Risk Bounds for Mixture Density Estimation

In this paper we focus on the problem of estimating a bounded density using a finite combination of densities from a given class. We consider the Maximum Likelihood Procedure (MLE) and the greedy procedure described by Li and Barron. Approximation and estimation bounds are given for the above methods. We extend and improve upon the estimation results of Li and Barron, and in particular prove an $O(\\frac{1}{\\sqrt{n}})$ bound on the estimation error which does not depend on the number of densities in the estimated combination.

Carbon Nanotube Growth Using Ni Catalyst in Different Layouts

Vertically aligned carbon nanotubes have been grown using Ni as catalyst by plasma enhanced chemical vapor deposition system (PECVD) in various pre-patterned substrates. Ni was thermally evaporated on silicon substrates with anodized alumina mask prepared in different methods including 2 step anodization of porous alumina template and interference lithography assisted array of pores. The templates helped to define Ni nanodots inside the pores which in turn catalyzed the growth of carbon nanotubes inside the PECVD system at temperature of 700-750C using mixture of ammonia and acetylene gases. The resulting well-aligned multi-walled carbon nanotubes were further investigated using SEM, TEM and Raman spectroscopy. The size, shape and structure of the grown carbon nanotubes were also discussed.

Plasma polymerization of C[subscript 4]F[subscript 8] thin film on high aspect ratio silicon molds

High aspect ratio polymeric micro-patterns are ubiquitous in many fields ranging from sensors, actuators, optics, fluidics and medical. Second generation PDMS molds are replicated against first generation silicon molds created by deep reactive ion etching. In order to ensure successful demolding, the silicon molds are coated with a thin layer of C[subscript 4]F[subscript 8] plasma polymer to reduce the adhesion force. Peel force and demolding status are used to determine if delamination is successful. Response surface method is employed to provide insights on how changes in coil power, passivating time and gas flow conditions affect plasma polymerization of C[subscript 4]F[subscript 8].