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A punctuated equilibrium model of biological evolution with relative fitness between different species being the fundamental driving force of evolution is introduced. Mutation is modeled as a fitness updating cellular automaton process…
A first principles approach to the theoretical description of the development of biological forms, from a fertilized egg to a functioning embryo, remains a central challenge to applied physics and theoretical biology. Rather than refer to…
Automated algorithm discovery in scientific computing faces fundamental challenges: vast design spaces with expensive evaluations, domain-specific physical constraints requiring expert knowledge, and the necessity for interpretable…
The growth of evolutionary computing (EC) methods in the exploration of complex potential energy landscapes of atomic and molecular clusters, as well as crystals over the last decade or so is reviewed. The trend of growth indicates that…
Explicit coupling property and gradient estimates are investigated for the linear evolution equations on Hilbert spaces driven by an additive cylindrical L\'evy process. The results are efficiently applied to establish the exponential…
Several exoplanets have been discovered to date, and the next step is the search for extraterrestrial life. However, it is difficult to estimate the number of life-bearing exoplanets because our only template is based on life on Earth. In…
Discrete time, spatially extended models play an important role in ecology, modelling population dynamics of species ranging from micro-organisms to birds. An important question is how 'bottom up', individual-based models can be…
The existence of exponential dichotomies has been well-established as a powerful tool to study existence, stability, and bifurcations of coherent structures. Currently, the application of exponential dichotomies to elliptic problems posed…
Finding the most powerful node in a dynamic random network, the largest set in a partition-valued stochastic process, or the largest family in an evolving population at a given time, can be a very difficult problem. This is particularly the…
This thesis develops and expands upon known techniques of mathematical physics relevant to the analysis of the popular Markov model of phylogenetic trees required in biology to reconstruct the evolutionary relationships of taxonomic units…
Astrocladistics, a methodology borrowed from biology, is an objective way of understanding galaxy diversity through evolutionary relationships. It is based on the evolution of all the available parameters describing galaxies and thus…
Biological evolution in a sequence space with random fitnesses is studied within Eigen's quasispecies model. A strong selection limit is employed, in which the population resides at a single sequence at all times. Evolutionary trajectories…
Cosmologists wish to explain how our Universe, in all its complexity, could ever have come about. For that, we assess the number of states in our Universe now. This plays the role of entropy in thermodynamics of the Universe, and reveals…
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…
A new definition of entropy is introduced using a model that simulates an expanding space-time compatible with the fundamental principle of cosmology. The entropy is obtained by mean of a state function that measures the variation of the…
Stochastic thermodynamics is the field of study relating fluctuations in stochastic systems to thermodynamic quantities. The total entropy production (EP), is central to the thermodynamic classification of systems. Non-equilibrium systems…
We study the convergence of stochastic time-discretization schemes for evolution equations driven by random velocity fields, including examples like stochastic gradient descent and interacting particle systems. Using a unified framework…
We propose a generic model of eco-systems, with a {\it hierarchical} food web structure. In our computer simulations we let the eco-system evolve continuously for so long that that we can monitor extinctions as well as speciations over…
For over 30 years, mode-coupling theory (MCT) has been the de facto theoretic description of dense fluids and the liquid-glass transition. MCT, however, is limited by its ad hoc construction and lacks a mechanism to institute corrections.…
We present results for the equilibrium statistics and dynamic evolution of moderately large ($n = {\mathcal{O}}(10^2 - 10^3)$) numbers of interacting point vortices on the unit sphere under the constraint of zero mean angular momentum. We…