p-Adic mathematics and theoretical biology.

The principal objective of this article is a brief overview of the main parts of p-adic mathematics, which have already had valuable applications and may have a significant impact in the near future on the further development of some fields of theoretical and mathematical biology. In particular, we present the basics of ultrametrics, p-adic numbers and p-adic analysis, as well as insight into their applications for modeling some cognitive processes, genetic code and protein dynamics. We also argue that ultrametric concepts and p-adic mathematics are natural tools for the viable description of biological systems and phenomena with a hierarchical structure.

Entropy, externality and human evolution.

Considering biosphere as a closed thermodynamical system, inside it, biological organisms may be considered as open thermodynamical systems exchanging energy and matter with ecosystem. Making appeal to non-equilibrium thermodynamics, anthropology, biology, sociology and cliodynamics, we discuss, from an interdisciplinary stance, some main moments of human evolution from either the phylogenetic and the ontogenetic standpoint, highlighting the crucial bifurcation which saw the rising of the modern societies with respect to primitive ones.

Indications of a possible symmetry and its breaking in a many-agent model obeying quantum statistics.

The results of computer simulations are presented which give evidence for the existence of an interesting symmetry in a many-agent model which demonstrates, in special cases, both Bose-Einstein and Fermi-Dirac statistics. This symmetry is expressed in the close vicinity of the mean values of the degree of ultrametricity and the fraction of isosceles of the sets of agent memories (histories) coded by two different information-loss coding schemes. It is shown that this (in some sense) approximate statistical supersymmetry is probably broken at low temperatures--below some condensation limit. This breaking leads to the appearance of specific coding schemes for boson and fermion histories. The meaning of this specificity is revealed by applying the interpretation of the many-agent model described earlier [A. A. Ezhov and A. Yu. Khrennikov, Phys. Rev. E 71, 016138 (2005)].

Toward an adequate mathematical model of mental space: conscious/unconscious dynamics on m-adic trees.

We try to perform geometrization of cognitive science and psychology by representing information states of cognitive systems by points of mental space given by a hierarchic m-adic tree. Associations are represented by balls and ideas by collections of balls. We consider dynamics of ideas based on lifting of dynamics of mental points. We apply our dynamical model for modeling of flows of unconscious and conscious information in the human brain. In a series of models, Models 1-3, we consider cognitive systems with increasing complexity of psychological behavior determined by structure of flows of associations and ideas.

Agents with left and right dominant hemispheres and quantum statistics.

We present a multiagent model illustrating the emergence of two different quantum statistics, Bose-Einstein and Fermi-Dirac, in a friendly population of individuals with the right-brain dominance and in a competitive population of individuals with the left-brain hemisphere dominance, correspondingly. Doing so, we adduce the arguments that Lefebvre's "algebra of conscience" can be used in a natural way to describe decision-making strategies of agents simulating people with different brain dominance. One can suggest that the emergence of the two principal statistical distributions is able to illustrate different types of society organization and also to be used in order to simulate market phenomena and psychic disorders, when a switching of hemisphere dominance is involved.