Results for "Jian Ding"

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Exponential and double exponential tails for maximum of two-dimensional discrete Gaussian free fieldMay 29 2011Sep 25 2012We study the tail behavior for the maximum of discrete Gaussian free field on a 2D box with Dirichlet boundary condition after centering by its expectation. We show that it exhibits an exponential decay for the right tail and a double exponential decay ... More
Scaling window for mean-field percolation of averagesOct 14 2011Feb 15 2013For a complete graph of size $n$, assign each edge an i.i.d. exponential variable with mean $n$. For $\lambda>0$, consider the length of the longest path whose average weight is at most $\lambda$. It was shown by Aldous (1998) that the length is of order ... More
On cover times for 2D latticesOct 15 2011Jun 05 2012We study the cover time $\tau_{\mathrm{cov}}$ by (continuous-time) random walk on the 2D box of side length $n$ with wired boundary or on the 2D torus, and show that in both cases with probability approaching 1 as $n$ increases, $\sqrt{\tau_{\mathrm{cov}}}=\sqrt{2n^2}[\sqrt{2/\pi} ... More
Asymptotics of cover times via Gaussian free fields: Bounded-degree graphs and general treesMar 22 2011Feb 25 2014In this paper we show that on bounded degree graphs and general trees, the cover time of the simple random walk is asymptotically equal to the product of the number of edges and the square of the expected supremum of the Gaussian free field on the graph, ... More
Extreme values for two-dimensional discrete Gaussian free fieldJun 02 2012Apr 07 2013We consider in this paper the collection of near maxima of the discrete, two dimensional Gaussian free field in a box with Dirichlet boundary conditions. We provide a rough description of the geometry of the set of near maxima, estimates on the gap between ... More
Liouville first passage percolation: geodesic length exponent is strictly larger than 1 at high temperaturesOct 10 2016Mar 16 2019Let $\{\eta(v): v\in V_N\}$ be a discrete Gaussian free field in a two-dimensional box $V_N$ of side length $N$ with Dirichlet boundary conditions. We study the Liouville first passage percolation, i.e., the shortest path metric where each vertex is given ... More
Sensitivity of mixing timesMar 31 2013In this note, we demonstrate an instance of bounded-degree graphs of size $n$, for which the total variation mixing time for the random walk is decreased by a factor of $\log n/ \log\log n$ if we multiply the edge-conductances by bounded factors in a ... More
Localization for random walks among random obstacles in a single Euclidean ballJul 21 2018Nov 02 2018Place an obstacle with probability $1-p$ independently at each vertex of $\mathbb Z^d$, and run a simple random walk until hitting one of the obstacles. For $d\geq 2$ and $p$ strictly above the critical threshold for site percolation, we condition on ... More
Mixing time for the Ising model: a uniform lower bound for all graphsSep 28 2009Sep 25 2013Consider Glauber dynamics for the Ising model on a graph of $n$ vertices. Hayes and Sinclair showed that the mixing time for this dynamics is at least $n\log n/f(\Delta)$, where $\Delta$ is the maximum degree and $f(\Delta) = \Theta(\Delta \log^2 \Delta)$. ... More
Liouville first-passage percolation: subsequential scaling limits at high temperatureMay 13 2016Sep 15 2018Let $\{Y_{\mathfrak{B}}(x)\,:\,x\in\mathfrak{B}\}$ be a discrete Gaussian free field in a two-dimensional box $\mathfrak{B}$ of side length $S$ with Dirichlet boundary conditions. We study Liouville first-passage percolation: the shortest-path metric ... More
Non-universality for first passage percolation on the exponential of log-correlated Gaussian fieldsJun 10 2015Oct 25 2017We consider first passage percolation (FPP) where the vertex weight is given by the exponential of two-dimensional log-correlated Gaussian fields. Our work is motivated by understanding the discrete analog for the random metric associated with \emph{Liouville ... More
Exploring the Self-enhanced Mechanism of Interactive Advertising Phenomenon---Based on the Research of Three CasesMay 18 2015Under the background of the new media era with the rapid development of interactive advertising, this paper used case study method based on the summary of the research of the communication effect of interactive advertising from both domestic and foreign ... 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
