Results for "Haotian Chi"
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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 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 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 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 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 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 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 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 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 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 FDR control for multiple hypothesis testing on composite nullsJul 30 2008Multiple hypothesis testing often involves composite nulls, i.e., nulls that are associated with two or more distributions. In many cases, it is reasonable to assume that there is a prior distribution on the distributions despite it is unknown. When the ... More Integral criteria for Strong Renewal Theorems with infinite meanDec 20 2013Apr 15 2014Let $F$ be a probability measure on $\mathbb{R}$ in the domain of attraction of a stable law with exponent $\alpha\in (0, 1)$. We establish integral criteria on $F$ that significantly expand the probabilistic approach to Strong Renewal Theorems (SRTs). ... 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 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 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 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 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 Invariant ideals of twisted crossed productsJun 03 2002Jun 25 2002We prove a result concerning the inclusion of non-trivial invariant ideals inside non-trivial ideals of a twisted crossed product. We will also give results concerning the primeness and simplicity of crossed products of twisted actions of locally compact ... More Adams operations on classical compact Lie groupsOct 07 2015Aug 05 2016Let $G$ be $U(n)$, $SU(n)$, $Sp(n)$ or $Spin(n)$. In this short note we give explicit general formulas for Adams operations on $K^*(G)$, and eigenvectors of Adams operations on $K^*(U(n))$. On the Efficiency of Quantum Algorithms for Hamiltonian SimulationMay 08 2010Oct 11 2010We study the efficiency of algorithms simulating a system evolving with Hamiltonian $H=\sum_{j=1}^m H_j$. We consider high order splitting methods that play a key role in quantum Hamiltonian simulation. We obtain upper bounds on the number of exponentials ... More Crater Property in Two-Particle Bound States: When and WhyOct 26 1999Crater has shown that, for two particles (with masses $m_1$ and $m_2$) in a Coulombic bound state, the charge distribution is equal to the sum of the two charge distributions obtained by taking $m_1\to\infty$ and $m_2\to\infty$ respectively, while keeping ... More Heavy Baryons and Multiquark Exotics in the Large $N_c$ limitNov 10 1995In the large $N_c$ limit, one can describe normal heavy baryons $Qqq$ and heavy pentaquarks $\bar Qqqqq$ as bound states of heavy mesons to chiral (anti)solitons. In this picture, the strong and electromagnetic decay parameters of these hadrons can be ... More A Transversality Theorem for some Classical VarietiesNov 14 2011Nov 18 2011In 2009, de Fernex and Hacon proposed a generalization of the notion of the singularities to normal varieties that are not Q-Gorenstein. Based on their work, we generalize Kleiman's transversality theorem to subvarieties with log terminal or log canonical ... More Mathematical pendulum and its variantsMay 27 2009In this paper we show that there are applications that transform the movement of a pendulum into movements in $\mathbb{R}^3$. This can be done using Euler top system of differential equations. On the constant level surfaces, Euler top system reduces to ... More MOND's Problem in Local GroupJan 14 2011I use the distances and motions of Local Group galaxies to test Modified Newtonian Dynamics (MOND). The old Local Group timing argument of Kahn & Woltjer, which assumed Newtonian gravity and a simple radial orbit, indicated that the total mass of M31 ... More On quaternionic functional analysisSep 06 2006In this article, we will show that the category of quaternion vector spaces, the category of (both one-sided and two sided) quaternion Hilbert spaces and the category of quaternion $B^*$-algebras are equivalent to the category of real vector spaces, the ... More Oscillations of the Inner Regions of Viscous Accretion DisksDec 11 2008Although quasi-periodic oscillations (QPOs) have been discovered in different X-ray sources, their origin is still a matter of debate. Analytical studies of hydrodynamic accretion disks have shown three types of trapped global modes with properties that ... More Thermodynamics of the System of Distinguishable ParticlesMar 27 2009Jun 29 2009The issue of the thermodynamics of a system of distinguishable particles is discussed in this paper. In constructing the statistical mechanics of distinguishable particles from the definition of Boltzmann entropy, it is found that the entropy is not extensive. ... More AdS_5 Supersymmetry in N=1 SuperspaceMay 24 2011Aug 21 2011We use N=1 superspace to construct the supersymmetric matter couplings of vector and hyper multiplets in a five-dimensional anti-de Sitter spacetime background. For hypermultiplets, we find that AdS_5 supersymmetry requires the scalar fields to lie on ... More Examples of Amenable Kac systemOct 27 2000By giving an interesting characterisation of amenable multiplicative unitaries in term of one dimensional representations, we show in a simple way that bicrossproducts of amenable locally compact groups is both amenable and coamenable. $KR$-theory of compact Lie groups with group anti-involutionsMay 14 2014Oct 17 2015Let $G$ be a compact, connected, and simply-connected Lie group, equipped with an anti-involution $a_G$ which is the composition of a Lie group involutive automorphism $\sigma_G$ and the group inversion. We view $(G, a_G)$ as a Real $(G, \sigma_G)$-space ... More Notes on Scattering Amplitudes as Differential FormsJul 29 2018Aug 31 2018Inspired by the idea of viewing amplitudes in ${\cal N}=4$ SYM as differential forms on momentum twistor space, we introduce differential forms on the space of spinor variables, which combine helicity amplitudes in any four-dimensional gauge theory as ... 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 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 Quantum Bit Commitment can be Unconditionally SecureDec 20 2001Jul 28 2003It is generally believed that unconditionally secure quantum bit commitment (QBC) is proven impossible by a "no-go theorem". We point out that the theorem only establishes the existence of a cheating unitary transformation in any QBC scheme secure against ... More Insecurity of Quantum Bit Commitment with Secret ParametersJan 31 2006The impossibility proof of unconditionally secure quantum bit commitment is crucially dependent on the assertion that Bob is not allowed to generate probability distributions unknown to Alice. This assertion is actually not meaningful, because Bob can ... More Secret parameters in quantum bit commitmentAug 24 2005Sep 28 2005The no-go theorem of unconditionally secure quantum bit commitment depends crucially on the assumption that Alice knows in detail all the probability distributions generated by Bob. We show that if a protocol is concealing, then the cheating unitary transformation ... More Spectral Compressed Sensing via Structured Matrix CompletionApr 16 2013May 01 2013The paper studies the problem of recovering a spectrally sparse object from a small number of time domain samples. Specifically, the object of interest with ambient dimension $n$ is assumed to be a mixture of $r$ complex multi-dimensional sinusoids, while ... 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 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 On isolated log canonical centersApr 15 2013In this paper, we show that the depth of an isolated log canonical center is determined by the cohomology of the -1 discrepancy diviors over it. A similar result also holds for normal isolated Du Bois singularities. 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 Fluid Invasion in Porous Media: Viscous Gradient PercolationMay 12 2004We suggest that the dynamics of stable viscous invasion fronts in porous media depends on the volume capacitance of the media. At high volume capacitance, our network simulations provide numerical evidence of a scaling relation between the front width ... 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 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 Secure Quantum Bit Commitment Using Unstable ParticlesMar 17 2006Mar 28 2006Using unstable particles which decay by emitting neutrinos, we propose a quantum bit commitment protocol that is humanly impossible to break. Neutrinos carry away quantum information, but their interaction with matter is so weak that it would take an ... More