Preliminary Transformation Research Articles

Selective Processing of the Kaolinite Fraction of High-Silicon Bauxite

When processing low-quality gibbsite–kaolinite bauxites, technologies that involve different methods of mechanical and chemical enrichment with the separation of a difficult-to-utilize fine kaolinite fraction for disposal are used. Before production, problems related to waste storage and disposal arise. To solve the problem of utilization, it is necessary to develop an effective technology for the selective processing of the kaolinite fraction. The efficiency of the technology will depend on the quality of pretreatment of raw materials prior to processing for Al2O3 extraction. Preliminary preparation of kaolinite fraction is associated with the maximum removal of excess silica during chemical enrichment by treatment with an alkaline solution. The presence of silica reduces the quality of final alumina products and requires a large consumption of reagents during the desiliconization of aluminate solutions. During the chemical enrichment of kaolinite fraction in alkaline solution, a serious problem of the co-dissolution of Al2O3 with silica arises. The solution to this problem can be the transformation of phase composition with the transformation of kaolin into a chemically resistant compound corundum, which will create conditions for the selective removal of silica. Kazakhstan’s alumina refinery, Pavlodar Aluminum Smelter, processes low-quality gibbsite–kaolinite bauxite from the Krasnogorsk deposit. To improve the quality of bauxite, preliminary gravity enrichment is carried out to separate the kaolinite fraction to a quantity greater than 50%. The purpose of this work was to study the possibility of the selective processing of the kaolinite fraction via various techniques, including preliminary thermal transformation, through sintering, chemical enrichment, autoclave leaching in a circulating aluminate solution, and low-temperature desiliconization, to obtain a solution for decomposition. As a result of this study, the possibility of obtaining a corundum phase after sintering at a temperature of 900–1000 °C was established, which made it possible to obtain 58.8% chemical enrichment through the extraction of SiO2 into solution. Further use of the enriched kaolinite fraction in autoclave leaching in a circulating aluminate solution with low-temperature desiliconization made it possible to obtain an aluminate solution with a caustic modulus of 1.65–1.7, which is suitable for decomposition.

Microbiota and Long-Term Prognosis in Liver Cirrhosis

Purpose. To compare the gut microbiota in patients with an anamnesis of liver cirrhosis of less than and more than 10 years. Materials and methods. A one-stage study and metagenomic fecal sequencing of 40 hospitalized patients with liver cirrhosis were conducted, of which 35 were with a history of cirrhosis of less than 10 years and 5 — more than 10 years. High-throughput sequencing was performed using a MiSeq genetic analyzer (Illumina, USA) and a protocol based on analysis of 16s rRNA gene variable regions. The study was registered in Clinicaltrials.gov (NCT05335213). Data analysis was performed using Kraken2 algorithm. The analysis of the difference in the proportional composition of the microbiome between the groups was carried out using polynomial Dirichlet modeling (Likelihood-Ratio-Test Statistics: Several Sample Dirichlet-Multinomial Test Comparison), the Mann-Whitney test with preliminary data transformation by CLR transformation (Centered log ratio transform), differential analysis of gene expression based on negative binomial distribution (DESeq2). The significance level α assumed to be 0.05. Results. In patients with liver cirrhosis, the dominant phylotypes of fecal microbiota are Firmicutes, Bacteroidetes, Proteobacteria, Actinobacteria, minor components include taxa Aquificae, Coprothermobacterota, Tenericutes, Verrucomicrobia, Chloroflexi, Deinococcus-Thermus, Thermotogae, Chlorobi. Significant differences have been established in the density of dominant and minor philotypes of gut bacteria, such as Actinobacteria, Proteobacteria, Tenericutes, Coprothermobacterota, as well as some classes, genera, bacterial species in patients with different disease duration (p < 0.05). Conclusion. There is no doubt about the effect of gut microbiota on compensation for liver function. The established differences in the composition of the microbiota in patients with liver cirrhosis depending on survival over 10 years are of scientific and practical importance for the formation of an evidence-based approach to the use of microbiome-associated interventions

