Maximizing information exchange between complex networks
详细信息    查看全文
文摘
Science is not merely the smooth progressive interaction of hypothesis, experiment and theory, although it sometimes has that form. More realistically the scientific study of any given complex phenomenon generates a number of explanations, from a variety of perspectives, that eventually requires synthesis to achieve a deep level of insight and understanding. One such synthesis has created the field of out-of-equilibrium statistical physics as applied to the understanding of complex dynamic networks. Over the past forty years the concept of complexity has undergone a metamorphosis. Complexity was originally seen as a consequence of memory in individual particle trajectories, in full agreement with a Hamiltonian picture of microscopic dynamics and, in principle, macroscopic dynamics could be derived from the microscopic Hamiltonian picture. The main difficulty in deriving macroscopic dynamics from microscopic dynamics is the need to take into account the actions of a very large number of components. The existence of events such as abrupt jumps, considered by the conventional continuous time random walk approach to describing complexity was never perceived as conflicting with the Hamiltonian view. Herein we review many of the reasons why this traditional Hamiltonian view of complexity is unsatisfactory. We show that as a result of technological advances, which make the observation of single elementary events possible, the definition of complexity has shifted from the conventional memory concept towards the action of non-Poisson renewal events. We show that the observation of crucial processes, such as the intermittent fluorescence of blinking quantum dots as well as the brain’s response to music, as monitored by a set of electrodes attached to the scalp, has forced investigators to go beyond the traditional concept of complexity and to establish closer contact with the nascent field of complex networks. Complex networks form one of the most challenging areas of modern research overarching all of the traditional scientific disciplines. The transportation networks of planes, highways and railroads; the economic networks of global finance and stock markets; the social networks of terrorism, governments, businesses and churches; the physical networks of telephones, the Internet, earthquakes and global warming and the biological networks of gene regulation, the human body, clusters of neurons and food webs, share a number of apparently universal properties as the networks become increasingly complex. Ubiquitous aspects of such complex networks are the appearance of non-stationary and non-ergodic statistical processes and inverse power-law statistical distributions. Herein we review the traditional dynamical and phase–space methods for modeling such networks as their complexity increases and focus on the limitations of these procedures in explaining complex networks. Of course we will not be able to review the entire nascent field of network science, so we limit ourselves to a review of how certain complexity barriers have been surmounted using newly applied theoretical concepts such as aging, renewal, non-ergodic statistics and the fractional calculus. One emphasis of this review is information transport between complex networks, which requires a fundamental change in perception that we express as a transition from the familiar stochastic resonance to the new concept of complexity matching.

© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号

地址：北京市海淀区学院路29号 邮编：100083

电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700