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Normal and anomalous diffusion are ubiquitous in many complex systems [1] . Here, we define a time and space generalized diffusion equation (GDE), which uses fractional-time derivatives and transformed d-path Laplacian operators on…
We consider a Moran-type model of cultural evolution, which describes how traits emerge, are transmitted, and get lost in populations. Our analysis focuses on the underlying cultural genealogies; they were first described by Aguilar and…
The number of people able to end Earth's technical civilization has heretofore been small. Emerging dual-use technologies, such as biotechnology, may give similar power to thousands or millions of individuals. To quantitatively investigate…
We apply the theory of learning to physically renormalizable systems in an attempt to develop a theory of biological evolution, including the origin of life, as multilevel learning. We formulate seven fundamental principles of evolution…
The aim of this paper is two-fold. First, we propose a new computational method to investigate the particularities of evolution. Second, we apply this method to a model of gene regulatory networks (GRNs) and explore the evolution of…
Recent cosmological observations show hints for possible deviations from the standard $\Lambda$CDM paradigm at late times. To study such deviation, we introduce a minimal phenomenological framework in which the total equation of state of…
The recent interest in human dynamics has led researchers to investigate the stochastic processes that explain human behaviour in various contexts. Here we propose a generative model to capture the dynamics of survival analysis,…
We are interested in modeling Darwinian evolution resulting from the interplay of phenotypic variation and natural selection through ecological interactions. The population is modeled as a stochastic point process whose generator captures…
Biological entities are inherently dynamic. As such, various ecological disciplines use mathematical models to describe temporal evolution. Typically, growth curves are modelled as sigmoids, with the evolution modelled by ordinary…
This brief discusses evolutionary game theory as a powerful and unified mathematical tool to study evolution of collective behaviours. It summarises some of my recent research directions using evolutionary game theory methods, which include…
These lectures contain a brief description of evolutionary models inspired by the statistical mechanics of disordered systems. After an introduction describing the Darwinian paradigm of evolving populations, the deterministic quasispecies…
The dynamics of molecular collisions in a macroscopic body are encoded by the parameter Thermodynamic entropy - a statistical measure of the number of molecular configurations that correspond to a given macrostate. Directionality in the…
Evolution in finite populations is often modelled using the classical Moran process. Over the last ten years this methodology has been extended to structured populations using evolutionary graph theory. An important question in any such…
Natural selection explains how life has evolved over millions of years from more primitive forms. The speed at which this happens, however, has sometimes defied formal explanations when based on random (uniformly distributed) mutations.…
Evolutionary computing (EC) is an exciting development in Computer Science. It amounts to building, applying and studying algorithms based on the Darwinian principles of natural selection. In this paper we briefly introduce the main…
Exponentiated gradient descent (EGD), a biologically motivated optimisation algorithm that respects Dale's law, produces log-normally distributed synaptic weights at convergence, in alignment with experimental observations in neuroscience.…
Inspired by biological evolution, we explain the rationality of Vision Transformer by analogy with the proven practical Evolutionary Algorithm (EA) and derive that both of them have consistent mathematical representation. Analogous to the…
Nowadays, sustained development of different social media can be observed worldwide. One of the relevant research domains intensively explored recently is analysis of social communities existing in social media as well as prediction of…
The dynamics of adaptation is difficult to predict because it is highly stochastic even in large populations. The uncertainty emerges from number fluctuations, called genetic drift, arising in the small number of particularly fit…
We provide a review on semi-empirical models of galaxy formation and evolution. We present a brief census of the three main modeling approaches to galaxy evolution, namely hydrodynamical simulations, semi-analytic models, and semi-empirical…