Related papers: Phase Transitions on Fractals and Networks
Three solvable models are set out in some detail in reviewing different types of phase transitions. Two of these relate directly to emergent critical phenomena, viz. melting and magnetic transitions in heavy rare-earth metals, and secondly,…
This review was written for the Encyclopedia of Complexity and System Science (Springer-Verlag, Berlin, 2008), and is intended as a guide to the growing literature which approaches the phenomena of cell biology from a more theoretical point…
Networks and network computations have become a primary mathematical tool for analyzing the structure of many kinds of complex systems, ranging from the Internet and transportation networks to biochemical interactions and social networks. A…
The review is a survey of the present status of research in social networks highlighting the topics of small world property, degree distributions, community structure, assortativity, modelling, dynamics and searching in social networks.
This paper is written as one chapter in a collection of essays on neutrino physics for beginning graduate students. The text presents important experimental methods and issues for those interested in searches for sterile neutrinos. Other…
Percolation in complex networks is viewed as both: a process that mimics network degradation and a tool that reveals peculiarities of the underlying network structure. During the course of percolation, networks undergo non-trivial…
Percolation theory allows simple description of the phase transition based on the scaling properties of the network clusters with respect to a single parameter - site or bond occupation probability. How to design a network exhibiting the…
This is a natural generalization of the previous work by Dan, "Modeling and Simulation of Diffusion Phenomena on Social Networks," to appear in The proceedings of 2011 Third International Conference on Computer Modeling and Simulation. In…
Complex networks describe a wide range of systems in nature and society. Frequently cited examples include Internet, WWW, a network of chemicals linked by chemical reactions, social relationship networks, citation networks, etc. The…
The fractal nature of graphs has traditionally been investigated by using the nodes of networks as the basic units. Here, instead, we propose to concentrate on the graph edges, and introduce a practical and computationally not demanding…
We use a simplified model which is based on the same physics as inherent in most statistical models for nuclear multifragmentation. The simplified model allows exact calculations for thermodynamic properties of systems of large number of…
This text is a slightly edited version of lecture notes for a course I gave at ETH, during the Winter term 2000-2001, to undergraduate Mathematics and Physics students. Contents: Chapter 1 - Examples of Dynamical Systems Chapter 2 -…
The transformer is a neural network component that can be used to learn useful representations of sequences or sets of data-points. The transformer has driven recent advances in natural language processing, computer vision, and…
This chapter provides a general introduction of network modeling in psychometrics. The chapter starts with an introduction to the statistical model formulation of pairwise Markov random fields (PMRF), followed by an introduction of the PMRF…
These lecture notes give an introduction to the theory of interacting particle systems. The main subjects are the construction using generators and graphical representations, the mean field limit, stochastic order, duality, and the relation…
We present an introduction to fractal interpolation beginning with a global set-up and then extending to a local, a non-stationary, and finally the novel quaternionic setting. Emphasis is placed on the overall perspective with references…
This article was prepared in connection with the 2009 Barnett lecture at the University of Cincinnati, and deals with various classes of fractal sets and analysis on them.
A network is a typical expressive form of representing complex systems in terms of vertices and links, in which the pattern of interactions amongst components of the network is intricate. The network can be static that does not change over…
We review what is known about fracton phases of quantum matter. Fracton phases are characterized by excitations that exhibit restricted mobility, being either immobile under local Hamiltonian dynamics, or mobile only in certain directions.…
The optical model is a fundamental tool to describe scattering processes in nuclear physics. The basic input is an optical model potential, which describes the refraction and absorption processes more or less schematically. Of special…