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Exponential decay of correlations in the two-dimensional random field Ising model at positive temperaturesMay 14 2019We study random field Ising model on $\mathbb Z^2$ where the external field is given by i.i.d.\ Gaussian variables with mean zero and positive variance. We show that at any positive temperature the effect of boundary conditions on the magnetization in ... More

Exponential decay of correlations in the two-dimensional random field Ising model at zero temperatureFeb 08 2019We study random field Ising model on $\mathbb Z^2$ where the external field is given by i.i.d.\ Gaussian variables with mean zero and positive variance. We show that at zero temperature the effect of boundary conditions on the magnetization in a finite ... More

Exponential decay of correlations in the two-dimensional random field Ising model at zero temperatureFeb 08 2019Feb 17 2019We study random field Ising model on $\mathbb Z^2$ where the external field is given by i.i.d.\ Gaussian variables with mean zero and positive variance. We show that at zero temperature the effect of boundary conditions on the magnetization in a finite ... More

The stable cohomology of the Satake compactification of $\mathcal{A}_g$Aug 23 2015Sep 10 2016Charney and Lee have shown that the rational cohomology of the Satake-Baily-Borel compactification the moduli space of principally polarized abelian varieties of dimension g stabilizes as g grows and they computed this stable cohomology as a Hopf algebra. ... More

Statistical-Computational Tradeoffs in Planted Problems and Submatrix Localization with a Growing Number of Clusters and SubmatricesFeb 06 2014Mar 13 2015We consider two closely related problems: planted clustering and submatrix localization. The planted clustering problem assumes that a random graph is generated based on some underlying clusters of the nodes; the task is to recover these clusters given ... More

The homotopy type of the Baily-Borel and allied compactificationsAug 23 2015Nov 05 2015A number of compactifications familiar in complex-analytic geometry, in particular, the Baily-Borel compactification and its toroidal variants, as well as the Deligne-Mumford compactifications, can be covered by open subsets whose nonempty intersections ... More

Statistical Problems with Planted Structures: Information-Theoretical and Computational LimitsMay 31 2018Aug 12 2018Over the past few years, insights from computer science, statistical physics, and information theory have revealed phase transitions in a wide array of high-dimensional statistical problems at two distinct thresholds: One is the information-theoretical ... More

Reconstruction of Cloud Geometry from High-Resolution Multi-Angle ImagesNov 10 2015We consider the reconstruction of the interface of compact, connected "clouds" from satellite or airborne light intensity measurements. In a two dimensional setting, the cloud is modeled by an interface, locally represented as a graph, and an outgoing ... More

Computational Lower Bounds for Community Detection on Random GraphsJun 25 2014Mar 11 2015This paper studies the problem of detecting the presence of a small dense community planted in a large Erd\H{o}s-R\'enyi random graph $\mathcal{G}(N,q)$, where the edge probability within the community exceeds $q$ by a constant factor. Assuming the hardness ... More

Minimax-optimal Inference from Partial RankingsJun 21 2014This paper studies the problem of inferring a global preference based on the partial rankings provided by many users over different subsets of items according to the Plackett-Luce model. A question of particular interest is how to optimally assign items ... More

Edge Label Inference in Generalized Stochastic Block Models: from Spectral Theory to Impossibility ResultsJun 26 2014The classical setting of community detection consists of networks exhibiting a clustered structure. To more accurately model real systems we consider a class of networks (i) whose edges may carry labels and (ii) which may lack a clustered structure. Specifically ... More

The Relevance of Bayesian Layer Positioning to Model Uncertainty in Deep Bayesian Active LearningNov 29 2018One of the main challenges of deep learning tools is their inability to capture model uncertainty. While Bayesian deep learning can be used to tackle the problem, Bayesian neural networks often require more time and computational power to train than deterministic ... More

Weakly-Interacting Massive Particles in Non-supersymmetric SO(10) Grand Unified ModelsSep 02 2015Non-supersymmetric SO(10) grand unified theories provide a framework in which the stability of dark matter is explained while gauge coupling unification is realized. In this work, we systematically study this possibility by classifying weakly interacting ... More

