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Published since 1998
ISSN 1562-5419
16+
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Sorting problem on graths in programming contests

Mihail Ivanovich Kinder, Andrei Kazantsev
384-391
Abstract: The problem of sorting data is analyzed, the order relation between which is described as the adjacency relation of vertices on an arbitrary graph. Subtasks and issues related to the ‘neighborhood‘ of the problem are highlighted; their solution is the level of ‘immersion‘ in the solution of the general problem. Algorithms for solving individual subtasks for graphs of a special kind are discussed, as well as various approaches to solving the sorting problem in the general case. A sorting task of this type was proposed at the ISI-Junior School Programming Cup in July 2019 (Innopolis).
Keywords: mathematical olympiads, programming contests, informatics olympiads, multilevel tasks in mathematics, multilevel tasks in informatics contests, sorting problem on graphs.

Inverse Problem of Identification of Thermophysical Parameters of the Green-Nagdi Type III Model for an Elastic Rod Based on a Physically Informed Neural Network

Yana Andreevna Vakhterova, Darya Andreevna Leontyeva
852-869
Abstract:

In this paper, we study the inverse problem of identifying the dimensionless thermal conductivity coefficient for the Green–Naghdi equation of type III, which describes the propagation of thermal disturbances with a finite velocity and takes into account the inertial effects of heat flux. For the inverse problem, the stability requirement (Hadamard criteria) is violated, as a result of which even minimal data distortions lead to significant errors in parameter identification. As a solution method, we use an approach based on physically informed neural networks (PINN), which combines the capabilities of deep learning with a priori knowledge of the structure of the differential equation. The parameter is included among the trained variables, and the loss function is formed based on the deviation from the differential equation, boundary conditions, initial conditions, and noisy experimental data from a point sensor. The results of computational experiments are presented, demonstrating high accuracy of parameter recovery (error less than 0.03%) and the stability of the method with respect to the presence of additive Gaussian noise in the data. The PINN method has proven itself to be an effective tool for solving ill-posed inverse problems of mathematical physics.

Keywords: inverse problem, Green-Naghdi model type III, thermoelasticity, deep machine learning, physics informed neural networks.

On Serious and Funny in Science (Based on Materials of Digital Libraries)

Yuri Evgenievich Polak
215-249
Abstract:

Digital libraries (DL) and archives accumulate gigantic volumes of various information. The goal of this work is, without trying to cover the immensity, to try, using a relatively small number of striking examples, to trace how issues of scientific creativity are reflected in DL; discuss and dispel stereotypical ideas about scientists as unsociable, pedantic formalists or eccentric, absent-minded persons; show how the peculiarities of their thought processes, combined with high intelligence, can cause misunderstanding in everyday life. At the same time, these qualities, combined with originality of thinking, sometimes turning into paradox, are manifested in non-standard approaches to problems, non-trivial solutions, and an ironic attitude towards the surrounding reality. As a result, along with serious results, unexpected associations and analogies; jokes, witticisms, and anecdotes are born. The paper provides examples of the creativity of scientists in the professional field, as well as works in such genres as science fiction, utopia, humor, and art song. Materials from 20+ electronic libraries were used.

Keywords: digital libraries, image of a scientist, scientific creativity, humor, art song.

On the Synonym Search Model

Olga Muratovna Ataeva, Vladimir Alekseevich Serebriakov, Natalia Pavlovna Tuchkova
1006-1022
Abstract:

The problem of finding the most relevant documents as a result of an extended and refined query is considered. For this, a search model and a text preprocessing mechanism are proposed, as well as the joint use of a search engine and a neural network model built on the basis of an index using word2vec algorithms to generate an extended query with synonyms and refine search results based on a selection of similar documents in a digital semantic library. The paper investigates the construction of a vector representation of documents based on paragraphs in relation to the data array of the digital semantic library LibMeta. Each piece of text is labeled. Both the whole document and its separate parts can be marked. The problem of enriching user queries with synonyms was solved, then when building a search model together with word2vec algorithms, an approach of "indexing first, then training" was used to cover more information and give more accurate search results. The model was trained on the basis of the library's mathematical content. Examples of training, extended query and search quality assessment using training and synonyms are given.

