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Exponential decay of correlations in the two-dimensional random field Ising model at positive temperaturesMay 14 2019May 23 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 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

Exponential decay of correlations in the two-dimensional random field Ising model at zero temperatureFeb 08 2019May 23 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

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

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 Extent of the Stop Coannihilation StripApr 22 2014Many supersymmetric models such as the CMSSM feature a strip in parameter space where the lightest neutralino \chi is identified as the lightest supersymmetric particle (LSP), the lighter stop squark \tilde t_1 is the next-to-lightest supersymmetric particle ... More

Multiple-parameter bifurcation analysis in a Kuramoto model with time delay and distributed shearAug 11 2016Apr 23 2018In this paper, time delay effect and distributed shear are considered in the Kuramoto model. On the Ott-Antonsen's manifold, through analyzing the associated characteristic equation of the reduced functional differential equation, the stability boundary ... 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

Are the silicate crystallinities of oxygen-rich evolved stars related to their mass loss rates?Sep 26 2018A sample of 28 oxygen-rich evolved stars is selected based on the presence of crystalline silicate emission features in their ISO/SWS spectra. The crystallinity, measured as the flux fraction of crystalline silicate features, is found not related to mass ... 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

Optimal Power Allocation over Multiple Identical Gilbert-Elliott ChannelsMar 27 2013We study the fundamental problem of power allocation over multiple Gilbert-Elliott communication channels. In a communication system with time varying channel qualities, it is important to allocate the limited transmission power to channels that will ... More

Optimal Distributed Beamforming for MISO Interference ChannelsNov 17 2010Nov 29 2010We consider the problem of quantifying the Pareto optimal boundary in the achievable rate region over multiple-input single-output (MISO) interference channels, where the problem boils down to solving a sequence of convex feasibility problems after certain ... More

Weakly-Supervised Hierarchical Text ClassificationDec 29 2018Hierarchical text classification, which aims to classify text documents into a given hierarchy, is an important task in many real-world applications. Recently, deep neural models are gaining increasing popularity for text classification due to their expressive ... More

On Hybrid Pilot for Channel Estimation in Massive MIMO UplinkAug 06 2016This paper introduces a hybrid pilot-aided channel estimation technique for mitigating the effect of pilot contamination for the uplink of multi-cell multiuser massive MIMO systems. The proposed hybrid pilot is designed such that it enjoys the complementary ... More

The ATLAS Diboson Resonance in Non-Supersymmetric SO(10)Dec 07 2015SO(10) grand unification accommodates intermediate gauge symmetries with which gauge coupling unification can be realized without supersymmetry. In this paper, we discuss the possibility that a new massive gauge boson associated with an intermediate gauge ... More

Broadcast Channels with Delayed Finite-Rate Feedback: Predict or Observe?May 18 2011Most multiuser precoding techniques require accurate transmitter channel state information (CSIT) to maintain orthogonality between the users. Such techniques have proven quite fragile in time-varying channels because the CSIT is inherently imperfect ... 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

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

Multi-Task Learning for Email Search Ranking with Auxiliary Query ClusteringSep 15 2018User information needs vary significantly across different tasks, and therefore their queries will also differ considerably in their expressiveness and semantics. Many studies have been proposed to model such query diversity by obtaining query types and ... 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

Eliciting Knowledge from Experts:Automatic Transcript Parsing for Cognitive Task AnalysisJun 26 2019Cognitive task analysis (CTA) is a type of analysis in applied psychology aimed at eliciting and representing the knowledge and thought processes of domain experts. In CTA, often heavy human labor is involved to parse the interview transcript into structured ... 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

Morphology of Flow Patterns Generated by Viscous Fingering from Miscible FluidsSep 18 2018A rest fluid displaced by a less viscous fluid in a porous medium triggers the so-called Saffman-Taylor instability at their contact front and hence forms complicated finger-like patterns. When the two fluids are miscible, the surface tension at their ... More

Probe CP violation in $H\to γZ$ through forward-backward asymmetryAug 27 2017We suggest that the forward-backward asymmetry $(A_{FB})$ of the charged lepton in $gg\to H\to\gamma Z\to\gamma \ell^-\ell^+$ process could be used to probe the CP violating $H\gamma Z$ coupling when the interference from $gg\to\gamma Z\to\gamma \ell^-\ell^+$ ... More

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

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

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

Inverse anisotropic mean curvature flow and a Minkowski type inequalityJun 30 2015May 27 2017In 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

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

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

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

Propagation of Nonlinear Acoustic Waves in the Suspension of Ultrasound Contrast Agents Part I: Equation for Counting Resonance Effects and Revealing Acoustic LocalizationOct 04 2018The oscillations of ultrasound contrast agents are of particular importance to the understanding of the propagation of acoustic waves in the bubbly liquids (suspensions of ultrasound contrast agents). Acoustic waves propagating in bubbly liquids have ... More

Sequence-based Multiscale Model (SeqMM) for High-throughput chromosome conformation capture (Hi-C) data analysisJul 12 2017Jul 31 2017In this paper, I introduce a Sequence-based Multiscale Model (SeqMM) for the biomolecular data analysis. With the combination of spectral graph method, I reveal the essential difference between the global scale models and local scale ones in structure ... 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

Quasiprimitive groups containing a transitive alternating groupAug 31 2015This paper classifies quasiprimitive permutation groups with a transitive subgroup which is isomorphic to $\A_n$ for some $n\geqslant5$.

