Results for "Cunhua Pan"

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Ergodic Rate Analysis of Cooperative Ambient Backscatter CommunicationAug 15 2019Ambient backscatter communication has shown great potential in the development of future wireless networks. It enables a backscatter transmitter (BTx) to send information directly to an adjacent receiver by modulating over ambient radio frequency (RF) ... More
Energy Efficient Transmission for Multicast Services in MISO Distributed Antenna SystemsMar 01 2016This paper aims to solve the energy efficiency (EE) maximization problem for multicast services in a multiple-input single-output (MISO) distributed antenna system (DAS). A novel iterative algorithm is proposed, which consists of solving two subproblems ... More
Resource Allocation for D2D Communications Underlaying a NOMA-Based Cellular NetworkOct 14 2017This letter investigates the power control and channel assignment problem in device-to-device (D2D) communications underlaying a non-orthogonal multiple access (NOMA) cellular network. With the successive interference cancellation decoding order constraints, ... More
A Caching Strategy Towards Maximal D2D Assisted Offloading GainAug 02 2019Device-to-Device (D2D) communications incorporated with content caching have been regarded as a promising way to offload the cellular traffic data. In this paper, the caching strategy is investigated to maximize the D2D offloading gain with the comprehensive ... More
Optimal Fairness-Aware Time and Power Allocation in Wireless Powered Communication NetworksFeb 14 2018In this paper, we consider the sum $\alpha$-fair utility maximization problem for joint downlink (DL) and uplink (UL) transmissions of a wireless powered communication network (WPCN) via time and power allocation. In the DL, the users with energy harvesting ... More
Energy Efficient Resource Allocation in Machine-to-Machine Communications with Multiple Access and Energy Harvesting for IoTNov 29 2017This paper studies energy efficient resource allocation for a machine-to-machine (M2M) enabled cellular network with non-linear energy harvesting, especially focusing on two different multiple access strategies, namely non-orthogonal multiple access (NOMA) ... More
Energy Efficient Resource Allocation in UAV-Enabled Mobile Edge Computing NetworksFeb 08 2019In this paper, we consider the sum power minimization problem via jointly optimizing user association, power control, computation capacity allocation and location planning in a mobile edge computing (MEC) network with multiple unmanned aerial vehicles ... More
Unified Offloading Decision Making and Resource Allocation in ME-RANMay 29 2017Jun 26 2018In order to support communication and computation cooperation, we propose ME-RAN architecture, which consists of mobile edge cloud (ME) as the computation provision platform and radio access network (RAN) as the communication interface. Cooperative offloading ... More
Tradeoff Caching Strategy of Outage Probability and Fronthaul Usage in Cloud-RANNov 08 2016Feb 05 2018In this paper, optimal content caching strategy is proposed to jointly minimize the cell average outage probability and fronthaul usage in cloud radio access network (Cloud-RAN). At first, an accurate closed form expression of the outage probability conditioned ... More
Tradeoff Caching Strategy of Outage Probability and Fronthaul Usage in Cloud-RANNov 08 2016In this paper, optimal content caching strategy is proposed to jointly minimize the cell average outage probability and fronthaul usage in cloud radio access network (Cloud-RAN). At first, an accurate closed form expression of the outage probability conditioned ... More
Energy Efficient Resource Allocation in UAV-Enabled Mobile Edge Computing NetworksFeb 08 2019Feb 13 2019In this paper, we consider the sum power minimization problem via jointly optimizing user association, power control, computation capacity allocation and location planning in a mobile edge computing (MEC) network with multiple unmanned aerial vehicles ... More
Joint Pilot Allocation and Robust Transmission Design for Ultra-dense User-centric TDD C-RAN with Imperfect CSIOct 22 2017This paper considers the unavailability of complete channel state information (CSI) in ultra-dense cloud radio access networks (C-RANs). The user-centric cluster is adopted to reduce the computational complexity, while the incomplete CSI is considered ... More