Keywords: search model, word2vec algorithm, synonyms, information query, query extension.

The Problem of the Existence of a Tree with a Characteristic Vector of Node Vertices

Ivan Nikolaevich Popov
474-484
Abstract:

The paper presents the problem of the existence of a tree with certain numerical characteristics. It is clear that if a tree is given, it is possible to determine the number of node vertices of the tree and leaves, as well as to determine their degrees. Thus, for a tree, you can define a set of pairs whose coordinates are numbers corresponding to the number of node vertices and their degrees. We can form the inverse problem: we give pairs of natural numbers whose second coordinates are greater than 1, and we should determine whether there is at least one tree that the numbers of its node vertices and their degrees coincide with these pairs. The solution to this problem is presented in this paper.

Keywords: algorithm, Python, graph-tree, Prufer code of the tree.

Analysis of the Distribution of Key Terms in Scientific Articles

Svetlana Aleksandrovna Vlasova, Nikolay Evgenievich Kalenov, Irina Nikolaevna Sobolevskaya
35-51
Abstract:

One of the Common Digital Space of Scientific Knowledge (CDSSK) main components are the subject ontologies of individual thematic subspaces, which include the basic concepts related to this scientific area. The constructing subject ontologies task at the initial phase requires the array of key terms formation in a given scientific are with the subsequent establishment of links between them. A similar task is in the encyclopedias formation in terms of the articles (slots) list generating that determines their content. One of the sources for the formation of the key terms array can be the metadata of articles published in the leading scientific journals. Namely, the author's key terms ("keywords" in the terminology of the journals editors) quoted by the article. To make a conclusion about the possibility of using this approach to the subject ontologies formation, it is necessary to conduct the author's key terms array preanalysis, both in terms of real correspondence to the main areas of research in this science branch and in terms of the distribution of the certain terms occurrence frequency. This article presents the results of the occurrence frequency analysis of the author's key terms in Russian and English, carried out on the software processing basis of several thousand articles from leading Russian journals in mathematics, computer science and physics, reflected in the MathNet database. An assessment was made of the distribution of key terms correspondence (as phrases) and individual words to the Bradford's law, and the key terms cores within the thematic direction were identified.

Keywords: digital space of scientific knowledge, subject ontologies, encyclopedia articles, key terms, article metadata, frequency analysis.

Digital Platform for Supercomputer Mathematical Modeling of Spraying Processes

Nikita Igorevich Tarasov, Viktoriia Olegovna Podryga, Sergey Vladimirovich Polyakov, Alexey Valerievich Timakov
697-721
Abstract:

The work presents a digital platform for supercomputer modeling the problems of spraying the particles on substrates. The purpose of this work is to discuss the general architecture, technology stack and implementation features of the platform's user interface. The platform is based on web technologies for access and management of calculations, which allow implementing a user system for conducting a full cycle of a computational experiment, including the configuration of applied applications, their launch on remote computing resources, monitoring the completion of tasks, analysis and interactive visualization of results. User interaction with computing resources is implemented through the graphical interface that does not require the client computer to have any additional software, except actual version of a modern web browser. An important advantage of the platform is the ability to make large-scale computer research in a multi-user mode that is based on the natural principles of building client-server applications. The presented digital web platform was successfully tested on computing clusters of the KIAM RAS in solving a number of the topical mathematical problems of nanotechnology. Also, with its help, for the last 3 years, group training of MIPT students in modern information technologies has been carried out.

Keywords: supercomputer modeling, digital platform, web interface, gas-dynamic spraying of particles.

