145 research outputs found
A p-Adic Model of DNA Sequence and Genetic Code
Using basic properties of p-adic numbers, we consider a simple new approach
to describe main aspects of DNA sequence and genetic code. Central role in our
investigation plays an ultrametric p-adic information space which basic
elements are nucleotides, codons and genes. We show that a 5-adic model is
appropriate for DNA sequence. This 5-adic model, combined with 2-adic distance,
is also suitable for genetic code and for a more advanced employment in
genomics. We find that genetic code degeneracy is related to the p-adic
distance between codons.Comment: 13 pages, 2 table
Some aspects of the -adic analysis and its applications to -adic stochastic processes
In this paper we consider a generalization of analysis on -adic numbers
field to the case of -adic numbers ring. The basic statements, theorems
and formulas of -adic analysis can be used for the case of -adic analysis
without changing. We discuss basic properties of -adic numbers and consider
some properties of -adic integration and -adic Fourier analysis. The
class of infinitely divisible -adic distributions and the class of -adic
stochastic Levi processes were introduced. The special class of -adic CTRW
process and fractional-time -adic random walk as the diffusive limit of it
is considered. We found the asymptotic behavior of the probability measure of
initial distribution support for fractional-time -adic random walk.Comment: 18 page
Prebiotic Homochirality as a Critical Phenomenon
The development of prebiotic homochirality on early-Earth or another
planetary platform may be viewed as a critical phenomenon. It is shown, in the
context of spatio-temporal polymerization reaction networks, that environmental
effects -- be them temperature surges or other external disruptions -- may
destroy any net chirality previously produced. In order to understand the
emergence of prebiotic homochirality it is important to model the coupling of
polymerization reaction networks to different planetary environments.Comment: 6 Pages, 1 Figure, In Press: Origins of Life and Evolution of
Biosphere
Dissociation in a polymerization model of homochirality
A fully self-contained model of homochirality is presented that contains the
effects of both polymerization and dissociation. The dissociation fragments are
assumed to replenish the substrate from which new monomers can grow and undergo
new polymerization. The mean length of isotactic polymers is found to grow
slowly with the normalized total number of corresponding building blocks.
Alternatively, if one assumes that the dissociation fragments themselves can
polymerize further, then this corresponds to a strong source of short polymers,
and an unrealistically short average length of only 3. By contrast, without
dissociation, isotactic polymers becomes infinitely long.Comment: 16 pages, 6 figures, submitted to Orig. Life Evol. Biosp
Phase transitions for -adic Potts model on the Cayley tree of order three
In the present paper, we study a phase transition problem for the -state
-adic Potts model over the Cayley tree of order three. We consider a more
general notion of -adic Gibbs measure which depends on parameter
\rho\in\bq_p. Such a measure is called {\it generalized -adic quasi Gibbs
measure}. When equals to -adic exponent, then it coincides with the
-adic Gibbs measure. When , then it coincides with -adic quasi
Gibbs measure. Therefore, we investigate two regimes with respect to the value
of . Namely, in the first regime, one takes for some
J\in\bq_p, in the second one . In each regime, we first find
conditions for the existence of generalized -adic quasi Gibbs measures.
Furthermore, in the first regime, we establish the existence of the phase
transition under some conditions. In the second regime, when we prove the existence of a quasi phase transition. It turns out that
if and \sqrt{-3}\in\bq_p, then one finds the existence
of the strong phase transition.Comment: 27 page
Homochiral growth through enantiomeric cross-inhibition
The stability and conservation properties of a recently proposed
polymerization model are studied. The achiral (racemic) solution is linearly
unstable once the relevant control parameter (here the fidelity of the
catalyst) exceeds a critical value. The growth rate is calculated for different
fidelity parameters and cross-inhibition rates. A chirality parameter is
defined and shown to be conserved by the nonlinear terms of the model. Finally,
a truncated version of the model is used to derive a set of two ordinary
differential equations and it is argued that these equations are more realistic
than those used in earlier models of that form.Comment: 20 pages, 6 figures, Orig. Life Evol. Biosph. (accepted
Toward homochiral protocells in noncatalytic peptide systems
The activation-polymerization-epimerization-depolymerization (APED) model of
Plasson et al. has recently been proposed as a mechanism for the evolution of
homochirality on prebiotic Earth. The dynamics of the APED model in
two-dimensional spatially-extended systems is investigated for various
realistic reaction parameters. It is found that the APED system allows for the
formation of isolated homochiral proto-domains surrounded by a racemate. A
diffusive slowdown of the APED network such as induced through tidal motion or
evaporating pools and lagoons leads to the stabilization of homochiral bounded
structures as expected in the first self-assembled protocells.Comment: 10 pages, 5 figure
p-Adic Mathematical Physics
A brief review of some selected topics in p-adic mathematical physics is
presented.Comment: 36 page
Глубокая очистка теллура для производства материалов электроники и фотоники
The regularities of impurity distribution between the distillate and the still as well as the spatial distribution of impurities along the distillate length have been studied. We conclude that some impurities such as s−metals, Zn, Ni, V and rare metals distribute uniformly along the distillate length (20 cm). Contrarily, Se tends to concentrate in the distant (from the still) region of distillate with more than one order of magnitude higher concentration compared to the nearest region.Для проведения процесса получе ния высокочистого теллура методом вакуумной дистилляции предложена конструкция реактора из высокочистых кварцевого стекла и графита. В ходе процесса расплав теллура испаряется, пар переносится из горячей части системы в более холодную и конденсируется в виде твердой фазы (дистиллята) без образования жидкости. Изучены закономерности перераспределения примесей между дистиллятом и кубовым остатком, а также пространственное распределение примесей в дистилляте при проведении очистки металлического теллура. Установлено, что часть примесей, например щелочные металлы, Zn, Ni, V, редкоземельные металлы распределены равномерно по длине дистиллята (20 см). В то же время концентрация Se в дальней (от перегонного куба) части дистиллята превышает концентрацию в ближней части на порядок
Network Geometry and Complexity
(28 pages, 11 figures)Higher order networks are able to characterize data as different as functional brain networks, protein interaction networks and social networks beyond the framework of pairwise interactions. Most notably higher order networks include simplicial complexes formed not only by nodes and links but also by triangles, tetrahedra, etc. More in general, higher-order networks can be cell-complexes formed by gluing convex polytopes along their faces. Interestingly, higher order networks have a natural geometric interpretation and therefore constitute a natural way to explore the discrete network geometry of complex networks. Here we investigate the rich interplay between emergent network geometry of higher order networks and their complexity in the framework of a non-equilibrium model called Network Geometry with Flavor. This model, originally proposed for capturing the evolution of simplicial complexes, is here extended to cell-complexes formed by subsequently gluing different copies of an arbitrary regular polytope. We reveal the interplay between complexity and geometry of the higher order networks generated by the model by studying the emergent community structure and the degree distribution as a function of the regular polytope forming its building blocks. Additionally, we discuss the underlying hyperbolic nature of the emergent geometry and we relate the spectral dimension of the higher-order network to the dimension and nature of its building blocks
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