Numerical algorithms for solving an elliptic optimal control problem with a power-law nonlinearity

The paper is devoted to the development and analysis of approximation-iteration algorithms based on the method of grids and the method of lines for solving an elliptic optimal control problem with a power-law nonlinearity. For the numerical solution of the main boundary value problem and the adjoint one, the second order of accuracy difference schemes are applied using the implicit method of simple iteration. Computational schemes of the method of lines for solving the above-mentioned elliptic boundary value problems are implemented in combination with the shooting method for the approximate solution of boundary value problems for the corresponding ordinary differential equations systems arising in the considered domain after lattice approximation. To minimize the objective functional, well-known gradient-type methods (gradient projection and conditional gradient methods) of constrained optimization are used. The essence of the proposed approximation-iteration approach consists in replacing the original extremal problem with a sequence of grid problems that approximate it on a set of refining grids, and applying an iterative gradient-type method to each of the "approximate" extremal problems. In this case, we propose to construct only a few approximations to the solution for each of the "approximate" problems and to take the last of these approximations, using piecewise linear interpolation, as the initial approximation in the iterative process for the next "approximate" problem. The sequence of the corresponding piecewise linear interpolants is considered as a sequence of approximations to the solution of the original extremal problem. The paper discusses the theoretical foundations of this combined approach, as well as its advantages over traditional methods using the example of solving a model optimal control problem

Recognition and calculation of objects in images using YOLOv3 architecture

Program that searches for five types of fruits in the images of fruit trees, classifies them and counts their quantity is presented. Its creation took into account the requirement to be able to work both in the background and in real time and to identify the desired objects at a sufficiently high speed. The program should also be able to learn from available computers (including laptops) and within a reasonable time. In carrying out this task, the possibilities of several existing approaches to the recognition and identification of visual objects based on the use of convolutional neural networks were analyzed. Among the considered network archi-tectures were R-CNN, Fast R-CNN, Faster R-CNN, SSD, YOLO and some modifications based on them. Based on the analysis of the peculiarities of their work, the YOLO architecture was used to perform the task, which allows the analy-sis of visual objects in real time with high speed and reliability. The software product was implemented by modifying the YOLOv3 architecture implemented in TensorFlow 2.1. Object recognition in this architecture is performed using a trained Darknet-53 network, the parameters of which are freely available. The modification of the network was to replace its original classification layer. The training of the network modified in this way was carried out on the basis of Transfer learning technology using the Agrilfruit Dataset. There was also a study of the peculiarities of the learning process of the network under the use of different types of gradient descent (stochastic and with the value of the batch 4 and 8), as a result of which the optimal version of the trained network weights was selected for further use. Tests of the modified and trained network have shown that the system based on it with high reliability distin-guishes objects of the corresponding classes of different sizes in the image (even with their significant masking) and counts their number. The ability of the program to distinguish and count the number of individual fruits in the analyzed image can be used to visually assess the yield of fruit trees

Search for identical regions in images using invariant moments

One of the ways to describe objects on images is to identify some of their characteristic points or points of attention. Areas of neighborhoods of attention points are described by descriptors (lots of signs) in such way that they can be identified and compared. These signs are used to search for identical points in other images. The article investigates and establishes the possibility of searching for arbitrary local image regions by descriptors constructed with using invariant moments. A feature of the proposed method is that the calculation of the invariant moments of local areas is carried out with using the integral representation of the geometric moments of the image. Integral representation is a matrix with the same size as the image. The elements of the matrix is the sums of the geometric moments of individual pixels, which are located above and to the left with respect to the coordinates of this element. The number of matrices depends on the order of the geometric moments. For moments up to the second order (inclusively), there will be six such matrices. Calculation of one of six geometric moments of an arbitrary rectangular area of the image comes down up to 3 operations such as summation or subtraction of elements of the corresponding matrix located in the corners of this area. The invariant moments are calculated on base of six geometric moments. The search is performed by scanning the image coordinate grid with a window of a given size. In this case, the invariant moments and additional parameters are calculated and compared with similar parameters of the neighborhoods of the reference point of different size (taking into account the possible change in the image scale). The best option is selected according to a given condition. Almost all mass operations of the procedures for calculating the parameters of standards and searching of identical points make it possible explicitly perform parallel computations in the SIMD mode. As a result, the integral representation of geometric moments and the possibility of using parallel computations at all stages will significantly speed up the calculations and allow you to get good indicators of the search efficiency for identical points and the speed of work

Hybrid method of intellectual diagnosis and forecasting of complex technical systems

