Least-squares bilinear clustering of three-way data

A least-squares bilinear clustering framework for modelling three-way data, where each observation consists of an ordinary two-way matrix, is introduced. The method combines bilinear decompositions of the two-way matrices with clustering over observations. Different clusterings are defined for each part of the bilinear decomposition, which decomposes the matrix-valued observations into overall means, row margins, column margins and row–column interactions. Therefore up to four different classifications are defined jointly, one for each type of effect. The computational burden is greatly reduced by the orthogonality of the bilinear model, such that the joint clustering problem reduces to separate problems which can be handled independently. Three of these sub-problems are specific cases of k-means clustering; a special algorithm is formulated for the row–column interactions, which are displayed in clusterwise biplots. The method is illustrated via an empirical example and interpreting the interaction biplots are discussed. Supplemental materials for this paper are available online, which includes the dedicated R package, .

Balance Model of COVID-19 Epidemic Based on Percentage Growth Rate

The paper examines the possibility of using an alternative approach to predicting statistical indicators of a new COVID-19 virus type epidemic. A systematic review of models for predicting epidemics of new infections in foreign and Russian literature is presented. The accuracy of the SIR model for the spring 2020 wave of COVID-19 epidemic forecast in Russia is analyzed. As an alternative to modeling the epidemic spread using the SIR model, a new CIR discrete stochastic model is proposed based on the balance of the epidemic indicators at the current and past time points. The new model describes the dynamics of the total number of cases (C), the total number of recoveries and deaths (R), and the number of active cases (I). The system parameters are the percentage increase in the C(t) value and the characteristic of the dynamic balance of the epidemiological process, first introduced in this paper. The principle of the dynamic balance of epidemiological process assumes that any process has the property of similarity between the value of the total number of cases in the past and the value of the total number of recoveries and deaths at present. To calculate the values of the dynamic balance characteristic, an integer linear programming problem is used. In general, the dynamic characteristic of the epidemiological process is not constant. An epidemiological process the dynamic characteristic of which is not constant is called non-stationary. To construct mid-term forecasts of indicators of the epidemiological process at intervals of stationarity of the epidemiological process, a special algorithm has been developed. The question of using this algorithm on the intervals of stationarity and non-stationarity is being examined. Examples of the CIR model application for making forecasts of the considered indicators for the epidemic in Russia in May-June 2020 are given.

Algorithm of Estimating Import-Substitution Based on Costs – Output Tables

The article studies problems and prospects of managerial decisions dealing with the process of import-substitution of certain products and puts forward the method of raising its efficiency. This research is based on costs – output tables, as a result of which a special algorithm is designed to estimate the efficiency and accompanying effects for different lines of import-substitution. The authors analyze in what way the process of import-substitution can affect the output of certain industries (both inside the country and for other countries) and how it can change import and export by each industry of each country. By using this algorithm two tests were carried out based on computer modeling, where a proportion of import in a chosen industry of the country was replaced by home production, at first for one type of products and then for another. Results of these tests show a number of predicted values of macro-economic indices as a result of import-substitution of one or another product, whose analysis helps identify the best variant of importing such product, which should be substituted by home produce in order to reach the set criterion of efficiency. The designed algorithm can be used as a support system for decision-making in importsubstitution policy.

Application of Identification Reference Nets for the Preliminary Modeling on the Example of Electrical Machines

This paper presents the use of identification reference nets (IRNs) for modeling electric power system (EPS) components using electrical machines (EMs) as an example. To perform this type of task, a database of reference nets is necessary, to which the identification net (IN) of the modeled machine is adjusted. Both the IRN and IN are obtained by using a special algorithm that allows the relevant transfer function (TF) to be converted to the rounded trajectory. This type of modeling can be a useful tool for the initial determination of parameters included in the TF associated with the EM, preceding advanced parametric identification procedures, e.g., those based on artificial intelligence methods. Two types of electrical machines are considered, i.e., the squirrel-cage asynchronous (SCA) and brushless direct-current (BLDC) machines. The solution proposed in this paper is a new approach intended for modeling EPS components.

