ARTM advantages: ARTM is much simpler that Bayesian Inference ARTM focuses on formalizing task-specific requirements ARTM simplifies the multi-objective PTMs learning ARTM reduces barriers to entry into PTMs research field ARTM encourages the development of regularization library ARTM restrictions: Choosing a regularization path is a new open issue for PTMs

By applying methods of power geometry, we find all asymptotic expansions of solutions to the fifth Painlevé equation near its nonsingular point for all values of its four complex parameters. More specifically, 10 families of expansions of solutions to the equation areobtained, of which one was not previously known. Three expansions are Laurent series, while the remaining seven expansions are Taylor series. All of them converge in a (deleted) neighborhood of the nonsingular point.

Results related to extended formulations of convex polygons are discussed. In particular, it turns out that six linear inequalities are sufficient to describe a convex heptagon up to a linear projection.

We consider the time-dependent 1D Schrödinger equation on the half-axis with variable coefficients becoming constant for large x. We study a two-level symmetric in time (i.e. the Crank-Nicolson) and any order finite element in space numerical method to solve it. The method is coupled to an approximate transparent boundary condition (TBC). We prove uniform in time stability with respect to initial data and a free term in two norms, under suitable conditions on an operator in the approximate TBC. We also consider the corresponding method on an infinite mesh on the half-axis. We derive explicitly the discrete TBC allowing us to restrict the latter method to a finite mesh. The operator in the discrete TBC is a discrete convolution in time; in turn its kernel is a multiple discrete convolution. The stability conditions are justified for it. The accomplished computations confirm that high order finite elements coupled to the discrete TBC are effective even in the case of highly oscillating solutions and discontinuous potentials. The study is carried out by the first author within The National Research University Higher School of Economics' Academic Fund Program in 2012-2013, research grant No. 11-01-0051.

In the framework of modular metric spaces, introduced by the author in 2006, we define a new notion of modular convergence, which is more weak than the metric convergence, and establish the necessary and sufficient condition on the modular under consideration, under which the modular convergence is equivalent to the metric one. We introduce the notion of modular contractive maps, study their relationship with Lipschitz continuous maps with respect to the corresponding metrics and present the main result of the paper concerning the existence of fixed points of modular contractive maps. As an application of the fixed point theorem, we prove the existence of solutions to a Caratheodory-type differential equation with the right hand side from the Orlicz space.

It is known that by means of minimal values of tolerances one can obtain necessary and sufficient conditions for the uniqueness of the optimal solution of a combinatorial optimization problem (COP) with an additive objective function and the set of nonembedded feasible solutions. Moreover, the notion of a tolerance is defined locally, i.e., with respect to a chosen optimal solution. In this paper we introduce the notion of a global tolerance with respect to the whole set of optimal solutions and prove that the nonembeddedness assumption on the set of feasible solutions of the COP can be relaxed, which generalizes the well known rela- tions for the extremal values of the tolerances. In particular, we formulate a new criterion for the uniqueness of the optimal solution of the COP with an additive objective function, which is based on certain equalities between locally and globally defined tolerances.

In contrast to all analysis methods available for multicriterial decisionmaking problems that use criteria importance estimates, criteria importance theory is based on rigorously defined concepts of equality and superiority of one criterion over others in terms of their importance. In this theory, decision rules for combinations of various types of information on the importance of criteria and their scale have been developed that specify corresponding binary preference relations. In this paper, we propose several fundamentally new decision rules that cover previously uncovered combinations of types of information or are computationally simpler than known decision rules.

The quasigasdynamic (QGD) approach makes it possible to construct convenient and reliable difference schemes for the numerical solution of various gasdynamic problems. Its description can be found in several books. In particular, the Boltzmann kinetic equation for a mixture of monatomic gases is used to derive and test QGD equations for binary mixtures of nonreactive ideal polytropic gases. In this paper, we analyze and expand the capabilities of the QGD approach in this area. The original equations are rewritten as conservation laws, which are more conventional in viscous gas dynamics and convenient for discretization. Additionally, an external force and a heat source are taken into account. We briefly discuss the parabolicity of the system in the sense of Petrovskii, which ensures that the system is well defined. An entropy balance equation is derived, and the entropy production for a gas mixture is shown to be nonnegative, which ensures that the system is physically consistent (but does not hold in all available descriptions of gas mixtures). Importantly, to achieve the latter property, the expressions for the exchange terms in the total energy balance equation (initially derived only for monatomic gas mixtures) are properly generalized. Additionally, we introduce a simplification of the QGD system for binary mixtures, which is referred to as a quasihydrodynamic system and is used for the numerical simulation of weakly compressible sub and transonic flows. At the end of this paper, we present simplified barotropic versions of both systems and derive a corresponding energy balance equation with nonpositive energy production.

A concept of k-stable alternatives is introduced. Relationship of classes of k-stable alternatives with dominant, uncovered and weakly stable sets is established.

In a neighborhood of a singular point, we consider autonomous systems of ordinary differential equations for which one eigenvalue of the matrix of the linear part is zero and the remaining eigenvalues do not belong to the imaginary axis. We study the reducibility of such systems to normal form. We prove that the problem of finitely smooth equivalence can be solved for such systems by using finite segments of the Taylor series of their right-hand sides.

In a neighborhood of a singular point, we consider autonomous systems of ordinary differential equations such that the matrix of their linear part has two purely imaginary eigenvalues, while the other eigenvalues lie outside the imaginary axis. We study the reducibility of such systems to pseudonormal form. We prove that the problem of finitely smooth equivalence can be solved for such systems by using finite segments of the Taylor series of their right-hand sides.

In a neighborhood of a singular point, we consider autonomous systems of ordinary differential equations such that the matrix of their linear part has two purely imaginary eigenvalues, while the other eigenvalues lie outside the imaginary axis. We study the reducibility of such systems to pseudonormal form. We prove that the problem of finitely smooth equivalence can be solved for such systems by using finite segments of the Taylor series of their right-hand sides.

We show that a pointwise precompact sequence of maps from the ndimensional rectangle into a metric semigroup, whose total variations in the sense of Vitali, Hardy and Krause are uniformly bounded, contains a pointwise convergent subsequence. We present a variant of this result for maps with values in a reflexive separable Banach space with respect to the weak pointwise convergence of maps.

Using a model of traffic flow dynamics as an example, we study the phenomenon of self-organization in large systems under the influence of a random force.

It is shown that the discrete spectrum of the Dirichlet problem for the Laplacian on the union of two mutually perpendicular circular cylinders consists of a single eigenvalue, while the homogeneous problem with a threshold value of the spectral parameter has no bounded solutions. As a consequence, an adequate one-dimensional model of a square lattice of thin quantum waveguides is presented and the asymptotic behavior of the spectral bands and lacunas (zones of wave transmission and deceleration) and the oscillatory processes they generate is described. © 2015, Pleiades Publishing, Ltd.