Mixing under monotone censoringNov 23 2013Dec 02 2013We initiate the study of mixing times of Markov chain under monotone censoring. Suppose we have some Markov Chain $M$ on a state space $\Omega$ with stationary distribution $\pi$ and a monotone set $A \subset \Omega$. We consider the chain $M'$ which ... More
Poly-logarithmic localization for random walks among random obstaclesMar 20 2017Jul 21 2018Place an obstacle with probability $1-p$ independently at each vertex of $\mathbb Z^d$, and run a simple random walk until hitting one of the obstacles. For $d\geq 2$ and $p$ strictly above the critical threshold for site percolation, we condition on ... More
Three favorite sites occurs infinitely often for one-dimensional simple random walkDec 06 2016Oct 25 2017For a one-dimensional simple random walk $(S_t)$, for each time $t$ we say a site $x$ is a favorite site if it has the maximal local time. In this paper, we show that with probability 1 three favorite sites occurs infinitely often. Our work is inspired ... More
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
Upper bounds on Liouville first passage percolation and Watabiki's predictionOct 31 2016Aug 01 2018Given a planar continuum Gaussian free field $h^{\mathcal U}$ in a domain $\mathcal U$ with Dirichlet boundary condition and any $\delta>0$, we let $\{h_\delta^{\mathcal U}(v): v\in \mathcal U\}$ be a real-valued smooth Gaussian process where $h_\delta^{\mathcal ... More
Subsequential scaling limits for Liouville graph distanceDec 17 2018Apr 01 2019For $0<\gamma<2$ and $\delta>0$, we consider the Liouville graph distance, which is the minimal number of Euclidean balls with Liouville quantum gravity measure at most $\delta$ whose union contains a continuous path between two endpoints. In this paper, ... More
Percolation for level-sets of Gaussian free fields on metric graphsJul 29 2018Mar 12 2019We study level-set percolation for Gaussian free fields on metric graphs. In two dimensions, we give an upper bound on the chemical distance between the two boundaries of a macroscopic annulus. Our bound holds with high probability conditioned on connectivity ... More
A sharp estimate for cover times on binary treesApr 03 2011We compute the second order correction for the cover time of the binary tree of depth $n$ by (continuous-time) random walk, and show that with probability approaching 1 as $n$ increases, $\sqrt{\tau_{\mathrm{cov}}}=\sqrt{|E|}[\sqrt{2\log 2}\cdot n - {\log ... More
Percolation of averages in the stochastic mean field model: the near-supercritical regimeJan 15 2015Nov 19 2015For a complete graph of size $n$, assign each edge an i.i.d.\ exponential variable with mean $n$. For $\lambda>0$, consider the length of the longest path whose average weight is at most $\lambda$. It was shown by Aldous (1998) that the length is of order ... More
Nonconvex Approach for Sparse and Low-Rank Constrained Models with Dual MomentumJun 06 2019In this manuscript, we research on the behaviors of surrogates for the rank function on different image processing problems and their optimization algorithms. We first propose a novel nonconvex rank surrogate on the general rank minimization problem and ... More
Supercritical minimum mean-weight cyclesApr 03 2015We study the weight and length of the minimum mean-weight cycle in the stochastic mean-field distance model, i.e., in the complete graph on $n$ vertices with edges weighted by independent exponential random variables. Mathieu and Wilson showed that the ... More
Persistence of iterated partial sumsMay 15 2012Let $S_n^{(2)}$ denote the iterated partial sums. That is, $S_n^{(2)}=S_1+S_2+ ... +S_n$, where $S_i=X_1+X_2+ ... s+X_i$. Assuming $X_1, X_2,....,X_n$ are integrable, zero-mean, i.i.d. random variables, we show that the persistence probabilities $$p_n^{(2)}:=\PP(\max_{1\le ... More
On multiple peaks and moderate deviations for supremum of Gaussian fieldNov 21 2013Nov 25 2013We prove two theorems concerning extreme values of general Gaussian fields. Our first theorem concerns with the concept of multiple peaks. A theorem of Chatterjee states that when a centered Gaussian field admits the so-called superconcentration property, ... More
On level sets of Gaussian fieldsOct 18 2013In this short note, we present a theorem concerning certain "additive structure" for the level sets of non-degenerate Gaussian fields, which yields the multiple valley phenomenon for extremal fields with exponentially many valleys.
