Abstract: In this article the task of clustering operons (special units of genetic information) is solved. The authors describe its use for the identification of groups of operons with similar functions. The specifics of the open bases of operons used as sources of initial data for the study are considered. The authors describe the selection and preparation of data for clustering, the features of the clustering process, and its relationship with the approaches traditionally used for the analysis of natural languages. Based on the clustering performed, the quality and composition of the obtained groups is analyzed. To convert the raw data into vectors, the classical implementation of the word2vec algorithm and a number of features of the original data are used. The resulting representation is clustered by the DBScan algorithm based on the cosine distance. The novelty of the proposed method is associated with the use of non-standard algorithms for the initial data. The approach used effectively manifests itself when working with a large amount of data, does not require additional data markup and independently forms factors for clustering. The obtained results show the possibility of using the proposed approach for the implementation of services that allow comparative analysis of bacterial genomes.

Keywords: clustering, DBScan, word embeddings, word2vec, machine learning, methods, algorithms, operons, natural language processing, open access databases

Abstract: The study is devoted tp algorithms of segmentation of satellite images for various systems of technical vision. For the segmentation of images authors use sections on graphs. Preliminary segmentation is performed based on the minimal spanning tree to improve performance. When describing the properties of super pixels, information about the height and color of the regions is taken into account. The height of the areas is calculated based on the stereo images. The color of segments is calculated on the basis of color invariants. All super pixels in accordance with their characteristics belong to the areas of buildings, grass cover, trees and shrubs, shaded areas, etc. The image is an undirected weighted graph, the nodes of which are segments of the image. The weights of the vertices of a graph are numbers that determine the membership of a certain class. To divide regions into clusters, the method of cuts on graphs is used. The novelty of the study is the algorithm for segmenting satellite imagery based on super pixels and graphs. The segmentation time on the basis of the developed algorithm decreases several times in comparison with the method of cuts on graphs. The developed algorithm is used to allocate buildings to images. Comparison of the developed algorithm with existing approaches of building allocation is shown, its advantages are shown. Examples of the operation of the algorithm are given by the authors of the article and the results of the research are described.

Keywords: pattern recognition, computer vision, image processing, satellite imagery, graph cuts, spectral graph theory, superpixels, image segmentation, scene analysis, color invariants

Abstract: The subject of the study is the concept of hierarchical bitmap-indexes proposed by the authors. In order to improve the processing performance of queries on the time filter, the indices are supported not only for the values of the basic unit of time, but also for arbitrary larger multiple units. The object of the study is to construct a probabilistic model that makes it possible to evaluate the effectiveness of decision making: what bitwise operation to apply at the next level of the hierarchy when constructing the resulting sample is a disjunction or an exclusive OR. The author focuses on justifying the validity of the model and comparing the results with the previously constructed minimax model, in which the decision was made according to a pre-established rule and did not depend on the current state of the system. The methodology of the study is probability theory, methods multicriteria optimization and computational experiment, as well as related methods of intuitive evaluation of the likelihood of the results. Main conclusions of the study: an analytical model of the dynamic selection of an index operation has been constructed and verified; It is shown that the proposed discipline of choice gives higher productivity in comparison with the minimax model and software is developed to obtain a numerical estimate of this difference; a model for estimating the costs of dynamic decision making and a weight function that allows one to evaluate the efficiency of the model with decision making and to choose one of the two models is proposed for this or that choice of weights.

Keywords: multi-criterial optimization, binning, minimax rule, exclusive OR, disjunction, exponential distribution, total probability, random flow of events, hierarchical bitmap-indexes, weighted function

Abstract: The paper shows the solution of the problem of constructing an ontological model for the choice of software development tools. The classes of the constructed ontological model form a taxonomy. Questions of representation of the developed ontological model in the form of the non-uniform oriented graph are considered. To support the ontology and solve on its basis the tasks of selecting software development tools on the constructed model, operations of adding and modifying the main ontology concepts are defined, which are the criteria for evaluating software quality. To evaluate and decide on the choice of tools based on the developed ontological model, an algorithm based on the method for estimating the similarity of objects in the intellectual space of knowledge is proposed. The novelty of the presented work is to build an ontological model of knowledge for making decisions on the choice of software development tools that allows to expand the composition of concepts and relationships between them, which provides the opportunity to describe various objects, subjects and processes of the software life cycle.

