Penrose mosaic as a quasistochastic tree-graph lattice

Yudin, V. V.; Pisarenko, T. A.; Lyubchenko, Elena; Chudnova, Olga; Karygina, Yu. A.

doi:10.1134/1.1466491

Cited by 10 publications

(39 citation statements)

References 6 publications

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“…But along with the alphabet of segregates as structure units, the notion of neighborhood (adjacency, incidence) plays a main role in grid systems [11]. Grid and lattice systems can then be conveniently represented by coordination Cayley tree graphs (CTGs), which we have systematically studied in a series of works [11]- [15].…”

Section: Introductionmentioning

confidence: 99%

“…Grid and lattice systems can then be conveniently represented by coordination Cayley tree graphs (CTGs), which we have systematically studied in a series of works [11]- [15].…”

Section: Introductionmentioning

confidence: 99%

“…For our coordination graphs, there is evidently an intercluster local overlap, but the Markov property is then preserved. Previously, we introduced the term "Markov thicket," which is much more complicated and excessive compared with generalized Bethe-Cayley trees [11], [12].…”

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confidence: 99%

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Entropic measure of the order-disorder character in lattice systems in the representation of coordination Cayley tree graphs

2010

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We systematically expound the infodynamical method for analyzing lattice and grid systems. We establish the logic and algorithm for mapping given objects to coordination Cayley tree graphs and present their main properties. Tree graphs of grid systems are complicated objects, and the principle of cluster-type simplicial decomposition can be used to study them. Based on a simplicial decomposition, we construct the enumerating structures, from which we construct entropy-type functionals. We pose the percolation problem on Cayley tree graphs in a nonconventional sense, which may be considered for both enumerating structures and their entropies. The corresponding entropy percolational dependences and their critical indices can be considered sufficiently universal measures of order in lattice systems. The simpliciality also implies an analogy with the fractality principle. We introduce three types of fractal characteristics and give analytic expressions for fractal dimensions for the tangential and streamer representations and for the Mandelbrot shell.

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Section: Introductionmentioning

confidence: 99%

“…Grid and lattice systems can then be conveniently represented by coordination Cayley tree graphs (CTGs), which we have systematically studied in a series of works [11]- [15].…”

Section: Introductionmentioning

confidence: 99%

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Entropic measure of the order-disorder character in lattice systems in the representation of coordination Cayley tree graphs

2010

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“…While applying these technologies to the process modeling, an IDEF notations set, which includes such notations as IDEF0, IDEF1Х, IDEF3, IDEF9, etc., and DFD notation are regarded as the basic ones [18][19][20][21][22]. The other notations set, Workflow, is focused on modeling of rules and demands, which should be followed during the operations.…”

Section: Adaptation Of Integrated Platform Of Modeling System Prmentioning

confidence: 99%

Modeling material flows as basic tool for enhancing company's efficiency during crisis

Chudnova¹,

Lubchenko²

2017

Proceedings of the International Conference "Actual Issues of Mechanical Engineering" 2017 (AIME 2017)

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Abstract-The article reviews the problems, emerging while planning, managing and evaluating the efficiency of material flows of enterprises, identifies and justifies the necessity of using integrated platform of management on the basis of systems and process theories. Moreover, the article provides the conceptual framework of models of systems decomposition and types of processes description and distinguishes the key steps for developing an integrated model of material flows. In addition, the article describes how the model of material flows, based on the integrated platform with the use of SADT-and ARIStechnologies, may be adapted in practice and shows the viability of developed models, collected in the albums of processes. The material flow model will provide an opportunity to conduct indepth analysis and point out some details, which remain unnoticed by employees as well as by management team, so that it will help to identify problem areas and enhance the quality.Keywords-Material flows, processes-flows, systems theory, process theory, dynamic stability, enhancement of efficiency, integrated platform/integrated platform of management, SADTtechnologies, ARIS-technologies, the album of processes, quality control, process approach, system approach to management, "AS-IS" model, "TO-BE" model.

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“…For the considered organizations, it is necessary to sustain maximum feasibility for as long as possible, meaning to stay in market for a prolonged period of time, and this is nothing less then the concept of critical path in the theory of net graphs [15][16]. Surely, lately this given concept is mainly used for evaluation of duration of implementation of innovative projects and optimization of deadlines.…”

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confidence: 99%

Comparative study on economic security of enterprises depending on implemented business activities quantity

2017

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Abstract.The results of a comparative study on economic security of enterprises depending on the quantity of business activities are published in the article. The sampling for analysis was conducted based on statistic data of Primorsky Region of the Russian Federation. The control points are the years of the most thorough data collection on the business activities of one-field and diversified enterprises:

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Penrose mosaic as a quasistochastic tree-graph lattice

Cited by 10 publications

References 6 publications

Entropic measure of the order-disorder character in lattice systems in the representation of coordination Cayley tree graphs

Entropic measure of the order-disorder character in lattice systems in the representation of coordination Cayley tree graphs

Modeling material flows as basic tool for enhancing company's efficiency during crisis

Comparative study on economic security of enterprises depending on implemented business activities quantity

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