Persistence versus stability for auto-regressive processesJun 02 2019The stability of an Auto-Regressive (AR) time sequence of finite order $L$, is determined by the maximal modulus $r^\star$ among all zeros of its generating polynomial. If $r^\star<1$ then the effect of input and initial conditions decays rapidly in time, ... More
Electron heating and acceleration by magnetic reconnection in hot accretion flowsNov 24 2009Both analytical and numerical works show that magnetic reconnection must occur in hot accretion flows. This process will effectively heat and accelerate electrons. In this paper we use the numerical hybrid simulation of magnetic reconnection plus test-electron ... More
Anatomy of the giant component: The strictly supercritical regimeFeb 28 2012In a recent work of the authors and Kim, we derived a complete description of the largest component of the Erd\H{o}s-R\'enyi random graph $G(n,p)$ as it emerges from the critical window, i.e. for $p = (1+\epsilon)/n$ where $\epsilon^3 n \to\infty$ and ... More
Cover times, blanket times, and majorizing measuresApr 25 2010Oct 07 2011We exhibit a strong connection between cover times of graphs, Gaussian processes, and Talagrand's theory of majorizing measures. In particular, we show that the cover time of any graph $G$ is equivalent, up to universal constants, to the square of the ... More
Censored Glauber Dynamics for the mean field Ising ModelDec 03 2008We study Glauber dynamics for the Ising model on the complete graph on $n$ vertices, known as the Curie-Weiss Model. It is well known that at high temperature ($\beta < 1$) the mixing time is $\Theta(n\log n)$, whereas at low temperature ($\beta > 1$) ... More
The mixing time evolution of Glauber dynamics for the mean-field Ising modelJun 11 2008Jun 12 2008We consider Glauber dynamics for the Ising model on the complete graph on $n$ vertices, known as the Curie-Weiss model. It is well-known that the mixing-time in the high temperature regime ($\beta < 1$) has order $n\log n$, whereas the mixing-time in ... More
Occluded Face Recognition Using Low-rank Regression with Generalized Gradient DirectionJun 06 2019In this paper, a very effective method to solve the contiguous face occlusion recognition problem is proposed. It utilizes the robust image gradient direction features together with a variety of mapping functions and adopts a hierarchical sparse and low-rank ... More
Convergence of the centered maximum of log-correlated Gaussian fieldsMar 16 2015We show that the centered maximum of a sequence of log-correlated Gaussian fields in any dimension converges in distribution, under the assumption that the covariances of the fields converge in a suitable sense. We identify the limit as a randomly shifted ... More
Heat kernel for Liouville Brownian motion and Liouville graph distanceJul 02 2018We show the existence of the scaling exponent $\chi\in (0,4[(1+\gamma^2/4)- \sqrt{1+\gamma^4/16}]/\gamma^2]$ of the graph distance associated with subcritical two-dimensional Liouville quantum gravity of paramater $\gamma<2$ on $\mathbb V =[0,1]^2 $. ... More
Total-variation cutoff in birth-and-death chainsJan 17 2008Oct 06 2008The cutoff phenomenon describes a case where a Markov chain exhibits a sharp transition in its convergence to stationarity. In 1996, Diaconis surveyed this phenomenon, and asked how one could recognize its occurrence in families of finite ergodic Markov ... More
Return probability and recurrence for the random walk driven by two-dimensional Gaussian free fieldNov 11 2016Given any $\gamma>0$ and for $\eta=\{\eta_v\}_{v\in \mathbb Z^2}$ denoting a sample of the two-dimensional discrete Gaussian free field on $\mathbb Z^2$ pinned at the origin, we consider the random walk on $\mathbb Z^2$ among random conductances where ... More
Convergence in law of the maximum of the two-dimensional discrete Gaussian free fieldJan 28 2013Jul 03 2015We consider the two-dimensional Gaussian Free Field on a box of side length $N$, with Dirichlet boundary data, and prove the convergence of the law of the recentered maximum of the field.