CONCEPT OF BUILDING A LIBRARY OF TASKS AND SOLUTIONS

The article develops the concept of building a library of tasks and their solutions in the form of computational processes (CPs) and Petri nets (PNs) with the preliminary transformation of CPs into PNs. The conversion includes the extraction of macro operations (MOs) from CPs as a result of their analysis, the construction of PNs and their fragments as models of CPs and MOs, and the modeling of PNs and their fragments. The architecture, structure and interface of the library are proposed. Computational process is a sequence of time-ordered operations and procedures of varying degrees of complexity. The set of PNs, as well as the set of problems for which PNs are solutions, is divided into classes and subclasses. A class includes problems such as Combinatorial, Linear Algebraic Equations, etc.; the Combinatorial class includes subclasses of problems such as Sorting, Search, Sets, Graphs, etc. A macro operation is a fragment of a GP that is a functionally complete computational construct. MOs can have different levels of complexity, starting with the elementary one; they can be built hierarchically. A Petri net is a bipartite graph with two interconnected objects: event-condition, process-resource, etc. Fragments of the PN are models of the MO. The components of the library are tree nodes supplemented with files of their verbal descriptions built according to certain rules. The architecture, structure, interface, and operations of the library provide convenient management, editing, and expansion of knowledge about computational processes and macro operations, making the library open for further research and development by the developer. All files are available to the user, but without the right to edit. The paper presents an example of the initial filling of the library for the Sorting task.

О ВЛИЯНИИ ЛОГАРИФМИРОВАНИЯ ДАННЫХ НА ОЦЕНКУ ДЛИНЫ,ПРИ КОТОРОЙ НАСТУПАЕТ ПОЛОВАЯ ЗРЕЛОСТЬ У РЫБ

To characterize fish sexual maturity, such parameter as the length at which 50 % of individuals are sexually mature is widely applied. The conventional practice is to use the fish length values directly, without their preliminary logarithmic transformation. However, based on theoretical considerations, such logarithmic transformation should be expected to improve the quality of approximation of the relationship between the percentage of mature individuals and their length. This study is aimed at the testing of the hypothesis that logarithmic transformation improves the quality of approximation of the data on fish maturity, as well as at the assessment of practicability and expedience of the logarithmic transformation when estimating the length at which 50 % of the individuals are sexually mature. This research is conducted based on the published data. Approximation was carried out using two methods: by the probability integral of a normal distribution and by the logistic function. Following the data analysis involving an original two-level approach, it has been found out that the preliminary logarithmic transformation of the length values statistically significantly improves the quality of approximation. However, this pattern manifests only in the case of analyzing a certain volume of data sets. The difference between the results obtained using transformed and non-transformed length values is not big and, oftentimes, unsubstantial. Nevertheless, in some cases, such a difference is noticeable, which provides a reason to recommend the logarithmic transformation of the fish length values when conducting the analysis. It is also demonstrated that, during the estimation of the length at which 50 % of the individuals are sexually mature, both tested functions are equally suitable for approximation.

Special Economic Zones of Russia: Forecasting Decisions of Potential Residents and Resident Generation Process Modeling

