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The work is devoted to the construction and analysis of difference schemes for a system of hemodynamic equations obtained by averaging the hydrodynamic equations of a viscous incompressible fluid over the vessel cross-section. Models of blood as an ideal and as a viscous Newtonian fluid are considered. Difference schemes that approximate equations with second order on the spatial variable are proposed. The computational algorithms of the constructed schemes are based on the method of splitting on physical processes. According to this approach, at one time step, the model equations are considered separately and sequentially. The practical implementation of the proposed schemes at each time step leads to a sequential solution of two linear systems with tridiagonal matrices. It is demonstrated that the schemes are $\rho$-stable under minor restrictions on the time step in the case of sufficiently smooth solutions.

For the problem with a known analytical solution, it is demonstrated that the numerical solution has a second order convergence in a wide range of spatial grid step. The proposed schemes are compared with well-known explicit schemes, such as the Lax – Wendroff, Lax – Friedrichs and McCormack schemes in computational experiments on modeling blood flow in model vascular systems. It is demonstrated that the results obtained using the proposed schemes are close to the results obtained using other computational schemes, including schemes constructed by other approaches to spatial discretization. It is demonstrated that in the case of different spatial grids, the time of computation for the proposed schemes is significantly less than in the case of explicit schemes, despite the need to solve systems of linear equations at each step. The disadvantages of the schemes are the limitation on the time step in the case of discontinuous or strongly changing solutions and the need to use extrapolation of values at the boundary points of the vessels. In this regard, problems on the adaptation of splitting schemes for problems with discontinuous solutions and in cases of special types of conditions at the vessels ends are perspective for further research.

A new method of statistical analysis of texts is suggested. The frequency distribution of the first significant digits in numerals of English-language texts is considered. We have taken into account cardinal as well as ordinal numerals expressed both in figures, and verbally. To identify the author’s use of numerals, we previously deleted from the text all idiomatic expressions and set phrases accidentally containing numerals, as well as itemizations and page numbers, etc. Benford’s law is found to hold approximately for the frequencies of various first significant digits of compound literary texts by different authors; a marked predominance of the digit 1 is observed. In coherent authorial texts, characteristic deviations from Benford’s law arise which are statistically stable significant author peculiarities that allow, under certain conditions, to consider the problem of authorship and distinguish between texts by different authors. The text should be large enough (at least about 200 kB). At the end of $\{1, 2, \ldots, 9\}$ digits row, the frequency distribution is subject to strong fluctuations and thus unrepresentative for our purpose. The aim of the theoretical explanation of the observed empirical regularity is not intended, which, however, does not preclude the applicability of the proposed methodology for text attribution. The approach suggested and the conclusions are backed by the examples of the computer analysis of works by W.M. Thackeray, M. Twain, R. L. Stevenson, J. Joyce, sisters Bront¨e, and J.Austen. On the basis of technique suggested, we examined the authorship of a text earlier ascribed to L. F. Baum (the result agrees with that obtained by different means). We have shown that the authorship of Harper Lee’s “To Kill a Mockingbird” pertains to her, whereas the primary draft, “Go Set a Watchman”, seems to have been written in collaboration with Truman Capote. All results are confirmed on the basis of parametric Pearson’s chi-squared test as well as non-parametric Mann –Whitney U test and Kruskal –Wallis test.

