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A Newton-bracketing method for a simple conic optimization problemMay 30 2019For the Lagrangian-DNN relaxation of quadratic optimization problems (QOPs), we propose a Newton-bracketing method to improve the performance of the bisection-projection method implemented in BBCPOP [to appear in ACM Tran. Softw., 2019]. The relaxation ... More

A Geometrical Analysis of a Class of Nonconvex Conic Programs for Convex Conic Reformulations of Quadratic and Polynomial Optimization ProblemsJan 08 2019We present a geometrical analysis on the completely positive programming reformulation of quadratic optimization problems and its extension to polynomial optimization problems with a class of geometrically defined nonconvex conic programs and their covexification. ... More

Doubly nonnegative relaxations are equivalent to completely positive reformulations of quadratic optimization problems with block-clique graph structuresMar 18 2019We study the equivalence among a nonconvex QOP, its CPP and DNN relaxations under the assumption that the aggregated and correlative sparsity of the data matrices of the CPP relaxation is represented by a block-clique graph $G$. By exploiting the correlative ... 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

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

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 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 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

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 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

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

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

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

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 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 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

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

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 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

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

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

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 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

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

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

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

BBCPOP: A Sparse Doubly Nonnegative Relaxation of Polynomial Optimization Problems with Binary, Box and Complementarity ConstraintsApr 02 2018The software package BBCPOP is a MATLAB implementation of a hierarchy of sparse doubly nonnegative (DNN) relaxations of a class of polynomial optimization (minimization) problems (POPs) with binary, box and complementarity (BBC) constraints. Given a POP ... 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

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

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

A proximal point algorithm for sequential feature extraction applicationsAug 04 2011We propose a proximal point algorithm to solve LAROS problem, that is the problem of finding a "large approximately rank-one submatrix". This LAROS problem is used to sequentially extract features in data. We also develop a new stopping criterion for ... 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

A New Homotopy Proximal Variable-Metric Framework for Composite Convex MinimizationDec 13 2018This paper suggests two novel ideas to develop new proximal variable-metric methods for solving a class of composite convex optimization problems. The first idea is a new parameterization of the optimality condition which allows us to develop a class ... More

A bounded degree SOS hierarchy for polynomial optimizationJan 25 2015Jun 26 2015We consider a new hierarchy of semidefinite relaxations for the general polynomial optimization problem $(P):\:f^{\ast}=\min \{\,f(x):x\in K\,\}$ on a compact basic semi-algebraic set $K\subset\R^n$. This hierarchy combines some advantages of the standard ... 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 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

Sparse-BSOS: a bounded degree SOS hierarchy for large scale polynomial optimization with sparsityJul 05 2016May 27 2017We provide a sparse version of the bounded degree SOS hierarchy BSOS [7] for polynomial optimization problems. It permits to treat large scale problems which satisfy a structured sparsity pattern. When the sparsity pattern satisfies the running intersection ... More

A bounded degree SOS hierarchy for large scale polynomial optimization with sparsityJul 05 2016We provide a sparse version of the bounded degree SOS (BSOS) hierarchy for polynomial optimization problems. The presented version permits to handle large scale problems which satisfy a structured sparsity pattern. When the sparsity pattern satisfies ... 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

Addressing learning difficulties in Newtons 1st and 3rd Laws through problem based inquiry using Easy Java SimulationMar 01 2013Sep 25 2013We develop an Easy Java Simulation (EJS) model for students to visualize Newtons 1st and 3rd laws, using frictionless constant motion equation and a spring collision equation during impact. Using Physics by Inquiry instructional (PbI) strategy, the simulation ... More

Charge and CP asymmetries of $B_q$ meson in unparticle physicsDec 01 2010Dec 02 2010Recently the D{\O} Collaboration reported an observation of like-sign charge asymmetry (CA), which is about $3.2 \sigma$ deviation from the standard model (SM) prediction. Inspired by the observation we investigate the scalar unparticle effects, under ... More

A new model of turbulent relative dispersion: a self-similar telegraph equation based on persistently separating motionsOct 21 2005Turbulent relative dispersion is studied theoretically with a focus on the evolution of probability distribution of the relative separation of two passive particles. A finite separation speed and a finite correlation of relative velocity, which are crucial ... More

