Using Rounding Errors in Modern Computer Technologies

Introduction. When solving problems of transcomputational complexity, the problem of evaluating the rounding error is relevant, since it can be dominant in evaluating the accuracy of solving the problem. The ways to reduce it are important, as are the reserves for optimizing the algorithms for solving the problem in terms of accuracy. In this case, you need to take into account the rounding-off rules and calculation modes. The article shows how the estimates of the rounding error can be used in modern computer technologies for solving problems of computational, applied mathematics, as well as information security. The purpose of the article is to draw the attention of the specialists in computational and applied mathematics to the need to take into account the rounding error when analyzing the quality of the approximate solution of problems. This is important for mathematical modeling problems, problems using Bigdata, digital signal and image processing, cybersecurity, and many others. The article demonstrates specific estimates of the rounding error for solving a number of problems: estimating the mathematical expectation, calculating the discrete Fourier transform, using multi-digit arithmetic and using the estimates of the rounding error in algorithms for solving computer steganography problems. The results. The estimates of the rounding error of the algorithms for solving the above-mentioned classes of problems are given for different rounding-off rules and for different calculation modes. For the problem of constructing computer steganography, the use of the estimates of the rounding error in computer technologies for solving problems of hidden information transfer is shown. Conclusions. Taking into account the rounding error is an important factor in assessing the accuracy of the approximate solution of problems of the complexity above average. Keywords: rounding error, computer technology, discrete Fourier transform, multi-digit arithmetic, computer steganography.

Development of a Subsystem for Supporting a Complex of Diagnostic Procedures for the Information-Analytical System TISP

Introduction. During the implementation of the project "Transdisciplinary Intelligent Information-Analytical System for Supporting Rehabilitation Processes in a Pandemic (TISP)", all the capabilities of the basic cognitive information technology were focused on the implementation of the strategy of rehabilitation measures, which consists in taking into account the pathogenetic features of the development of the disease. In the subsystem of information and analytical support of the complex of diagnostic procedures, the central is the assessment of the effectiveness of rehabilitation based on the indicators of the electrocardiogram (ECG) and heart rate variability (HRV), control of the patient's condition using psychophysiological (PF) and psychological testing, the use of biological feedback (BF) to improve the efficiency of rehabilitation, as well as the use of PF testing for the implementation of BF. The purpose of the article is detailing the composition and functionality of a complex of diagnostic procedures for supporting rehabilitation processes in a pandemic. Results. The composition and functionality of the complex of diagnostic procedures are presented. It includes three components: first, an innovative technique for scaling electrocardiograms and heart rate variability (Universal Scoring System) with software and a miniature electrocardiograph (with the ability to use on-line mode). Secondly, the study of psychophysiological testing tools based on the software-hardware complex "Psykholot-1" with the prospect of its addition by means of Biological Feedback (BF). Thirdly, the analysis of existing means of BF therapy and their application for rehabilitation with the proposed method of rehabilitation based on BF using artificial intelligence tools that are being developed within the framework of this project. In the future, it is planned to monitor patients undergoing rehabilitation in order to develop new rules specially adapted for assessing and monitoring the current state of patients undergoing rehabilitation, as well as the effectiveness of BF for rehabilitation. To implement the BF, the Psykholot-1 complex should be used in a trainer mode with a visual presentation of PF tests to the patient in real time. Conclusions. Hardware and software systems of biomanagement must be present at every workplace of a doctor, psychologist, coach, teacher. They can not only help in the treatment of patients, but also can change motivation, mobilize personal resources, and this is what many of us lack today. Keywords: rehabilitation, diagnosis, psychophysiological testing, electrocardiogram, heart rate variability, biological feedback.

