### Article

## New versions of evolutionary models with lethal mutations

In this paper, the impact of lethal mutations on evolutionary dynamics of asexual populations is analyzed. We suggest distinguishing different definitions of lethality, which lead to different mathematical formalizations of the microscopic model. Most of the studies focus on polyphasic lethality, meaning that individuals carrying lethal mutations have no offspring but consume common resources. In an alternative problem setting, monophasic lethal mutants die without giving offspring on the first stage of development. In the third case, semi-lethal mutations are considered when the lethal mutants survive with some probability. We suggest and investigate mathematical models for these cases, deriving the evolutionary characteristics of the steady state. We found that the peak sequence probability drastically depends on the version of lethality. The results obtained here can be used to solve the error threshold paradox at the origin of life.

This volume of Advances in Intelligent Systems and Computing contains papers presented in the main track of IITI 2016, the First International Conference on Intelligent Information Technologies for Industry held in May 16-21 in Sochi, Russia. The conference was jointly co-organized by Rostov State Transport University (Russia) and VŠB – Technical University of Ostrava (Czech Republic) with the participation of Russian Association for Artificial Intelligence (RAAI) and Russian Association for Fuzzy Systems and Soft Computing (RAFSSC). The volume is devoted to practical models and industrial applications related to intelligent information systems. The conference has been a meeting point for researchers and practitioners to enable the implementation of advanced information technologies into various industries. Nevertheless, some theoretical talks concerning the-state-of-the-art in intelligent systems and soft computing are included in the proceedings as well.

A strategy of "customer-centricity" as well as topical models of customer-centric companies is described. Propositions of effective social network technology application for various business aspects in such companies are suggested. Recommendations for theoretical description, analysis, modeling of customer-centric social networks and also for their monitoring with the aim of qualitative development are given. A case study of the WeChat mobile application is presented.

We study the planar matching problem, defined by a symmetric random matrix with independent identically distributed entries, taking values 0 and 1. We show that the existence of a perfect planar matching structure is possible only above a certain critical density of allowed contacts, $p_{c}$. This problem has an important application for the prediction of the optimal folding of RNA-type polymers. Using an alternative formulation of the problem in terms of Dyck paths and a matrix model of planar contact structures, we provide an analytical estimation for the value of the transition point, $p_{c}$, in the thermodynamic limit. This estimation is close to the critical value, $p_{c}\approx 0.38$, obtained in numerical simulations based on an exact dynamic-programming algorithm. We characterize the corresponding critical behavior of the model and discuss the relation of the perfect-imperfect matching transition to the known molten-glass transition in the context of random RNA secondary structure's formation. In particular, we provide strong evidence supporting the conjecture that the molten-glass transition at $T=0$ occurs at $p_{c}$

We study the fraction f of nucleotides involved in the formation of a cactuslike secondary structure of random heteropolymer RNA-like molecules. In the low-temperature limit, we study this fraction as a function of the number c of different nucleotide species. We show, that with changing c, the secondary structures of random RNAs undergo a morphological transition:f(c)→1 for c≤ccr as the chain length n goes to infinity, signaling the formation of a virtually perfect gapless secondary structure; while f(c)<1 for c>ccr, which means that a nonperfect structure with gaps is formed. The strict upper and lower bounds 2≤ccr≤4 are proven, and the numerical evidence for ccr is presented. The relevance of the transition from the evolutional point of view is discussed.

A simple sociophysical model is proposed to describe the transition between a chaotic and a coherent state of a microblogging social network. The model is based on the equations of evolution of the order parameter, the conjugated field, and the control parameter. The self-consistent evolution of the networks is presented by equations in which the correlation function between the incoming information and the subsequent change of the number of microposts plays the role of the order parameter; the conjugate field is equal to the existing information; and the control parameter is given by the number of strategically oriented users. Analysis of the adiabatic approximation shows that the second-order phase transition, which means following a definite strategy by the network users, occurs when their initial number exceeds a critical value equal to the geometric mean of the total and critical number of users.

In this work, we explore the properties of antiferromagnetic cycloid and the phase transitions between commensurate and incommensurate magnetic states in epitaxial BiFeO3 film. Additional magnetic anisotropy induced by strain effects in the films allocates cycloids with the definite directions of spin rotation. Peculiar feature of the cycloids propagating in the films whose symmetry is different from the single crystals is the orientation of spin rotational plane that does not contain electric polarization in contrast with the bulk materials. We construct a diagram of phase transitions induced by magnetic field applied along normal to the surface and show considerable decrease of the strength of magnetic field destroying cycloid in films compared with the bulk.

A method based on the spectral analysis of thermowave oscillations formed under the effect of radiation of lasers operated in a periodic pulsed mode is developed for investigating the state of the interface of multilayered systems. The method is based on high sensitivity of the shape of the oscillating component of the pyrometric signal to adhesion characteristics of the phase interface. The shape of the signal is quantitatively estimated using the correlation coefficient (for a film–interface system) and the transfer function (for multilayered specimens).

Let k be a field of characteristic zero, let G be a connected reductive algebraic group over k and let g be its Lie algebra. Let k(G), respectively, k(g), be the field of k- rational functions on G, respectively, g. The conjugation action of G on itself induces the adjoint action of G on g. We investigate the question whether or not the field extensions k(G)/k(G)^G and k(g)/k(g)^G are purely transcendental. We show that the answer is the same for k(G)/k(G)^G and k(g)/k(g)^G, and reduce the problem to the case where G is simple. For simple groups we show that the answer is positive if G is split of type A_n or C_n, and negative for groups of other types, except possibly G_2. A key ingredient in the proof of the negative result is a recent formula for the unramified Brauer group of a homogeneous space with connected stabilizers. As a byproduct of our investigation we give an affirmative answer to a question of Grothendieck about the existence of a rational section of the categorical quotient morphism for the conjugating action of G on itself.

Let G be a connected semisimple algebraic group over an algebraically closed field k. In 1965 Steinberg proved that if G is simply connected, then in G there exists a closed irreducible cross-section of the set of closures of regular conjugacy classes. We prove that in arbitrary G such a cross-section exists if and only if the universal covering isogeny Ĝ → G is bijective; this answers Grothendieck's question cited in the epigraph. In particular, for char k = 0, the converse to Steinberg's theorem holds. The existence of a cross-section in G implies, at least for char k = 0, that the algebra k[G]G of class functions on G is generated by rk G elements. We describe, for arbitrary G, a minimal generating set of k[G]G and that of the representation ring of G and answer two Grothendieck's questions on constructing generating sets of k[G]G. We prove the existence of a rational (i.e., local) section of the quotient morphism for arbitrary G and the existence of a rational cross-section in G (for char k = 0, this has been proved earlier); this answers the other question cited in the epigraph. We also prove that the existence of a rational section is equivalent to the existence of a rational W-equivariant map T- - - >G/T where T is a maximal torus of G and W the Weyl group.