Practical Matrix Completion and Corruption Recovery using Proximal Alternating Robust Subspace MinimizationSep 06 2013Oct 28 2014Low-rank matrix completion is a problem of immense practical importance. Recent works on the subject often use nuclear norm as a convex surrogate of the rank function. Despite its solid theoretical foundation, the convex version of the problem often fails ... 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

Max-Norm Optimization for Robust Matrix RecoverySep 24 2016This paper studies the matrix completion problem under arbitrary sampling schemes. We propose a new estimator incorporating both max-norm and nuclear-norm regularization, based on which we can conduct efficient low-rank matrix recovery using a random ... More

Wafer-scale graphene/ferroelectric hybrid devices for low-voltage electronicsJan 07 2011Preparing graphene and its derivatives on functional substrates may open enormous opportunities for exploring the intrinsic electronic properties and new functionalities of graphene. However, efforts in replacing SiO$_{2}$ have been greatly hampered by ... More

Topological characterization of classical waves: the topological origin of magnetostatic surface spin wavesMay 20 2019We propose a topological characterization of Hamiltonians describing classical waves. Applying it to the magnetostatic surface spin waves that are important in spintronics applications, we settle the speculation over their topological origin. For a class ... More

Venn GAN: Discovering Commonalities and Particularities of Multiple DistributionsFeb 09 2019We propose a GAN design which models multiple distributions effectively and discovers their commonalities and particularities. Each data distribution is modeled with a mixture of $K$ generator distributions. As the generators are partially shared between ... More

Telegraph-type versus diffusion-type models of turbulent relative dispersionNov 10 2007Apr 30 2008Properties of two equations describing the evolution of the probability density function (PDF) of the relative dispersion in turbulent flow are compared by investigating their solutions: the Richardson diffusion equation with the drift term and the self-similar ... More

Deterministic Stretchy RegressionJun 09 2018An extension of the regularized least-squares in which the estimation parameters are stretchable is introduced and studied in this paper. The solution of this ridge regression with stretchable parameters is given in primal and dual spaces and in closed-form. ... More

Inverse resonance problems for the Schroedinger operator on the real line with mixed given dataMar 06 2017Sep 13 2017In this work, we study inverse resonance problems for the Schr\"odinger operator on the real line with the potential supported in $[0,1]$. In general, all eigenvalues and resonances can not uniquely determine the potential. (i) It is shown that if the ... More

Low-threshold optically pumped lasing in highly strained Ge nanowiresAug 15 2017The integration of efficient, miniaturized group IV lasers into CMOS architecture holds the key to the realization of fully functional photonic-integrated circuits. Despite several years of progress, however, all group IV lasers reported to date exhibit ... More

Geometric theory of inversion and seismic imagingJun 01 2015The goal of inversion is to estimate the model which generates the data of observations with a specific modeling equation. One general approach to inversion is to use optimization methods which are algebraic in nature to define an objective function. ... More

L0+L1+L2 mixed optimization: a geometric approach to seismic imaging and inversion using concepts in topology and semigroupJul 12 2010The mathematical interpretation of L0, L1 and L2 is needed to understand how we should use these norms for optimization problems. The L0 norm is combinatorics which is counting certain properties of an object or an operator. This is the least amplitude ... More

Quantitative and Qualitative Seismic Imaging and Seismic InversionJun 16 2017We consider seismic imaging to include seismic inversion. Imaging could use approximate operator or time instead of depth. Processing in time is an important part of seismic imaging as well as processing in depth. We can classify seismic imaging as quantitative ... More

Seismic Solvability ProblemsDec 06 2012Classical approach of solvability problem has shed much light on what we can solve and what we cannot solve mathematically. Starting with quadratic equation, we know that we can solve it by the quadratic formula which uses square root. Polynomial is a ... More

On Anomaly Identification and the Counterfeit Coin ProblemMay 01 2009We address a well-known problem in combinatorics involving the identification of counterfeit coins with a systematic approach. The methodology can be applied to cases where the total number of coins is exceedingly large such that brute force or enumerative ... More

The Googly Amplitudes in Gauge TheoryMar 10 2004The googly amplitudes in gauge theory are computed by using the off shell MHV vertices with the newly proposed rules of Cachazo, Svrcek and Witten. The result is in agreement with the previously well-known results. In particular we also obtain a simple ... More

