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A Secure Proxy-based Access Control Scheme for Implantable Medical DevicesMar 21 2018Jun 30 2018With the rapid development of health equipments, increasingly more patients have installed the implantable medical devices (IMD) in their bodies for diagnostic, monitoring, and therapeutic purposes. IMDs are extremely limited in computation power and ... More

Robustness of Information Diffusion Algorithms to Locally Bounded AdversariesOct 17 2011Mar 28 2012We consider the problem of diffusing information in networks that contain malicious nodes. We assume that each normal node in the network has no knowledge of the network topology other than an upper bound on the number of malicious nodes in its neighborhood. ... More

Joint Stochastic Approximation learning of Helmholtz MachinesMar 20 2016Sep 28 2018Though with progress, model learning and performing posterior inference still remains a common challenge for using deep generative models, especially for handling discrete hidden variables. This paper is mainly concerned with algorithms for learning Helmholz ... More

Near-optimal Repair of Reed-Solomon Codes with Low Sub-packetizationJul 09 2019Minimum storage regenerating (MSR) codes are MDS codes which allow for recovery of any single erased symbol with optimal repair bandwidth, based on the smallest possible fraction of the contents downloaded from each of the other symbols. Recently, certain ... More

Time delay of timelike particles in gravitational lensing of Schwarzschild spacetimeJun 27 2019Time delay in Schwarzschild spacetime for null and timelike signals with arbitrary velocity $v$ is studied. The total travel time $t_\mathrm{if}$ is evaluated both exactly and approximately in the weak field limit, with the result given as functions of ... More

Cross-App Interference Threats in Smart Homes: Categorization, Detection and HandlingAug 06 2018Oct 10 2018A number of Internet of Things (IoTs) platforms have emerged to enable various IoT apps developed by third-party developers to automate smart homes. Prior research mostly concerns the overprivilege problem in the permission model. Our work, however, reveals ... More

e-SAFE: Secure, Efficient and Forensics-Enabled Access to Implantable Medical DevicesApr 06 2018To facilitate monitoring and management, modern Implantable Medical Devices (IMDs) are often equipped with wireless capabilities, which raise the risk of malicious access to IMDs. Although schemes are proposed to secure the IMD access, some issues are ... More

Privacy Leakage in Smart Homes and Its Mitigation: IFTTT as a Case StudyFeb 08 2019The combination of smart home platforms and automation apps introduces much convenience to smart home users. However, this also brings the potential for privacy leakage. If a smart home platform is permitted to collect all the events of a user day and ... More

Privacy Leakage in Smart Homes and Its Mitigation: IFTTT as a Case StudyFeb 08 2019Feb 14 2019The combination of smart home platforms and automation apps introduces much convenience to smart home users. However, this also brings the potential for privacy leakage. If a smart home platform is permitted to collect all the events of a user day and ... More

Joint Bayesian Gaussian discriminant analysis for speaker verificationDec 13 2016Jan 19 2017State-of-the-art i-vector based speaker verification relies on variants of Probabilistic Linear Discriminant Analysis (PLDA) for discriminant analysis. We are mainly motivated by the recent work of the joint Bayesian (JB) method, which is originally proposed ... More

Smart wing rotation and ingenious leading edge vortex control modulate the unconventional forces during insects flightsNov 13 2018Jun 18 2019Compared with fixed-wing flight, flapping flight can generate a higher lift and is also more maneuverable, largely resulting from the benefits of wing rotation. By analyzing the real wing kinematics of fruit flies, we found that the wing rotation is smart ... More

Multivariate Signal Modelling with Applications to Inertial Sensor CalibrationMay 04 2019Jul 23 2019The common approach to inertial sensor calibration for navigation purposes has been to model the stochastic error signals of individual sensors independently, whether as components of a single inertial measurement unit (IMU) in different directions or ... More