Modern studies widely discuss the role of special economic zones in stimulating the economic growth and development of Russia, generating the necessary investment flows and increasing the country's innovative potential by expanding production in high-tech sectors of the economy with high added value. The purpose of the study is to model the process of generating residents and to determine quantitative factors that have a statistically significant effect on the average annual growth rate of companies participating in special economic zones in the Russian Federation. The paper describes modern approaches to predicting the choice of potential residents to start doing business in the territory of the SEZ using classification approaches (Support Vector Machines, Decision Trees, Random Forest, Naive Bayes, K-Nearest Neighbor, Gradient Boosting) and regression approaches (logistic regression). A modern classification algorithm was applied in practice - Histogram-based Gradient Boosting Classification Tree, which is stable for analyzing large data with missing variable values and does not require preliminary sample transformation. The paper confirms the hypothesis that there is a positive relationship between the location of the organization and its financial result forming by the end of the year. On average, in the sample, resident companies located near the centers of the constituent entities of the Russian Federation are more successful in terms of generated revenue. The hypothesis that there is a strong relationship between indicators of spatial differentiation of the regions of the Russian Federation and indicators characterizing the process of generating residents and private investment has not been fully confirmed. From a practical point of view, the results of the study could be applied by both resident organizations, potential residents, and SEZ management companies. The theoretical significance of the study lies in the specification of the proposed binary choice model for potential residents, which can be expanded and generalized in future works. At present, there are all the necessary prerequisites for creating conditions for the development of industry, high-tech sectors of the economy and the production of high value-added products in order to increase the stability of the Russian economy.

OPERATOR SPECTRUM TRANSFORMATION IN HARTREE<i>–</i>FOCK AND KOHN–SHAM EQUATIONS

The paper proposes a method for preliminary transformation of the spectrum of the equation operator both in the Hartree–Fock method and in density functional theory. This method makes it possible to solve a partial eigenvalue problem instead of the complete one, and the eigenfunctions turn out to be ordered in a way convenient for calculation. The transformation makes an old idea of grid approximation of a solution competitive in terms of computational speed as compared to widely used approaches based on basis sets methods.

Performance of wetland applied to ecological remediation of abandoned fish ponds: A case study in Gonghu Bay, Tai lake

To restore the abandoned fish ponds to “near natural” state, the wetland restoration was carried out in Gonghu Bay lakeside, and its long-term performance of controlling external load was studied for 5 years. The findings showed that water quality and biodiversity had been improved dramatically after the preliminary transformation. The concentrations of permanganate index (CODMn), total nitrogen (TN), and total phosphorus (TP) obviously decreased from 12.91 mg L−1 to 4.32 mg L−1, from 3.46 mg L−1 to 1.42 mg L−1, and from 0.27 mg L−1 to 0.04 mg L−1, respectively. The proportion of Cyanophyta was effectively reduced from 31.82% to 18.89%, and favored the growth of diatoms (31.82%–37.78%) to be the dominant algae species. Aquatic plant species and coverage gradually increased from 16 to 56 and from 5% to 60%, respectively. An in-deep monitoring done for 5 years (2013–2017) showed that the wetland achieved a satisfactory removal efficiency of 58.95% for TN, 64.60% for TP, and up to 77.83% for chlorophyll-a. Besides, three pollution scenarios, such as stormwater runoff, algal bloom, and continuous water transfer, were selected to explore the tolerance of the wetland to the suddenly increased pollution loads. The results dedicated that even if the inlet load was up to 1.0 × 105 m3 d−1, the removal rate coefficients of wetland for chlorophyll-a, TP, and TN were 0.135–0.239 d−1, 0.041–0.112 d−1, and 0.030–0.109 d−1, respectively, which were equivalent to the well-running wetlands. This study confirmed that the wetland was not only a promising ecological remediation technique to contaminated abandoned fish ponds, but also could withstand high pollution load, which had the prospect of sustainable utilization.

