修正的Newman-Watts小世界及其上随机游走的混合时

在一个常规构建的图中加"长边(shortcuts)"会得到一个小世界模型,这是经典的构造小世界模型的方法.最近,吴宪远在文[Internet Mathematics,DOI:10.1080/15427951,2015.101208]中指出,在加"长边"过程中加的所有边,只有与图的直径成正比才会对小世界模型的构造起决定性作用.我们依据此文的加边机制,对体积为n~d的d(d≥1)维格点图,只添加起决定性作用的长边,得到的小世界模型修正了原始的Newman-Watts小世界模型,并证明该模型的直径和混合时是log n阶的.     

Diameter of P.A. random graphs with edge‐step functions

In this work we prove general bounds for the diameter of random graphs generated by a preferential attachment model whose parameter is a function f:N→[0,1] that drives the asymptotic proportion between the numbers of vertices and edges. These results are sharp when f is a regularly varying function at infinity with strictly negative index of regular variation ?γ. For this particular class, we prove a characterization for the diameter that depends only on ?γ. More specifically, we prove that the diameter of such graphs is of order 1/γ with high probability, although its vertex set order goes to infinity polynomially. Sharp results for the diameter for a wide class of slowly varying functions are also obtained.     

高校女性知识分子体成分与骨密度的相关研究

应用GE Insight和INBODY3．0测试不同年龄段高校女性知识分子的骨密度与身体成分，结果显示随着年龄的增加，体重、身体质量指数（BMI）、肌肉、脂肪百分比也随之增大，且这些指标存在统计学差异性；各年龄段骨强度（STI）、T值、Z值无显著性差异；骨总量（BMC）、体脂百分比、去脂体重均随BMI的增加而增大，存在统计学的差异性；骨强度、T、Z随着BMI的增加而呈现橄榄型．相关性检验还表明身高与骨强度、T、Z存在负相关，脂肪百分比与STI、T值存在负相关，无统计学上差异；体重、BMI、去脂体重、骨总量与Z值间存在显著的相关性．     

Structured information in sparse-code metric neural networks

Sparse-code networks have retrieval abilities which are strongly dependent on the firing threshold for the neurons. If the connections are spatially uniform, the macroscopic properties of the network can be measured by the overlap between neurons and learned patterns, and by the global activity. However, for nonuniform networks, for instance small-world networks, the neurons can retrieve fragments of patterns without performing global retrieval. Local overlaps are needed to describe the network. We characterize the structure type of the neural states using a parameter that is related to fluctuations of the local overlaps, with distinction between bump and block phases. Simulation of neural dynamics shows a competition between localized (bump), structured (block) and global retrieval. When the network topology randomness increases, the phase-diagram shows a transition from local to global retrieval. Furthermore, the local phase splits into a bump phase for low activity and a block phase for high activity. A theoretical approach solves the asymptotic limit of the model, and confirms the simulation results which predicts the change of stability from bumps to blocks when the storage ratio increases.     

适应创新教育的“3＋1”大学物理实验教学模式的探索与实践

分析了我校大学物理实验教学现状和民族院校学生特点,提出了针对不同层次、不同专业学生的＂3＋1＂大学物理实验教学模式,在实验教学中注重创新教育,培养学生科学实践能力和科技创新精神。     

Mathematical programming models for some smallest-world problems

Given a weighted graph G, in the minimum-cost-edge-selection problem (MCES), a minimum weighted set of edges is chosen subject to an upper bound on the diameter of graph G. Similarly, in the minimum-diameter-edge-selection problem (MDES), a set of edges is chosen to minimize the diameter subject to an upper bound on their total weight. These problems are shown to be equivalent and proven to be NP-complete. MCES is then formulated as a 0–1 integer programming problem. The problems MCES and MDES provide models for determining smallest-world networks and for measuring the “small-worldness” of graphs.     

光测力学技术：连接虚拟空间和现实世界的纽带

在轿车的整个开发过程中，零部件、总成和整车产品都必须根据试验结果验证和优化，在轿车开发的过程中测试技术是连接设计师思维空间和现实空间的纽带，现代光学测试技术以数字图象数据处理技术为基础，融汇贯通高速宽带数字采样、数据库和数据自动分析以及计算机智能工程及专家系统等最新技术，巧妙应用于轿车开发过程，在满足计算机虚拟开发工程对测试技术新要求的同时，还可以优化轿车开发程序，提高开发质量，本文以作者多年来在德国轿车开发部门主持的现代测试技术项目的实例介绍采用光测技术解决开发程序中的问题的构想，方法和手段。     

Spatial and Temporal Behaviors in a Modified Evolution Model Based on Small World Network

In this paper, we introduce a new modified evolution model on a small world network. In our model,the spatial and temporal correlations and the spatial-temporal evolve pattern of mutating nodes exhibit some particular behaviors different from those of the original BS evolution model. More importantly, these behaviors will change with φ, the density of short paths in our network.     

The impact of network structure on innovation efficiency: An agent‐based study in the context of innovation networks

This article investigates the impact of network structure on innovation efficiency by establishing a simulation model of innovation process in the context of innovation networks. The results indicate that short path lengths between vertices are conductive to high efficiency of explorative innovations, dense clusters are conductive to high efficiency of exploitative innovations, and high small‐worldness is conductive to high efficiency of the hybrid of these two innovations. Moreover, we discussed the reason of the results and give some suggestions to innovators and innovation policy makers. © 2014 Wiley Periodicals, Inc. Complexity 21: 111–122, 2015     

False vacuum decay in a brane world cosmological model

The false vacuum decay in a brane world model is studied in this work. We investigate the vacuum decay via the Coleman-de Luccia instanton, derive explicit approximative expressions for the Coleman-de Luccia instanton which is close to a Hawking-Moss instanton and compare the results with those already obtained within Einstein's theory of relativity.