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Individualized Group LearningJun 13 2019Many massive data are assembled through collections of information of a large number of individuals in a population. The analysis of such data, especially in the aspect of individualized inferences and solutions, has the potential to create significant ... More

Reinforcement Learning for Nested Polar Code ConstructionApr 16 2019In this paper, we model nested polar code construction as a Markov decision process (MDP), and tackle it with advanced reinforcement learning (RL) techniques. First, an MDP environment with state, action, and reward is defined in the context of polar ... More

Faster Algorithms for High-Dimensional Robust Covariance EstimationJun 11 2019We study the problem of estimating the covariance matrix of a high-dimensional distribution when a small constant fraction of the samples can be arbitrarily corrupted. Recent work gave the first polynomial time algorithms for this problem with near-optimal ... More

Minimal Realization Problems for Hidden Markov ModelsNov 13 2014Dec 14 2015Consider a stationary discrete random process with alphabet size d, which is assumed to be the output process of an unknown stationary Hidden Markov Model (HMM). Given the joint probabilities of finite length strings of the process, we are interested ... More

Intersecting Faces: Non-negative Matrix Factorization With New GuaranteesJul 08 2015Non-negative matrix factorization (NMF) is a natural model of admixture and is widely used in science and engineering. A plethora of algorithms have been developed to tackle NMF, but due to the non-convex nature of the problem, there is little guarantee ... More

Non-Convex Matrix Completion Against a Semi-Random AdversaryMar 28 2018Sep 07 2018Matrix completion is a well-studied problem with many machine learning applications. In practice, the problem is often solved by non-convex optimization algorithms. However, the current theoretical analysis for non-convex algorithms relies heavily on ... More

Rich Component AnalysisJul 14 2015In many settings, we have multiple data sets (also called views) that capture different and overlapping aspects of the same phenomenon. We are often interested in finding patterns that are unique to one or to a subset of the views. For example, we might ... More

Explaining Landscape Connectivity of Low-cost Solutions for Multilayer NetsJun 14 2019Mode connectivity is a surprising phenomenon in the loss landscape of deep nets. Optima---at least those discovered by gradient-based optimization---turn out to be connected by simple paths on which the loss function is almost constant. Often, these paths ... More

Pulse phase-resolved analysis of SMC X-3 during its 2016--2017 super-Eddington outburstJan 08 2018The Be X-ray pulsar SMC X-3 underwent an extra long and ultraluminous giant outburst from 2016 August to 2017 March. The peak X-ray luminosity is up to $\sim 10^{39}$ erg/s, suggesting a mildly super-Eddington accretion onto the strongly magnetized neutron ... More

On the Optimization Landscape of Tensor DecompositionsJun 18 2017Non-convex optimization with local search heuristics has been widely used in machine learning, achieving many state-of-art results. It becomes increasingly important to understand why they can work for these NP-hard problems on typical data. The landscape ... More

Efficient approaches for escaping higher order saddle points in non-convex optimizationFeb 18 2016Local search heuristics for non-convex optimizations are popular in applied machine learning. However, in general it is hard to guarantee that such algorithms even converge to a local minimum, due to the existence of complicated saddle point structures ... More

Decomposing Overcomplete 3rd Order Tensors using Sum-of-Squares AlgorithmsApr 21 2015Tensor rank and low-rank tensor decompositions have many applications in learning and complexity theory. Most known algorithms use unfoldings of tensors and can only handle rank up to $n^{\lfloor p/2 \rfloor}$ for a $p$-th order tensor in $\mathbb{R}^{n^p}$. ... More

Understanding Composition of Word Embeddings via Tensor DecompositionFeb 02 2019Word embedding is a powerful tool in natural language processing. In this paper we consider the problem of word embedding composition \--- given vector representations of two words, compute a vector for the entire phrase. We give a generative model that ... More

A Practical Algorithm for Topic Modeling with Provable GuaranteesDec 19 2012Topic models provide a useful method for dimensionality reduction and exploratory data analysis in large text corpora. Most approaches to topic model inference have been based on a maximum likelihood objective. Efficient algorithms exist that approximate ... More