Evaluation Method of Innovative Education Model of E-Commerce Video Live Broadcast Based on Big Data Analysis Technology

In the environment of education big data, how colleges and universities make good use of these data not only affects the orderly operation of the whole education and teaching system of colleges and universities. It will also become an inexhaustible driving force to help colleges and universities promote the reform and innovation of the education and teaching system. This paper takes student evaluation data and student online learning data as research objects. Focusing on the teaching operation and students’ autonomous learning, this paper uses the improved k-mode algorithm to cluster analyze the classroom teaching operation. This paper uses neural network algorithm based on machine learning to predict and compare students’ online course learning. It is hoped that it can provide meaningful reference for the construction of teaching management system and the reform and innovation of teaching management system in colleges and universities. Two research works are mainly carried out through the preliminary analysis and transformation of the data of student evaluation of teaching in a certain university. The improved cosine dissimilarity algorithm is used to eliminate the abnormal teaching evaluation data. The normalization method was used to standardize the teaching evaluation data. The traditional k-mode algorithm is used to cluster the teaching evaluation data. Some problems of k-mode algorithm are pointed out, and the traditional k-mode algorithm is improved. Experimental results show that the improved algorithm is more reasonable and effective.

Electrochemical Cyclization of Alkynyl Enaminones: Controllable Synthesis of Indeno[1,2-c]pyrroles or Indanones.

We report an electrochemical intramolecular [3 + 2] cyclization of alkynyl enaminones in a user-friendly undivided cell under constant current conditions without an oxidant and catalyst, and indeno[1,2-c]pyrrole derivatives could be obtained in good to excellent yields. Notably, preliminary substituent-controlled selective transformation is also achieved under electrocatalysis alone, and indeno[1,2-c]pyrrole (R4 ≠ H) or indanone derivatives (R4 = H) could be prepared directly under electrocatalysis without adding a base and heating process.

Evaluation of Mathematical Models for Teaching Precision in the Framework of Big Data

With the continuous development and application of data computing in the whole society in the construction of digital campus and intelligent campus of each higher education institution. In the environment of education, universities use these data well, which not only affects the orderly operation of higher education but also will become an inexhaustible power to help higher education promote the reform and innovation of education and teaching system. In this paper, we focus on the teaching operation and students’ independent learning by taking students’ evaluation data and students’ online learning data of Y school as the research objects. We conducted a preliminary analysis and transformation of students’ evaluation data of a university, eliminated the abnormal evaluation data by using the improved cosine phase dissimilarity algorithm, standardized the evaluation data by using the normalization method, and used the traditional K -modes algorithm. Based on these three problems, the traditional K -modes algorithm was improved in three aspects, including the determination of the number of clustering families, the determination of the measurement of clustering distances, and the experimental results showed that the improved algorithm was more reasonable and effective.

Processing of Low-Quality Gibbsite-Kaolinite Bauxites

The results of studies on the processing of gibbsite-kaolinite bauxite are presented. The developed technology includes preliminary chemical activation and thermal transformation during enrichment to obtain a concentrate suitable for processing by the Bayer method. As a result of the chemical activation of gibbsite-kaolinite bauxite in a solution of sodium bicarbonate, a change in the phase composition occurs, which made it possible to improve the results of gravity enrichment with the production of a coarse-grained gibbsite fraction. The transformation of bauxite in the temperature range of 900–1000 °C is explained by the decomposition reactions of siderite, gibbsite, kaolinite, calcite, dolomite and sodium ferro-sulfide oxide, as well as the formation of sodium aluminosilicate, hematite, quartz and the chemically stable phase of corundum. The optimum firing temperature of bauxite is 950 °C, after which, as a result of alkaline treatment during chemical enrichment, the extraction of SiO2 into solution was 74.9%. A silicon modulus of enriched bauxite 10.9 units was obtained. As a result of the autoclave leaching of gibbsite-kaolinite bauxite after a two-stage enrichment, the maximum extraction of alumina into solution was 87.4%. The yield of red mud during the processing of bauxite enriched and calcined at 950 °C was 37.62%. During the autoclave leaching of bauxite without enrichment, the yield of red mud was 71%.

