Главной целью журнала является публикация высококачественных научных статей и обзоров, отражающих передовые достижения фундаментальной науки в области вычислительной математики и информатики. Издательство: Издательский центр ЮУрГУ Главный редактор: Л.Б. Соколинский, д.ф.-м.н., профессор Редакционная коллегия Редакционный совет Тематика Редакционная этика журнала Правила для авторов Порядок рецензирования статей Регистрация Подача статьи Контакты Научный журнал «Вестник Южно-Уральского государственного университета. Серия: Вычислительная математика и информатика» включен в RSCI (К1), «Белый список» РЦНИ и входит в Перечень ВАК (К2) рецензируемых научных изданий, в которых должны быть опубликованы основные результаты диссертаций на соискание ученых степеней кандидата и доктора наук по следующим специальностям: 1.2.3. Теоретическая информатика, кибернетика (физико-математические науки); 2.3.5. Математическое и программное обеспечение вычислительных систем, комплексов и компьютерных сетей (физико-математические науки). Статьи, поданные в журнал, проходят одностороннее слепое рецензирование внешними экспертами и/или членами редакционного совета. Плата с авторов не взимается, авторские гонорары не выплачиваются. Журнал индексируется в следующих библиографических базах данных: РИНЦ (входит в ядро РИНЦ), Math-Net, DOAJ. Журнал предоставляет бесплатный открытый доступ ко всему контенту на условиях лицензии Creative Commons Attribution 4.0 License (авторы сохраняют права на свои статьи, но разрешают всем беспрепятственно скачивать, повторно использовать, перепечатывать, изменять, распространять и/или копировать статьи, при условии упоминания их авторства, без специального разрешения авторов/издателя).
Supercomputer Modeling of Supersonic Flow around Rotation Bodies of Different Shapes
The numerical approach and its parallel software implementation for studying the processes of flow around solids of complex geometry by supersonic gas flows are discussed. The aim of the study is to analyze the effectiveness of numerical schemes on unstructured hybrid grids approximating quasi-gasdynamic (QGD) equations. As an example, the problem of flowing around bodies of rotation of various shapes is chosen. The gaseous medium is represented by dry air. The system of QGD equations is considered in a one-component formulation. It is supplemented by equations of state of an ideal gas and the dependencies of kinetic coefficients on temperature and pressure. Axisymmetric gas flows around a cylinder, an ellipsoid, and a composite body are considered in numerical experiments. Calculations are performed for three values of the input flow velocity. The obtained results confirm the correctness of the developed computing technology.
Copyright (c) 2025 Computational Mathematics and Software Engineering
Distributed Computational Experiments in the MLOps Platform of HSE University
Despite the wide spread and successful application of data mining and processing tools for solving individual applied problems, the problem of developing a technology for creating such software tools has not yet been solved. In the context of a unified MLOps process for creating machine learning technologies, this paper considers the emerging problems of automating and executing distributed computing experiments on a hybrid cloud computing platform. The MLOps platform being developed at HSE University is designed to deploy intelligent services and data analysis software. The platform shall manage heterogeneous resources available locally and in the cloud environment and combine them with the resources of the HSE cHARISMa computing cluster managed with Slurm. Thus, relevant is the problem of integrating the specified resources for conducting computational experiments, implementing pipelines for setting up machine learning models, solving problems of data processing and analysis. The features of the problem being solved are the consideration of the computation process as an integral part of the technology for creating intelligent services, the need for using heterogeneous resources for this technology, and the use of the hybrid platform for the execution of computations. The paper proposes a solution to the problem of integrating computations and presents the results of testing the solution for intelligent services. We show the feasibility of such integration of heterogeneous resources in the same computational experiment based on an object model of the experiment extended by the user and a domain-specific language for its specification, and resolve the issues of dynamic management of the deployment of intelligent applications, integration of data processing pipelines, services and data sets for performing distributed computational experiments.
Searching of Optimal Weights for the Akushsky Core Function
Modern computational tasks involving the processing of large numbers require not only high accuracy but also significant speed. In this context, the use of the residue number system offers an approach to parallel big data processing used in cryptography, signal processing and artificial neural networks. Despite the advantages of the residue number system, its diffusion has been slow due to the computational complexity of the so-called non-modular operations of the residual class system. One of the universal tools for realising non-modular operations is the Akushsky core function. This paper studies the Akushsky core function as a tool for determining the positional characteristic of a number in the residue number system. The application of Monte Carlo method and genetic algorithm is proposed to find the optimal weights of the core function. Experimental results demonstrate that the genetic algorithm provides more stable results when the number of moduli increases, while the Monte Carlo method is effective on small dimensions. The genetic algorithm is on average 38% faster than the Monte Carlo method, making it the preferred choice. Additionally, the computation time of the core function with optimal weights and the Pirlo function were compared. The results showed that the core function with optimal weights is on average 14% faster than the Pirlo function.
