A box-covering algorithm for fractal scaling in scale-free networks

A random sequential box-covering algorithm recently introduced to measure the fractal dimension in scale-free (SF) networks is investigated. The algorithm contains Monte Carlo sequential steps of choosing the position of the center of each box; thereby, vertices in preassigned boxes can divide subsequent boxes into more than one piece, but divided boxes are counted once. We find that such box-split allowance in the algorithm is a crucial ingredient necessary to obtain the fractal scaling for fractal networks; however, it is inessential for regular lattice and conventional fractal objects embedded in the Euclidean space. Next, the algorithm is viewed from the cluster-growing perspective that boxes are allowed to overlap; thereby, vertices can belong to more than one box. The number of distinct boxes a vertex belongs to is, then, distributed in a heterogeneous manner for SF fractal networks, while it is of Poisson-type for the conventional fractal objects.     

基于散射量子行走的完全图上结构异常搜索算法

完全图K_N 上某个顶点连接到图G将破坏其对称性. 为加速定位这类结构异常, 基于散射量子行走模型设计搜索算法, 首先给出了算法酉算子的定义, 在此基础上利用完全图的对称性, 将算法的搜索空间限定为一个低维的坍缩图空间. 以G为一个顶点的情况为例, 利用硬币量子行走模型上的研究结论简化了坍缩图空间中酉算子的计算, 并借助矩阵扰动理论分析算法演化过程. 针对星图S_N 上结构异常的研究表明, 以星图中心节点为界将整个图分为左右两个部分, 当且仅当两部分在N→∞时具有相同的特征值, 搜索算法可以获得量子加速. 本文说明星图上的分析方法和结论可以推广至完全图的坍缩图上. 基于此, 本文证明无论完全图连接的图G结构如何, 搜索算法均可在O(√N) 时间内定位到目标顶点, 成功概率为1-O(1√N), 即量子行走搜索该类异常与经典搜索相比有二次加速.     

Diagram technique for finding of vertex functions in the Landau theory of heteropolymer liquids

The problem on finding the coefficients of the Landau free energy expansion into the power series of parameter of order has been considered for solutions and melts of linear heteropolymers whose molecules comprise several types monomeric units arranged stochastically. The presence of such a quenched structural disorder places this problem outside the framework of the traditional statistical physics inviting for its solution special approaches. One of them, based on the replica concept and actively engaged in theoretical physics of disordered systems, has been invoked in this paper to derive expressions for the vertex functions in the Landau theory of heteropolymer liquids. An algorithm has been formulated which permits one resorting to the simple diagram technique to write down expressions for these functions of any order in terms of the statistical characteristics of chemical quenched structure of polymer molecules. Explicit expressions for the contributions to the Landau free energy up to the fourth degree of order parameters for polymer systems with an arbitrary structural disorder have been presented to illustrate this general algorithm. Its potentialities have been also exemplified for the melt of random m-component copolymer where exact analytical formulas for these contributions up to n=6 at an arbitrary m have been derived for the first time.     

Full fermion-boson vertex function derived in terms of symmetry relations in Abelian gauge theory

Nonperturbative studies such as confinement and dynamical chiral symmetry breaking need the nonperturbative interacting vertex functions. In this paper, an approach to determining the full fermion-boson vertex function in four-dimensional Abelian gauge theory is presented: this full vertex function is derived in terms of a set of normal (longitudinal) and transverse Ward-Takahashi relations for the fermion-boson (vector) and axial-vector vertices in the momentum space in the case of massless fermion. Such a derived fermion-boson vertex function should be satisfied both perturbatively and nonperturbatively. The fact that such a derived full fermion-boson vertex function to one-loop order holds indeed is proven and the nonperturbative form of this vertex is also under discussion.     

The Multilevel Splitting algorithm for graph colouring with application to the Potts model

Calculating the partition function of the zero-temperature antiferromagnetic model is an important problem in statistical physics. However, an exact calculation is hard since it is strongly connected to a fundamental combinatorial problem of counting proper vertex colourings in undirected graphs, for which an efficient algorithm is not known to exist. Thus, one has to rely on approximation techniques. In this paper, we formulate the problem of the partition function approximation in terms of rare-event probability estimation and investigate the performance of a particle-based algorithm, called Multilevel Splitting, for handling this setting. The proposed method enjoys a provable probabilistic performance guarantee and our numerical study indicates that this algorithm is capable of delivering accurate results using a relatively modest amount of computational resources.     

基于NURBS曲线插值的实时大气折射误差修正

提出了一种采用传统的逐点描迹法和NURBS曲线插值方法相结合的技术，对多种可见光测量设备进行高准确度的实时大气折射误差修正方法.该方法克服了逐点描迹法计算量大、无法达到实时计算要求等缺点，尤其适用于全自动胶片判读仪或光电经纬仪中实时数据的大气折射误差修正.     

