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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

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 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

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 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

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 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 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 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

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 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 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

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

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 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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 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

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

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

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

A Fast Globally Linearly Convergent Algorithm for the Computation of Wasserstein BarycentersSep 12 2018Jul 28 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 areas such as statistics, machine learning and image processing. When the ... 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

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 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

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

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

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.

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.

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

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

Note on geodesic rays tamed by simple test configurationsJun 17 2008Nov 08 2009In this short note, we give a new proof of a theorem of Arezzo-Tian on the existence of smooth geodesic rays tamed by a special degeneration.

Large Two-loop Effects in the Higgs Sector as New Physics ProbesOct 08 2015We consider a simple Higgs portal model in beyond the standard model scenario: an extra real gauge singlet scalar that couples to the Higgs. We calculate the higher-loop corrections to the cross section of the Higgsstrahlung process $e^+e^- \rightarrow ... More

Little Flavor: Heavy Leptons, Z' and Higgs PhenomenologyNov 01 2014Jan 22 2016The Little Flavor model is a close cousin of the Little Higgs theory which aims to generate flavor structure around TeV scale. While the original Little Flavor only included the quark sector, here we build the lepton part of the Little Flavor model and ... More

Multi-view Laplacian Support Vector MachinesJul 26 2013We propose a new approach, multi-view Laplacian support vector machines (SVMs), for semi-supervised learning under the multi-view scenario. It integrates manifold regularization and multi-view regularization into the usual formulation of SVMs and is a ... More

Size Information Obtained by Using Static Light Scattering TechniqueJul 01 2004Dec 08 2004Detailed investigation of static light scattering $(SLS) $ has been attempted in this work using dilute water dispersions of homogenous spherical particles, poly($N$-isopropylacrylamide) microgels and simulated data. When Rayleigh-Gan-Debye approximation ... More

Analysis of Fully Preconditioned ADMM with Relaxation in Hilbert SpacesNov 15 2016Alternating direction method of multipliers (ADMM) is a powerful first order methods for various applications in signal processing and imaging. However, there is no clear result on the weak convergence of ADMM with relaxation studied by Eckstein and Bertsakas ... More

Co-iterative augmented Hessian method for orbital optimizationOct 26 2016Orbital 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

Stability of direct images under Frobenius morphismAug 02 2006Aug 18 2006Let $X$ be a smooth projective variety over an algebraically field $k$ with ${\rm char}(k)=p>0$ and $F:X\to X_1$ be the relative Frobenius morphism. When ${\rm dim}(X)=1$, we prove that $F_*W$ is a stable bundle for any stable bundle $W$ (Theorem \ref{thm1.3}). ... More

Root Mean Square Minimum Distance: a Quality Metric for Localization Nanoscopy ImagingJan 06 2018A localization algorithm in optical localization nanoscopy plays an important role in obtaining a high-quality image. A universal and objective metric, which is crucial and necessary to evaluate qualities of nanoscopy images and performances of localization ... More

Cohen-Lyndon type theorem for group theoretic Dehn fillingsSep 24 2018Nov 13 2018The classical Cohen-Lyndon property of a free group describes the structure of the normal closure of a non-trivial element, and computes the relation module of the corresponding quotient group. Realizing that this result is, in fact, about the kernel ... More

Bounded t-structures on the bounded derived category of coherent sheaves over a weighted projective lineAug 17 2017Jun 20 2018We use recollement and HRS-tilt to describe bounded t-structures on the bounded derived category $\mathcal{D}^b(\mathbb{X})$ of coherent sheaves over a weighted projective line $\mathbb{X}$ of virtual genus $\leq 1$. We will see from our description that ... More

Anonymous Information DeliveryJun 14 2018We introduce the problem of anonymous information delivery (AID), comprised of $K$ messages, a user, and $N$ servers (each holds $M$ messages) that wish to deliver one out of $K$ messages to the user anonymously, i.e., without revealing the delivered ... More

Zero-Entropy Dynamical Systems with Gluing Orbit PropertyOct 21 2018Apr 06 2019We show that a dynamical system with gluing orbit property and zero topological entropy is equicontinuous, hence it is topologically conjugate to a minimal rotation. Moreover, we show that a dynamical system with gluing orbit property has zero topological ... More

A Stock Selection Method Based on Earning Yield Forecast Using Sequence Prediction ModelsMay 13 2019Long-term investors, different from short-term traders, focus on examining the underlying forces that affect the well-being of a company. They rely on fundamental analysis which attempts to measure the intrinsic value an equity. Quantitative investment ... More

Exponential Decay of Expansive ConstantsJan 04 2011A map $f$ on a compact metric space is expansive if and only if $f^n$ is expansive. We study the exponential rate of decay of the expansive constant of $f^n$. A major result is that this rate times box dimension bounds topological entropy.