Conditional Electrocardiogram Generation using Hierarchical Variation-al Autoencoders

Ivan Anatolevich Sviridov, Konstantin Sergeevich Egorov
1186-1206
Abstract:

Cardiovascular diseases remain the leading cause of mortality, and automated electrocardiogram (ECG) analysis can ease clinical workloads but is limited by scarce and imbalanced data. Synthetic ECG can mitigate these issues, and while most methods use Generative Adversarial Networks (GANs), recent work show variational autoencoders (VAEs) perform comparably. We introduce cNVAE-ECG, a conditional Nouveau VAE (NVAE) that generates high-resolution, 12-lead, 10-second ECGs with multiple pathologies. Leveraging a compact channel-generation scheme and class embeddings for multi-label conditioning, cNVAE-ECG improves downstream binary and multi-label classification, achieving up to a 2% AUROC gain in transfer learning over GAN-based models.

Keywords: ECG, variational autoencoder, conditional generation, GAN.

Analysis of Word Embeddings for Semantic Role Labeling of Russian Texts

Leysan Maratovna Kadermyatova, Elena Victorovna Tutubalina
1026-1043
Abstract: Currently, there are a huge number of works dedicated to semantic role labeling of English texts [1–3]. However, semantic role labeling of Russian texts was an unexplored area for many years due to the lack of train and test corpora. Semantic role labeling of Russian Texts was widely disseminated after the appearance of the FrameBank corpus [4]. In this approach, we analyzed the influence of the word embedding models on the quality of semantic role labeling of Russian texts. Micro- and macro- F1 scores on word2vec [5], fastText [6], ELMo [7] embedding models were calculated. The set of experiments have shown that fastText models averaged slightly better than word2vec models as applied to Russian FrameBank corpus. The higher micro- and macro- F1 scores were obtained on deep tokenized word representation model ELMo in relation to classical shallow embedding models.
Keywords: machine learning, ML-model, natural language processing, word embedding, semantic role labeling.

Using the Co-Authority Graph for the Thematic Search of Conferences on Scientometric Data

Alexander Sergeevich Kozitsyn, Sergey Alexandrovich Afonin, Dmitry Alekseevich Shachnev
600-615
Abstract:

Thematic information search is used in various fields of activity. The use of thematic analysis tools to search for conferences allows you to increase the completeness of the search and coverage of conferences, helps to expand the circle of scientific communication of young scientists and the formation of closer scientific connections. The search algorithms developed by the authors use the co-authorship graph and the reference set of authors. The set can be obtained using methods of thematic search of experts or based on given samples. The developed algorithms are language insensitive and take into account the authority of conferences in the scientific community. Approbation was carried out on the data of the scientometric system IAS ISTINA.

Keywords: thematic search, bibliographic data, conference search, co-authorship graph, information systems, scientometrics.

Computed knowledge base for descrbing information resources in molecular spectroscopy. 5. Expert data quality

А.Ю. Ахлёстин, Н.А. Лаврентьев, А.И. Привезенцев, А.З. Фазлиев
Abstract: It is shown that trust in the content of information resources can be assessed by means of a publishing criterion, with the information recourses being of the trusted and distrusted type. The task of assessment of trust consists of four subtasks: (1) building multisets of physical quantities available in primary data sources, (2) alignment of values of physical quantities, (3) formulation of quantitative restrictions for publishing criterion in different ranges of change of physical quantities, and (4) decomposition of expert data. Spectral data publishing criteria and restrictions required for solving data alignment tasks are outlined. Alignment results have been tabulated. Using vacuum wavenumbers as an example, restrictions inherent in publishing criteria are formulated. The assessment of the content trust obtained from solutions to the tasks of decomposition f expert data are presented as the OWL-ontologies. Building knowledge bases of this kind at virtual data centers intended for data intensive science will provide realization of an automatic selection of spectroscopic information resources exhibiting a high degree of trust.
Keywords: quantitative spectroscopy, data alignment, content trust, publishing criterion.