Robust Beamforming Design for Ultra-dense User-Centric C-RAN in the Face of Realistic Pilot Contamination and Limited FeedbackApr 06 2018The ultra-dense cloud radio access network (UD-CRAN), in which remote radio heads (RRHs) are densely deployed in the network, is considered. To reduce the channel estimation overhead, we focus on the design of robust transmit beamforming for user-centric ... More
Joint Blocklength and Location Optimization for URLLC-enabled UAV Relay SystemsJan 16 2019This letter considers the unmanned aerial vehicle (UAV)-enabled relay system to deliver command information under ultra-reliable and low-latency communication (URLLC) requirements. We aim to jointly optimize the blocklength allocation and the UAV's location ... More
Energy Efficiency Optimization for MIMO Distributed Antenna SystemsNov 12 2015In this paper, we propose a transmit covariance optimization method to maximize the energy efficiency (EE) for a single-user distributed antenna system, where both the remote access units (RAUs) and the user are equipped with multiple antennas. Unlike ... More
User-centric C-RAN Architecture for Ultra-dense 5G Networks: Challenges and MethodologiesSep 20 2017Ultra-dense networks (UDN) constitute one of the most promising techniques of supporting the 5G mobile system. By deploying more small cells in a fixed area, the average distance between users and access points can be significantly reduced, hence a dense ... More
Efficient Resource Allocation for Mobile-Edge Computing Networks with NOMA: Completion Time and Energy MinimizationAug 12 2019This paper investigates an uplink non-orthogonal multiple access (NOMA)-based mobile-edge computing (MEC) network. Our objective is to minimize a linear combination of the completion time of all users' tasks and the total energy consumption of all users ... More
Joint Time Allocation and Power Control in Multi-Cell Networks with Load Coupling: Energy Saving and Rate ImprovementJul 01 2017In this paper, we consider the problems of minimizing sum power and maximizing sum rate for multi-cell networks with load coupling, where coupling relation occurs among cells due to inter-cell interference. This coupling relation is characterized by the ... More
Joint User Selection and Energy Minimization for Ultra-Dense Multi-channel C-RAN with Incomplete CSIMay 17 2017This paper provides a unified framework to deal with the challenges arising in dense cloud radio access networks (C-RAN), which include huge power consumption, limited fronthaul capacity, heavy computational complexity, unavailability of full channel ... More
Joint Precoding and RRH selection for User-centric Green MIMO C-RANFeb 10 2017This paper jointly optimizes the precoding matrices and the set of active remote radio heads (RRHs) to minimize the network power consumption (NPC) for a user-centric cloud radio access network (C-RAN), where both the RRHs and users have multiple antennas ... More
Compressive Sensing Based User Clustering for Downlink NOMA Systems with Decoding PowerMar 13 2018This letter investigates joint power control and user clustering for downlink non-orthogonal multiple access systems. Our aim is to minimize the total power consumption by taking into account not only the conventional transmission power but also the decoding ... More
Cache Placement in Two-Tier HetNets with Limited Storage Capacity: Cache or Buffer?Jun 06 2018In this paper, we aim to minimize the average file transmission delay via bandwidth allocation and cache placement in two-tier heterogeneous networks with limited storage capacity, which consists of cache capacity and buffer capacity. For average delay ... More
Cache Placement in Two-Tier HetNets with Limited Storage Capacity: Cache or Buffer?Jun 06 2018Jul 17 2019In this paper, we aim to minimize the average file transmission delay via bandwidth allocation and cache placement in two-tier heterogeneous networks with limited storage capacity, which consists of cache capacity and buffer capacity. For average delay ... More
On Consideration of Content Preference and Sharing Willingness in D2D Assisted OffloadingFeb 01 2017Device-to-device (D2D) assisted offloading heavily depends on the participation of human users. The content preference and sharing willingness of human users are two crucial factors in the D2D assisted offloading. In this paper, with consideration of ... More