Genetic Algorithms as Computational Methods for Finite-Dimensional Optimization

Introduction. As early as 1744, the great Leonhard Euler noted that nothing at all took place in the universe in which some rule of maximum or minimum did not appear [12]. Great many today’s scientific and engineering problems faced by humankind are of optimization nature. There exist many different methods developed to solve optimization problems, the number of these methods is estimated to be in the hundreds and continues to grow. A number of approaches to classify optimization methods based on various criteria (e.g. the type of optimization strategy or the type of solution obtained) are proposed, narrower classifications of methods solving specific types of optimization problems (e.g. combinatorial optimization problems or nonlinear programming problems) are also in use. Total number of known optimization method classes amounts to several hundreds. At the same time, methods falling into classes far from each other may often have many common properties and can be reduced to each other by rethinking certain characteristics. In view of the above, the pressing task of the modern science is to develop a general approach to classify optimization methods based on the disclosure of the involved search strategy basic principles, and to systematize existing optimization methods. The purpose is to show that genetic algorithms, usually classified as metaheuristic, population-based, simulation, etc., are inherently the stochastic numerical methods of direct search. Results. Alternative statements of optimization problem are given. An overview of existing classifications of optimization problems and basic methods to solve them is provided. The heart of optimization method classification into symbolic (analytical) and numerical ones is described. It is shown that a genetic algorithm scheme can be represented as a scheme of numerical method of direct search. A method to reduce a given optimization problem to a problem solvable by a genetic algorithm is described, and the class of problems that can be solved by genetic algorithms is outlined. Conclusions. Taking into account the existence of a great number of methods solving optimization problems and approaches to classify them it is necessary to work out a unified approach for optimization method classification and systematization. Reducing the class of genetic algorithms to numerical methods of direct search is the first step in this direction. Keywords: mathematical programming problem, unconstrained optimization problem, constrained optimization problem, multimodal optimization problem, numerical methods, genetic algorithms, metaheuristic algorithms.

Biosensor Devices in the Production of Alcoholic and Non-Alcoholic Beverages

"Smart" multisensors and biosensor systems based on modern information and communication technologies make it possible to qualitatively improve the parameters of testing systems for biologically active, chemical and toxic substances and biological or biophysical objects, improve parameter control, data processing and analysis in digital agriculture, food industry, environmental monitoring and other areas of human activity. These next-generation devices combine biologically sensitive elements with converters of biophysical signals into electrical digital signals. The article reveals the basic principles of construction of biosensor devices, their practical implementation and application. The own results of development of a wireless network of "smart" multisensors and biosensor devices for express diagnostics of a condition of grape and fruit crops and control of process of production of wine are presented. In order to test the capabilities of the unit of measurement, a number of experimental works were performed. To perform such work, it was first necessary to develop a new embedded software for the microprocessor of Analog Devices ADuCM350, and the corresponding user software for the OS Windows 10. Experiments were performed using disposable sensors based on the enzyme glucose oxidase to measure the sugar content in glucose and wine solution. A review and analysis of modern biosensor devices used in the production of alcoholic and Non-Alcoholic Beverages were done. The comparative table of analyzers for different studies based on biosensors is made. Development and preparation for mass production of "smart" biosensors, biosensor devices and networks based on them is in line with global scientific and technological trends of today and, of course, the near future. Keywords: biosensors, ammetric transducers, wireless sensor network, express diagnostics of grape and berry crops.

Comparative Analysis of the Application of Multilayer and Convolutional Neural Networks for Recognition of Handwritten Letters of the Azerbaijani Alphabet

Introduction. The implementation of information technologies in various spheres of public life dictates the creation of efficient and productive systems for entering information into computer systems. In such systems it is important to build an effective recognition module. At the moment, the most effective method for solving this problem is the use of artificial multilayer neural and convolutional networks. The purpose of the paper. This paper is devoted to a comparative analysis of the recognition results of handwritten characters of the Azerbaijani alphabet using neural and convolutional neural networks. Results. The analysis of the dependence of the recognition results on the following parameters is carried out: the architecture of neural networks, the size of the training base, the choice of the subsampling algorithm, the use of the feature extraction algorithm. To increase the training sample, the image augmentation technique was used. Based on the real base of 14000 characters, the bases of 28000, 42000 and 72000 characters were formed. The description of the feature extraction algorithm is given. Conclusions. Analysis of recognition results on the test sample showed: as expected, convolutional neural networks showed higher results than multilayer neural networks; the classical convolutional network LeNet-5 showed the highest results among all types of neural networks. However, the multi-layer 3-layer network, which was input by the feature extraction results; showed rather high results comparable with convolutional networks; there is no definite advantage in the choice of the method in the subsampling layer. The choice of the subsampling method (max-pooling or average-pooling) for a particular model can be selected experimentally; increasing the training database for this task did not give a tangible improvement in recognition results for convolutional networks and networks with preliminary feature extraction. However, for networks learning without feature extraction, an increase in the size of the database led to a noticeable improvement in performance. Keywords: neural networks, feature extraction, OCR.