Block Coordinate Regularization by DenoisingMay 13 2019We consider the problem of estimating a vector from its noisy measurements using a prior specified only through a denoising function. Recent work on plug-and-play priors (PnP) and regularization-by-denoising (RED) has shown the state-of-the-art performance ... More

Growth and Properties of Quaternary Alloy Magnetic Semiconductor (InGaMn)AsNov 09 2001We have studied growth and properties of quaternary alloy magnetic semiconductor (InGaMn)As grown both on GaAs substrates and on InP substrates by low-temperature molecular-beam epitaxy (LT-MBE). (InGaMn)As thin films were ferromagnetic below ~30 K, exhibiting ... More

A Medical Literature Search System for Identifying Effective Treatments in Precision MedicineApr 16 2019The Precision Medicine Initiative states that treatments for a patient should take into account not only the patient's disease, but his/her specific genetic variation as well. The vast biomedical literature holds the potential for physicians to identify ... More

A FISTA-type accelerated gradient algorithm for solving smooth nonconvex composite optimization problemsMay 16 2019In this paper, we describe and establish iteration-complexity of two accelerated composite gradient (ACG) variants to solve a smooth nonconvex composite optimization problem whose objective function is the sum of a nonconvex differentiable function $ ... More

On the Limits of Learning Representations with Label-Based SupervisionMar 07 2017Advances in neural network based classifiers have transformed automatic feature learning from a pipe dream of stronger AI to a routine and expected property of practical systems. Since the emergence of AlexNet every winning submission of the ImageNet ... More

On the Lambek Calculus with an Exchange ModalityApr 15 2019In this paper we introduce Commutative/Non-Commutative Logic (CNC logic) and two categorical models for CNC logic. This work abstracts Benton's Linear/Non-Linear Logic by removing the existence of the exchange structural rule. One should view this logic ... More

Vacuum Stability and Radiative Electroweak Symmetry Breaking in an SO(10) Dark Matter ModelFeb 17 2016Jul 01 2016Vacuum stability in the Standard Model is problematic as the Higgs quartic self-coupling runs negative at a renormalization scale of about $10^{10}$ GeV. We consider a non-supersymmetric SO(10) grand unification model for which gauge coupling unification ... More

Concept Learning through Deep Reinforcement Learning with Memory-Augmented Neural NetworksNov 15 2018Deep neural networks have shown superior performance in many regimes to remember familiar patterns with large amounts of data. However, the standard supervised deep learning paradigm is still limited when facing the need to learn new concepts efficiently ... More

Discriminative Nonparametric Latent Feature Relational Models with Data AugmentationDec 07 2015We present a discriminative nonparametric latent feature relational model (LFRM) for link prediction to automatically infer the dimensionality of latent features. Under the generic RegBayes (regularized Bayesian inference) framework, we handily incorporate ... More

End-to-End Reinforcement Learning for Automatic Taxonomy InductionMay 10 2018We present a novel end-to-end reinforcement learning approach to automatic taxonomy induction from a set of terms. While prior methods treat the problem as a two-phase task (i.e., detecting hypernymy pairs followed by organizing these pairs into a tree-structured ... More

Efficient random graph matching via degree profilesNov 19 2018Random graph matching refers to recovering the underlying vertex correspondence between two random graphs with correlated edges; a prominent example is when the two random graphs are given by Erd\H{o}s-R\'{e}nyi graphs $G(n,\frac{d}{n})$. This can be ... More

Chern Classes of Logarithmic Derivations for Free Divisors with Jacobian Ideal of Linear TypeOct 22 2012Let $X$ be a nonsingular variety defined over an algebraically closed field of characteristic 0, and $D$ be a free divisor with Jacobian ideal of linear type. We compute the Chern class of the sheaf of logarithmic derivations along $D$ and compare it ... More