Improving Value-at-Risk Estimation for Multivariate Portfolios Using a Mixture of Probabilistic Principal Component Analyzers
This paper proposes a novel approach for estimating the Value-at-Risk (VaR) of multidimensional portfolios, based on a mixture of probabilistic principal component analyzers (mPPCA) and the Akaike information criterion. The effectiveness of the proposed approach is evaluated on historical data, accounting for various numbers of mixture components in the mPPCA method. The study is performed on 100 highly diversified and 100 weakly diversified stock portfolios of the S&P 500 index over the 2009–2023 period, using rolling windows of 350 trading days. Probabilistic principal component analysis (PPCA) can model complex dependencies among assets while capturing the “heavy” tails of return distributions. As a result, the mPPCA method surpasses conventional principal component analysis (PCA) in the accuracy of VaR estimation. In addition, by reducing dimensionality, the model is computationally much more efficient and stable than a mixture of Gaussian distributions (GMM). The paper demonstrates how portfolio return volatility and tail heaviness depend both on the optimal number of components in mPPCA and on the minimal sufficient number of principal components in PCA and PPCA needed to explain 80 % of the variance in the data. The new approach, which optimizes the number of components in mPPCA, consistently achieves higher performance than GMM, PCA, or PPCA, especially for less diversified portfolios. The paper describes methods for optimizing mPPCA training and provides an extensive historical performance evaluation (backtesting). By employing just-in-time compilation, a “warm start” for mPPCA with each new window position, and a three-step algorithm for VaR estimation, the experiments are significantly accelerated compared with the standard implementation.
Fault Diagnosis of Rolling Bearings Using Spectral Peaks and Neural Networks
The most important components of machine parts are rolling bearings, the condition of which is necessary to control, since possible defects in their design can lead to incorrect operation or general failure of machines. Modern solutions on fault diagnosis of bearings typically use complex feature extraction processes, such as their Hilbert spectrum imaging and a further powerful neural network to classify them. In this article, we propose a simple, but, nevertheless, an effective algorithm for solving this problem. To extract features from a signal, we divide the signal spectrum into equal subintervals and find the amplitude maximum and the corresponding frequency value in each of them. In the article, based on the t-SNE method, it is shown that the features selected in this way, despite their small size, represent different types of signals well. At the second stage, the selected features are fed to the input of a simple classifier neural network. The proposed method is computationally simple, both at the stage of feature extraction and at the stage of neural network training. Despite this, the method gives 100% accuracy for all types of signals on short data from the IMS dataset.
Copyright (c) 2022 Computational Mathematics and Software Engineering
Innovation Ecosystem of a World-Class Inter-University Campus: Management and Educational Aspects
Thе article is devoted to the current issues of forming an ecosystem of a modern world-class inter-university campus. The article focuses on the significance of the campus as an important element of the scientific and technological development system of the Russian state; considers the process of modeling an effective management system of a world-class inter-university campus using the example of the campus in the Chelyabinsk region; outlines the potential structure of the innovative ecosystem of such a campus, ensuring the success of educational and management processes implemented within the framework of the campus project by its participants and partners in the interests of economic, industrial and social development of the region. The authors analyze in detail the Strategy for Scientific and Technological Development of the Russian Federation, approved by Decree of the President of the Russian Federation dated February 28, 2024 No. 145, as well as the materials of the strategic session “Formation of Effective Campus Management Models”, held on December 11–13, 2024 in Ufa and also undertake a review of existing models of digital platforms and innovative ecosystems used to implement management and other processes in various large-scale projects. Based on the results of the conducted research, conclusions were made about the need and directions for improving the studied ecosystem, its management and educational aspects, as well as the need for further scientific understanding of the indicated issues, which is ultimately intended to contribute, among other things, to the achievement of technological sovereignty of the Russian Federation.