The paper provides a comparative analysis of the results obtained by various approaches to modeling the process of artillery shot. In this connection, the main problem of internal ballistics and its particular case of the Lagrange problem are formulated in averaged parameters, where, within the framework of the assumptions of the thermodynamic approach, the distribution of pressure and gas velocity over the projectile space for a channel of variable cross section is taken into account for the first time. The statement of the Lagrange problem is also presented in the framework of the gas-dynamic approach, taking into account the spatial (one-dimensional and two-dimensional axisymmetric) changes in the characteristics of the ballistic process. The control volume method is used to numerically solve the system of Euler gas-dynamic equations. Gas parameters at the boundaries of control volumes are determined using a selfsimilar solution to the Riemann problem. Based on the Godunov method, a modification of the Osher scheme is proposed, which allows to implement a numerical calculation algorithm with a second order of accuracy in coordinate and time. The solutions obtained in the framework of the thermodynamic and gas-dynamic approaches are compared for various loading parameters. The effect of projectile mass and chamber broadening on the distribution of the ballistic parameters of the shot and the dynamics of the projectile motion was studied. It is shown that the thermodynamic approach, in comparison with the gas-dynamic approach, leads to a systematic overestimation of the estimated muzzle velocity of the projectile in the entire range of parameters studied, while the difference in muzzle velocity can reach 35%. At the same time, the discrepancy between the results obtained in the framework of one-dimensional and two-dimensional gas-dynamic models of the shot in the same range of change in parameters is not more than 1.3%.

A spatial gas-dynamic formulation of the backpressure problem is given, which describes the change in pressure in front of an accelerating projectile as it moves along the barrel channel. It is shown that accounting the projectile’s front, considered in the two-dimensional axisymmetric formulation of the problem, leads to a significant difference in the pressure fields behind the front of the shock wave, compared with the solution in the framework of the onedimensional formulation of the problem, where the projectile’s front is not possible to account. It is concluded that this can significantly affect the results of modeling ballistics of a shot at high shooting velocities.

Accurate segmentation of liver plays important in contouring during diagnosis and the planning of treatment. Imaging technology analysis and processing are wide usage in medical diagnostics, and therapeutic applications. Liver segmentation referring to the process of automatic or semi-automatic detection of liver image boundaries. A major difficulty in segmentation of liver image is the high variability as; the human anatomy itself shows major variation modes. In this paper, a proposed approach for computed tomography (CT) liver segmentation is presented by combining exponential entropy and fuzzy c-partition. Entropy concept has been utilized in various applications in imaging computing domain. Threshold techniques based on entropy have attracted a considerable attention over the last years in image analysis and processing literatures and it is among the most powerful techniques in image segmentation. In the proposed approach, the computed tomography (CT) of liver is transformed into fuzzy domain and fuzzy entropies are defined for liver image object and background. In threshold selection procedure, the proposed approach considers not only the information of liver image background and object, but also interactions between them as the selection of threshold is done by find a proper parameter combination of membership function such that the total fuzzy exponential entropy is maximized. Differential Evolution (DE) algorithm is utilizing to optimize the exponential entropy measure to obtain image thresholds. Experimental results in different CT livers scan are done and the results demonstrate the efficient of the proposed approach. Based on the visual clarity of segmented images with varied threshold values using the proposed approach, it was observed that liver segmented image visual quality is better with the results higher level of threshold.

The paper studies the problem of searching for fragments with missing bibliographic links in a scientific article using automatic binary classification. To train the model, we propose a new contrast resampling technique, the innovation of which is the consideration of the context of the link, taking into account the boundaries of the fragment, which mostly affects the probability of presence of a bibliographic links in it. The training set was formed of automatically labeled samples that are fragments of three sentences with class labels «without link» and «with link» that satisfy the requirement of contrast: samples of different classes are distanced in the source text. The feature space was built automatically based on the term occurrence statistics and was expanded by constructing additional features — entities (names, numbers, quotes and abbreviations) recognized in the text.

A series of experiments was carried out on the archives of the scientific journals «Law enforcement review» (273 articles) and «Journal Infectology» (684 articles). The classification was carried out by the models Nearest Neighbors, RBF SVM, Random Forest, Multilayer Perceptron, with the selection of optimal hyperparameters for each classifier.

Experiments have confirmed the hypothesis put forward. The highest accuracy was reached by the neural network classifier (95%), which is however not as fast as the linear one that showed also high accuracy with contrast resampling (91–94%). These values are superior to those reported for NER and Sentiment Analysis on comparable data. The high computational efficiency of the proposed method makes it possible to integrate it into applied systems and to process documents online.