Chern Classes Of Logarithmic Vector Fields For Locally-Homogenous Free DivisorsMay 17 2012Oct 22 2012Let $X$ be a nonsingular complex projective variety and $D$ a locally quasi-homogeneous free divisor in $X$. In this paper we study a numerical relation between the Chern class of the sheaf of logarithmic derivations on $X$ with respect to $D$, and the ... More

Deligne-Riemann-Roch Theorems I. Uniqueness of Deligne Pairings and Degree $1$ Part of Deligne-Riemann-Roch IsomorphismsOct 26 2017Jan 18 2018This is the first of a series of papers. Our final goal is to establish Deligne-Riemann-Roch isomorphisms in various settings. In this paper, we establish a uniqueness theorem for Deligne pairings and prove the degree $1$ part of the Deligne-Riemann-Roch ... More

Experiments and Modeling of Mass Transport Phenomena in SiGe DevicesSep 26 2018Recent experiments and continuum modeling work on dopant diffusion and segregation, Si-Ge interdiffusion, and defect engineering in SiGe material systems are reviewed. Doping impact on Ge thin film quality and interdiffusion is also discussed. These are ... More

Hyperbolic Invariant Sets With Positive MeasuresMar 21 2005Aug 26 2005If a $C^{1 + a}$, $a >0$, volume-preserving diffeomorphism on a compact manifold has a hyperbolic invariant set with positive volume, then the map is Anosov. We also give a direct proof of ergodicity of volume-preserving $CC^{1+a}$, $a>0$, Anosov diffeomorphism ... More

Moderate deviations and law of the iterated logarithm for intersections of the ranges of random walksAug 30 2005Let S_1(n),...,S_p(n) be independent symmetric random walks in Z^d. We establish moderate deviations and law of the iterated logarithm for the intersection of the ranges #{S_1[0,n]\cap... \cap S_p[0,n]} in the case d=2, p\ge 2 and the case d=3, p=2.

A Note on The Backfitting Estimation of Additive ModelsMar 20 2009The additive model is one of the most popular semiparametric models. The backfitting estimation (Buja, Hastie and Tibshirani, 1989, \textit{Ann. Statist.}) for the model is intuitively easy to understand and theoretically most efficient (Opsomer and Ruppert, ... More

The geodesic problem in quasimetric spacesJul 22 2008May 27 2009In this article, we study the geodesic problem in a generalized metric space, in which the distance function satisfies a relaxed triangle inequality $d(x,y)\leq \sigma (d(x,z)+d(z,y))$ for some constant $\sigma \geq 1$, rather than the usual triangle ... More

QoS Challenges and Opportunities in Wireless Sensor/Actuator NetworksJun 01 2008A wireless sensor/actuator network (WSAN) is a group of sensors and actuators that are geographically distributed and interconnected by wireless networks. Sensors gather information about the state of physical world. Actuators react to this information ... More

Reduce and Solve Boltzmann Equation on a Global Lie GroupDec 13 2010Aug 11 2011This paper has been withdrawn by the author due to a crucial sign error in equation 2.23 and a wrong author added.

Cyclotomic difference sets in finite fieldsJan 14 2015Sep 27 2015The problem of whether $m$th-powers with or without zero in a finite field GF($q$) form a difference set has been extensively studied, and is related to many topics, such as flag transitive finite projective planes. In this paper new necessary and sufficient ... More

Crystalline Hodge cycles and Shimura curves in positive characteristicsNov 05 2013In this paper, we seek an appropriate definition for a Shimura curve of Hodge type in positive characteristics, i.e. a characterization of curves in positive characteristics which are reduction of Shimura curve over the complex field. Specifically, we ... More

A Partial Order on Bipartitions From the Generalized Springer CorrespondenceJan 29 2018Feb 28 2018In \cite{Lusztig}, Lusztig gives an explicit formula for the bijection between the set of bipartitions and the set $\mathcal{N}$ of unipotent classes in a spin group which carry irreducible local systems equivariant for the spin group but not equivariant ... More

