Pretrees and Arborescent Convexities

Malyutin, A. V.

doi:10.1007/s10958-016-2689-1

Cited by 2 publications

(4 citation statements)

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“…Properties (23)- (25) imply that M is infinite. Therefore, an infinite number of P j 's contain I z , whence by property (23) it follows that all P j 's contain I z , which contradicts (25). Suppose to the contrary that it does not.…”

Section: Lemma Letmentioning

confidence: 94%

“…In [23] it was proved that the class of convexities corresponding to the pretrees coincides with the class of arborescent convexities introduced in [14]. In [23] it was proved that the class of convexities corresponding to the pretrees coincides with the class of arborescent convexities introduced in [14].…”

Section: 19mentioning

confidence: 99%

“…However, it can be shown (see [23]) that the restrictions of these maps to the images of the "duals" are mutually inverse bijections; furthermore, by restricting these maps further, to the class of the convex structures with Carathéodory number at most 2 and the corresponding class of interval spaces, we obtain mutually inverse functors (with respect to the corresponding categories, in which inclusions act as morphisms). However, it can be shown (see [23]) that the restrictions of these maps to the images of the "duals" are mutually inverse bijections; furthermore, by restricting these maps further, to the class of the convex structures with Carathéodory number at most 2 and the corresponding class of interval spaces, we obtain mutually inverse functors (with respect to the corresponding categories, in which inclusions act as morphisms).…”

Section: 19mentioning

confidence: 99%

“…The variety of convex structures generated by trees 4 was considered in the paper [14] by P. Duchet. In [23] it was shown that this variety is equivalent to the class of pretrees: there is a natural oneto-one correspondence between the elements of this variety and the pretrees. We remark that in the class of ternary structures as well as in the class of intervals, the subclass of pretrees is finitely based (it can be defined by a finite list of forbidden subspaces), while the variety of convex structures that is equivalent to the class of pretrees is no longer finitely based in the class of all convex structures.…”

Section: Introductionmentioning

confidence: 99%

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Pretrees and the shadow topology

Malyutin

2015

St. Petersburg Math. J.

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A further development of the theory of pretrees, started by the work of L. Ward, P. Duchet, B. Bowditch, S. Adeleke and P. Neumann, and others, is presented. In particular, a relationship between this theory and the theory of convex structures is established. The shadow topology is investigated in detail. This remarkable topology emerges on tree-like objects of various types and has broad application.2010 Mathematics Subject Classification. Primary 54F50.

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Section: Lemma Letmentioning

confidence: 94%

Section: 19mentioning

confidence: 99%

Section: 19mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Pretrees and the shadow topology

Malyutin

2015

St. Petersburg Math. J.

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Automated Identification of an Operator Anticipation on Marine Transport

Nosov

Popovych

Cherniavskyi

et al. 2020

RIC

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Context. The article discusses approaches to anticipation identification being an essential part of the decision-making process done by the operator by using the example of a sea captain in ergatic systems of critical infrastructures in the sea transport management. The mentioned above aspect of anticipation of operators can be regarded as being a complex form of human-machine interaction and, certainly, claims for further elaboration of information and tools to be used. Objective. The way to approach development is taken as being based on an information analysis of the full range of trajectories of decision-making by operators at the time of performing complex multi-stage actions. These items are rooting out of their adopted strategy of human-machine interaction. Besides, it leads to the formation of a metric being able to algorithmically represent the enormous number of variants. It can be done taking into account conditions of combinatorial representation in terms of the geometric theory of groups on the Cayley graph. Method. Being a part of the approach elaboration the having been obtained during the analysis of the database of navigation simulators mathematical model of experimental data collecting and processing succeeded to be constructed. To confirm the formalalgorithmic approach a simulation was challenged to be carried out helping to form the trajectory of the operator's decision making in critical situations. It was felicitously performed basing on the three-factor ERO-AEA-EAPI model. Thus, the algebraic and software representation of the metric decision space is noticed to uncover approximate complex human-machine interactions in uncertain environments. As a result, the converting process of data of the main subject of critical infrastructure (i.e. the operator) into knowledge is able to be coped with. In addition, factors possible to be gauged in the proposed metric are able to be uncovered. Results. In order to carry out the feasibility assessment of the developed approach as well as formal-algorithmic ones, an experiment was performed by using the Navi Trainer 5000 navigation simulator (NTPRO 5000). During having one of the most troublesome operations i.e. mooring we wanted the server data to be analyzed. As a result, data about anticipation being shaped as triangular constructs in the quasi-isometric space of Cayley graph is reported to have been obtained. The automated neural networks being used for result obtaining led to delivering of the possibility to get multiple data regression and to analyze the relationships of many independent variables. It is considered to be clear evidence due to having found out results of scattering and reliability diagrams. Conclusions. The having been presented in the investigations formal-algorithmic approach together with the developed software tools and the approaches of converting data into knowledge about operator anticipation are said to embrace the possibility to classify and to identify individual decision-making strategies when managing a vessel and to pre...

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Pretrees and Arborescent Convexities

Cited by 2 publications

References 5 publications

Pretrees and the shadow topology

Pretrees and the shadow topology

Automated Identification of an Operator Anticipation on Marine Transport

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