Related papers: Entropy and diffusion characterize mutation accumu…
There is sustained and widespread interest in understanding the limit, if any, to the human lifespan. Apart from its intrinsic and biological interest, changes in survival in old age have implications for the sustainability of social…
Robustness, the insensitivity of some of a biological system's functionalities to a set of distinct conditions, is intimately linked to fitness. Recent studies suggest that it may also play a vital role in enabling the evolution of species.…
Partial differential equations are ubiquitous in almost all applications of mathematics, where they provide a natural mathematical description of many phenomena involving change in physical, chemical, biological, and social processes. The…
Understanding the patterns and processes of diversification of life in the planet is a key challenge of science. The Tree of Life represents such diversification processes through the evolutionary relationships among the different taxa, and…
We consider the evolution of populations under the joint action of mutation and differential reproduction, or selection. The population is modelled as a finite-type Markov branching process in continuous time, and the associated…
In this work, with the help of fractional calculus, it is shown a time dependence of entropy more general than the well known Pesin relation is derived. Here the equiprobability postulate is not assumed, the system dynamic in the phase…
Information theory is a mathematical theory of learning with deep connections with topics as diverse as artificial intelligence, statistical physics, and biological evolution. Many primers on information theory paint a broad picture with…
Organizations generate vast amounts of interconnected content across various platforms. While language models enable sophisticated reasoning for use in business applications, retrieving and contextualizing information from organizational…
The fundamental question of how information spreads in closed quantum many-body systems is often addressed through the lens of the bipartite entanglement entropy, a quantity that describes correlations in a comprehensive (nonlocal) way.…
Biological systems reach organizational complexity that far exceeds the complexity of any known inanimate objects. Biological entities undoubtedly obey the laws of quantum physics and statistical mechanics. However, is modern physics…
Many real-world complex networks arise as a result of a competition between growth and rewiring processes. Usually the initial part of the evolution is dominated by growth while the later one rather by rewiring. The initial growth allows…
According to the second law of thermodynamics, the arrow of time points to an ever increasing entropy of the Universe. However, exactly how the entropy evolves with time and what drives the growth remain largely unknown. Here, for the first…
Probability distributions of money, income, and energy consumption per capita are studied for ensembles of economic agents. The principle of entropy maximization for partitioning of a limited resource gives exponential distributions for the…
Currently, 'time' does not play any essential role in quantum information theory. In this sense, quantum information theory is underdeveloped similarly to how quantum physics was underdeveloped before Erwin Schrodinger introduced his famous…
Many biological populations exhibit diversity in their strategy for survival and reproduction in a given environment, and microbes are an example. We explore the fate of different strategies under sustained environmental change by…
Generative diffusion models have emerged as a powerful class of models in machine learning, yet a unified theoretical understanding of their operation is still developing. This paper provides an integrated perspective on generative…
Macroevolution is considered as a problem of stochastic dynamics in a system with many competing agents. Evolutionary events (speciations and extinctions) are triggered by fitness records found by random exploration of the agents' fitness…
We examine the evolution of expression patterns and the organization of genetic information in populations of self-replicating digital organisms. Seeding the experiments with a linearly expressed ancestor, we witness the development of…
Living systems are subject to the arrow of time; from birth, they undergo complex transformations (self-organization) in a constant battle for survival, but inevitably ageing and disease trap them to death. Can ageing be understood and…
Mathematical models of infectious diseases, which are in principle analytically tractable, use two general approaches. The first approach, generally known as compartmental modeling, addresses the time evolution of disease propagation at the…