The technology of creating patterns from natural language words (concepts) based on text data in the bag of words model is considered. Patterns are used to reduce the dimension of the original space in the description of documents and search for semantically related words by topic. The process of dimensionality reduction is implemented through the formation of patterns of latent features. The variety of structures of document relations is investigated in order to divide them into themes in the latent space.

It is considered that a given set of documents (objects) is divided into two non-overlapping classes, for the analysis of which it is necessary to use a common dictionary. The belonging of words to a common vocabulary is initially unknown. Class objects are considered as opposition to each other. Quantitative parameters of oppositionality are determined through the values of the stability of each feature and generalized assessments of objects according to non-overlapping sets of features.

To calculate the stability, the feature values are divided into non-intersecting intervals, the optimal boundaries of which are determined by a special criterion. The maximum stability is achieved under the condition that the boundaries of each interval contain values of one of the two classes.

The composition of features in sets (patterns of words) is formed from a sequence ordered by stability values. The process of formation of patterns and latent features based on them is implemented according to the rules of hierarchical agglomerative grouping.

A set of latent features is used for cluster analysis of documents using metric grouping algorithms. The analysis applies the coefficient of content authenticity based on the data on the belonging of documents to classes. The coefficient is a numerical characteristic of the dominance of class representatives in groups.

To divide documents into topics, it is proposed to use the union of groups in relation to their centers. As patterns for each topic, a sequence of words ordered by frequency of occurrence from a common dictionary is considered.

The results of a computational experiment on collections of abstracts of scientific dissertations are presented. Sequences of words from the general dictionary on 4 topics are formed.

The paper outlines the approaches to mathematical modeling correlation adaptometry techniques widely used in biology and medicine. The analysis is based on models employed in descriptions of structured biological systems. It is assumed that the distribution density of the biological population numbers satisfies the equation of Kolmogorov-Fokker-Planck. Using this technique evaluated the effectiveness of treatment of patients with obesity. All patients depending on the obesity degree and the comorbidity nature were divided into three groups. Shows a decrease in weight of the correlation graph computed from the measured in the patients of the indicators that characterizes the effectiveness of the treatment for all studied groups. This technique was also used to assess the intensity of the training loads in academic rowing three age groups. It was shown that with the highest voltage worked with athletes for youth group. Also, using the technique of correlation adaptometry evaluated the effectiveness of the treatment of hormone replacement therapy in women. All the patients depending on the assigned drug were divided into four groups. In the standard analysis of the dynamics of mean values of indicators, it was shown that in the course of the treatment were observed normalization of the averages for all groups of patients. However, using the technique of correlation adaptometry it was found that during the first six months the weight of the correlation graph was decreasing and during the second six months the weight increased for all study groups. This indicates the excessive length of the annual course of hormone replacement therapy and the practicality of transition to a semiannual rate.

The method of the stochastic matrix spectrum analysis is used to build an indicator that allows to determine the subject of scientific texts without keywords usage. This matrix is a matrix of conditional probabilities of bigrams, built on the statistics of the alphabet characters in the text without spaces, numbers and punctuation marks. Scientific texts are classified according to the mutual arrangement of invariant subspaces of the matrix of conditional probabilities of pairs of letter combinations. The separation indicator is the value of the cosine of the angle between the right and left eigenvectors corresponding to the maximum and minimum eigenvalues. The computational algorithm uses a special representation of the dichotomy parameter, which is the integral of the square norm of the resolvent of the stochastic matrix of bigrams along the circumference of a given radius in the complex plane. The tendency of the integral to infinity testifies to the approximation of the integration circuit to the eigenvalue of the matrix. The paper presents the typical distribution of the indicator of identification of specialties. For statistical analysis were analyzed dissertations on the main 19 specialties without taking into account the classification within the specialty, 20 texts for the specialty. It was found that the empirical distributions of the cosine of the angle for the mathematical and Humanities specialties do not have a common domain, so they can be formally divided by the value of this indicator without errors. Although the body of texts was not particularly large, nevertheless, in the case of arbitrary selection of dissertations, the identification error at the level of 2 % seems to be a very good result compared to the methods based on semantic analysis. It was also found that it is possible to make a text pattern for each of the specialties in the form of a reference matrix of bigrams, in the vicinity of which in the norm of summable functions it is possible to accurately identify the theme of the written scientific work, without using keywords. The proposed method can be used as a comparative indicator of greater or lesser severity of the scientific text or as an indicator of compliance of the text to a certain scientific level.

