Markov Algorithm Research Articles

A METHOD FOR SYNTHESIZING TOPOS OF HASHES IN THE CATEGORICAL cN-SCHEME OF THE MARKOV ALGORITHM. Part 1

In organizational systems, economic interactions are studied. The purpose of this study is to synthesize a problem-oriented management subsystem for combating money laundering and terrorist financing. To achieve this goal, the problem of synthesizing a constructive way of processing such interactions is solved. The method is based on the development of the N-scheme of the Markov algorithm with an output that cannot be considered normal according to Markov. This algorithm scheme allows us to consider a quadruple consisting of words in the ordered and extended Markov alphabet A2, morphism numbers N, source numbers i, and the alphabet M. From the N-scheme of the Markov algorithm, its categorical version is synthesized. The need for this scheme of the Markov algorithm is due to the solution of the problem of folding Markov occurrences of words into each other of large length for their more compact representation. The idea of organizing a convolution for the entire topos is tested separately. The term “topos of hashes” is introduced into scientific circulation. This topos is considered as an alternative way to represent blocks of chains of Markov occurrences. The hash topos is formed from hash trees known in blockchain technology. This idea follows from previous studies of classifiers in topos, as well as the possibility of splitting chains of Markov occurrences into blocks. The convolution is considered using gamma and hash functions. In the course of the study, it was possible to theoretically show the connection between Markov algorithms and blockchain technology, taking into account the fact that each chain of occurrences of words in each other is considered as a category, and these chains are formed in different sources, otherwise worlds, and the way they are synthesized may have signs of a creative process, then a connection was found between the theories of categories, algorithms, blockchain technology and intuitionistic models by S. Kripke and L. E. Ya. Brouwer.

THE METHOD OF MARKING ITS CHAINS OF OCCURRENCES OF A WORD IN THE N-SCHEME OF THE MARKOV ALGORITHM

In order to detect and classify -voids in these sources, a method of labeling its chains of occurrences with a word is investigated using the N-scheme of the Markov algorithm. The keys of the database used by the N-schema of the Markov algorithm to record the classified objects and morphisms in the topos are considered as input data for the algorithm that performs the second pass through the data for classifying -voids. The idea of a second pass through the data, using the database, is subjected to critical analysis, in terms of the cost of its implementation and the search for ways to build an algorithm that does not require a second pass through the data. Marking your chains of occurrences in the N-scheme of the Markov algorithm can be done in two main ways, based on the morphism number and the first word in the chain. Marking your chains of occurrences in the N-scheme of the Markov algorithm can be done in two main ways, based on the morphism number and the first word in the chain. This property distinguishes the N-scheme of the Markov algorithm from other algorithms. The control implementation mechanism in the N-scheme of the Markov algorithm is considered for the case of organizing a repeated pass through the data in the database. The method proposed in the study for marking one’s chains of occurrences with a word is considered, in which, during the first pass through the data, the first word in the chain is entered into the database as its unique marker. The mechanism of “stitching” of chains of occurrences in a topos is studied with a different composition of words in chains, a case is highlighted in which the first words in the “stitched” chains are combined into a tuple and form compositions that are unique for each such chain and can be used to mark them. In the course of the study, it was found that in order to detect -voids, it is necessary to process the entire set of such tuples, so they will either have to be placed in memory, or in a file, or in a database, thus, one way or another, implement the algorithm for processing these tuples second pass through the data. Some negative aspects of this approach have been established, for example, the length of markers formed by words can be significant, so it is advisable to collapse them with respect to some function, for example, a hash, synthesizing topos hashes for all given data. It is concluded that it is expedient to study the properties of the hash topos using the alphabet of the M N-scheme of the Markov algorithm for encoding occurrences relative to the previous ones and to synthesize a method for marking own chains of occurrences in the hash topos.

