Biology is a constructive physics

Yuri Manin's approach to Zipf's law (Kolmogorov complexity as energy) is applied to investigation of biological evolution. Model of constructive statistical mechanics where complexity is a contribution to energy is proposed to model genomics. Scaling laws in genomics are discussed in relation to Zipf's law. This gives a model of Eugene Koonin's Third Evolutionary Synthesis (physical model which should describe scaling in genomics).Comment: 9 pages, commentaries adde

Dynamical systems where time is a quantum group and quantum ergodicity

We define dynamical systems where time is a quantum group. We give the definition of quantum ergodicity for the introduced dynamical system with noncommutative (or quantum) time, and discuss the examples.Comment: 4 pages, LaTe

Classification by Ensembles of Neural Networks

We introduce a new procedure for training of artificial neural networks by using the approximation of an objective function by arithmetic mean of an ensemble of selected randomly generated neural networks, and apply this procedure to the classification (or pattern recognition) problem. This approach differs from the standard one based on the optimization theory. In particular, any neural network from the mentioned ensemble may not be an approximation of the objective function.Comment: 8 pages, LaTe

The noncommutative replica procedure

The alternative to the replica procedure, which we call the noncommutative replica procedure, is discussed. The detailed comparison with the standard replica procedure is performed.Comment: 12 pages, LaTeX, Commentaries adde

Free coherent states and distributions on p-adic numbers

Free coherent states for a system with two degrees of freedom is defined. An isomorphism of the space of distributions on 2-adic disc and the space of free coherent states is constructed.Comment: 10 pages, LATEX, some correction

Rigged Hilbert space of the free coherent states and p-adic numbers

Rigged Hilbert space of the free coherent states is investigated. We prove that this rigged Hilbert space is isomorphous to the space of generalized functions on p-adic disk. We discuss the relation of the described isomorphism of rigged Hilbert spaces and noncommutative geometry and show, that the considered example realises the isomorphism of the noncommutative line and p-adic disk.Comment: 12 pages, LaTe

Free coherent states and pp-adic numbers

Free coherent states for a system with two degrees of freedom is defined. Existence of the homeomorphism of the ring of integer 2-adic numbers to the set of coherent states corresponding to an eigenvalue of the operator of annihilation is proved. It is shown that the metric of free Fock space induces the 2-adic topology on the set of coherent states.Comment: 5 pages, LATE

Model of vibrones in quantum photosynthesis as an analog of model of laser

Mechanism of vibronic amplification of transport of excitons was discussed in relation to quantum photosynthesis. Vibrones (some modes of vibrations of molecules) are observed experimentally in photosynthetic systems. In the present paper we discuss a model of vibronic amplification of quantum transfer where generation of vibrones as a coherent vibrational mode is described by an analog of semiclassical theory of laser. We consider two models --- a model of nonequilibrium three level system with vibronic mode, and some variant of a model of laser without inversion. We conjecture that dark states discussed in relation to quantum photosynthesis might be related to mechanism of vibronic "laser" without inversion which amplifies the transfer of excitons. We prove that in presence of vibronic mode transfer rate of excitons increases and compute dependence of the transfer rate on parameters of the model.Comment: 13 page

Model of protein fragments and statistical potentials

We discuss a model of protein conformations where the conformations are combinations of short fragments from some small set. For these fragments we consider a distribution of frequencies of occurrence of pairs (sequence of amino acids, conformation), averaged over some balls in the spaces of sequences and conformations. These frequencies can be estimated due to smallness of epsilon-entropy of the set of conformations of protein fragments. We consider statistical potentials for protein fragments which describe the mentioned frequencies of occurrence and discuss model of free energy of a protein where the free energy is equal to a sum of statistical potentials of the fragments. We also consider contribution of contacts of fragments to the energy of protein conformation, and contribution from statistical potentials of some hierarchical set of larger protein fragments. This set of fragments is constructed using the distribution of frequencies of occurrence of short fragments. We discuss applications of this model to problem of prediction of the native conformation of a protein from its primary structure and to description of dynamics of a protein. Modification of structural alignment taking into account statistical potentials for protein fragments is considered and application to threading procedure for proteins is discussed.Comment: 17 pages, some discussion is added or improve

p-Adic representation of the Cuntz algebra and the free coherent states

Representation of the Cuntz algebra in the space of (complex valued) functions on p-adic disk is introduced. The relation of this representation and the free coherent states is investigated.Comment: LaTeX, 10 page