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## On a regularization of the magnetic gas dynamics system of equations

A brief derivation of a specific regularization for the magnetic gas dynamic system of equations is given in the case of general equations of gas state (in presence of a body force and a heat source). The entropy balance equation in two forms is also derived for the system. For a constant regularization parameter and under a standard condition on the heat source, we show that the entropy production rate is nonnegative.

The study is carried out within The National Research University Higher School of Economics' Academic Fund Program, grant No. 13-09-0124.

The problem of reaching consensus in a MAC where there is no spanning tree in the dependency digraph is Considered.

In this research we compare the performance of different data mining techniques in the analysis of electroencephalogram (EEG) data. We study the question od predicting post-comatose neuro-developmental scores based mainly on statistical features of the EEG recordings. We compare results from applying different data mining techniques, such as the Elastic Net, Lasso, Gaussian Support Vector Regression and Random Forest Regression. We also compare the results produced with different matrix completion methods.

Homogeneous and isotropic with respect to horizontal variables random fields are useful for study of geophysical (in particular, meteorological) functions of spatial-temporal variables. The following horizontal scale (30 — 3000 km), which is induced by the spatial scale of the observing grid for the Earth’s atmosphere and by the power of modern computers for solutions of the system of hydrothermodynamics equations, which included water phase transformations etc, is important for the weather forecast problems.

The correlation functions (CFs) of the random fields may be applied for the following goals:

1) For the optimal interpolation of the meteorological information from the points of observation into the points of a regular finite-difference grid, as well as (for the checking of some observations by other ones) into another point of the observation.

2) For the models’ testing, if a climate model simulates adequately not only mean fields, but the fields of the relative dispersions and CFs, too, then we should consider the climate model as a certain one.

The CFs are evaluated by the global checked archive of meteorological observations by meteorological sounds. A special regularization procedure provides the strong positive definiteness of the CFs. The areas in the Earth atmosphere, where the isotropy hypothesis is essentially not fulfilled, were localized by a special algorithm.

Let us consider an algorithm, which can construct atmospheric fronts that separate so named homogeneous synoptic atmospheric volumes. Then we can evaluate separately CFs for the ensemble of the pairs of points, which are in a unite volume and CFs for the ensemble of the pairs of points, which are in a various volumes. We can see the difference between the different CFs. The difference will be more for a better algorithm. So, we obtain a quality criterion for such algorithms. The statistical approach given possibility to optimize the algorithm with respect to a lot of numerical parameters. The optimal algorithm was exploited in the operative regime in Hydrometeorological Center of Russia. The similar algorithms of numerical construction of boundaries between homogeneous volumes by a discrete set of observations can be realized for various physical media.

For the quasi-gasdynamic system of equations, there holds the law of nondecreasing entropy. Difference methods based on this system have been successfully used in numerous applications and test gasdynamic computations. In theoretical terms, however, for standard spatial discretizations of this system, the nondecreasing entropy law does not hold exactly even in the onedimensional case because of the mesh imbalance terms. For the quasigasdynamic equations, a new conservative spatial discretization is proposed for which the entropy balance equation has an appropriate form and the entropy production is guaranteed to be nonnegative (which also holds in the presence of body forces and heat sources). An important element of this discretization is that it makes use of nonstandard spaceaveraging techniques, including a nonlinear “logarithmic” averaging of the density and internal energy. The results hold on arbitrary nonuniform meshes.

The sixteen-volume set comprising the LNCS volumes 11205-11220 constitutes the refereed proceedings of the 15th European Conference on Computer Vision, ECCV 2018, held in Munich, Germany, in September 2018. The 776 revised papers presented were carefully reviewed and selected from 2439 submissions. The papers are organized in topical sections on learning for vision; computational photography; human analysis; human sensing; stereo and reconstruction; optimization; matching and recognition; video attention; and poster sessions.

In this paper, we propose several consensus protocols of the first and second order for networked multi-agent systems and provide explicit representations for their asymptotic states. These representations involve the eigenprojection of the Laplacian matrix of the dependency digraph.In particular, we study regularization models for the problem of coordination when the dependency digraph does not contain a converging tree. In such models of the first kind, the system is supplemented by a dummy agent, a ``hub" that uniformly, but very weakly influences the agents and, in turn, depends on them. In the models of the second kind, we assume the presence of very weak background links between the agents. Besides that, we present a description of the asymptotics of the classical second-order consensus protocol.

A model for organizing cargo transportation between two node stations connected by a railway line which contains a certain number of intermediate stations is considered. The movement of cargo is in one direction. Such a situation may occur, for example, if one of the node stations is located in a region which produce raw material for manufacturing industry located in another region, and there is another node station. The organization of freight traﬃc is performed by means of a number of technologies. These technologies determine the rules for taking on cargo at the initial node station, the rules of interaction between neighboring stations, as well as the rule of distribution of cargo to the ﬁnal node stations. The process of cargo transportation is followed by the set rule of control. For such a model, one must determine possible modes of cargo transportation and describe their properties. This model is described by a ﬁnite-dimensional system of diﬀerential equations with nonlocal linear restrictions. The class of the solution satisfying nonlocal linear restrictions is extremely narrow. It results in the need for the “correct” extension of solutions of a system of diﬀerential equations to a class of quasi-solutions having the distinctive feature of gaps in a countable number of points. It was possible numerically using the Runge–Kutta method of the fourth order to build these quasi-solutions and determine their rate of growth. Let us note that in the technical plan the main complexity consisted in obtaining quasi-solutions satisfying the nonlocal linear restrictions. Furthermore, we investigated the dependence of quasi-solutions and, in particular, sizes of gaps (jumps) of solutions on a number of parameters of the model characterizing a rule of control, technologies for transportation of cargo and intensity of giving of cargo on a node station.

Event logs collected by modern information and technical systems usually contain enough data for automated process models discovery. A variety of algorithms was developed for process models discovery, conformance checking, log to model alignment, comparison of process models, etc., nevertheless a quick analysis of ad-hoc selected parts of a journal still have not get a full-fledged implementation. This paper describes an ROLAP-based method of multidimensional event logs storage for process mining. The result of the analysis of the journal is visualized as directed graph representing the union of all possible event sequences, ranked by their occurrence probability. Our implementation allows the analyst to discover process models for sublogs defined by ad-hoc selection of criteria and value of occurrence probability

The dynamics of a two-component Davydov-Scott (DS) soliton with a small mismatch of the initial location or velocity of the high-frequency (HF) component was investigated within the framework of the Zakharov-type system of two coupled equations for the HF and low-frequency (LF) fields. In this system, the HF field is described by the linear Schrödinger equation with the potential generated by the LF component varying in time and space. The LF component in this system is described by the Korteweg-de Vries equation with a term of quadratic influence of the HF field on the LF field. The frequency of the DS soliton`s component oscillation was found analytically using the balance equation. The perturbed DS soliton was shown to be stable. The analytical results were confirmed by numerical simulations.