Stein's method and the distribution of the product of zero mean correlated normal random variables

Over the last 80 years there has been much interest in the problem of finding an explicit formula for the probability density function of two zero mean correlated normal random variables. Motivated by this historical interest, we use a recent technique from the Stein's method literature to obtain a simple new proof, which also serves as an exposition of a general method that may be useful in related problems.Comment: 6 pages. To appear in Communications in Statistics - Theory and Method

Synchronization in complex networks

Synchronization processes in populations of locally interacting elements are in the focus of intense research in physical, biological, chemical, technological and social systems. The many efforts devoted to understand synchronization phenomena in natural systems take now advantage of the recent theory of complex networks. In this review, we report the advances in the comprehension of synchronization phenomena when oscillating elements are constrained to interact in a complex network topology. We also overview the new emergent features coming out from the interplay between the structure and the function of the underlying pattern of connections. Extensive numerical work as well as analytical approaches to the problem are presented. Finally, we review several applications of synchronization in complex networks to different disciplines: biological systems and neuroscience, engineering and computer science, and economy and social sciences.Comment: Final version published in Physics Reports. More information available at http://synchronets.googlepages.com

Introducing Agility in Hybrid Communication Systems and Sensors

This paper presents a new approach in dealing with hybridization issues in communication systems or sensors. The thrust is to separate the logical network (sensor) infrastructure from the physical one. Here we show how we can exploit concepts such as persistent identification which we believe is crucial to be able to connect a variety of heterogeneous devices in a network that grows, and that is robust to failures. A vital characteristic of our architecture is the ability to accommodate a variety of heterogeneous devices and subsystems. Several examples of hybridization of sensors at the physical, logical, and network levels are presented and discussed