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This paper explores the optimal number of unique jobs for an industrial enterprise by using computer simulations to reduce overall costs of creating and operating these jobs through staff remuneration optimization. The study utilizes the author's mathematical models of workers' behavior in a stimulating environment and optimization of the number of similar jobs used in industrial enterprises. The paper employs computational mathematics and computer modeling to analyze potential solutions for organizing unique workplaces. The study demonstrates that the estimated number of unique jobs can be reduced by increasing work shifts, hiring qualified workers, and offering incentive wage rates. The paper presents the results of model computational experiments on the optimal number of jobs for performing a given amount of work in two shifts under three scenarios: attracting workers with average market qualifications, attracting more qualified workers with wages under average market conditions, and attracting more qualified workers with wages at increased rates., В данной работе проводится компьютерное обоснование оптимального выбора количества уникальных рабочих мест применительно к условиям промышленных предприятий. Снижение общих издержек на создание и на эксплуатацию рабочих мест достигается путем оптимизации оплаты труда персонала. Исследование выполнено с использованием авторских математических моделей поведения работников в стимулирующей среде и оптимизации количества используемых однотипных рабочих мест. Методами вычислительной математики и компьютерного моделирования проведено исследование возможных решений при организации уникальных рабочих мест. Показано, что имеются варианты сокращения их расчетной численности путем увеличении рабочих смен, найма квалифицированных работников и использования стимулирующих расценок оплаты труда. Приведены результаты модельных вычислительных экспериментов оптимальной численности рабочих мест при выполнении заданного объема работы в две смены в трех следующих вариантах: привлечение работников среднерыночной квалификации; привлечение более квалифицированных работников с оплатой труда по среднерыночным условиям; привлечение более квалифицированных работников с оплатой труда по повышенным расценкам.

The article deals with the problem of the reconciliation of observation results, which arises when solving problems of interval analysis of a database. It is found that the values of the set of input variables and the output variable are consistent if the graph of the desired dependence is located at the inner points of the interval hyper-rectangle in each observation. In this case, it is proposed to use special solutions of interval systems of linear algebraic equations (ISLAU) to analyze the data of linear processes. However, in real and model conditions, the specified property of the database is not always fulfilled a priori. In these cases, it is proposed to use the principle of robust estimation: inconsistent observations should either be excluded from the sample or adjusted. This paper presents the results of the study of these methods of matching the used experimental database on model linear processes under conditions when the basic assumptions of interval estimation of dependencies are fulfilled. In addition, variant computational experiments have been investigated to reveal the possibility of increasing the accuracy of interval analysis due to preliminary correction of observations, including the possibility of guaranteed estimation of the sought dependences.

Early diagnosis of tick-borne borreliosis determines the indications for etiotropic therapy, and the detection of borrelia in a tick that has bitten you serves as the basis for antibiotic prophylaxis. To determine the causative agent of borreliosis, PCR methods are most widely used, which requires special conditions for organizing the work of laboratories and the use of expensive equipment. In addition, the procedure for isolating bacterial DNA and subsequent amplification takes several hours of working time. At the same time, methods for detecting borrelia in the isothermal LAMP-reaction are described, which makes it possible to significantly speed up the diagnosis, does not require complex equipment and highly qualified personnel. It is also known that LAMP in some cases allows analysis without prior extraction of nucleic acids. The purpose was a development of a modified test for isothermal detection of DNA of borreliosis pathogens for an accelerated result and the possibility of excluding the stage of nucleic acid extraction. We used 40 samples of Borrelia DNA and 11 Ixodes persulcatus ticks. To shorten the detection time for Borrelia, the previously described LAMP method was modified by the introduction of additional loop primers. The copy number of the positive DNA sample of the borrelia plasmid was estimated using digital PCR. The results of the LAMP reaction were compared with those of the commercial PRC-RT test. The additional use of loop primers approximately halved the detection time for Borrelia DNA without affecting the comparative diagnostic efficiency. The analytical sensitivity limit of the modified LAMP method was 4 copies/μl or 21 molecules of the plasmid standard added to the reaction. In comparative testing with RT-PCR, the sensitivity of the LAMP method is 90%, and the specificity is 100%. The possibility of detecting borrelia in ticks without the stage of DNA extraction has been demonstrated for the first time. A modified isothermal method for the detection of pathogens of tick-borne borreliosis has been developed, which allows analysis within 20-30 minutes, including in ticks without preliminary DNA extraction.

