The range of tree-indexed random walk in low dimensions

We study the range $R_n$ of a random walk on the $d$-dimensional lattice $\mathbb{Z}^d$ indexed by a random tree with $n$ vertices. Under the assumption that the random walk is centered and has finite fourth moments, we prove in dimension $d\leq3$ that $n^{-d/4}R_n$ converges in distribution to the Lebesgue measure of the support of the integrated super-Brownian excursion (ISE). An auxiliary result shows that the suitably rescaled local times of the tree-indexed random walk converge in distribution to the density process of ISE. We obtain similar results for the range of critical branching random walk in $\mathbb{Z}^d$, $d\leq3$. As an intermediate estimate, we get exact asymptotics for the probability that a critical branching random walk starting with a single particle at the origin hits a distant point. The results of the present article complement those derived in higher dimensions in our earlier work.Comment: Published at http://dx.doi.org/10.1214/14-AOP947 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

A distributed multi-agent framework for shared resources scheduling

Nowadays, manufacturers have to share some of their resources with partners due to the competitive economic environment. The management of the availability periods of shared resources causes a problem because it is achieved by the scheduling systems which assume a local environment where all resources are on the same site. Therefore, distributed scheduling with shared resources is an important research topic in recent years. In this communication, we introduce the architecture and behavior of DSCEP framework (distributed, supervisor, customer, environment, and producer) under shared resources situation with disturbances. We are using a simple example of manufacturing system to illustrate the ability of DSCEP framework to solve the shared resources scheduling problem in complex systems

A ferrofluid-based homogeneous assay for highly sensitive and selective detection of single-nucleotide polymorphisms

10.1039/C3CC43281EChemical Communications49738114-811