Change analyses and prediction of land use and land cover changes in Bernam River Basin, Malaysia

Land use and land cover (LULC) change is a dynamic process which is significantly influenced by anthropogenic activities. Analysing historical LULC trends and predicting future dynamics is critical to provide insights for decision-makers and planners aiming for sustainable land management and development. This study focuses on the Bernam River Basin (BRB). It employs an integrated approach that combines the Multi-Layer Perceptron (MLP), the Cellular Automata (CA)-Markov algorithm, remote sensing, and Geographical Information System (GIS) techniques. Using multi-temporal 10m resolution Sentinel-2 Landsat imagery from 2010, 2020, and 2022, the study classified LULC into seven categories: water, forest, wetlands, agriculture, urban, barren, and rangeland areas. Change analysis from 2010 to 2020 was conducted, with 2022 validating predicted LULC transitions. The MLP model, trained on land change driver variables, facilitated the generation of transition potentials for simulating future LULC changes. A spatially explicit CA-Markov model implemented LULC change projections for 2022, 2025, 2050, and 2075, based on the transition potentials. The analysis reveals an annual increase of 0.24% in water, 0.61% in forest, and 2.11% in urban areas, while wetlands (2.69%), agriculture (2.47%), barren (3.51%), and rangeland (4.58%) experienced declines. The CA-Markov approach accurately predicted LULC transitions for 2022, validated through an error matrix with an overall accuracy of 91.56% based on 450 sampling points. Predictions for 2025–2075 indicate rising trends in water (1.76%), wetlands (29.18%), agriculture (60.08%), urban (96.53%), barren (0.59%), and rangeland areas (3.57%). Forests are expected to decrease by 12% (261.52 km2). The study identified agriculture and urban expansion as the primary drivers of LULC changes in the river basin. These findings provide critical information for regional authorities to formulate evidence-based policies and management strategies, ensuring the environmental sustainability of BRB. Furthermore, these predicted LULC patterns can be integrated into complementary models, such as the Soil and Water Assessment Tool, to assess the impacts of LULC changes on water resources.

Continuous Hidden Markov Algorithm-Based Multimedia Melody Retrieval System for Music Education

Education professionals receive instruction in Music Education (ME) to prepare for prospective jobs like secondary or primary music teachers, schools ensembles executives, or ensembles directors at music institutions. In the discipline of music education, educators do original research on different approaches to teaching and studying music. The most accurate and effective method of extracting music from huge music databases has become one of the most frequently discussed participants in contemporary multimedia information retrieval development. The essence of multimedia material is presented within a range of techniques since it is not bound to a single side. These several categories could consist of the song’s audio components and lyrics for musical information. Retrieving melodic information, subsequently, becomes the main focus of most recent studies. Aside from being an expensive deviate from academics, music programs are neither a viable profession neither a valid pastime. Therefore, in this study, we offer a Continuous Hidden Markov Algorithm (CHMA) related a novel method for recovering melodies from musical multimedia recordings. CHMA is considered to be the most basic dynamic Bayesian network. Two various types of audio frame features and audio example features are extracted throughout the feature extraction procedure from the audio signal according to unit length. Every music clip receives a unique approach that we implement with concurrently using various CHMA. The initial music gets processed using a trained CHMA that monitors fundamental frequencies, maps states, and generates retrieval outcomes. The training time for Traditional opera reached 455.76 minutes, the testing time for Narration achieved 56.10 minutes, and the recognition accuracy for advertisement reached an impressive 98.02%. A subsequently experimental result validates the applicability of the proposed approach.

THE METHOD OF MARKING ITS CHAINS OF OCCURRENCES WITH A MORPHISM NUMDER IN THE N-SCHEME OF THE MARKOV ALGORITHM

To detect and classify λ-voids, we study a way of marking own chains of occurrences of words in each other by the morphism number determined in the N-scheme of the Markov algorithm. In the framework of the category-theoretic approach, the N-scheme of the Markov algorithm is considered as a topos form of the Markov algorithm. The topos explores additional properties of classifiers. The idea of introducing the Markov control flow algorithm into the N-schema is subjected to a comprehensive theoretical analysis. The control flows in the Turing algorithm and the topos form of the Markov algorithm are subjected to a comparative analysis. From the standpoint of the theoretical provisions of the constructivist approach of the Soviet (Leningrad) school, the conditions for equivalence and non-equivalence of the Markov and Turing algorithms are considered. The form of the Markov algorithm equivalent and non-equivalent to the Turing algorithm is synthesized, substantiated and analyzed. To detect the final occurrences in its chain of occurrences, necessary for the detection and classification of λ-voids, the composition of the elements of the N-scheme of the Markov algorithm, which is responsible for this, is specified. For some unknown algorithm for numbering its chains of occurrences of words in each other using the database of the N-scheme of the Markov algorithm, the method of its implementation by the imitating Turing algorithm is considered. The idea of Turing's algorithm imitating some of the algorithms used for the synthesis of artificial intelligence is analyzed. In the context of this study, it is shown that the imitation of the Turing algorithm is due to the need for a second pass through the data, organized by accessing the database in the N-scheme of the Markov algorithm. A description is given for the method of marking own chains of occurrences with the morphism number in the N-scheme of the Markov algorithm. It is concluded that it is necessary to decompose the instruction for checking whether the chain of occurrences belongs to its own chain into fragments, the length of which will be relatively small, for which we consider the method of marking the chains of occurrences with a word, as well as convolution.