Towards better Validity: Dispersion based Clustering for Unsupervised Person Re-identificationJun 04 2019Person re-identification aims to establish the correct identity correspondences of a person moving through a non-overlapping multi-camera installation. Recent advances based on deep learning models for this task mainly focus on supervised learning scenarios ... More
New quantum codes from dual-containing cyclic codes over finite ringsAug 24 2016Let $R=\mathbb{F}_{2^{m}}+u\mathbb{F}_{2^{m}}+\cdots+u^{k}\mathbb{F}_{2^{m}}$ , where $\mathbb{F}_{2^{m}}$ is a finite field with $2^{m}$ elements, $m$ is a positive integer, $u$ is an indeterminate with $u^{k+1}=0.$ In this paper, we propose the constructions ... More
Capacitated Center Problems with Two-Sided Bounds and OutliersFeb 24 2017In recent years, the capacitated center problems have attracted a lot of research interest. Given a set of vertices $V$, we want to find a subset of vertices $S$, called centers, such that the maximum cluster radius is minimized. Moreover, each center ... More
Energy-Efficient Joint Congestion Control and Resource Optimization in Heterogeneous Cloud Radio Access NetworksFeb 17 2016The heterogeneous cloud radio access network (HCRAN) is a promising paradigm which integrates the advantages of cloud radio access network (C-RAN) and heterogeneous network (HetNet). In this paper, we study the joint congestion control and resource optimization ... More
Geometry of the random walk range conditioned on survival among Bernoulli obstaclesJun 21 2018We consider a discrete time simple symmetric random walk among Bernoulli obstacles on $\mathbb{Z}^d$, $d\geq 2$, where the walk is killed when it hits an obstacle. It is known that conditioned on survival up to time $N$, the random walk range is asymptotically ... More
Cut-off for lamplighter chains on tori: dimension interpolation and phase transitionDec 16 2013Aug 14 2018Given a finite, connected graph $G$, the lamplighter chain on $G$ is the lazy random walk $X^\diamond$ on the associated lamplighter graph $G^\diamond={\mathbf Z}_2 \wr G$. The mixing time of the lamplighter chain on the torus ${\mathbf Z}_n^d$ is known ... More
Cognitive Non-Orthogonal Multiple Access with Cooperative Relaying: A New Wireless Frontier for 5G Spectrum SharingJan 12 2018Two emerging technologies towards 5G wireless networks, namely non-orthogonal multiple access (NOMA) and cognitive radio (CR), will provide more efficient utilization of wireless spectrum in the future. In this article, we investigate the integration ... More
Scalable and Accurate Online Feature Selection for Big DataNov 30 2015Jul 28 2016Feature selection is important in many big data applications. Two critical challenges closely associate with big data. Firstly, in many big data applications, the dimensionality is extremely high, in millions, and keeps growing. Secondly, big data applications ... 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
Tightness of Liouville first passage percolation for $γ\in (0,2)$Apr 16 2019We study Liouville first passage percolation metrics associated to a Gaussian free field $h$ mollified by the two-dimensional heat kernel $p_t$ in the bulk, and related star-scale invariant metrics. For $\gamma \in (0,2)$ and $\xi = \frac{\gamma}{d_{\gamma}}$, ... More
The Fidelity of Measurement-Based Quantum Computation under a Boson EnvironmentApr 07 2014Oct 27 2014We investigate the fidelity of the measurement-based quantum computation (MBQC) when it is coupled with boson environment, by measuring cluster state fidelity and gate fidelity. Two different schemes of cluster state preparation are studied. In the Controlled-Z ... More
SRLA: A real time sliding time window super point cardinality estimation algorithm for high speed network based on GPUMar 28 2018Jul 04 2018Super point is a special host in network which communicates with lots of other hosts in a certain time period. The number of hosts contacting with a super point is called as its cardinality. Cardinality estimating plays important roles in network management ... More