Shikimate Kinase; Searching for Potential Novel Anti‐Tubercular Agents

Tuberculosis is a respiratory infection with over 10 million reported cases each year. This infection rate is responsible for over two million deaths annually, second only to HIV in fatalities among infectious diseases annually. Studies in the last decade have shown that tuberculosis rates have gradually increased. This observation suggests that there is an alarming increase in the prevalence of drug resistant strains of tuberculosis, thus the need for the discovery of novel antitubercular agents. The shikimate pathway is a seven step metabolic route that produces aromatic amino acids and other cellular metabolites. The target enzyme in this project, Mycobacterium tuberculosis Shikimate Kinase (MtSK), catalyzes the 5th step of this pathway. MtSK converts shikimate to shikimate 3 phosphate. The overall goal of this project is to express and characterize MtSK to screen for potential antitubercular agents. Initial methods included a bacterial transformation of XL1 blue competent E.coli cells. This preliminary transformation was performed using a pET‐21b plasmid with an aroK gene inserted into the multiple cloning site. Successfully transformed XL1 blue cells were cloned and a second transformation of BL21 DE3 competent cells was performed. Initial small scale expression showed the presence of a band around 20 kDa. The theoretical mass of the enzyme is 19.6 kDa which suggests MtSK was successfully expressed. Expression analysis for large scale supported data from small scale as a band of 20 kDa was present. The purity and molecular weight of MtSK were confirmed by nickel affinity chromatography as well as ESI‐LC‐MS. ATP‐dependent kinetic parameters determined via a spectrophotometric coupled assay showed a kcat of 50 ± 6 mM, KM of 0.2 ± 0.04 mM. shikimate dependent kinetic parameters showed a kcat of 55 ± 2 mM, KM of 1.8 ± 0.1 mM. Quenching intrinsic tyrosine fluorescence showed binding affinities similar to ATP and shikimate‐dependent parameters. The marine compound, avarone showed substantial quenching of intrinsic fluorescence. The inhibitory mechanism of avarone on MtSK is currently under investigation.

Method for Concurrent Identification of a Linear Dynamic Measurement System Based on Preliminary Nonlinear Transformation of the Input Signal

Method for Concurrent Identification of a Linear Dynamic Measurement System Based on Preliminary Nonlinear Transformation of the Input Signal

DYNAMIC HANDWRITTEN SIGNATURE IDENTIFICATION USING SPIKING NEURAL NETWORK

The article proposes a method for dynamic signature identification based on a spiking neural network. Three dynamic signature parameters l(t), xy(t), p(t) are used, which are invariant to the signature slope angle, and after their normalization, also to the signature spatial and temporal scales. These dynamic parameters are fed to the spiking neural network for recognition simultaneously in the form of time series without preliminary transformation into a vector of static features, which, on the one hand, simplifies the method due to the absence of complex computational transformation procedures, and on the other hand, prevents the loss of useful information, and therefore increases the accuracy and reliability of signature identification and recognition (especially when recognizing forged signatures that are highly correlated with the genuine). The spiking neural network used has a simple training procedure, and not all neurons of the network are trained, but only the output ones. If it is necessary to add new signatures, it is not necessary to retrain the entire network as a whole, but it is enough to add several output neurons and learn only their connections. In the results of experimental studies of the software implementation of the proposed system, it’s EER = 3.9% was found when identifying skilled forgeries and EER = 0.17% when identifying random forgeries.

Rainstorm Magnitude and Debris Flows in Pyroclastic Deposits Covering Steep Slopes of Karst Reliefs in San Martino Valle Caudina (Campania, Southern Italy)