Associative computing in algorithm theory

The article discusses associative calculations in the theory of algorithms. Explains associative calculations using ordered substitutions and graphical diagrams. In the theory of algorithms, the need arises for mathematical refinement of the algorithm. One of them is the regular Markov algorithm. Associative calculus is also used in the regular Markov algorithm.

METHODS FOR SYNTHESIZING SIGNS OF THE RISKS OF LAUNDERING PROCEEDS FROM CRIME

Methods for synthesizing risk features are being explored in the interest of creating a methodology for classifying MLB and TF risk typologies in big data from multiple data sources of organizational systems. A new space of risk features is investigated, consisting of words and their morphisms, represented by diagrams of Markov occurrences of words in each other, obtained by synthesis using the N-scheme of the Markov algorithm. Typologies of individual risks of money laundering and terrorist financing are considered as separate risk knowledge. When considering knowledge, it is taken into account that they are of a changeable nature, therefore, they must be reviewed and refined in the process of counteraction. Knowledge is treated with the assumption that some of them are quite far apart when viewed through the structure of the categories they form. The study shows synthesized methods for excluding and suspending risk features in a promising risk classifier. The method for excluding risk features from a promising classifier is considered and illustrated by an example of a valid feature in the classifier of the Central Bank of the Russian Federation, introduced by the Bank of Russia Regulation No. 375-P dated March 2, 2012 (as amended on October 20, 2020), which requires exclusion from it. The way to suspend the action of a risk attribute, without excluding it from a promising classifier, is presented in the study, using the example of a risk from the classifier of the Central Bank of the Russian Federation. Examples of refinement of a risk attribute, without excluding it from the classifier and synthesizing a risk typology for it, are presented in the form of categorical formulas with restrictions on some morphism parameters. The presented methods of excluding and suspending the action of risk features in the risk classifier allow a wider use of the acquired knowledge, which is understood as typologies of individual risks, and take into account the changing nature of this knowledge, understood as a specification of knowledge.

Research on Optimization Method for Fault-Tolerant Integration of Real-Time Dual-Computer Embedded Systems

Abstract This paper addresses the fault-tolerant performance of real-time dual-computer embedded systems. The article first emphasizes the importance of real-time and reliability in various fields and points out that improving fault-tolerant performance is a crucial topic. Based on the Markov chain algorithm, the study optimizes the fault-tolerant integration method for real-time dual-computer embedded systems. By constructing a model of Markov algorithm and using the deadline of the task as a benchmark, the passage and transfer probabilities of faults are calculated. The article also provides algorithmic proofs of fault-tolerant control of Markovian jump systems and calculates their stability levels. The results show that the fault passage rate of the system increases as the number of complex tasks increases, e.g., when the number of complex tasks is 4, the passage rate can reach 90%. In addition, in the scheduling test, it was found that the schedulability of the system increases with the increase in the number of processors. When the number of processors reaches 5, the system's schedulability is 43%. In conclusion, the system fault tolerance optimization method based on Markov algorithm proposed in the article can effectively improve the reliability and fault tolerance of the system.

