Two Approaches to the Problem of Sharing Delay Costs in Joint Projects

AMS classifications: 90D12; 90B35activity graph;bankruptcy problem;taxation problem;serial cost sharing method;delay cost

Non-trivial non-negative periodic solutions of a system of doubly degenerate parabolic equations with nonlocal terms

The aim of the paper is to provide conditions ensuring the ex- istence of non-trivial non-negative periodic solutions to a system of doubly degenerate parabolic equations containing delayed nonlocal terms and satis- fying Dirichlet boundary conditions. The employed approach is based on the theory of the Leray-Schauder topological degree theory, thus a crucial purpose of the paper is to obtain a priori bounds in a convenient functional space, here L 2(QT ), on the solutions of certain homotopies. This is achieved under different assumptions on the sign of the kernels of the nonlocal terms. The considered system is a possible model of the interactions between two biologi- cal species sharing the same territory where such interactions are modeled by the kernels of the nonlocal terms. To this regard the obtained results can be viewed as coexistence results of the two biological populations under different intra and inter specific interferences on their natural growth rates

Positive periodic solutions and optimal control for a distributed biological model of two interacting species

The paper deals with the existence of positive periodic solutions to a system of degenerate parabolic equations with delayed nonlocal terms and Dirichlet boundary conditions. Taking in each equation a meaningful function as a control parameter, we show that for a suitable choice of a class of such controls we have, for each of them, a time-periodic response of the system under different assumptions on the kernels of the nonlocal terms. Finally, we consider the problem of the minimization of a cost functional on the set of pairs: control-periodic response. The considered system may be regarded as a possible model for the coexistence problem of two biological populations, which dislike crowding and live in a common territory, under different kind of intra- and inter-specific interferences. \ua9 2010 Elsevier Ltd. All rights reserved

Linear Degenerate Parabolic Equations in Bounded Domains: Controllability and Observability

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Coexistence and optimal control problems for a degenerate predator-prey model

In this paper we present a predator-prey mathematical model for two biological populations which dislike crowding. The model consists of a system of two degenerate parabolic equations with nonlocal terms and drifts. We provide conditions on the system ensuring the periodic coexistence, namely the existence of two non-trivial non-negative periodic solutions representing the densities of the two populations. We assume that the predator species is harvested if its density exceeds a given threshold. A minimization problem for a cost functional associated with this process and with some other significant parameters of the model is also considered. \ua9 2010 Elsevier Inc

Combining Shapley value and statistics to the analysis of gene expression data in children exposed to air pollution

<p>Abstract</p> <p>Background</p> <p>In gene expression analysis, statistical tests for differential gene expression provide lists of candidate genes having, individually, a sufficiently low <it>p</it>-value. However, the interpretation of each single <it>p</it>-value within complex systems involving several interacting genes is problematic. In parallel, in the last sixty years, <it>game theory </it>has been applied to political and social problems to assess the power of interacting agents in forcing a decision and, more recently, to represent the relevance of genes in response to certain conditions.</p> <p>Results</p> <p>In this paper we introduce a Bootstrap procedure to test the null hypothesis that each gene has the same relevance between two conditions, where the relevance is represented by the Shapley value of a particular coalitional game defined on a microarray data-set. This method, which is called <it>Comparative Analysis of Shapley value </it>(shortly, CASh), is applied to data concerning the gene expression in children differentially exposed to air pollution. The results provided by CASh are compared with the results from a parametric statistical test for testing differential gene expression. Both lists of genes provided by CASh and t-test are informative enough to discriminate exposed subjects on the basis of their gene expression profiles. While many genes are selected in common by CASh and the parametric test, it turns out that the biological interpretation of the differences between these two selections is more interesting, suggesting a different interpretation of the main biological pathways in gene expression regulation for exposed individuals. A simulation study suggests that CASh offers more power than t-test for the detection of differential gene expression variability.</p> <p>Conclusion</p> <p>CASh is successfully applied to gene expression analysis of a data-set where the joint expression behavior of genes may be critical to characterize the expression response to air pollution. We demonstrate a synergistic effect between coalitional games and statistics that resulted in a selection of genes with a potential impact in the regulation of complex pathways.</p