The Algebraic View of Computation

We argue that computation is an abstract algebraic concept, and a computer is a result of a morphism (a structure preserving map) from a finite universal semigroup.Comment: 13 pages, final version will be published elsewher

From Simple to Complex and Ultra-complex Systems:\ud A Paradigm Shift Towards Non-Abelian Systems Dynamics

Atoms, molecules, organisms distinguish layers of reality because of the causal links that govern their behavior, both horizontally (atom-atom, molecule-molecule, organism-organism) and vertically (atom-molecule-organism). This is the first intuition of the theory of levels. Even if the further development of the theory will require imposing a number of qualifications to this initial intuition, the idea of a series of entities organized on different levels of complexity will prove correct. Living systems as well as social systems and the human mind present features remarkably different from those characterizing non-living, simple physical and chemical systems. We propose that super-complexity requires at least four different categorical frameworks, provided by the theories of levels of reality, chronotopoids, (generalized) interactions, and anticipation

Organismic Supercategories and Qualitative Dynamics of Systems

The representation of biological systems by means of organismic supercategories, developed in previous papers, is further discussed. The different approaches to relational biology, developed by Rashevsky, Rosen and by Baianu and Marinescu, are compared with Qualitative Dynamics of Systems which was initiated by Henri Poincaré (1881). On the basis of this comparison some concrete results concerning dynamics of genetic system, development, fertilization, regeneration, analogies, and oncogenesis are derived

Quantum Genetics and Quantum Automata Models of Quantum-Molecular Evolution Involved in the Evolution of Organisms and Species

Previous theoretical or general approaches to the problems of Quantum Genetics and Molecular Evolution are considered in this article from the point of view of Quantum Automata Theory first published by the author in 1971 and further developed in several recent articles. The representation of genomes and Interactome networks in categories of many-valued logic LMn –algebras that are naturally transformed during biological evolution, or evolve through interactions with the environment provide a new insight into the mechanisms of molecular evolution, as well as organismal evolution, in terms of sequences of quantum automata. Phenotypic changes are expressed only when certain environmentally-induced quantum-molecular changes are coupled with an internal re-structuring of major submodules of the genome and Interactome networks related to cell cycling and cell growth. Contrary to the commonly held view of `standard’ Darwinist models of evolution, the evolution of organisms and species occurs through coupled multi-molecular transformations induced not only by the environment but actually realized through internal re-organizations of genome and interactome networks. The biological, evolutionary processes involve certain epigenetic transformations that are responsible for phenotypic expression of the genome and Interactome transformations initiated at the quantum-molecular level. It can thus be said that only quantum genetics can provide correct explanations of evolutionary processes that are initiated at the quantum--multi-molecular levels and propagate to the higher levels of organismal and species evolution.

Biological evolution should be therefore regarded as a multi-scale process which is initiated by underlying quantum (coupled) multi-molecular transformations of the genomic and interactomic networks, followed by specific phenotypic transformations at the level of organism and the variable biogroupoids associated with the evolution of species which are essential to the survival of the species. The theoretical framework introduced in this article also paves the way to a Quantitative Biology approach to biological evolution at the quantum-molecular, as well as at the organismal and species levels. This is quite a substantial modification of the 'established’ modern Darwinist, and also of several so-called `molecular evolution’ theories

Computational universes

Suspicions that the world might be some sort of a machine or algorithm existing ``in the mind'' of some symbolic number cruncher have lingered from antiquity. Although popular at times, the most radical forms of this idea never reached mainstream. Modern developments in physics and computer science have lent support to the thesis, but empirical evidence is needed before it can begin to replace our contemporary world view.Comment: Several corrections of typos and smaller revisions, final versio

Quantum automata, braid group and link polynomials

The spin--network quantum simulator model, which essentially encodes the (quantum deformed) SU(2) Racah--Wigner tensor algebra, is particularly suitable to address problems arising in low dimensional topology and group theory. In this combinatorial framework we implement families of finite--states and discrete--time quantum automata capable of accepting the language generated by the braid group, and whose transition amplitudes are colored Jones polynomials. The automaton calculation of the polynomial of (the plat closure of) a link L on 2N strands at any fixed root of unity is shown to be bounded from above by a linear function of the number of crossings of the link, on the one hand, and polynomially bounded in terms of the braid index 2N, on the other. The growth rate of the time complexity function in terms of the integer k appearing in the root of unity q can be estimated to be (polynomially) bounded by resorting to the field theoretical background given by the Chern-Simons theory.Comment: Latex, 36 pages, 11 figure