Gesture Recognition Technology of VR Piano Playing Teaching Game based on Hidden Markov Model

Virtual Reality (VR) is a kind of simulation environment generated by computer simulation. It is a kind of isolation of users from the physical environment, and users are fully engaged in the simulation environment. In music teaching, especially in the learning of piano performance, VR technology can simulate the real playing experience without physical piano, so that learners can learn and practice piano anywhere. At present, the traditional way of learning piano often needs the guidance of professional piano teachers, and learners must study and practice beside the piano, which undoubtedly brings limitations to the time and space of learners. VR technology provides a more convenient way for learners to learn and practice without a physical piano, making learning more flexible and free. Firstly, a piano playing teaching game platform based on VR technology is constructed to provide a virtual piano playing scene. Then, by collecting a large number of piano players' gesture data, they are accurately marked. Finally, the Hidden Markov Model (HMM) is used to train and model the gesture data, and the key features of the gesture sequence are extracted to realize the recognition and real-time feedback of the piano player's gesture. According to the findings, the recognition accuracy of the Principal Component Analysis-HMM (PCA-HMM) without playing correction is very low after playing correction. Compared to the logarithmic likelihood ratio test, the recognition rate of the quadratic statistical model is only 15%. The results show that this method has good iterative convergence and convergence performance, which can effectively avoid falling into local optima. Compared with the traditional hidden Markov algorithm, it reduces 96.05% and 89.48% respectively. Compared with the fuzzy hidden Markov algorithm, it reduces 90.20% and 73.35% respectively. The average time and standard deviation for real-time positioning and map construction are 0.251s and 0.152s, respectively. The fitness of HMM based on fuzzy Particle Swarm Optimization (PSO) is 6.8% and 2.6% higher than that of the hidden Markov algorithm and the fuzzy hidden Markov algorithm, respectively. At the same time, in the comparison between the research model and other algorithm models, the accuracy and other parameter performance of the research model are better, with the highest error value of only 3.5, which is 5.9 lower than the lowest Convolutional Neural Network (CNN) algorithm model. It can be seen that the error value of the model used in the study is lower and the performance is better. Learners can receive real-time guidance and a more immersive playing experience through this technology. This provides useful reference for further exploring the combination of music teaching and VR technology

Neural integrated Markov model for effective script identification and classification in biometric system

Biometric scripts are required to be adaptable and robust for differentiating human input for preventing forging. However, based on the individual biometrics system's functionality, the script identification and classification are vital for input detection. Therefore, for improving the adaptability and improved analysis, this article introduces an Integrated Classification model (ICM) using Neural Markov Algorithm (NMA) for biometric systems. The proposed model jointly performs script detection and classification for different biometric functions. The flaws in the process are identified using output validation and the error between output and input. Therefore, this random change in error is computed using the Markov model for detection based on which the classification as robust or non-robust is decided. For improving the robust type classification, the current error level is accounted for and script flaws and improvements are recommended. Based on the script improvement further testing is performed for the detection phase using Markov stochastic computation. This detection is alone performed for preventing non-robust classifications for varying inputs. Therefore, the maximum robust combinations are identified across different biometric scripts that suit the design purpose.

Retracted: Cultivation of Students’ Independent Learning Ability in Teaching Chinese as a Foreign Language Based on the CDIO Model of Guiding Data Structures and Hidden Markov Algorithms

Retracted: Cultivation of Students’ Independent Learning Ability in Teaching Chinese as a Foreign Language Based on the CDIO Model of Guiding Data Structures and Hidden Markov Algorithms

MARKOV NETWORK MODEL

Markov networks synthesized from the N-scheme of the Markov algorithm, developed to replace his well-known y-scheme, are studied theoretically from the standpoint of theories of algorithms and categories. The provisions of the theory of Markov algorithms are developed in the direction of synthesizing methods for the joint processing of words and morphism values that are occurrences in these words. In Markov networks, morphisms are weighted according to the method adopted in artificial neural networks. The material for the synthesis of Markov networks are diagrams of Markov occurrences of words into each other, obtained from input data samples, by classifying occurrences in the alphabet M = λιτφпо1…оx/αβδγχκμ. The Markov network model and the activation function of its morphemes are synthesized and subjected to scientific analysis. The idea of joint consideration of category theory and the theory of Markov algorithms is developed for the control channel, so this control channel is understood as an n-category associator introduced into the N-scheme of the Markov algorithm. In Markov networks, chain termination mechanisms are studied, using the control channel command, using combined methods of classifying words and morphisms, previously studied for the N-scheme of his algorithm, the evolution of categories formed by words is considered due to their occurrences in each other. For the method of synthesizing training samples from diagrams of Markov occurrences, a scientific substantiation of prescriptions for processing samples is carried out. For activation functions, examples of their implementation are considered. The categorical representation of the activation function is synthesized for Markov networks and subjected to a separate scientific analysis. For single-layer and multi-layer Markov networks of direct distribution, a block diagram has been developed. In Markov networks, the concept of zero-nets is introduced. As a promising direction for further theoretical research in Markov networks, multilayer Markov networks of indirect propagation are singled out, which have a conclusion that cannot be considered normal according to Markov. In the conclusions to the study, it is noted that Markov networks have a category-theoretic representation and can be synthesized from Markov zero-nets.

