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Ricci-flat graphs with girth at least fiveJan 01 2013A graph is called Ricci-flat if its Ricci-curvatures vanish on all edges. Here we use the definition of Ricci-cruvature on graphs given in [Lin-Lu-Yau, Tohoku Math., 2011], which is a variation of [Ollivier, J. Funct. Math., 2009]. In this paper, we classified ... More

Zipf's Law Leads to Heaps' Law: Analyzing Their Relation in Finite-Size SystemsFeb 20 2010May 11 2010Background: Zipf's law and Heaps' law are observed in disparate complex systems. Of particular interests, these two laws often appear together. Many theoretical models and analyses are performed to understand their co-occurrence in real systems, but it ... More

On crown-free families of subsetsJun 27 2012The crown $\Oh_{2t}$ is a height-2 poset whose Hasse diagram is a cycle of length $2t$. A family $\F$ of subsets of $[n]:=\{1,2..., n\}$ is {\em $\Oh_{2t}$-free} if $\Oh_{2t}$ is not a weak subposet of $(\F,\subseteq)$. Let $\La(n,\Oh_{2t})$ be the largest ... More

Leaders in Social Networks, the Delicious CaseMar 27 2011Finding pertinent information is not limited to search engines. Online communities can amplify the influence of a small number of power users for the benefit of all other users. Users' information foraging in depth and breadth can be greatly enhanced ... More

Multivalued matrices and forbidden configurationsOct 01 2017An $r$-matrix is a matrix with symbols in $\{0,1,\ldots,r-1\}$. A matrix is simple if it has no repeated columns. Let ${\cal F}$ be a finite set of $r$-matrices. Let $\hbox{forb}(m,r,{\cal F})$ denote the maximum number of columns possible in a simple ... More

Information filtering via preferential diffusionFeb 27 2011Recommender systems have shown great potential to address information overload problem, namely to help users in finding interesting and relevant objects within a huge information space. Some physical dynamics, including heat conduction process and mass ... More

Role of Weak Ties in Link Prediction of Complex NetworksJul 10 2009Aug 14 2009Plenty of algorithms for link prediction have been proposed and were applied to various real networks. Among these works, the weights of links are rarely taken into account. In this paper, we use local similarity indices to estimate the likelihood of ... More

Strong Jumps and Lagrangians of Non-Uniform HypergraphsMar 05 2014The hypergraph jump problem and the study of Lagrangians of uniform hypergraphs are two classical areas of study in the extremal graph theory. In this paper, we refine the concept of jumps to strong jumps and consider the analogous problems over non-uniform ... More

An Upper Bound on Burning Number of GraphsJun 24 2016The burning number $b(G)$ of a graph $G$ was introduced by Bonato, Janssen, and Roshanbin [Lecture Notes in Computer Science 8882 (2014)] for measuring the speed of the spread of contagion in a graph. They proved for any connected graph $G$ of order $n$, ... More

Diameters of Graphs with Spectral Radius at most $3/2\sqrt{2}$Dec 21 2011The spectral radius $\rho(G)$ of a graph $G$ is the largest eigenvalue of its adjacency matrix. Woo and Neumaier discovered that a connected graph $G$ with $\rho(G)\leq 3/2{\sqrt{2}}$ is either a dagger, an open quipu, or a closed quipu. The reverse statement ... More

Connected Hypergraphs with Small Spectral RadiusFeb 21 2014Mar 07 2014In 1970 Smith classified all connected graphs with the spectral radius at most $2$. Here the spectral radius of a graph is the largest eigenvalue of its adjacency matrix. Recently, the definition of spectral radius has been extended to $r$-uniform hypergraphs. ... More

High-order Phase Transition in Random HypergrpahsSep 03 2014In this paper, we study the high-order phase transition in random $r$-uniform hypergraphs. For a positive integer $n$ and a real $p\in [0,1]$, let $H:=H^r(n,p)$ be the random $r$-uniform hypergraph on the vertex set $[n]$, where each $r$-set is an edge ... More

