### Article

## Seeding the UEFA Champions League Participants: Evaluation of the Reforms

We evaluate the sporting effects of the seeding system reforms in the Champions League, the major football club tournament organized by the Union of European Football Associations (UEFA). Before the 2015-16 season, the teams were seeded in the group stage by their ratings. Starting from the 2015-16 season, national champions

of the Top-7 associations are seeded in the first pot, whereas other teams are seeded by their rating as before. Taking effect from the season 2018-19, the team's rating will not longer include 20% of the rating of the association that the team represents. Using the prediction model, we simulate the whole UEFA season and obtain numerical

estimates for competitiveness changes in the UEFA tournaments caused by these seeding reforms. We report only marginal changes in tournament metrics that characterize ability of the tournament to select the best teams and competitive balance. Probability of changes in the UEFA national association ranking does not exceed several percent for any association.

The article presents the analysis of the measures of risk non-financial company. Identified key risk metrics. If justified the use of EVaR models. Developed methodical recommendations on the use of EVaR in stress-testing company.

Various Condorcet consistent social choice functions based on majority rule (tournament solutions) are considered in the general case, when ties are allowed: the core, the weak and strong top cycle sets, versions of the uncovered and minimal weakly stable sets, the uncaptured set, the untrapped set, classes of k-stable alternatives and k-stable sets. The main focus of the paper is to construct a unified matrix-vector representation of a tournament solution in order to get a convenient algorithm for its calculation. New versions of some solutions are also proposed.

This paper presents a simple bootstrap test to verify the existence of finite moments. The efficacy of the test relies on the fact that in the absence of a first moment and under certain general conditions, the arithmetic average of a sample grows at a rate greater than the growth rates of the arithmetic averages of the sub-samples. Firstly, we show test consistency analytically. Then, Monte-Carlo simulations are performed to compare our test with the Hill estimator.

A model for organizing cargo transportation between two node stations connected by a railway line which contains a certain number of intermediate stations is considered. The movement of cargo is in one direction. Such a situation may occur, for example, if one of the node stations is located in a region which produce raw material for manufacturing industry located in another region, and there is another node station. The organization of freight traﬃc is performed by means of a number of technologies. These technologies determine the rules for taking on cargo at the initial node station, the rules of interaction between neighboring stations, as well as the rule of distribution of cargo to the ﬁnal node stations. The process of cargo transportation is followed by the set rule of control. For such a model, one must determine possible modes of cargo transportation and describe their properties. This model is described by a ﬁnite-dimensional system of diﬀerential equations with nonlocal linear restrictions. The class of the solution satisfying nonlocal linear restrictions is extremely narrow. It results in the need for the “correct” extension of solutions of a system of diﬀerential equations to a class of quasi-solutions having the distinctive feature of gaps in a countable number of points. It was possible numerically using the Runge–Kutta method of the fourth order to build these quasi-solutions and determine their rate of growth. Let us note that in the technical plan the main complexity consisted in obtaining quasi-solutions satisfying the nonlocal linear restrictions. Furthermore, we investigated the dependence of quasi-solutions and, in particular, sizes of gaps (jumps) of solutions on a number of parameters of the model characterizing a rule of control, technologies for transportation of cargo and intensity of giving of cargo on a node station.

This proceedings publication is a compilation of selected contributions from the “Third International Conference on the Dynamics of Information Systems” which took place at the University of Florida, Gainesville, February 16–18, 2011. The purpose of this conference was to bring together scientists and engineers from industry, government, and academia in order to exchange new discoveries and results in a broad range of topics relevant to the theory and practice of dynamics of information systems. Dynamics of Information Systems: Mathematical Foundation presents state-of-the art research and is intended for graduate students and researchers interested in some of the most recent discoveries in information theory and dynamical systems. Scientists in other disciplines may also benefit from the applications of new developments to their own area of study.