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A mathematical model for behavioral changes by pair interactions (i.e. due to direct contact) of individuals is developed. Three kinds of pair interactions can be distinguished: Imitative processes, avoidance processes, and compromising…
People sometimes change their opinions when they discuss things with other people. Researchers can use mathematics to study opinion changes in simplifications of real-life situations. These simplified settings, which are examples of…
Random walks and related spatial stochastic models have been used in a range of application areas including animal and plant ecology, infectious disease epidemiology, developmental biology, wound healing, and oncology. Classical random walk…
We study the problem of reconstructing the probability measure of the Curie-Weiss model from a sample of the voting behaviour of a subset of the population. While originally used to study phase transitions in statistical mechanics, the…
In shared space environments, urban space is shared among different types of road users, who frequently interact with each other to negotiate priority and coordinate their trajectories. Instead of traffic rules, interactions among them are…
One widely-existed state --``harmony with diversity" in which individuals freely express various viewpoints to sustain integration of social diversity, but at the same time shared values ensure social coherence, can be considered as the…
A recently proposed model of social interaction in voting is investigated by simplifying it down into a version that is more analytically tractable and which allows a mathematical analysis to be performed. This analysis clarifies the…
Basic principles of statistical inference are commonly violated in network data analysis. Under the current approach, it is often impossible to identify a model that accommodates known empirical behaviors, possesses crucial inferential…
This paper presents a randomization-based framework for estimating causal effects under interference between units, motivated by challenges that arise in analyzing experiments on social networks. The framework integrates three components:…
A broad set of empirical phenomenon in the study of social, economic and machine behaviour can be modelled as complex systems with averaging dynamics. However many of these models naturally result in consensus or consensus-like outcomes. In…
The internal behaviour of a population is an important feature to take account of when modelling their dynamics. In line with kin selection theory, many social species tend to cluster into distinct groups in order to enhance their overall…
This paper studies a recently proposed continuous-time distributed self-appraisal model with time-varying interactions among a network of $n$ individuals which are characterized by a sequence of time-varying relative interaction matrices.…
A biological pathway represents a set of genes that serves a particular cellular or a physiological function. The genes within the same pathway are expected to function together and hence may interact with each other. It is also known that…
A model, applicable to a range of innovation diffusion applications with a strong peer to peer component, is developed and studied, along with methods for its investigation and analysis. A particular application is to individual households…
Addressing global challenges often involves stimulating the large-scale adoption of new products or behaviors. Research traditions that focus on individual decision making suggest that achieving this objective requires identifying the…
Many models in mathematical epidemiology are developed with the aim to provide a framework for parameter estimation and then prediction. It is well-known that parameters are not always uniquely identifiable. In this paper we consider…
We propose a method of estimating the linear-in-means model of peer effects in which the peer group, defined by a social network, is endogenous in the outcome equation for peer effects. Endogeneity is due to unobservable individual…
This paper investigates social interactions in endogenous groups. We specify a two-sided many-to-one matching model, where individuals select groups based on preferences, while groups admit individuals based on qualifications until reaching…
Understanding the movement behaviours of individuals and the way they react to the external world is a key component of any problem that involves the modelling of human dynamics at a physical level. In particular, it is crucial to capture…
This study introduces a new numerical model to simulate how information is comprehended and processed on social networks, using continuous "Phase Field Modeling" variables (phiA, phiB, phiC) to represent individual users' opinions. It…