The Stability of the Roommate Problem Revisited

The lack of stability in some matching problems suggests that alternative solution concepts to the core might be applied to find predictable matchings. We propose the absorbing sets as a solution for the class of roommate problems with strict preferences. This solution, which always exists, either gives the matchings in the core or predicts some other matchings when the core is empty. Furthermore, it satisfies an interesting property of outer stability. We also characterize the absorbing sets, determine their number and, in case of multiplicity, we find that they all share a similar structure.

Decomposing the Gender Wage Gap: The effect of firms, occupations and Job Stratification

This paper presents new evidence on the role of segregation into firms, occupations within a firm and stratification into professional categories within firm-occupations in explaining the gender wage gap. I use a generalized earnings model that allows observed and unobserved group characteristics to have different impact on wages of men and women within the same group. The database is a large sample of individual wage data from the 1995 Spanish Wage Structure Survey. Results indicate that firm segregation in our sample accounts for around one-fifth of the raw gender wage gap. Occupational segregation within firms accounts for about one-third of the raw wage gap, and stratification into different professional categories within firms and occupations explains another one-third of it. The remaining one-fifth of the overall gap arises from better outcomes of men relative to women within professional categories. It is also found that rewards to both observable and unobservable skills, particularly those related to education, are higher for males than for females within the same group. Finally, mean wages in occupations or job categories with a higher fraction of female co-workers are lower, but the negative impact of femaleness in higher for women.

Stability of Switched Feedback Time-Varying Dynamic Systems Based on the Properties of the Gap Metric for Operators

The stabilization of dynamic switched control systems is focused on and based on an operator-based formulation. It is assumed that the controlled object and the controller are described by sequences of closed operator pairs (L, C) on a Hilbert space H of the input and output spaces and it is related to the existence of the inverse of the resulting input-output operator being admissible and bounded. The technical mechanism addressed to get the results is the appropriate use of the fact that closed operators being sufficiently close to bounded operators, in terms of the gap metric, are also bounded. That philosophy is followed for the operators describing the input-output relations in switched feedback control systems so as to guarantee the closed-loop stabilization.

The Linear Ordering Problem Revisited

The Linear Ordering Problem is a popular combinatorial optimisation problem which has been extensively addressed in the literature. However, in spite of its popularity, little is known about the characteristics of this problem. This paper studies a procedure to extract static information from an instance of the problem, and proposes a method to incorporate the obtained knowledge in order to improve the performance of local search-based algorithms. The procedure introduced identifies the positions where the indexes cannot generate local optima for the insert neighbourhood, and thus global optima solutions. This information is then used to propose a restricted insert neighbourhood that discards the insert operations which move indexes to positions where optimal solutions are not generated. In order to measure the efficiency of the proposed restricted insert neighbourhood system, two state-of-the-art algorithms for the LOP that include local search procedures have been modified. Conducted experiments confirm that the restricted versions of the algorithms outperform the classical designs systematically. The statistical test included in the experimentation reports significant differences in all the cases, which validates the efficiency of our proposal.

The forward problem for the electromagnetic Helmholtz equation

157 p.

Unilateral vs. Bilateral link-formation: Bridging the gap

We provide a model that bridges the gap between two benchmark models of strategic network formation: Jackson and Wolinsky' s model based on bilateral formation of links, and Bala and Goyal's two-way fl ow model, where links can be unilaterally formed. In the model introduced and studied here a link can be created unilaterally. When it is only supported by one of the two players the fl ow through the link suffers a certain decay, but when it is supported by both the fl ow runs without friction. When the decay in links supported by only one player is maximal (i.e. there is no flow) we have Jackson and Wolinsky 's connections model without decay, while when flow in such links is perfect we have Bala and Goyal' s two-way flow model. We study Nash, strict Nash and pairwise stability for the intermediate models. Efficiency and dynamics are also examined.

A new solution for the roommate problem: The Q-stable matchings

The aim of this paper is to propose a new solution for the roommate problem with strict preferences. We introduce the solution of maximum irreversibility and consider almost stable matchings (Abraham et al. [2])and maximum stable matchings (Ta [30] [32]). We find that almost stable matchings are incompatible with the other two solutions. Hence, to solve the roommate problem we propose matchings that lie at the intersection of the maximum irreversible matchings and maximum stable matchings, which are called Q-stable matchings. These matchings are core consistent and we offer an effi cient algorithm for computing one of them. The outcome of the algorithm belongs to an absorbing set.

Addressing students' difficulties with Faraday's law: A guided problem solving approach

In traditional teaching, the fundamental concepts of electromagnetic induction are usually quickly analyzed, spending most of the time solving problems in a more or less rote manner. However, physics education research has shown that the fundamental concepts of the electromagnetic induction theory are barely understood by students. This article proposes an interactive teaching sequence introducing the topic of electromagnetic induction. The sequence has been designed based on contributions from physics education research. Particular attention is paid to the relationship between experimental findings (macroscopic level) and theoretical interpretation (microscopic level). An example of the activities that have been designed will also be presented, describing the implementation context and the corresponding findings. Since implementing the sequence, a considerable number of students have a more satisfactory grasp of the electromagnetic induction explicative model. However, difficulties are manifested in aspects that require a multilevel explanation, referring to deep structures where the system description is better defined.

Distribution of Healthcare resources II.Study and Comparison of a Linear Programming Problem and its Dual. Resolution and Evaluation of a Practical Case and its Programming using Excel and Win QSB.

[EN]This research had as primary objective to model different types of problems using linear programming and apply different methods so as to find an adequate solution to them. To achieve this objective, a linear programming problem and its dual were studied and compared. For that, linear programming techniques were provided and an introduction of the duality theory was given, analyzing the dual problem and the duality theorems. Then, a general economic interpretation was given and different optimal dual variables like shadow prices were studied through the next practical case: An aesthetic surgery hospital wanted to organize its monthly waiting list of four types of surgeries to maximize its daily income. To solve this practical case, we modelled the linear programming problem following the relationships between the primal problem and its dual. Additionally, we solved the dual problem graphically, and then we found the optimal solution of the practical case posed through its dual, following the different theorems of the duality theory. Moreover, how Complementary Slackness can help to solve linear programming problems was studied. To facilitate the solution Solver application of Excel and Win QSB programme were used.

Contributions to time series data mining departing from the problem of road travel time modeling

194 p.