Limit theorems for empirical Fréchet means of independent and non-identically distributed manifold-valued random variables

We prove weak laws of large numbers and central limit theorems of Lindeberg type for empirical centres of mass (empirical Fréchet means) of independent nonidentically distributed random variables taking values in Riemannian manifolds. In order to prove these theorems we describe and prove a simple kind of Lindeberg–Feller central approximation theorem for vector-valued random variables, which may be of independent interest and is therefore the subject of a self-contained section. This vector-valued result allows us to clarify the number of conditions required for the central limit theorem for empirical Fréchet means, while extending its scope

Feasibility of an electrostatic energy harvesting device for CFCs aircraft

A novel energy harvesting concept is proposed for treating local electrostatic energy produced on flying composite aircrafts. This work focuses on the feasibility research on collecting static charges with capacitive collectors. The existing energy harvesting system and the electrification of the typical carbon fibre composites (CFCs) aircraft has been reviewed. The detailed model experiments were then designed to characterize different configurations for electrostatic energy harvesting on aeroplane. In the lab, the static charge was produced by a corona discharging device, and a capacitor or a metal sheet was put in the electric field to collect the charges under four different configurations. After that, the rest results for these configurations were analysed, which is followed by the discussion about the results application on the aircraft. This work has proved that it is feasible to collect the local static electricity on flying aircraft, and it could provide a new direction of energy harvesting system in aviation field

A diffusion process associated with Fréchet means

This paper studies rescaled images, under exp−1μ, of the sample Fréchet means of i.i.d. random variables {Xk|k≥1} with Fréchet mean μ on a Rie-mannian manifold. We show that, with appropriate scaling, these images converge weakly to a diffusion process. Similar to the Euclidean case, this limiting diffusion is a Brownian motion up to a linear transformation. However, in addition to the covariance structure of exp−1μ(X1), this linear transformation also depends on the global Riemannian structure of the manifol

Benefits of postponement for fashion products with forecast updates

Thesis (M. Eng. in Logistics)--Massachusetts Institute of Technology, Engineering Systems Division, 2005.Includes bibliographical references (leaves 67-69).This thesis examines the benefit of postponement of fashion products by considering the overage cost of the intermediate product and the correlation between the demand for each end products produced from it. The benefit of postponement is measured by the percentage increase in maximum expected profit after demand is realized. the production process is modelled as a two stage newsvendor problem and the forecast update path follows an additive martingale. An optimal solution and a myopic solution are proposed to solve this problem. Numerical results indicate that the benefit of postponement decreases with the overage cost of the intermediate product and the correlation between demand for each end products. It becomes less sensitive to the overage cost of the intermediate product when end products are more negatively correlated. It is also less sensitive to the demand correlation between end products when the overage cost of the intermediate product is low. In addition, the benefit of postponement is sensitive to the additional unit costs introduced by postponement. A case study to NFL Jerseys purchase planning indicates that an increase of unit cost by 10% can reduce the benefit of postponement by over 50%.by Huiling Gong.M.Eng.in Logistic

Grassroots Emergency Health Risk Communication and Transmedia Public Participation: H1N1 Flu, Travelers from Epicenters, and Cyber Vigilantism

Grassroots risk reduction tactics took new forms in the era of social media. Chinese netizens mobilized human flesh searches (HFS), or cyber vigilantism, to reduce the risks posed by international travelers who might import the H1N1 flu virus into China. My study suggests that at the beginning of the H1N1 flu epidemic, rigorous transmedia intervention efforts were made to discipline the early irresponsible overseas Chinese who traveled extensively after arriving in China, but much less attention was paid to risks posed by foreign travelers. The grassroots risk tactics employed emotional appeals, valuative judgment, and moral condemnation to criticize the irresponsible travel of the earliest imported H1N1 flu cases. These transmedia risk tactics got quickly appropriated by regional and national governments to reduce alienation of overseas Chinese and to discipline overseas returnees. Analysis of the HFS episodes reveals the need to create an interface of interaction between authorities and the public for open systems of communication and to consider local public health practices, emotion needs, and values and beliefs when designing health risk communication messages