Multivariate Signal Modelling with Applications to Inertial Sensor CalibrationMay 04 2019May 12 2019The common approach to inertial sensor calibration for navigation purposes has been to model the stochastic error signals of individual sensors independently, whether as components of a single inertial measurement unit (IMU) in different directions or ... More

Stability of complex hyperbolic space under curvature-normalized Ricci flowJun 02 2011Oct 26 2012Using the maximal regularity theory for quasilinear parabolic systems, we prove two stability results of complex hyperbolic space under the curvature-normalized Ricci flow in complex dimensions two and higher. The first result is on a closed manifold. ... More

An Attempt to Design a Better Algorithm for the Uncapacitated Facility Location ProblemOct 24 2016The uncapacitated facility location has always been an important problem due to its connection to operational research and infrastructure planning. Byrka obtained an algorithm that is parametrized by $\gamma$ and proved that it is optimal when $\gamma>1.6774$. ... More

On type-II singularities in Ricci flow on $\mathbb{R}^{N}$Oct 15 2012Sep 19 2015In each dimension $N\geq 3$ and for each real number $\lambda\geq 1$, we construct a family of complete rotationally symmetric solutions to Ricci flow on $\mathbb{R}^{N}$ which encounter a global singularity at a finite time $T$. The singularity forms ... More

Two Stage Optimization with Recourse and RevocationOct 21 2016Two-stage optimization with recourse model is an important and widely used model, which has been studied extensively these years. In this article, we will look at a new variant of it, called the two-stage optimization with recourse and revocation model. ... More

Point-Voxel CNN for Efficient 3D Deep LearningJul 08 2019We present Point-Voxel CNN (PVCNN) for efficient, fast 3D deep learning. Previous work processes 3D data using either voxel-based or point-based NN models. However, both approaches are computationally inefficient. The computation cost and memory footprints ... More

K-semistability is equivariant volume minimizationDec 22 2015Sep 27 2016This is a continuation to the paper \cite{Li15a} in which a problem of minimizing normalized volumes over $\mathbb{Q}$-Gorenstein klt singularities was proposed. Here we consider the case when there is a $\mathbb{C}^*$-action on $(X,o)$. In particular, ... More

From the Fourth Color to Spin-charge Separation - Neutrinos and SpinonsMar 31 2015We introduce the spin-charge separation mechanism to the quark-lepton unification models which consider the lepton number as the fourth color. In certain finite-density systems, quarks and leptons are decomposed into spinons and chargons, which carry ... More

Data volume and power of multiple tests with small sample size per nullOct 22 2008Jun 05 2009In multiple hypothesis testing, the volume of data, defined as the number of replications per null times the total number of nulls, usually defines the amount of resource required. On the other hand, power is an important measure of performance for multiple ... More

False discovery rate control with multivariate $p$-valuesJun 04 2007May 21 2008Multivariate statistics are often available as well as necessary in hypothesis tests. We study how to use such statistics to control not only false discovery rate (FDR) but also positive FDR (pFDR) with good power. We show that FDR can be controlled through ... More

A local stochastic Lipschitz condition with application to Lasso for high dimensional generalized linear modelsSep 06 2010For regularized estimation, the upper tail behavior of the random Lipschitz coefficient associated with empirical loss functions is known to play an important role in the error bound of Lasso for high dimensional generalized linear models. The upper tail ... More

Effects of statistical dependence on multiple testing under a hidden Markov modelApr 09 2009Mar 09 2011The performance of multiple hypothesis testing is known to be affected by the statistical dependence among random variables involved. The mechanisms responsible for this, however, are not well understood. We study the effects of the dependence structure ... More

On the asymptotic of likelihood ratios for self-normalized large deviationsSep 10 2007Jan 30 2008Motivated by multiple statistical hypothesis testing, we obtain the limit of likelihood ratio of large deviations for self-normalized random variables, specifically, the ratio of $P(\sqrt{n}(\bar X +d/n) \ge x_n V)$ to $P(\sqrt{n}\bar X \ge x_n V)$, as ... More