The method for mapping of intermediate representations (IR) set of C, C++ programs to vector embedding space is considered to create an empirical estimation framework for static performance prediction using LLVM compiler infrastructure. The usage of embeddings makes programs easier to compare due to avoiding Control Flow Graphs (CFG) and Data Flow Graphs (DFG) direct comparison. This method is based on transformation series of the initial IR such as: instrumentation — injection of artificial instructions in an instrumentation compiler’s pass depending on load offset delta in the current instruction compared to the previous one, mapping of instrumented IR into multidimensional vector with IR2Vec and dimension reduction with t-SNE (t-distributed stochastic neighbor embedding) method. The D1 cache miss ratio measured with perf stat tool is considered as performance metric. A heuristic criterion of programs having more or less cache miss ratio is given. This criterion is based on embeddings of programs in 2D-space. The instrumentation compiler’s pass developed in this work is described: how it generates and injects artificial instructions into IR within the used memory model. The software pipeline that implements the performance estimation based on LLVM compiler infrastructure is given. Computational experiments are performed on synthetic tests which are the sets of programs with the same CFGs but with different sequences of offsets used when accessing the one-dimensional array of a given size. The correlation coefficient between performance metric and distance to the worst program’s embedding is measured and proved to be negative regardless of t-SNE initialization. This fact proves the heuristic criterion to be true. The process of such synthetic tests generation is also considered. Moreover, the variety of performance metric in programs set in such a test is proposed as a metric to be improved with exploration of more tests generators.

In the development of the previously obtained result on modeling the dynamics of vegetation cover, due to variations in the temperature background, a new scheme for the interval analysis of the dynamics of floristic images of formations is presented in the case when the parameter of the response rate of the model of the dynamics of each counting plant species is set by the interval of scatter of its possible values. The detailed description of the functional parameters of macromodels of biodiversity, desired in fundamental research, taking into account the essential reasons for the observed evolutionary processes, may turn out to be a problematic task. The use of more reliable interval estimates of the variability of functional parameters “bypasses” the problem of uncertainty in the primary assessment of the evolution of the phyto-resource potential of the developed controlled territories. The solutions obtained preserve not only a qualitative picture of the dynamics of species diversity, but also give a rigorous, within the framework of the initial assumptions, a quantitative assessment of the degree of presence of each plant species. The practical significance of two-sided estimation schemes based on the construction of equations for the upper and lower boundaries of the trajectories of the scatter of solutions depends on the conditions and measure of proportional correspondence of the intervals of scatter of the initial parameters with the intervals of scatter of solutions. For dynamic systems, the desired proportionality is not always ensured. The given examples demonstrate the acceptable accuracy of interval estimation of evolutionary processes. It is important to note that the constructions of the estimating equations generate vanishing intervals of scatter of solutions for quasi-constant temperature perturbations of the system. In other words, the trajectories of stationary temperature states of the vegetation cover are not roughened by the proposed interval estimation scheme. The rigor of the result of interval estimation of the species composition of the vegetation cover of formations can become a determining factor when choosing a method in the problems of analyzing the dynamics of species diversity and the plant potential of territorial systems of resource-ecological monitoring. The possibilities of the proposed approach are illustrated by geoinformation images of the computational analysis of the dynamics of the vegetation cover of the Yamal Peninsula and by the graphs of the retro-perspective analysis of the floristic variability of the formations of the landscapelithological group “Upper” based on the data of the summer temperature background of the Salehard weather station from 2010 to 1935. The developed indicators of floristic variability and the given graphs characterize the dynamics of species diversity, both on average and individually in the form of intervals of possible states for each species of plant.