Моделирование приемной кампании: вузы различного качества и абитуриенты с квадратичной функцией полезности
In Russia from 2009 College admission is based on results of Unified State Exam. Entrant applies to no more than five universities. Admission mechanism is defined by government for all state universities. In the paper the authors model how entrant chooses university for application and, based on the entrant's choice prediction, the shortages of the current admission mechanism are revealed.
Matching problem with preferences being simplest semiorders is analysed. It is proved that a stable matching always exists. Furthermore, for any stable matching there exists a linear extension of preferences, which does not sontradict stability of a matching. In the college admission problem common goal is to find student-optimal stable matching. We provide a simple criteria (Stable Improvement Cycle existence), that allows to check, whether some particular stable matching is student-side Pareto optimal.
A common feature of the Hungarian, Irish, Spanish and Turkish higher education admission systems is that students apply for programmes and are ranked according to their scores. Students who apply for a programme with the same score are tied. Ties are broken by lottery in Ireland, by objective factors in Turkey (such as date of birth) and by other precisely defined rules in Spain. In Hungary, however, an equal treatment policy is used, students applying for a programme with the same score are all accepted or rejected together. In such a situation there is only one decision to make, whether or not to admit the last group of applicants with the same score who are at the boundary of the quota. Both concepts can be described in terms of stable score-limits. The strict rejection of the last group with whom a quota would be violated corresponds to the concept of H-stable (i.e. higher-stable) score-limits that is currently used in Hungary. We call the other solutions based on the less strict admission policy as L-stable (i.e. lower-stable) score-limits. We show that the natural extensions of the Gale–Shapley algorithms produce stable score-limits, moreover, the applicant-oriented versions result in the lowest score-limits (thus optimal for students) and the college-oriented versions result in the highest score-limits with regard to each concept. When comparing the applicant-optimal H-stable and L-stable score-limits we prove that the former limits are always higher for every college. Furthermore, these two solutions provide upper and lower boundaries for any solution arising from a tie-breaking strategy. Finally we show that both the H-stable and the L-stable applicant-proposing score-limit algorithms are manipulable.
On the basis of a monitoring of educational and working trajectories of graduates of schools and higher education institutions The authors think it expedient for studying problems in adaptation of first-year students to training in higher education institutions to sort out groups of fundamentally different students on the basis of the cluster analysis. With the use of a comprehensive survey of Moscow first-year students seven groups are sorted out, and specific difficulties in learning are analyzed in each case, as well as differences between students from different groups in terms of their certainty when selecting Statistics and Sociology of Education an occupation, when assessing social life in a higher education institution, in terms of peculiarities of their goals in life and education.
The book contains the necessary information from the algorithm theory, graph theory, combinatorics. It is considered partially recursive functions, Turing machines, some versions of the algorithms (associative calculus, the system of substitutions, grammars, Post's productions, Marcov's normal algorithms, operator algorithms). The main types of graphs are described (multigraphs, pseudographs, Eulerian graphs, Hamiltonian graphs, trees, bipartite graphs, matchings, Petri nets, planar graphs, transport nets). Some algorithms often used in practice on graphs are given. It is considered classical combinatorial configurations and their generating functions, recurrent sequences. It is put in a basis of the book long-term experience of teaching by authors the discipline «Discrete mathematics» at the business informatics faculty, at the computer science faculty of National Research University Higher School of Economics, and at the automatics and computer technique faculty of National research university Moscow power engineering institute. The book is intended for the students of a bachelor degree, trained at the computer science faculties in the directions 09.03.01 Informatics and computational technique, 09.03.02 Informational systems and technologies, 09.03.03 Applied informatics, 09.03.04 Software Engineering, and also for IT experts and developers of software products.
Let G = (V,E) be an undirected graph, T ⊆ V be a set of terminals. Then a natural combinatorial problem consists in finding the maximum number of vertex-disjoint paths connecting distinct terminals. For this problem, a clever construction suggested by Gallai reduces it to computing a maximum non-bipartite matching and thus gives an O ( m √n log n 2 /m log n ) -Time algorithm (hereinafter n := |V |, m := |E|). Now let us consider the fractional relaxation, i.e. allow T-path packings with arbitrary nonnegative real weights. It is known that there always exists a half-integral solution, that is, one only needs to assign weights 0, 1/2 , 1 to maximize the total weight of T-paths. It is also known that an optimum half-integral packing can be found in strongly-polynomial time but the actual time bounds are far from being satisfactory. In this paper we present a novel algorithm that solves the half-integral problem within O ( m √n log n 2 /m log n )time, thus matching the complexities of integral and half-integral versions.
Smoking is a problem, bringing signifi cant social and economic costs to Russiansociety. However, ratifi cation of the World health organization Framework conventionon tobacco control makes it possible to improve Russian legislation accordingto the international standards. So, I describe some measures that should be taken bythe Russian authorities in the nearest future, and I examine their effi ciency. By studyingthe international evidence I analyze the impact of the smoke-free areas, advertisementand sponsorship bans, tax increases, etc. on the prevalence of smoking, cigaretteconsumption and some other indicators. I also investigate the obstacles confrontingthe Russian authorities when they introduce new policy measures and the public attitudetowards these measures. I conclude that there is a number of easy-to-implementanti-smoking activities that need no fi nancial resources but only a political will.
One of the most important indicators of company's success is the increase of its value. The article investigates traditional methods of company's value assessment and the evidence that the application of these methods is incorrect in the new stage of economy. So it is necessary to create a new method of valuation based on the new main sources of company's success that is its intellectual capital.