Debris flows that have occurred in the area of San Martino Valle Caudina (Campania, Southern Italy) are described by geomorphological and hydrological analyses, focusing on the recent event of December 2019. This area can be considered a key example for studying debris-flow phenomena involving the pyroclastic mantle that covers the karstified bedrock along steep slopes. A hydrological analysis of the time series of the maximum annual rainfall, of durations of 1, 3, 6, 12 and 24 h, was carried out based on a new approach to assess rainstorm magnitude. It was quantified by measuring the deviation of the rainfall intensity from the normal conditions, within a specified time period. As the time series of annual maxima are typically skewed, a preliminary transformation is needed to normalize the distribution; to obtain the Z-value of the standard normal distribution, with mean µ = 0 and standard deviation σ = 1, different probability distribution functions were fitted to the actual data. A specific boxplot was used, with box width Z = ±1 and whiskers length Z = ±2. The deviations from these values provide the performance of the distribution fits. For the normalized time series, the rates shown by the trends and relative significance were investigated for the available time series of 11 rain gauges covering the Western–Central Campania region. The most critical condition for the debris-flow initiation appears to occur when a severe or extreme rainfall has a duration ≥ 12 h. The trend analysis did not detect statistically significant increases in the intensity of the rainfall of duration ≥ 6 h.

The Concurrent Error-Detection Systems Organization Based on the Boolean Complement Method with the Preliminary Transformation of Operating Functions into Check Vectors of Berger Codes

The article describes a new way of concurrent error-detection (CED) systems organization using the Boolean complement method, which involves the use of pre-compression of signals from the diagnostic object using encoders of classical sum codes (Berger codes). Control of compressed signals is carried out using the constant-weight "1-out-of-4" code. In comparison with the known methods of the CED systems organization, it is possible to implement a self-checking digital device using one such circuit, and this significantly reduces the structural redundancy. The article suggests using the encoders of modified Berger codes with improved error detection characteristics as a compression scheme.

Tuberculosis shikimate kinase as a target for the development of new antimycobacterials

Tuberculosis is a respiratory infection with over 10 million reported cases each year. This infection rate is responsible for over two million deaths annually, second only to HIV in fatalities among infectious diseases. Since 1960 tuberculosis rates have steadily declined worldwide as medical technology has advanced to produce more effective antibiotics. However, recent studies have shown that tuberculosis rates have seen a steady increase. This observation suggests that there is an alarming increase in the prevalence of drug-resistant strains of tuberculosis, thus the need for the discovery of novel anti-tubercular agents. Targeting potential enzymatic pathways for drug discovery requires the pathway to possess minimal overlap with the host. The shikimate pathway is a seven-step metabolic route that produces aromatic amino acids and other cellular metabolites. This pathway is typically present in microorganisms and has no mammalian counterpart, making any of the enzymes in this pathway suitable targets for screening of potential anti-tubercular agents. The target enzyme here, Mycobacterium tuberculosis Shikimate Kinase (MtSK), catalyzes the 5th step of this pathway, converting shikimate to shikimate-3-phosphate. The overall goal of this project is to express and characterize MtSK in order to screen for potential anti-tubercular agents. Initial methods included a bacterial transformation of XL-1 blue competent E.coli cells. This preliminary transformation was performed using a pET-21b plasmid with an aroK gene inserted at the multiple cloning site. Successfully transformed XL-1 blue cells were cloned and a second transformation using BL21 DE3 competent cells as an expression host was performed. Small scale expression showed the presence of a band around 20 kDa. The theoretical mass of the enzyme is 19.6 kDa which suggests MtSK was successfully expressed within the transformed cells. Expression analysis for large-scale supported data from small scale as a band of 20 kDa once again appeared in the verification SDS-PAGE gel. Purification of MtSK was carried out through nickel affinity chromatography. Subsequently, kinetic characterization and inhibitors studies will be performed using inhibitors like avarone and hymenidin.