Direct photon production in Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV at STARAug 11 2014We present the direct photon production for $1<p_{T}<10$ GeV/$c$ derived from continuum in the dielectron invariant mass region $0.1<M_{ee}<0.3$ GeV/$c^{2}$ from one billion $\sqrt{s_{NN}}=200$ GeV Au+Au events taken in year 2010 and 2011. A clear excess ... More

Two-phase flow of ferrofluidsJul 26 2016Ferrofluids currently are the only type of magnetic liquid materials with wide practical use. The theory on ferrofluids is an example of success to apply statistics to science. Ferrofluids are two-phase liquids consisting of dispersed nanoscale ferromagnetic ... More

QCD strings and the U(1) problemNov 30 2018We promote the usual QCD $\theta$-parameter to a field and interpret it as the phase of the quark condensate, which becomes nontrivial when topological defects, vortices in our formulation, are induced in the quark condensate by the QCD strings (chromoelectric ... More

On Multivariate Strong Renewal TheoremDec 05 2014Mar 15 2017This paper takes the so-called probabilistic approach to the Strong Renewal Theorem (SRT) for multivariate distributions in the domain of attraction of a stable law. A version of the SRT is obtained that allows any kind of lattice-nonlattice composition ... More

Uniform convergence of exact large deviations for renewal reward processesJul 31 2007Let (X_n,Y_n) be i.i.d. random vectors. Let W(x) be the partial sum of Y_n just before that of X_n exceeds x>0. Motivated by stochastic models for neural activity, uniform convergence of the form $\sup_{c\in I}|a(c,x)\operatorname {Pr}\{W(x)\gecx\}-1|=o(1)$, ... More

Large deviations for template matching between point processesMar 22 2005We study the asymptotics related to the following matching criteria for two independent realizations of point processes X\sim X and Y\sim Y. Given l>0, X\cap [0,l) serves as a template. For each t>0, the matching score between the template and Y\cap [t,t+l) ... More

Gemini: Reducing DRAM Cache Hit Latency by Hybrid MappingsJun 03 2018Die-stacked DRAM caches are increasingly advocated to bridge the performance gap between on-chip Cache and main memory. It is essential to improve DRAM cache hit rate and lower cache hit latency simultaneously. Prior DRAM cache designs fall into two categories ... More

On Multivariate Strong Renewal TheoremDec 05 2014Dec 09 2014This paper takes the so-called probabilistic approach to the Strong Renewal Theorem (SRT) on $\mathbb{R}^d$ for distributions in the domain of attraction without centering of a nondegenerate stable law of exponent $\alpha \in (0, 2]\cap (0,d)$. We obtain ... More

Subspace Learning From BitsJul 23 2014Jul 24 2014This paper proposes a simple sensing and estimation framework to faithfully recover the principal subspace of high-dimensional datasets or data streams from a collection of one-bit measurements from distributed sensors based on comparing accumulated energy ... More

Law of the first passage triple of a spectrally positive strictly stable processJan 21 2018May 28 2018For a spectrally positive and strictly stable process with index in (1, 2), a series representation is obtained for the joint distribution of the "first passage triplet", i.e., the time, the undershoot, and the overshoot of first passage. The representation ... More

Dark fermions from the Standard Model via spin-charge separationMay 31 2016We study a new composite scenario of the lepton sector in the Standard Model by a de-gauging procedure called spin-charge separation and propose that leptons are bound states of some neutral fermions and Higgs bosons. Continuing this procedure we may ... More

A de-gauging approach to physics beyond the Standard ModelJun 06 2016By studying the t-J model for superconductivity, the Pati-Salam model and the Haplon model for particle unifications, we extract their common feature which is the spin-charge separation of fermions. This becomes a de-gauging process for charged fermions ... More

Phase of Quark Condensate and Topological Current in QCDOct 31 2013We propose a new topological charge term in QCD based on flux-tube models. It couples a superflow of the phase of the quark condensate to the Chern-Simons current. The usual $\theta$-parameter is replaced by the phase of the quark condensate, which becomes ... More

