RANDOM graph theory originated with seminal work by Erdös and Re nyi in the 1950s. Until then, graph theory analyzed either specific graph instances or deterministically defined graph classes. Erdös and Re nyi considered graph classes where the existence of edges between nodes was determined probabilistically. Their results were theoretically interesting and found applications in many practical...

Real-world complex systems may be mathematically modeled as graphs, revealing properties of the system. Here we study graphs of functional brain organization in healthy adults using resting state functional connectivity MRI. We propose two novel brain-wide graphs, one of 264 putative functional areas, the other a modification of voxelwise networks that eliminates potentially artificial short-di...

Rigidity theory has helped in our understanding of the properties of network glasses. We analyze the connection between rigidity and various non-random features in the network structure. Lack of small rings in the network can lead to a sharper rigidity transition. We review a model of network self-organization that we have proposed, in which the existence of an intermediate phase that is rigid,...

Although the metabolic networks of the three domains of life consist of different constituents and metabolic pathways, they exhibit the same scale-free organization. This phenomenon has been hypothetically explained by preferential attachment principle that the new-recruited metabolites attach preferentially to those that are already well connected. However, since metabolites are usually small ...

At the dawn of the 3rd millennium, the world is quite different from 25 years ago, when TDR was created. Scientifi c and technological advances, as well as economic, political, social, cultural and environmental changes, have dramatically modifi ed the global landscape. We live today in an Internet village, supported by powerful information and communication technologies. Biology has become ‘bi...

As networks and their structure have become a major field of research, a strong demand to visualize these networks has emerged. We address this challenge by formalizing the well established spring layout in terms of dynamic equations. We thus opening up the design space for new algorithms. Drawing from the knowledge of systems design, we derive a layout algorithm that remedies several drawbacks...

Ghosh, A., and S.K. Pal, Neural network, self-organization and object extraction, Paitern Recognition Letters l3 (1992) 387-397. Algorithms for object extraction nsing a nenral network are proposed. A single nenron (processor) is assigned here to every pixel for its operalion in order to implement {he concept of self-organized fealnre mapping. Both global and local information have been used as...

It is pointed out that the entropies of structure, information and the effectiveness entropy between knowledge and organization structure are main entropy sources of supply chain network in this paper. Firstly, establish entropy model of fractal supply chain network organization structure. Secondly, fractal knowledge management network outside independently organization structure is set up. Mor...