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

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

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

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

Large deviations and laws of the iterated logarithm for the local times of additive stable processesMar 07 2006Jul 25 2007We study the upper tail behaviors of the local times of the additive stable processes. Let $X_1(t),...,X_p(t)$ be independent, d-dimensional symmetric stable processes with stable index $0<\alpha\le 2$ and consider the additive stable process $\bar{X}(t_1,...,t_p)=X_1(t_1)+... ... 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

On an anisotropic Minkowski problemMar 06 2012In this paper, we study the anisotropic Minkowski problem. It is a problem of prescribing the anisotropic Gauss-Kronecker curvature for a closed strongly convex hypersurface in Euclidean space as a function on its anisotropic normals in relative or Minkowski ... 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

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

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

Multiscale virtual particle based elastic network model (MVP-ENM) for biomolecular normal mode analysisJul 31 2017In this paper, a multiscale virtual particle based elastic network model (MVP-ENM) is proposed for biomolecular normal mode analysis. The multiscale virtual particle model is proposed for the discretization of biomolecular density data in different scales. ... More

2D materials coated plasmonic structures for SERS applicationsFeb 26 2018Two-dimensional (2D) materials, such as graphene and hexagonal boron nitride, are new kind of materials that can serve as substrates for surface enhanced Raman spectroscopy (SERS). When combined with traditional metallic plasmonic structures, the hybrid ... More

A Note on the Nonlinear Attenuation of an Ultrasound Contrast Agent Calculated by Rayleigh-Plesset EquationSep 25 2018The dynamics of microbubble-based Ultrasound contrast agents (UCAs) is governed by the Rayleigh-Plesset equation, of which the linearization is used to formulate the attenuation of an UCA under the excitation of ultrasound. Recent experimental observations ... More

Analysis on the Integrability of the Rayleigh-Plesset Equation with Painlevé Test and Lie Symmetry GroupsSep 20 2018The Rayleigh-Plesset equation (RPE) is a nonlinear ordinary differential equation (ODE) of second order that governs the dynamics of a spherical bubble and plays an essential role in interpreting many real-world phenomena involving the presence of bubbles ... 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

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

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

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

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

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

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

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.

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

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

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.

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

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

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

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

A multiresolution triangular plate-bending element methodOct 13 2017Jun 14 2018A triangular plate-bending element with a new multi-resolution analysis (MRA) is proposed and a novel multiresolution element method is hence presented. The MRA framework is formulated out of a displacement subspace sequence whose basis functions are ... 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

On cubic graphical regular representations of finite simple groupsSep 26 2017Jun 10 2019A 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

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

Integration by parts formula for non-pluripolar productJul 15 2019In this paper, we prove the integration by parts formula for the non-pluripolar product on a compact K\"ahler manifold. Our result generalizes the special case of potentials with small unbounded loci proved in [BEGZ10].

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

Integration by parts formula for non-pluripolar productJul 15 2019Jul 16 2019In this paper, we prove the integration by parts formula for the non-pluripolar product on a compact K\"ahler manifold. Our result generalizes the special case of potentials with small unbounded loci proved in [BEGZ10].

Mabuchi geometry of big cohomology classes with prescribed singularitiesJul 16 2019Let $X$ be a compact K\"ahler manifold. Fix a big class $\alpha$ with smooth representative $\theta$ and a model potential $\phi$ with positive mass. We study the space $\mathcal{E}^p(X,\theta;[\phi])$ of finite energy K\"ahler potentials with prescribed ... 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

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

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

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

Data-dependent Confidence Regions of Singular SubspacesJan 02 2019Jun 10 2019Matrix singular value decomposition (SVD) is popular in statistical data analysis which shows superior efficiency of extracting unknown low-rank singular subspaces embedded in noisy matrix observations. This paper is on the statistical inference for singular ... More

Acoustic Nonlinearity Parameter B/A in the Suspension of Ultrasound Contrast Agents Part I: A Thermodynamic ApproachOct 05 2018May 23 2019The acoustic nonlinearity parameter B/A plays a significant role in the characterization of acoustic properties of various biomaterials and biological tissues. It has the potential to be a favorable imaging modality in the contrast ultrasound imaging ... More

Derivations on almost complex manifoldsSep 20 2018Mar 31 2019In this short note, we propose an unified method to derive formulas for derivations conjugated by exponential functions on an almost complex manifold. In v3, we corrected some mistakes in previous versions.

Non-asymptotic bounds for percentiles of independent non-identical random variablesAug 24 2018Feb 02 2019This note displays an interesting phenomenon for percentiles of independent but non-identical random variables. Let $X_1,\cdots,X_n$ be independent random variables obeying non-identical continuous distributions and $X^{(1)}\geq \cdots\geq X^{(n)}$ be ... More

Confidence Region of Singular Subspaces for Low-rank Matrix RegressionMay 24 2018Jan 23 2019Low-rank matrix regression refers to the instances of recovering a low-rank matrix based on specially designed measurements and the corresponding noisy outcomes. In the last decade, numerous statistical methodologies have been developed for efficiently ... More

Persistent homology analysis of ion aggregation and hydrogen-bonding networkFeb 26 2018Despite the great advancement of experimental tools and theoretical models, a quantitative characterization of the microscopic structures of ion aggregates and its associated water hydrogen-bonding networks still remains a challenging problem. In this ... More