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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…
Evidence for exocomets, icy bodies in extrasolar planetary systems, has rapidly increased over the past decade. Volatiles are detected through the gas that exocomets release as they collide and grind down within their natal belts, or as…
A birth-death-move process with mutations is a Markov model for a system of marked particles in interaction, that move over time, with births and deaths. In addition the mark of each particle may also change, which constitutes a mutation.…
We demonstrate that there exists a class of cyclic cosmological models, such that these models can in principle solve the problem of the entropy growth, and are at the same time geodesically complete. We thus show that some recently stated…
We define a new variant of exclusion processes in discrete time that has jump probabilities that depend on the last jump performed. In a particular limit for the jump probabilities and in suitable scaling limits for space and time, we…
The large number of observed exoplanets ($\gtrsim $ 700) provides important constraints on their origin as deduced from the mass-period diagram of planets. The most surprising features in the diagram are 1) the (apparent) pile up of gas…
We develop a new methodology for model-based clustering. Optimizing the log-likelihood provides a principled statistical framework for clustering, with solutions found via the EM algorithm. However, because the log-likelihood is nonconvex,…
Time evolution of number of species (genera, families, and others), population of them, and size distribution of present ones and life times are studied in terms of a new model, where population of each genetic taxon increases by a (random)…
Massive volumes of high-dimensional data that evolves over time is continuously collected by contemporary information processing systems, which brings up the problem of organizing this data into clusters, i.e. achieve the purpose of…
Systems evolving according to the standard concept of biological or technological evolution are often described by catalytic evolution equations. We study the structure of these equations and find a deep relationship to classical…
Planetary obliquity and eccentricity influence climate by shaping the spatial and temporal patterns of stellar energy incident at a planet's surface, affecting both the annual mean climate and magnitude of seasonal variability. Previous…
In the field of Astrobiology, the precise location, prevalence and age of potential extraterrestrial intelligence (ETI) have not been explicitly explored. Here, we address these inquiries using an empirical galactic simulation model to…
Epigenetic Tracking is a mathematical model of biological cells, originally conceived to study embryonic development. Computer simulations proved the capacity of the model to generate complex 3-dimensional cellular structures, and the…
Molecular phenotypes are important links between genomic information and organismic functions, fitness, and evolution. Complex phenotypes, which are also called quantitative traits, often depend on multiple genomic loci. Their evolution…
We study the evolution of star clusters on circular and eccentric orbits using direct $N$-body simulations. We model clusters with initially $N=8{\rm k}$ and $N=16{\rm k}$ single stars of the same mass, orbiting around a point-mass galaxy.…
A simple stochastic model for evolution, based upon the need to pass a sequence of n critical steps (Carter 1983, Watson 2008) is applied to both terrestrial and extraterrestrial origins of life. In the former case, the time at which humans…
We investigate the interaction between an eccentric planet and a less massive external debris disc. This scenario could occur after planet-planet scattering or merging events. We characterise the evolution over a wide range of initial…
Following a recent proof of Shannon's entropy power inequality (EPI), a comprehensive framework for deriving various EPIs for the R\'enyi entropy is presented that uses transport arguments from normal densities and a change of variable by…
We investigate a new model for populations evolving in a spatial continuum. This model can be thought of as a spatial version of the Lambda-Fleming-Viot process. It explicitly incorporates both small scale reproduction events and large…
We propose a novel definition of life in terms of which its emergence in the universe is expected, and its ever-creative open-ended evolution is entailed by no law. Living organisms are Kantian Wholes that achieve Catalytic Closure,…