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Protein evolution underpins life, and understanding its behavior as a system is of great importance. However, our current models of protein evolution are arguably too simplistic to allow quantitative interpretation and prediction of…
We calculate the power spectrum of density fluctuations in the statistical non-equilibrium field theory for classical, microscopic degrees of freedom to first order in the interaction potential. We specialise our result to cosmology by…
This paper develops a new method for identifying econometric models with partially latent covariates. Such data structures arise in industrial organization and labor economics settings where data are collected using an input-based sampling…
Laboratory experiments with bacterial colonies, under well-controlled conditions often lead to evolutionary diversification, where at least two ecotypes emerge from an initially monomorphic population. Empirical evidence suggests that such…
Phylogenetic mixture models, in which the sites in sequences undergo different substitution processes along the same or different trees, allow the description of heterogeneous evolutionary processes. As data sets consisting of longer…
Model uncertainties and simulation uncertainties occur in mathematical modeling of multiscale complex systems, since some mechanisms or scales are not represented (i.e., "unresolved") due to lack in our understanding of these mechanisms or…
Drug gradients are believed to play an important role in the evolution of bacteria resistant to antibiotics and tumors resistant to anti-cancer drugs. We use a statistical physics model to study the evolution of a population of malignant…
Evolutionary algorithms have been frequently applied to constrained continuous optimisation problems. We carry out feature based comparisons of different types of evolutionary algorithms such as evolution strategies, differential evolution…
This article examines the decoherence of a macroscopic body using a simple model of the environment and following the evolution of the pure state for the whole system. We found that decoherence occurs for very general initial conditions and…
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…
Recent studies on epistatic networks of model organisms have unveiled a certain type of modular property called monochromaticity in which the networks are clusterable into functional modules that interact with each other through the same…
Estimation of molecular evolutionary divergence times requires models of rate change. These vary with regard to the assumption of what quantity is penalized. The possibilities considered are the rate of evolution, the log of the rate of…
Phylogenetic mixtures model the inhomogeneous molecular evolution commonly observed in data. The performance of phylogenetic reconstruction methods where the underlying data is generated by a mixture model has stimulated considerable recent…
We suggest a novel proposal to express decoherence in open quantum systems by jointly employing spectral and stochastic methods. This proposal, which basically perturbs the unitary evolution operator in a random fashion, allows us to…
In the article "Stochastic evolution equations for large portfolios of Stochastic Volatility models" (Arxiv:1701.05640) there is a mistake in the proof of Theorem 3.1. In this erratum we establish a weaker version of this Theorem and then…
Stochastic fluctuations of molecule numbers are ubiquitous in biological systems. Important examples include gene expression and enzymatic processes in living cells. Such systems are typically modelled as chemical reaction networks whose…
We study the evolution of sexual and asexual populations in general fitness landscapes. We find deep relations between the mathematics of biological evolution and the formalism of quantum mechanics. We give the general structure of the…
The Fredkin spin chain serves as an interesting theoretical example of a quantum Hamiltonian whose ground state exhibits a phase transition between three distinct phases, one of which violates the area law. Here we consider a classical…
The time-dependence of correlation functions under the influence of classical equations of motion is described by an exact evolution equation. For conservative systems thermodynamic equilibrium is a fixed point of these equations. We show…
We consider the time evolution of systems in which a spatially homogeneous scalar field is coupled to fermions. The quantum back-reaction is taken into account in one-loop approximation. We set up the basic equations and their…