Abstract For systems of ordinary differential equations (ODEs) with a nondegenerate linear part in the general and Hamiltonian cases, the problem of finding invariant coordinate subspaces in the coordinates of the normal form calculated in the vicinity of the equilibrium is stated. Conditions for the existence of such invariant subspaces in terms of the resonant relations between the eigenvalues of

Abstract On the basis of Newton’s recurrent formulas, an algorithm for constructing the resultant of two entire functions is described. This algorithm helps eliminate unknowns from systems of nonalgebraic equations. This algorithm is implemented in the computer algebra system Maple. Examples demonstrating the operation of the algorithm are discussed.

Abstract Polynomial factorization is a classical algorithmic algebra problem with a wide range of applications. Of particular interest is factorization over finite fields, among which fields of order two are probably the most important ones when representing Boolean functions by Zhegalkin polynomials. In particular, factorization of Boolean polynomials corresponds to conjunctive decomposition of Boolean

Abstract In this paper, we propose a package for symbolic construction of exponential–logarithmic solutions to linear differential equations whose coefficients are represented in incomplete form, i.e., as power series for which only a finite number of initial terms is known. The series involved in the solutions are also represented in incomplete form. For each such series, the maximum possible number

Abstract This paper proposes two simple methods for determining equilibrium orientations of a satellite moving in a central Newtonian force field along a circular orbit under the action of the gravitational torque. The first method uses linear algebra approaches, while the second one employs computer algebra algorithms. The equilibrium orientations of the satellite in the orbital coordinate system

Abstract In this paper, we investigate the behavior of quantum entanglement in the process of unitary evolution in constructive models of multicomponent quantum systems. Symmetry groups of quantum systems that admit the occurrence of geometric structures associated with quantum entanglement are described. Algorithms for dynamic simulation of quantum entanglement are based on methods of computer algebra

Abstract Recently, the place of the main programming language for scientific and engineering computations has been little by little taken by Julia. Some users want to work completely within the Julia ecosystem like they work within the Python ecosystem. There are libraries for Julia that cover the majority of scientific and engineering computations demands. The aim of this paper is to combine the usage

Abstract Computer algebra is increasingly used in research and applied computations. An example is tensor computations or, in a wide sense, simplification of expressions containing indices. In this paper, the method of colored graphs designed for simplifying abstract expressions containing indices is developed for the case when the indices are of different types. An example of such indices are upper

Abstract An algorithm for finding the solution to the Cauchy problem for a two-dimensional difference equation with constant coefficients at a point using computer algebra is described. In the one-dimensional case, solving the Cauchy problem is easy; however, already in the two-dimensional case the number of unknowns rapidly increases at each step. To automate the process of computing the solution

Abstract In this paper, we consider the problem of constructing the first terms of formal Laurent series that act as solutions to a given component yk (\(1 \leqslant k \leqslant m\)) of a vector of unknowns y for a differential system \(y{\kern 1pt} ' = Ay\), where \(y = {{({{y}_{1}}, \ldots ,{{y}_{m}})}^{T}}\) and A is an m × m matrix whose elements are d-truncations of formal Laurent series, i.e

Abstract This paper investigates the problem of symbolic representation for the general solution of a system of ordinary differential equations (ODEs) with symbolically defined constant coefficients in the case where some symbolic constants can vanish. In addition, the symbolic representation of eigenvectors for the system’s coefficient matrix is not unique. It is shown that standard procedures of

Abstract We consider the task of capturing the result of a researcher-driven stereo visualization of a complex dynamic virtual scene into a video sequence of stereo pairs (stereo clip) of ultrahigh resolution. An efficient technology of deferred synthesis of stereo clips is proposed. It allows one to create stereo clips without interfering with real-time visualization. The technology includes real-time

Abstract In this paper, we discuss the problem of searching for equilibrium states of Atwood’s machine in which a pulley of a finite radius is replaced by two separate small pulleys and both masses can oscillate in a vertical plane. Differential equations of motion for the system are derived, and their solutions are computed in the form of power series in a small parameter. It is shown that, in the

Abstract In research problems that involve the use of numerical methods for solving systems of ordinary differential equations (ODEs), it is often required to select the most efficient method for a particular problem. To solve a Cauchy problem for a system of ODEs, Runge–Kutta methods (explicit or implicit ones, with or without step-size control, etc.) are employed. In that case, it is required to