Keywords: estimation of similarity of objects, decision-making algorithm, concept, class, non-uniform oriented graph, taxonomy, ontological model, intellectual space of knowledge, evaluation criterion, life cycle

Abstract: The authors consider the problem of choosing a wavelet for its application in a continuous wavelet transformation. The whole advantage of wavelet analysis lies in the possibility of choosing a basis among a large number of wavelets. The choice of the analyzing wavelet is usually determined by what information needs to be extracted from the signal under study. Each wavelet has characteristic features, both in time and in frequency space. Therefore, with the help of different wavelets, it is possible to reveal more fully and emphasize certain properties of the analyzed signal. The choice of the analyzing wavelet function for creating a basis for wavelet transform is one of the issues whose successful solution affects the success of using wavelet analysis in the problem being solved. Bypassing this question repels the beginners in this field of researchers from using wavelet analysis or significantly lends the field of its application. The choice of the wavelet function is especially important for a continuous wavelet transform, where the result of the transformation is a three-dimensional continuous wavelet spectrum. This makes it difficult to analyze it, which is often limited to a visual analysis of the projection of the wavelet spectrum on the scale-time axis. This also complicates the choice of the wavelet function, since when changing the wavelet in the projection of the wavelet spectrum, numerous changes that can not be analyzed sometimes occur.The purpose of this work is to show the method of substantiating the choice of the analyzing wavelet-function for its use in continuous wavelet transformation using the example of the problem of localizing the points of extrema of a digital signal. The work uses continuous wavelet transform. We consider wavelet coefficients on different scales for analyzing the changes not on the wavelet spectrum as a whole, but on its individual parts. The proposed technique shows an algorithm for analyzing continuous wavelet spectra with different wavelet functions in order to evaluate their suitability for searching for extrema. An important point in this technique is the transition from a visual analysis of three-dimensional wavelet spectra to a quantitative analysis of two-dimensional wavelet coefficients on different scales. Such a transition shows how the wavelet analysis works inside three-dimensional wavelet spectra (analyzed primarily visually) and automates signal analysis. This also allows us to numerically estimate the accuracy of finding extrema when using a particular wavelet. As a result, the article shows that the Haar wavelet is the most accurate in the problem of searching for signal extrema by means of continuous wavelet analysis.This method of choosing a basis can be used in problems where an acceptable quantitative estimate of the accuracy of the operation of a continuous wavelet transform is possible. This will allow the authors to analyze three-dimensional wavelet spectra not only qualitatively (visually), but also quantitatively.

Keywords: arterial blood pressure signal, scale, extrema definition, basis selection, wavelet, wavelet analysis, modelling, wavelet Haar, continuous wavelet transform, method

Abstract: The subject of the study is the filtration problem, which describes the distribution of suspended solids in a loose porous soil. The urgency of constructing a model is determined by the need to strengthen loose soil by pumping under pressure a solution in the form of a suspension that, when hardened, forms a waterproof layer. The author's main goal is to construct a model for the motion of suspended particles of a suspension and colloids and to form a sediment in a porous ground for various filtration regimes. The distributions of solid particles of various sizes carried by the carrier liquid and settled on the framework of the porous medium are studied at different rates of precipitate growth.The one-dimensional filtration model with the particle retention mechanism includes a hyperbolic system of first-order equations with inconsistent initial and boundary conditions that generate discontinuous solutions. For polydisperse media, a modified mathematical model describing the competition of particles of different sizes for small pores is considered. The computer circuit for finding the numerical solution is constructed by the method of finite differences. The optimization of the method is used to improve convergence and reduce computation time. The main results of the study are a multi-particle model of solution filtration in a porous soil, taking into account the variety of sizes of suspended particles. A numerical calculation of the problem is performed for various blocking filter coefficients. Solutions are obtained with a discontinuity at the concentration front. Approbation of the found numerical solutions is carried out. Plots of the dependence of the concentrations of suspended and sedimented particles on time and coordinates are constructed.

Keywords: finite-difference methods, numerical solution, mathematical model, suspended particles, porous medium, deep bed filtration, grout, discontinuous solutions, retained particles, Euler's method

Abstract: To date, the introduction of electronic document management and records management in the executive bodies of state power remains one of the most urgent tasks. The authors consider the use of "soft" mathematical modeling in developing a mathematical model for assessing the implementation of electronic document management systems and records management. By mathematical modeling, the work is understood as the process of establishing correspondence to the real object of a certain mathematical object, which is called a mathematical model. The object of modeling is the system of electronic document circulation and records management. The main objectives of modeling the study of document flow in the executive bodies of state power are: to increase the effectiveness of management activities, accelerate the movement of documents, reduce the complexity of processing documents.In this work, the authors used the formalization method, which consists in studying objects by displaying their content and structure in sign form. The main conclusions of the study are that, using "soft" mathematical modeling, a mathematical model for assessing the implementation of the electronic document management system and office work in the executive bodies of state power is constructed. After studying the constructed oriented graph, a system of differential equations is written that corresponds to the following rules: equations as many as there are unknown quantities, model parameters (system coefficients) are found as a result of application of computational methods.

