Related papers: The 2005 Neyman Lecture: Dynamic Indeterminism in …
This essay provides a critical overview of the mathematical kinetic theory of active particles, which is used to model and study collective systems consisting of interacting living entities, such as those involved in behavior and evolution.…
Recently, progress has been made in the theory of turbulence, which provides a framework on how a deterministic process changes to a stochastic one owing to the change in thermodynamic states. It is well known that, in the framework of…
100 years after Smoluchowski introduces his approach to stochastic processes, they are now at the basis of mathematical and physical modeling in cellular biology: they are used for example to analyse and to extract features from large…
Scientists often think of the world (or some part of it) as a dynamical system, a stochastic process, or a generalization of such a system. Prominent examples of systems are (i) the system of planets orbiting the sun or any other classical…
Current theories from biosocial (e.g.: the role of neurotransmitters in behavioral features), ecological (e.g.: cultural, political, and institutional conditions), and interpersonal (e.g.: attachment) perspectives have grounded…
The objective of this work is the investigation of complexity, asymmetry, stochasticity and non-linearity of the financial and economic systems by using the tools of statistical mechanics and information theory. More precisely, this thesis…
Quantitative understanding of human behaviors provides elementary comprehension of the complexity of many human-initiated systems. A basic assumption embedded in the previous analyses on human dynamics is that its temporal statistics are…
The socioeconomic impact of pollution naturally comes with uncertainty due to, e.g., current new technological developments in emissions' abatement or demographic changes. On top of that, the trend of the future costs of the environmental…
Increasing pressures on the environment are generating an ever-increasing need to manage animal and plant populations sustainably, and to protect and rebuild endangered populations. Effective management requires reliable mathematical…
Stochastic resetting has been a subject of considerable interest within statistical physics, both as means of improving completion times of complex processes such as searches and as a paradigm for generating nonequilibrium stationary…
Unlike equilibrium statistical mechanics, with its well-established foundations, a similar widely-accepted framework for non-equilibrium statistical mechanics (NESM) remains elusive. Here, we review some of the many recent activities on…
The conventional economic approaches explore very little about the dynamics of the economic systems. Since such systems consist of a large number of agents interacting nonlinearly they exhibit the properties of a complex system. Therefore…
We demonstrate a comprehensive framework that accounts for citation dynamics of scientific papers and for the age distribution of references. We show that citation dynamics of scientific papers is nonlinear and this nonlinearity has…
Social dynamics is concerned primarily with interactions among individuals and the resulting group behaviors, modeling the temporal evolution of social systems via the interactions of individuals within these systems. In particular, the…
Stochastic mathematical models are essential tools for understanding and predicting complex phenomena. The purpose of this work is to study the exit times of a stochastic dynamical system-specifically, the mean exit time and the…
Some stochastic systems are particularly interesting as they exhibit critical behavior without fine-tuning of a parameter, a phenomenon called self-organized criticality. In the context of driven-dissipative steady states, one of the main…
Regression adjustments are often made to experimental data. Since randomization does not justify the models, bias is likely; nor are the usual variance calculations to be trusted. Here, we evaluate regression adjustments using Neyman's…
Nonlinear systems with model uncertainty are often described by stochastic differential equations. Some techniques from random dynamical systems are discussed. They are relevant to better understanding of solution processes of stochastic…
Stochastic dynamic models have been extensively used for the description of processes with uncertainties arising in the operations research, behavioral sciences, and many other application areas. A large class of the problems from these…
Stochastic resetting breaks detailed balance and drives the formation of nonequilibrium steady states . Here, we consider a chain of diffusive processes $x_i(t)$ that interact unilaterally: at random time intervals, the process $x_n$…