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.

An Approach to the stability of international environmental agreements: the absorbing sets solution

We study international environmental negotiations when agreements between countries can not be binding. A problem with this kind of negotiations is that countries have incentives for free-riding from such agreements. We develope a notion of equilibrium based on the assumption that countries can create and dissolve agreements in their seeking of a larger welfare. This approach leads to a larger degree of cooperation compared to models based on the internal-external stability approach.

Stability of the factorial structure of metabolic syndrome from childhood to adolescence : a 6-year follow-up study

Background: Metabolic syndrome (MS) is a clustering of cardiometabolic risk factors that is considered a predictor of cardiovascular disease, type 2 diabetes and mortality. There is no consistent evidence on whether the MS construct works in the same way in different populations and at different stages in life. Methods: We used confirmatory factor analysis to examine if a single-factor-model including waist circumference, triglycerides/HDL-c, insulin and mean arterial pressure underlies metabolic syndrome from the childhood to adolescence in a 6-years follow-up study in 174 Swedish and 460 Estonian children aged 9 years at baseline. Indeed, we analyze the tracking of a previously validated MS index over this 6-years period. Results: The estimates of goodness-of-fit for the single-factor-model underlying MS were acceptable both in children and adolescents. The construct stability of a new model including the differences from baseline to the end of the follow-up in the components of the proposed model displayed good fit indexes for the change, supporting the hypothesis of a single factor underlying MS component trends. Conclusions: A single-factor-model underlying MS is stable across the puberty in both Estonian and Swedish young people. The MS index tracks acceptably from childhood to adolescence.

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.

Hyers-Ulam-Rassias Stability of Functional Differential Systems with Point and Distributed Delays

This paper investigates stability and asymptotic properties of the error with respect to its nominal version of a nonlinear time-varying perturbed functional differential system subject to point, finite-distributed, and Volterra-type distributed delays associated with linear dynamics together with a class of nonlinear delayed dynamics. The boundedness of the error and its asymptotic convergence to zero are investigated with the results being obtained based on the Hyers-Ulam-Rassias analysis.