Multi-level Chunk-based Constituent-to-Dependency Treebank Transformation for Tibetan Dependency Parsing

Dependency parsing is an important task for Natural Language Processing (NLP). However, a mature parser requires a large treebank for training, which is still extremely costly to create. Tibetan is a kind of extremely low-resource language for NLP, there is no available Tibetan dependency treebank, which is currently obtained by manual annotation. Furthermore, there are few related kinds of research on the construction of treebank. We propose a novel method of multi-level chunk-based syntactic parsing to complete constituent-to-dependency treebank conversion for Tibetan under scarce conditions. Our method mines more dependencies of Tibetan sentences, builds a high-quality Tibetan dependency tree corpus, and makes fuller use of the inherent laws of the language itself. We train the dependency parsing models on the dependency treebank obtained by the preliminary transformation. The model achieves 86.5% accuracy, 96% LAS, and 97.85% UAS, which exceeds the optimal results of existing conversion methods. The experimental results show that our method has the potential to use a low-resource setting, which means we not only solve the problem of scarce Tibetan dependency treebank but also avoid needless manual annotation. The method embodies the regularity of strong knowledge-guided linguistic analysis methods, which is of great significance to promote the research of Tibetan information processing.

Improvement of Video Measuring Systems for Electric Traction Network Diagnostics

Purpose. The purpose of the article is system analysis of the state of electric traction networks, as well as methods of complex diagnostics of the contact network from a moving laboratory car to increase the resolution capability of the systems for monitoring the quality of interaction between the contact network and current collectors. Methodology. The problem was solved by theoretical analysis and experimental studies of the current collection parameters, a generalized model of the device for monitoring the wear of the overhead wire and its functional units in order to determine the factors affecting the control error, as well as the development of methods that reduce the specified error. The apparatus of factor analysis, the theory of optoelectronic circuits and methods of statistical information processing were used. Findings. Innovative approaches and qualitatively new diagnostic tools are proposed that allow expanding the functionality of the laboratory cars for testing the contact network for power supply enterprises of electrified railways, industrial and urban electric transport. Hardware and software have been developed to improve the system for measuring the parameters of the overhead wire and other components of the contact network. Originality. The theoretical maximum permissible, from the point of view of the contact network operation, error in monitoring the wear of the overhead wire and other components of the electric traction network has been determined. A method for increasing the resolution capability of a stereo television system and an adaptive lighting system is proposed. It consists in preliminary image transformation and expansion of the dynamic range of image measurement. The ways of introducing a high-speed real-time compression algorithm and using LED backlighting are proposed. Practical value. The quality of the contact network diagnostics in difficult conditions for video surveillance has been improved. A camera with a built-in image compression module without losing its performance is proposed, which allows capturing and transmitting full-frame images to a computing complex for the application of new diagnostic algorithms for contact network components. The modernized video measuring systems for the wear of the overhead wire for monitoring the grounding of the contact network supports are proposed, as well as elements of track facilities located in the visibility zone of specialized cameras, which ensure the operability of the systems at any time of the day at speeds up to 160 km/h. An air curtain subsystem was implemented to protect the cameras.

Многомерный алгоритм кумулятивных сумм для обнаружения изменений характеристик временных рядов

The article presents a cumulative sum algorithm intended to detect a sudden step-like change in the probabilistic characteristics of a monitored time series when such a change (“disorder”) is associated with a simultaneous change in both the location characteristics and the dispersion characteristics of the corresponding distribution functions. In the general case of a multidimensional time series, the disorder is associated with a jump in the values of the mathematical expectation vector (the vector of means) and covariance matrix entries. To solve this problem, it is proposed to use a preliminary linear transformation of the time series values, as a result of which the covariance matrix is transformed to the unity form before disordering and to the diagonal form after disordering. The change in the vector of means is analyzed, and the main relations describing the considered detection algorithm are derived. It is noted that by using the above-mentioned linear transformation it is possible to simplify the obtaining of the reference data necessary for synthesizing the monitoring algorithm with the predetermined properties. As an example, a particular case of a one-dimensional time series and a disorder in the form of a simultaneous change in the mean and variance is considered. For this case, reference data obtained by applying the simulation method are given, using which it is possible to find the monitoring algorithm triggering threshold and estimate the average delay time of detecting the specified disorder from the given interval between false alarms. This study is a logical continuation and further development of the approach to construction of multidimensional algorithms for detecting disorders [1].