A New Kind of Absolute Magnetic Encoder

To fulfill the requirement of fields such as robotics, aviation, and special machining, motors with quill shafts or outer rotors have been used. For these special motors, the photoelectric encoder’s volume is normally too big and easy to be polluted by oil or dust; magnetic encoder normally has poor accuracy, and alnico piece may not provide enough magnetic field coverage area. The aim of this essay is to find a new structure of magnetic encoder to improve the precision and magnetic field coverage area. By using two multi-pole alnico rings with a different number of pole pairs to provide a magnetic field, the coverage area could be improved. The position differences between two alnicos pole positions are used to calculate absolute angle value, so the accuracy of the encoder could be absolute and no less than that of a combined magnetic encoder with the same number of pole pairs. A special algorithm is proposed for decoding. This new kind of magnetic encoder could be used on special motors with quill shafts or outer rotors. Its volume and weight are less than the photoelectric encoder and have better performance on antipollution. The alnico ring is easy to modify to suit the structure of the motor.

Therapy of coronavirus infection

Background: The computer apparatus for electro-acupuncture diagnostics and medicated testing "IMEDIS-EXPERT" made in Russia was used for the purposes of this work to detect SARS-CoV-2 (COVID-19) or to prove its absence, and to select homoeopathic preparations, nosodes, and their relevant doses. The methods of the system-nosological approach (SNA) were used for the therapy of patients, which included recording and appliance of relevant control signals (C.S.) of homoeopathic preparations, both native and informational (electronic) copies. Aims: 1. Develop an algorithm to select preparations from the group of nosodes and homoeopathy to prevent the development of SARS-CoV-2 (COVID-19); 2. Evaluate the possibility of preventing treatment and therapy of coronavirus infection employing an "electronic vaccine" produced employing coronavirus C.S. Methodology: The electronic preventing "immunization" was made for patients as the preventing treatment of COVID-19, which was an adaptation to coronavirus C.S. conducted in accordance with a special algorithm. The three-block scheme of SNA therapy was used for the therapy of ill patients, which was composed of three preparations, which were used sequentially: 1. Control signal of coronavirus targeted on a patient's CMH; 2. Cerebral response (C.R.) with a patient's cumulative impact of: C.S. of coronavirus and the sum of target organs (blood-forming system, lymphatic systems, lungs, bronchus, gastrointestinal system) and test-indicators of immune regulation targeted on the second CMH marker amplification; 3. Drainages in the form of homeopathic preparations were used (after the impact of two previous preparations), which were: Arsenicum, Arsenicum iod, Carbo vegetabilis, Spongia, Drosera, Naya, Rhus Toxicodendron, and Ferrum met. The preparations were selected to compensate the third impact of CMH. Results: At present, 175 people have asked for help due to COVID-19, an electronic preventing vaccine ("immunization") made for 112 people on the SNA algorithm. According to the diagnostic testing results made for 63 ill patients and who asked for treatment: 47 people tested coronavirus infection, 16 people tested ARVI, and 12 people tested pneumonia caused by a virus. The coincidence of VRT tests (vegetative resonance tests) and PCR was found ranged from 68 to 75%. 4 people got ill by coronavirus among those who got preventing immunization (112 people) by "the electronic sensibilization method" (that was proved by VRT and PCR tests). The illness had the light form among 2 of them, and two people had moderate severity of illness without hospital admission. Conclusion: An algorithm is developed, which allows to select C.S. of therapeutic nosodes and homoeopathic preparations to prevent the development of SARS-CoV-2. The efficiency of applying the electronic immunization method according to the algorithms of SNA using coronavirus C.S. is 95%.