Power Control for Multi-Cell Networks with Non-Orthogonal Multiple AccessJun 14 2017Nov 02 2017In this paper, we investigate the problems of sum power minimization and sum rate maximization for multi-cell networks with non-orthogonal multiple access. Considering the sum power minimization, we obtain closed-form solutions to the optimal power allocation ... More
Totally Distributed Energy-Efficient Transmission in MIMO Interference ChannelsMar 13 2015Jul 01 2015In this paper, we consider the problem of maximizing the energy efficiency (EE) for multi-input multi-output (MIMO) interference channels, subject to the per-link power constraint. To avoid extensive information exchange among all links, the optimization ... More
Robust Transmission Design for Multi-Cell D2D Underlaid Cellular NetworksApr 14 2018This paper investigates the robust transmission design (RTD) of a multi-cell device-to-device (D2D) underlaid cellular network with imperfect channel state information (CSI). The bounded model is adopted to characterize the CSI impairment and the aim ... More
Multiple Antenna Assisted Non-Orthogonal Multiple AccessJan 24 2018Non-orthogonal multiple access (NOMA) is potentially capable of circumventing the limitations of the classic orthogonal multiple access schemes, hence it has recently received significant research attention both in industry and academia. This article ... More
Intelligent Reflecting Surface for Multicell MIMO CommunicationsJul 25 2019Intelligent reflecting surface (IRS) is envisioned to be a disruptive and revolutionizing technology that can achieve both spectral and energy efficient wireless communications and provide a radio-controllable environment. In specific, IRS is a planar ... More
Joint Altitude, Beamwidth, Location and Bandwidth Optimization for UAV-Enabled CommunicationsJun 06 2018This letter investigates an uplink power control problem for unmanned aerial vehicles (UAVs) assisted wireless communications. We jointly optimize the UAV's flying altitude, antenna beamwidth, UAV's location and ground terminals' allocated bandwidth and ... More
Pricing-based Distributed Energy-Efficient Beamforming for MISO Interference ChannelsDec 15 2015In this paper, we consider the problem of maximizing the weighted sum energy efficiency (WS-EE) for multi-input single-output (MISO) interference channels (ICs) which is well acknowledged as general models of heterogeneous networks (HetNets), multicell ... More
Reconfigurable Antenna Multiple Access for 5G mmWave SystemsMar 27 2018This paper aims to realize a new multiple access technique based on recently proposed millimeter-wave reconfigurable antenna architectures. To this end, first we show that integration of the existing reconfigurable antenna systems with the well-known ... More
Robust Beamforming with Pilot Reuse Scheduling in a Heterogeneous Cloud Radio Access NetworkApr 23 2018This paper considers a downlink ultra-dense heterogeneous cloud radio access network (H-CRAN) which guarantees seamless coverage and can provide high date rates. In order to reduce channel state information (CSI) feedback overhead, incomplete inter-cluster ... More
Widely-Linear Precoding for Large-Scale MIMO with IQI: Algorithms and Performance AnalysisFeb 28 2017In this paper we study widely-linear precoding techniques to mitigate in-phase/quadrature-phase (IQ) imbalance (IQI) in the downlink of large-scale multiple-input multiple-output (MIMO) systems. We adopt a real-valued signal model which takes into account ... More
Improving Wireless Physical Layer Security via D2D CommunicationSep 08 2018This paper investigates the physical layer security issue of a device-to-device (D2D) underlaid cellular system with a multi-antenna base station (BS) and a multi-antenna eavesdropper. To investigate the potential of D2D communication in improving network ... More
Intelligent Reflecting Surface for Multicell MIMO CommunicationsJul 25 2019Jul 26 2019Intelligent reflecting surface (IRS) is envisioned to be a disruptive and revolutionizing technology that can achieve both spectral and energy efficient wireless communications as well as provide a radio-controllable environment. In specific, IRS is a ... More
Intelligent Reflecting Surface Enhanced MIMO Broadcasting for Simultaneous Wireless Information and Power TransferAug 13 2019In this paper, we propose to deploy an intelligent reflecting surface (IRS) to enhance the energy harvesting performance for a simultaneous wireless information and power transfer (SWIPT) system. Specifically, an IRS-assisted SWIPT wireless communication ... More