The Ablowitz-Ladik system on a graphMar 21 2019This paper presents an approach to study initial-boundary value (IBV) problems for integrable nonlinear differential-difference equations (DDEs) posed on a graph. As an illustrative example, we consider the Ablowitz-Ladik system posed on a graph that ... More

Base collapse of holographic algorithmsNov 04 2015A holographic algorithm solves a problem in domain of size $n$, by reducing it to counting perfect matchings in planar graphs. It may simulate a $n$-value variable by a bunch of $t$ matchgate bits, which has $2^t$ values. The transformation in the simulation ... More

A Minkowski type inequality in space formsAug 14 2015Sep 22 2015In this note we apply the general Reilly formula established in \cite{QX} to the solution of a Neumann boundary value problem to prove an optimal Minkowski type inequality in space forms.

Local gradient estimate for harmonic functions on Finsler manifoldsAug 16 2013Dec 17 2013In this paper, we prove the local gradient estimate for harmonic functions on complete, noncompact Finsler measure spaces under the condition that the weighted Ricci curvature has a lower bound. As applications, we obtain Liouville type theorem on Finsler ... More

Chern Classes Of Logarithmic Vector Fields For Locally-Homogenous Free DivisorsMay 17 2012Sep 02 2017Let $X$ be a nonsingular complex projective variety and $D$ a locally quasi-homogeneous free divisor in $X$. In this paper we study a numerical relation between the Chern class of the sheaf of logarithmic derivations on $X$ with respect to $D$, and the ... More

Chern Classes of Logarithmic Vector FieldsJan 30 2012Oct 22 2012Let $X$ be a nonsingular complex variety and $D$ a reduced effective divisor in $X$. In this paper we study the conditions under which the formula $c_{SM}(1_U)=c(\textup{Der}_X(-\log D))\cap [X]$ is true. We prove that this formula is equivalent to a ... More

Cyclotomic difference sets in finite fieldsJan 14 2015Jul 04 2017The classical problem of whether $m$th-powers with or without zero in a finite field $\mathbb{F}_q$ form a difference set has been extensively studied, and is related to many topics, such as flag transitive finite projective planes. In this paper new ... More

The Ablowitz-Ladik system on a graphMar 21 2019Mar 26 2019This paper presents an approach to study initial-boundary value (IBV) problems for integrable nonlinear differential-difference equations (DDEs) posed on a graph. As an illustrative example, we consider the Ablowitz-Ladik system posed on a graph that ... More

The Ablowitz-Ladik system on a finite set of integersMar 05 2017Jun 29 2018We show how to solve initial-boundary value problems for integrable nonlinear differential-difference equations on a finite set of integers. The method we employ is the discrete analogue of the unified transform (Fokas method). The implementation of this ... More

The covering radius of $\mathrm{PGL}_2(q)$Feb 15 2017Jun 02 2017The covering radius of a subset $C$ of the symmetric group $\mathrm{S}_n$ is the maximal Hamming distance of an element of $\mathrm{S}_n$ from $C$. This note determines the covering radii of the finite projective general linear groups. It turns out that ... More

Simplification of Boltzmann Equation on S^{3}(1)Mar 28 2011Aug 11 2011Simple form of Boltzmann equation will be proposed after introducing a three-dimensional closed Lie group to simplify its collision term.

Ramified optimal transportation in geodesic metric spacesJul 31 2009An optimal transport path may be viewed as a geodesic in the space of probability measures under a suitable family of metrics. This geodesic may exhibit a tree-shaped branching structure in many applications such as trees, blood vessels, draining and ... More

Mean-variance Hedging in the Discontinuous CaseJul 30 2006The results on the mean-variance hedging problem in Gouri\'eroux, Laurent and Pham (1998), Rheinl\"ander and Schweizer (1997) and Arai (2005) are extended to discontinuous semimartingale models. When the num\'eraire method is used, we only assume the ... More

On Local Convexity of Quadratic TransformationsMay 23 2014In this paper, we improve Polyak's local convexity result for quadratic transformations. Extension and open problems are also presented.

