从统计物理学看复杂网络研究

从统计物理学来看，网络是一个包含了大量个体及个体之间相互作用的系统。本文从统计物理学的角度整理与总结了复杂网络目前的主要研究结果，并对将来的研究工作做了一个展望。文章把网络分为三个层次——无向网络、有向网络与加权网络，对不同网络的静态几何量研究的现状分别做了综述，并结合网络机制模型设计与评价的需要，提出了新的有待研究的静态几何量；对网络机制模型做了总结与分析，提出了有待解决的关于双向幂律网络的机制模型的问题；部分地概括了网络演化性质，网络的结构稳定性以及网络上的动力学模型的研究。然后，以我们目前正在进行的两个方面的工作—科学家网络和产品生产关系网络一为例，粗略地介绍了网络研究在一些实际问题中的应用。最后，作为一个简单的补充和索引，我们整理了复杂网络研究中部分常用的解析与数值计算的方法。     

On the Clique-Transversal Number in （Claw,K4）-Free 4-Regular Graphs

A clique-transversal set D of a graph G is a set of vertices of G such that D meets all cliques of G.The clique-transversal number,denoted by τC(G),is the minimum cardinality of a clique-transversal set in G.In this paper,we first present a lower bound on τC(G) and characterize the extremal graphs achieving the lower bound for a connected(claw,K4)-free 4-regular graph G.Furthermore,we show that for any 2-connected(claw,K4)-free 4-regular graph G of order n,its clique-transversal number equals to [n/3].     

几类图的匹配唯一性

若图G的匹配多项式为M(G;W),对任何图H,M(G;W)=M(H;W)推出G与H同构,则称G是匹配唯一的.本文讨论了下面的几种图类:(i)B_(m,n,r);(ii)D_(m,n,r);(iii)T_(m,n)的匹配唯一性问题,从而得到一些较为满意的结果.     

Injective coloring of planar graphs with girth 5

A coloring of a graph G is injective if its restriction to the neighbour of any vertex is injective. The injective chromatic number X_i\left(G\right) of a graph G is the leastk such that there is an injective k-coloring. In this paper, we prove that for each planar graph with g\ge 5 and \Delta \left(G\right)\ge 20, {\chi }_i\left(G\right)\le \Delta \left(G\right)+3.     

High‐Performance Colorful Semitransparent Polymer Solar Cells with Ultrathin Hybrid‐Metal Electrodes and Fine‐Tuned Dielectric Mirrors

Polymer solar cells (PSCs) possess the unique features of semitransparency and coloration, which make them potential candidates for applications in aesthetic windows. Here, the authors fabricate inverted semitransparent PSCs with high‐quality hybrid Au/Ag transparent top electrodes and fine‐tuned dielectric mirrors (DMs). It is demonstrated that the device color can be tailored and the light harvesting in the PSCs can be enhanced by matching the bandgap of the polymer donors in the active layer with the specifically designed maximum‐reflection‐center‐wavelengths of the DMs. A detailed chromaticity analysis of the semitransparent PSCs from both bottom and top (mirror) views is also carried out. Furthermore, the inverted semitransparent PSCs based on PTB7‐Th:PC₇₁BM with six pairs of DMs demonstrate a maximum power conversion efficiency (PCE) of 7.0% with an average visible transmittance (AVT) of 12.2%. This efficiency is one of the highest reported for semitransparent PSCs, corresponding to 81.4% of the PCE from opaque counterpart devices. The device design and processing method are also successfully adapted to a flexible substrate, resulting in a device with a competitive PCE of 6.4% with an AVT of 11.5%. To the best of our knowledge, this PCE value is the highest value reported for a flexible semitransparent PSC.     

High-performance simple-encoding generator-based systematic irregular LDPC codes and resulted product codes

Low-Density Parity-Check (LDPC) code is one of the most exciting topics among the coding theory community.It is of great importance in both theory and practical communications over noisy channels.The most advantage of LDPC codes is their relatively lower decoding complexity compared with turbo codes,while the disadvantage is its higher encoding complexity.In this paper,a new ap- proach is first proposed to construct high performance irregular systematic LDPC codes based on sparse generator matrix,which can significantly reduce the encoding complexity under the same de- coding complexity as that of regular or irregular LDPC codes defined by traditional sparse parity-check matrix.Then,the proposed generator-based systematic irregular LDPC codes are adopted as con- stituent block codes in rows and columns to design a new kind of product codes family,which also can be interpreted as irregular LDPC codes characterized by graph and thus decoded iteratively.Finally, the performance of the generator-based LDPC codes and the resultant product codes is investigated over an Additive White Gaussian Noise (AWGN) and also compared with the conventional LDPC codes under the same conditions of decoding complexity and channel noise.     

无线网络中兼顾业务类型及公平性的无线资源共享问题研究

基于图染色理论提出了2种无线网络中的无线资源共享算法C_TDRS和S_TDGRS.这2种算法分别从子信道和业务流角度考虑,以尽力满足业务需求为目标,兼顾了业务类型和资源共享的公平性.仿真结果表明,2种算法的共享结果在系统吞吐率和比例公平方面比现有算法更接近最优值,并且S_TDGRS算法对2个指标有很好的折衷.     

A multi-cell graph based dynamic resource allocation scheme for multi-user wireless networks

Dynamic resource allocation being a computationally difficult problem, static spectrum management is more commonly used in large-scale networks. The combination of virtualization technologies, where powerful centralized allocation algorithms can be implemented, and recent advances in graph coloring algorithms prompts the revisiting of this view. We describe a new graph based framework to maximize the number of simultaneously communicating mobiles in a wireless network. Since the considered problem is NP-hard, we propose various heuristic algorithms and analyze their performance, in comparison with standard decentralized channel assignment strategies such as Fractional Frequency Reuse (FFR). We consider the LTE uplink and downlink with the WINNER channel as the reference model. We show that for blocking probabilities below 2%, our scheme typically increases the number of mobile users by 25%. For example with 25 base stations and 120 channels, running the resource allocation scheme takes one second on a PC and permits to increase the number of mobiles requiring one single channel each from 750 to 950, a 25% increase in efficiency compared to FFR.     

Texture separation via a reference set

Patch-based de-noising algorithms and patch manifold smoothing have emerged as efficient de-noising methods. This paper provides a new insight on these methods. We show how to extend them to separate oscillatory patterns that could be entangled. A collection of particular patches, that we call reference set, is selected by the user. We define a notion of similarity relative to this reference set that is used to extend the Non-Local Means (see Buades et al., 2005) [1] and the graph-based de-noising method (see Szlam et al., 2008) [12].     

Journal of Mathematical Research with Applications Vol.34, No.1–5 Contents

正~~