Generative Models for Learning from CrowdsJun 13 2017Oct 03 2017In this paper, we propose generative probabilistic models for label aggregation. We use Gibbs sampling and a novel variational inference algorithm to perform the posterior inference. Empirical results show that our methods consistently outperform state-of-the-art ... More

On equivariantly uniform stability and Yau-Tian-Donaldson conjecture for singular Fano varietiesJul 22 2019Let $X$ be a $\mathbb{Q}$-Fano variety and ${\rm Aut}(X)_0$ be the identity component of the automorphism group of $X$. Let $\mathbb{G}$ denote a connected reductive subgroup of ${\rm Aut(X)}_0$. We prove that if $X$ is $\mathbb{G}$-uniformly K-stable, ... More

On exact sampling of the first passage event of Levy process with infinite Levy measure and bounded variationJul 10 2012We present an exact sampling method for the first passage event of a Levy process. The idea is to embed the process into another one whose first passage event can be sampled exactly, and then recover the part belonging to the former from the latter. The ... More

Law of two-sided exit by a spectrally positive strictly stable processJun 19 2018For a spectrally positive strictly stable process with index in (1,2), the paper obtains i) the density of the time when the process makes first exit from an interval by hitting the interval's lower end point before jumping over its upper end point, and ... More

Stochastic Lipschitz continuity for high dimensional Lasso with multiple linear covariate structures or hidden linear covariatesNov 05 2010Two extensions of generalized linear models are considered. In the first one, response variables depend on multiple linear combinations of covariates. In the second one, only response variables are observed while the linear covariates are missing. We ... More

On $\ell_1$-regularized estimation for nonlinear models that have sparse underlying linear structuresNov 25 2009In a recent work (arXiv:0910.2517), for nonlinear models with sparse underlying linear structures, we studied the error bounds of $\ell_0$-regularized estimation. In this note, we show that $\ell_1$-regularized estimation in some important cases can achieve ... More

Sample size and positive false discovery rate control for multiple testingMar 08 2007May 09 2007The positive false discovery rate (pFDR) is a useful overall measure of errors for multiple hypothesis testing, especially when the underlying goal is to attain one or more discoveries. Control of pFDR critically depends on how much evidence is available ... More

Joint Sparsity Recovery for Spectral Compressed SensingNov 09 2013Feb 03 2014Compressed Sensing (CS) is an effective approach to reduce the required number of samples for reconstructing a sparse signal in an a priori basis, but may suffer severely from the issue of basis mismatch. In this paper we study the problem of simultaneously ... More

Lorentz Violation by Quark CondensationAug 02 2010At the TeV scale, heavy quarks, for example the 4th generation quarks of the Standard Model with four generations, can form condensates which dynamically break the electroweak symmetry. A dense quark system may form other types of condensates which dynamically ... More

Geometry of Kottwitz-Viehmann VarietiesMay 22 2018We study basic geometric properties of Kottwitz-Viehmann varieties, which are certain generalizations of affine Springer fibers that encode orbital integrals of spherical Hecke functions. Based on previous work of A. Bouthier and the author, we show that ... More

On the performance of FDR control: Constraints and a partial solutionOct 17 2007The False Discovery Rate (FDR) paradigm aims to attain certain control on Type I errors with relatively high power for multiple hypothesis testing. The Benjamini--Hochberg (BH) procedure is a well-known FDR controlling procedure. Under a random effects ... More

Molecular Clock Dating using MrBayesMar 17 2016There are two modern approaches on dating species divergence using molecular data: node dating (e.g., Yang and Rannala, 2006; Drummond et al., 2006) and total-evidence dating (e.g., Ronquist et al., 2012a; Zhang et al., 2016). In a Bayesian framework, ... More

Minimizing normalized volumes of valuationsNov 25 2015Apr 10 2016We propose a problem of minimizing normalized volumes of valuations. For a $\mathbb{Q}$-Gorenstein klt singularity, by proving a key properness estimate, we prove that the set of valuations with uniformly bounded normalized volumes is compact. Under a ... More