Tronquée Solutions of the Third and Fourth Painlevé EquationsMar 29 2018Sep 08 2018Recently in a paper by Lin, Dai and Tibboel, it was shown that the third and fourth Painlev\'e equations have tronqu\'ee and tritronqu\'ee solutions. We obtain global information about these tronqu\'ee and tritronqu\'ee solutions. We find their sectors ... More

The massive Thirring system in the quarter planeOct 29 2018The unified transform method (UTM) for analyzing initial-boundary value (IBV) problems provides an important generalization of the inverse scattering transform (IST) method for analyzing initial value problems. In comparison with the IST, a major difficulty ... More

Exploring Sparsity in Multi-class Linear Discriminant AnalysisDec 26 2014Jan 09 2015Recent studies in the literature have paid much attention to the sparsity in linear classification tasks. One motivation of imposing sparsity assumption on the linear discriminant direction is to rule out the noninformative features, making hardly contribution ... More

How Many Vote Operations Are Needed to Manipulate A Voting System?Apr 05 2012Aug 14 2012In this paper, we propose a framework to study a general class of strategic behavior in voting, which we call vote operations. We prove the following theorem: if we fix the number of alternatives, generate $n$ votes i.i.d. according to a distribution ... More

On the Ohno-Nakagawa TheoremAug 02 2016In this paper we give a new proof of the Ohno-Nakagawa Theorem using the techniques of $L$-series. By applying Eisenstein's parametrization of binary cubic forms on the one hand, and a class field theory interpretation of Datskovsky \& Wright's Theorem ... More

Inverse anisotropic mean curvature flow and a Minkowski type inequalityJun 30 2015In this paper, we show that the inverse anisotropic mean curvature flow in $\mathbb{R}^{n+1}$, initiating from a star-shaped, strictly $F$-mean convex hypersurface, exists for all time and after rescaling the flow converges exponentially fast to a rescaled ... More

Estimation of low rank density matrices by Pauli measurementsOct 16 2016Density matrices are positively semi-definite Hermitian matrices with unit trace that describe the states of quantum systems. Many quantum systems of physical interest can be represented as high-dimensional low rank density matrices. A popular problem ... More

l-adic Monodromy and Shimura curves in positive characteristicsMar 01 2014In this paper, we seek an appropriate definition for a Shimura curve of Hodge type in positive characteristics, i.e. a characterization, in terms of geometry mod p, of curves in positive characteristics which are reduction of Shimura curves over the complex ... More

A Characterization of Mumford Curves with Good ReductionJun 02 2013Mumford defines a certain type of Shimura curves of Hodge type, parameterizing polarized complex abelian fourfolds. In this paper, we study the good reduction of such a curve in positive characteristic and give a characterization in the generically ordinary ... More

On the deformation of a Barsotti-Tate group over a curveMar 12 2013In this paper, we study deformations of pairs (C,G) where G is a height 2 BT(or BT_n) group over a complete curve on algebraically closed field k of characteristic p. We prove that, if the curve C is a versal deformation of G, then there exists a unique ... More

Chern Classes of Logarithmic Derivations for Free Divisors with Jacobian Ideal of Linear TypeOct 22 2012Oct 17 2017Let $X$ be a nonsingular variety defined over an algebraically closed field of characteristic $0$, and $D$ be a free divisor with Jacobian ideal of linear type. We compute the Chern class of the sheaf of logarithmic derivations along $D$ and compare it ... More

Interdiffusion in Group IV Semiconductor Material Systems: Applications, Methods and DiscoveriesJan 29 2019Group IV semiconductor alloys, heterostructures and solid solutions such as SiGe, GeSn, Ge/Si and SiGe:C have been widely used and under extensive research for applications in major microelectronic and photonic devices. In the growth and processing of ... More