Neurographics as a Means of Developing the Creative Thinking of Future Teachers

The urgency of the problem of developing the creative thinking of future teachers is due to a number of factors provoking the emergence of new requirements for a modern person: the ability to make decisions quickly, independently model their own future and take responsibility for it; learn throughout life, successfully build relationships with others, be creative. In the article, the author makes an attempt to substantiate the expediency of using neurographics as an art-therapeutic method for the development of an important feature of the thinking of a modern student of a pedagogical profile ‒ creativity. The essence of the concepts «creative thinking», «neurographics» is determined. The leading concept of the work ‒ neurographics ‒ is defined as an art-technology for working with the subconscious of a person, when, in the process of drawing according to a special algorithm, new neural connections are formed in a person, creative thinking develops, which allows you to look at the problem in a new way and solve it more effectively. The principles of neurographic drawing (neuroplasticity, reliance on the inner meaning of the personality, a high degree of independence), its content, an algorithm for using it for the development of students' creative thinking (working with a request, forming a composition, combining elements / rounding, searching for new forms, field lines, fixing new results, reflection), the interpretation of the leading figures (circle, triangle, square, as well as a neurographic line) in a neurographic drawing is given. The effectiveness of using the neurographic method in the educational process of higher educational institutions for the development of creative thinking of future teachers has been proved.

The Two-Level Semi-Synchronous Parallelization Method for the Caustic and Indirect Luminance Calculation in Realistic Rendering

The paper considers an original approach to the semi-synchronous calculation of the luminance of caustic and indirect illumination for the group of methods based on the bidirectional stochastic ray tracing with backward pho-ton maps. The designed parallelization method uses the two-level threads hierarchy. The low level of this thread hierarchy is synchronous calculations of the part of the whole image defined by a randomly generated pixel mask which is applied to the whole image. The top level is semi-synchronous parallelization level that consists groups of the low level threads which of them calculate own part of the whole image in a way similar to asynchronous calculations. As the top level is semi-synchronous it means that when calculating the luminance of the caustic and indirect illumination, the threads of the low level have access to the data accumulated in the backward photon maps of the other parallel threads of the semi-synchronous level. A special algorithm for organizing an access to data of the upper-level threads avoids de-lays associated with data synchronization. The comparison of the developed solution with purely synchronous and asynchronous parallelization methods is presented.

CLASSIFICATION OF SORBENTS USED IN TECHNOLOGIES FOR PURIFICATION OF WASTE WATER FROM PETROLEUM PRODUCTS

Currently, there is no a generally accepted classifi cation of the sorbents used in the technologies for wastewater treatment from oil products. The purpose of this work is to more fully systematize the sorbents used in wastewater treatment, depending on their main characteristics, as well as on the economy and environmental friendliness. Based on the existing classifi cations, the generalized classifi cation of the sorbents designed for wastewater treatment from oil products in the dissolved and emulsifi ed forms, and additionally in the fi lm form, was developed and supplemented with the new parameters. A special algorithm, that allows one to make an informed choice of the sorbent in terms of its application effi ciency, environmental protection and material costs, is formed. In this regard, as an example, the classifi cation of pine sawdust has been performed. It can be considered as an eff ective sorbent base.

Architecture neural network deep optimizing based on self organizing feature map algorithm

Forward neural network (FNN) execution relying on the algorithm of training and architecture selection. Different parameters using for nip out the architecture of FNN such as the connections number among strata, neurons hidden number in each strata hidden and hidden strata number. Feature architectural combinations exponential could be uncontrollable manually so specific architecture can be design automatically by using special algorithm which build system with ability generalization better. Determination of architecture FNN can be done by using the algorithm of optimization numerous. In this paper methodology new proposes achievement where FNN neurons respective with hidden layers estimation work where in this work collect algorithm training self organizing feature map (SOFM) with advantages to explain how the best architectural selected automatically by SOFM from criteria error testing based on architecture populated. Different size of dataset benchmark of 4 classifications tested for approach proposed.