Related papers: Comment on 'Classification scheme for phenomenolog…
In the theoretical biology framework one fundamental problem is the so-called error catastrophe in Darwinian evolution models. We reexamine Eigen's fundamental equations by mapping them into a polymer depinning transition problem in a…
This is a short commentary piece that discusses how the methods used in the natural sciences can apply to economics in general and financial markets specifically.
We conjecture recurrence relations satisfied by the degrees of some linearizable lattice equations. This helps to prove linear growth of these equations. We then use these recurrences to search for lattice equations that have linear growth…
A general model for the ontogenetic growth of living organisms has been recently proposed. Here we investigate the extension of this model to the growth of solid malignant tumors. A variety of in vitro and in vivo data are analyzed and…
In this paper a mathematically precise global (i.e. not the usual local) approach is presented to the variational principles of general relativistic classical field theories. Problems of the classic (usual) approaches are also discussed in…
Relationships between sediment flux and geomorphic processes are combined with statements of mass conservation, in order to create continuum models of hillslope evolution. These models have parameters which can be calibrated using available…
This paper introduces a variational formulation of natural selection, paying special attention to the nature of "things" and the way that different "kinds" of "things" are individuated from - and influence - each other. We use the Bayesian…
New Planck scale physics may solve the singularity problems of classical general relativity and may lead to interesting consequences for very early Universe cosmology. Two approaches to these questions are reviewed in this article. The…
In this article, the notion of a mathematical model in science is attempted to be enlightened from several points of view. In particular, it is shown that mathematical models are introduced differently and used differently in different…
The unique fluctuation-dissipation theorem for equilibrium stands in contrast with the wide variety of nonequilibrium linear response formulae. Their most traditional approach is "analytic", which, in the absence of detailed balance,…
Schemata theory, Markov chains, and statistical mechanics have been used to explain how evolutionary algorithms (EAs) work. Incremental success has been achieved with all of these methods, but each has been stymied by limitations related to…
Planck scale physics represents a future challenge, located between particle physics and general relativity. The Planck scale marks a threshold beyond which the old description of spacetime breaks down and conceptually new phenomena must…
We describe a general scheme of derivation of the Vlasov-type equations for Markov evolutions of particle systems in continuum. This scheme is based on a proper scaling of corresponding Markov generators and has an algorithmic realization…
In this talk we go over several new developments regarding the techniques for a large class of non-hermitian matrix models with unitary randomness (complex random numbers). In particular, we discuss: (a) - A diagrammatic approach based on a…
A popular science article designed to introduce people familiar with basic cosmological nomenclature with models alternative to cosmological inflation. The paper briefly discusses the modern view of the Big Bang model, inflation (both its…
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…
A general nonlinear logistic equation has been proposed to model long-time saturation in industrial growth. An integral solution of this equation has been derived for any arbitrary degree of nonlinearity. A time scale for the onset of…
The Darwinian paradigm of biological evolution is based on the separability of the variation and selection processes. As a result, the population thinking had always been an integral part of the Darwinian approach. I propose an alternative…
We research the natural causality of the Universe. We find that the equation of causality provides very good results on physics. That is our first endeavour and success in describing a quantitative expression of the law of causality. Hence,…
The aim of "A glance beyond the quantum model" [arXiv:0907.0372] to modernize the Correspondence Principle is compromised by an assumption that a classical model must start with the idea of particles, whereas in empirical terms particles…