Online Learning with Composite Loss FunctionsMay 18 2014We study a new class of online learning problems where each of the online algorithm's actions is assigned an adversarial value, and the loss of the algorithm at each step is a known and deterministic function of the values assigned to its recent actions. ... More
Testing for high-dimensional geometry in random graphsNov 20 2014Nov 22 2015We study the problem of detecting the presence of an underlying high-dimensional geometric structure in a random graph. Under the null hypothesis, the observed graph is a realization of an Erd\H{o}s-R\'enyi random graph $G(n,p)$. Under the alternative, ... More
Anatomy of a young giant component in the random graphJun 10 2009Jul 31 2009We provide a complete description of the giant component of the Erd\H{o}s-R\'enyi random graph $G(n,p)$ as soon as it emerges from the scaling window, i.e., for $p = (1+\epsilon)/n$ where $\epsilon^3 n \to \infty$ and $\epsilon=o(1)$. Our description ... More
Likelihood Ratio Based Scheduler for Secure Detection in Cyber Physical SystemsJul 27 2015This paper is concerned with a binary detection problem over a non-secure network. To satisfy the communication rate constraint and against possible cyber attacks, which are modeled as deceptive signals injected to the network, a likelihood ratio based ... More
Efficient Cross-Validation for Semi-Supervised LearningFeb 13 2019Manifold regularization, such as laplacian regularized least squares (LapRLS) and laplacian support vector machine (LapSVM), has been widely used in semi-supervised learning, and its performance greatly depends on the choice of some hyper-parameters. ... More
Biased random walk conditioned on survival among Bernoulli obstacles: subcritical phaseApr 16 2019We consider a discrete time biased random walk conditioned to avoid Bernoulli obstacles on ${\mathbb Z}^d$ ($d\geq 2$) up to time $N$. This model is known to undergo a phase transition: for a large bias, the walk is ballistic whereas for a small bias, ... More
Densely Connected Bidirectional LSTM with Applications to Sentence ClassificationFeb 03 2018Deep neural networks have recently been shown to achieve highly competitive performance in many computer vision tasks due to their abilities of exploring in a much larger hypothesis space. However, since most deep architectures like stacked RNNs tend ... More
Hidden Hamiltonian Cycle Recovery via Linear ProgrammingApr 15 2018We introduce the problem of hidden Hamiltonian cycle recovery, where there is an unknown Hamiltonian cycle in an $n$-vertex complete graph that needs to be inferred from noisy edge measurements. The measurements are independent and distributed according ... More
Escaping in couples facilitates evacuation: Experimental study and modelingDec 16 2015In this paper, the impact of escaping in couples on the evacuation dynamics has been investigated via experiments and modeling. Two sets of experiments have been implemented, in which pedestrians are asked to escape either in individual or in couples. ... More
Analytical and simulation studies of pedestrian flow at a crossing with random update ruleMar 03 2017The intersecting pedestrian flow on the 2D lattice with random update rule is studied. Each pedestrian has three moving directions without the back step. Under periodic boundary conditions, an intermediate phase has been found at which some pedestrians ... More
Faster super-resolution imaging with auto-correlation two-step deconvolutionSep 19 2018Sep 27 2018Despite super-resolution fluorescence blinking microscopes break the diffraction limit, the intense phototoxic illumination and long-term image sequences thus far still pose to major challenges in visualizing live-organisms. Here, we proposed a super-resolution ... More
Upper bounds on Liouville first passage percolation and Watabiki's predictionOct 31 2016Given a planar continuous Gaussian free field $h$ in a domain $D$ with Dirichlet boundary condition and any $\delta>0$, we let $\{h_\delta(v): v\in D\}$ be a real-valued smooth Gaussian field where $h_\delta(v)$ is the average of $h$ in a circle of radius ... More