Bibliographic Database Ratings and White Lists

Tatyana Alekseevna Polilova
640-670
Abstract:

Currently, Russian institutions are almost completely disconnected from Western information resources and services related to the publication of scientific journals. In such conditions, the task of replacing the departed services, reorientation to domestic scientific journals, Russian online library resources has become particularly actual. In the largest bibliographic database the eLibrary.ru, focused on Russian-language scientific publications, collected information about almost 15 thousand Russian-language journals. In the eLibrary.ru there is an analytical system "Russian Science Citation Index" that processes metadata of articles from more than 5 thousand Russian scientific journals. Is the eLibrary.ru ready to serve as a national bibliographic database? For what reason "white lists" of journals appear in Russian organizations?


The main problem of the RSCI is the quality of the constructed ratings of scientific journals. The methods of calculating ratings over the past years have caused certain criticisms. The paper provides an example of a rating of journals from the section "Mathematics" built in the RSCI. Journals that are little known among professional mathematicians were in the first positions. Serious deformations in the ratings of the eLibrary.ru undermine the confidence of scientists in the assessments of the credibility of Russian journals proposed by the eLibrary.ru. The reaction of some universities and scientific organizations is quite expected: organizations are beginning to introduce their own criteria for the success of the publication activities of employees associated with the publication of articles in journals from the so-called "white lists". The white list of journals is compiled, as a rule, by the expert councils of the organization specifically for each discipline and scientific direction. Scientometric indicators may be taken into account when compiling white lists, but they are not the primary criterion for the selection of journals. White lists can now become a reasonable addition to the ratings of bibliographic databases.

Keywords: scientific publication, rating of journals, thematic classification, impact factor, multidisciplinary, bibliographic reference, white list of scientific journals.

Of Neural Network Model Robustness Through Generating Invariant to Attributes Embeddings

Marat Rushanovich Gazizov, Karen Albertovich Grigorian
1142-1154
Abstract:

Model robustness to minor deviations in the distribution of input data is an important criterion in many tasks. Neural networks show high accuracy on training samples, but the quality on test samples can be dropped dramatically due to different data distributions, a situation that is exacerbated at the subgroup level within each category. In this article we show how the robustness of the model at the subgroup level can be significantly improved with the help of the domain adaptation approach to image embeddings. We have found that application of a competitive approach to embeddings limitation gives a significant increase of accuracy metrics in a complex subgroup in comparison with the previous models. The method was tested on two independent datasets, the accuracy in a complex subgroup on the Waterbirds dataset is 90.3 {y : waterbirds;a : landbackground}, on the CelebA dataset is 92.22 {y : blondhair;a : male}.

Keywords: robust classification, image classification, generative adversarial networks, domain adaptation.

Electronic libraries in the Computing Center of Russian Rcademy of Sciences – main developments

Владимир Алексеевич Серебряков
534-566
Abstract: The main projects that have been implemented in the Computing Center named A.A. Dorodnitsyna of the Russian Academy of Sciences (CC RAS) for the last 20 years, that is, since 1998, are analyzed. One of the first was the implementation of the pilot project “Integrated Information Resource System (ISIR) RAS”. The successful completion of this project allowed the development of work on the integration of heterogeneous scientific information resources into the general academic scientific information system. An important stage was the project of creating the Unified Scientific Information Space (ENIP) of the RAS. This project was based on the subsystem “Scientific Institute of the Russian Academy of Sciences”, created at the CC of the Russian Academy of Sciences and the Center for Scientific Telecommunications (CNTK) of the Russian Academy of Sciences. Considering the importance of building digital libraries, in 2006 the Russian Academy of Sciences adopted the target scientific program “Creating the Central Bank “Scientific Heritage of Russia”, in accordance with which the digital library was implemented. The created GeoMeta Portal is a standardized and decentralized spatial information management environment designed to access geodatabases, map products and associated metadata from various sources, facilitating the exchange of spatial information between organizations and its sharing via the Internet. Currently, the main line of work is the LibMeta digital personal semantic library. The main task of this system is to provide the user with a unified view for the possibility of automated extraction of information of interest to him on a particular subject area.
Keywords: subject area, scientific subject area, scientific information, scientific knowledge, generalized representation of scientific subject area, taxonomy, thesaurus, global ontology, search engines, organization of scientific knowledge, digital libraries.