International Level Campus: Creating Complex Digital Platforms for Implementation of Inclusive Processes in the Academic Environment and Beyond
The study’s major hypothesis suggests the presence of a need for digitalization of an international-level campus by creating a complex digital platform on its basis. The following are proposed as components of such a platform: an internal social network, educational services and units, special-purpose services and units, a campus dashboard with possibility of online interaction with the city (representatives of the business community, industries and citizens). Based on the results of the latest multidisciplinary studies by domestic and foreign scientists, the authors prove that the introduction of such components will contribute to increasing the efficiency of the implementation of inclusive processes in the academic environment and beyond, increasing the prestige and competitiveness of beneficiaries, academic mobility, improving the psychological well-being of students, as well as attracting additional funding for both the platform itself and the educational institutions included in the inter-university union. The novelty of the research conducted within the framework of this article lies in the possibility of using existing domestic programs to create new types of multi-component digital platforms operating in a single window mode, the functionality of which will be able to satisfy a number of needs of the population, business and the state, reflected in national and regional strategic development programs.
Integration of Missing Data Imputation Tools for Time Series in Real-Time Mode into a Relational DBMS
The article addresses the problem of integrating time series imputation into relational database management systems (RDBMS). A method called ImputeDB is proposed, which enables the real-time integration of neural network-based imputation models into the PostgreSQL RDBMS. The imputation of missing values is carried out through triggers (stored functions automatically executed by the RDBMS kernel when new data is inserted). When a trigger is activated, missing values are replaced by synthetic ones generated by a neural network model. Using the proposed method, a database application programmer can integrate the process of imputing missing values into the standard time series processing pipeline within the PostgreSQL RDBMS, without relying on external services. The proposed approach includes a set of components implemented as user-defined functions (UDFs) in Python and PL/Python: Trigger Constructor, Model Manager, Model Storage, and Imputer. The Trigger Constructor is used to create triggers that automatically perform imputation of missing values in inserted data. The Model Manager is responsible for training neural network models, while the Model Storage is used to save these models in a file-based repository. The Imputer, in turn, synthesizes missing values using the trained models. Experiments were conducted to evaluate the performance of the ImputeDB method. The experiments measured the processing time of data insertion with automatic gap imputation as a function of the time series dimensionality. Experiments were performed under two scenarios: single and multiple insertions. Neural network-based imputation models with various architectures, including recurrent neural networks, autoencoders, and transformers, were employed. The experimental results demonstrated that under conditions of increasing time series dimensionality and rising overhead from network requests and data transfer, ImputeDB exhibits superior performance. Specifically, the system achieved an efficiency gain of 22.5% compared to another approach, while maintaining the accuracy of the employed imputation methods.
Intelligent Binocular Compound Eye Vision System for Detecting Azimuth and Distance to Object on Plane
The article is devoted to the prototype of an artificial binocular compound eye vision system for detecting the azimuth and distance to an object on a plane using an artificial neural network. A analytical review of modern distance and azimuth detection systems based on active and passive sensors is given. An intelligent binocular vision system is proposed, which is a passive optical sensor that allows you to determine the azimuth and distance to a round object of arbitrary size, emitting in the visible or infrared ranges of the electromagnetic spectrum. The general architecture of the compound eye vision system is considered. The main structural elements of the system are: an optical module, a hardware and software controller and a neural network module. The optical module uses a pair of lenses to convert the light signal from the object into two pixel Fourier images, which are fed to the input of the hardware and software controller. The controller performs primary processing of pixel Fourier images and converts them into two bit masks, the elements of which correspond to separate facets (each facet integrates four adjacent columns of the pixel image). The resulting bit masks are fed into a neural network module, which, based on their analysis, determines the coordinates of the object in the form of distance and azimuth.
Precise Localization of PDF417 Code Based on Fast Hough Transform
The PDF417 is a popular barcode symbology which is widely used in a huge variety of business processes. In this paper, we propose an original method for precise PDF417 code localization. It can successfully process projectively distorted images captured via the mobile device cameras. The core of this method is the analysis of the Fast Hough Transform image. This analysis is aimed to: (a) determine the line, corresponding to the vanish point of vertical symbol sides, using the RANSAC algorithm; (b) select the best pair of Hough-points corresponding to the horizontal symbol sides. We also propose the evaluation methodology for assessing the accuracy of precise PDF417 localization and a new dataset SE-PDF417-SYN-400, which consists of 400 synthesized PDF417 images and is publicly available. The accuracy of the proposed method on SE-PDF417-SYN-400 is equal to 0.948, and its error rate is about four times less than the one obtained by the popular ZXing detector. The average running times on iPhone 8 and iPhone 14 Pro Max mobile devices are equal to 77 and 34 ms per image correspondingly.