Mollow "quintuplets" from coherently-excited quantum dotsFeb 14 2013Charge-neutral excitons in semiconductor quantum dots have a small finite energy separation caused by the anisotropic exchange splitting. Coherent excitation of neutral excitons will generally excite both exciton components, unless the excitation is parallel ... More

Stochastic Gradient Descent Escapes Saddle Points EfficientlyFeb 13 2019This paper considers the perturbed stochastic gradient descent algorithm and shows that it finds $\epsilon$-second order stationary points ($\left\|\nabla f(x)\right\|\leq \epsilon$ and $\nabla^2 f(x) \succeq -\sqrt{\epsilon} \mathbf{I}$) in $\tilde{O}(d/\epsilon^4)$ ... More

Realistic Channel Models Pre-trainingJul 22 2019In this paper, we propose a neural-network-based realistic channel model with both the similar accuracy as deterministic channel models and uniformity as stochastic channel models. To facilitate this realistic channel modeling, a multi-domain channel ... More

Violation of Leggett-Garg inequalities in single quantum dotOct 25 2011Oct 26 2011We investigate the violation of Leggett-Garg (LG) inequalities inquantum dots with the stationarity assumption. By comparing two types of LG inequalities, we find a better one which is easier to be tested in experiment. In addition, we show that the fine-structure ... More

Quasinormal mode theory and modelling of electron energy loss spectroscopy for plasmonic nanostructuresOct 05 2015Mar 20 2016Understanding light-matter interactions using localized surface plasmons (LSPs) is of fundamental interest in classical and quantum plasmonics and has a wide range of applications. In order to understand the spatial properties of LSPs, electron energy ... More

Design of an efficient single photon source from a metallic nanorod dimer: a quasinormal mode finite-difference time-domain approachJan 23 2015We describe how the finite-difference time-domain (FDTD) technique can be used to compute the quasinormal mode (QNM) for metallic nano-resonators, which is important for describing and understanding light-matter interactions in nanoplasmonics. We use ... More

Quantum dynamics of two quantum dots coupled through localized plasmons: An intuitive and accurate quantum optics approach using quasinormal modesMay 08 2015Nov 17 2015We study the quantum dynamics of two quantum dots (QDs) or artificial atoms coupled through the fundamental localized plasmon of a gold nanorod resonator. We derive an intuitive and efficient time-local master equation, in which the effect of the metal ... More

Swift observations of SMC X-3 during its 2016-2017 super-Eddington outburstJan 11 2017Jun 02 2017The Be X-ray pulsar, SMC X-3 underwent a giant outburst from 2016 August to 2017 March, which was monitored with the Swift satellite. During the outburst, its broadband flux increased dramatically, and the unabsorbed X-ray luminosity reached an extreme ... More

Towards a better approximation for sparsest cut?Apr 11 2013We give a new $(1+\epsilon)$-approximation for sparsest cut problem on graphs where small sets expand significantly more than the sparsest cut (sets of size $n/r$ expand by a factor $\sqrt{\log n\log r}$ bigger, for some small $r$; this condition holds ... More

Beyond Log-concavity: Provable Guarantees for Sampling Multi-modal Distributions using Simulated Tempering Langevin Monte CarloOct 07 2017Nov 06 2017A key task in Bayesian statistics is sampling from distributions that are only specified up to a partition function (i.e., constant of proportionality). However, without any assumptions, sampling (even approximately) can be #P-hard, and few works have ... More

Learning One-hidden-layer Neural Networks with Landscape DesignNov 01 2017Nov 03 2017We consider the problem of learning a one-hidden-layer neural network: we assume the input $x\in \mathbb{R}^d$ is from Gaussian distribution and the label $y = a^\top \sigma(Bx) + \xi$, where $a$ is a nonnegative vector in $\mathbb{R}^m$ with $m\le d$, ... More

