Related papers: Coalgebraic analysis of social systems
This research addresses a new tool for data analysis known as Topological Data Analysis TDA It underlies an area of Mathematics known as Combinatorial Algebra or more recently Algebraic Topology which through making strong use of…
The spatial metaphor of the network along with its accompanying abstractions, such as flow, movement, and connectivity, have been central themes throughout the relational turn in human geography. However, to date networks in geography have…
Hypergraphs offer a natural modeling language for studying polyadic interactions between sets of entities. Many polyadic interactions are asymmetric, with nodes playing distinctive roles. In an academic collaboration network, for example,…
Polygraphs are a higher-dimensional generalization of the notion of directed graph. Based on those as unifying concept, this monograph on polygraphs revisits the theory of rewriting in the context of strict higher categories, adopting the…
In this paper we present a proof system that operates on graphs instead of formulas. Starting from the well-known relationship between formulas and cographs, we drop the cograph-conditions and look at arbitrary undirected) graphs. This…
Algebraic characterizations of the computational aspects of functions defined over the real numbers provide very effective tool to understand what computability and complexity over the reals, and generally over continuous spaces, mean. This…
The mathematical formalisms used to model biological systems induce both latent and ambiguous assumptions that can limit or distort their representational capabilities. Developing formalisms that can represent systems more precisely is…
Graphs are widely used as a popular representation of the network structure of connected data. Graph data can be found in a broad spectrum of application domains such as social systems, ecosystems, biological networks, knowledge graphs, and…
The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of…
There has been a great deal of attention recently to graphs whose vertex set is a group, defined using the group structure. (The commuting graph, where two elements are joined if they commute, is the oldest and most famous example.) The…
Social hierarchy (i.e., pyramid structure of societies) is a fundamental concept in sociology and social network analysis. The importance of social hierarchy in a social network is that the topological structure of the social hierarchy is…
Traditional graph analysis focuses on nodes and edges, that is, pairwise relationships. Yet many real-world networks, including biological, social, and communication networks, involve higher-order relationships in which multiple nodes…
Community detection is a fundamental problem in social network analysis consisting in unsupervised dividing social actors (nodes in a social graph) with certain social connections (edges in a social graph) into densely knitted and highly…
Social networks existing among employees, customers or users of various IT systems have become one of the research areas of growing importance. A social network consists of nodes - social entities and edges linking pairs of nodes. In…
Modeling relation between actors is important for recognizing group activity in a multi-person scene. This paper aims at learning discriminative relation between actors efficiently using deep models. To this end, we propose to build a…
From social to biological systems, many real-world systems are characterized by higher-order, non-dyadic interactions. Such systems are conveniently described by hypergraphs, where hyperedges encode interactions among an arbitrary number of…
Topology identification and inference of processes evolving over graphs arise in timely applications involving brain, transportation, financial, power, as well as social and information networks. This chapter provides an overview of graph…
Multi-agent models are a suitable starting point to model complex social interactions. However, as the complexity of the systems increase, we argue that novel modeling approaches are needed that can deal with inter-dependencies at different…
Techniques from higher categories and higher-dimensional rewriting are becoming increasingly important for understanding the finer, computational properties of higher algebraic theories that arise, among other fields, in quantum…
Sampling algorithms, hypergraph degree sequences, and polytopes play a crucial role in statistical analysis of network data. This article offers a brief overview of open problems in this area of discrete mathematics from the point of view…