Abstract This paper discusses automated software testing technologies for industrial systems of computer graphics and optical modeling. Test automation becomes vital in the case of limited resources and frequent releases of program versions, which is a typical situation for software developers. In this paper, we consider both regression testing methods for computing kernels of software complexes and

Abstract In this paper, we propose some heuristic probabilistic polynomial time algorithms with one-sided error for recognition of cubic hypersurfaces the singular loci of which do not contain any linear subspace of sufficiently large dimension. These algorithms are easy to implement in computer algebra systems. The algorithms are based on checking the condition that the Hessian determinant of a cubic

Abstract In this work, we present purely subword-based alternatives to fastText word embedding algorithm The alternatives are modifications of the original fastText model, but rely on subword information only, eliminating the reliance on word-level vectors and at the same time helping to dramatically reduce the size of embeddings. Proposed models differ in their subword information extraction method:

Abstract Graph data models are widely employed in different areas of computer science, e.g., graph databases, bioinformatics, social network analysis, and static code analysis. Querying for specific paths is one of the main problems solved in graph data analysis. Path queries are usually performed by means of a formal grammar that describes admissible edge labeling of the paths. A path query is said

Abstract This paper proposes an algorithmic implementation of the elementary version of Runge’s method for a family of fourth-degree Diophantine equations in two unknowns. Any Diophantine equation of the fourth degree the leading homogeneous part of which is decomposed into a product of linear and cubic polynomials can be reduced to equations of the type considered in this paper. The corresponding

This article has been retracted. Please see the Retraction Notice for more detail: https://doi.org/10.1134/S0361768820220016

Abstract In the last years Autonomous vehicle navigation has had considerable improvements; however, this technology has not yet been able to effectively be integrated with mobile systems that work inside buildings, houses or without the influence of absolute references such as GPS. It is for this reason that this paper provides a methodological proposal that allows the integration of the use of object

Abstract Scientific applications requires to process, analyze and transfer large volumes of data in the shortest possible time from distributed data sources. In order to improve their performance, it is necessary to provide them with specific QoS parameters. On the other hand, SDN is presented as a new paradigm of communications networks that facilitates the management of the communications infrastructure

Abstract The article discusses the search for a global extremum in the training of artificial neural networks using a correlation indicator. A method based on a mathematical model of an artificial neural network presented as an information transmission system is proposed. Drawing attention to the fact that in information transmission systems widely used methods that allow effective analysis and recovery

Abstract Underwater Wireless Sensor Networks (UWSNs) is an emerging technology for the monitoring of aquatic assets and frequently applied in several domains like underwater information gathering, ocean sampling network, anonymous vehicles, disaster prevention and submarine detection. Recently, UWSNs have been getting significant attention of researchers from both academia and industry. As a result

Abstract Mental disorders like depression represent 28% of global disability. It affects around 7.5% percent of global disability. Depression is a common disorder that affects the state of mind, normal activities, emotions, and produces sleep disorders. It is estimated that approximately 50% of depressive patients suffering from sleep disturbances. In this paper, a data mining process to classify depressive

Abstract Most of the software model checker tools do not scale well on complicated software. Our goal was to develop a tool, which provides an adjustable balance between precise and slow software model checkers and fast and imprecise static analyzers. The key idea of the approach is an abstraction over the precise thread interaction and analysis for each thread in a separate way, but together with

Abstract Advanced computing brings opportunities for innovation in a broad gamma of applications. Traditional practices based on visual and manual methods tend to be replaced by cyber-physical systems to automate processes. The present work introduces an example of this, a machine vision system research based on deep learning to classify bridge load, to give support to an optical scanning system for

Abstract An approach to the static verification of the program source code for correct memory usage is considered. The method is based on the use of symbolic graphs for representing the program memory. An extension of symbolic memory graphs that makes it possible to use predicates over symbolic values to improve the precision of analysis is proposed. These predicates cut off the unreachable paths thus

Abstract This article presents an approach for the participation of datacenters and supercomputing facilities in smart electricity markets. This is a relevant problem in modern smart grid systems to implement demand response strategies for a better use of resources to guarantee energy efficiency. The proposed approach includes a datacenter model based on empirical information to determine the power

Abstract This paper proposes a first approach based on wavelet analysis inside image processing for object detection with a repetitive pattern and binary classification in the image plane, in particular for navigation in simulated environments. To date, it has become common to use algorithms based on convolutional neural networks (CNNs) to process images obtained from the on-board camera of unmanned

