Asymptotic distribution of the maximum interpoint distance in a sample of random vectors with a spherically symmetric distribution

Extreme value theory is part and parcel of any study of order statistics in one dimension. Our aim here is to consider such large sample theory for the maximum distance to the origin, and the related maximum "interpoint distance," in multidimensions. We show that for a family of spherically symmetric distributions, these statistics have a Gumbel-type limit, generalizing several existing results. We also discuss the other two types of limit laws and suggest some open problems. This work complements our earlier study on the minimum interpoint distance.Comment: Published at http://dx.doi.org/10.1214/14-AAP1082 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

The use of Mean Residual Life in testing departures from Esxponentiality.

vita media residua; test di esponenzialità; processo di wiener; processo di quantili

Nanogels for pharmaceutical and biomedical applications and their fabrication using 3D printing technologies

Nanogels are hydrogels formed by connecting nanoscopic micelles dispersed in an aqueous medium, which give an opportunity for incorporating hydrophilic payloads to the exterior of the micellar networks and hydrophobic payloads in the core of the micelles. Biomedical and pharmaceutical applications of nanogels have been explored for tissue regeneration, wound healing, surgical device, implantation, and peroral, rectal, vaginal, ocular, and transdermal drug delivery. Although it is still in the early stages of development, due to the increasing demands of precise nanogel production to be utilized for personalized medicine, biomedical applications, and specialized drug delivery, 3D printing has been explored in the past few years and is believed to be one of the most precise, efficient, inexpensive, customizable, and convenient manufacturing techniques for nanogel production

The Tightness of the Kesten-Stigum Reconstruction Bound of Symmetric Model with Multiple Mutations

It is well known that reconstruction problems, as the interdisciplinary subject, have been studied in numerous contexts including statistical physics, information theory and computational biology, to name a few. We consider a $2q$-state symmetric model, with two categories of $q$ states in each category, and 3 transition probabilities: the probability to remain in the same state, the probability to change states but remain in the same category, and the probability to change categories. We construct a nonlinear second order dynamical system based on this model and show that the Kesten-Stigum reconstruction bound is not tight when $q \geq 4$.Comment: Accepted, to appear Journal of Statistical Physic

Journal Staff

A human body can carry out many physiological complex processes which can be mechanical, electrical or bio-chemical. Each mechanical activity generates a signal that describes the characteristics of the particular action in the form of pressure or temperature. Any irregularity in the process changes the usual functioning thus affecting the performance of the system. Several techniques were introduced to evaluate these muscular signals in order to get a deeper understanding of the medical abnormalities. Displacement sensors, laser optics, electrodes, accelerometers and microphones are some of the widely used devices in measuring the electrical and mechanical activities produced in the muscles. The aim of this thesis project was to find and implement a simple non-contact optical method to measure and monitor the displacements caused on the surface of the skin due to muscular movements. In this study, a device was developed using photo electric sensors that can record surface changes caused on the skin due to the movements forearm muscles