Introduction: local treatment of metastases is an integral part of colon cancer treatment. However, there is not enough data on the efficacy of surgical resection of metastases in patients with a BRAF gene mutation to recom‑mend this approach in routine practice. We initiated a retrospective multicenter study to assess the incidence of BRAF gene mutations in patients with metastatic colon cancer and to study the efficacy of metastasectomy in this group of patients.Materials and methods: we selected all patients who underwent surgical resection of metastases in various sites from the database of patients with BRAF gene mutations created as a result of a multicenter retrospective study with participation of 7 clinics in the Russian Federation. All 57 patients with RAS gene mutations and 43 patients with wild‑type RAS and BRAF genes who also underwent surgical resection of metastases at any stage of treatment were selected from the register of the Chemotherapy Department No. 2 of the NMRC of Oncology named after N. N. Blokhin for comparative analysis. Disease‑free survival and overall survival were used as primary efficacy criteria.Results: we found 26 patients with BRAF gene mutations who underwent surgical resection of metastases. When comparing disease‑free survival, the worst median was achieved in the group of patients with BRAF gene mutations: 7 months versus 14 months in patients with RAS gene mutations (HR 0.4, 94 % CI 0.23–0.7, P = 0.006); median disease‑free survival was not achieved in the wild‑type RAS and BRAF group (HR 0.2, 95 % CI 0.11–0.45, P The median overall survival in the BRAF gene mutation group was 26 months versus 38 months in the RAS gene mutations group (HR 0.8, 95 % CI 0.33–1.98, P = 0.6) and 49 months in the wtRAS/wtBRAF group (RR 0.46, 95 % CI 0.17–1.24, P = 0.1). Resection of recurrent tumors in patients with metastases in retroperitoneal lymph nodes was associated with extremely low disease‑free survival (2 months); at the same time, disease‑free survival was 7 months after resection of isolated metastases in the liver and 8 months for metastases in the peritoneum.Conclusion: prognosis of patients with a BRAF gene mutation after surgical resection of metastases is worse than in patients with a different mutation phenotype. Nevertheless, literature data, as well as the results of our study, confirm the possibility of performing metastasectomy with careful selection of patients.

Conformally Killing fields play an important role in the theory of Ricci solitons and also generate an important class of locally conformally homogeneous (pseudo) Riemannian manifolds. In the Riemannian case, V. V. Slavsky and E.D. Rodionov proved that such spaces are either conformally flat or conformally equivalent to locally homogeneous Riemannian manifolds. In the pseudo-Riemannian case, the question of their structure remains open. Pseudo-Riemannian symmetric spaces of order k, where k 2, play an important role in research in pseudo-Riemannian geometry. Currently, they have been investigated in cases k=2,3 by D.V. Alekseevsky, A.S. Galaev and others. For arbitrary k, non-trivial examples of such spaces are known: generalized Kachen - Wallach manifolds. In the case of small dimensions, these spaces and Killing vector fields on them were studied by D.N. Oskorbin, E.D. Rodionov, and I.V. Ernst with the helpof systems of computer mathematics. In this paper, using the Sagemath SCM, we investigate conformally Killing vector fields on five-dimensional indecomposable 2- symmetric Lorentzian manifolds, and construct an algorithm for their computation.