The impact of fill patterns on the fast ion instability in the ILC damping ringMay 31 2012The ions produced via collisional ionization of the residual gas molecules in vacuum pipe with the circulating electron beam have deleterious effect on the beam properties and may become a limiting factor for the machine's performance. For the electron ... More

Hilbert scheme of twisted cubics as simple wall-crossingAug 16 2016We study the Hilbert scheme of twisted cubics in the three-dimensional projective space by using Bridgeland stability conditions. We use wall-crossing techniques to describe its geometric structure and singularities, which reproves the classical result ... More

Lie Subalgebras and Invariant Solutions to the Equation of Fluid Flows in Toroidal FieldAug 11 2011Sep 15 2018In the present report, by using the Stokes-Helmholtz decomposition theorem the 3-dimensional Navier-Stokes equation (NSE) is uncoupled and transformed into a scalar equation for the velocity potential when the flow field is toroidal. The dynamics of the ... More

Separation of variables for local symmetrical flowsAug 11 2011Jan 09 2016Separation of variables is effective method for solving ordinary and partial differential equations. We examine some topological manifolds in flows and get a conclusion that it can be applied in separating variables of differential equations. Then we ... More

A new multiresolution finite element method based on a multiresolution quadrilateral plate elementApr 04 2014Oct 21 2014A new multiresolution quadrilateral plate element is proposed and a multiresolution finite element method is hence presented. The multiresolution analysis (MRA) framework is formulated out of a mutually nesting displacement subspace sequence, whose basis ... More

Multilevel Monte Carlo method for jump-diffusion SDEsJun 23 2011We investigate the extension of the multilevel Monte Carlo path simulation method to jump-diffusion SDEs. We consider models with finite rate activity, using a jump-adapted discretisation in which the jump times are computed and added to the standard ... More

Deterministic generation of bright multicolor entanglement from optomechanical systemsJul 27 2015Entangled continuous variable (CV) Gaussian states with different wavelengths plays a central role in recent CV-based approaches to quantum network, quantum information processing and quantum metrology. Typically, experiments demonstrating CV entanglement ... More

Tunable slowing, storing and releasing of a weak microwave fieldNov 01 2013Jan 17 2014We study the slowing, storing and releasing of microwave pulses in a superconducting circuits composed of two coplanar waveguide resonators and a superconducting transmon-type qubit. The quantum interference analogy to electromagnetically induced transparency ... More

Optimal Schatten-q and Ky-Fan-k Norm Rate of Low Rank Matrix EstimationMar 25 2014Apr 03 2014In this paper, we consider low rank matrix estimation using either matrix-version Dantzig Selector $\hat{A}_{\lambda}^d$ or matrix-version LASSO estimator $\hat{A}_{\lambda}^L$. We consider sub-Gaussian measurements, $i.e.$, the measurements $X_1,\ldots,X_n\in\mathbb{R}^{m\times ... More

Revealing the missing heritability via cross-validated genome-wide association studiesJul 30 2013Aug 07 2013Presented here is a simple method for cross-validated genome-wide association studies (cvGWAS). Focusing on phenotype prediction, the method is able to reveal a significant amount of missing heritability by properly selecting a small number of loci with ... More

K-theoretic defect in Chern class identity for a free divisorDec 22 2016Let $X$ be a nonsingular variety defined over an algebraically closed field of characteristic $0$, and $D$ be a free divisor. We study the motivic Chern class of $D$ in the Grothendieck group of coherent sheaves $G_0(X)$, and another class defined by ... More

A dichotomy for CLT in total variationJun 17 2016Let $\eta_i$, $i\ge 1$, be a sequence of independent and identically distributed random variables with finite third moment, and let $\Delta_n$ be the total variation distance between the distribution of $S_n:=\sum_{i=1}^n\eta_i$ and the normal distribution ... More

Tensor decomposition of isocrystals characterizes Mumford curvesOct 10 2013We seek an appropriate definition for a Shimura curve of Hodge type in positive characteristics via characterizing curves in positive characteristics which are reduction of Shimura curve over $\mathbb{C}$. In this paper, we study the liftablity of a curve ... More

