{"title":"超图模型解释中的一些离散断层扫描问题","authors":"Hasmik Sahakyan","doi":"10.1134/s1054661824010176","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In this paper we consider discrete tomography problems with an additional requirement of non-repeatability of rows of the binary matrix to be reconstructed; as well as discrete tomography problems with given pairwise projections. Representing the problems in the hypergraph model and pointing out their equivalence to the basic definitions, we state the following results: (i) nonconvexity of the set of hypergraphic sequences of simple hypergraphs with <span>\\(n\\)</span> vertices and <span>\\(m\\)</span> hyperedges in the <span>\\(n\\)</span>-dimensional <span>\\(m + 1\\)</span>-valued lattice, (ii) characterization of monotone Boolean functions associated with degree sequences of 3-/(<i>n</i>–3)-uniform hypergraphs, (iii) formulation of discrete tomography problems with paired projections, their connection to hypergraph degree sequence problem with generalized degrees, a solution for a particular case.</p>","PeriodicalId":35400,"journal":{"name":"PATTERN RECOGNITION AND IMAGE ANALYSIS","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2024-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Some Discrete Tomography Problems in Hypergraph Model Interpretation\",\"authors\":\"Hasmik Sahakyan\",\"doi\":\"10.1134/s1054661824010176\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<h3 data-test=\\\"abstract-sub-heading\\\">Abstract</h3><p>In this paper we consider discrete tomography problems with an additional requirement of non-repeatability of rows of the binary matrix to be reconstructed; as well as discrete tomography problems with given pairwise projections. Representing the problems in the hypergraph model and pointing out their equivalence to the basic definitions, we state the following results: (i) nonconvexity of the set of hypergraphic sequences of simple hypergraphs with <span>\\\\(n\\\\)</span> vertices and <span>\\\\(m\\\\)</span> hyperedges in the <span>\\\\(n\\\\)</span>-dimensional <span>\\\\(m + 1\\\\)</span>-valued lattice, (ii) characterization of monotone Boolean functions associated with degree sequences of 3-/(<i>n</i>–3)-uniform hypergraphs, (iii) formulation of discrete tomography problems with paired projections, their connection to hypergraph degree sequence problem with generalized degrees, a solution for a particular case.</p>\",\"PeriodicalId\":35400,\"journal\":{\"name\":\"PATTERN RECOGNITION AND IMAGE ANALYSIS\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2024-04-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"PATTERN RECOGNITION AND IMAGE ANALYSIS\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1134/s1054661824010176\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"PATTERN RECOGNITION AND IMAGE ANALYSIS","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1134/s1054661824010176","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
Some Discrete Tomography Problems in Hypergraph Model Interpretation
Abstract
In this paper we consider discrete tomography problems with an additional requirement of non-repeatability of rows of the binary matrix to be reconstructed; as well as discrete tomography problems with given pairwise projections. Representing the problems in the hypergraph model and pointing out their equivalence to the basic definitions, we state the following results: (i) nonconvexity of the set of hypergraphic sequences of simple hypergraphs with \(n\) vertices and \(m\) hyperedges in the \(n\)-dimensional \(m + 1\)-valued lattice, (ii) characterization of monotone Boolean functions associated with degree sequences of 3-/(n–3)-uniform hypergraphs, (iii) formulation of discrete tomography problems with paired projections, their connection to hypergraph degree sequence problem with generalized degrees, a solution for a particular case.
期刊介绍：
The purpose of the journal is to publish high-quality peer-reviewed scientific and technical materials that present the results of fundamental and applied scientific research in the field of image processing, recognition, analysis and understanding, pattern recognition, artificial intelligence, and related fields of theoretical and applied computer science and applied mathematics. The policy of the journal provides for the rapid publication of original scientific articles, analytical reviews, articles of the world''s leading scientists and specialists on the subject of the journal solicited by the editorial board, special thematic issues, proceedings of the world''s leading scientific conferences and seminars, as well as short reports containing new results of fundamental and applied research in the field of mathematical theory and methodology of image analysis, mathematical theory and methodology of image recognition, and mathematical foundations and methodology of artificial intelligence. The journal also publishes articles on the use of the apparatus and methods of the mathematical theory of image analysis and the mathematical theory of image recognition for the development of new information technologies and their supporting software and algorithmic complexes and systems for solving complex and particularly important applied problems. The main scientific areas are the mathematical theory of image analysis and the mathematical theory of pattern recognition. The journal also embraces the problems of analyzing and evaluating poorly formalized, poorly structured, incomplete, contradictory and noisy information, including artificial intelligence, bioinformatics, medical informatics, data mining, big data analysis, machine vision, data representation and modeling, data and knowledge extraction from images, machine learning, forecasting, machine graphics, databases, knowledge bases, medical and technical diagnostics, neural networks, specialized software, specialized computational architectures for information analysis and evaluation, linguistic, psychological, psychophysical, and physiological aspects of image analysis and pattern recognition, applied problems, and related problems. Articles can be submitted either in English or Russian. The English language is preferable. Pattern Recognition and Image Analysis is a hybrid journal that publishes mostly subscription articles that are free of charge for the authors, but also accepts Open Access articles with article processing charges. The journal is one of the top 10 global periodicals on image analysis and pattern recognition and is the only publication on this topic in the Russian Federation, Central and Eastern Europe.
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