A Self-tuning Exact Solution and the Non-existence of Horizons in 5d Gravity-Scalar SystemMay 25 2000Jun 24 2000We present an exact thick domain wall solution with naked sigularities to five dimensional gravity coupled with a scalar field with exponential potential. In our solution we found exactly the special coefficient of the exponent as coming from compactification ... More

The BRST quantization of the nonlinear $WB_2$ and $W_4$ algebrasJun 04 1993Jun 11 1993We construct the BRST operator for the nonlinear $WB_2$ and $W_4$ algebras. Contrary to the general belief, the nilpotent condition of the BRST operator doesn't determine all the coefficients. We find a three and seven parameter family of nilpotent BRST ... More

A Formula for Multi-Loop 4-Particle Amplitude in Superstring TheoryMar 01 2005Based on the recent developments of explicit computations at 2 loops in superstring theory in the covariant RNS formalism, we propose an explicit formula for the arbitrary loop 4-particle amplitude in superstring theory. We prove that this formula passes ... More

Transformation Semigroup and Complex Topology: a study of inversion with increasing complexityAug 11 2010This paper is a continuation of our 2005 paper on complex topology and its implication on invertibility (or non-invertibility). In this paper, we will try to classify the complexity of inversion into 3 different classes. We will use synthetic models based ... More

Edge-following topological statesAug 26 2019Aug 28 2019We prove that Chern insulators have topologically protected edge states which not only propagate unidirectionally along a straight line boundary, but also swerve around arbitrary-angled corners and geometric imperfections of the material boundary. This ... More

On the Alternative Relaying Diamond Channel with Conferencing LinksFeb 03 2012May 05 2012In this paper, the diamond relay channel is considered, which consists of one source-destination pair and two relay nodes connected with rate-limited out-of-band conferencing links. In particular, we focus on the half-duplex alternative relaying strategy, ... More

Solvability by semigroup : Application to seismic imaging with complex decomposition of wave equations and migration operators with idempotentsJan 28 2011The classical approach of solvability using group theory is well known and one original motivation is to solve polynomials by radicals. Radicals are square, cube, square root, cube root etc of the original coefficients for the polynomial. A polynomial ... More

Practical approach to solvability: Geophysical application using complex decomposition into simple part (solvable) and complex part (interpretable) for seismic imagingDec 02 2010The classical approach to solvability of a mathematical problem is to define a method which includes certain rules of operation or algorithms. Then using the defined method, one can show that some problems are solvable or not solvable or undecidable depending ... More

Two-Loop Computation in Superstring TheoryJan 06 2003In this paper I review some old and new works on the computation of two-loop 4-particle amplitude in superstring theory. I also present the proof by Iengo, showing the vanishing of the term related to the two-loop correction to the $R^4$ term. Finally ... More

A quick estimation of luminosity function based on the luminosity-distance diagramJan 12 2017Based on the luminosity-distance diagram, we propose a method to quickly estimate the luminosity function for any certain astrophysical objects. Giving the mean distance between any two objects at a given luminosity range, we can find the relation between ... More

Dynamics of weighted translations on Orlicz spacesAug 17 2018Let $G$ be a locally compact group, and let $\Phi$ be a Young function. In this paper, we give sufficient and necessary conditions for weighted translation operators on the Orlicz space $L^\Phi(G)$ to be chaotic and topologically multiply recurrent. In ... More

Direct and indirect seismic inversion: interpretation of certain mathematical theoremsNov 04 2017Quantitative methods are more familiar to most geophysicists with direct inversion or indirect inversion. We will discuss seismic inversion in a high level sense without getting into the actual algorithms. We will stay with meta-equations and argue pros ... More

The Complete structure of the nonlinear $W_4$ and $W_5$ algebras from quantum Miura transformationJun 04 1993Jun 11 1993Starting from the well-known quantum Miura transformation for the Lie algebra $A_n$, we compute explicitly the OPEs for $n=3$ and 4. The primary fields with spin 3, 4 and 5 are found (for general $n$). By using these primary fields and the OPEs from quantum ... More

Bifidelity data-assisted neural networks in nonintrusive reduced-order modelingFeb 01 2019Feb 05 2019In this paper, we present a new nonintrusive reduced basis method when a cheap low-fidelity model and expensive high-fidelity model are available. The method relies on proper orthogonal decomposition (POD) to generate the high-fidelity reduced basis and ... More