Gauged Nambu-Jona-Lasinio model and axionic QCD stringDec 30 2014We propose an axionic QCD string scenario based on the original flux-tube model by Kogut and Susskind, and then incorporate it into a gauged Nambu-Jona-Lasinio (NJL) model. Axial anomaly is studied by a new topological coupling from the string side, and ... More

QCD Flux Tubes and Anomaly InflowFeb 28 2013Jul 17 2013We apply the Callan-Harvey anomaly inflow mechanism to the study of QCD (chromoelectric) flux tubes, quark (pair)-creation and chiral magnetic effect, using new variables from the Cho-Faddeev-Niemi decomposition of the gauge potential. A phenomenological ... More

The geometry of some generalized affine Springer fibersOct 30 2017May 23 2018We study basic geometric properties of some group analogue of affine Springer fibers and compare with the classical Lie algebra affine Springer fibers. The main purpose is to formulate a conjecture that relates the number of irreducible components of ... More

Yau-Tian-Donaldson correspondence for K-semistable Fano manifoldsFeb 27 2013Feb 23 2015In this note, using the recent compactness results of Tian and Chen-Donaldson-Sun, we prove the K-semistable version of Yau-Tian-Donaldson correspondence for Fano manifolds.

Law of the first passage triple of a spectrally positive strictly stable processJan 21 2018Apr 02 2019For a spectrally positive and strictly stable process with index in (1,2), a series representation is obtained for the joint distribution of the "first passage triple" that consists of the time of first passage and the undershoot and the overshoot at ... More

Nonnormal small jump approximation of infinitely divisible distributionsApr 23 2013We consider a type of nonnormal approximation of infinitely divisible distributions that incorporates compound Poisson, Gamma, and normal distributions. The approximation relies on achieving higher orders of cumulant matching, to obtain higher rates of ... More

Limit laws of estimators for critical multi-type Galton-Watson processesMar 24 2005We consider the asymptotics of various estimators based on a large sample of branching trees from a critical multi-type Galton-Watson process, as the sample size increases to infinity. The asymptotics of additive functions of trees, such as sizes of trees ... More

Random reversible Markov matrices with tunable extremal eigenvaluesMay 08 2015Sep 08 2015Random sampling of large Markov matrices with a tunable spectral gap, a nonuniform stationary distribution, and a nondegenerate limiting empirical spectral distribution (ESD) is useful. Fix $c>0$ and $p>0$. Let $A_n$ be the adjacency matrix of a random ... More

Mean curvature flow of noncompact hypersurfaces with Type-II curvature blow-upMar 05 2016May 07 2017We study the phenomenon of Type-II curvature blow-up in mean curvature flows of rotationally symmetric noncompact embedded hypersurfaces. Using analytic techniques based on formal matched asymptotics and the construction of upper and lower barrier solutions ... More

Joint Stochastic Approximation learning of Helmholtz MachinesMar 20 2016Though with progress, model learning and performing posterior inference still remains a common challenge for using deep generative models, especially for handling discrete hidden variables. This paper is mainly concerned with algorithms for learning Helmholz ... More

Degenerate neckpinches in mean curvature flow on noncompact hypersurfacesMar 05 2016Mar 13 2016We study the formation of Type-II singularities in mean curvature flows of rotationally symmetric noncompact embedded hypersurfaces. Using analytic techniques based on formal matched asymptotics and the construction of upper and lower barrier solutions ... More

Integrating Lexical and Temporal Signals in Neural Ranking Models for Searching Social Media StreamsJul 25 2017Time is an important relevance signal when searching streams of social media posts. The distribution of document timestamps from the results of an initial query can be leveraged to infer the distribution of relevant documents, which can then be used to ... More