First passage percolation on the exponential of two-dimensional branching random walkNov 21 2015Sep 14 2016We consider the branching random walk $\{\mathcal R^N_z: z\in V_N\}$ with Gaussian increments indexed over a two-dimensional box $V_N$ of side length $N$, and we study the first passage percolation where each vertex is assigned weight $e^{\gamma \mathcal ... More
Chemical distances for percolation of planar Gaussian free fields and critical random walk loop soupsMay 14 2016Aug 29 2016We initiate the study on chemical distances of percolation clusters for level sets of two-dimensional discrete Gaussian free fields as well as loop clusters generated by two-dimensional random walk loop soups. One of our results states that the chemical ... 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
Threshold resummation effects in Higgs boson pair production at the LHCJan 07 2013Jul 31 2013We investigate the resummation effects in the Standard Model Higgs boson pair production through gluon-gluon fusion at the LHC with soft-collinear effective theory. We calculate the total cross section and the invariant mass distribution at Next-to-Next-to-Leading-Logarithmic ... More
First passage percolation on the exponential of two-dimensional branching random walkNov 21 2015Dec 06 2017We consider the branching random walk $\{\mathcal R^N_z: z\in V_N\}$ with Gaussian increments indexed over a two-dimensional box $V_N$ of side length $N$, and we study the first passage percolation where each vertex is assigned weight $e^{\gamma \mathcal ... More
The fractal dimension of Liouville quantum gravity: universality, monotonicity, and boundsJul 03 2018Apr 22 2019We prove that for each $\gamma \in (0,2)$, there is an exponent $d_\gamma > 2$, the "fractal dimension of $\gamma$-Liouville quantum gravity (LQG)", which describes the ball volume growth exponent for certain random planar maps in the $\gamma$-LQG universality ... More
Impurity effect and suppression to superconductivity in Na(Fe$_{0.97-x}$Co$_{0.03}$T$_x$)As (T=Cu, Mn)Aug 06 2013We report the successful growth and the impurity scattering effect of single crystals of Na(Fe$_{0.97-x}$Co$_{0.03}$T$_x$)As (T=Cu, Mn). The temperature dependence of DC magnetization at high magnetic fields is measured for different concentrations of ... More
Model independent analysis of top quark forward-backward asymmetry at the Tevatron up to $\mathcal{O}(\as^2/Λ^2)$Jul 20 2011Oct 24 2011We present the complete calculations of the forward-backward asymmetry ($A_{\rm FB}$) and the total cross section of top quark pair production induced by dimension-six four quark operators at the Tevatron up to $\mathcal{O}(\as^2/\Lambda^2)$. Our results ... More
A new coherence measure based on fidelityJun 24 2017Jul 05 2017Quantifying coherence is an essential endeavor for both quantum foundations and quantum technologies. In this paper, we put forward a quantitative measure of coherence by following the axiomatic definition of coherence measures introduced in [T. Baumgratz, ... More
Optimal Solution Predictions for Mixed Integer ProgramsJun 23 2019Mixed Integer Programming (MIP) is one of the most widely used modeling techniques to deal with combinatorial optimization problems. In many applications, a similar MIP model is solved on a regular basis, maintaining remarkable similarities in model structures ... More
Phenomenological Description of the Spectral Function for the Pseudogap and Superconducting Phases of High-T$_c$ CupratesMay 13 2019May 15 2019We present a phenomenological Green's function to characterize the superconducting and pseudogap phases of the cuprates based on a microscopic theory of doped Mott insulators. In this framework, the "Fermi arc" and "kink" phenomena observed by angle-resolved ... More
Glauber Dynamics for the mean-field Potts ModelApr 19 2012Jun 11 2012We study Glauber dynamics for the mean-field (Curie-Weiss) Potts model with $q\geq 3$ states and show that it undergoes a critical slowdown at an inverse-temperature $\beta_s(q)$ strictly lower than the critical $\beta_c(q)$ for uniqueness of the thermodynamic ... More