Evolution of Electronic Structure in Atomically Thin Sheets of WS2 and WSe2Dec 21 2012Geometrical confinement effect in exfoliated sheets of layered materials leads to significant evolution of energy dispersion with decreasing layer thickness. Molybdenum disulphide (MoS2) was recently found to exhibit indirect to direct gap transition ... More

Atomically Thin Resonant Tunnel Diodes built from Synthetic van der Waals HeterostructuresMar 18 2015Vertical integration of two-dimensional van der Waals materials is predicted to lead to novel electronic and optical properties not found in the constituent layers. Here, we present the direct synthesis of two unique, atomically thin, multi-junction heterostructures ... More

Realization of Probabilistic Identification and Clone of Quantum-States II Multiparticles SystemJul 31 1999We realize the probabilistic cloning and identifying linear independent quantum states of multi-particles system, given prior probability, with universal quantum logic gates using the method of unitary representation. Our result is universal for separate ... More

Lattice study on kaon nucleon scattering length in the I=1 channelSep 12 2003Nov 14 2003Using the tadpole improved clover Wilson quark action on small, coarse and anisotropic lattices, $KN$ scattering length in the I=1 channel is calculated within quenched approximation. The results are extrapolated towards the chiral and physical kaon mass ... More

Radiatively scotogenic type-II seesaw and a relevant phenomenological analysisJun 25 2019When a small vacuum expectation value of Higgs triplet ($v_\Delta$) in the type-II seesaw model is required to explain neutrino oscillation data, a fine-tuning issue occurs on the mass-dimension lepton-number-violation (LNV) scalar coupling. Using the ... More

Entanglement as the symmetric portion of correlated coherenceMay 28 2018We show that the symmetric portion of correlated coherence is always a valid quantifier of entanglement, and that this property is independent of the particular choice of coherence measure. This leads to an infinitely large class of coherence based entanglement ... More

Nonclassical Light and Metrological Power: An Introductory ReviewSep 03 2019In this review, we introduce the notion of quantum nonclassicality of light, and the role of nonclassicality in optical quantum metrology. The first part of the paper focuses on defining and characterizing the notion of nonclassicality and how it may ... More

Kernel Transformer Networks for Compact Spherical ConvolutionDec 07 2018Apr 09 2019Ideally, 360{\deg} imagery could inherit the deep convolutional neural networks (CNNs) already trained with great success on perspective projection images. However, existing methods to transfer CNNs from perspective to spherical images introduce significant ... More

Learning Spherical Convolution for Fast Features from 360° ImageryAug 02 2017Dec 07 2018While 360{\deg} cameras offer tremendous new possibilities in vision, graphics, and augmented reality, the spherical images they produce make core feature extraction non-trivial. Convolutional neural networks (CNNs) trained on images from perspective ... More

A hybrid LBM-DEM numerical approach with an improved immersed moving boundary method for complex particle-liquid flows involving adhesive particlesJan 28 2019This paper presents a hybrid numerical framework for modelling solid-liquid flow with particle adhesion based on a coupled single-relaxation-time lattice Boltzmann method (LBM) and a discrete element method (DEM) for adhesive particles. The LBM is implemented ... More

Lorentz Factor Constraint from the very early external shock of the gamma-ray burst ejectaAug 30 2009While it is generally agreed that the emitting regions in Gamma-Ray Bursts (GRBs) move ultra relativistically towards the observer, different estimates of the initial Lorentz factors, $\Gamma_0$, lead to different, at times conflicting estimates. We show ... More

Good Wannier bases in Hilbert modules associated to topological insulatorsApr 30 2019For a large class of physically relevant operators on a manifold with discrete group action, we prove general results on the existence of a basis of smooth well-localised Wannier functions for their spectral subspaces. This turns out to be equivalent ... More

Lattice study on kaon pion scattering length in the $I=3/2$ channelMar 28 2004Using the tadpole improved Wilson quark action on small, coarse and anisotropic lattices, $K\pi$ scattering length in the $I=3/2$ channel is calculated within quenched approximation. The results are extrapolated towards the chiral and physical kaon mass ... More

Internal particle width effects on the the triangle singularity mechanism in the study of the $η(1405)$ and $η(1475)$ puzzleMay 10 2019Jul 25 2019In this article, the analyticity of triangle loop integral with complex masses of internal particles is discussed in a new perspective, base on which we obtain the explicit width dependence of the absorptive part of the triangle amplitude. We reanalyze ... More