一门新兴的交叉学科--经济物理

从上世纪90年代后期，美国科学家H．Stanley等人第一次使用“经济物理”(Econophysics国内有些论文与著作将其译为“金融物理”)这个名词以来，这个领域吸引了许多物理学家与数学家的关心，并召开了多次有关这方面的学术会议．“经济物理”顾名思义就是用物理学中的概念、方法和理论来定量地研究经济领域中，特别是金融市场内存在的复杂关系，并希望能从中寻找出某些内在的规律．面对这样一个新的研究领域，必然会有一些最基本的问题摆在人们的面前．一个问题是复杂的金融市场有什么特点，为什么可以用研究自然现象的物理工具来研究它?     

网络"建筑学"

复杂网络系统普遍地存在于自然界与人类社会中，对它们的研究也具有广泛而重要的意义．我们如何来认识和区分晶格、Internet和一个生态食物链?它们又是如何演化的?在这些网络背后，是否隐藏着某种无形的组织原理?近年来，借助强大的计算工具，人们对网络的认识发生了巨大的改变，文章以小世界、集团化和无标度等新的概念为中心，介绍了其中的研究进展．     

复杂网络思想方法在大学物理教学中的应用

复杂网络是近年来复杂性研究的热点领域,与物理学的发展有密切的联系.让学生了解该领域的基本概念、方法及其与物理之间的关系大有裨益.本文对复杂网络中的一些基本概念和思想进行了简要介绍,并利用复杂网络的基本概念和思想对物理教学中两个较复杂的典型问题进行了分析.     

《对玻恩及其学派的系列研究》连载③——玻恩的大学求学生涯

20世纪伟大的理论物理学家马克斯·玻恩,直到开始准备做博士论文时还没想过成为一位物理学家.那么他在几年的大学学习期间,都学习了什么?他最初的理想是什么?什么促使他最终转向学习和研究物理学?在玻恩的整个大学学习成长过程中,有什么对于今天的老师和学生有一定的启发意义?本文将详细解答这些问题.     

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。     

动态复杂网络中节点影响力的研究进展

节点影响力的识别和预测具有重要的理论意义和应用价值,是复杂网络的热点研究领域.目前大多数研究方法都是针对静态网络或动态网络某一时刻的快照进行的,然而在实际应用场景中,社会、生物、信息、技术等复杂网络都是动态演化的.因此在动态复杂网络中评估节点影响力以及预测节点未来影响力,特别是在网络结构变化之前的预测更具意义.本文系统地总结了动态复杂网络中节点影响力算法面临的三类挑战,即在增长网络中,节点影响力算法的计算复杂性和时间偏见;网络实时动态演化时,节点影响力算法的适应性;网络结构微扰或突变时,节点影响力算法的鲁棒性,以及利用网络结构演变阐释经济复杂性涌现的问题.最后总结了这一研究方向几个待解决的问题并指出未来可能的发展方向.     

如何使一本书能成为畅销书？

一本书藉的畅销究竟是聪明商人在促销呢，还是它真正是一本具有社会价值的书藉?它的销售额会迅速地下降呢，还是会是一本影响几代人的经典著作?这些问题好像不是自然科学领域应该研究的课题．但物理学家们却能利用统计物理的方法对这个现象提供真知灼见．它能预言将要发生的事件的几率有多大．就像在大地震后能确定随后将会有多少次余震，或者在沙滩上堆沙子时，会有多少次将会坍塌一样。     

复杂网络可控性研究现状综述

控制复杂系统是人们对复杂系统模型结构及相关动力学进行研究的最终目标, 反映人们对复杂系统的认识能力. 近年来, 通过控制理论和复杂性科学相结合,复杂网络可控性的研究引起了人们的广泛关注. 在过去的几年内, 来自国内外不同领域的研究人员从不同的角度对复杂网络可控性进行了深入的分析研究, 取得了丰硕的成果. 本文重点讨论了复杂网络的结构可控性研究进展, 详细介绍了基于最大匹配方法的复杂网络结构可控性分析框架, 综述了自2011年以来复杂网络可控性的相关研究成果, 具体论述了不同类型的可控性、可控性与网络拓扑结构统计特征的关联、基于可控性的网络及节点度量、控制的鲁棒性和可控性的相关优化方法. 最后, 对网络可控性未来的研究动态进行了展望, 有助于国内同行开展网络可控性的相关研究.     