Achievable Data Rate for URLLC-Enabled UAV Systems with 3-D Channel ModelJul 15 2019In this paper, we investigate the average achievable data rate (AADR) of the control information delivery from the ground control station (GCS) to unmanned-aerial-vehicle (UAV) under a 3-D channel, which requires ultra-reliable and low-latency communications ... More
Power-and Rate-Adaptation Improves the Effective Capacity of C-RAN for Nakagami-$m$ Fading ChannelsApr 06 2017Jun 13 2018We propose a power-and rate-adaptation scheme for cloud radio access networks (C-RANs), where each radio remote head (RRH) is connected to the baseband unit (BBU) pool through optical links. The RRHs jointly support the users by efficiently exploiting ... More
Unified Offloading Decision Making and Resource Allocation in ME-RANMay 29 2017Jul 01 2019In order to support communication and computation cooperation, we propose ME-RAN architecture, which consists of mobile edge cloud (ME) as the computation provision platform and radio access network (RAN) as the communication interface. Cooperative offloading ... More
Factors of Some Lacunary q-Binomial SumsJan 28 2012Jun 03 2012In this paper, we prove a divisibility result for the lacunary $q$-binomial sum $$ \sum_{k\equiv r\pmod{c}}(-1)^kq^{\binom{k}{2}}\qbinom{n}{k}{q}\qbinom{(k-r)/c}{l}{q^{c}}. $$
p-adic deformation of graph cyclesOct 12 2016Oct 14 2016In this paper, we show that the infinitesimal Torelli theorem implies the existence of deformations of automorphisms. We give a positive answer to Bloch-Esnault-Kerz conjecture for some graph cycles if the infinitesimal Torelli theorem holds.
SAT problem and statistical distanceFeb 26 2015Sep 22 2015In this paper with two equivalent representations of the information contained by a SAT formula, the reason why string generated by succinct SAT formula can be greatly compressed is firstly presented based on Kolmogorov complexity theory. Then what strings ... More
T2Ku: Building a Semantic Wiki of MathematicsJan 27 2012We introduce T2Ku, an open source project that aims at building a semantic wiki of mathematics featuring automated reasoning(AR) techniques. We want to utilize AR techniques in a way that truly helps mathematical researchers solve problems in the real ... More
A simple proof of Gopakumar-Vafa conjecture for local toric Calabi-Yau manifoldsOct 26 2004Dec 15 2004We prove Gopakumar-Vafa conjecture for local toric Calabi-Yau manifolds. It's also proved that the local Gopakumar-Vafa invariants of a given class at large genus vanish.
Magnetosphere structure of a Kerr black hole: marginally force-free equatorial boundary conditionJul 15 2018Sep 23 2018The role of equatorial boundary condition in the structure of a force-free black hole magnetosphere was rarely discussed, since previous studies have been focused on the field lines entering the horizon. However, recent high-accuracy force-free electrodynamics ... More
Emergence from Symmetry: A New Type of Cellular AutomataMar 17 2010Jul 25 2010In this paper, a different perspective of constructing the CA models is proposed. Its kernel, the Local Symmetric Distribution Principle, relates to some fundamental concepts in physics, which maybe raise a wide interest. With a rich palette of configurations, ... More
Physical Integrity Attack Detection of Surveillance Camera with Deep Learning Based Video Frame InterpolationJun 15 2019Surveillance cameras, which is a form of Cyber Physical System, are deployed extensively to provide visual surveillance monitoring of activities of interest or anomalies. However, these cameras are at risks of physical security attacks against their physical ... More
Relative derived equivalences and relative homological dimensionsJan 25 2014Let $\mathscr{A}$ be a small abelian category. For a closed subbifunctor $F$ of $\Ext_{\mathscr{A}}^{1}(-,-)$, Buan has generalized the construction of the Verdier's quotient category to get a relative derived category, where he localized with respect ... More
On divisibility of sums of Apery polynomialsAug 07 2011For any positive integers $m$ and $\alpha$, we prove that $$\sum_{k=0}^{n-1}\epsilon^k(2k+1)A_k^{(\alpha)}(x)^m\equiv0\pmod{n}, $$ where $\epsilon\in\{1,-1\}$ and $$ A_n^{(\alpha)}(x)=\sum_{k=0}^n\binom{n}{k}^{\alpha}\binom{n+k}{k}^{\alpha}x^k.$$
Lehmer's type congruences for lacunary harmonic sumsMay 07 2009Oct 10 2009In this paper, we study the Lehmer's type congruences for lacunary harmonic sums.