The article presents the results of the approximation of the set of solutions of interval systems of linear algebraic equations. These systems are used in the problems of modeling linear deterministic processes. It is assumed that the modeled process is described by an output variable and a set of input variables, the measurement errors of which are assumed to be set by known intervals symmetric with respect to the zero value. Traditionally, the sets of solutions of interval systems of linear algebraic equations in applied problems are approximated by a hyper-rectangular whose sides are parallel to the axes of the selected coordinate system. In this paper, we propose to use an ellipsoidal approximation of these sets, which is more efficient. The main results of the work include the substantiation of assumptions about the properties of the modeled process, the choice of a mathematical method for constructing an approximating ellipsoid, the proposed method for forming boundary points, and a numerical method for solving the problem. A computer simulation of the problem of estimating the parameters of a linear process is performed in Excel, which is used for a comparative study of approximations of solutions of interval systems of linear algebraic equations by a hyper-rectangular and an ellipse., Представлены результаты аппроксимации множества решений интервальных систем линейных алгебраических уравнений (ИСЛАУ), которые используются в задачах моделирования линейных по параметрам детерминированных процессов. Предполагается, что моделируемый процесс описывается выходной переменной и совокупностью входных переменных, ошибки измерения которых по предположению задаются известными интервалами, симметричными относительно нулевого значения. Традиционно множества решений ИСЛАУ в прикладных задачах аппроксимируются внешне моделью бруса, минимального гиперпрямоугольника, стороны которого параллельны осям выбранной системы координат. В данной работе предлагается использовать эллипсоидную аппроксимацию этих множеств, которая является более эффективной. К основным результатам работы относятся обоснование предположений относительно свойств моделируемого процесса, выбор математического метода построения аппроксимирующего эллипсоида, предложенный способ формирования граничных точек и численный метод решения задачи. Выполнено компьютерное моделирование в среде Excel задачи оценки параметров линейного процесса, которое использовано для сравнительного исследования аппроксимаций решений ИСЛАУ брусом и эллипсом.

The paper is devoted to the implementation of an algorithm for calculating the functionals of the Minkowski set in a three-dimensional digital space. The algorithm is based on the calculation of the values of these functionals for various types of node neighborhoods into which a set in a digital space can be divided. The concept of Minkowski functionals appeared in the theory of convex sets in n-dimensional Euclidean space; they are coefficients in the expansion of the volume function ε of a neighborhood of a convex set in powers of ε. Subsequently, it turned out that the concept of functionals can be generalized to the case of sets with singularities, including the case of a set in a digital space. Minkowski functionals of a digital image representing a union cubic voxel intersecting along edges and vertices are statistical measures based on the Euler-Poincare characteristic of n-dimen-sional space, show sensitivity to the morphology of disordered structures, which is confirmed by applied research. They are used in calculating density measures for a number of unordered microstructural models; particle-based models, amorphous microstructures, cellular and foamlike structures. The results of calculations for various microstructures demonstrate a number of qualitative characteristics. The paper studies the implementation of the algorithm for finding the Minkowski functionals for a set in a threedimensional digital space., Статья посвящена реализации алгоритма вычисления функционалов Минковского множества в трехмерном цифровом пространстве на основе расчетов значений этих функционалов у различных типов окрестностей узлов, на которые можно разбить множество в цифровом пространстве. Понятие функционалов Минковского появилось в теории выпуклых множеств в n-мерном евклидовом пространстве, они представляют собой коэффициенты в разложении функции объема ε-окрестности выпуклого множества по степеням ε. Впоследствии оказалось, что понятие функционалов можно обобщить на случай множеств с особенностями, в том числе на случай множества в цифровом пространстве. Функционалы Минковского цифрового изображения, представляющего объединение кубических вокселей, пересекающихся по ребрам и вершинам, являются статистическими мерами, основанными на характеристике Эйлера-Пуанкаре n-мерного пространства, показывают чувствительность к морфологии неупорядоченных структур, что подтверждают прикладные исследования. Они используются при вычислении мер с плотностью для ряда неупорядоченных микроструктур-ных моделей; моделей на основе частиц, аморфных микроструктур, ячеистых и пеноподобных структур. Результаты расчетов для различных микроструктур демонстрируют ряд качественных характеристик. В работе изучаются вопросы реализации алгоритма нахождения функционалов Минковского для множества в трехмерном цифровом пространстве.

One of the promising areas for using Prolog-systems is to solve logical tasks. This study outlines a solution approach based on the state generation procedure and the verification procedure. A solution to a logical task is presented, which demonstrates in practice the proposed approach and method of specifying a procedure for generating states. In the proposed example, a bit chain is generated that defines the code of a particular letter in the solution of the applied problem. Building a solution by means of code generation with verification allows not storing in the knowledge base a binary tree of all possible codes. The process of generating new states can be associated with the training of the program, with the dynamic formation of the knowledge base. The approach is based on the capabilities of software environments for adding facts and rules to existing ones, which were obtained as the results of the program or its stages. In this case, the entire program is the generating rule. An analysis of the constructed and tested procedures for the dynamic generation of states and the generation of facts allows us to talk about the applicability of such a solution for certain applied problems.

