1,911 research outputs found

### 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

### Free coherent states and $p$-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 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

### 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

### 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

### 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

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