Parameter vertex method and its parallel solution for evaluating the dynamic response bounds of structures with interval parameters

In this article, we propose a parameter vertex method to determine the upper and lower bounds of the dynamic response of structures with interval parameters, which can be regarded as an extension of the matrix vertex method proposed by Qiu and Wang. The matrix vertex method requires considerable computation time and encounters the dependency problem in practice, thereby limiting its application in engineering. The proposed parameter vertex method can avoid the dependency problem, and the number of possible vertex combinations in the proposed method is significantly less than that in the matrix vertex method. The parameter vertex method requires that each matrix element in the dynamic differential equation is monotonic with respect to the uncertain parameter, and that the dynamic response reaches its extreme value when the uncertain parameter is at its endpoint. To further reduce the runtime, both vertical and transversal parallel algorithms are introduced and integrated into the parameter vertex method to improve its computational efficiency. Two numerical examples are presented to demonstrate the proposed method combined with both parallel algorithms. The performances of the two parallel algorithms are thoroughly studied. The parameter vertex method combined with parallel algorithm can be used for large-scale computing.     

Influence of transport corrections on the infrared absorption in superconductors

In order to study the magnitude of the vertex correction in the infrared absorption in a superconductor, we have calculated the

and ω dependent response function for a simple Debye model of a superconductor. We have carried out our calculations for no vertex correction and also for the first vertex correction in both the high q and low q limits. The vertex correction calculation includes the influence of transport modifications due to the interference between quasiparticle scattering by phonons and the quasiparticle-external field interaction. This correction is small for all frequencies except those just above the gap. Our calculations indicate that, with vertex corrections, the theory for lead would be in even better agreement with experiment.     

Structure of the pairing interaction in the two-dimensional Hubbard model

Dynamic cluster Monte Carlo calculations for the doped two-dimensional Hubbard model are used to study the irreducible particle-particle vertex responsible for dx2-y2 pairing in this model. This vertex increases with increasing momentum transfer and decreases when the energy transfer exceeds a scale associated with the Q=(pi, pi) spin susceptibility. Using an exact decomposition of this vertex into a fully irreducible two-fermion vertex and charge and magnetic exchange channels, the dominant part of the effective pairing interaction is found to come from the magnetic, spin S=1 exchange channel.     

Use of symmetry plane fragmentation and graph squaring techniques to express the eigenspectra for some vertex-weighted graphs of linear chains and cycles in analytical form

Three types of graphs of linear chains, viz. linear chains with unit increment or decrement in weight on one terminal vertex, linear chains with unit increment or decrement in weight on both the terminal vertices and linear chains with unit increment in weight on one terminal vertex and decrement in that on the other terminal vertex, have been considered. The symmetry plane fragmentation and graph squaring techniques have been exploited to express the eigenspectra of such graphs of linear chains in analytical form, and have subsequently been used to express the eigenspectra of graphs of linear chains and cycles with alternant vertex weights. The derived expressions for the eigenspectra have been used to obtain the eigenspectra of linear polyacenes, methylene-substituted linear polyacenes and cylindrical polyacene strips in analytical form.     

基于垂直平分线的非测距定位算法

在无线传感器网络定位机制中,近似三角形内点测试(APIT)定位算法因思想简单、硬件成本低、定位精度高而被广泛应用,但算法性能会因锚节点分布不均匀受到严重影响。为提高节点定位精度和解决APIT定位算法边缘效应的问题,提出一种基于垂直平分线的非测距定位算法。该算法利用接收信号强度指示值(RSSI)值筛选锚节点并与等腰三角形底边中垂线过顶点的几何原理结合进行定位,可以得到比较合理的定理精度,性能相对稳定。仿真结果表明,该算法可有效提高无线传感器网络定位的精度和覆盖率。     

Ordered community structure in networks

Community structure in networks is often a consequence of homophily, or assortative mixing, based on some attribute of the vertices. For example, researchers may be grouped into communities corresponding to their research topic. This is possible if vertex attributes have unordered discrete values, but many networks exhibit assortative mixing by some ordered (discrete or continuous) attribute, such as age or geographical location. In such cases, the identification of discrete communities may be difficult or impossible. We consider how the notion of community structure can be generalized to networks that have assortative mixing by ordered attributes. We propose a method of generating synthetic networks with ordered communities and investigate the effect of ordered community structure on the spread of infectious diseases. We also show that current community detection algorithms fail to recover community structure in ordered networks, and evaluate an alternative method using a layout algorithm to recover the ordering.     

Decay vertex reconstruction and 3-dimensional lifetime determination at BESⅢ

This paper focuses mainly on the vertex reconstruction of resonance particles with a relatively long lifetime such as KSO, A, as well as on lifetime measurements using a 3-dimensional fit. The kinematic constraints between the production and decay vertices and the decay vertex fitting algorithm based on the least squares method are both presented. Reconstruction efficiencies including experimental resolutions are discussed. The results and systematic errors are calculated based on a Monte Carlo simulation.     

