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This chapter focuses on the mathematical modelling of active particles (or agents) in crowded environments. We discuss several microscopic models found in literature and the derivation of the respective macroscopic partial differential…
Trust evaluation is an important topic in both research and applications in sociable environments. This paper presents a model for trust evaluation between agents by the combination of direct trust, indirect trust through neighbouring links…
In human societies, people's willingness to compete and strive for better social status as well as being envious of those perceived in some way superior lead to social structures that are intrinsically hierarchical. Here we propose an…
The proliferation of ideological movements into extremist factions via social media has become a global concern. While radicalization has been studied extensively within the context of specific ideologies, our ability to accurately…
The abrupt outbreak and transmission of biological diseases has always been a long-time concern of humankind. For long, mathematical modeling has served as a simple and yet efficient tool to investigate, predict, and control spread of…
We propose a dynamical model for group formation and switching behavior in systems where each group competes for members through attraction functions that are inversely proportional to their current sizes. This attraction is modulated by…
Pedestrians are often encountered walking in the company of some social relations, rather than alone. The social groups thus formed, in variable proportions depending on the context, are not randomly organised but exhibit distinct features,…
The objective of this exploratory study was to examine the interpersonal dynamics of an afterschool math club for middle schoolers. Using social network analysis, two networks were identified and analyzed: (a) a network of friendship…
A local culture denotes a commonly shared behaviour within a cluster of firms. Similar to social norms or conventions, it is an emergent feature resulting from the firms' interaction in an economic network. To model these dynamics, we…
This paper presents a new approach to behavioral-social dynamics of pedestrian crowds by suitable development of methods of the kinetic theory. It is shown how heterogeneous individual behaviors can modify the collective dynamics, as well…
Traffic jams on roadways, echo chambers on social media, crowds of moving pedestrians, and opinion dynamics during elections are all complex social systems. These applications may seem disparate, but some of the questions that they motivate…
We present a toy model of opinion spreading in a society which combines a self-reinforcing mechanism with diffusion. The relative strength of these two mechanisms - called the affectability of the system - is a free parameter of the model.…
Confirmation bias is a cognitive bias that adversely affects management decisions, and mathematical modelling is an aid to its detailed understanding. Bias in opinion update about the value of a parameter is modelled here assuming that…
We present a strategy capable of describing basic features of the dynamics of crowds. The behaviour of the crowd is considered from a twofold perspective. We examine both the large scale behaviour of the crowd, and phenomena happening at…
We propose a compartmental model for epidemiology wherein the population is split into groups with either comply or refuse to comply with protocols designed to slow the spread of a disease. Parallel to the disease spread, we assume that…
Two prevailing theories for explaining social group or community structure are cohesion and identity. The social cohesion approach posits that social groups arise out of an aggregation of individuals that have mutual interpersonal…
In present paper we propose the consistent statistical approach which appropriate for a number of models describing both behavior of biological populations and various social groups interacting with each other.The approach proposed based on…
Under the sociological theory of homophily, people who are similar to one another are more likely to interact with one another. Marketers often have access to data on interactions among customers from which, with homophily as a guiding…
Evolution of cooperation is a widely studied problem in biology, social science, economics, and artificial intelligence. Most of the existing approaches that explain cooperation rely on some notion of direct or indirect reciprocity. These…
We provide a quantitative formulation of the equivalence between hyperlinearity and soficity for amenable groups, effectively showing how every hyperlinear approximation to such a group is simulated by a suitable sofic approximation. The…