Link Prediction in Complex Networks: A SurveyOct 04 2010Link prediction in complex networks has attracted increasing attention from both physical and computer science communities. The algorithms can be used to extract missing information, identify spurious interactions, evaluate network evolving mechanisms, ... More

Turan Problems on Non-uniform HypergraphsJan 09 2013A non-uniform hypergraph $H=(V,E)$ consists of a vertex set $V$ and an edge set $E\subseteq 2^V$; the edges in $E$ are not required to all have the same cardinality. The set of all cardinalities of edges in $H$ is denoted by $R(H)$, the set of edge types. ... More

Link Prediction Based on Local Random WalkJan 14 2010The problem of missing link prediction in complex networks has attracted much attention recently. Two difficulties in link prediction are the sparsity and huge size of the target networks. Therefore, the design of an efficient and effective method is ... More

Spectra of edge-independent random graphsApr 27 2012Let $G$ be a random graph on the vertex set $\{1,2,..., n\}$ such that edges in $G$ are determined by independent random indicator variables, while the probability $p_{ij}$ for $\{i,j\}$ being an edge in $G$ is not assumed to be equal. Spectra of the ... More

Loose Laplacian spectra of random hypergraphsSep 15 2011Dec 05 2011Let $H=(V,E)$ be an $r$-uniform hypergraph with the vertex set $V$ and the edge set $E$. For $1\leq s \leq r/2$, we define a weighted graph $G^{(s)}$ on the vertex set ${V\choose s}$ as follows. Every pair of $s$-sets $I$ and $J$ is associated with a ... More

High-ordered Random Walks and Generalized Laplacians on HypergraphsFeb 22 2011Despite of the extreme success of the spectral graph theory, there are relatively few papers applying spectral analysis to hypergraphs. Chung first introduced Laplacians for regular hypergraphs and showed some useful applications. Other researchers treated ... More

Ricci-flat cubic graphs with girth fiveFeb 08 2018We classify all connected, simple, 3-regular graphs with girth at least 5 that are Ricci-flat. We use the definition of Ricci curvature on graphs given in Lin-Lu-Yau, Tohoku Math., 2011, which is a variation of Ollivier, J. Funct. Anal., 2009. A graph ... More

The Randic index and the diameter of graphsApr 03 2011The {\it Randi\'c index} $R(G)$ of a graph $G$ is defined as the sum of 1/\sqrt{d_ud_v} over all edges $uv$ of $G$, where $d_u$ and $d_v$ are the degrees of vertices $u$ and $v,$ respectively. Let $D(G)$ be the diameter of $G$ when $G$ is connected. Aouchiche-Hansen-Zheng ... More

Coarse Graining for Synchronization in Directed NetworksDec 01 2010Mar 23 2011Coarse graining model is a promising way to analyze and visualize large-scale networks. The coarse-grained networks are required to preserve the same statistical properties as well as the dynamic behaviors as the initial networks. Some methods have been ... More

Hypergraphs with Spectral Radius at most $(r-1)!\sqrt[r]{2+\sqrt{5}}$Dec 03 2014In our previous paper, we classified all $r$-uniform hypergraphs with spectral radius at most $(r-1)!\sqrt[r]{4}$, which directly generalizes Smith's theorem for the graph case $r=2$. It is nature to ask the structures of the hypergraphs with spectral ... More

The Fractional Chromatic Number of Triangle-free Graphs with $Δ\leq 3$Nov 10 2010Jul 25 2012Let $G$ be any triangle-free graph with maximum degree $\Delta\leq 3$. Staton proved that the independence number of $G$ is at least 5/14n. Heckman and Thomas conjectured that Staton's result can be strengthened into a bound on the fractional chromatic ... More

Monochromatic 4-term arithmetic progressions in 2-colorings of $\mathbb Z_n$Jul 14 2011This paper is motivated by a recent result of Wolf \cite{wolf} on the minimum number of monochromatic 4-term arithmetic progressions(4-APs, for short) in $\Z_p$, where $p$ is a prime number. Wolf proved that there is a 2-coloring of $\Z_p$ with 0.000386% ... More