Analyzing Tensor Power Method Dynamics in Overcomplete RegimeNov 06 2014Sep 14 2015We present a novel analysis of the dynamics of tensor power iterations in the overcomplete regime where the tensor CP rank is larger than the input dimension. Finding the CP decomposition of an overcomplete tensor is NP-hard in general. We consider the ... More

No Spurious Local Minima in Nonconvex Low Rank Problems: A Unified Geometric AnalysisApr 03 2017In this paper we develop a new framework that captures the common landscape underlying the common non-convex low-rank matrix problems including matrix sensing, matrix completion and robust PCA. In particular, we show for all above problems (including ... More

Learning Topic Models - Going beyond SVDApr 09 2012Apr 10 2012Topic Modeling is an approach used for automatic comprehension and classification of data in a variety of settings, and perhaps the canonical application is in uncovering thematic structure in a corpus of documents. A number of foundational works both ... More

Learning Mixtures of Gaussians in High DimensionsMar 02 2015Mar 10 2015Efficiently learning mixture of Gaussians is a fundamental problem in statistics and learning theory. Given samples coming from a random one out of k Gaussian distributions in Rn, the learning problem asks to estimate the means and the covariance matrices ... More

Matrix Completion has No Spurious Local MinimumMay 24 2016Sep 16 2016Matrix completion is a basic machine learning problem that has wide applications, especially in collaborative filtering and recommender systems. Simple non-convex optimization algorithms are popular and effective in practice. Despite recent progress in ... More

Simulated Tempering Langevin Monte Carlo II: An Improved Proof using Soft Markov Chain DecompositionNov 29 2018A key task in Bayesian machine learning is sampling from distributions that are only specified up to a partition function (i.e., constant of proportionality). One prevalent example of this is sampling posteriors in parametric distributions, such as latent-variable ... More

Sample Complexity Analysis for Learning Overcomplete Latent Variable Models through Tensor MethodsAug 03 2014Dec 16 2014We provide guarantees for learning latent variable models emphasizing on the overcomplete regime, where the dimensionality of the latent space can exceed the observed dimensionality. In particular, we consider multiview mixtures, spherical Gaussian mixtures, ... More

Guaranteed Non-Orthogonal Tensor Decomposition via Alternating Rank-$1$ UpdatesFeb 21 2014Mar 04 2015In this paper, we provide local and global convergence guarantees for recovering CP (Candecomp/Parafac) tensor decomposition. The main step of the proposed algorithm is a simple alternating rank-$1$ update which is the alternating version of the tensor ... More

High-Dimensional Robust Mean Estimation in Nearly-Linear TimeNov 23 2018We study the fundamental problem of high-dimensional mean estimation in a robust model where a constant fraction of the samples are adversarially corrupted. Recent work gave the first polynomial time algorithms for this problem with dimension-independent ... More

$β$-expansion: A Theoretical Framework for Fast and Recursive Construction of Polar CodesApr 19 2017In this work, we introduce $\beta$-expansion, a notion borrowed from number theory, as a theoretical framework to study fast construction of polar codes based on a recursive structure of universal partial order (UPO) and polarization weight (PW) algorithm. ... More

Matrix Completion has No Spurious Local MinimumMay 24 2016Jul 22 2018Matrix completion is a basic machine learning problem that has wide applications, especially in collaborative filtering and recommender systems. Simple non-convex optimization algorithms are popular and effective in practice. Despite recent progress in ... More

New Algorithms for Learning Incoherent and Overcomplete DictionariesAug 28 2013May 26 2014In sparse recovery we are given a matrix $A$ (the dictionary) and a vector of the form $A X$ where $X$ is sparse, and the goal is to recover $X$. This is a central notion in signal processing, statistics and machine learning. But in applications such ... More

Conditional estimates on small distances between ordinates of zeros of $ζ(s)$ and $ζ'(s)$Apr 14 2016Let $\beta'+i\gamma'$ be a zero of $\zeta'(s)$. In \cite{GYi} Garaev and Y{\i}ld{\i}r{\i}m proved that there is a zero $\beta+i\gamma$ of $\zeta(s)$ with $ \gamma'-\gamma \ll \sqrt{|\beta'-1/2|} $. Assuming RH, we improve this bound by saving a factor ... More

