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Existing theoretical models of evolution focus on the relative fitness advantages of different mutants in a population while the dynamic behavior of the population size is mostly left unconsidered. We here present a generic stochastic model…
We propose and study a stochastic binary opinion model where agents in a group are considered to hold an opinion of 0 or 1 at each moment. An agent in the group updates his/her opinion based on the group's opinion configuration and his/her…
In this paper, a first sample-based formulation of the recently considered population observers, or ensemble observers, which estimate the state distribution of dynamic populations from measurements of the output distribution is…
Coevolutionary dynamics is investigated in chemical catalysis, biological evolution, social and economic systems. The dynamics of these systems can be analyzed within the unifying framework of evolutionary game theory. In this Letter, we…
In this paper, we consider stochastic versions of three classical growth models given by ordinary differential equations (ODEs). Indeed we use stochastic versions of Von Bertalanffy, Gompertz, and Logistic differential equations as models.…
Stochastic diffusion is the noisy and uncertain process through which dynamics like epidemics, or agents like animal species, disperse over a larger area. Understanding these processes is becoming increasingly important as we attempt to…
A general maximum principle is proved for optimal controls of abstract semilinear stochastic evolution equations. The control variable, as well as linear unbounded operators, acts in both drift and diffusion terms, and the control set need…
We consider particles that are conditioned to initial and final states. The trajectory of these particles is uniquely shaped by the intricate interplay of internal and external sources of randomness. The internal randomness is aptly…
Social consensus is important for society. Sometimes the success of society depends on a consensus (e.g. the decision to pay taxes or to commit to the constitution). Examples for continuous opinion dynamics are discussions about tax rates…
The model of a non-Bayesian agent who faces a repeated game with incomplete information against Nature is an appropriate tool for modeling general agent-environment interactions. In such a model the environment state (controlled by Nature)…
Global strategies to contain a pandemic, such as social distancing and protective measures, are designed to reduce the overall transmission rate between individuals. Despite such measures, essential institutions, including hospitals,…
This paper presents a new approach to behavioral-social dynamics of human crowds. First order models are derived based on mass conservation at the macroscopic scale, while methods of the kinetic theory are used to model the decisional…
Multi-stage stochastic optimization is a well-known quantitative tool for decision-making under uncertainty. It is broadly used in financial and investment planning, inventory control, and also natural disaster risk management. Theoretical…
Scaling limits are analyzed for stochastic continuous opinion dynamics systems, also known as gossip models. In such models, agents update their vector-valued opinion to a convex combination (possibly agent- and opinion-dependent) of their…
In this paper, we reconsider the spin model suggested recently to understand some features of collective decision making among higher organisms [A.T. Hartnett et al., Phys. Rev. Lett. 116 (2016) 038701]. Within the model, the state of an…
The growth of a population divided among spatial sites, with migration between the sites, is sometimes modelled by a product of random matrices, with each diagonal elements representing the growth rate in a given time period, and…
Any organism is embedded in an environment that changes over time. The timescale for and statistics of environmental change, the precision with which the organism can detect its environment, and the costs and benefits of particular protein…
We consider a stochastic control problem where the set of strict (classical) controls is not necessarily convex and the the variable control has two components, the first being absolutely continuous and the second singular. The system is…
We consider a susceptible-infected-susceptible (SIS) epidemic model in which a large group of individuals decide whether to adopt partially effective protection without being aware of their individual infection status. Each individual…
We study the voting game where agents' preferences are endogenously decided by the information they receive, and they can collaborate in a group. We show that strategic voting behaviors have a positive impact on leading to the ``correct''…