统计物理与复杂系统前沿进展

（2015年8月11日，中国科学院理论物理研究所，新楼6520会议室）

09:20—09:30开幕式

09:30—10:15李振鹏（大理大学，应用统计系，云南）

Global Opinions Bi-polarization and Local Structure Balance

在社会认同理论基础上区分出群体决策过程具体的三种社会影响，进一步赋予了Hopfield网络模型二元组间社会连带(social ties)的具体社会学内涵。基于此模型仿真研究了群体在具有自我认同、社会归属条件下的群体观点分化现象。模型仿真得到群体外生变量的干涉和负社会影响是推动群体观点极化的主要因素。特别地，仿真结果表明群体观点极化与三元组(社会学中研究的基本结构)影响模块结构平衡密切相关，从社会心理学角度解释了具有符号关系的群体宏观动态模式和微观结构变化之间的联系。

10:15—11:00管曙光（华东师范大学，理论物理研究所，上海）

The Frequency-Weighted Kuramoto Model

Kuramoto model turns out to be one of the mostsuccessful prototypes in the study of synchronization. It has many generalizedforms that have been investigated for decades. Recently, a frequency-weightedKuramoto model was proposed to study the explosive synchronization, i.e., anabrupt and irreversible phase transition in dynamical systems. In this talk, I will introduce some recent works ofECNU group on the frequency-weighted Kuramoto model, including

1）Exact solution for first-order synchronizationtransition in the frequency-weighted Kuramoto model;

2) Explosive synchronization with asymmetric frequencydistribution;

3) Landau damping effects in the synchronization ofconformist and contrarian oscillators. These results are helpful to enhance ourunderstanding of the collective behaviors in coupled oscillator systems.

References

[1] X. Hu, et al., Sci. Rep. 4, 7262 (2014).

[2] W. Zhou, et al., PRE 92, 012812 (2015).

[3] T. Qiu, et al., arXiv:1507.05383 (2015).

11:00—11:15茶歇

11:15—12:00邹勇（华东师范大学，理论物理研究所，上海）

Basin of Attraction and Explosive Synchronization

In the last several years, explosive synchronizationhas attracted much attention in the literature. In this talk, I will show theoreticallythat the basin of attraction determines the size of the hysteresis area. Morespecifically, The critical coupling associated with loss of coherence isdetermined by the existence of a locking manifold, whereas the criticalcoupling responsible for attaining coherence starting from an incoherent stateis related to a change in the basin of attraction of the locking manifold. Wehave uncovered the distinct dependence of both coupling thresholds on thenetwork size, revealing that the hysteresis is stronger in large networks.

12:00—14:00午餐及讨论

14:00—14:45周涛（电子科技大学，成都）

Degree, H-index and Coreness

Identifying influential nodes in dynamical processesis a crucial challenge in understanding network structure and function. Degree,H-index, and coreness are widely used, but previously treated as unrelated.Here we show their relation by constructing an operator H, in terms of whichdegree, H-index and coreness are the initial, intermediate and steady states ofthe sequence, respectively. We obtain a family of H-indices that can be used tomeasure a node's importance. We also prove that the convergence to coreness canbe guaranteed even under an asynchronous updating process, allowing adecentralized local method of calculating a node's coreness in large-scaleevolving networks. Extensive numerical analyses of thesusceptible-infected-removed spreading dynamics on disparate real networkssuggest that the H-index is a good tradeoff, which in many cases shows betterperformance in quantifying node influence than either degree or coreness.

14:45—15:30荣智海（电子科技大学，成都）

Zero-determinant Strategies of Game Theory

Recently, a new class of probabilistic and conditionalstrategies, called zero-determinant (ZD) strategies, attracts considerableattention to the two-player repeated prisoner’s dilemma game. A player adopting ZD strategies isable to enforce a linear relationship between his own payoff and the opponent'spayoff, in a unilateral way. Moreover, two kinds of ZD strategies, namedpinning strategy and extortion strategy, have been carefully investigated. Aplayer using the pinning strategy canindependently set his opponent's payoff. Aplayer with the extortion strategy can unilaterally ensure that his surplus is ­χ-times (χ≥1) of that of his opponent. The famous tit-for-tat strategy is a fairstrategy with χ= 1. This talk will review the recent results about ZDstrategies and their evolution in networked systems.

15:30—15:45茶歇

15:45—16:30孙怡帆（中国人民大学，统计学院，北京）

Statistical-Physical View on Network Game

In this talk, I will introduce our recent work onnetwork game from the viewpoint of statistical physics. The first example isthe network public goods game, of which the issue of equity and efficiency hasbeen investigated. The second example is the Rock-scissors-paper (RSP) onnetwork. I will demonstrate some preliminary results on the synchronous andasynchronous updating mechanism.

16:30—17:15周海军（中国科学院理论物理研究所，北京）

网络反馈节点集与支配集及其可能应用

网络的一个反馈节点集（feedback vertex set）包含网络的一部分节点，当这些节点被删除后，剩下的网络就不存在环了。而网络的一个支配集（dominating set）则包含网络的一部分节点，网络的所有其它节点都至少有一个最近邻节点属于该集合。我将介绍对这两个问题的统计物理处理方法，并讨论这两个问题在网络动力学性质研究中的可能应用。

17:15—18:00讨论与总结