Intrinsic Universal Measurements of Non-linear EmbeddingsNov 05 2018A basic problem in machine learning is to find a mapping $f$ from a low dimensional latent space to a high dimensional observation space. Equipped with the representation power of non-linearity, a learner can easily find a mapping which perfectly fits ... More

Cohomology of group theoretic Dehn fillings II: A spectral sequenceJul 29 2019This is the second paper in a series of three papers aiming to study cohomology of group theoretic Dehn fillings. In the present paper, we derive a spectral sequence for Cohen-Lyndon triples which can be thought of as a refined version of the classical ... More

Minimal rational curves in moduli spaces of stable bundlesOct 06 2003In this short note, we show that any rational curve passing through the generic point in a moduli space of stable bundles with rank $r$ and fixed determinant on a smooth projective curve of genus $g\ge 4$ has degree (with respect to the anti-canonical ... More

Elliptic curves in moduli space of stable bundlesNov 19 2010Let $M$ be the moduli space of rank $2$ stable bundles with fixed determinant of degree $1$ on a smooth projective curve $C$ of genus $g\ge 2$. When $C$ is generic, we show that any elliptic curve on $M$ has degree (respect to anti-canonical divisor $-K_M$) ... More

A mixed FEM for the quad-curl eigenvalue problemOct 24 2013The quad-curl problem arises in the study of the electromagnetic interior transmission problem and magnetohydrodynamics (MHD). In this paper, we study the quad-curl eigenvalue problem and propose a mixed method using edge elements for the computation ... More

Cyclotomic Temperley-Lieb algebra of type D and its representation theoryNov 17 2010Nov 19 2010We define a new class of algebras, cyclotomic Temperley-Lieb algebras of type D, in a diagrammatic way, which is a generalization of Temperley-Lieb algebras of type D. We prove that the cyclotomic Temperley-Lieb algebras of type D are cellular. In fact, ... More

The Capacity of Anonymous CommunicationsApr 04 2018We consider the communication scenario where K transmitters are each connected to a common receiver with an orthogonal noiseless link. One of the transmitters has a message for the receiver, who is prohibited from learning anything in the information ... More

A new class of refined Eulerian polynomialsFeb 27 2018May 21 2018In this note we introduce a new class of refined Eulerian polynomials defined by $$A_n(p,q)=\sum_{\pi\in\mathfrak{S}_n}p^{{\rm odes}(\pi)}q^{{\rm edes}(\pi)},$$ where ${\rm odes}(\pi)$ and ${\rm edes}(\pi)$ enumerate the number of descents of permutation ... More

Degree of W-operator and Noncrossing PartitionOct 20 2016Jun 15 2019Goulden and Jackson first introduced the cut-and-join operator. The cut-and-join is widely used in studying the Hurwitz number and many other topological recursion problems. Mironov, Morosov and Natanzon give a more general construction and call it W-operator ... More

Virtual homological eigenvalue and mapping torus of pseudo-Anosov mapsAug 25 2016Oct 18 2016In this note, we show that, if a pseudo-Anosov map $\phi:S\to S$ admits a finite cover whose action on the first homology has spectral radius greater than $1$, then the monodromy of any fibered structure of any finite cover of the mapping torus $M_{\phi}$ ... More

Geometric Structure of Pseudo-plane Quadratic FlowsJan 18 2017Quadratic flows have the unique property of uniform strain and are commonly used in turbulence modeling and hydrodynamic analysis. While previous application focused on two-dimensional homogeneous fluid, this study examines the geometric structure of ... More

A note on equivariantization of additive categories and triangulated categoriesAug 17 2017Apr 10 2019In this article, we investigate the category $\mathcal{A}^G$ of equivariant objects of an additive category $\mathcal{A}$ with respect to an action of a finite group $G$. We show that if $G$ is solvable then we can reconstruct $\mathcal{A}$ from $\mathcal{A}^G$ ... More

Minimality and Gluing Orbit PropertyAug 02 2018Aug 21 2018We show that a topological dynamical system is either minimal or have positive topological entropy. Moreover, for equicontinuous systems, we show that topological transitivity, minimality and orbit gluing property are equivalent. These facts reflect the ... More

Performance Analysis of Quantum ChannelsJul 12 2018We study the quality of service in quantum channels. We regard the quantum channel as a queueing system, and present queueing analysis of both the classical information transmission and quantum information transmission in the quantum channel. For the ... More

Comment on 'Perfect drain for the Maxwell fish eye lens'Oct 16 2012Mar 08 2013The non-magnetic loss material has been proposed (2011 New J. Phys. 13 023038) to mimic a passive perfect drain in the Maxwell's fish eye lens (MFL). In this comment, we argue that this passive medium can only be treated as a perfect absorber which can ... More