Sublunar-Mass Primordial Black Holes from Closed Axion Domain WallsMay 29 2019We study the formation of primordial black holes (PBHs) from the collapse of closed domain walls (DWs) which naturally arise in QCD axion models near QCD scale as part of the string-wall network. Size distribution of the closed DWs is determined by percolation ... More

DDVV-type inequality for skew-symmetric matrices and Simons-type inequality for Riemannian submersionsSep 30 2011Mar 12 2013In this paper, we will first derive a DDVV-type optimal inequality for real skew-symmetric matrices, then we apply it to establish a Simons-type integral inequality for Riemannian submersions with totally geodesic fibres and Yang-Mills horizontal distributions. ... More

Improved Accent Classification Combining Phonetic Vowels with Acoustic FeaturesFeb 24 2016Researches have shown accent classification can be improved by integrating semantic information into pure acoustic approach. In this work, we combine phonetic knowledge, such as vowels, with enhanced acoustic features to build an improved accent classification ... More

First CT-MRI Scanner for Multi-dimensional Synchrony and Multi-physical CouplingFeb 11 2014We propose to prototype the first CT-MRI scanner for radiation therapy and basic research, demonstrate its transformative biomedical potential, and initiate a paradigm shift in multimodality imaging. Our design consists of a double donut-shaped pair of ... More

Integral Basis Theorem of cyclotomic Khovanov-Lauda-Rouquier algebras of Type ADec 11 2014In this paper we prove that the cyclotomic Khovanov-Lauda-Rouquier algebras in type A, $\mathscr R_n^\Lambda$, are $\mathbb{Z}$-free. We then extend the graded cellular basis of $\mathscr R_n^\Lambda$ constructed by Hu and Mathas to $\mathscr R_n$ and ... More

Constructing the scattering matrix for optical microcavities as a nonlocal boundary value problemAug 16 2017We develop a numerical scheme to construct the scattering ($S$) matrix for optical microcavities, including the special cases with parity-time and other non-Hermitian symmetries. This scheme incorporates the explicit form of a nonlocal boundary condition, ... More

Mode Selection and Single-mode Lasing by Active Transformation OpticsAug 20 2014Nov 17 2015Using the correspondence between (saturated) nonlinear and (unsaturated) linear dielectric constants, we propose a simple and systematic method to achieve selective excitation of lasing modes that would have been dwarfed by more dominant ones of lower ... More

A splitting property for subalgebras of tensor productsJan 01 1995We prove a basic result about tensor products of a $\text{II}_1$ factor with a finite von Neumann algebra and use it to answer, affirmatively, a question asked by S. Popa about maximal injective factors.

Soul Theorem for 4-dimensional Topologically Regular Open Nonnegatively Curved Alexandrov SpacesOct 09 2010In this paper, we study the topology of topologically regular 4-dimensional open non-negatively curved Alexandrov spaces. These spaces occur naturally as the blow-up limits of compact Riemannian manifolds with lower curvature bound. These manifolds have ... More

Homotopy Analysis for Tensor PCAOct 28 2016Nov 02 2016Developing efficient and guaranteed nonconvex algorithms has been an important challenge in modern machine learning. Algorithms with good empirical performance such as stochastic gradient descent often lack theoretical guarantees. In this paper, we analyze ... More

Un-regularizing: approximate proximal point and faster stochastic algorithms for empirical risk minimizationJun 24 2015We develop a family of accelerated stochastic algorithms that minimize sums of convex functions. Our algorithms improve upon the fastest running time for empirical risk minimization (ERM), and in particular linear least-squares regression, across a wide ... More

Online Service with DelayAug 18 2017In this paper, we introduce the online service with delay problem. In this problem, there are $n$ points in a metric space that issue service requests over time, and a server that serves these requests. The goal is to minimize the sum of distance traveled ... More