On families of subsets with a forbidden subposetJul 23 2008Let $\F\subset 2^{[n]}$ be a family of subsets of $\{1,2,..., n\}$. For any poset $H$, we say $\F$ is $H$-free if $\F$ does not contain any subposet isomorphic to $H$. Katona and others have investigated the behavior of $\La(n,H)$, which denotes the maximum ... More

Unavoidable Multicoloured Families of ConfigurationsSep 15 2014Sep 29 2014Balogh and Bollob\'as [{\em Combinatorica 25, 2005}] prove that for any $k$ there is a constant $f(k)$ such that any set system with at least $f(k)$ sets reduces to a $k$-star, an $k$-costar or an $k$-chain. They proved $f(k)<(2k)^{2^k}$. Here we improve ... More

Repeated columns and an old chestnutMay 03 2013Let $t\ge 1$ be a given integer. Let ${\cal F}$ be a family of subsets of $[m]=\{1,2,\ldots,m\}$. Assume that for every pair of disjoint sets $S,T\subset [m]$ with $|S|=|T|=k$, there do not exist $2t$ sets in ${\cal F}$ where $t$ subsets of ${\cal F}$ ... More

Set families with forbidden subposetsAug 04 2014Let $F$ be a family of subsets of $\{1,\ldots,n\}$. We say that $F$ is $P$-free if the inclusion order on $F$ does not contain $P$ as an induced subposet. The \emph{Tur\'an function} of $P$, denoted $\pi^*(n,P)$, is the maximum size of a $P$-free family ... More

A new asymptotic enumeration technique: the Lovasz Local LemmaMay 25 2009Feb 23 2014Our previous paper applied a lopsided version of the Lov\'asz Local Lemma that allows negative dependency graphs to the space of random injections from an $m$-element set to an $n$-element set. Equivalently, the same story can be told about the space ... More

Efficient Image Reconstruction and Practical Decomposition for Dual-energy Computed TomographyJul 06 2016Jul 29 2016Dual-energy computed tomography (DECT) has shown great potential and promising applications in advanced imaging fields for its capabilities of material decomposition. However, image reconstructions and decompositions under sparse views dataset suffers ... More

Scaling Laws in Human LanguageFeb 14 2012Zipf's law on word frequency is observed in English, French, Spanish, Italian, and so on, yet it does not hold for Chinese, Japanese or Korean characters. A model for writing process is proposed to explain the above difference, which takes into account ... More

Unrolling residues to avoid progressionsSep 12 2012We consider the problem of coloring $[n]={1,2,...,n}$ with $r$ colors to minimize the number of monochromatic $k$ term arithmetic progressions (or $k$-APs for short). We show how to extend colorings of $\mathbb{Z}_m$ which avoid nontrivial $k$-APs to ... More

Predicting Missing Links via Local InformationJan 05 2009Jun 01 2009Missing link prediction of networks is of both theoretical interest and practical significance in modern science. In this paper, we empirically investigate a simple framework of link prediction on the basis of node similarity. We compare nine well-known ... More

Boolean algebras and Lubell functionsJul 12 2013Let $2^{[n]}$ denote the power set of $[n]:=\{1,2,..., n\}$. A collection $\B\subset 2^{[n]}$ forms a $d$-dimensional {\em Boolean algebra} if there exist pairwise disjoint sets $X_0, X_1,..., X_d \subseteq [n]$, all non-empty with perhaps the exception ... More

A combinatorial identity on Galton-Watson processJun 28 2015Let $f(m,c)=\sum_{k=0}^{\infty} (km+1)^{k-1} c^k e^{-c(km+1)/m} / (m^kk!)$. For any positive integer $m$ and positive real $c$, the identity $f(m,c)=f(1,c)^{1/m}$ arises in the random graph theory. In this paper, we present two elementary proofs of this ... More