Designing a Tool for Creating Gameplay through the Systematization of Game Mechanics

Aleksey Vitalevich Shubin, Vlada Vladimirovna Kugurakova
774-795
Abstract:

A new approach to the development of a tool aimed at simplifying the workflow of a game designer is presented. The requirements are elaborated, the work scenario is developed and the main parameters for the developed tool are specified. The main objective of the tool is to speed up and facilitate the selection of proper game mechanics without the need to spend valuable time on lengthy analysis of other videogame projects.


To provide more effective work of game designers in the selection of game mechanics, we analyzed a variety of approaches to the classification of game mechanics. In the process of the research various methods of classification of game mechanics were considered, the analysis revealed which classifications are more suitable for decomposition of game mechanics. The results of the research allowed us to identify key aspects of game mechanics, which will serve as a foundation for the development of the tool.


This research represents an important step in creating a tool that will optimize the game design process and increase the speed of videogame development.

Keywords: game design, classification, game mechanics, automatization, videogame.

Neuro-Fuzzy Image Segmentation with Learning Function

Maksim Vladimirovich Bobyr, Bogdan Andreevich Bondarenko
601-621
Abstract:

This paper presents a neuro-fuzzy algorithm for high-speed grayscale image segmentation based on a modified defuzzification method using triangular membership functions. The aim of the study is to analyze the effect of simplifying the defuzzification formula on the accuracy and contrast of object selection. The proposed approach includes adaptive learning of the weight coefficient, which allows dynamically adjusting the defuzzification process depending on the target values. The paper compares the basic method of averaging membership values and a modified version taking into account nonlinear weights. Experiments conducted on 1024x720 images demonstrate that the developed algorithm provides high segmentation accuracy and improved object contrast with minimal computational costs. The results confirm the superiority of the proposed method over traditional approaches, emphasizing the prospects for applying artificial intelligence in computer vision problems.

Keywords: IAS, neuro-fuzzy algorithm, image segmentation, defuzzification, artificial intelligence, area ratio method.

Stability Studies of a Coupled Model to Perturbation of Initial Data

Konstantin Pavlovich Belyaev, Gury Mikhaylovich Mikhaylov, Alexey Nikolaevich Salnikov, Natalia Pavlovna Tuchkova
615-633
Abstract: The stability problem is considered in terms of the classical Lyapunov definition. For this, a set of initial conditions is set, consisting of their preliminary calculations, and the spread of the trajectories obtained as a result of numerical simulation is analyzed. This procedure is implemented as a series of ensemble experiments with a joint MPI-ESM model of the Institute of Meteorology M. Planck (Germany). For numerical modeling, a series of different initial values of the characteristic fields was specified and the model was integrated, starting from each of these fields for different time periods. Extreme ocean level characteristics over a period of 30 years were studied. The statistical distribution was built, the parameters of this distribution were estimated, and the statistical forecast for 5 years in advance was studied. It is shown that the statistical forecast of the level corresponds to the calculated forecast obtained by the model. The localization of extreme level values was studied and an analysis of these results was carried out. Numerical calculations were performed on the Lomonosov-2 supercomputer of Lomonosov Moscow State University.
Keywords: non-linear circulation models, Ensemble numerical experiments, analysis of stability of the model trajectories.

Method for Expert Search using Scientometric System Data

Alexander Sergeevich Kozitsyn, Sergey Alexandrovich Afonin
870-888
Abstract:

The use of modern methods of thematic analysis for the analytical processing of information is currently used in almost all areas of human activity, including scientometrics. Many scientometric and citation systems, including the world famous WoS, Scopus, Google Shcolar, develop thematic categories for searching and processing information. Most important tasks that can be solved using thematic classification methods are: assessment of the dynamics of the development of thematic areas in the organization, country and in world science; search for articles on a given topic; search and assessment of the authority of experts; search for journal for publication and other relevant tasks. The Lomonosov Moscow State University is currently developing and using the system ISTINA. In this project, algorithms have been created that solve some of the problems listed. Scientific research is underway to create new effective mathematical models and algorithms in this area.