Evolving Agents for the Hanabi 2018 CIG CompetitionSep 26 2018Hanabi is a cooperative card game with hidden information that has won important awards in the industry and received some recent academic attention. A two-track competition of agents for the game will take place in the 2018 CIG conference. In this paper, ... More

Generating Sentiment-Preserving Fake Online Reviews Using Neural Language Models and Their Human- and Machine-based DetectionJul 22 2019Advanced neural language models (NLMs) are widely used in sequence generation tasks because they are able to produce fluent and meaningful sentences. They can also be used to generate fake reviews, which can then be used to attack online review systems ... More

The topology on Berkovich affine lines over complete valuation ringsMar 16 2017In this article, we give a full description of the topology of the one dimensional affine analytic space $\mathbb{A}_R^1$ over a complete valuation ring $R$ (i.e. a valuation ring with "real valued valuation" which is complete under the induced metric), ... More

A Model-based Approach for Effective Service DeliveryApr 19 2016May 31 2016With the prevalence of X-as-a-Service (e.g., software as a service, platform as a service, infrastructure as a service, etc.) and users' growing demand on good services, QoS (Quality of Service) assurance is becoming increasingly important to service ... More

Property $(T)$ and strong Property $(T)$ for unital $C^*$-algebrasJan 14 2009In this paper, we will give a thorough study of the notion of Property $(T)$ for $C^*$-algebras (as introduced by M.B. Bekka in \cite{Bek-T}) as well as a slight stronger version of it, called "strong property $(T)$" (which is also an analogue of the ... More

Berkovich spectra of elements in Banach RingsOct 22 2014Adapting the notion of the spectrum $\Sigma_a$ for an element $a$ in an ultrametric Banach algebra (as defined by Berkovich), we introduce and briefly study the Berkovich spectrum $\sigma^{Ber}_R(u)$ of an element $u$ in a Banach ring $R$. This spectrum ... More

Dynamical stability of algebraic Ricci solitonsSep 21 2013Sep 10 2014We consider dynamical stability for a modified Ricci flow equation whose stationary solutions include Einstein and Ricci soliton metrics. Our focus is on homogeneous metrics on non-compact manifolds. Following the program of Guenther, Isenberg, and Knopf, ... More

On tensor products of positive representations of split real quantum Borel subalgebra $U_{q\tilde{q}}(b_R)$May 19 2014May 29 2014We studied the positive representations $P_\lambda$ of split real quantum groups $U_{q\tilde{q}}(g_R)$ restricted to the Borel subalgebra $U_{q\tilde{q}}(b_R)$. We proved that the restriction is independent of the parameter $\lambda$. Furthermore, we ... More

Conical Kahler-Einstein metric revisitedJul 20 2012Oct 07 2012In this paper we introduce the "interpolation-degneration" strategy to study Kahler-Einstein metrics on a smooth Fano manifold with cone singularities along a smooth divisor that is proportional to the anti-canonical divisor. By "interpolation" we show ... More

Multiple Testing under Dependence with Approximate Conditional LikelihoodDec 25 2014Apr 09 2016It has long been recognized that statistical dependence in data poses a significant challenge to large-scale multiple testing. Failure to take the dependence into account can result in severe drop in performance of multiple testing. In particular, the ... More

Geometric Bijections Between Spanning Trees and Break DivisorsSep 09 2015The Jacobian group ${\rm Jac}(G)$ of a finite graph $G$ is a group whose cardinality is the number of spanning trees of $G$. $G$ also has a tropical Jacobian which has the structure of a real torus; using the notion of break divisors, An et al. obtained ... More

A unified composite model of inflation and dark matter in the Nambu-Jona-Lasinio theorySep 15 2016In this work, we propose a cosmological scenario inherently based on the effective Nambu-Jona-Lasinio (NJL) model that comic inflation and dark matter can be successfully described by a single framework. On the one hand, the scalar channel of the NJL ... More