Graphs with Diameter $n-e$ Minimizing the Spectral RadiusOct 11 2011The spectral radius $\rho(G)$ of a graph $G$ is the largest eigenvalue of its adjacency matrix $A(G)$. For a fixed integer $e\ge 1$, let $G^{min}_{n,n-e}$ be a graph with minimal spectral radius among all connected graphs on $n$ vertices with diameter ... More

A Fractional Analogue of Brooks' TheoremMar 17 2011Nov 13 2011Let $\Delta(G)$ be the maximum degree of a graph $G$. Brooks' theorem states that the only connected graphs with chromatic number $\chi(G)=\Delta(G)+1$ are complete graphs and odd cycles. We prove a fractional analogue of Brooks' theorem in this paper. ... More

Similarity-Based Classification in Partially Labeled NetworksMar 03 2010We propose a similarity-based method, using the similarity between nodes, to address the problem of classification in partially labeled networks. The basic assumption is that two nodes are more likely to be categorized into the same class if they are ... More

Computing Diffusion State Distance using Green's Function and Heat Kernel on GraphsOct 13 2014The diffusion state distance (DSD) was introduced by Cao-Zhang-Park-Daniels-Crovella-Cowen-Hescott [{\em PLoS ONE, 2013}] to capture functional similarity in protein-protein interaction networks. They proved the convergence of DSD for non-bipartite graphs. ... More

Effective spreading from multiple leaders identified by percolation in social networksAug 18 2015Social networks constitute a new platform for information propagation, but its success is crucially dependent on the choice of spreaders who initiate the spreading of information. In this paper, we remove edges in a network at random and the network segments ... More

Empirical analysis of web-based user-object bipartite networksSep 27 2009Dec 24 2011Understanding the structure and evolution of web-based user-object networks is a significant task since they play a crucial role in e-commerce nowadays. This Letter reports the empirical analysis on two large-scale web sites, audioscrobbler.com and del.icio.us, ... More

Duplication Models for Biological NetworksAug 31 2002Are biological networks different from other large complex networks? Both large biological and non-biological networks exhibit power-law graphs (number of nodes with degree k, N(k) ~ k-b) yet the exponents, b, fall into different ranges. This may be because ... More

Diamond-free FamiliesOct 26 2010Sep 06 2011Given a finite poset P, we consider the largest size La(n,P) of a family of subsets of $[n]:=\{1,...,n\}$ that contains no subposet P. This problem has been studied intensively in recent years, and it is conjectured that $\pi(P):= \lim_{n\rightarrow\infty} ... More

Quantifying the influence of scientists and their publications: Distinguish prestige from popularitySep 06 2011Oct 13 2011The number of citations is a widely used metric to evaluate the scientific credit of papers, scientists and journals. However, it does happen that a paper with fewer citations from prestigious scientists is of higher influence than papers with more citations. ... More

Small world yields the most effective information spreadingJul 03 2011Nov 23 2011Spreading dynamics of information and diseases are usually analyzed by using a unified framework and analogous models. In this paper, we propose a model to emphasize the essential difference between information spreading and epidemic spreading, where ... More

Enhancing topology adaptation in information-sharing social networksJul 22 2011Apr 13 2012The advent of Internet and World Wide Web has led to unprecedent growth of the information available. People usually face the information overload by following a limited number of sources which best fit their interests. It has thus become important to ... More

Identifying Influential Spreaders by Weighted LeaderRankJun 21 2013Nov 28 2013Identifying influential spreaders is crucial for understanding and controlling spreading processes on social networks. Via assigning degree-dependent weights onto links associated with the ground node, we proposed a variant to a recent ranking algorithm ... More

On the integrated squared error of the linear wavelet density estimatorOct 29 2012Linear wavelet density estimators are wavelet projections of the empirical measure based on independent, identically distributed observations. We study here the law of the iterated logarithm (LIL) and a Berry-Esseen type theorem. These results are proved ... More

Recommender SystemsFeb 06 2012The ongoing rapid expansion of the Internet greatly increases the necessity of effective recommender systems for filtering the abundant information. Extensive research for recommender systems is conducted by a broad range of communities including social ... More

