摘要:

Networks with complex topology describe systems as diverse as the cell or the World Wide Web. The emergence of these networks is driven by self‐organizing processes that are governed by simple but generic laws. In the last three years it became clear that many complex networks, such as the Internet, the cell, or the world wide web, share the same large‐scale topology. Here we review recent advances in the characterization of complex networks, focusing the emergence of the scale‐free and the hierarchical architecture. We also present empirical results to demonstrate that the scale‐free and the hierarchical property are shared by a wide range of complex networks. Finally, we discuss the impact of the network topology on our ability to stop the spread of viruses in complex networks. © 2003 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1571285

出版商:AIP    

年代:1903

数据来源: AIP

摘要:

We present here an introduction to the ideas and models that physicist developed in order to describe the graph or network structure in a variety of different systems. Firstly we give a very basic list of definition that can be of some help in approaching this field. After that we present a brief review of the state of art for the models. © 2003 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1571286

出版商:AIP    

年代:1903

数据来源: AIP

ISSN:0094-243X    

DOI:10.1063/1.1571287

出版商:AIP    

年代:1903

数据来源: AIP

摘要:

In the quest of quantitatively understanding risk‐regulatory behavior of financial agents we propose a physical model of interacting agents where interactions are defined by trades of financial derivatives. Consequences arising from various types of interaction‐network topologies are shown for system safety and efficiency. We demonstrate that the model yields characteristic features of actually observed wealth timeseries. Further we study the dependence of global system safety as a function of a risk‐control parameter (Basle multiplier). We find a phase transition‐like phenomenon, where the Basle parameter plays the role of temperature and safety serves as the order parameter. This work is done together with R. Hanel and S. Pichler. © 2003 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1571288

出版商:AIP    

年代:1903

数据来源: AIP

摘要:

Recent research on complex networks has had a great development thanks to a great abundance of data. Here we address the problem of whether the methods used to obtain these data can influence the data themselves and, as a consequence, the topology of the observed networks. © 2003 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1571289

出版商:AIP    

年代:1903

数据来源: AIP

摘要:

The incipient infinite cluster appearing at the bond percolation threshold can be decomposed into singly‐connected “links” and multiply‐connected “blobs.” Here we decompose blobs into objects known in graph theory as 3‐blocks. A 3‐block is a graph that cannot be separated into disconnected subgraphs by cutting the graph at 2 or fewer vertices. Clusters, blobs, and 3‐blocks are special cases ofk‐blocks withk= 1, 2, and 3, respectively. We study bond percolation clusters at the percolation threshold on 2‐dimensional square lattices and 3‐dimensional cubic lattices and, using Monte‐Carlo simulations, determine the distribution of the sizes of the 3‐blocks into which the blobs are decomposed. We find that the 3‐blocks have fractal dimensiond3= 1.2 ± 0.1 in 2D and 1.15 ± 0.1 in 3D. These fractal dimensions are significantly smaller than the fractal dimensions of the blobs, making possible more efficient calculation of percolation properties. © 2003 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1571290

出版商:AIP    

年代:1903

数据来源: AIP

摘要:

Networks are constructed from gene expression data using a procedure that uses the maximum number of neighborsKof a vertex as a single tunable parameter. In some range of the parameter, the degree distribution of the networks shows scale‐free behavior with an exponent of unity in the tails. The cumulative degree distributions for all the values ofKin this range collapse together very well showing good scaling when plotted against normalized degree. Implication of this finding in understanding the biological process, especially, the origin of carcinomas, are discussed. Specifically, the present observation confirms the “biologically expected/known” result that various carcinomas are a consequence of malfunction of (a few) genes that either regulate the expression of large number of genes or form the hubs of the genetic regulatory pathways. © 2003 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1571291

出版商:AIP    

年代:1903

数据来源: AIP

摘要:

Recently reaction‐diffusion type of models were introduced that involve particle (or pair) production and annihilation at pairs, while lonely particles follow annihilating random walks, hence they may be described by a system with a coupled diffusive field. Different numerical studies have found that this kind of models in 1d exhibit continuous phase transitions to absorbing states with new type of universal behavior for which neither bosonic field theoretical treatment nor arguments based on symmetries provided full understanding. Site restricted (fermionic) and unrestricted (bosonic) versions of these models exhibit different critical behaviors. In 2d large scale simulations (using grid network) show that mean‐field type of behavior (with logarithmic corrections) emerges. In 1d it is debated whether the critical behavior changes by varying the diffusion rate or not. I show some recent simulation results in one and two dimensions that clarifies the situation to some extent. I give an outlook to generalizations of these models. © 2003 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1571292

出版商:AIP    

年代:1903

数据来源: AIP

ISSN:0094-243X    

DOI:10.1063/1.1571293

出版商:AIP    

年代:1903

数据来源: AIP

摘要:

The lattice dynamics of the reactionA + A → A + Sis treated using a Boolean model inspired by a Monte Carlo algorithm. In the diffusionless case, we solve the relevant set of moment equations and show that the coverage &thgr; inAparticles decays exponentially to an initial‐condition‐dependent steady state. The same moment equations are recovered in the framework of a Master equation approach. Diffusion drives the system into the empty state predicted by the classical mean field law, but an anomalous slowing down is observed due to reaction‐induced transient fluctuations. © 2003 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1571294

出版商:AIP    

年代:1903

数据来源: AIP