Copyright (c) 2024 Computational Mathematics and Software Engineering
Towards a loss function for training neural network models of time series imputation
In the article, we touch upon the problem of choosing a loss function for training neural network models for imputation of missing values of multidimensional time series and introduce a novel loss function called MPDE (Mean Profile Distance Error). The MPDE function for real and reconstructed m-length subsequences is calculated as the average of the distances between all pairs of ℓ-length sliding windows of these subsequences, where ℓ ⩽ m and above windows have the same starting points. The distance between two windows is a modification of the MPdist (matrix profile distance) similarity measure and is defined as the weighted sum of the Euclidean and z-normalized Euclidean distances between these windows. The above weights are taken from the range [0,1] and are the hyper-parameters of the loss function. When training a neural network model, MPDE allows taking into account the behavioral similarity of the compared subsequences through the presence of similar windows in them, regardless of the relative locations of these windows. Since MPDE has a high computational complexity, we implement a parallel algorithm for its calculation on a GPU to incorporate MPDE into deep learning frameworks. The algorithm is implemented using the PyTorch framework, where MPDE is represented as a sequence of automatically parallelizable operations with multidimensional tensors. Experiments over multidimensional time series from various subject domains showed that in 78% of cases state-of-the-art neural network models achieve their highest imputation accuracy (in terms of the RMSE metric) when using the proposed loss function; at the same time, the above models demonstrate imputation accuracy 40% higher than the average value achieved when using other loss functions.
Deep Learning Method for Anomaly Detection in Streaming Multivariate Time Series
The article touches upon the problem of detecting anomalous subsequences of multivariate streaming time series, where the elements arrive in real time, which currently arises in a wide range of subject domains: industrial Internet of Things, personal healthcare, etc. In the article, we introduce a novel method to solve such a problem, called mDiSSiD (Discord, Snippet, and Siamese Neural Network-based Detector of multivariate anomalies). The mDiSSiD method employs the time series discord concept (a subsequence with the most dissimilar nearest neighbor), which is generalized to the multivariate case. Multivariate discord refers to the N-dimensional subsequence of a d-dimensional time series (where 1 ⩽ N ⩽ d), which is the most dissimilar to all other subsequences of N-dimensional time series obtained by composing all the possible combinations of d series of N. Anomaly detection is implemented through a deep learning model based on the Siamese neural network architecture. Experimental evaluation of mDiSSiD over real time series from various subject domains showed that the proposed method is on average ahead of state-of-the-art analogs based on other deep learning approaches (convolutional and recurrent neural networks, autoencoders, and generative-adversarial networks) in terms of anomaly detection accuracy.
On Numerical Method for the Stokes Problem with Neumann Boundary Conditions in Non-convex Domain
The Stokes problem with Neumann boundary conditions with an incoming angle at the boundary of the two-dimensional domain is considered. The concept of an R_v-generalized solution in sets of weighted Sobolev spaces is introduced. A weighted finite element method on a uniform grid is constructed based on the secondorder Taylor-Hood finite element pair and the introduction to the basis of a weight function in some powers v* and μ* for the components of the velocity field and the scalar pressure function, respectively. The weight function in the domain coincides with the function of the distance from the point to the vertex of the incoming angle in some δ-neighborhood and the constant δ outside it. Numerical experiments in the non-convex domain is carried out. The convergence rate of the approximate solution to the exact one is obtained, which is independent of an incoming angle value and exceeds the convergence rate for the classical FEM. The convergence result is achieved without geometric refinement of the mesh in the vicinity of the singularity point. A series of numerical experiments for different values of an incoming angle was carried out and the domain of suitable free parameters of the proposed approach is found. For any point of the constructed domain, an optimal result, from the point of view of convergence, is achieved. The area of choice of suitable free parameters differs from the area for the considered problem with Dirichlet boundary conditions.
Classification of Streaming Time Series Based on Neural Network Technologies and Behavioral Patterns
Data mining of streaming time series is a topical task that occurs in a wide range of subject areas. This article presents the SALTO method (Snippet and Autoencoder based Labeling of Time series coming Online), which combines a neural network model for classifying streaming time series and an analytical method for automatic labeling of training set based on behavioral patterns (snippets). The lightweight architecture of the neural network model used makes it possible to achieve low latency when classifying streaming data. The method involves two stages: preprocessing and classification. At the preprocessing stage, the Preprocessor searches for the optimal value of the length of the subsequence of the input series and performs its labeling. The resulting labels are used to create a training set for the Extractor. The Extractor performs the extraction of the snippet of the input subsequence and assigns it a class based on the similarity of the extracted snippet with snippets from the training set. The experimental results showed that the proposed method performs the classification of a single subsequence in less than 10 ms, which allows SALTO, unlike other competitors, to be used in industrial Internet of Things applications with high performance requirements in accordance with the URLLC (Ultra-Reliable Low Latency Communications) standard.