Stronger generalization bounds for deep nets via a compression approachFeb 14 2018Nov 26 2018Deep nets generalize well despite having more parameters than the number of training samples. Recent works try to give an explanation using PAC-Bayes and Margin-based analyses, but do not as yet result in sample complexity bounds better than naive parameter ... More

Escaping From Saddle Points --- Online Stochastic Gradient for Tensor DecompositionMar 06 2015We analyze stochastic gradient descent for optimizing non-convex functions. In many cases for non-convex functions the goal is to find a reasonable local minimum, and the main concern is that gradient updates are trapped in saddle points. In this paper ... More

Competing with the Empirical Risk Minimizer in a Single PassDec 20 2014Feb 25 2015In many estimation problems, e.g. linear and logistic regression, we wish to minimize an unknown objective given only unbiased samples of the objective function. Furthermore, we aim to achieve this using as few samples as possible. In the absence of computational ... More

On the Local Minima of the Empirical RiskMar 25 2018Oct 17 2018Population risk is always of primary interest in machine learning; however, learning algorithms only have access to the empirical risk. Even for applications with nonconvex nonsmooth losses (such as modern deep networks), the population risk is generally ... More

Normalization of quasinormal modes in leaky optical cavities and plasmonic resonatorsJan 23 2015Dec 02 2015We discuss three formally different formulas for normalization of quasinormal modes currently in use for modeling optical cavities and plasmonic resonators and show that they are complementary and provide the same result. Regardless of the formula used ... More

The Step Decay Schedule: A Near Optimal, Geometrically Decaying Learning Rate ProcedureApr 29 2019There is a stark disparity between the step size schedules used in practical large scale machine learning and those that are considered optimal by the theory of stochastic approximation. In theory, most results utilize polynomially decaying learning rate ... More

DynIMS: A Dynamic Memory Controller for In-memory Storage on HPC SystemsSep 29 2016In order to boost the performance of data-intensive computing on HPC systems, in-memory computing frameworks, such as Apache Spark and Flink, use local DRAM for data storage. Optimizing the memory allocation to data storage is critical to delivering performance ... More

Efficient Quantum RatchetJun 16 2012Quantum resonance is one of the main characteristics of the quantum kicked rotor, which has been used to induce accelerated ratchet current of the particles with a generalized asymmetry potential. Here we show that by desynchronizing the kicked potentials ... More

Simple, Efficient, and Neural Algorithms for Sparse CodingMar 02 2015Sparse coding is a basic task in many fields including signal processing, neuroscience and machine learning where the goal is to learn a basis that enables a sparse representation of a given set of data, if one exists. Its standard formulation is as a ... More

Provable ICA with Unknown Gaussian Noise, and Implications for Gaussian Mixtures and AutoencodersJun 23 2012Nov 12 2012We present a new algorithm for Independent Component Analysis (ICA) which has provable performance guarantees. In particular, suppose we are given samples of the form $y = Ax + \eta$ where $A$ is an unknown $n \times n$ matrix and $x$ is a random variable ... More

Finding Overlapping Communities in Social Networks: Toward a Rigorous ApproachDec 08 2011A "community" in a social network is usually understood to be a group of nodes more densely connected with each other than with the rest of the network. This is an important concept in most domains where networks arise: social, technological, biological, ... More

Provable Algorithms for Inference in Topic ModelsMay 27 2016Recently, there has been considerable progress on designing algorithms with provable guarantees -- typically using linear algebraic methods -- for parameter learning in latent variable models. But designing provable algorithms for inference has proven ... More

Reply to "Comment on "Normalization of quasinormal modes in leaky optical cavities and plasmonic resonators" " by E. A. Muljarov and W. LangbeinMay 16 2016We refute all claims of the "Comment on "Normalization of quasinormal modes in leaky optical cavities and plasmonic resonators" " by E. A. Muljarov and W. Langbein (arXiv:1602.07278v1). Based entirely on information already contained in our original article ... More

