Dynamic network model based on the use of hypercomplex number systems
In recent years, the direction of the study of networks in which the links in terms of content correspond to the mutual impact of the nodes has been developed. Many works have been devoted to the study of such complex networks but most often they relate to the distribution of one type of activity (i...
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| Формат: | Стаття |
| Мова: | Ukrainian |
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Інститут проблем реєстрації інформації НАН України
2020
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| Назва журналу: | Data Recording, Storage & Processing |
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drspiprikievua-article-2259182021-03-10T16:12:52Z Dynamic network model based on the use of hypercomplex number systems Модель динамічної мережі на базі застосування гіперкомплексних числових систем Ланде, Д. В. Боярінова, Ю. Є. Каліновський, Я. О. complex systems, complex networks, hypercomplex number system, isomorphism of hypercomplex systems, impact model складні системи, складні мережі, гіперкомплексна числова система, ізоморфізм гіперкомплексних систем, модель впливу In recent years, the direction of the study of networks in which the links in terms of content correspond to the mutual impact of the nodes has been developed. Many works have been devoted to the study of such complex networks but most often they relate to the distribution of one type of activity (impact). In the process of development of the newest technologies various mathematical models are developed and investigated: models with thresholds, models of independent cascades, models of distribution of epidemics, models of Markov processes, etc. It is proposed to use hypercomplex number systems (HNS), which are a mathematical apparatus that allows you to model some network problems and solve them at a new level, i.e. to consider a complex network with several properties in each node. In this paper, we consider networks where the edges correspond to the mutual impact of the nodes. It is suggested to match the number of properties in each node and the measurability of a hypercomplex number system with the appropriate number of basic elements. Each HNS corresponds to a Kelly table showing the multiplication law of these HNS. The properties of the HNS allow one to build an isomorphic transition from a filled Kelly table to a less filled one, which simplifies the calculation. To model the problem using hypercomplex number systems, a specialized software of hypercomplex computing (SSHC) is proposed, which is a software tool that can be called, connected to a program and transported to other computers and is based on the Maple computer algebra system. This made it easy to model a complex network with several impact. Fig.: 5. Refs: 16 titles. Запропоновано використання гіперкомплексних числових систем для опису динамічної мережі та різноманітних впливів у цих мережах. Для спрощення обчислень запропоновано використання ізоморфних гіперкомплексних числових систем, таблиця Келі однієї з яких має діагональний вигляд. Інститут проблем реєстрації інформації НАН України 2020-12-29 Article Article application/pdf http://drsp.ipri.kiev.ua/article/view/225918 10.35681/1560-9189.2020.22.4.225918 Data Recording, Storage & Processing; Vol. 22 No. 4 (2020); 79-90 Регистрация, хранение и обработка данных; Том 22 № 4 (2020); 79-90 Реєстрація, зберігання і обробка даних; Том 22 № 4 (2020); 79-90 1560-9189 uk http://drsp.ipri.kiev.ua/article/view/225918/226093 Авторське право (c) 2021 Реєстрація, зберігання і обробка даних |
| institution |
Data Recording, Storage & Processing |
| collection |
OJS |
| language |
Ukrainian |
| topic |
complex systems complex networks hypercomplex number system isomorphism of hypercomplex systems impact model складні системи складні мережі гіперкомплексна числова система ізоморфізм гіперкомплексних систем модель впливу |
| spellingShingle |
complex systems complex networks hypercomplex number system isomorphism of hypercomplex systems impact model складні системи складні мережі гіперкомплексна числова система ізоморфізм гіперкомплексних систем модель впливу Ланде, Д. В. Боярінова, Ю. Є. Каліновський, Я. О. Dynamic network model based on the use of hypercomplex number systems |
| topic_facet |
complex systems complex networks hypercomplex number system isomorphism of hypercomplex systems impact model складні системи складні мережі гіперкомплексна числова система ізоморфізм гіперкомплексних систем модель впливу |
| format |
Article |
| author |
Ланде, Д. В. Боярінова, Ю. Є. Каліновський, Я. О. |
| author_facet |
Ланде, Д. В. Боярінова, Ю. Є. Каліновський, Я. О. |
| author_sort |
Ланде, Д. В. |
| title |
Dynamic network model based on the use of hypercomplex number systems |
| title_short |
Dynamic network model based on the use of hypercomplex number systems |
| title_full |
Dynamic network model based on the use of hypercomplex number systems |
| title_fullStr |
Dynamic network model based on the use of hypercomplex number systems |
| title_full_unstemmed |
Dynamic network model based on the use of hypercomplex number systems |
| title_sort |
dynamic network model based on the use of hypercomplex number systems |
| title_alt |
Модель динамічної мережі на базі застосування гіперкомплексних числових систем |
| description |
In recent years, the direction of the study of networks in which the links in terms of content correspond to the mutual impact of the nodes has been developed. Many works have been devoted to the study of such complex networks but most often they relate to the distribution of one type of activity (impact). In the process of development of the newest technologies various mathematical models are developed and investigated: models with thresholds, models of independent cascades, models of distribution of epidemics, models of Markov processes, etc.
It is proposed to use hypercomplex number systems (HNS), which are a mathematical apparatus that allows you to model some network problems and solve them at a new level, i.e. to consider a complex network with several properties in each node. In this paper, we consider networks where the edges correspond to the mutual impact of the nodes.
It is suggested to match the number of properties in each node and the measurability of a hypercomplex number system with the appropriate number of basic elements. Each HNS corresponds to a Kelly table showing the multiplication law of these HNS.
The properties of the HNS allow one to build an isomorphic transition from a filled Kelly table to a less filled one, which simplifies the calculation.
To model the problem using hypercomplex number systems, a specialized software of hypercomplex computing (SSHC) is proposed, which is a software tool that can be called, connected to a program and transported to other computers and is based on the Maple computer algebra system. This made it easy to model a complex network with several impact. Fig.: 5. Refs: 16 titles. |
| publisher |
Інститут проблем реєстрації інформації НАН України |
| publishDate |
2020 |
| url |
http://drsp.ipri.kiev.ua/article/view/225918 |
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2024-04-21T19:34:19Z |
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