TASC Software for HPC Performance Analysis: Current State and Latest Developments
To ensure high operating efficiency of modern supercomputers, it is necessary to constantly analyze and control various aspects of their behavior, paying special attention to the flow of supercomputer applications running on these machines. To solve this problem, the TASC (Tuning Applications for SuperComputers) software suite was previously developed. It automatically detects performance issues in HPC applications and evaluates the efficiency of using supercomputer resources, provides supercomputer administrators with a flexible report tool for analyzing different aspects of supercomputer functioning with the desired level of detail, and estimates the noise level on compute nodes. This paper provides full-scale description of current TASC structure and capabilities, including the stages of data processing and storing, as well as performing different types of analysis. It also describes new results obtained and methods developed within one of the main TASC components — assessment system for quick and accurate evaluation of HPC resources usage efficiency.
Optimal Control of Three Work-Stealing Deques Located in Two-Level Memory
The problem of even balancing of tasks between threads may arise during parallel computations. One way to resolve this issue is to implement distributed dynamic load balancing. In this balancing method each worker thread has its own task queue, and threads themselves distribute further tasks. One of the widely used distributed dynamic balancing methods is “work-stealing”: a thread that runs out of tasks begins to “steal” them from another thread. To utilize this method, each thread must have its own specialized deque where pointers to tasks are stored. In this paper, we propose and examine a new method for representing three work stealing deques in two-level memory. We consider the case of working with three deques, where one section of fast memory contains two LIFO parts of the deques, i.e., two stacks that grow towards each other. Third LIFO part and three FIFO parts are located in the other section of fast memory. FIFO parts are combined into one FIFO queue, from which elements are only deleted (being stolen). The middle parts of the deques are located in slow memory. They are accessed when LIFO or FIFO parts located in fast memory are empty or overflowed. We consider the problem of finding optimal partition of fast memory for three deques with predetermined probabilities of operations. This choice depends on the characteristics of memory levels, operation probabilities, and optimality criteria. The optimality criterion is the maximum mean system operating time (the average number of operations) before memory reallocation.
Designing the Optimal Trajectory for Monitoring Objects
The article considers the task of developing a system for modeling the trajectories of a robot monitoring in a closed area from the ground: inspection of premises, survey of industrial facilities, assessment of the condition of fruit trees, etc. During monitoring, some obstacles may arise in the robot’s path: temporary and removable (people, small furniture, household appliances, emergency zone) or permanent (walls, permanently installed equipment, fixed furniture). The robot is controlled using a program developed by the authors, which stores a database of routes successfully overcome by the robot earlier, for the most accurate determination of the trajectory of the robot, taking into account obstacles encountered along the constructed path. The article considers an algorithm for constructing a graph model of the monitoring area for the subsequent search for the shortest route of the robot, which consists in discretization the area, identifying possible ways to move the robot, analyzing existing obstacles and setting distances between the objects of study. It is shown that after obtaining such a graph, it is possible to apply one of the algorithms for finding the Hamiltonian path in a graph. It connects the vertices of the graph corresponding to the monitoring points. The result of applying the algorithm is the shortest route of the robot, or a message about the impossibility of monitoring (partial or complete insolubility of the problem) if a number of obstacles do not allow you to plot a route passing through some (or all) vertices.
Discrete Mathematics and Mathematical Cybernetics
Numerical Implementation of Surface Movement Method in Linear Programming
The article is devoted to the numerical implementation of a new linear programming method called the surface movement method. The implementation is based on the AlFaMove algorithm, which builds, on the surface of the feasible polytope, the optimal objective path from an arbitrary boundary point to a point that is a solution to the linear programming problem. The optimality of the path lies in the fact that the direction of movement along the face of the polytope corresponds to the maximum increase in the value of the objective function. To calculate the optimal direction of movement, a method based on the operation of pseudoprojection onto a linear manifold is used. The pseudoprojection operation is a generalization of the notion of orthogonal projection. Pseudo projection is implemented using an iterative projection-type algorithm. The proposition is proved that the pseudoprojection coincides with the orthogonal projection in the case of a linear manifold that is the intersection of hyperplanes. It is also proved that, in the case of a linear manifold, the pseudoprojection method calculates a movement vector that coincides with the direction of maximum increase of the objective function. A parallel implementation of the AlFaMove algorithm is performed. The results of computational experiments on a cluster computing system are presented, which demonstrate the high scalability of the proposed numerical implementation.