Homoclinic Points For Area-Preserving Surface DiffeomorphismsJun 13 2006We show a $C^r$ connecting lemma for area-preserving surface diffeomorphisms and for periodic Hamiltonian on surfaces. We prove that for a generic $C^r$, $r=1, 2, ...$, $\infty$, area-preserving diffeomorphism on a compact orientable surface, homotopic ... More

Generic ill-posedness for wave equation of power type on 3D torusJul 26 2015Aug 19 2015In this article, we prove that the equation \begin{equation*} \left\{\begin{split} &(\partial^2_t-\Delta)u+|u|^{p-1}u=0,\ \ \ 3\leq p<5 &\big(u(0),\partial_tu(0)\big)=(u_0,u_1)\in H^{s}(\mathbb{T}^3)\times H^{s-1}(\mathbb{T}^3)=:\mathcal{H}^s(\mathbb{T}^3) ... More

A Constructive Approach to the Estimation of Dimension Reduction DirectionsJan 26 2007In this paper, we propose two new methods to estimate the dimension-reduction directions of the central subspace (CS) by constructing a regression model such that the directions are all captured in the regression mean. Compared with the inverse regression ... More

An approach to Lagrangian specialisation through MacPherson's graph constructionAug 29 2018Let $f: M \to N$ be a holomorphic map between two complex manifolds. Assume $f$ is flat and sans \'{e}clatement en codimension 0 (no blowup in codimension 0). We study the theory of Lagrangian specialisation for such $f$, and prove a Gonz\'{a}lez-Sprinberg ... More

Numerical simulation of optimal transport pathsJul 23 2008This article provides numerical simulation of an optimal transport path from a single source to an atomic measure of equal total mass. We first construct an initial transport path, and then modify the path as much as possible by using both local and global ... More

Local analysis of cyclotomic difference setsJul 18 2017Jul 31 2018We develop a local analysis method to study cyclotomic difference sets in finite fields. This is by applying a general existence criterion for cyclotomic difference sets via Gauss sums and Gauss periods to various underlying local fields. With this local ... More

Estimation of low rank density matrices by Pauli measurementsOct 16 2016Jan 05 2017Density matrices are positively semi-definite Hermitian matrices with unit trace that describe the states of quantum systems. Many quantum systems of physical interest can be represented as high-dimensional low rank density matrices. A popular problem ... More

A survey of hidden convex optimizationFeb 28 2019Motivated by the fact that not all nonconvex optimization problems are difficult to solve, we survey in this paper three widely-used ways to reveal the hidden convex structure for different classes of nonconvex optimization problems. Finally, ten open ... More

Squeezing giant spin states via geometric phase control in cavity-assisted Raman transitionsOct 18 2016Squeezing ensemble of spins provides a way to surpass the standard quantum limit (SQL) in quantum metrology and test the fundamental physics as well, and therefore attracts broad interest. Here we propose an experimentally accessible protocol to squeeze ... More

Spatial asymptotics for the parabolic Anderson models with generalized time-space Gaussian noiseMar 30 2016Partially motivated by the recent papers of Conus, Joseph and Khoshnevisan [Ann. Probab. 41 (2013) 2225-2260] and Conus et al. [Probab. Theory Related Fields 156 (2013) 483-533], this work is concerned with the precise spatial asymptotic behavior for ... More

Risk Aversion and Portfolio Selection in a Continuous-Time ModelMay 05 2008Dec 30 2011The comparative statics of the optimal portfolios across individuals is carried out for a continuous-time complete market model, where the risky assets price process follows a joint geometric Brownian motion with time-dependent and deterministic coefficients. ... More

Data-dependent Confidence Regions of Singular SubspacesJan 02 2019Matrix singular value decomposition (SVD) is popular in statistical data analysis which shows superior efficiency of extracting the unknown low-rank singular subspaces embedded in noisy matrix observations. This article is about the statistical inference ... More