Quasi-normal mode approach to the local-field problem in quantum opticsJan 23 2015Apr 13 2015The local-field (LF) problem of a finite-size dipole emit- ter radiating inside a lossy inhomogeneous structure is a long-standing and challenging quantum optical problem, and it now is becoming more important due to rapid advances in solid-state fabrication ... More

Common Origin of Soft mu-tau and CP Breaking in Neutrino Seesaw and the Origin of MatterJan 06 2010Apr 01 2010Neutrino oscillation data strongly support mu-tau symmetry as a good approximate flavor symmetry of the neutrino sector, which has to appear in any viable theory for neutrino mass-generation. The mu-tau breaking is not only small, but also the source ... More

Provable Bounds for Learning Some Deep RepresentationsOct 23 2013We give algorithms with provable guarantees that learn a class of deep nets in the generative model view popularized by Hinton and others. Our generative model is an $n$ node multilayer neural net that has degree at most $n^{\gamma}$ for some $\gamma ... More

On the ability of neural nets to express distributionsFeb 22 2017Jun 02 2017Deep neural nets have caused a revolution in many classification tasks. A related ongoing revolution---also theoretically not understood---concerns their ability to serve as generative models for complicated types of data such as images and texts. These ... More

Computing a Nonnegative Matrix Factorization -- ProvablyNov 03 2011In the Nonnegative Matrix Factorization (NMF) problem we are given an $n \times m$ nonnegative matrix $M$ and an integer $r > 0$. Our goal is to express $M$ as $A W$ where $A$ and $W$ are nonnegative matrices of size $n \times r$ and $r \times m$ respectively. ... More

Stabilized SVRG: Simple Variance Reduction for Nonconvex OptimizationMay 01 2019Variance reduction techniques like SVRG provide simple and fast algorithms for optimizing a convex finite-sum objective. For nonconvex objectives, these techniques can also find a first-order stationary point (with small gradient). However, in nonconvex ... More

Learning Two-layer Neural Networks with Symmetric InputsOct 16 2018Feb 03 2019We give a new algorithm for learning a two-layer neural network under a general class of input distributions. Assuming there is a ground-truth two-layer network $$ y = A \sigma(Wx) + \xi, $$ where $A,W$ are weight matrices, $\xi$ represents noise, and ... More

AI Coding: Learning to Construct Error Correction CodesJan 17 2019In this paper, we investigate an artificial-intelligence (AI) driven approach to design error correction codes (ECC). Classic error correction code was designed upon coding theory that typically defines code properties (e.g., hamming distance, subchannel ... More

Global Convergence of Policy Gradient Methods for the Linear Quadratic RegulatorJan 15 2018Oct 21 2018Direct policy gradient methods for reinforcement learning and continuous control problems are a popular approach for a variety of reasons: 1) they are easy to implement without explicit knowledge of the underlying model 2) they are an "end-to-end" approach, ... More

Homotopy Analysis for Tensor PCAOct 28 2016Jun 14 2017Developing efficient and guaranteed nonconvex algorithms has been an important challenge in modern machine learning. Algorithms with good empirical performance such as stochastic gradient descent often lack theoretical guarantees. In this paper, we analyze ... More

Spin dynamics in the XY modelOct 18 2010Oct 21 2010We study the evolution of entanglement, quantum correlation and classical correlation for the one dimensional XY model in external transverse magnetic field. The system is initialized in the full polarized state along the z axis, after annealing, different ... More

Global Convergence of Policy Gradient Methods for the Linear Quadratic RegulatorJan 15 2018Mar 23 2019Direct policy gradient methods for reinforcement learning and continuous control problems are a popular approach for a variety of reasons: 1) they are easy to implement without explicit knowledge of the underlying model 2) they are an "end-to-end" approach, ... More

Generalization and Equilibrium in Generative Adversarial Nets (GANs)Mar 02 2017Aug 01 2017We show that training of generative adversarial network (GAN) may not have good generalization properties; e.g., training may appear successful but the trained distribution may be far from target distribution in standard metrics. However, generalization ... More

