Multipoint-to-multipoint network communication

We have formulated an exact ILP model for the problem of communicating on a virtual network. While this ILP model was successful in solving small problems, it is not recommended to handle larger instances, due to the fact that the number of variables in the model grows exponentially as the graph size grows. However, this ILP model can provide a benchmark for heuristic algorithms developed for this problem. We have also described a heuristic approach, and explored several variants of the algorithm. We found a solution that seems to perform well with reasonable computation time. The heuristic is able to find solutions that respect the degree constraints, but show a small number of violations of the desired time constraints. Tests on small problems show that heuristic is not always able to find feasible solutions, even though the exact method has shown they exist. It would be interesting in the future to look at whether insights gained by looking at exact solutions can be used to improve the heuristic

The propagation of a cultural or biological trait by neutral genetic drift in a subdivided population

We study fixation probabilities and times as a consequence of neutral genetic drift in subdivided populations, motivated by a model of the cultural evolutionary process of language change that is described by the same mathematics as the biological process. We focus on the growth of fixation times with the number of subpopulations, and variation of fixation probabilities and times with initial distributions of mutants. A general formula for the fixation probability for arbitrary initial condition is derived by extending a duality relation between forwards- and backwards-time properties of the model from a panmictic to a subdivided population. From this we obtain new formulae, formally exact in the limit of extremely weak migration, for the mean fixation time from an arbitrary initial condition for Wright's island model, presenting two cases as examples. For more general models of population subdivision, formulae are introduced for an arbitrary number of mutants that are randomly located, and a single mutant whose position is known. These formulae contain parameters that typically have to be obtained numerically, a procedure we follow for two contrasting clustered models. These data suggest that variation of fixation time with the initial condition is slight, but depends strongly on the nature of subdivision. In particular, we demonstrate conditions under which the fixation time remains finite even in the limit of an infinite number of demes. In many cases - except this last where fixation in a finite time is seen - the time to fixation is shown to be in precise agreement with predictions from formulae for the asymptotic effective population size.Comment: 17 pages, 8 figures, requires elsart5p.cls; substantially revised and improved version; accepted for publication in Theoretical Population Biolog

Composability of Markov Models for Processing Sensor Data

We show that it is possible to apply the divide-and-conquer principle in constructing a Markov model for sensor data from available sensor logs. The state space can be partitioned into clusters, for which the required transition counts or probabilities can be acquired locally. The combination of these local parameters into a global model takes the form of a system of linear equations with a confined solution space. Expected advantages of this approach lie for example in reduced (wireless) communication costs

A bi-objective hub-and-spoke approach for reconfiguring Web communities

Web communities in general grow naturally, thus creating unbalanced network structures where a few domains centralise most of the linkups. When one of them breaks down, a significant part of the community might be unable to communicate with the remaining domains. Such a situation is highly inconvenient, as in the case of wishing to pursue distribution policies within the community, or for marketing purposes. In order to reduce the damages of such an occurrence, the Web community should be reconfigured, in such a way that a complete sub-network of main domains -the hubs - is identified and that each of the other domains of the community - the spokes - is doubly linked at least with a hub. This problem can be modellised through a bi-objective optimisation problem, the Web Community Reconfiguring Problem, which will be presented in this paper. A bi-objective mixed binary formulation will also be shown, along with a brief description of GRASP, tabu search and hybrid heuristics which were developed to find feasible solutions to the problem, possibly efficient solutions to the bi-objective problem. A computational experiment is reported, involving comparison of these metaheuristics when applied to several Web communities, obtained by crawling the Web and using epistemic boundaries and to other randomly generated ones. The heuristics revealed excellent quality for the small dimension cases whose efficient solutions were roughly all determined. As for the other medium and higher dimension instances, the heuristics were successful in building a wide variety of feasible solutions that are candidate efficient solutions. The best behaviour was attained with the GRASP and the GRASP and tabu hybrid search. Comparison of some metrics before and after reconfiguration confirmed that the final structures are more balanced in terms of degree distribution reinforcing the connecting effect imposed by the reconfiguration process