An exact algorithm with the time complexity of $O^*(1.299^m)$ for the weighed mutually exclusive set cover problemFeb 23 2013In this paper, we will introduce an exact algorithm with a time complexity of $O^*(1.299^m)$ for the {\sc weighted mutually exclusive set cover} problem, where $m$ is the number of subsets in the problem. This problem has important applications in recognizing ... More

A Class of Diffusion Algorithms with Logarithmic Cost over Adaptive Sparse Volterra NetworkJun 28 2016Jun 29 2016In this Letter, we present a novel class of diffusion algorithms that can be used to estimate the coefficients of sparse Volterra network. The development of the algorithms is based on the logarithmic cost and l0-norm constraint. To further overcome the ... More

Diffusion leaky LMS algorithm: analysis and implementationFeb 13 2016Jul 30 2016The diffusion least-mean square (dLMS) algorithms have attracted much attention owing to its robustness for distributed estimation problems. However, the performance of such filters may change when they are implemented for suppressing noises from speech ... More

An exact algorithm for the weighed mutually exclusive maximum set cover problemJan 24 2014In this paper, we introduce an exact algorithm with a time complexity of $O^*(1.325^m)$ for the {\sc weighted mutually exclusive maximum set cover} problem, where $m$ is the number of subsets in the problem. This is an NP-hard motivated and abstracted ... More

An Unsupervised Homogenization Pipeline for Clustering Similar Patients using Electronic Health Record DataDec 30 2017Electronic health records (EHR) contain a large variety of information on the clinical history of patients such as vital signs, demographics, diagnostic codes and imaging data. The enormous potential for discovery in this rich dataset is hampered by its ... More

Sequential Convex Programming Methods for A Class of Structured Nonlinear ProgrammingOct 10 2012In this paper we study a broad class of structured nonlinear programming (SNLP) problems. In particular, we first establish the first-order optimality conditions for them. Then we propose sequential convex programming (SCP) methods for solving them in ... More

Harmonic map heat flow with rough boundary dataOct 16 2010Let $B_1$ be the unit open disk in $\Real^2$ and $M$ be a closed Riemannian manifold. In this note, we first prove the uniqueness for weak solutions of the harmonic map heat flow in $H^1([0,T]\times B_1,M)$ whose energy is non-increasing in time, given ... More

Reducts of the Generalized Random Bipartite GraphJul 20 2011Let \Gamma be the generalized random bipartite graph that has two sides Rl and Rr with edges for every pair of vertices between R1 and Rr but no edges within each side, where all the edges are randomly colored by three colors P1; P2; P3. In this paper, ... More

Unsupervised Learning on Neural Network Outputs: with Application in Zero-shot LearningJun 02 2015May 23 2016The outputs of a trained neural network contain much richer information than just an one-hot classifier. For example, a neural network might give an image of a dog the probability of one in a million of being a cat but it is still much larger than the ... More

Geometry of Two-dimensional Self-shrinkersMay 01 2015We prove a local graphical theorem for two-dimensional self-shrinkers away from the origin. As applications, we study the asymptotic behavior of noncompact self-shrinkers with finite genus. Also, we show uniform boundedness on the second fundamental form ... More

Small Amplitude Periodic Solutions of Klein-Gordon EquationsSep 19 2013Oct 14 2014We consider a class of nonlinear Klein-Gordon equations $u_{tt}=u_{xx}-u+f(u)$ and obtain a family of small amplitude periodic solutions, where the temporal and spatial period have different scales.