Kähler-Einstein metrics and volume minimizationFeb 16 2016Apr 11 2016We prove that if a $\mathbb{Q}$-Fano variety $V$ specially degenerates to a K\"ahler-Einstein $\mathbb{Q}$-Fano variety $V$, then for any ample Cartier divisor $H=-r^{-1} K_V$ with $r\in \mathbb{Q}_{>0}$, the normalized volume $\widehat{\rm vol}(v)=A_X^n(v)\cdot ... More

Behavior of zeros of $X_{1}$-Jacobi and $X_{1}$-Laguerre exceptional polynomialsJun 29 2018Dec 09 2018The $X_1$-Jacobi and the $X_1$-Laguerre exceptional orthogonal polynomials have been introduced and studied by G\'omez-Ullate, Kamran and Milson in a series of papers. In this note, we establish some properties, such as interlacing, monotonicity with ... More

Moduli Space of Paired Punctures, Cyclohedra and Particle Pairs on a CircleDec 27 2018In this paper, we study a new moduli space $\mathcal{M}_{n+1}^{\mathrm{c}}$, which is obtained from $\mathcal{M}_{0,2n+2}$ by identifying pairs of punctures. We find that this space is tiled by $2^{n-1}n!$ cyclohedra, and construct the canonical form ... More

Some remarks on groupoids and small categoriesOct 18 2007This unpublished note contains some materials taken from my old study note on groupoids and small categories. It contains a proof for the fact that any groupoid is a group bundle over an equivalence relation. Moreover, the action of a category $G$ on ... More

Properties of post-shock solar wind deduced from geomagnetic indices responses after sudden impulsesAug 16 2016Interplanetary (IP) shock plays a key role in causing the global dynamic changes of the geospace environment. For the perspective of Solar-Terrestrial relationship, it will be of great importance to estimate the properties of post-shock solar wind simply ... More

An n-to-1 Bidder Reduction for Multi-item Auctions and its ApplicationsJun 12 2014Jun 23 2014In this paper, we introduce a novel approach for reducing the $k$-item $n$-bidder auction with additive valuation to $k$-item $1$-bidder auctions. This approach, called the \emph{Best-Guess} reduction, can be applied to address several central questions ... More

Domains of Injectivity for the Gross-Hopkins Period MapNov 29 2013Mar 11 2015We determine the domain of injectivity of the Gross-Hopkins Period map around each points in the deformation space for a fixed formal module $\bar{F}$ of height 2 that defined over a finite field. And then we will use this to conclude some local analyticity ... More

A new look at Condition AJul 02 2009Ozeki and Takeuchi \cite[I]{OT} introduced the notion of Condition A and Condition B to construct two classes of inhomogeneous isoparametric hypersurfaces with four principal curvatures in spheres, which were later generalized by Ferus, Karcher and M\"unzner ... More

False Discovery Variance Reduction in Large Scale Simultaneous Hypothesis TestsDec 25 2014Oct 12 2018Statistical dependence between hypotheses poses a significant challenge to the stability of large scale multiple hypotheses testing. Ignoring it often results in an unacceptably large spread in the false positive proportion even though the average value ... More

Universal programmable devices for unambiguous discriminationJun 22 2006We discuss the problem of designing unambiguous programmable discriminators for any $n$ unknown quantum states in an $m$-dimensional Hilbert space. The discriminator is a fixed measurement which has two kinds of input registers: the program registers ... More

Interior continuity of two-dimensional weakly stationary-harmonic multiple-valued functionsAug 01 2011May 09 2013In his big regularity paper, Almgren has proven the regularity theorem for mass-minimizing integral currents. One key step in his paper is to derive the regularity of Dirichlet-minimizing $\mathbf{Q}_{Q}(\mathbb{R}^{n})$-valued functions in the Sobolev ... More

Low-energy Effective Theory for Spin Dynamics of Fluctuating StripesOct 20 2005We derive an effective Hamiltonian for spin dynamics of fluctuating smectic stripes from the t-J model in the weak coupling limit t >> J. Besides the modulation of spin magnitude, the high energy hopping term would induce a low-energy anti-ferromagnetic ... More