Provable learning of Noisy-or NetworksDec 28 2016Many machine learning applications use latent variable models to explain structure in data, whereby visible variables (= coordinates of the given datapoint) are explained as a probabilistic function of some hidden variables. Finding parameters with the ... More

More Algorithms for Provable Dictionary LearningJan 03 2014In dictionary learning, also known as sparse coding, the algorithm is given samples of the form $y = Ax$ where $x\in \mathbb{R}^m$ is an unknown random sparse vector and $A$ is an unknown dictionary matrix in $\mathbb{R}^{n\times m}$ (usually $m > n$, ... More

A Tensor Approach to Learning Mixed Membership Community ModelsFeb 12 2013Oct 24 2013Community detection is the task of detecting hidden communities from observed interactions. Guaranteed community detection has so far been mostly limited to models with non-overlapping communities such as the stochastic block model. In this paper, we ... More

On the canonical maps of nonsingular threefolds of general typeDec 21 2016Dec 28 2016Let $S$ be a nonsingular minimal complex projective surface of general type and the canonical map of $S$ is generically finite. Beauville showed that the geometric genus of the image of the canonical map is vanishing or equals the geometric genus of $S$ ... More

Smooth solution to higher dimensional complex Plateau problemDec 07 2017Dec 14 2017Let $X$ be a compact connected strongly pseudoconvex $CR$ manifold of real dimension $2n-1$ in $\mathbb{C}^{N}$. For $n\ge 3$, Yau solved the complex Plateau problem of hypersurface type by checking a bunch of Kohn-Rossi cohomology groups in 1981. In ... More

The Briot-Bouquet systems and the center families for holomorphic dynamical systemsJul 15 2013We give a complete solution to the existence of isochronous center families for holomorphic dynamical systems. The study of center families for n-dimensional holomorphic dynamical systems naturally leads to the study of (n-1)-dimensional Briot-Bouquet ... More

On automorphisms of quasi-circular domains fixing the originMar 30 2014Jan 27 2015It is known that automorphisms of quasi-circular domains fixing the origin are polynomial mappings. By introducing the so-called resonance order and quasi-resonance order, we provide a uniform upper bound for the degree of such polynomial automorphisms. ... More

Localisation, Communication and Networking with VLC: Challenges and OpportunitiesSep 06 2017The forthcoming Fifth Generation (5G) era raises the expectation for ubiquitous wireless connectivity to enhance human experiences in information and knowledge sharing as well as in entertainment and social interactions. The promising Visible Light Communications ... More

Gradient-based Sampling: An Adaptive Importance Sampling for Least-squaresMar 02 2018In modern data analysis, random sampling is an efficient and widely-used strategy to overcome the computational difficulties brought by large sample size. In previous studies, researchers conducted random sampling which is according to the input data ... More

Recent Experimental Results on Leptonic $D^+_{(s)}$ Decays, Semileptonic $D$ Decays and Extraction of $|V_{cd(s)}|$Nov 14 2014The recent experimental results on leptonic $D^+_{(s)}$ decays, semileptonic $D$ decays, determinations of decay constants and form factors, as well as extractions of $|V_{cd}|$ and $|V_{cs}|$ are briefly reviewed. Global analysis of all existing measurements ... More

Programmatic Control of a Compiler for Generating High-performance Spatial HardwareNov 21 2017Dec 13 2017This methodology paper addresses high-performance high-productivity programming on spatial architectures. Spatial architectures are efficient for executing dataflow algorithms, yet for high-performance programming, the productivity is low and verification ... More

Review and Report on Results of Leptonic Decays of $D^+$ and $D^+_s$ MesonsSep 01 2012In the last 25 years, many $e^+e^-$ experiments and fixed-target experiments performed to search for and study the leptonic decays of the $D^+$ and $D^+_s$ mesons. By 2012, more than 530 signal events of the $D^+$ leptonic decays and about $4\times10^3$ ... More