The effect of intelligent tour guide system based on attraction positioning and recommendation to improve the experience of tourists visiting scenic spots

With the advancement of technology and economic development, human living standards have been substantially improved. The demand for tourism has also increased. Smart tourism uses information technology to integrate tourism resources. Tourists are provided with the right travel solutions for their needs. To further enhance the tourist experience, a smart tour guide system based on attraction positioning and recommendation is proposed. The RankSVM+time algorithm and K-means clustering algorithm are used to achieve attraction recommendation. The tourist flow path planning method of scenic spots is combined with D*algorithm to realize dynamic programming of tourist routes. A smart tour guide system based on tourist demand analysis is established to achieve data interaction and attraction positioning. The tour guide system is built based on analyzing the needs of tourists, realizing the functions of data interaction and attraction location. Tour guide services are provided in the form of voice or image. The experimental data shows that the F-value of RankSVM+time algorithm reaches 0.75. The recommendation accuracy is higher than that of RankSVM+Markov algorithm. The shortest running time is 81 s, which is faster than other methods. The intelligent tour guide system also dynamically adjusts the route visit scheme when dynamic changes occur in the attractions. The results show that the intelligent tour guide system based on attraction location and recommendation is highly accurate, fast and adaptable, which can enhance the tourist experience of visitors.

DEFINITION OF MARKOV NETWORKS FROM THE POSITION OF THE THEORIES OF CATEGORIES AND N-CATEGORIES

The study develops new provisions of the theory of Markov algorithms. The area of use of the N-scheme of the Markov algorithm, developed to replace its wellknown y-scheme, is being expanded. The study solves the scientific problem of developing the Markov algorithm in the direction of processing not only words, but also morphisms. Such a problem has not been posed or solved before in the theory of Markov algorithms. Morphisms that differ from each other by types, where some are numeric and others are categorical, are proposed to be processed together. In the study of methods for processing morphisms in the Markov algorithm, it is proposed to use the wellknown in science and practice idea of weighing numerical morphisms. The very idea of weighting morphisms is considered more broadly as a task for the synthesis of a Markov network from separate components, such as an N-schema Markov algorithm for a single data source and a Markov system for many sources of big data. Markov networks are introduced into scientific circulation using the methodology adopted for artificial neural networks. This approach allows us to reduce the time for comprehending the main theoretical provisions of Markov networks, in comparison with artificial neural networks. The same technique is used to classify diagrams of Markov occurrences of words in each other, which are the basis for the synthesis of Markov networks. Approaches to weighting the values of morphisms in Markov networks do not fundamentally differ from those used in artificial neural networks. Diagrams of Markov occurrences are considered from category-theoretic positions, where words are assumed to be associated categories, otherwise, n-categories. For Markov networks, theoretical considerations are given on the activation of their elements by a secret morphism. The use of category-theoretic positions in Markov networks allows us to say that these networks are also activated by all associators used in the N-scheme of the Markov algorithm, as well as by the control channel, which is also an associator. At the same time, associators are considered as n-category objects, which distinguishes Markov networks from artificial neural networks. An N-scheme of the Markov algorithm and a Markov system with weight coefficients and thresholds for weighting the values of morphisms are synthesized. It is concluded that Markov networks provide joint processing of words and morphisms, and it is in the network that additional methods of processing morphisms are implemented that were not previously taken into account in the theory of Markov algorithms.

