Springer

Distributions of in-degree and out-degree in directed graphs evolving by the linear preferential attachment (PA) without edge and node deletion were derived in Bollob\'{a}s, Riordan (2002). The same distributions, but in undirected graphs evolving by the PA with edge and node deletion, were obtained in Ghoshal et al. (2013). Our paper is devoted to a modeling %an empirical study of in- and out-degree distributions in directed graphs evolving by the PA and with edge and node deletion. The PA model is taken the same way as in Ghoshal et al. (2013). We show by a simulation study that the in- and out-degree distributions can be modeled by a power-law distribution or a power-law distribution with an exponential correction depending on the PA parameters.

The problem of drawing up a bypass plan for targets moving rectilinearly to one point for simple movements of an interceptor (traveling salesman) is considered. A new criterion of the problem is proposed based on the initial partition of the possible intercept area, as well as an algorithm for finding a sub-optimal bypass plan based on the construction of a solution search tree by the Monte Carlo method. A numerical implementation of the algorithm has been developed, modeling has been carried out and the obtained plans for bypassing targets have been statistically analyzed.

A preferential attachment (PA) has been suggested to model network evolution and to explain conjectured power-law node degree distributions in real-world networks. In Markovich, Ryzhov (2022a,b), the schemes of the linear PA proposed in Wan et al. (2020) for the network evolution were suggested for information spreading. The PA and the well-known algorithm SPREAD proposed in Mosk-Aoyama, Shah (2006) were compared regarding the minimum number of evolution steps K ∗ required to spread a single message among a fixed number of nodes in non-homogeneous directed networks. This comparison was done in Markovich, Ryzhov (2022a,b) without node and edge deletion during the evolution. The objective of the current study is to investigate the AQ3 impact of the PA parameters on spreading of a single message to a fixed number of nodes in the graph when an existing node or edge is uniformly deleted at each step of the PA evolution. The results are provided for simulated and real graphs.

In this study, a pursuit-evasion game of two players, known as a game of two identical cars, is examined. It is assumed that the game proceeds in a two-dimensional plane. Both players have a constant speed and a limited turn radius. The goal of the first player (pursuer) is to ensure that the second player (evader) enters the capture circle as quickly as possible. The goal of the evader is to avoid or delay capturing for as long as possible. The kinematics of both players are described using the same equations. Thus, the game has only one free parameter: capture radius. This study aims to provide an exhaustive analytical description of the barrier surface for all values of capture radius. Previously, Merz analytically investigated the barrier in a game of two identical cars. In this work, it was found that there is a certain critical value of the capture radius, above which the barrier is qualitatively different from Merz’s example. In addition, we obtained an explicit analytical description of the optimal feedback controls for the barrier.

We study the degree of individual and coalitional manipulability of q-Paretian social choice rules under Impartial Culture. Manipulability is defined as a situation, when an agent or a coalition, which consists of some agents, misrepresents her/their preferences to obtain a better outcome of the social choice rule. We study a class of q-Paretian social choice rules, which consists of four rules: Strong q-Paretian simple majority rule, Strong q-Paretian plurality rule, Strongest q-Paretian simple majority rule, and Condorcet practical rule. For the cases of 3, 4, and 5 alternatives and for the cases from 3 to 100 agents, we use computer modeling to calculate a number of manipulability indices. We provide the analysis of the results for different cases.

A new model of inventory control with returns is considered, when it is possible for consumers to return (under certain conditions) the products they have purchased and a similar model of multi-channel controlled queueing system with switching of service channels. An optimal inventory control strategy in such a system turns out to be four-level. Then we investigate a model of a multilinear queueing system (QS) with channel switching under uncertainty and study the analogy of this model with the model of inventory control with returns.

As of February 07, 2022, more than 395 million cases of COVID-19 had been identified in the world, with 5.74 million deaths. The paper considers methodology for predicting the number of cases in the short term using a preliminary assessment of countries based on three indicators: expert assessments of the law-abiding population, the level of education and restrictive measures taken in the country. The description and composition of the groups obtained are given. An assessment of the accuracy of the forecast results is made. A comparison of the considered models of 2020 with 2022 is given.

In the present paper we analyze data obtained in experiments of resource allocation games with two mechanisms: the Yang-Hajek’s mechanism (YH) and mechanism based on the alternating direction method of multipliers (ADMM). Previous research has shown that there is some correlation between consensus achievement and share of certain types of behavior. This paper considers behavior models based on best response and Pareto improvement. The aim of the research was to investigate individuals’ behavior variation on mechanism change. A behavior based on Pareto improvement is demonstrated by players in both mechanisms slightly more often than only in one mechanism. At the same time, more players demonstrate behavior based on best response in either YH or in ADMM than in both mechanisms. Players had an opportunity to subjectively rank mechanisms; dependence between players behavior and subjective ranking is also studied. It is possible that players give higher rank to the mechanism where they behave according to the best-response and Pareto improvement models more often. There can be inverse relationship between the ranking of YH mechanism and the share of Pareto improvement behavior.

Evolution of random undirected graphs by the clustering attachment (CA) without node and edge deletion and with uniform node deletion is investigated. The CA causes clusters of consecutive exceedances of the modularity over a sufficiently high threshold. The modularity is a measure that allows us to divide graphs into communities. It shows the connectivity of nodes in the community. An extremal index (a local dependence measure) approximates the mean cluster size of exceedances over a sufficiently high threshold. Considering the change of the modularity at each evolution step, the extremal index of the latter random sequence indicates the consecutive large connectivity of nodes and thus, it reflects the community appearance during the network evolution. This allows to consider the community structure of the network from perspectives of the extreme value analysis. By simulation study we show that estimates of the extremal index of the modularity and the tail index of node degrees depend on the CA parameters. The latter estimates are compared both for evolution without node and edge deletion and with uniform node deletion.

Superstar nodes to which a large proportion of nodes attach in the evolving graphs are considered. We attract results of the extreme value theory regarding sums and maxima of non-stationary random length sequences to predict the tail index of the PageRanks and Max-linear models as influence measures of superstar nodes. To this end, the graphs are divided into mutually weakly dependent communities. Maxima and sums of the PageRanks over communities are used as weakly independent block-data. Tail indices of the block-maxima and block-sums and hence, of the PageRanks and the Max-linear models are found to be close to the minimum tail index of series of representative nodes taken from the communities. The graph evolution is provided by a linear preferential attachment. The tail indices are estimated by data of simulated and real temporal graphs.