Development and Conformity Assessment of ECG-Photometric Complex Software

Introduction. The article is devoted to the software "PulseWave", which is used as part of the ECG-photometric complex for research in medical institutions. For further implementation of the complex in medical practice, it is necessary to assess the compliance of this software in accordance with the requirements of the technical regulations for medical devices. There are two ways to perform software conformity assessment: as part of the ECG photometric complex or separately from it (stand alone). In this paper, the option of conducting a stand alone conformity assessment was chosen, i.e. as a separate product. This approach is the most promising, given the development of "cloud" storage and data processing environments and the need to introduce into medical practice of treatment and prevention facilities in Ukraine. The purpose of the article is to develop software and prepare it for conformity assessment in accordance with the requirements of the technical regulations for medical devices. Results. The authors consider the structure and principle of operation of the software "PulseWave" ECG-photometric complex. The main stages of the life cycle of this software according to international standards are given. A risk assessment report has been developed, which shows and evaluates the main errors that may occur in the work of the software; and ways to eliminate them. Conclusions. The software development, development of its life cycle and risk analysis provide an opportunity to start the procedure of assessing its compliance with the requirements of the technical regulations for medical devices in accordance with international standards. Keywords: software, conformity assessment, life cycle, application risks.

Experience of OpenStack Test Deployment and Comparison of Virtual and Real Cluster Environments

Introduction. A brief overview of the properties and architecture of one of the components of the National Cloud of Open Science prototype – the cloud platform OpenStack is given. The list of software and hardware components of the OpenStack test cloud environment and the sequence of actions required for the deployment of both OpenStack itself and the Slurm virtual cluster environment for portable, scalable, reproducible scientific biomedical computing are presented. The purpose of the paper is a description of the experience of test deployment of OpenStack to create a scalable computing environment for reproducible scientific computing using modern technological solutions, which can be applied to both cloud (OpenStack, AWS, Google) and cluster platforms (Slurm). Results. The structure of the created test containerized (using Singularity technology) biomedical application, which contains modern software and libraries and can be used in conventional and cloud virtual cluster environments is briefly described. The results of a comparative test of this application in the virtual cluster environment Slurm under the control of OpenStack and in the node of cluster SKIT-4.5 in the V.M. Glushkov Institute of Cybernetics of the NAS of Ukraine are given. Information on solving the problem of finding the optimal in terms of saving resources scaling parameters for the developed application in two comparable cluster environments is given. Some features of the use of these cluster environments are clarified, in particular, a comparison of the dependence of the application speed on the number of parallel processes for two cluster environments is presented. Empirical data are presented in graphical form, which illustrate the nature of the load on the OpenStack server and the use of RAM on the number of parallel processes. Possibilities of portability between the specified cluster environments, scaling of calculations and maintenance of reproducibility of calculations for the offered test application are demonstrated. The advantages of using OpenStack technology for scientific biomedical calculations are pointed out. Conclusions. The described example of test deployment and use of OpenStack gives an idea of the requirements for the necessary technical base to ensure the reproducibility of scientific biomedical calculations in cloud and cluster environments. Keywords: cloud technologies, reproducible calculations, cluster platform.

Bayesian Recognition Procedures with Independent Signs of Inflammatory Processes in Gliomas, Metastases and Meningiomas by Indicators of Erythrocyte Sedimentation Rate

Introduction. The article discusses the application of Bayesian recognition procedures with independent signs in relation to the data of the modified erythrocyte sedimentation rate, which were taken from patients with gliomas, metastases, meningiomas, craniocerebral concussion and from a group of healthy people. Purpose of the article. Improving the efficiency of recognition of inflammatory processes in gliomas, metastases and meningiomas by indicators of erythrocyte sedimentation rate using optimal recognition procedures with independent signs. Results. In previous articles by the authors, an attempt was made to recognize inflammatory processes by indicators of the modified erythrocyte sedimentation rate caused by brain cancer using Bayesian recognition procedures based on a single substance. In this work, a new model was built using several independent signs (different substances) at once. The results obtained on the basis of the new model significantly increased their efficiency in relation to the models that were used earlier. Such an increase in all comparisons ranged from 3 to 12 %, and up to almost 94 %. If earlier it was possible to recognize only combinations of diagnoses in which there were no more than two diagnoses, then in this work for the first time it was possible to recognize three diagnoses at once. At the same time, the recognition efficiency became slightly more than 70 %. An attempt was also made to recognize more than three diagnoses, but the new model did not give significant results, slightly exceeding 50 % when recognizing four diagnoses at once. Conclusions. Thanks to the use of Bayesian recognition procedures with independent signs, it was possible to significantly increase the recognition of inflammatory processes caused by brain cancer. The modified erythrocyte sedimentation rate, which is an auxiliary tool in the diagnosis of gliomas, allows one or another pathology to be determined in the preoperative period, since the pathology is finally determined only when studying a surgically removed tumor. In the postoperative period, such a modification is an indicator of repeated recurrence of gliomas. It was also possible to significantly increase the recognition of inflammatory processes caused by non-oncological disease (traumatic brain injury) in relation to oncological processes in gliomas, metastases and meningiomas. Keywords: Bayesian recognition procedure, independent signs, gliomas, metastases, meningiomas, modified erythrocyte sedimentation rate, complex parameter.