Keywords: thematic search, bibliographic data, expert search, information systems, scientometrics.

International Virtual Observatory: 10 years after

О.Ю. Малков, О.Б. Длужневская, О.С. Бартунов, И.Ю. Золотухин
Abstract: International Virtual Observatory (IVO) is a collection of integrated astronomical data archives and software tools that utilize computer networks to create an environment in which research can be conducted. Several countries have initiated national virtual observatory programs that will combine existing databases from ground-based and orbiting observatories and make them easily accessible to researchers. As a result, data from all the world's major observatories will be available to all users and to the public. This is significant not only because of the immense volume of astronomical data but also because the data on stars and galaxies have been compiled from observations in a variety of wavelengths: optical, radio, infrared, gamma ray, X-ray and more. Each wavelength can provide different information about a celestial event or object, but also requires a special expertise to interpret. In a virtual observatory environment, all of this data is integrated so that it can be synthesized and used in a given study. The International Virtual Observatory Alliance (IVOA) represents 17 international projects working in coordination to realize the essential technologies and interoperability standards necessary to create a new research infrastructure. Russian Virtual Observatory is one of the founders and important members of the IVOA. The International Virtual Observatory project was launched about ten years ago, and major IVO achievements in science and technology in recent years are discussed in this presentation. Standards for accessing large astronomical data sets were developed. Such data sets can accommodate the full range of wavelengths and observational techniques for all types of astronomical data: catalogues, images, spectra and time series. The described standards include standards for metadata, data formats, query language, etc. Services for the federation of massive, distributed data sets, regardless of the wavelength, resolution and type of data were developed. Effective mechanisms for publishing huge data sets and data products, as well as data analysis toolkits and services are provided. The services include source extraction, parameter measurements and classification from data bases, data mining from image, spectra and catalogue domains, multivariate statistical tools and multidimensional visualization techniques. Development of prototype VO services and capabilities implemented within the existing data centers, surveys and observatories are also discussed. We show that the VO has evolved beyond the demonstration level to become a real research tool. Scientific results based on end-to-end use of VO tools are discussed in the presentation.
Keywords: virtual observatory, e-science, astronomical data.

Procedural Methods for Skinning Humanoid Characters

Rim Radikovich Gazizov, Aleksey Vitalevich Shubin
404-440
Abstract:

The procedure for setting vertex weights is a very time consuming and difficult task for any 3D model artist. Therefore, the use of procedural methods to facilitate this procedure is very important.


This article analyzes various skinning techniques and identifies their advantages and disadvantages. The most frequent variants of skinning defects that arise when using standard approaches are described. The analysis of tools for skinning in the Maya 3D modeling environment has been carried out. Methods for solving some of the existing problems are proposed, but do not imply a procedural solution. Also, on the basis of neural networks, an idea of their own solution was proposed as an additional tool for the Maya program. This tool will overcome most of the disadvantages of other methods and speed up the skinning process of the model.

Keywords: 3D modeling, vertexes, rigging, neural networks.

Automation of the creation of the schedule at the university: the mathematical model and methods of implementation

Ришат Ильшатович Хабипов
461-470
Abstract:

The construction of the schedule is the distribution of a discrete set of events in a given time interval, subject to the specified restrictions. The aim of the work is to describe a mathematical model of the automation of the scheduling process in an educational institution. Also the approaches to the compilation of the optimal schedule are considered. In the studied tasks a large amount of initial original information is used, which differs in its composition, and contains a large number of requirements that must be taken into account. Therefore, scheduling refers to the class of NP-complete integer programming problems, which implies that as the number of values of given variables increases, the complexity of the solution will grow exponentially. Note that the quality of the established lesson schedule directly affects the efficiency of the educational process of the university.