Spectral estimation of the percolation transition in clustered networksOct 04 2017There have been several spectral bounds for the percolation transition in networks, using spectrum of matrices associated with the network such as the adjacency matrix and the non-backtracking matrix. However they are far from being tight when the network ... More
Evaluating accuracy of community detection using the relative normalized mutual informationJan 15 2015Oct 28 2015The Normalized Mutual Information (NMI) has been widely used to evaluate the accuracy of community detection algorithms. However in this article we show that the NMI is seriously affected by systematic errors due to finite size of networks, and may give ... More
Inference of kinetic Ising model on sparse graphsJul 23 2012Based on dynamical cavity method, we propose an approach to the inference of kinetic Ising model, which asks to reconstruct couplings and external fields from given time-dependent output of original system. Our approach gives an exact result on tree graphs ... More
Automorphism and Cohomology I: Fano variety of lines and CubicNov 17 2015Oct 12 2016In this paper, we prove a general principle of lifting an automorphism from positive characteristic to zero characteristic. We based on the principle to prove the automorphism group of Fano variety of cubic threefold (fourfold) acts on its cohomology ... More
The augmentation category map induced by exact Lagrangian cobordismsJun 19 2016May 23 2017To a Legendrian knot, one can associate an $\mathcal{A}_{\infty}$ category, the augmentation category. An exact Lagrangian cobordism between two Legendrian knots gives a functor of the augmentation categories of the two knots. We study the functor and ... More
Effective equidistribution of circles in the limit sets of Kleinian groupsJan 31 2016Consider a general circle packing $\mathcal{P}$ in the complex plane $\mathbb{C}$ invariant under a Kleinian group $\Gamma$. When $\Gamma$ is convex-cocompact or its critical exponent is greater than 1, we obtain an effective equidistribution for small ... More
On a conjecture of SunMay 24 2010May 25 2010We confirm a conjecture of Sun on the expansions of $n(m^k-1)/(m-1)$ in base $m$.
A note on enumerating colored integer partitionsSep 21 2015In this short note, we give basic enumerative results on colored integer partitions.