Non-universality for first passage percolation on the exponential of log-correlated Gaussian fieldsJun 10 2015Jan 20 2016We consider first passage percolation(FPP) where the vertex weight is given by the exponential of two-dimensional log-correlated Gaussian fields. Our work is motivated by understanding the discrete analog for the random metric associated with \emph{Liouville ... More
Subsequential scaling limits for Liouville graph distanceDec 17 2018For $0<\gamma<2$ and $\delta>0$, we consider the Liouville graph distance, which is the minimal number of Euclidean balls with Liouville quantum gravity measure at most $\delta$ whose union contains a continuous path between two endpoints. In this paper, ... More
Momentum-space threshold resummation in $tW$ production at the LHCMar 05 2019We calculate the soft-gluon corrections for $tW$ production to all orders. The soft limit is defined in the pair invariant mass or one particle inclusive kinematic schemes. We find that at NLO the contribution of the soft-gluon effect dominates in the ... More
Measurement-based Quantum Computation Under Different Types of NoisesOct 01 2013Nov 24 2013Measurement based quantum computation (MBQC) is an effective paradigm for universal quantum computation. In this scheme, the universal set of quantum gates are realized by only local measurements on the prior prepared cluster states. The inevitable decoherence ... More
Chemical distances for percolation of planar Gaussian free fields and critical random walk loop soupsMay 14 2016Feb 25 2018We initiate the study on chemical distances of percolation clusters for level sets of two-dimensional discrete Gaussian free fields as well as loop clusters generated by two-dimensional random walk loop soups. One of our results states that the chemical ... More
Capacity lower bound for the Ising perceptronSep 20 2018We consider the Ising perceptron with gaussian disorder, which is equivalent to the discrete cube $\{-1,+1\}^N$ intersected by $M$ random half-spaces. The perceptron's capacity is $\alpha_N \equiv M_N/N$ for the largest integer $M_N$ such that the intersection ... More
Liouville first passage percolation: the weight exponent is strictly less than 1 at high temperaturesMay 26 2016Jun 03 2016Let $\{\eta_{N, v}: v\in V_N\}$ be a discrete Gaussian free field in a two-dimensional box $V_N$ of side length $N$ with Dirichlet boundary conditions. We study the Liouville first passage percolation, i.e., the shortest path metric where each vertex ... More
Dunhuang Grottoes Painting Dataset and BenchmarkJul 10 2019Jul 11 2019This document introduces the background and the usage of the Dunhuang Grottoes Dataset and the benchmark. The documentation first starts with the background of the Dunhuang Grotto, which is widely recognised as an priceless heritage. Given that digital ... More
Practical phase-modulation stabilization in quantum key distribution via machine learningJun 16 2019In practical implementation of quantum key distributions (QKD), it requires efficient, real-time feedback control to maintain system stability when facing disturbance from either external environment or imperfect internal components. Usually, a "scanning-and-transmitting" ... More
Possible gapless spin liquid in a rare-earth kagomé lattice magnet Tm$_{3}$Sb$_{3}$Zn$_{2}$O$_{14}$Feb 03 2018Nov 08 2018We report the thermodynamic and muon spin relaxation ($\mu$SR) evidences for a possible gapless spin liquid in Tm$_{3}$Sb$_{3}$Zn$_{2}$O$_{14}$, with the rare-earth ions Tm$^{3+}$ forming a two-dimensional kagom\'{e} lattice. We extract the magnetic specific ... 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
Distances in critical long range percolationMar 16 2013Nov 07 2015We study the long range percolation model on $\mathbb{Z}$ where sites $i$ and $j$ are connected with probability $\beta |i-j|^{-s}$. Graph distances are now well understood for all exponents $s$ except in the case $s=2$ where the model exhibits non-trivial ... More
Three favorite sites occurs infinitely often for one-dimensional simple random walkDec 06 2016For a one-dimensional simple random walk $(S_t)$, for each time $t$ we say a site $x$ is a favorite site if it has the maximal local time. In this paper, we show that with probability 1 three favorite sites occurs infinitely often. Our work is inspired ... More