The article describes the process of forming the schedule of classes: at the first stage, you need to create an initial schedule based on the existing student contingent and teachers, audiences, as well as a number of additional restrictions; at the second stage, the initial schedule is optimized; at the third stage, it is allowed to adjust the received schedule by university staff.

Keywords: the task of scheduling, algorithms of integer linear programming, educational plans, class schedule.

Software for forest fire simulation with respect to weather and environmental conditions

Арслан Альфирович Гиниятов, Влада Владимировна Кугуракова, Ринат Султанович Якушев
180-192
Abstract: Prediction of forest fire dynamics is no easy task, requiring thoughtful examination of many factors involved, such as landscape, vegetation, climate and weather conditions, humidity, urbanization of land, and many others. One of the best approaches to this problem is a computer simulation. In this paper, we describe the thought process and the development of a forest fire simulator that means to address all of those difficulties.
Keywords: 3D, virtual reality, virtual simulation, forest fire simulation.

Automated System for Numerical Similarity Evaluation of Android Applications

Valery Vladimirovich Petrov
336-365
Abstract:

This paper is devoted to the design and development of a system for automating numerical similarity assessment of Android applications. The task of application similarity evaluation is reduced to the similarity evaluation of sets of control flow graphs constructed based on code from classes.dex files of applications. The similarity value was calculated based on the similarity matrix. The algorithms of graph editing and Levenshtein distance were used to compare control flow graphs. Application similarity criteria were formulated and their representation forms were investigated. Types of Android application models and methods of their construction are presented. A prototype of the system for automating the numerical evaluation of Android-applications similarity is developed. Optimization of the software solution is performed with the help of parallel programming tools. Experiments are carried out and the conclusion is made about the ability of the developed system to detect similarities between Android applications.

Keywords: Android application similarity, program similarity, similarity matrix, control flow graph edit distance, similarity matrix visualisation, control flow graph.

Signature Methods for Time Series Analysis

Kirill Alekseevich Mashchenko
681-700
Abstract:

Signature methods are a powerful tool for time series analysis, transforming them into a form suitable for machine learning tasks. The article examines the fundamental concepts of path signatures, their properties, and geometric interpretation, as well as computational methods for various types of time series. Examples of signature method applications in different fields, including finance, medicine, and education, are presented, highlighting their advantages over traditional approaches. Special attention is given to synthetic data generation based on signatures, which is particularly relevant when working with limited datasets. The experimental results on generating and predicting student digital learning trajectories demonstrate the effectiveness of signature methods for machine learning applications in time series analysis and forecasting.

Keywords: signature, signature methods, time series, data generation, trajectory analysis, digital footprint.

Formalization of Processes for Forming User Collections in the Digital Space of Scientific Knowledge

Nikolay Evgenvich Kalenov, Irina Nikolaevna Sobolevskaya, Aleksandr Nikolaevich Sotnikov
433-450
Abstract: The task of forming a digital space of scientific knowledge (DSSK) is analyzed in the paper. The difference of this concept from the general concept of the information space is considered. DSSK is presented as a set containing objects verified by the world scientific community. The form of a structured representation of the digital knowledge space is a semantic network, the basic organization principle of which is based on the classification system of objects and the subsequent construction of their hierarchy, in particular, according to the principle of inheritance. The classification of the objects that make up the content of the DSSK is introduced. A model of the central data collection system is proposed as a collection of disjoint sets containing digital images of real objects and their characteristics, which ensure the selection and visualization of objects in accordance with multi-aspect user requests. The concept of a user collection is defined, and a hierarchical classification of types of user collections is proposed. The use of the concepts of set theory in the construction of DSSK allows you to break down information into levels of detail and formalize the algorithms for processing user queries, which is illustrated by specific examples.
Keywords: recursive link, knowledge cyberdomain, digital library, detail levels, data entries hierarchy.
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