Analysis of the Execution of Fragmented Programs Based on SLOW Factors
When executing parallel programs based on the task parallelism paradigm, several issues need to be addressed, such as choosing the order in which tasks are started, considering the dependencies between them, distributing data and tasks across parallel processes, and balancing resource utilization. These issues fall under the category of system-level parallel programming and are typically handled by a dedicated execution system. The final performance of a parallel program depends on how effectively these issues are addressed, as well as the structure and characteristics of the underlying algorithm. If the program’s performance is insufficient, optimization may be required, which necessitates identifying the bottlenecks that hinder its performance. Profiling can be used to pinpoint program bottlenecks by collecting performance metrics that may reveal the source of performance issues. However, the conventional tools commonly used for profiling parallel programs are not able to provide an answer in terms of the required concepts, due to the difficulty in analyzing the asynchronous execution of multiple tasks, as well as the inability to differentiate between application (multiple tasks) and system (operating system) components within an executing program. Consequently, such programs necessitate the development of novel profiling and analysis techniques. The paper discusses the problem of obtaining comprehensible performance characteristics of task-based parallel programs for performance analysis and optimization. It is suggested to evaluate the influence of the following factors: Starvation, Latency, Overhead andWaiting for contention resolution (SLOW). An algorithm for obtaining the corresponding characteristics for the LuNA fragmented programming system is presented, as well as a method for analyzing them to optimize LuNA programs. The correctness of the approach has been demonstrated on a number of synthetic tests. The application of the approach to the analysis of the “real-world” numerical simulation program is shown.
Building Recognition Hybrid Algorithm for Satellite Images Based on the Beetle Method and the Area Exclusion Algorithm
The article proposes a new method for recognizing buildings on satellite images. The proposed method is a hybrid, it is based on the region exclusion algorithm and the beetle method. The region exclusion algorithm is a well-known and effective approach to object detection on the image. Its main idea is to segment an image into regions of similar pixels based on various characteristics: color, texture, brightness, shape, etc. The beetle method is a classic contour analysis method that sequentially draws the boundary between an object and its background. As part of the proposed method, the beetle method first identifies potential areas where buildings may be located. The region exclusion method then eliminates unwanted elements in the image (vegetation, water surfaces and roads) that could be falsely identified as buildings, and accurately determines the location and outline of buildings. The offered algorithm shows good recognition accuracy regardless of image quality and does not require a training sample. The article also describes the software implementation of the proposed method and discusses the results of computational experiments to assess the quality of the method and compare it with three well-known recognition algorithms.
Imputation of Multivariate Time Series Based on the Behavioral Patterns and Autoencoders
Currently, in a wide range of subject domains, the problem of imputation missing points or blocks of time series is topical. In the article, we present SAETI (Snippet-based Autoencoder for Time-series Imputation), a novel method for imputation of missing values in multidimensional time series that is based on the combined use of autoencoders and a time series of behavioral patterns (snippets). The imputation of a multidimensional subsequence is performed using the following two neural network models: The Recognizer, which receives a subsequence as input, where the gaps are pre-replaced with zeros, and determines the corresponding snippet for each dimension; and the Reconstructor, which takes as input a subsequence and a set of snippets received from the Recognizer, and replaces the missing elements with plausible synthetic values. The Reconstructor is implemented as a combination of the following two models: An Encoder that forms a hidden state for a set of input sequences and recognized snippets; and a Decoder that receives a hidden state as input, which imputes the original subsequence. In the article, we present a detailed description of the above models. The results of experiments over time series from real-world subject domains showed that SAETI is on average ahead of state-of-the-art analogs in terms of accuracy and shows better results when input time series reflect the activity of a certain subject.
Multimodal Dynamic Graph CNN for 3D Semantic Segmentation
In this paper, a semantic segmentation method of point clouds in the form of terrain using a new multimodal convolutional neural network architecture based on a regular dynamic weighted graph, which allows to obtain an accurate solution to the segmentation problem based on a fusion of geometric and color features. The method can be effectively used for sparse, noisy, inhomogeneous and non convex point clouds. The computer modeling of state-of-the-art methods for 3D semantic segmentation was carried out using the reference data collection ModelNet 40 and a data set of archaeological sites of the Bronze Age of the Southern Trans-Urals, namely data obtained as a result of a total station survey (the Trimble 3300 total station) of a complex of archaeological sites in the valley of the Sintashta river. A comparative analysis of the proposed method and state-of-the-art methods for 3D semantic segmentation with different combinations of input features of point clouds was carried out, and the method influence of forming a point cloud on the accuracy of 3D semantic segmentation was also investigated: in the first case, a point cloud from a reference dataset was studied, in the second case, variants using 3D registration based on NICP and FICP algorithms were applied.