Interplay of collective excitations in quantum-well intersubband resonances

Intersubband resonances in a semiconductor quantum well (QW) display fascinating features involving various collective excitations such as Fermi-edge singularity (FES) and intersubband plasmon (ISP). Using a density matrix approach, we treated many-body effects such as depolarization, vertex correction, and self-energy consistently for a two-subband system. We found a systematic change in resonance spectra from FES- to ISP-dominated features, as QW width or electron density is varied. Such an interplay between FES and ISP significantly changes both line shape and peak position of the absorption spectrum. We found that a cancellation of FES and ISP undresses the resonant responses and recovers the single-particle features of absorption for semiconductors with a strong nonparabolicity such as InAs, leading to a dramatic broadening of the absorption spectrum.     

Local Statistics of Realizable Vertex Models

We study planar “vertex” models, which are probability measures on edge subsets of a planar graph, satisfying certain constraints at each vertex, examples including the dimer model, and 1-2 model, which we will define. We express the local statistics of a large class of vertex models on a finite hexagonal lattice as a linear combination of the local statistics of dimers on the corresponding Fisher graph, with the help of a generalized holographic algorithm. Using an n × n torus to approximate the periodic infinite graph, we give an explicit integral formula for the free energy and local statistics for configurations of the vertex model on an infinite bi-periodic graph. As an example, we simulate the 1-2 model by the technique of Glauber dynamics.     

An efficient approach for feature-preserving mesh denoising

With the growing availability of various optical and laser scanners, it is easy to capture different kinds of mesh models which are inevitably corrupted with noise. Although many mesh denoising methods proposed in recent years can produce encouraging results, most of them still suffer from their computational efficiencies. In this paper, we propose a highly efficient approach for mesh denoising while preserving geometric features. Specifically, our method consists of three steps: initial vertex filtering, normal estimation, and vertex update. At the initial vertex filtering step, we introduce a fast iterative vertex filter to substantially reduce noise interference. With the initially filtered mesh from the above step, we then estimate face and vertex normals: an unstandardized bilateral filter to efficiently smooth face normals, and an efficient scheme to estimate vertex normals with the filtered face normals. Finally, at the vertex update step, by utilizing both the filtered face normals and estimated vertex normals obtained from the previous step, we propose a novel iterative vertex update algorithm to efficiently update vertex positions. The qualitative and quantitative comparisons show that our method can outperform the selected state of the art methods, in particular, its computational efficiency (up to about 32 times faster).     

Framed Vertex Operator Algebras, Codes and the Moonshine Module

For a simple vertex operator algebra whose Virasoro element is a sum of commutative Virasoro elements of central charge ?, two codes are introduced and studied. It is proved that such vertex operator algebras are rational. For lattice vertex operator algebras and related ones, decompositions into direct sums of irreducible modules for the product of the Virasoro algebras of central charge ? are explicitly described. As an application, the decomposition of the moonshine vertex operator algebra is obtained for a distinguished system of 48 Virasoro algebras. Received: 14 July 1997 / Accepted: 8 September 1997     

Characteristics of the network of scientific journals pertaining to Chinese patents

We present the network of scientific journals pertaining to Chinese patent data in the period of 1995-2002, in which two journals are considered linked if they have been cited by a common patent. We study a variety of statistical properties of the network of scientific journals of China (NSJC), including degree distribution, local clustering and average degree of the nearest neighbors in the one-mode projected network. Besides this, we generate a weighted network for the NSJC in which the number of common patents citing two particular journals is mapped to line weights. For such a weighted network, distributions of weight, vertex strength, weight per degree, and the relationship between the vertex strength and degree have been analyzed. The above findings show that for the NSJC, small-world behavior is not distinct, while properties of random networks are observed.     

Solving the undirected feedback vertex set problem by local search

An undirected graph consists of a set of vertices and a set of undirected edges between vertices. Such a graph may contain an abundant number of cycles, in which case a feedback vertex set (FVS) is a set of vertices intersecting with each of these cycles. Constructing a FVS of cardinality approaching the global minimum value is an optimization problem in the nondeterministic polynomial-complete complexity class, and therefore it might be extremely difficult for some large graph instances. In this paper we develop a simulated annealing local search algorithm for the undirected FVS problem by adapting the heuristic procedure of Galinier et al. [P. Galinier, E. Lemamou, M.W. Bouzidi, J. Heuristics 19, 797 (2013)], which worked for the directed FVS problem. By defining an order for the vertices outside the FVS, we replace the global cycle constraints by a set of local vertex constraints on this order. Under these local constraints the cardinality of the focal FVS is then gradually reduced by the simulated annealing dynamical process. We test this heuristic algorithm on large instances of Erdös-Rényi random graph and regular random graph, and find that this algorithm is comparable in performance to the belief propagation-guided decimation algorithm.     

Geometrical event reconstruction in the COMPASS experiment

The procedure of geometrical event reconstruction used at the setup COMPASS (CERN/SPS) including the algorithm of charged particle tracks reconstruction and the algorithm of the search of the vertex of beam muon-target interaction is presented. The results of the calculation of the accuracy of reconstructed objects and efficiency of the track reconstruction algorithm are given.