A generalized Tian-Todorov theoremOct 27 2013May 24 2016Let X be a smooth proper variety with torsion canonical bundle. Suppose L is a line bundle on X. We prove the pair (X,L) is unobstructed if one of the following conditions holds, (1) the line bundle L is ample, (2) the fundamental group {\pi}_1(X) of ... More
Effective equidistribution of circles in the limit sets of Kleinian groupsJan 31 2016Feb 21 2017Consider a general circle packing $\mathcal{P}$ in the complex plane $\mathbb{C}$ invariant under a Kleinian group $\Gamma$. When $\Gamma$ is convex-cocompact or its critical exponent is greater than 1, we obtain an effective equidistribution for small ... More
Non-trivial Kazhdan-Lusztig coefficients of affine Weyl groupsApr 06 2018In this paper we show that the leading coefficients $\mu(y,w)$ of some Kazhdan-Lusztig polynomials $P_{y,w}$ with $y,w$ in the affine Weyl group of type $\widetilde{B_n}$ can be $n$; in the cases of types $\widetilde{C_n}$ and $\widetilde{D_n}$ they can ... More
SAT is a problem with exponential complexity measured by negentropyDec 03 2014Sep 21 2015In this paper the reason why entropy reduction (negentropy) can be used to measure the complexity of any computation was first elaborated both in the aspect of mathematics and informational physics. In the same time the equivalence of computation and ... More
Dragon: A Computation Graph Virtual Machine Based Deep Learning FrameworkJul 26 2017Deep Learning has made a great progress for these years. However, it is still difficult to master the implement of various models because different researchers may release their code based on different frameworks or interfaces. In this paper, we proposed ... More
Landslide Monitoring based on Terrestrial Laser Scanning: A Novel Semi-automatic WorkflowSep 01 2018In this paper, we propose a workflow that uses Terrestrial Laser Scanning(TLS) to semi-automatically monitor landslide and then test it in practice. Firstly, several groups of TLS stations are set on different time to collect the raw point cloud of the ... More
Nonnegative Ricci curvature, almost stability at infinity, and structure of fundamental groupsSep 26 2018Jan 31 2019We study the fundamental group of an open $n$-manifold $M$ of nonnegative Ricci curvature with additional stability condition on $\widetilde{M}$, the Riemannian universal cover of $M$. We prove that if any tangent cone of $\widetilde{M}$ at infinity is ... More
A Proof of Milnor conjecture in dimension 3Mar 23 2017We present a proof of Milnor conjecture in dimension 3 based on Cheeger-Colding theory on limit spaces of manifolds with Ricci curvature bounded below. It is different from [Liu] that relies on minimal surface theory.
Colour Dependence of the Distribution of IRAS Galaxies revealed by Multifractal MeasuresApr 11 2006Jul 04 2006Multifractal measures are applied to three IRAS galaxy subsamples selected by colour from the PSCz catalogue. As shown by generalised dimension spectrum, hot IRAS galaxies are found less clustered than cold galaxies, but the difference is very weak. An ... More
Secure Communication through Wireless-Powered Friendly Jamming: Jointly Online Optimization over Geography, Energy and TimeFeb 17 2016Exploring the interference-emitting friendly jammers to protect the sensitive communications in the presence of eavesdroppers has increasingly being investigated in literature. In parallel, scavenging energy from abient radio signals for energy-constrained ... More
Derived equivalences for Cohen-Macaulay Auslander algebrasSep 20 2010Mar 29 2011Let $A$ and $B$ be Gorenstein Artin algebras of Cohen-Macaulay finite type. We prove that, if $A$ and $B$ are derived equivalent, then their Cohen-Macaulay Auslander algebras are also derived equivalent.
Non-backtracking operator for Ising model and its application in attractor neural networksSep 10 2014The non-backtracking operator was recently shown to give a redemption for spectral clustering in sparse graphs. In this paper we consider non-backtracking operator for Ising model on a general graph with a general coupling distribution by linearizing ... More
A remark on Zoloterav's theoremJan 02 2006Let n>=3 be an odd integer. For any integer a prime to n, define the permutation gamma_{a,n} of {1,...,(n-1)/2} by gamma_{a,n}(x)=n-\dec{ax}_n if {ax}_n>=(n+1)/2, and {ax}_n if {ax}_n<=(n-1)/2, where {x}_n denotes the least nonnegative residue of x modulo ... More
Exact Lagrangian Fillings of Legendrian $(2,n)$ torus linksJul 11 2016For a Legendrian $(2,n)$ torus knot or link with maximal Thurston-Bennequin number, Ekholm, Honda, and K\'alm\'an constructed $C_n$ exact Lagrangian fillings, where $C_n$ is the $n$-th Catalan number. We show that these exact Lagrangian fillings are pairwise ... More
Vague partition, fuzzy sets and their axiomatical foundationsJun 24 2015Based on the in-depth analysis of the nature and features of vague phenomenon, this paper focuses on establishing the axiomatical foundation of the membership degree theory for vague phenomenon, presents an axiomatic system of governing membership degrees ... More
Spaces of conics on low degree complete intersectionsOct 13 2013Jan 09 2017Let X be a smooth complete intersection. Suppose p and q are general points of X, we consider conics in X passing through p and q. We show the moduli space of these conics is a smooth complete intersection. The main ingredients of the proof are a criterion ... More
A generalization of Carlitz's congruenceMar 21 2006Jul 03 2006In this paper, we propose a generalization of a congruence due to Carlitz.