Image Reconstruction by the Method of Reverse Projection Using Wavelet Filtering of Projection Data in X-ray Computed Tomography
The article presents a method for reducing the error of image reconstruction for X-ray computer tomography by using wavelet filtering of noisy projection data. The wavelet transformation and the wavelet filtering of one-dimensional signals based on it makes it possible to determine a specific place of correspondence between the frequency and time (in this case, the spatial coordinate of the detectors) region. This makes it possible to uniquely determine the transition from the frequency domain to the spatial domain and vice versa. To filter the projection data, the wavelet transform is used, which makes it possible, through coefficients defining scaling functions and wavelet functions, to determine in the frequency and spatial domain the place of noise in a noisy signal and to isolate a non-noisy signal by assigning filtering thresholds to the above coefficients. To enhance the filtering properties of the wavelet transform, it is proposed to divide the projection data into intervals, for each of which its coefficients are determined. Wavelet filtering is carried out using Daubeshi wavelets. The research results were confirmed by mathematical modeling of noisy projection data, their wavelet filtering and reconstruction of the test tomographic image based on them. The mathematical model of the test object of the study and the software reconstructor of the tomographic image developed by the authors made it possible to simulate direct (obtaining projection data on the test object), reverse (obtaining a test tomographic image from the projection data of the object) tomography tasks and to carry out a comparative analysis of the quality of image reconstruction with “ideal” and noisy projection data.
Classification of Multimodal Lung Disease Data Based on Late Fusion of Modalities
With the development of technology, high-quality X-rays have become available for the diagnosis of lung diseases with the help of radiologists. However, the diagnostic process takes a lot of time and depends on the availability of specialists in a medical institution. At the same time, patient information may include not only chest X-rays of different quality, but also the results of medical tests, doctor’s notes and prescriptions, information about taking medications, and others. In this study, we propose a model for the classification of pulmonary diseases based on multimodal data on clinical studies of patients and radiographic images. When preparing the data, we used various methods of generating artificial samples for both images and tabular data on the results of laboratory studies. We have proposed a method for establishing a correspondence for generated samples between modals. The proposed multimodal model has a late fusion architecture. We conducted experiments on datasets with one modality and two modalities. Our model showed accuracy 5.5% higher than models based on single-modality (91.3% vs. 86.11% on a dataset of 1,156 patients).
The Laplace–Stieltjes Transformation of the Distribution Function of the Peak Age of Information in a Multichannel Transmission Group
This article continues the author’s cycle of works devoted to the problem of the Age of Information (AoI), a metric used in information systems for monitoring and managing remote sources of information from the control center. The theoretical analysis of information transmission systems requires a quantitative assessment of the “freshness” of information delivered to the control center. In this paper, we consider a model of a two-node transmission group consisting of an information source (sender node), a control center (recipient node) and several communication channels between them. It is assumed that the channel capacities may be different. At the same time, the network protocol requires that the information received by the recipient node be read in the same sequence as it was transmitted from the sending node. As a result, packets that violate the established order are delayed at the sending node for the time required to restore order. In this paper, the information transfer process is modeled using a multichannel queuing system with a limited storage, Poisson flow of applications, exponential maintenance and reordering of applications. At the same time, applications simulate packets of transmitted information, the system storage is a queue of packets for transmission, the service of applications on devices of varying intensity is the process of transmitting packets over communication channels. This model was used for the first time to estimate the age of information. As a result of the conducted research, expressions for the Laplace–Stieltjes transformation of the stationary distribution function and the initial moments of the maximum value of the information age, called the peak age, were obtained. A numerical study of system performance indicators has been conducted, including an analysis of the peak age of information at various system loads. The correctness of the analytical results is confirmed by the results of simulation modeling.
On the Non-existence of a Simple Version of the Polynomial Algorithm for Extracting the Root from the Language
For the usual operation of concatenation of words considered as multiplication, the concatenation of languages is obviously determined, and on the basis of the last operation, the degree of the language and the root of a given degree (if available) is determined. When describing algorithms for constructing a language that is a root of degree M from a given language, so called potential roots are of great importance: these are the words (not the languages) whose considered M-th degree is included in a given language. It is easily to show that all potential roots for a given language are constructed using a polynomial algorithm. This task, apparently, is not simplified when considering words and languages over the 1-letter alphabet, which is done in this paper. So called taboo pair of potential roots is a pair whose word concatenation is not included in the language. In previous publications on the topic of describing algorithms for extracting roots from a language, the hypothesis arose that a polynomial algorithm for extracting a root from a language can be described on the basis of considering the set of taboo pairs only, by iterating over specially described subsets of the set of potential roots. This paper shows, that such an algorithm (called “simple”) is impossible, i.e., if there is a polynomial algorithm for extracting the root from the language, then this algorithm must use some additional information.