Problems on Shortest k-Node Cycles and Paths

The paper is devoted to the construction of mathematical models for problems on the shortest cycles and paths, that pass through a given number of nodes of a directed graph. Such cycles and paths are called k-node, where 1<k <n, n is the number of nodes in the graph. Section 1 formulates two problems for finding the shortest k-node cycle – a mixed Boolean and linear programming problem and a discrete programming problem. Both problems include constraints from the classical assignment problem, describing a one-time entry into a node and a one-time exit from a node for those nodes through which the cycle passes. The cycle connectivity in the first problem is ensured by modeling the flow problem, and in the second problem, it is ensured by using the A. Tucker constraints for the travelling salesman problem. Section 2 establishes a connection between the formulations of both problems from Section 1 and the travelling salesman problem and investigates the efficiency of their solution using modern versions of gurobi and cplex programs and the AMPL modeling language. Section 3 contains the formulation of the shortest k-node path problem, which is represented by a mixed Boolean and linear programming problem. With its help, the optimal routes were found for visiting the wine-making points of the Malopolskie Wine Route in the direction Lviv-Wroclaw-Lviv (Section 4). Here a map for the 20 most visited wine-making points of the Malopolskie Wine Route and a table of the distances between them and the distances from them to Lviv and Wroclaw, calculated using the Google Maps web service, are presented. The developed mathematical models of the problems of finding the shortest k-node paths and cycles and the developed software in the AMPL modeling language can be used for the design and arrangement of technical objects, optimization of the transportation of products, analysis and forecasting of economic processes, determination of optimal routes when planning passenger and freight traffic, optimal organization of the process of managing a set of transactions and queries during their implementation in network databases and other classes of applied optimization problems. Keywords: digraph, shortest path, Boolean variable, linear programming, Hamiltonian cycle, Hamiltonian path, travelling salesman problem, AMPL, gurobi, cplex.

Decision Making Models on the Market of Cloud Services

Introduction. Optimization can be applied in developing profitability management tools for a cloud service broker working according to a certain business model. On behalf of the managing telecommunications holding company (telecommunications operator), this broker integrates, aggregates and configures software and data storage services of third-party Internet software vendors. Such a broker receives only fixed commissions from this company, based on the subscription fee, but does not pay royalties to an Internet software vendor and does not receive payments from the sale of service packages. The purpose. The cloud broker faces the problem of limited human resources required to carry out the relevant legal, technical and economic activities. In addition, the broker faces the problem of uncertainty in sales, service prices, the share of resource use, or the risk of losing operational and financial goals. Results. To run a broker?s business efficiently, one needs to find services and their bundles that increase profitability and reduce financial risk by solving certain optimization problems. Information on such services is needed to support negotiations on fixed and variable commissions, as well as to prioritize services and their packages to be provided. Thus, for the cloud services broker, both profitability management tools and services portfolio development tools are useful. In general, a cloud service broker is an organization that negotiates the relationships between cloud service clients and Internet software vendors. Cloud broker can be created on the basis of different business models regarding the type of service (platform, infrastructure, software), type of clients (enterprise, household), functions performed (identity management, accounting, billing, location, etc.), the degree of rebranding, measures of aggregation of services and other criteria. Conclusions. Different cloud brokers have different attitudes to choice of important solutions for their businesses. Solutions can relate to pricing, capacity planning and utilization in combination with service quality, security, scalability and other issues. Keywords: optimization, portfolio, uncertainty, Boolean variables, revenue generation.