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This paper presents a new formulation and solution of a mixed-integer program for the hierarchical orthogonal hypergraph drawing problem, and the number of hyperedge crossings is minimized. The novel feature of the model is in combining several stages of the Sugiyama framework for graph drawing: vertex ordering, the assignment of vertices’ x-coordinates, and orthogonal hyperedge routing. The hyperedges of a hypergraph are assumed to be multi-source and multi-target, and vertices are depicted as rectangles with ports on their top and bottom sides. Such hypergraphs are used in data-flow diagrams and in a scheme of cooperation. The numerical results demonstrate the correctness and effectiveness of the proposed approach compared to mathematical heuristics. For instance, the proposed exact approach yields a 67.3% reduction of the number of crossings compared to that obtained by using a mathematical heuristic for a dataset of non-planar graphs.

The GMOS (Global Mercury Observation System) project has the overall goal to develop a coordinated observing system to monitor mercury on a global scale. Here we present the long-term (2011–2020) air mercury monitoring data obtained at the Listvyanka station located at a shore of Lake Baikal, Siberia. The long-term monitoring shows obvious seasonal variation of the background mercury concentration in air, which increases in the cold and decreases in the warm season. The short-term anomalies are associated with the wind carrying the air from the industrial areas where several big coal-fired power plants are located. A positive correlation between the mercury, SO2 and NO2 concentrations is observed both in the short-term variations and in the monthly average concentrations. The analysis of forward and backward trajectories obtained with the HYSPLIT model demonstrates revealing of the mercury emissions sources. During the cruise of 2018, the continuous air mercury survey over Lake Baikal covered 1800 km. The average mercury concentration over Baikal is notably less in comparison with the average value obtained at the onshore Listvyanka station during the same days of the cruise. That can lead to the conclusion that Baikal is a significant sink of the atmospheric mercury.

This work proposes an innovative approach to evaluate the functional characteristics of a heterogeneous underwater wireless acoustic sensor network (UWASN) using a stochastic model and the network connectivity criterion. The connectivity criterion is probabilistic and considers inherently distinct groups of parameters: technical parameters that determine the network function at specific levels of the communication stack and physical parameters that describe the environment in the water area. The proposed approach enables researchers to evaluate the network characteristics in terms of energy efficiency and reliability while considering specific network and environmental parameters. Moreover, this approach is a simple and convenient tool for analyzing the effectiveness of protocols in various open systems interconnection model levels. It is possible to assess the potential capabilities of any protocol and include it in the proposed model. This work presents the results of modeling the critical characteristics of heterogeneous three-dimensional UWASNs of different scales consisting of stationary sensors and a wave glider as a mobile gateway, using specific protocols as examples. Several alternative routes for the wave glider are considered to optimize the network’s functional capabilities. Optimal trajectories of the wave glider’s movement have been determined in terms of ensuring the efficiency and reliability of the hybrid UWASN at various scales. In the context of the problem, an evaluation of different reference node placement was to ensure message transmission to a mobile gateway. The best location of reference nodes has been found.

Glider-type autonomous underwater vehicles are today one of the most promising areas of marine robotics. This is confirmed by the frequent and remarkable results of various research missions and projects. The cumulative group application of underwater and no less innovative wave gliders can significantly reduce the time of obtaining oceanographic data. Together with wave gliders, one group of such robotic objects can significantly increase the efficiency, time and volume of obtaining oceanographic data. There is big interest in increasing the functionality of such a group. This article presents one of the possible alternatives to increase the functionality of a group of underwater and waveguide hang gliders. We present the process of upgrading the existing design, control algorithms and software of the SHADOW underwater glider, which was developed by the teams of the St. Petersburg State Marine Technical University (SMTU) and Okeanos JSC in order to jointly study the monitoring of underwater potentially dangerous objects with the St. Petersburg State Fire Service EMERCOM of Russia. A structural-functional approach to the group application of underwater and waveguides is also proposed, which is capable of providing oceanographic, meteorological and environmental monitoring data online, based on the developed multilayer system for planning the trajectories of group movement of objects. The results of full-scale sea trials and the developed algorithms are demonstrated.