Abstract Digital twins of processes and devices use information from sensors to synchronize their state with the entities of the physical world. The concept of stream computing enables effective processing of events generated by such sensors. However, the need to track the state of an instance of the object leads to the impossibility of organizing instances of digital twins as stateless services. Another

Abstract Automatic detection of bugs in programs is an extremely important direction of current research and development in the field of program reliability and security assurance. Earlier studies covered, methods for program analysis that combine the dynamic symbolic execution, randomized testing, and static analysis. In this paper, a formal model for detecting bugs using the symbolic execution of

Abstract This paper presents the automation of a Web advertising recognition algorithm, using regular expressions. Currently, the use of regular expressions, optical character recognition, Databases, and automation tests have been critical for multiple Software implementations. The tests were carried out in three Web browsers. As a result, the detection of advertisements in Spanish, that distract attention

Abstract An acceptable level of quality in data is nowadays a paramount for any kind of organization or enterprise that wishes its business processes to prosper. Thus, introducing activities focused in the data quality management is a crucial requirement for the analysts if the level of quality of data for the functionality or service at hand is to be ensured. Such specialized data quality management

Abstract Currently, in Scrum, there are different methods to estimate user stories in terms of effort or complexity. Most of the existing techniques consider factors in a fine grain level; these techniques are not always accurate. Although Planning Poker is the most used method in Scrum to estimate user stories, it is primarily effective in experienced teams since the estimation mostly depends on the

Abstract In this paper, we study the possibility of using a certain cloud computing model supplied with cryptoservers to obfuscate software programs. Earlier, we proposed this cloud computing model in our study of some information security problems for multi-client distributed computing over encrypted data. Based on this model, we proposed a new approach involving the use of threshold homomorphic cryptosystems

Abstract Designing a trusted access control mechanism of an operating system (OS) is a complex task if the goal is to achieve high level of security assurance and guarantees of unwanted information flows absence. Even more complex it becomes when the integration of several heterogeneous mechanisms, like role-based access control (RBAC), mandatory integrity control (MIC), and multi-level security (MLS)

Abstract This paper describes an approach to testing artificial neural networks that is implemented in a C++ program as a set of data structures and algorithms for their processing. C++ classes are used as data structures that implement the processing of the following objects: vertex, edge, directed and undirected graphs, spanning tree, and circuit. Interfaces for the most important overloaded operations

Abstract Rendering of 3D scenes with a large number of objects is computationally intensive. Occlusion culling methods are used to improve rendering performance by reducing the number of objects to be processed on the GPU. In this paper, we consider occlusion culling methods that employ spatial and temporal coherence of visibility. Some of the most efficient methods are based on hardware occlusion

Abstract This paper is devoted to the problem of mapping parallel computations to distributed systems based on RapidIO communications. A distributed system is represented as a set of hosts with given levels of performance and a set of switches interconnected by links with known bandwidths. Parallel computation is specified as a number of processes that communicate by passing data streams. Each process

Abstract In this paper, a software system for image processing with parallel computing based on the geometrized histograms method developed for the concise description and segmentation of color images and for designing real-time image understanding systems is described. The parallel processing leans on the fact that, in contrast to the majority of the existing image segmentation methods, the proposed

Abstract In this paper, we propose an algorithm for detection and recognition of all information fields at the bank card front side based on video sequences. The algorithm is intended for use on mobile devices. This algorithm consists of the following basic steps: detection of the card boundaries in a frame, segmenting the information fields, improving the quality of segments, localizing the boundaries

Abstract In this paper, we prove that a k-tape Minsky machine operating with time \(T(n)\) can be modeled by a three-tape Minsky machine in a time not exceeding \(T{{(n)}^{k}} \times \log T(n)\). It is shown that multitape Turing machines can be modeled by three-tape Minsky machines with optimal word encoding.

Abstract The problem of lazy visualization of ontological graphs has certain constraints. Visualization of structures that contain blank nodes is especially challenging. In this paper, we propose an approach to visualization of these structures that is implemented in Ontodia, analyze the limitations of this approach, and consider some alternative solutions.