The Stretch Factor of the Delaunay Triangulation Is Less Than 1.998Mar 22 2011Jun 04 2013Let $S$ be a finite set of points in the Euclidean plane. Let $D$ be a Delaunay triangulation of $S$. The {\em stretch factor} (also known as {\em dilation} or {\em spanning ratio}) of $D$ is the maximum ratio, among all points $p$ and $q$ in $S$, of ... More

Area-Preserving Surface DiffeomorphismsMar 11 2005We prove some generic properties for $C^r$, $r=1, 2, ..., \infty$, area-preserving diffeomorphism on compact surfaces. The main result is that the union of the stable (or unstable) manifolds of hyperbolic periodic points are dense in the surface. This ... More

On cubic graphical regular representations of finite simple groupsSep 26 2017A recent conjecture of the author and Teng Fang states that there are only finitely many finite simple groups with no cubic graphical regular representation. In this paper, we make a crucial progress towards this conjecture by giving an affirmative answer ... More

Which Facial Expressions Can Reveal Your Gender? A Study With 3D FacesMay 01 2018Human exhibit rich gender cues in both appearance and behavior. In computer vision domain, gender recognition from facial appearance have been extensively studied, while facial behavior based gender recognition studies remain rare. In this work, we first ... More

Exponential asymptotics and law of the iterated logarithm for intersection local times of random walksMar 25 2005Let \alpha ([0,1]^p) denote the intersection local time of p independent d-dimensional Brownian motions running up to the time 1. Under the conditions p(d-2)<d and d\ge 2, we prove lim_{t\to\infty}t^{-1}\log P\bigl{\alpha([0,1]^p)\ge t^{(d(p-1))/2}\bigr}=-\gamma_{\alpha}(d,p) ... More

Moderate deviations and laws of the iterated logarithm for the local times of additive Lévy processes and additive random walksJul 30 2007We study the upper tail behaviors of the local times of the additive L\'{e}vy processes and additive random walks. The limit forms we establish are the moderate deviations and the laws of the iterated logarithm for the L_2-norms of the local times and ... More

Wikidata Vandalism Detection - The Loganberry Vandalism Detector at WSDM Cup 2017Dec 19 2017Wikidata is the new, large-scale knowledge base of the Wikimedia Foundation. As it can be edited by anyone, entries frequently get vandalized, leading to the possibility that it might spread of falsified information if such posts are not detected. The ... More

An Empirical Analysis of Proximal Policy Optimization with Kronecker-factored Natural GradientsJan 17 2018In this technical report, we consider an approach that combines the PPO objective and K-FAC natural gradient optimization, for which we call PPOKFAC. We perform a range of empirical analysis on various aspects of the algorithm, such as sample complexity, ... More

Stop Coannihilation in the CMSSM and SubGUT ModelsJan 30 2018Stop coannihilation may bring the relic density of heavy supersymmetric dark matter particles into the range allowed by cosmology. The efficiency of this process is enhanced by stop-antistop annihilations into the longitudinal (Goldstone) modes of the ... More

Improved queue-size scaling for input-queued switches via graph factorizationMar 01 2019This paper studies the scaling of the expected total queue size in an $n\times n$ input-queued switch, as a function of both the load $\rho$ and the system scale $n$. We provide a new class of scheduling policies under which the expected total queue size ... More

Securing Distributed Machine Learning in High DimensionsApr 26 2018Jun 08 2018Standard distributed machine learning frameworks require collecting the training data from data providers and storing it in a datacenter. To ease privacy concerns, alternative distributed machine learning frameworks (such as {\em Federated Learning}) ... More

Clustering and Inference From Pairwise ComparisonsFeb 16 2015Dec 17 2015Given a set of pairwise comparisons, the classical ranking problem computes a single ranking that best represents the preferences of all users. In this paper, we study the problem of inferring individual preferences, arising in the context of making personalized ... More