Part I: We set the stage for our homotopical work with preliminary chapters on the point-set topology necessary to parametrized homotopy theory, the base change and other functors that appear in over and under categories, and generalizations of several classical results about equivariant bundles and fibrations to the context of proper actions of non-compact Lie groups.Part II: Despite its long history, the homotopy theory of ex-spaces requires further development before it can serve as the starting point for a rigorous modern treatment of parametrized stable homotopy theory. We give a leisurely account that emphasizes several issues that are of independent interest in the theory and applications of topological model categories. The essential point is to resolve problems about the homotopy theory of ex-spaces that are absent from the homotopy theory of spaces. In contrast to previously encountered situations, model theoretic techniques are intrinsically insufficient to a full development of the basic foundational properties of the homotopy category of ex-spaces. Instead, a rather intricate blend of model theory and classical homotopy theory is required. However, considerable new material on the general theory of topologically enriched model categories is also required.Part III: We give a systematic treatment of the foundations of parametrized stable homotopy theory, working equivariantly and with highly structured smash products and function spectra. The treatment is based on equivariant orthogonal spectra, which are simpler for the purpose than alternative kinds of spectra. Again, the parametrized context introduces many difficulties that have no nonparametrized counterparts and cannot be dealt with using standard model theoretic techniques. The space level techniques of Part II only partially extend to the spectrum level, and many new twists are encountered. Most of the difficulties are already present in the nonequivariant special case. Equivariantly, we show how change of universe, passage to fixed points, and passage to orbits behave in the parametrized setting.Part IV: We give a fiberwise duality theorem that allows fiberwise recognition of dualizable and invertible parametrized spectra. This allows direct application of the formal theory of duality in symmetric monoidal categories to the construction and analysis of transfer maps. The relationship between transfer for general Hurewicz fibrations and for fiber bundles is illuminated by the construction of fiberwise bundles of spectra, which are like bundles of tangents along fibers, but with spectra replacing spaces as fibers. Using this construction, we obtain a simple conceptual proof of a generalized Wirthmüller isomorphism theorem that calculates the right adjoint to base change along an equivariant bundle with manifold fibers in terms of a shift of the left adjoint. Due to the generality of our bundle theoretic context, the Adams isomorphism theorem relating orbit and fixed point spectra is a direct consequence. ContentsPrologue Part I. Point-set topolo...

Bayesian belief nets (BBNs) provide an effective way of reasoning under uncertainty. They have a firm mathematical background in probability theory and have been used in a variety of application areas, including reliability. BBNs can provide alternative representations of fault trees and reliability block diagrams. BBNs can be used to incorporate expert judgement formally into the modelling process. It has been claimed BBNs may overcome some of the limitations of standard reliability techniques. This paper presents an overview of BBNs and illustrates their use through a simple tutorial on system reliability modelling. The use of BBNs in reliability to date is reviewed. The challenge of using BBNs in reliability practice is explored and areas of research are identified

In this paper, we present a deep learning based method for blind hyperspectral unmixing in the form of a neural network autoencoder. We show that the linear mixture model implicitly puts certain architectural constraints on the network, and it effectively performs blind hyperspectral unmixing. Several different architectural configurations of both shallow and deep encoders are evaluated. Also, deep encoders are tested using different activation functions. Furthermore, we investigate the performance of the method using three different objective functions. The proposed method is compared to other benchmark methods using real data and previously established ground truths of several common data sets. Experiments show that the proposed method compares favorably to other commonly used hyperspectral unmixing methods and exhibits robustness to noise. This is especially true when using spectral angle distance as the network's objective function. Finally, results indicate that a deeper and a more sophisticated encoder does not necessarily give better results.

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Hyperspectral images (HSI) are composed of hundreds of spectral bands, covering a broad range of the electromagnetic spectrum. However, images can only be visualized using three spectral channels for red, green, and blue (RGB) colors. Generating realistic RGB images using HSI is seldom the main focus of remote sensing researchers, and is therefore sometimes lacking. In this paper, we present an algorithm which creates realistic color images of HSI, using standardized methods. Research, conducted on the human perception of color in the 1920s culminated in the CIE 1931 XYZ color space. The algorithm maps every spectral band in the visible spectrum to the XYZ color space, using D65 as the reference illuminant, and then maps the XYZ to the sRGB (standard Red Green Blue) color space. The image is gamma-corrected and finally thresholded to improve contrast. The method was validated using two HSIs, creating realistic color images.