Функциональные соответствия Галуа для классов дискретных функций и свойство Эрроу для симметричных классов решающих правил
One of the main tasks of the theory of collective choice is formulated in the language of functional Galois correspondences. A convenient characterization of symmetric classes of decision rules without the Arrow property is proposed.
A complete classification of symmetric sets of choice functions with the Arrow property is obtained.
In this paper, we explain how Galois connection and related operators between sets of users and items naturally arise in user-item data for forming neighbourhoods of a target user or item for Collabora- tive Filtering. We compare the properties of these operators and their ap- plicability in simple collaborative user-to-user and item-to-item setting. Moreover, we propose a new neighbourhood-forming operator based on pair-wise similarity ranking of users, which takes intermediate place be- tween the studied closure operators and its relaxations in terms of neigh- bourhood size and demonstrates comparatively good Precision-Recall trade-off. In addition, we compare the studied neighbourhood-forming operators in the collaborative filtering setting against simple but strong benchmark, the SlopeOne algorithm, over bimodal cross-validation on MovieLens dataset.
We give an effective description of symmetric closed classes of discrete functions preserving any unary predicate.
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.
This article is talking about state management and cultural policy, their nature and content in term of the new tendency - development of postindustrial society. It mentioned here, that at the moment cultural policy is the base of regional political activity and that regions can get strong competitive advantage if they are able to implement cultural policy successfully. All these trends can produce elements of new economic development.