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Natural ecosystems are characterized by striking diversity of form and functions and yet exhibit deep symmetries emerging across scales of space, time and organizational complexity. Species-area relationships and species-abundance…
Usually, opinion formation models assume that individuals have an opinion about a given topic which can change due to interactions with others. However, individuals can have different opinions in different topics and therefore n-dimensional…
The dynamics of casual group formation has long been a subject of interest in social sciences. While early stochastic models offered foundational insights into group size distributions, they often simplified individual behaviors and lacked…
A person's decision to adopt an idea or product is often driven by the decisions of peers, mediated through a network of social ties. A common way of modeling adoption dynamics is to use threshold models, where a node may become an adopter…
Inter-city interactions are critical for the transmission of infectious diseases, yet their effects on the scaling of disease cases remain largely underexplored. Here, we use the commuting network as a proxy for inter-city interactions,…
In the environmental modeling field, the exploratory analysis of responses often exhibits spatial correlation as well as some non-Gaussian attributes such as skewness and/or heavy-tailedness. Consequently, we propose a general spatial model…
We consider a discrete-time model for random interface growth which admits exact formulas and converges to the Polynuclear growth model in a particular limit. The height of the interface is initially flat and the evolution involves the…
We extensively study the evolution and distinct signatures of cosmological models, in which dark energy interacts directly with dark matter. We first focus on the imprints of these coupled models on the cosmic microwave background…
Despite growing interest in probabilistic modeling approaches and availability of learning tools, people with no or less statistical background feel hesitant to use them. There is need for tools for communicating probabilistic models to…
Reactions in solution require "contact" between the reagents. We can predict the rate at which reagents come into "contact" (at least in dilute conditions), but if the initial collision does not lead to reaction, what happens then? The…
Species interactions (ranging from direct predator prey relationships to indirect effects mediated by the environment) are central to ecosystem balance and biodiversity. While empirical methods for measuring these interactions exist, their…
An extension of coupled maps is given which allows for the growth of the number of elements, and is inspired by the cell differentiation problem. The growth of elements is made possible first by clustering the phases, and then by…
Existing models of network growth typically have one or two parameters or strategies which are fixed for all times. We introduce a general framework where feedback on the current state of a network is used to dynamically alter the values of…
We study the dynamics of individual agents in some kinetic models of wealth exchange, particularly, the models with savings. For the model with uniform savings, agents perform simple random walks in the "wealth space". On the other hand, we…
We have studied the island size distribution and spatial correlation function of an island growth model under the effect of an elastic interaction of the form $1/r^{3}$. The mass distribution $P_n(t)$ that was obtained presents a pronounced…
Networks of person-person contacts form the substrate along which infectious diseases spread. Most network-based studies of the spread focus on the impact of variations in degree (the number of contacts an individual has). However, other…
Publicly traded companies are fundamental units of contemporary economies and markets and are important mechanisms through which humans interact with their environments. Understanding the general properties that underlie the processes of…
Typically, the plastic yield stress of a sample is determined from a stress-strain curve by defining a yield strain and reading off the stress required to attain it. However, it is not a priori clear that yield strengths of microscale…
A version of the Schelling model on $\mathbb{Z}$ is defined, where two types of agents are allocated on the sites. An agent prefers to be surrounded by other agents of its own type, and may choose to move if this is not the case. It then…
We investigate the dynamics following a global parameter quench for two 1D models with variable-range power-law interactions: a long-range transverse Ising model, which has recently been realised in chains of trapped ions, and a long-range…