanese fiber dimension twoNov 28 2012Feb 23 2014In this paper we prove that for any smooth projective variety of Albanese fiber dimension two and of general type, the 6-canonical map is birational. And we also show that the 5-canonical map is birational for any such variety with some geometric restrictions. ... More

Orlicz-Besov imbedding and globally $n$-regular domainsOct 09 2018Denote by $ {\bf\dot B}^{\alpha,\phi}(\Omega)$ the Orlicz-Besov space, where $\alpha\in\mathbb{R}$, $\phi$ is a Young function and $\Omega\subset\mathbb{R}^n$ is a domain. For $\alpha\in(-n,0)$ and optimal $\phi$, in this paper we characterize domains ... More

A Transcendental Invariant of Pseudo-Anosov MapsSep 12 2012May 09 2013For each pseudo-Anosov map $\phi$ on surface $S$, we will associate it with a $\mathbb{Q}$-submodule of $\mathbb{R}$, denoted by $A(S,\phi)$. $A(S,\phi)$ is defined by an interaction between the Thurston norm and dilatation of pseudo-Anosov maps. We will ... More

A representation-theoretic proof of the branching rule for Macdonald polynomialsDec 01 2014We give a new representation-theoretic proof of the branching rule for Macdonald polynomials using the Etingof-Kirillov Jr. expression for Macdonald polynomials as traces of intertwiners of U_q(gl_n). In the Gelfand-Tsetlin basis, we show that diagonal ... More

Rank $n$ swapping algebra for the $\operatorname{PSL}(n, \mathbb{R})$ Hitchin componentNov 11 2014Oct 24 2015F. Labourie [arXiv:1212.5015] characterized the Hitchin components for $\operatorname{PSL}(n, \mathbb{R})$ for any $n>1$ by using the swapping algebra, where the swapping algebra should be understood as a ring equipped with a Poisson bracket. We introduce ... More

Shifted convolution sums involving theta seriesMay 02 2017Let $f$ be a cuspidal newform (holomorphic or Maass) of arbitrary level and nebentypus and denote by $\lambda_f(n)$ its $n$-th Hecke eigenvalue. Let $$ r(n)=\#\left\{(n_1,n_2)\in \mathbb{Z}^2:n_1^2+n_2^2=n\right\}. $$ In this paper, we study the shifted ... More

Co-iterative augmented Hessian method for orbital optimizationOct 26 2016Jan 10 2017Orbital optimization procedure is widely called in electronic structure simulation. To efficiently find the orbital optimization solution, we developed a new second order orbital optimization algorithm, co-iteration augmented Hessian (CIAH) method. In ... More

Shifted convolution sums of $GL_3$ cusp forms with $θ$-seriesSep 25 2015Sep 10 2016Let $A_f(1,n)$ be the normalized Fourier coefficients of a Hecke-Maass cusp form $f$ for $SL_3(\mathbb{Z})$ and $$ r_3(n)=\#\left\{(n_1,n_2,n_3)\in \mathbb{Z}^3:n_1^2+n_2^2+n_3^2=n\right\}. $$ Let $1\leq h\leq X$ and $\phi(x)$ be a smooth function compactly ... More

Gaussian Approximations for Maxima of Random Vectors under $(2+ι)$-th MomentsMay 27 2019We derive a Gaussian approximation result for the maximum of a sum of random vectors under $(2+\iota)$-th moments. Our main theorem is abstract and nonasymptotic, and can be applied to a variety of statistical learning problems. The proof uses the Lindeberg ... More

Graphene oxide adsorptive power from better to more via an enhanced route in perspectiveApr 25 2017Adsorption is one important way applied to water decontamination, where carbon is commonly used as highly effective absorbent. Carbon of different morphologies and structures normally demonstrate distinct capabilities to adsorption-typed decontaminations. ... More

Compactness of Constant Mean Curvature Surfaces in Three Manifold with Positive Ricci CurvatureApr 25 2018Dec 06 2018In this paper we prove a compactness theorem for constant mean curvature surfaces with area and genus bound in three manifold with positive Ricci curvature. As an application, we give a lower bound of first eigenvalue of constant mean curvature surfaces ... More

Exact Controllability of linear KP-I equationFeb 28 2018We prove the exact controllability of linear KP-I equation if the control input is added on a vertical domain. More generally, we have obtained the least dispersion needed to insure observability for fractional linear KP I equation.

Two laws of large numbers for sublinear expectationsNov 18 2015In this paper, we consider the sublinear expectation on bounded random vari- ables. With the notion of uncorrelatedness for random variables under the sublinear expectation, a weak law of large numbers is obtained. With the no- tion of independence for ... More

Chebyshev Interpolation for Function in 1DSep 24 2018This research is concerned with finding the roots of a function in an interval using Chebyshev Interpolation. Numerical results of Chebyshev Interpolation are presented to show that this is a powerful way to simultaneously calculate all the roots in an ... More

An estimate on energy of min-max Seiberg-Witten Floer generatorsJan 08 2018Jan 20 2018Previously, Cristofaro-Gardiner, Hutchings and Ramos have proved that embedded contact homology (ECH) capacities can recover the volume of a contact 3-manifod in their paper "the asymptotics of ECH capacities" . There were two main steps to proving this ... More