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The article is devoted to a structure of topological spaces related with topological quasigroups. Regular and complete spaces over topological quasigroups are studied. Separations and embeddings are also investigated for them. Their…
The discovery of small world and scale free properties of many real world networks has revolutionized the way we study, analyze, model and process networks. An important way to analyze these complex networks is to visualize them using graph…
The aim of this chapter is twofold. In the first part we will provide a brief overview of the mathematical and statistical foundations of graphical models, along with their fundamental properties, estimation and basic inference procedures.…
Topological metrics of graphs provide a natural way to describe the prominent features of various types of networks. Graph metrics describe the structure and interplay of graph edges and have found applications in many scientific fields. In…
As an alternative view to the graph formation models in the statistical physics community, we introduce graph formation models using \textit{network formation} through selfish competition as an approach to modeling graphs with particular…
Group theory involves the study of symmetry, and its inherent beauty gives it the potential to be one of the most accessible and enjoyable areas of mathematics, for students and non-mathematicians alike. Unfortunately, many students never…
We exploit the theory of $\infty$-stacks to provide some basic definitions and calculational tools regarding stratified homotopy theory of stratified topological stacks.
Graphs are nowadays ubiquitous in the fields of signal processing and machine learning. As a tool used to express relationships between objects, graphs can be deployed to various ends: I) clustering of vertices, II) semi-supervised…
We study properties of Cartesian products of digital images, using a variety of adjacencies that have appeared in the literature.
We introduce a new class of network allocation games called graphical distance preservation games. Here, we are given a graph, called a topology, and a set of agents that need to be allocated to its vertices. Moreover, every agent has an…
In 20th century mathematics, the field of topology, which concerns the properties of geometric objects under continuous transformation, has proved surprisingly useful in application to the study of discrete mathematics, such as…
The theory of pictures between posets is known to encode much of the combinatorics of symmetric group representations and related topics such as Young diagrams and tableaux. Many reasons, com-binatorial (e.g. since semi-standard tableaux…
Games can be a powerful tool for learning about statistical methodology. Effective game design involves a fine balance between caricature and realism, to simultaneously illustrate salient concepts in a controlled setting and serve as a…
Expander graphs have been, during the last five decades, the subject of a most fruitful interaction between pure mathematics and computer science, with influence and applications going both ways (cf. [Lub94], [HLW06], [Lub12] and the…
In this paper, we view the Internet under a game-theoretic lens in an effort to explain and overcome the Internet's innovation slump. Game Theory is used to model Internet environments as problems of technological competition toward the end…
In recent years, studies in different areas have used gamification to improve users' flow experience. However, due to the high variety of the conducted studies and the lack of secondary studies (e.g., systematic literature reviews) in this…
The information technology explosion has dramatically increased the application of new mathematical ideas and has led to an increasing use of mathematics across a wide range of fields that have been traditionally labeled "pure" or…
The article is devoted to mathematical methods of experimental detection of interactive phenomena in complex systems and their analysis.
Immersions of graphs to the projective plane are studied. A classification of immersions up to regular homotopy is given. A complete invariant of immersions up to regular homotopy is constructed. Equivalence classes are described.
These notes are an introduction to higher dimensional local fields and higher dimensional adeles. As well as the foundational theory, we summarise the theory of topologies on higher dimensional local fields and higher dimensional local…