Distribution of Squares and Hypothesis Verification in Odd Integer Partitions
The article considers partitions of a natural number n whose parts are distinct, odd and their product is not a square. Such partitions are applicable for determining the rank of the group of central units of an integral group ring of an alternating group. The number of partitions grows exponentially, hence the enumeration task is computationally expensive. The article proposes a parallel algorithm in shared memory for finding the number of partitions of the n with additional conditions. The algorithm is based on the concept of data parallelism and the use of nested parallelism. A set of lengths K of the partition of the n is obtained, the elements of which are processed in parallel. During the processing of the length k of the partition of the n, the set of levels L is obtained, the elements of which are processed in parallel as well. Acceptable values of speedup and parallel efficiency of the proposed algorithm are obtained by using two threads per parallel length region and two threads per parallel level region. Thus, the speedup for distinct n increases to 2.1, and the parallel efficiency does not decrease below 50 %. The results obtained were used to check Kargapolov’s hypotheses and analyze the distribution of the number of odd partition in certain ranges. An algorithm for finding the optimal coefficient c is proposed. Using this algorithm, an asymptotic formula for the number of partitions of the n is obtained, in which the parts are distinct, odd and their product is a square. This formula is based on experimental data and formulated as a conjecture.
A Program Study of Semilattices Connected with the Waterloo Automaton
The paper is devoted to the study of semilattices containing covering automata for the Waterloo automaton. In the initial sections of the paper, the process of constructing covering automata on the basis of subsets of the grids of the original automaton is described (each grid represents some set of arcs associated with the original automaton), and also the properties of semilattices formed by covering automata are considered. The main result of the paper is a complete description of the obtained semilattices from the point of view of equivalence of the covering automata included in them to the original Waterloo automaton. Three classes of semilattices are distinguished, each of which has special properties. For the semilattice constructed on the basis of a minimal covering automaton, a graphical representation is obtained, which allows us to visualize the relations between its sets consisting of pairwise equivalent automata. In addition, a criterion of equivalence of the covering automaton to the Waterloo automaton is formulated in terms of the properties of the subset of grids defining the covering automaton. The study was carried out using the NFALib library for analysis of nondeterministic finite automata, implemented by the author in the C# language. The relevance of the study of the Waterloo automaton is connected with its role in the study of the problem of vertex minimization of nondeterministic finite automata and the development of real-time heuristic algorithms used for its solution.
Investigation of the Possibilities of Parallelism for Forecasting Using a Quasi-linear Recurrent Equation
Time series analysis and forecasting are one of the widely researched areas nowadays. Identification using various statistical methods, neural networks or mathematical models has long been used in various fields of research from industry, to medicine, the social sphere, and the agricultural researches. The article considers a parallel version of the algorithm for identifying the parameters of a quasi-linear recurrent equation for solving the task of regression analysis with interdependent observable variables, based on the generalized least modules method (GLDM). Unlike neural networks, which are widely used nowadays in various forecasting systems, this approach allows us to explicitly obtain qualitative quasi-linear difference equations that adequately describe the considered process. This makes it possible to improve the quality of the studied processes analysis. A significant advantage of the model using the generalized least deviation method, in comparison with numerous neural network approaches, is the possibility of interpreting the coefficients of the model from the point of view of the research task and using the resulting equation as a model of a dynamic process. The conducted computational experiments using time series show that the maximum acceleration of the algorithm occurs when using the number of threads equal to half of the possible threads for a given device.
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Control Methods of Work-stealing Deques in Dynamic Schedulers of Multiprocessor Parallel Computations
In parallel task schedulers, which are using the work-stealing strategy, each processor has own task deque. One end of the deque is used for insertion and deletion of tasks only by the owner, and the other is used for stealing of tasks by other processors. The article offers an overview of work-stealing deque’s description of the deque’s optimal management problems, which our team had solved for the work-stealing strategy. The idea of the algorithm for deque’s managing in two-level memory is that if the memory allocated to the deques becomes overflow, elements are redistributed between memory levels. Elements from the deque’s ends are stored in fast memory, since they will be worked with in the near time, and elements from the deque’s middle part are stored in slow memory. In this case, it is necessary to determine the required number of elements that need to be left in fast memory, depending on the optimal criteria and system parameters.