Collaborative Management of Resource Allocation and Precoding for Dual-Mode Networks

A sub-6GHz (μWave) and millimeter wave (mmWave) dual-mode network can deliver high data rates while maintaining dependable coverage. This paper proposes a novel resource allocation and precoding algorithm based on collaborative sensing in the dual-mode network. We formulated the collaborative optimization problem of resource allocation and precoding, which maximizes the sum of data rates while meeting minimum acceptable rate requirements and ensuring proportional fairness. Considering the spatial similarity between mmWave channel and μWave channel, the prior information of mmWave channel predicted by μWave band is generated to process sensing weight (i.e., subchannel allocation weight of Markov algorithm), which realizes fast dual-mode network resource allocation. Furthermore, a low complexity two-stage precoding scheme for dual-mode networks is proposed based on μWave spatial information. Low-complexity analog precoding is realized in the first stage based on μWave spatial information. In the second stage, inspired by the correlation between minimum mean square error (MMSE) and mutual information, this paper proposes an alternating optimization algorithm to find a local weighted sum-rate (WSR) optimum with low complexity. Compared with other heuristic algorithms, simulation results demonstrate the apparent advantages of the proposed collaborative sensing optimization algorithm. Most importantly, it can be seen that we can achieve a performance that approaches an upper bound.

PHONEMES, MORPHEMES, MORPHS AND ALLOMORPHS IN THE MARKOV ALPHABET OF A SET OF DATA SOURCES

For artificial languages formed by many sources of big data, in the Markov alphabet, a prescription is investigated that provides linkage between the word and the source, through the consideration of phonemes, morphemes, morphs and allomorphs in this language. The artificial language is studied in the context of solving the problem of synthesizing a methodology for classifying the risks of laundering proceeds from crime and financing terrorism in big data of organizational systems. New provisions of the theory of Markov algorithms are being developed. Methods of data decomposition using the N-scheme of the Markov algorithm, developed to replace his well-known g-scheme, are studied. A method for decomposing words into phonemes in the Markov alphabet is considered. It has been established that Markov phonemes are formed on the basis of terminal symbols of the alphabet M = litjпо1…оx /abdgckm for big data input samples and the alphabet MK = litj/abdgckm for the control channel. The method of synthesizing morphemes from Markov phonemes is studied from the positions of both the theory of algorithms and linguistics. The properties of roots and affixes of morphemes are considered from the standpoint of the theory of algorithms, in particular, in the N-scheme of the Markov algorithm. A scientific contradiction in the linguistic approach to the formation of morphemes is revealed, a way to overcome it is proposed. The results of the theoretical substantiation of the method of determining (assigning) for morphemes morphs and allomorphs within the framework of the theory of algorithms are given. New properties of Markov phonemes in the Markov alphabets AM±2 and KMK±2 not previously seen in linguistics are established. Some scientific conclusions previously obtained in linguistics are confirmed from the position of the theory of algorithms. A generalized, reference model of a morpheme has been developed, its abstract nature has been confirmed, methods for synthesizing morphs and allomorphs in a categorical representation format have been given. The statement is synthesized in the form of a Markov diagram of occurrences, its comprehensive analysis is carried out. It is concluded from the above research results that the decomposition of big data into phonemes and morphs provides the representation of statements in the form of chains of occurrences that can be recoded into a categorical presentation format, and by analyzing numbers-types and numbers of morphisms, it is possible to extract their signatures from morphs, which are allomorphs.

METHODOLOGY FOR CLASSIFYING MONEY LAUNDERING RISKS TYPOLOGIES

The method of classifying the typologies of money laundering and terrorist financing risks in big data from a variety of data sources of organizational systems is investigated. The main provisions of this technique are theoretically substantiated, reference models and calculation formulas are given. An algebraic approach for the synthesis of the method is proposed, a theoretical justification of the feasibility of its use is given. The algebraic approach to the synthesis of the methodology is implemented on the basis of category theory and the theory of algorithms, in particular the theory of Markov algorithms, which is considered outside of normal algorithms. The N-scheme of the Markov algorithm is considered, which was developed to replace its well-known g-scheme and provides processing of words in natural, artificial and combined languages, which can be represented in an ordered and extended Markov alphabet A±2, which takes into account many sources of big data. Methods for inputting incomplete, heterogeneous (heterogeneous) and non-representative input data samples are given. A method is proposed for converting input data samples into cycles of the Big Data Transfer Protocol. A reference model of the legal economic activity of the organizational system has been synthesized. This reference model is subjected to analysis and signs of illegal economic activity of mutually interacting organizational systems are highlighted. A reference model of the system for classifying the risks of laundering proceeds from crime and financing of terrorism has been developed. To combat money laundering, the N-scheme of the Markov algorithm for one data source and the Markov system, consisting of such schemes, for a variety of big data sources are theoretically substantiated. It is concluded that the synthesized Markov system provides a decomposition of words and their morphisms, contains a common data input control channel, and provides a classification of money laundering risks.