The papers of many mathematicians are devoted to the study of conformally Killing vector fields. Being a natural generalization of the concept of Killing vector fields, these fields generate a Lie algebra corresponding to the Lie group of conformal transformations of the manifold. Moreover, they generate the class of locally conformally homogeneous (pseudo) Riemannian manifolds studied by V.V. Slavsky and E.D. Rodionov. Ricci solitons, which R. Hamilton first considered, are another important area of research. Ricci solitons are a generalization of Einstein's metrics on (pseudo) Riemannian manifolds. The Ricci soliton equation has been studied on various classes of manifolds by many mathematicians. In particular, a general solution of the Ricci soliton equation was found on 2-symmetric Lorentzian manifolds of low dimension, and the solvability of this equation in the class of 3-symmetric Lorentzian manifolds was proved. The Killing vector fields make it possible to find the general solution of the Ricci soliton equation in the case of the constancy of the Einstein constant in the Ricci soliton equation. However, the role of the Killing fields is played by conformally Killing vector fields for different values of the Einstein constant. In this paper, we investigate conformal Killing vector fields on 5-dimensional 2-symmetric Lorentzian manifolds. The general solution of the conformal analog of the Killing equation on five-dimensional locally indecomposable 2-symmetric Lorentzian manifolds is described in local coordinates, discovered by A.S. Galaev and D.V. Alekseevsky.

The article substantiates the need for integration interaction between educational institutions and enterprises of the real sector of the economy, defines its modern directions. The article analyzes one of the practices of interaction between universities and industrial enterprises of the Altai territory. The article describes the activities of the Altai state University in cooperation with industrial enterprises of the region. A study of the interaction of the University and industrial organizations of the Altai territory in the field of personnel training, as well as in the field of research and development works is being conducted. The article describes the main results of the work of the Altai state University, carried out in the interests of the development of industrial production in the Altai territory. The article describes the results of the University's activities in terms of: modernization of its educational system, creation of innovative enterprises, research activities to develop new technological solutions for the development of industrial production in the region.

We developed a new test system to detect the omicron variant of SARS-CoV-2 using allele-specific reverse transcription PCR and estimated the frequency of its detection in patients living in the Novosibirsk Region. Clinical samples were divided into 3 groups: samples collected from December 1 to December 30, 2021 (group 1; n=66), from December 30, 2021 to January 10, 2022 (group 2; n=20), and from January 11 to January 22, 2022 (group 3; n=101). Based on the identification of 5 mutations specific to SARS-CoV-2 (B.1.1.529), two systems of oligonucleotide primers and probes were developed for detecting this coronavirus genotype in clinical samples. Limit of detection (LOD

Solid tumors resulting from oncogenic stimulation of neurotrophin receptors (TRK) by chimeric proteins are a group of rare tumors of various localization that respond to therapy with targeted drugs entrectinib and larotrectinib. The standard method for detecting chimeric TRK genes in tumor samples today is considered to be next generation sequencing with the determination of the prime structure of the chimeric transcripts. We hypothesized that expression of the chimeric tyrosine kinase proteins in tumors can determine the specific transcriptomic profile of tumor cells. We detected differentially expressed genes allowing distinguishing between TRK-dependent tumors papillary thyroid cancer (TC) from other molecular variants of tumors of this type. Using PCR with reverse transcription (RT-PCR), we identified 7 samples of papillary TC carrying a EVT6-NTRK3 rearrangement (7/215, 3.26%). Using machine learning and the data extracted from TCGA, we developed of a recognition function for predicting the presence of rearrangement in NTRK genes based on the expression of 10 key genes: AUTS2, DTNA, ERBB4, HDAC1, IGF1, KDR, NTRK1, PASK, PPP2R5B, and PRSS1. The recognition function was used to analyze the expression data of the above genes in 7 TRK-dependent and 10 TRK-independent thyroid tumors obtained by RT-PCR. On the test samples from TCGA, the sensitivity was 72.7%, the specificity - 99.6%. On our independent validation samples tested by RT-PCR, sensitivity was 100%, specificity - 70%. We proposed an mRNA profile of ten genes that can classify TC in relation to the presence of driver NTRK-chimeric TRK genes with acceptable sensitivity and specificity.