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Nonlinearity and non-Hermiticity, for example due to environmental gain-loss processes, are a common occurrence throughout numerous areas of science and lie at the root of many remarkable phenomena. For the latter, parity-time-reflection…
The large amount of data on galaxies, up to higher and higher redshifts, asks for sophisticated statistical approaches to build adequate classifications. Multivariate cluster analyses, that compare objects for their global similarities, are…
Asymptotically entropy of chaotic systems increases linearly and the sensitivity to initial conditions is exponential with time: these two behaviors are related. Such relationship is the analogous of and under specific conditions has been…
We extend the evolution mapping approach, originally proposed by Sanchez (2022) to describe non-linear matter density fluctuations, to statistics of the cosmic velocity field. This framework classifies cosmological parameters into shape…
Despite their claimed biological plausibility, most self organizing networks have strict topological constraints and consequently they cannot take into account a wide range of external stimuli. Furthermore their evolution is conditioned by…
The report considers the dynamics of the global population as the unique case of the Socio-Economic Soft Matter system. This category was introduced for complex systems dominated by mesoscale assemblies, emerging due to the inherent…
We describe work in progress by a collaboration of astronomers and statisticians developing a suite of Bayesian data analysis tools for extrasolar planet (exoplanet) detection, planetary orbit estimation, and adaptive scheduling of…
The evolutionary process has been modelled in many ways using both stochastic and deterministic models. We develop an algebraic model of evolution in a population of asexually reproducing organisms in which we represent a stochastic walk in…
An increasing number of dissident voices claim that the standard neo-Darwinian view of genes as 'leaders' and phenotypes as 'followers' during the process of adaptive evolution should be turned on its head. This idea is older than the…
In this survey, we provide an in-depth exposition of our recent results on the well-posedness theory for stochastic evolution equations, employing maximal regularity techniques. The core of our approach is an abstract notion of critical…
Cells generally convert external nutrient resources to support metabolismand growth. Understanding the thermodynamic efficiency of this conversion is essential to determine the general characteristics of cellular growth. Using a simple…
We study the evolution of the configuration entropy for different combinations of $\Omega_{m0}$ and $\Omega_{\Lambda0}$ in the flat $\Lambda$CDM universe and find that the cosmological constant plays a decisive role in controlling the…
We are interested in modelling Darwinian evolution, resulting from the interplay of phenotypic variation and natural selection through ecological interactions. Our models are rooted in the microscopic, stochastic description of a population…
Production of energy is a foundation of life. Metabolic rate of organisms (amount of energy produced per unit time) generally increases slower than organisms' mass, which has important implications for life organization. This phenomenon,…
We develop a generally covariant description of evolutionary dynamics that operates consistently in both genotype and phenotype spaces. We show that the maximum entropy principle yields a fundamental identification between the inverse…
Biological evolution is realised through the same mechanisms of birth and death that underlie change in population density. The deep interdependence between ecology and evolution is well-established, and recent models focus on integrating…
In most data-scientific approaches, the principle of Maximum Entropy (MaxEnt) is used to a posteriori justify some parametric model which has been already chosen based on experience, prior knowledge or computational simplicity. In a…
The stochastic processes underlying the growth and stability of biological and psychological systems reveal themselves when far from equilibrium. Far from equilibrium, nonergodicity reigns. Nonergodicity implies that the average outcome for…
Search for different life-forms elsewhere is the fascinating area of research in astrophysics and astrobiology. Nearly 3500 exoplanets are discovered according to NASA exoplanet archive database. Earth Similarity Index (ESI) is defined as…
We consider a generic class of stochastic particle-based models whose state at an instant in time is described by a set of continuous degrees of freedom (e.g. positions), and the length of this set changes stochastically in time due to…