Improved Hidden Markov Algorithm Based on Bayes in Low Dose CT Images

Improved Hidden Markov Algorithm Based on Bayes in Low Dose CT Images

Assessing overdiagnosis of fecal immunological test screening for colorectal cancer with a digital twin approach

Evaluating the magnitude of overdiagnosis associated with stool-based service screening for colorectal cancer (CRC) beyond a randomized controlled trial is often intractable and understudied. We aim to estimate the proportion of overdiagnosis in population-based service screening programs for CRC with the fecal immunochemical test (FIT). The natural process of overdiagnosis-embedded disease was first built up to learn transition parameters that quantify the pathway of non-progressive and progressive screen-detected cases calibrated with sensitivity, while also taking competing mortality into account. The Markov algorithms were then developed for estimating these transition parameters based on Taiwan FIT service CRC screening data on 5,417,699 residents aged 50–69 years from 2004 to 2014. Following the digital twin design with the parallel universe structure for emulating the randomized controlled trial, the screened twin, mirroring the control group without screening, was virtually recreated by the application of the above-mentioned trained parameters to predict CRC cases containing overdiagnosis. The ratio of the predicted CRCs derived from the screened twin to the observed CRCs of the control group minus 1 was imputed to measure the extent of overdiagnosis. The extent of overdiagnosis for invasive CRCs resulting from FIT screening is 4.16% (95% CI: 2.61–5.78%). The corresponding figure is increased to 9.90% (95% CI: 8.41–11.42%) for including high grade dysplasia (HGD) and further inflated to 15.83% (95% CI: 15.23–16.46%) when the removal adenoma is considered. The modest proportion of overdiagnosis modelled by the digital twin method, dispensing with the randomized controlled trial design, suggests the harm done to population-based FIT service screening is negligible.

ASSOCIATORS IN THE N-SCHEME OF THE MARKOV ALGORITHM

The prescriptions defining the association of words and morphisms in the N-scheme of the Markov algorithm synthesized to replace its well–known g-scheme are investigated. The prescriptions for processing words from the expanded and ordered Markov alphabet using the N-scheme of his algorithm are considered. The analysis of consequences for algorithms arising from some prescriptions used in the N-scheme of the Markov algorithm is carried out. Examples of Markov occurrences of words using word associators and morphisms are illustrated with figures showing the structure of n-category associators. The homology of Markov systems defined by associators is found. One of the Markov systems, which is a homology, consisting of N-schemes of the Markov algorithm, in which the control channel is also an N-scheme of the Markov algorithm, is singled out. It is shown that the alphabets M and MK together with the numbers-types should be used to increase the reliability of algorithms, since these alphabets provide for overcoming loops, in other words, do not allow algorithms to enter an infinite cycle. This variant of the Markov system is analyzed in order to study its properties. The distinctive properties of such a system are highlighted. The method of association of several homogeneous morphisms is considered. A method for setting the tuning mode using the control channel in the Markov system is proposed. It is noted that the method can be extended in case of entering initial, controlled parameters in order to check the safety and technical condition of the equipment. It is indicated that there are several prescriptions responsible for the association of words and morphisms in the N-scheme of the Markov algorithm, which are structurally related to the composition of associators. It is noted that the composition of the Markov alphabet word associators is sufficient, but perhaps not necessary for solving some applied problems, therefore, no restrictions are imposed on its composition and methods of expansion or ordering. It is concluded that in systems where clear and fuzzy (isolated morphisms) are used together, it is allowed to determine the composition of the associators of isolated morphisms by introducing new prescriptions.