Generalized low solution of $\mathsf{RT}_k^1$ problemFeb 19 2016Feb 28 2016We study the "coding power" of an arbitrary $\mathsf{RT}_k^1$-instance. We prove that every $\mathsf{RT}_k^1$-instance admit non trivial generalized low solution. This is somewhat related to a problem proposed by Patey. We also answer a question proposed ... More

Covariate adjustment in randomization-based causal inference for 2K factorial designsJun 17 2016Jul 12 2016We develop finite-population asymptotic theory for covariate adjustment in randomization-based causal inference for 2K factorial designs. In particular, we confirm that both the unadjusted and covariate-adjusted estimators of the factorial effects are ... More

On Randomization-based and Regression-based Inferences for 2^K Factorial DesignsFeb 12 2016We extend the randomization-based causal inference framework in Dasgupta et al. (2015) for general 2^K factorial designs, and demonstrate the equivalence between regression-based and randomization-based inferences. Consequently, we justify the use of ... More

Exotic Meson Decay to $ωπ^{0}π^{-}$May 17 2004A partial-wave analysis of the mesons from the reaction $\pi^{-}% p\to\pi^{+}\pi^{-}\pi^{-}\pi^{0}\pi^{0}p$ has been performed. The data show $b_{1}\pi$ decay of the spin-exotic states $\pi_{1}(1600)$ and \ $\pi_{1}(2000)$. Three isovector $2^{-+}$ states ... More

Optimization over Sparse Symmetric Sets via a Nonmonotone Projected Gradient MethodSep 29 2015Nov 29 2015We consider the problem of minimizing a Lipschitz differentiable function over a class of sparse symmetric sets that has wide applications in engineering and science. For this problem, it is known that any accumulation point of the classical projected ... More

Iterative Hard Thresholding Methods for $l_0$ Regularized Convex Cone ProgrammingOct 31 2012Nov 02 2012In this paper we consider $l_0$ regularized convex cone programming problems. In particular, we first propose an iterative hard thresholding (IHT) method and its variant for solving $l_0$ regularized box constrained convex programming. We show that the ... More

Remarks on the Bottcher-Wenzel InequalityJun 09 2011Mar 19 2014In 2005, B\"ottcher and Wenzel raised the conjecture that if $X,Y$ are real square matrices, then $||XY-YX||^2\leq 2||X||^2||Y||^2$, where $||\cdot||$ is the Frobenius norm. Various proofs of this conjecture were found in the last few years by several ... More

Proof of the normal scalar curvature conjectureNov 22 2007In this paper, we proved the normal scalar curvature conjecture and the Bottcher-Wenzel conjecture.

Single-spin asymmetries in electroproduction of pions on the longitudinally polarized nucleon targetsApr 16 2014Jul 25 2014We study the single-spin asymmetries of pions produced in semi-inclusive deep-inelastic scattering on the longitudinally polarized nucleon targets. We particularly consider the effects of the twist-3 transverse-momentum dependent distribution functions ... More

K Energy and K stability on HypersurfacesAug 02 2001In this paper, we study the limiting properties of the $K$ energy for smooth hypersurfaces in the projective spaces. Our result generalizes the result of Ding-Tian (W. Ding and G. Tian. K\"ahler-Einstein metrics and the generalized Futaki invariant. {\em ... More

No Quantum Brooks' TheoremNov 27 2014First, I introduce quantum graph theory. I also discuss a known lower bound on the independence numbers and derive from it an upper bound on the chromatic numbers of quantum graphs. Then, I construct a family of quantum graphs that can be described as ... More

Comparison of hadron shower data with simulationsJul 17 2010An analog hadron calorimeter (AHCAL) prototype of 5.3 nuclear interaction lengths thickness has been designed and constructed by members of the CALICE Collaboration. The AHCAL prototype consists of a 38-layer sandwich structure of steel plates and 7608 ... More

GPS Information and Rate Tolerance - Clarifying Relationship between Rate Distortion and Complexity DistortionApr 17 2012I proposed rate tolerance and discussed its relation to rate distortion in my book "A Generalized Information Theory" published in 1993. Recently, I examined the structure function and the complexity distortion based on Kolmogorov's complexity theory. ... More

New Approaches to Identify Gene-by-Gene Interactions in Genome Wide Association StudiesMay 07 2016Genetic variants identified to date by genome-wide association studies only explain a small fraction of total heritability. Gene-by-gene interaction is one important potential source of unexplained heritability. In the first part of this dissertation, ... More

