Amorphous carbon is an important and ubiquitous material, yet the understanding of the optical properties
as a function of frequency and temperature remains a challenge. In particular, a comprehensive physics-based
model has been a long term need. Building on past work on diamond and pyrolytic graphite, a new
model of the optical properties of soot is developed. The model includes frequency and temperature
dependence. Current progress is presented.
There are a number of challenging estimation, tracking, and decision theoretic problems that require the estimation of
Probability Density Functions (PDFs). When using a traditional parametric approach, the functional model of the PDF is
assumed to be known. However, these models often do not capture the complexity of the underlying distribution.
Furthermore, the problems of validating the model and estimating its parameters are often complicated by the sparsity of
prior examples. The need for exemplars grows exponentially with the dimension of the feature space. These methods
may yield PDFs that do not generalize well to unseen data because these tend to overfit or underfit the training
exemplars. We investigate and compare alternate approaches for estimating a PDF and consider instead kernel based
estimation methods which generalize the Parzen estimator and use a Linear Mixture of Kernels (LMK) model. The
methods reported here are derived from machine learning methods such as the Support Vector Machines and the
Relevance Vector Machines. These PDF estimators provide the following benefits: (a) they are data driven; (b) they do
not overfit the data and consequently have good generalization properties; (c) they can accommodate highly irregular
and multi-modal data distributions; (d) they provide a sparse and succinct description of the underlying data which leads
to efficient computation and communication. Comparative experimental results are provided illustrating these properties
using simulated Mixture of Gaussian-distributed data.
Normal cornea transmits greater than 90% of visible light, but its transmission would be less than 30% if the stroma's collagen fibrils scattered independently of one another. Thus modern transparency theories are based on there being sufficient order in fibril positions for destructive interference to cause cancellation among the scattered fields. Two types of structure have been proposed: long-range crystalline order as used in the earliest theory, and short-range liquid-like order such as that depicted by electron microscopy. Of course structures depicted in electron micrographs may be distorted and other tests are required to determine the nature of the order. Light scattering measurements can afford such a test. Specifically, the two types of order produce different dependencies on wavelength for the scattering cross-section (angular or total) in the long-wavelength limit. Measurements must be analyzed appropriately to obtain the long-wavelength limit. The results reported in this paper demonstrate that measurements of both angular and total scattering cross-sections support short-range order of fibril positions.
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