Recent Bes Results on psi(3770) and D Meson Production and DecayJun 10 2004Using a data sample of 17.7 $\rm pb^{-1}$ collected at 3.773 GeV with the BES-II detector at the BEPC, the cross sections for $D^0 \bar D^{0}$ and $D^+D^-$ productions at 3.773 GeV have been measured. From the data sample about 33 $\rm pb^{-1}$ taken ... More

The Fatou Set for Critically Finite MapsAug 19 2006It is a classical result in complex dynamics of one variable that the Fatou set for a critically finite map on $\mathbf{P}^1$ consists of only basins of attraction for superattracting periodic points. In this paper we deal with critically finite maps ... More

Attractors on $\mathbf{P}^k$Oct 29 2005Aug 21 2006We show that special perturbations of a particular holomorphic map on $\mathbf{P}^k$ give us examples of maps that possess chaotic nonalgebraic attractors. Furthermore, we study the dynamics of the maps on the attractors. In particular, we construct invariant ... More

PP-wave String Interactions from String Bit ModelAug 30 2002Nov 27 2002We construct the string states $|O_{p}^J>_J$, $|O_{q}^{J_1}>_{{J_1}{J_2}}$ and $|O_{0}^{J_{1}J_{2}}>_{{J_1}{J_2}}$ in the Hilbert space of the quantum mechanical orbifold model so as to calculate the three point functions and the matrix elements of the ... More

Perturbative and non-perturbative parts of eigenstates and local spectral density of states: the Wigner band random matrix modelDec 07 1998A generalization of Brillouin-Wigner perturbation theory is applied numerically to the Wigner Band Random Matrix model. The perturbation theory tells that a perturbed energy eigenstate can be divided into a perturbative part and a non-perturbative part ... More

X-ray Fluorescence SectioningOct 26 2012In this paper, we propose an x-ray fluorescence imaging system for elemental analysis. The key idea is what we call "x-ray fluorescence sectioning". Specifically, a slit collimator in front of an x-ray tube is used to shape x-rays into a fan-beam to illuminate ... More

Comment on "Atomic Scale Structure and Chemical Composition across Order-Disorder Interfaces"Feb 17 2011Interfaces have long been known to be the key to many mechanical and electric properties. To nickel base superalloys which have perfect creep and fatigue properties and have been widely used as materials of turbine blades, interfaces determine the strengthening ... More

A New Class of Solvable Many-Body ProblemsOct 02 2012A new class of solvable $N$-body problems is identified. They describe $N$ unit-mass point particles whose time-evolution, generally taking place in the complex plane, is characterized by Newtonian equations of motion "of goldfish type" (acceleration ... More

Precise measurement of coupling strength and high temperature quantum effect in a nonlinearly coupled qubit-oscillator systemAug 05 2017Jan 16 2018We study the coherence dynamics of a qubit coupled to a harmonic oscillator with both linear and quadratic interactions. As long as the linear coupling strength is much smaller than the oscillator frequency, the long time behavior of the coherence is ... More

Ground states of a mixture of two species of spin-1 Bose gases with interspecies spin exchange in a magnetic fieldNov 11 2011We consider a mixture of two species of spin-1 atoms with both interspecies and intraspecies spin exchanges in a weak magnetic field. Under the usual single mode approximation, it can be reduced to a model of coupled giant spins. We find most of its ground ... More

A Discrete Ricci Flow on Surfaces in Hyperbolic Background GeometryMay 19 2015In this paper, we generalize our results in \cite{GX3} to triangulated surfaces in hyperbolic background geometry, which means that all triangles can be embedded in the standard hyperbolic space. We introduce a new discrete Gaussian curvature by dividing ... More

An exotic sphere with positive curvatureDec 02 2014Dec 04 2014A metric with positive sectional curvature on the Gromoll-Meyer exotic 7-sphere is constructed explicitly. The proof relies on a 2-parameter family of left invariant metrics on Sp(2) and a one-parameter family of conformal deformations via an isoparametric ... More