Global existence and asymptotic behavior of solutions to the Euler equations with time-dependent dampingSep 20 2016We study the isentropic Euler equations with time-dependent damping, given by $\frac{\mu}{(1+t)^\lambda}\rho u$. Here, $\lambda,\mu$ are two non-negative constants to describe the decay rate of damping with respect to time. We will investigate the global ... More
The redshift and geometrical aspect of photonsApr 09 2007The cosmological redshift phenomenon can be described by the dark matter field fluid model, the results deduced from this model agree very well with the observations. The observed cosmological redshift of light depends on both the speed of the emitter ... More
Spaces of conics on low degree complete intersectionsOct 13 2013May 23 2016Let X be a smooth complete intersection. Suppose p and q are general points of X, we consider conics in X passing through p and q. We show the moduli space of these conics is a smooth complete intersection. The main ingredients of the proof are a criteria ... More
Joining measures for horocycle flows on abelian coversJul 12 2016Dec 06 2017A celebrated result of Ratner from the eighties says that two horocycle flows on hyperbolic surfaces of finite area are either the same up to algebraic change of coordinates, or they have no non-trivial joinings. Recently, Mohammadi and Oh extended Ratner's ... More
Collaborative Recommendation with Auxiliary Data: A Transfer Learning ViewJul 09 2014Intelligent recommendation technology has been playing an increasingly important role in various industry applications such as e-commerce product promotion and Internet advertisement display. Besides users' feedbacks (e.g., numerical ratings) on items ... More
Robust Clustering Oracle and Local Reconstructor of Cluster Structure of GraphsApr 22 2019Due to the massive size of modern network data, local algorithms that run in sublinear time for analyzing the cluster structure of the graph are receiving growing interest. Two typical examples are local graph clustering algorithms that find a cluster ... More
jQuery.Feyn: Drawing Feynman Diagrams with SVGNov 26 2013jQuery.Feyn is a tool for drawing Feynman diagrams with Scalable Vector Graphics (SVG), written in JavaScript and runs in modern browsers. It features predefined propagator styles, vertex types, and symbols. Math formulae can be included as external graphics, ... More
First covering of Drinfel'd upper half plane and Banach representations of GL_2(Q_p)Oct 11 2015Dec 05 2016We construct some admissible Banach representations of GL_2(Q_p) that conjecturally should correspond to some 2-dimensional tamely ramified, potentially Barsotti-Tate representations of G_{Q_p} via the p-adic local Langlands correspondence. To achieve ... More
Stable equivalences of Morita type for $Φ$-Beilinson-Green algebrasJul 02 2019In this paper, we present a method to construct new stable equivalences of Morita type. Suppose that a stable equivalence of Morita type between finite dimensional algebras $A$ and $B$ is defined by a $B$-$A$-bimodule $N$. Then, for any finite admissible ... More
Calculating Vacuum Energy as a Possible Explanation of the Dark EnergyJan 20 2011Jun 15 2011We carried out a study of the properties of the $\lambda \phi^4$ field solutions. By constructing Gaussian wave packets to calculate the $S$ matrix, we show that the probability of the vacuum unbroken state transfers to the broken state is about $10^{-52}$. ... More
Meson Mass Spectrum of Heavy-Light Quarks Combinations with Dirac EquationJun 15 2011Nov 23 2011We use the Dirac equation to study the mass spectrum of mesons with heavy-light quark combinations. First we study the Dirac equation with spherically symmetry and funnel potential, and apply them on the hydrogen-like atom problem to check the correctness ... More