复杂网络上动力系统同步的研究进展

本文简要介绍复杂网络的基本概念并详细总结了近年来复杂网络上动力学系统的同步的研究进展，主要内容有复杂网络同步的稳定性分析，复杂网络上动力学系统同步的特点，网络的几何特征量对同步稳定性的影响，以及提高网络同步能力的方法等。最后文章提出了这一领域的几个有待解决的问题及可能的发展方向。     

T形网络与П形网络的等效变换法

电阻的T形网络与П形网络间的等效变换是电路计算中经常遇到的问题．一般教材都根据等效的概念采用基尔霍夫定律得到转换公式，过程复杂，不利于学生的理解和掌握．这里介绍一种更为简便易懂的推导方法．     

The Transformation of Physics from 1900 to 1945

Historians of science have analyzed in detail the conceptual transformations that gave physics its modern character in the first half of the twentieth century. Rarely provided in these narratives, however, is a feeling for the global scene of the physics community. How many publishing physicists were there around 1900? How many in 1925 or 1939? Did most physicists publish as single authors or in teams, and how did they compare with chemists or mathematicians in terms of scientific collaborations? What are the links between these disciplines? I propose to undertake such a global analysis of the trends that can be captured through a bibliometric analysis of hundreds of thousands of scientific papers and the more than one million references in them.     

Neural networks: A biased overview

An overview of recent activity in the field of neural networks is presented. The long-range aim of this research is to understand how the brain works. First some of the problems are stated and terminology defined; then an attempt is made to explain why physicists are drawn to the field, and their main potential contribution. In particular, in recent years some interesting models have been introduced by physicists. A small subset of these models is described, with particular emphasis on those that are analytically soluble. Finally a brief review of the history and recent developments of single- and multilayer perceptrons is given, bringing the situation up to date regarding the central immediate problem of the field: search for a learning algorithm that has an associated convergence theorem.     

Synchronization in simple network motifs with negligible correlation and mutual information measures

Can different or even identical coupled oscillators be completely uncorrelated and still be synchronized? What can be concluded from the absence of correlations or even mutual information in networks of dynamical elements about their connectivity? These are fundamental and far-reaching questions arising in many complex systems. In this Letter, we address these two questions and demonstrate in simple and generic network motifs that synchronized behavior in the generalized sense can be realized and constructed such that no correlations and even negligible mutual information remain. Our findings raise new questions, in particular, whether and to what extent indirect connections are being underestimated, since the related collective behavior and even synchronization are less likely to be detected.     

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—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。     

The politics of physicists' social models

I give an overview of the topic of this dossier, the “applications of (statistical) physics to social sciences at large.” I discuss several examples of simple social models put forward by physicists and examine their interest. I argue that while they may be conceptually useful to correct our intuitive models of social mechanisms, their relevance for real social systems is moot. What is more, since physicists have always needed to ‘tame’ the world inside laboratories to make their models relevant, I suggest that social modeling might be linked to human taming, a smashing political project.     

Recommender systems

The 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 and computer scientists, physicists, and interdisciplinary researchers. Despite substantial theoretical and practical achievements, unification and comparison of different approaches are lacking, which impedes further advances. In this article, we review recent developments in recommender systems and discuss the major challenges. We compare and evaluate available algorithms and examine their roles in the future developments. In addition to algorithms, physical aspects are described to illustrate macroscopic behavior of recommender systems. Potential impacts and future directions are discussed. We emphasize that recommendation has great scientific depth and combines diverse research fields which makes it interesting for physicists as well as interdisciplinary researchers.     

Hyperbolic regularizations of conservation laws

One of the problems of the kinetics of nonequilibrium processes is related to the lack of information concerning most of the nonequilibrium variables, namely, those which have no intuitive physical meaning, i.e., cannot be defined from the experiment. Moreover, the number of nonequilibrium variables is so large that a reasonable amount (from the physical point of view) of boundary conditions is insufficient for posing the mixed problem. What do the initial data for the Cauchy problem and the boundary conditions for the mixed problem mean in this case? In fact, we must assume that the initial-boundary data for most of the nonequilibrium variables (the higher-order momenta) are arbitrary! The British physicists Chapman and Enskog conjectured that, for “physically correct” models of continuum mechanics, the influence of the higher-order momenta is “inessential.” There are some postulates of physical correctness, but we do not dwell on them. For us it is of importance to understand what the fact that the influence of the higher-order momenta is “inessential” means from the mathematical point of view. The paper is devoted to this very topic.     

A Survey of Information Entropy Metrics for Complex Networks

Information entropy metrics have been applied to a wide range of problems that were abstracted as complex networks. This growing body of research is scattered in multiple disciplines, which makes it difficult to identify available metrics and understand the context in which they are applicable. In this work, a narrative literature review of information entropy metrics for complex networks is conducted following the PRISMA guidelines. Existing entropy metrics are classified according to three different criteria: whether the metric provides a property of the graph or a graph component (such as the nodes), the chosen probability distribution, and the types of complex networks to which the metrics are applicable. Consequently, this work identifies the areas in need for further development aiming to guide future research efforts.