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• ## Modeling of automated monitoring systems

The article presents a set-theoretic model that generalizes the concept of a monitoring system. The model is a tuple that includes a monitoring object, the infrastructure of the monitoring system, initial data and monitoring results, and a set of relationships between the components of the model. Each component of the model is detailed at 1-2 levels of detail. For some elements of the model, examples from existing monitoring systems are given. The model can be used to create new or modify existing monitoring systems.

Keywords: monitoring system, monitoring object, set-theoretic model, tuple, data processing, infrastructure, sensor, software

• ## Algorithm of nonparametric estimation of transition probability distribution density for Markov model of university staff dynamics

The paper deals with the construction of an algorithm for nonparametric estimation of the transition probability distribution density for the Markov model of the dynamics of the number of university employees. The problem of reconstruction of transition probability distribution density on a retrospective sample of small volume is solved. The result of the solution is the transition probability matrix, the elements of which are random variables with distribution laws obtained from retrospective data. A distinctive feature of the algorithm is the simultaneous consideration of regional and functional constraints on the values of transition probabilities. The convergence of the algorithm has been experimentally confirmed.

Keywords: probability density, nonparametric estimation, Markov model, simulation modeling, university staff movement, publication activity

• ## Access points locations evaluation of the indoor positioning system in mines

In this paper, we review a number of algorithms for solving the problem of building a map and the problem of SLAM - Simultaneous localization and mapping - in various formulations. These tasks are solved on a graph structure that describes a mine working, in which a localization system from stationary access points is installed. To solve the SLAM problem, the FastSLAM algorithm is used in various modifications, depending on the method for estimating the positions of access points. In all the proposed solutions, it was possible to achieve an error in estimating the positions of access points of no more than 2 meters. The problem of building a map is solved as a combinatorial problem of searching for a permutation of access points by known positions. The proposed permutation search algorithm showed tangible advantages in terms of execution time over the exhaustive search method on systems with 5 or more access points.

Keywords: graph, mining, localization, map construction, SLAM, MCMC, particle filter, Kalman filter, Bayes method

• ## Local search algorithm for the problem of covering a polygon with a forest of rooted trees

The article considers the problem of optimizing the scheme of portages in a cutting area. The mathematical model of the cutting area is a polygon - a bounded closed broken part of the plane. The portage scheme corresponds to a root graph (forest, tree) of a special type. We have introduced the concept of covering a polygon with a rooted forest. The cover is interpreted as the possibility of cutting and collecting all the trees in the cutting area while moving the harvester and forwarder along the trails. The trails are laid according to the found covering root forest. Two variants of the algorithm for solving the problem are proposed, which are a modification of the local search. The first algorithm uses the greedy method we described earlier[18] to find the underlying solution. The second algorithm uses the branch and bound method to find the basic solution. Comparative experiments were carried out on polygons sized 12x12 and 18x18. Experimental results show that both modifications of the algorithm improve the basic solution. The first algorithm improves the solution by an average of 11% for a 12x12 polygon and by 24% for a 18x18 polygon.

Keywords: portage schemes, cutting area, polygon covering the root forest, local search, coverage

• ## Construction of a road graph for routing mobile robot in a closed system of corridors

Two approaches are proposed for constructing a road graph for routing mobile robot in a closed system of corridors with a focus on the use of the robot computer vision to identify the entrances to the rooms from the hallway. In the first version of the graph the vertices correspond to the two types of objects: connection points (branching intersection) corridors and location of entrances - each input corresponds to only one vertex. The second version for the formation of the graph allows to concider returns of the robot and the robot motion in the joints of the corridors. For each room's entry formed two vertices to describe the robot motion in all directions.

Keywords: routing, road graph, mobile robot