Exact solutions, finite time singularities and non-singular universe models from a variety of $Λ(t)$ cosmologiesDec 04 2017Jan 05 2018Cosmological models with time dependent $\Lambda$ (read as $\Lambda (t)$) have been investigated widely in the literature. Models that solve background dynamics analytically, are of special interest. Additionally, the allowance of past or future singularities ... More
Propagation of Delayed Lattice Differential Equations without Local QuasimonotonicityMay 06 2014This paper is concerned with the traveling wave solutions and asymptotic spreading of delayed lattice differential equations without quasimonotonicity. The spreading speed is obtained by constructing auxiliary equations and using the theory of lattice ... More
Rational homotopy theory and nonnegative curvatureJun 29 2001In this note, we answer positively a question by Belegradek and Kapovitch about the relation between rational homotopy theory and a problem in Riemannian geometry which asks that total spaces of which vector bundles over compact nonnegative curved manifolds ... More
A q-analogue of Lehmer's congruenceJul 25 2005Aug 17 2005We establish the q-analogue of a classical congruence of Lehmer. Also, the q-analogues of two congruences of Morley and Granville are given.
On consecutive happy numbersJul 08 2006Jul 27 2006Let e>=1 and b>=2 be integers. For a positive integer n=\sum_{j=0}^ka_jb^j with 0<=a_j<b, define T_{e,b}(n)=\sum_{j=0}^ka_j^e. n is called (e,b)-happy if T_{e,b}^r(n)=1 for some r>=0, where T_{e,b}^r is the r-th iteration of T_{e,b}. In this paper, we ... More
Robust Spectral Detection of Global Structures in the Data by Learning a RegularizationSep 09 2016Spectral methods are popular in detecting global structures in the given data that can be represented as a matrix. However when the data matrix is sparse or noisy, classic spectral methods usually fail to work, due to localization of eigenvectors (or ... More
Regularity of Solution to Axis-symmetric Navier-Stokes Equations with a Slightly Supercritical ConditionOct 23 2014Consider an axis-symmetric suitable weak solution of 3D incompressible Navier-Stokes equation with nontrivial swirl. If the solution satisfies a slightly supercritical assumption, we will prove that v is regular. This extends the results of Chen-Strain-Tsai-Yau, ... More
Regularity and geometric character of solution of a degenerate parabolic equationApr 07 2015This work studies the regularity and the geometric significance of solution of the Cauchy problem for a degenerate parabolic equation $u_{t}=\Delta{}u^{m}$. Our main objective is to improve the H$\ddot{o}$lder estimate obtained by pioneers and then, to ... More
First covering of Drinfel'd upper half plane and Banach representations of GL_2(Q_p)Oct 11 2015We construct some admissible Banach representations of GL_2(Q_p) that conjecturally should correspond to some 2-dimensional tamely ramified, potentially Barsotti-Tate representations of G_{Q_p} via the p-adic local Langlands correspondence. To achieve ... More
The evolution of the Earth-Moon system based on the dark matter field fluid modelApr 01 2007Jan 13 2008The evolution of Earth-Moon system is described by the dark matter field fluid model proposed in the Meeting of Division of Particle and Field 2004, American Physical Society. The current behavior of the Earth-Moon system agrees with this model very well ... More
Local mixing on abelian covers of hyperbolic surfaces with cuspsDec 16 2017We prove the local mixing theorem for geodesic flows on abelian covers finite volume hyperbolic surfaces with cusps, which is a continuation of the work of Oh-Pan. We also describe applications to counting problems and the prime geodesic theorem.
Using Malware Self-Defence Mechanism to Harden Defence and Remediation ToolsJan 06 2018Malware are becoming a major problem to every individual and organization in the cyber world. They are advancing in sophistication in many ways. Besides their advanced abilities to penetrate and stay evasive against detection and remediation, they have ... More