Observational Effects of Strange StarsJul 06 1998In this talk, after briefly reviewing some historical remarks concerning strange stars, the achievements in physics and dynamical behavior of strange stars are discussed. Especially, various observational effects in distinguishing strange stars from neutron ... More

Gromov-Witten invariants and rigidity of Hamiltonian loops with compact support on noncompact symplectic manifoldsMay 12 1999Jul 20 2003In this paper the Gromov-Witten invariants on a class of noncompact symplectic manifolds are defined by combining Ruan-Tian's method with that of McDuff-Salamon. The main point of the arguments is to introduce a method dealing with the transversality ... More

The Weinstein conjecture in the uniruled manifoldsJan 25 2000Dec 12 2000In this note we prove the Weinstein conjecture for a class of symplectic manifolds including the uniruled manifolds based on Liu-Tian's result.

The Conley conjecture for Hamiltonian systems on the cotangent bundle and its analogue for Lagrangian systemsJun 03 2008Jun 30 2008In this paper, the Conley conjecture, which were recently proved by Franks and Handel \cite{FrHa} (for surfaces of positive genus), Hingston \cite{Hi} (for tori) and Ginzburg \cite{Gi} (for closed symplectically aspherical manifolds), is proved for $C^1$-Hamiltonian ... More

Finiteness of the Hofer-Zehnder capacity of neighborhoods of symplectic submanifoldsOct 09 2005Dec 07 2006We use the minimal coupling procedure of Sternberg and Weinstein and our pseudo-symplectic capacity theory to prove that every closed symplectic submanifold in any symplectic manifold has an open neighborhood with finite ($\pi_1$-sensitive) Hofer-Zehnder ... More

Discrete Polymatroids satisfying a stronger symmetric exchange propertyDec 15 2014Sep 22 2015In this paper we introduce discrete polymatroids satisfying the one-sided strong exchange property and show that they are sortable (as a consequence their base rings are Koszul) and that they satisfy White's conjecture. Since any pruned lattice path polymatroid ... More

The splitting lemmas for nonsmooth functionals on Hilbert spaces INov 06 2012Jun 11 2014The Gromoll-Meyer's generalized Morse lemma (so called splitting lemma) near degenerate critical points on Hilbert spaces, which is one of key results in infinite dimensional Morse theory, is usually stated for at least $C^2$-smooth functionals. It obstructs ... More

Some critical point theorems and applicationsFeb 10 2011This paper is a continuation of \cite{Lu1}. In Part I, applying the new splitting theorems developed therein we generalize previous some results on computations of critical groups and some critical point theorems to weaker versions. In Part II (in progress), ... More

An extension of Biran's Lagrangian barrier theoremNov 16 2001May 21 2004We use the Gromov-Witten invariants and a nonsqueezing theorem by the author to affirm a conjecture by P.Biran on the Lagrangian barriers.

Symmetric confidence regions and confidence intervals for normal map formulations of stochastic variational inequalitiesJun 26 2014Stochastic variational inequalities (SVI) model a large class of equilibrium problems subject to data uncertainty, and are closely related to stochastic optimization problems. The SVI solution is usually estimated by a solution to a sample average approximation ... More

Effects of Data Resolution and Human Behavior on Large Scale Evacuation SimulationsDec 30 2014Traffic Analysis Zones (TAZ) based macroscopic simulation studies are mostly applied in evacuation planning and operation areas. The large size in TAZ and aggregated information of macroscopic simulation underestimate the real evacuation performance. ... More

Reflected BSDE with stochastic Lipschitz coefficientDec 11 2009Dec 15 2009In this paper, we deal with a class of one-dimensional reflected backward stochastic differential equations with stochastic Lipschitz coefficient. We derive the existence and uniqueness of the solutions for those equations via Snell envelope and the fixed ... More

Symplectic capacities of toric manifolds and related resultsDec 29 2003May 03 2006In this paper we give concrete estimations for the pseudo symplectic capacities of toric manifolds in combinatorial data. Some examples are given to show that our estimates can compute their pseudo symplectic capacities. As applications we also estimate ... More