Keywords: the system of differential equations, criterial values system of electronic document circulation and Office work, the criteria for assessing the implementation of the system, mathematical modeling, model, electronic document management system, mathematical model, electronic document management, Document management, documentation.

Abstract: The presented article deals with the application of affine transformations in solving problems with second-order curves, namely, stretching and contraction with respect to a straight line, that is, transforming a circle into an ellipse and vice versa.Ellipse finds the widest application in various fields due to the grace of form and its properties: in art, design, architecture, physics and technology, astronomy, its properties are described in fiction. The construction of an ellipse can be done very accurately with the help of improvised tools (pegs, threads, kinks of the circle, using a strip of paper), special adaptations and modern computer systems of mathematical modeling and CAD. The methods of constructing an ellipse are based on its properties, which also determines its shape.Using the laws of affine transformation will help to strengthen the skills of applying the properties of an ellipse and solving problems in determining its basic parameters. Method of work. The article presents methods of transformations aimed at determining the large and small axes of an ellipse, constructing tangents to an ellipse, and determining the points of intersection of a straight line with an ellipse.As a result of the work, algorithms for solving problems have been obtained that allow the authors to determine the intersection point of a straight line with surfaces of the second order (paraboloid, hyperboloid of one sheet) and a truncated cone using the method of a related transformation. The authors also determine the axes of the ellipse, the points of tangency and the intersection of the line with the ellipse. Scientific novelty. A method is proposed that makes it possible to simplify the solution of design problems on the intersection of a second-order surface with a straight line and a second-order surface, which will contribute to an increase in the accuracy and adequacy of their construction.The properties and essence of the affine transformation of an ellipse into a circle are shown and vice versa. The algorithms for solving various geometric problems based on the application of related transformations are demonstrated. The materials of the work are of practical importance, since they significantly broaden the concept of how to solve various problems with second-order curves.

Keywords: perpendicular straight lines, related points, conjugated diameters, axis of kinship, ellipse, affine transformation, circle, tangent, curves, intersection

Abstract: The goal of the presented study is to increase the effectiveness of recreating realistic shadows of dynamic 3D movie characters at the stage of digital post-processing of film and video material due to mathematically justified temporary replacement of high-poly three-dimensional surface modeling by low-polygonal without compromising the quality of the final product in the cinematographic industry. The object of this scientific research is the filmed and mounted film and video material and individual graphic images of film frames. The subject of the article are models, methods and algorithms for digital processing of video material. The methods of three-dimensional surface modeling by various polygons, program algorithms for geometric calculations of invisible lines and projections of 3D objects onto a three-dimensional surface are studied. New effective methods and software algorithms for reducing the dimensionality of the polygonal 3D model have been developed, which are justified mathematically and have made it possible to significantly reduce the amount of computer calculations of dynamic shadows without degrading the quality of the video material. An example of the practical implementation of new models and methods for recreating shadows in cinematography is given.

Keywords: Low-polygonal Modeling, 3D Model, Dynamic 3D Object, Shadows Recreation, Digital Video Post-processing, Cinematography, Video Frame, Geometric Computation, Efficiency Improvement, Mathematical Justification

Abstract: The article discusses electronic resources with support for the visually impaired interface, and also analyzes their compliance with the Web Content Accessibility Guidelines (WCAG) 2.0 standard and the user interface for visually impaired users of different levels. The purpose of the article is to check electronic resources for compliance with the information adaptation standard for visually impaired users and to comply with the requirements of the Resolution of the Government of the Russian Federation "On Approval of the State Program of the Russian Federation" Affordable Environment "for 2011-2020." The article considers models and methods for assessing the quality characteristics of the user interface , evaluation criteria for the identification of user groups of the visually impaired user in the user interface groups, and adaptation recommendations for the electron based on the standard WCAG 2.0 The results of usability testing on the criteria for assessing the user interface for visually impaired Internet users were obtained with the help of the results obtained in this article: without a tiflotechnical means, a disabled person with a color perception problem and a visually impaired user have limited access capabilities to the information, the sites of the Russian Internet space correspond to the minimum level of the standard WCAG 2.0.

Keywords: interface evaluation, user's interface, WCAG, hyposeeing user, usability, special interface, WCAG levels, electronic resources adaptation, web accessibility, web content