Optimal control of a stochastic hybrid system with discounted cost

We address the optimal control problem of a very general stochastic hybrid system with both autonomous and impulsive jumps. The planning horizon is infinite and we use the discounted-cost criterion for performance evaluation. Under certain assumptions, we show the existence of an optimal control. We then derive the quasivariational inequalities satisfied by the value function and establish well-posedness. Finally, we prove the usual verification theorem of dynamic programming.

Population genetic structure and conservation of Asian elephants (Elephas maximus) across India

This study examines the population genetic structure of Asian elephants (Elephas maximus) across India, which harbours over half the world's population of this endangered species. Mitochondrial DNA control region sequences and allele frequencies at six nuclear DNA microsatellite markers obtained from the dung of free-ranging elephants reveal low mtDNA and typical microsatellite diversity. Both known divergent clades of mtDNA haplotypes in the Asian elephant are present in India, with southern and central India exhibiting exclusively the β clade of Fernando et al. (2000), northern India exhibiting exclusively the α clade and northeastern India exhibiting both, but predominantly the α clade. A nested clade analysis revealed isolation by distance as the principal mechanism responsible for the observed haplotype distributions within the α and β clades. Analyses of molecular variance and pairwise population FST tests based on both mitochondrial and microsatellite DNA suggest that northern-northeastern India, central India, Nilgiris (in southern India) and Anamalai-Periyar (in southern India) are four demographically autonomous population units and should be managed separately. In addition, evidence for female philopatry, male-mediated gene flow and two possible historical biogeographical barriers is described.

Determining Top K Nodes in Social Networks using the Shapley Value

In this paper, we consider the problem of selecting, for any given positive integer k, the top-k nodes in a social network, based on a certain measure appropriate for the social network. This problem is relevant in many settings such as analysis of co-authorship networks, diffusion of information, viral marketing, etc. However, in most situations, this problem turns out to be NP-hard. The existing approaches for solving this problem are based on approximation algorithms and assume that the objective function is sub-modular. In this paper, we propose a novel and intuitive algorithm based on the Shapley value, for efficiently computing an approximate solution to this problem. Our proposed algorithm does not use the sub-modularity of the underlying objective function and hence it is a general approach. We demonstrate the efficacy of the algorithm using a co-authorship data set from e-print arXiv (www.arxiv.org), having 8361 authors.