Duality of Hopf $C^*$-algebrasJun 03 2002In this paper, we study the duality theory of Hopf $C^*$-algebras in a general ``Hilbert-space-free'' framework. Our particular interests are the ``full duality'' and the ``reduced duality''. In order to study the reduced duality, we define the interesting ... More

Mathematical analysis of stochastic models for tumor-immune systemsJun 15 2009In this paper we investigate some stochastic models for tumor-immune systems. To describe these models we used a Wiener process, as the noise has a stabilization effect. Their dynamics are studied in terms of stochastic stability in the equilibrium points, ... More

Positive Casimir and Central Characters of Split Real Quantum GroupsMar 02 2015Mar 30 2015We describe the generalized Casimir operators and their actions on the positive representations $P_{\lambda}$ of the modular double of split real quantum groups $U_{q\tilde{q}}(g_R)$. We introduce the notion of virtual highest and lowest weights, and ... More

Stochastic Fractional HP EquationsJun 24 2009In this paper we established the condition for a curve to satisfy stochas- tic fractional HP (Hamilton-Pontryagin) equations. These equations are described using It^o integral. We have also considered the case of stochastic fractional Hamiltonian equa- ... More

Microwave-mediated heat transport through a quantum dotFeb 06 2012The thermoelectric effect in a quantum dot (QD) attached to two leads in the presence of microwave fields is studied by using the Keldysh nonequilibrium Green function technique. When the microwave is applied only on the QD and in the linear-response ... More

Isoparametric hypersurfaces with four principal curvatures, IVMay 03 2016We prove that an isoparametric hypersurface with four principal curvatures and multiplicity pair $(7,8)$ is either the one constructed by Ozeki and Takeuchi, or one of the two constructed by Ferus, Karcher, and M\"{u}nzner. This completes the classification ... More

Picard group of isotropic realizations of twisted Poisson manifoldsNov 12 2015Let $B$ be a twisted Poisson manifold with a fixed tropical affine structure given by a period bundle $P$. In this paper, we study the classification of almost symplectically complete isotropic realizations (ASCIRs) over $B$ in the spirit of \cite{DD}. ... More

Generalized Cluster Trees and Singular MeasuresNov 08 2016In this paper, we study the $\alpha$-cluster tree ($\alpha$-tree) under both singular and nonsingular measures. The $\alpha$-tree uses probability contents within a level set to construct a cluster tree so that it is well-defined for singular measures. ... More

Coordinating Dynamical Routes with Statistical Physics on Space-time NetworksJun 25 2018Mar 27 2019Coordination of dynamical routes can alleviate traffic congestion and is essential for the coming era of autonomous self-driving cars. However, dynamical route coordination is difficult and many existing routing protocols are either static or without ... More

Do recommender systems benefit users?Jul 05 2015Recommender systems are present in many web applications to guide our choices. They increase sales and benefit sellers, but whether they benefit customers by providing relevant products is questionable. Here we introduce a model to examine the benefit ... More

On the extension of holomorphic sections from reduced unions of strata of divisorsMay 16 2019In this paper we study the problem of extension of holomorphic sections of line bundles/vector bundles from reduced unions of strata of divisors. An extension theorem of Ohsawa--Takegoshi type is proved. As consequences we deduce several qualitative results ... More

Graviton Bending in Quantum Gravity from One-Loop AmplitudesMar 19 2019We study the bending of gravitons that pass near a massive object like the Sun, using scattering amplitudes in which the Sun is represented by a massive scalar particle. Our results complete previous work on the bending angles of massless spin-0, spin-$\frac{1}{2}$ ... More

Coevolution Maintains Diversity in the Stochastic "Kill the Winner" ModelJun 08 2017The "Kill the Winner" hypothesis is an attempt to address the problem of diversity in biology. It argues that host-specific predators control the population of each prey, preventing a winner from emerging and thus maintaining the coexistence of all species ... More