Modern control and diagnostic systems (CDS) usually determine only the technical condition (TC) at the current time, ie the CDS answers the question: a complex technical system (CTS) should be considered operational or not, and may provide little information on performance CTS even in the near future. Therefore, the existing scenarios of CDS operation do not provide for the assessment of the possibility of gradual failures, ie there is no forecasting of the technical condition. The processes of parameter degradation and degradation prediction are stochastic processes, the “behavior” of which is influenced by a combination of external and internal factors, so the deg-radation process can be described as a function that depends on changes in the internal parameters of CTS. The hybrid method involves the following steps. The first is to determine the set of initial characteristics that characterize the CTS vehicle. The second is the establishment of precautionary tolerances of degradation values of the characteristics that characterize the pre-failure technical con-dition of the CTS. The third is to determine the rational composition of informative indicators, which maximally determine the "behavior" of the initial characteristics. The fourth — implementa-tion of multiparameter monitoring, fixation of values of the controlled characteristics, formation of an information array of values of characteristics. Fifth — the adoption of a general model of the process of changing the characteristics of the CTS. Sixth — the formation of a real model of the process of changing the characteristics of Y(t) on the basis of an information array of values of char-acteristics obtained by multi-parameter monitoring. Seventh — forecasting the time of possible oc-currence of the pre-failure state of the CTS, which is carried out by extrapolating the obtained real model of the process of changing the characteristics of Y(t). It is proposed to use two types of mod-els: for medium- and long-term forecasting - polynomial models, for short-term forecasting — a lin-ear extrapolation model. At the final stage, forecast errors are determined for all types of models of degradation of pa-rameters and characteristics. Based on the results of the forecast verification, the models are adjust-ed

Intelligent system for assessing the harmfulness of food products based on the processing of textual and graphic information

The paper substantiates the need to assess the harm of food for consumers with chronic diseases or allergies, which is important to prevent possible deterioration of the disease or eliminate acute allergic reactions of the human body to harmful ingredients present in the product. It is proved that currently there is no convenient intelligent system that could recognize the composition of products on the Ukrainian market, provide product characteristics and assess the harmfulness of the product. It is proposed to use food labels and packaging as primary sources of food information that is available to the consumer. It is shown that the printed information on the packages is presented in text-graphic form. The development of a mobile system as a software solution for the detection and analysis of textual and graphical information on the composition of products based on the use of artificial intelligence methods is proposed and substantiated. The block diagram of the intelligent mobile system for detection and analysis of food composition has been developed. The MSER algorithm is used to select text regions on the input image matrix in the presented algorithmic software. The solution to the problem of character recognition was based on the use of convolutional neural network MobileNet-V2, which is currently the best option in the classification of images by mobile applications that do not have a server part, and therefore large computing resources. Alignment of text on the image was carried out using the method of finding a rectangle with the smallest area Developed algorithms for grouping words. A decision support algorithm has been proposed to assess the harmfulness of products. The developed system allows personalized selection of food for each individual user, ie, the assessment of the composition of products is calculated taking into account the state of health of use, existing threats, diseases, restrictions or allergies

Data processing algorithms for the in silico SARS-CoV-2 epitope prediction and vaccine development

Based on literature analysis and own bioinformatics and virology research experience, authors propose multistep data processing algorithms, designed for the objectives of assisting the SARS-CoV-2 epitope vaccine production. Epitope vaccines are expected to provoke a weaker but safer response of the vaccinated person. Methodologies of reverse bioengineering, vaccinology and synthetic peptide manufacturing have a promising future to combat COVID-19 brutal disease. The significant mutational variability and evolution of the SARS-CoV-2, which is more typical for natural animal-borne viruses, are the hurdle for the effective and robust vaccine application and therefore require multidisciplinary research and prevention measures on the international level of cooperation. However, we can expect that other viruses with different nature and content may be labelled as SARS-CoV-2. In this case metagenomics is an important discipline for COVID-19 discovery. High quality reliable virus detection is still an unresolved question for improvement and optimization. It is of upmost importance to develop the in silico and in vitro methods for the vaccine recipient reaction prediction and monitoring as techniques of the so-called modern personalized medicine. Many questions can`t be solved applying exclusively in silico techniques and only can be discovered in vitro and in vivo, demanding significant time and money investments. Future experiments also should be directed at the discovery of optimal vaccine adjuvants, vectors and epitope ensembles, as well as the personal characteristics of citizens of a certain region. This research would require several more years of meticulous large-scale laboratory and clinical work in various centers of biomedical institutions worldwide

Software architecture of the question-answering subsystem with elements of self-learning