Percolation for level-sets of Gaussian free fields on metric graphsJul 29 2018We study level-set percolation for Gaussian free fields on metric graphs. In two dimensions, we give an upper bound on the chemical distance between the two boundaries of a macroscopic annulus. Our bound holds with high probability conditioned on connectivity ... More
The fractal dimension of Liouville quantum gravity: universality, monotonicity, and boundsJul 03 2018Aug 22 2018We prove that for each $\gamma \in (0,2)$, there is an exponent $d_\gamma > 2$, the "fractal dimension of $\gamma$-Liouville quantum gravity (LQG)", which describes the ball volume growth exponent for certain random planar maps in the $\gamma$-LQG universality ... 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
Soft gluon resummation in the signal-background interference process of $gg(\to h^*) \to ZZ$Apr 09 2015Aug 18 2015We present a precise theoretical prediction for the signal-background interference process of $gg(\to h^*) \to ZZ$, which is useful to constrain the Higgs boson decay width and to measure Higgs couplings to the SM particles. The approximate NNLO $K$-factor ... More
Understanding the Importance of Single Directions via Representative SubstitutionNov 27 2018Dec 06 2018Understanding the internal representations of deep neural networks (DNNs) is crucal to explain their behavior. The interpretation of individual units, which are neurons in MLPs or convolution kernels in convolutional networks, has been paid much attention ... More
Confronting Tri-direct CP-symmetry models to neutrino oscillation experimentsMay 30 2019Tri-direct CP symmetry is an economical neutrino model building paradigm, and it allows to describe neutrino masses, mixing angles and CP violation phases in terms of four free parameters. Viability of a class of tri-direct CP models is examined with ... More
A double neutron star merger origin for the cosmological relativistic fading source PTF11agg?Aug 06 2013Jan 07 2014The Palomar Transient Factory (PTF) team recently reported the discovery of a rapidly fading optical transient source, PTF11agg. A long-lived scintillating radio counterpart was identified, but the search for a high energy counterpart showed negative ... More
Liouville first-passage percolation: subsequential scaling limit at high temperatureMay 13 2016Let $\{Y_{\mathfrak{B}}(v):v\in\mathfrak{B}\}$ be a discrete Gaussian free field in a two-dimensional box $\mathfrak{B}$ of side length $S$ with Dirichlet boundary conditions. We study the Liouville first-passage percolation, in which each vertex is given ... More
Upper bounds on Liouville first passage percolation and Watabiki's predictionOct 31 2016Nov 01 2016Given a planar continuous Gaussian free field $h$ in a domain $D$ with Dirichlet boundary condition and any $\delta>0$, we let $\{h_\delta(v): v\in D\}$ be a real-valued smooth Gaussian field where $h_\delta(v)$ is the average of $h$ in a circle of radius ... More
Liouville first passage percolation: geodesic dimension is strictly larger than 1 at high temperaturesOct 10 2016Let $\{\eta(v): v\in V_N\}$ be a discrete Gaussian free field in a two-dimensional box $V_N$ of side length $N$ with Dirichlet boundary conditions. We study the Liouville first passage percolation, i.e., the shortest path metric where each vertex is given ... More
Exceptional points and their coalescence of PT-symmetric interface states in photonic crystalsJun 10 2019The existence of surface electromagnetic waves in the dielectric-metal interface is due to the sign change of real parts of permittivity across the interface. In this work, we demonstrate that the interface constructed by two semi-infinite photonic crystals ... More
Thermodynamics of charged AdS black holes in rainbow gravityMay 31 2018Jan 03 2019In this paper, the thermodynamic property of charged AdS black holes is studied in rainbow gravity. By the Heisenberg Uncertainty Principle and the modified dispersion relation, we obtain deformed temperature. Moreover, in rainbow gravity we calculate ... More