Abstract Traffic is a major challenge for electronic cities and coping with it requires analyzing traffic congestion in the city road network. In this paper, the performance index of vehicle speed was estimated to evaluate the conditions of road networks. This study analyzes the traffic density for the main network of Hamedan communication routes based on the collected data of Speed performance of

Abstract A software application’s menu is an important part of its user interface. User satisfaction and application usage efficiency depend on how well the menu is designed. Application menus designed by the developer are intended for the average user and do not take into account the needs and characteristics of individual users. A solution to this problem is the creation of user interfaces capable

Abstract This paper describes some live virtual machine (VM) migration schemes used in modern hypervisors and provides a comparative analysis of their potential capabilities based on the following criteria: eviction time, total migration time, downtime, total amount of data transmitted during migration, and decrease in performance of a migrating VM.

Abstract In the era of information technology, the use of computer technology for both work and personal use is growing rapidly with time. Unfortunately, with the increasing number and size of computer networks and systems, their vulnerability also increases. Protecting web applications of organizations is becoming increasingly relevant as most of the transactions are carried out over the Internet

Abstract Intelligent energy saving and energy efficient technologies are a modern large-scale global trend in the development of energy systems. Accurate estimates of energy savings are important for promoting energy-efficient construction projects and demonstrating their economic potential. The growing digital measurement infrastructure used in commercial buildings increases the availability of high-frequency

Abstract Modern functional programming languages, such as Haskell, Scala, ML, and F#, have properties that make it possible to implement logically complicated algorithms relatively easily. Among such properties is the composition of functions, currying, metafunctions (functions over functions), and some others. This makes it possible to obtain complex functions by combining simpler functions. An example

Abstract This paper discusses problems associated with modern user interfaces, analyzes interfaces built on the implementation paradigm, identifies the weaknesses of this paradigm, estimates some existing methodologies for interface development, and justifies the use of metaphoric or idiomatic methodologies when creating or improving user interfaces. At an annual meeting, Kenneth Olsen, an engineer

Abstract Refactoring is an integral part of the modern software development process. Often, the refactoring must be performed at the global level with modifications in a large number of files. Making these modifications is a long and painstaking work. However, users rarely employ automated tools for this purpose because they consider them unreliable and difficult to use. In this paper, a new tool for

Abstract Data replication is used to enhance the reliability, availability, and throughput of database systems at a price of increased complexity and cost of data updates. In many cases, data storage systems that exploit replication use relaxed consistency criteria. This survey describes different replication schemes and discusses several consistency models, protocols, and techniques designed to support

An implementation of associative memory based on a Hopfield network is described. In the proposed approach, memory addresses are regarded as training vectors of the artificial neural network. The efficiency of memory search is directly associated with solving the overfitting problem. A method for dividing the training and input network vectors into parts, the processing of which requires a smaller

AbstractThis paper presents an approach to developing ontologies of scientific subject domains (SSDs) that is based on the application of a system of heterogeneous ontology design patterns (ODPs), which are documented descriptions of proven solutions to typical problems of ontological modeling. This system includes both universal patterns used to describe typical ontology constructions and patterns

AbstractThis paper presents a new two-step verification method for control software. The novelty of the method is that it reduces the verification of the temporal properties of a control program to the deductive verification of an imperative program in the Hoare style, which explicitly models the time and history of the control program. The method is applied to programs written in the Reflex language

AbstractEver increasing software security requirements, the growing size of software projects, and the desire to reduce the time of software development and release require tools for the dynamic analysis that would detect vulnerabilities in С and С++ programs and prevent their exploitation. Two types of dynamic analysis tools implemented in the gcc and clang compilers are considered; these tools are

AbstractNvidia RTX is a proprietary hardware-accelerated ray tracing technology. Since implementation details are unknown, there were many questions in the development community about the hardware implementation: which stages of the ray tracing pipeline are hardware-accelerated and which of them can be efficiently implemented in software. In this paper we present the results of our experiments with

AbstractIn the paper, we study a family of testing equivalences in interleaving, partial-order semantics, and combined semantics in the context of safe time Petri nets (elementary net systems whose transitions are labeled with time firing intervals, can fire only if their lower time bounds are attained, and are forced to fire when their upper time bounds are reached). For this purpose, the following

AbstractThe quantitative analysis of the blood flow in the brain tissue is one of the important problems in neurosurgery. It arises when diagnosing acute ischemic stroke. This problem can be solved using computed tomography (CT) perfusion imaging. There are various methods for extracting quantitative characteristics of cerebral blood flow from CT perfusion data, which differ in degrees of their noise