Gromov-Witten invariants and pseudo symplectic capacitiesMar 28 2001Dec 07 2006We introduce the concept of pseudo symplectic capacities which is a mild generalization of that of symplectic capacities. As a generalization of the Hofer-Zehnder capacity we construct a Hofer-Zehnder type pseudo symplectic capacity and estimate it in ... More

Reconstructing directed networks for better synchronizationJun 29 2011In this paper, we studied the strategies to enhance synchronization on directed networks by manipulating a fixed number of links. We proposed a centrality-based reconstructing (CBR) method, where the node centrality is measured by the well-known PageRank ... More

Farrell cohomology of low genus pure mapping class groups with puncturesJul 22 2002In this paper, we calculate the p-torsion of the Farrell cohomology for low genus pure mapping class groups with punctures, where p is an odd prime. Here, `low genus' means g=1,2,3; and `pure mapping class groups with punctures' means the mapping class ... More

Observability Estimate and State Observation Problems for Stochastic Hyperbolic EquationsMay 03 2013Jun 09 2013In this paper, we derive a boundary and an internal observability inequality for stochastic hyperbolic equations with nonsmooth lower order terms. The required inequalities are obtained by global Carleman estimate for stochastic hyperbolic equations. ... More

Parametrizing Program Analysis by Lifting to Cardinal Power DomainsMay 25 2010A parametric analysis is an analysis whose input and output are parametrized with a number of parameters which can be instantiated to abstract properties after analysis is completed. This paper proposes to use Cousot and Cousot's Cardinal power domain ... More

Knowware: the third star after Hardware and SoftwareNov 27 2007This book proposes to separate knowledge from software and to make it a commodity that is called knowware. The architecture, representation and function of Knowware are discussed. The principles of knowware engineering and its three life cycle models: ... More

Two-Monopole Systems and the Formation of Non-Abelian CloudsJun 29 1998Nov 20 1998We study the energy density of two distinct fundamental monopoles in SU(3) and Sp(4) theories with an arbitrary mass ratio. Several special limits of the general result are checked and verified. Based on the analytic expression of energy density the coefficient ... More

GRBS: Standard Model & BeyondJan 03 2001There have been great and rapid progresses in the field of $\gamma$-ray bursts since BeppoSAX and other telescopes discovered their afterglows in 1997. In this talk, the main observational facts of $\gamma$-ray bursts and their afterglows, and the standard ... More

What do $γ$-ray bursts look like?Feb 08 2000There have been great and rapid progresses in the field of $\gamma$-ray bursts (denoted as GRBs) since BeppoSAX and other telescopes discovered their afterglows in 1997. Here, we will first give a brief review on the observational facts of GRBs and direct ... More

Symplectic fixed points and Lagrangian intersections on weighted projective spacesJan 12 2006In this note we observe that Arnold conjecture for the Hamiltonian maps still holds on weighted projective spaces $\CP^n({\bf q})$, and that Arnold conjecture for the Lagrange intersections for $(\CP^n({\bf q}), \RP^n({\bf q}))$ is also true if each weight ... More

Synthesis of Self-assembled Iron Silicon Oxide Nanowires onto Single-crystalline Si(100)Jul 30 2013Iron silicon oxide nanowire has been synthesized by putting single crystalline Si(100) wafer into ammonium iron sulfate, hydrogen peroxide, and triethylamine solution heated to from 70 to 100 degree in the air. The prepared iron silicon oxide nanowires ... More

Periodic motion of a charge on a manifold in the magnetic fieldsMay 24 1999May 25 2000In this paper we prove the existence of a periodic motion of a charge on a large class of manifolds under the action of the magnetic fields. Our methods also give a class of closed manifolds whose cotangent bundle contain no the closed exact Lagrangian ... More

Semantic Information Measure with Two Types of Probability for Falsification and ConfirmationSep 26 2016Logical Probability (LP) is strictly distinguished from Statistical Probability (SP). To measure semantic information or confirm hypotheses, we need to use sampling distribution (conditional SP function) to test or confirm fuzzy truth function (conditional ... More