Artificial Intelligence (hereinafter referred to as AI) systems have recently found great application and use in various industries, such as data processing, data analysis, and the operation control of marine robotic complexes, etc. In view of the ever-increasing degree of complexity of the missions assigned to marine robotic systems, it is becoming obvious that the AI technologies should be used as combined systems which can provide control of marine robotic complexes (hereinafter referred to as MRCs), their navigation in sea, logic formation of MRC behaviour in uncertain environments, path planning, and processing optimization of the received MRC payload data. All the areas mentioned above are within the field of MRC development, and currently do not have a general solution. This article discusses the development process of an intelligent system for path planning of a group of marine robotic complexes. The architecture of the intelligent system is based on a cascade approach, which includes the consistent use of functional modules designed as various “organs of perception” of the system. A detailed description of the development of each module and mathematical modelling of the presented algorithms are provided in this paper, and the main results of the conducted full-scale experiments are demonstrated.

The paper develops a theory of spectral boundary value problems from the perspective of general theory of linear operators in Hilbert spaces. An abstract form of spectral boundary value problem with generalized boundary conditions is suggested and results on its solvability complemented by representations of weak and strong solutions are obtained. Existence of a closed linear operator defined by a given boundary condition and description of its domain are studied in detail. These questions are addressed on the basis of Krein's resolvent formula derived from the explicit representations of solutions also obtained here. Usual resolvent identities for two operators associated with two different boundary conditions are written in terms of the so called M-function. Abstract considerations are complemented by illustrative examples taken from the theory of partial differential operators. Other applications to boundary value problems of analysis and mathematical physics are outlined. (Initial version title \"Spectral Boundary Value Problems and their Linear Operators\", 2009)

Results and discussion During the experiments it was found that after 4 hours only a liquid extract from hawthorn blood-red leaves at a dose of 100 pl / kg contributed to a significant increase in diuresis (by 20%), natriuresis (by 38%) and kaliuresis (by 77%) in the animal experimental group relative to indicators of water-alcohol control, which indicates a decrease in tubular reabsorption (Table 2). [...]a liquid extract of hawthorn blood-red leaves at a dose of 100 pi / kg with a single intragastric administration for 4 hours of experiment promoted an increase in diuresis and natriuresis similarly to the action of furosemide at a threshold dose of 1 mg/kg. [...]within 24 hours of the experiment, the liquid extract of the hawthorn blood-red leaves in the animals experimental group resulted in an increase in renal excretion of water (by 29%), sodium (by 30%) and creatinine (by 36%) relative to the water-alcohol control which indicates a decrease in tubular reabsorption and an increase in glomerular filtration (Table 4). Conclusions Because of the study of the diuretic and antidepressant action of phytopharmaceutical products, a number of features of their pharmacological action were revealed. [...]the liquid extract of hawthorn blood-red leaves at a dose of 100 pl/kg had a rapid progress of diuretic and saluretic action (tubular effect), a prolonged effect, showing an additional creatininurative effect (glomerular effect) by the end of 24 hours of the experiment.

The article deals with the artificial mind specifics as compared to the human one. The authors show that artificial mind development is defined by the computer processing power. The artificial mind inability for scientific creativity at the current level of technologies development is established.

This is an overview of mathematical heritage of Sergey Naboko in the area of functional models of non-self-adjoint operators. It covers the works by Sergey in model construction, the analysis of absolutely continuous and singular spectra and the construction of the scattering theory in model terms.

We give an overview of operator-theoretic tools that have recently proved useful in the analysis of boundary-value and transmission problems for second-order partial differential equations, with a view to addressing, in particular, the asymptotic behaviour of resolvents of physically motivated parameter-dependent operator families. We demonstrate the links of this rich area, on the one hand, to functional frameworks developed by S. N. Naboko and his students, and on the other hand, to concrete applications of current interest in the physics and engineering communities.