Within the framework of this paper, the analysis of software systems of question-answering type and their basic architectures has been carried out. With the development of machine learning technologies, creation of natural language processing (NLP) engines, as well as the rising popularity of virtual personal assistant programs that use the capabilities of speech synthesis (text-to-speech), there is a growing need in developing question-answering systems which can provide personalized answers to users' questions. All modern cloud providers proposed frameworks for organization of question answering systems but still we have a problem with personalized dialogs. Personalization is very important, it can put forward additional demands to a question-answering system’s capabilities to take this information into account while processing users’ questions. Traditionally, a question-answering system (QAS) is developed in the form of an application that contains a knowledge base and a user interface, which provides a user with answers to questions, and a means of interaction with an expert. In this article we analyze modern approaches to architecture development and try to build system from the building blocks that already exist on the market. Main criteria for the NLP modules were: support of the Ukrainian language, natural language understanding, functions of automatic definition of entities (attributes), ability to construct a dialogue flow, quality and completeness of documentation, API capabilities and integration with external systems, possibilities of external knowledge bases integration After provided analyses article propose the detailed architecture of the question-answering subsystem with elements of self-learning in the Ukrainian language. In the work you can find detailed description of main semantic components of the system (architecture components)

In the footsteps of Einstein end Wiener

To date the recognition of universal, a priori inherent in them connection between the objects of the world around us is quite rightly considered almost an accomplished fact. But on what laws do these or those sometimes rather variegated systems function in live and inert nature (including - in modern computer clusters)? Where are the origins of their self-organization activity lurked: whether at the level of still hypothetical quantum-molecular models, finite bio-automata or hugely fashionable now artificial neural networks? Answers to all these questions if perhaps will ever appear then certainly not soon. That is why the bold innovative developments presented in following article are capable in something, possibly, even to refresh the database of informatics so familiar to many of us. And moreover, in principle, the pivotal idea developed here, frankly speaking, is quite simple in itself: if, for example, the laws of the universe are one, then all the characteristic differences between any evolving objects should be determined by their outwardly-hidden informative (or, according to author’s terminology - “mental") rationale. By the way, these are not at all empty words, as it might seem at first glance, because they are fully, where possible, supported with the generally accepted physical & mathematical foundation here. So as a result, the reader by himself comes sooner or later to the inevitable conclusion, to wit: only the smallest electron-neutrino ensembles contain everything the most valuable and meaningful for any natural system! At that even no matter, what namely global outlook paradigm we here hold

Construction of subsystem determination of attacks in cyberphysical systems by neural network methods

In this research work analyzes and compares existing methods for describing data from cyberphysical systems, methods for detecting network attacks targeting cyberphysical systems, analyzes fundamental approaches and solutions in the field of cyberphysical systems security, and makes recommendations for supplementing existing approaches using new algorithms. The considered application of the neuroevolutionary algorithm of NeuroEvolution of Augmenting Topology using a hypercube for the analysis of multivariate time series describing the state of cyberphysical systems in order to identify abnormal conditions. After the modification, the algorithm allows almost completely configuring the target neural network without user intervention according to the specified parameters, including additionally creating intermediate network layers that were previously unavailable in the primary version of the algorithm. The method is verified on the TON_IOT DATASETS dataset. The system topology is the structure of the Internet of Things. The data are relevant, verified and correct, which allows them to be used for analysis and assessment of the accuracy of the approach under consideration. The obtained overall accuracy, proximity of solutions, values of False Positive Rate and False Negative Rate indicate the lack of retraining of the model and the high reliability of this method for detecting attacks in cyberphysical systems

To the question about remote sensing of the earth for precision farming tasks and assessment of the consequences of techno-environmental events

Some issues of the use of unmanned aircraft and space vehicles in monitoring the consequences of technical and environmental events and precision farming are considered. The proposed technology is aimed at improving the recognition accuracy of infrastructure objects with obtaining the numerical values of their 3D coordinates. The aim of the research is to improve the quality of monitoring using neural network identification and classification of objects in multi-zone satellite images obtained from unmanned aerial vehicles (UAV). Research includes both theoretical research and applied problem solving. The mathematical basis of image processing is the image recognition computer. Practical research is based on experimentation, software implementation, testing of algorithms and technology. An effective method of video surveillance of the territory has been improved. The task of the authors' research is to improve the accuracy of objects recognition on the earth's surface (specific infrastructure objects, the sky, the state of vegetation of agricultural land). The authors have experience in this area. The solution to this problem occurs simultaneously in two directions. The first direction: the technical result is ensured by the fact that the technology offers the use of a UAV equipped with two video cameras. The second direction is the use of scientific idea consisting in the development of a method for joint computer processing of digital and analog images obtained from UAVs, as well as quasi-simultaneous and reusable multi-zone satellite images. A new result of the research is the developed data structure for storing the model of the recognition process, which allows to jointly save dissimilar characteristics and membership functions of different types in the same tables