Algebraic K-Theory and Modular SymbolsApr 16 2016In this paper, we calculate the differential $d^1$ of the rank spectral sequence. We generalize Quillen's spectral sequence from Dedekind domain to general integral Noetherian ring $A$ by considering the Q-construction $Q^{tf}(A)$ of the category of finitely ... More

Crossed Product $C^*$-algebras of Minimal Dynamical Systems on the Product of the Cantor Set and the TorusFeb 14 2011This paper studies the relationship between minimal dynamical systems on the product of the Cantor set ($X$) and torus ($\T^2$) and their corresponding crossed product $C^*$-algebras. For the case when the cocycles are rotations, we studied the structure ... More

G-frames and G-Riesz BasesAug 05 2005G-frames are generalized frames which include ordinary frames, bounded invertible linear operators, as well as many recent generalizations of frames, e.g., bounded quasi-projectors and frames of subspaces. G-frames are natural generalizations of frames ... More

A Functional Central Limit Theorem for the Becker-Döring modelOct 11 2017Feb 23 2018We investigate the fluctuations of the stochastic Becker-D\"oring model of polymerization when the initial size of the system converges to infinity. A functional central limit problem is proved for the vector of the number of polymers of a given size. ... More

Physical Angular Momentum Separation for QEDAug 18 2016Apr 10 2017We study the non-uniqueness problem of the gauge-invariant angular momentum separation for the case of QED, which stems from the recent controversy concerning the proper definitions of the orbital angular momentum and spin operator of the individual parts ... More

Inversion Formula for the Windowed Fourier TransformJun 20 2010Sep 20 2011In this paper, we study the inversion formula for recovering a function from its windowed Fourier transform. We give a rigorous proof for an inversion formula which is known in engineering. We show that the integral involved in the formula is convergent ... More

Sarnak's Conjecture for nilsequences on arbitrary number fields and applicationsFeb 26 2019We formulate the generalized Sarnak's M\"obius disjointness conjecture for an arbitrary number field $K$, and prove a quantitative disjointness result between polynomial nilsequences $(\Phi(g(n)\Gamma))_{n\in\mathbb{Z}^{D}}$ and aperiodic multiplicative ... More

On a class of fully nonlinear elliptic equations on closed Hermitian manifolds II: $L^\infty$ estimateJul 29 2014We study a class of fully nonlinear elliptic equations on closed Hermitian manifolds. Under the assumption of cone condition, we derive the $L^\infty$ estimate directly.

A structure theorem for multiplicative functions over the Gaussian integers and applicationsMay 01 2014Dec 03 2014We prove a structure theorem for multiplicative functions on the Gaussian integers, showing that every bounded multiplicative function on the Gaussian integers can be decomposed into a term which is approximately periodic and another which has a small ... More

Parabolic Complex Monge-Ampère Type Equations on Closed Hermitian ManifoldsNov 13 2013We study the parabolic complex Monge-Amp\`ere type equations on closed Hermitian manfolds. We derive uniform $C^\infty$ {\em a priori} estimates for normalized solutions, and then prove the $C^\infty$ convergence. The result also yields a way to carry ... More

Golden Ratio estimate of success probability based on one and only sampleJul 22 2012This paper proposes iterative Bayesian method to estimate success probability based on unique sample. The procedure is replacing the distribution characteristic of prior with Bayes estimate on the every iteration until they coincide. Iterative Bayes estimate ... More

Swapping algebra, Virasoro algebra and discrete integrable systemDec 14 2014Sep 22 2016We induce a Poisson algebra $\{\cdot,\cdot\}_{\mathcal{C}_{n,N}}$ on the configuration space $\mathcal{C}_{n,N}$ of $N$ twisted polygons in $\mathbb{RP}^{n-1}$ from the swapping algebra \cite{L12}, which is found coincide with Faddeev-Takhtajan-Volkov ... More

Weak ergodic averages over dilated measuresSep 18 2018Oct 18 2018Let $m\in\mathbb{N}$ and $\textbf{X}=(X,\mathcal{X},\mu,(T_{\alpha})_{\alpha\in\mathbb{R}^{m}})$ be a measure preserving system with an $\mathbb{R}^{m}$-action. We say that a Borel measure $\nu$ on $\mathbb{R}^{m}$ is weakly equidistributed for $\textbf{X}$ ... More

Averages of shifted convolution sums for $GL(3) \times GL(2)$Jan 08 2017Let $A_f(1,n)$ be the normalized Fourier coefficients of a $GL(3)$ Maass cusp form $f$ and let $a_g(n)$ be the normalized Fourier coefficients of a $GL(2)$ cusp form $g$. Let $\lambda(n)$ be either $A_f(1,n)$ or the triple divisor function $d_3(n)$. It ... More