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This is an overview of various aspects of the 6-vertex model in statistical mechanics and related models.
This paper is a short introduction to orthogonal polynomials, both the general theory and some special classes. It ends with some remarks about the usage of computer algebra for this theory.
This paper introduces topological data analysis. Starting from notions of a metric space and some elementary graph theory, we take example sets of data and demonstrate some of their topological properties. We discuss simplicial complexes…
This chapter provides an overview of the different techniques and methods that exist for the analysis and visualization of dynamic networks. Basic definitions and formal notations are discussed and important references are cited. A major…
Network (as a general notion) is not a mathematical object - there is no even any definition. However, there is a lot of good rigorous mathematics for well-defined classes of networks. In sections 1-3 we give a short overview of classes of…
We review a study of the Internet traffic properties. We analyze under what conditions the reported results could be reproduced. Relations of results of passive measurements and those of modelling are also discussed. An example of the…
Some aspects and applications of $ \sigma$-models in particle and condensed matter physics are briefly reviewed.
A basic problem in the analysis of social networks is missing data. When a network model does not accurately capture all the actors or relationships in the social system under study, measures computed on the network and ultimately the final…
The development of modern information technologies permits to collect and to analyze huge amounts of statistical data in different spheres of life. The main problem is not to only to collect but to process all relevant information. The…
The approach for a network behavior description in terms of numerical time-dependant functions of the protocol parameters is suggested. This provides a basis for application of methods of mathematical and theoretical physics for information…
A brief presentation of basic definitions and notation used in permutation patterns research.
Network performance modeling is a field that predates early computer networks and the beginning of the Internet. It aims to predict the traffic performance of packet flows in a given network. Its applications range from network planning and…
This is a replacement paper. There are 6 chapters. The first two chapters are introductory. The third chapter is on extremal graph theory. The fourth chapter is about algebra in graph theory. The fifth chapter is focused on algorithms. The…
Network analysis has a crucial need for tools to compare networks and assess the significance of differences between networks. We propose a principled statistical approach to network comparison that approximates networks as probability…
We propose a method for characterizing large complex networks by introducing a new matrix structure, unique for a given network, which encodes structural information; provides useful visualization, even for very large networks; and allows…
Network topology inference is a prominent problem in Network Science. Most graph signal processing (GSP) efforts to date assume that the underlying network is known, and then analyze how the graph's algebraic and spectral characteristics…
In this chapter, concepts related to information and computation are reviewed in the context of human computation. A brief introduction to information theory and different types of computation is given. Two examples of human computation…
A brief review of the Standard Model of particle physics is presented.
Lecture-notes: introducing and discussing basic kp concepts related to bands interaction at an elementary level to beginners
Our comments are in two parts. First, we make some observations regarding the methodology in Chambers et al. [arXiv:0708.0302]. Second, we briefly describe another interesting network monitoring problem that arises in the context of…