Fast matrix computations for functional additive models

It is common in functional data analysis to look at a set of related functions: a set of learning curves, a set of brain signals, a set of spatial maps, etc. One way to express relatedness is through an additive model, whereby each individual function $g_{i}\left(x\right)$ is assumed to be a variation around some shared mean $f(x)$. Gaussian processes provide an elegant way of constructing such additive models, but suffer from computational difficulties arising from the matrix operations that need to be performed. Recently Heersink & Furrer have shown that functional additive model give rise to covariance matrices that have a specific form they called quasi-Kronecker (QK), whose inverses are relatively tractable. We show that under additional assumptions the two-level additive model leads to a class of matrices we call restricted quasi-Kronecker, which enjoy many interesting properties. In particular, we formulate matrix factorisations whose complexity scales only linearly in the number of functions in latent field, an enormous improvement over the cubic scaling of na\"ive approaches. We describe how to leverage the properties of rQK matrices for inference in Latent Gaussian Models

Model Order Selection in DoA Scenarios via Cross-Entropy based Machine Learning Techniques

In this paper, we present a machine learning approach for estimating the number of incident wavefronts in a direction of arrival scenario. In contrast to previous works, a multilayer neural network with a cross-entropy objective is trained. Furthermore, we investigate an online training procedure that allows an adaption of the neural network to imperfections of an antenna array without explicitly calibrating the array manifold. We show via simulations that the proposed method outperforms classical model order selection schemes based on information criteria in terms of accuracy, especially for a small number of snapshots and at low signal-to-noise-ratios. Also, the online training procedure enables the neural network to adapt with only a few online training samples, if initialized by offline training on artificial data

Up-rating underground sedimentation tanks subject to hydraulic overloading

A project report submitted to the Faculty of Engineering, University of the Witwatersrand, Johannesburg, in partial fulfilment of the requirements for the degree of Master of Science in Engineering. Johannesburg, 1987The research in this project report is aimed at improving effluent q u a l ities of existing sedimentation tanks which are overloaded either because the incoming flow rate is higher than the design flow or because the incoming suspended solids concentration is higher than that which was predicted in the design stages of the clarifier. Conventional methods of up-rating tanks, usually in the form of rectangular tube modules, were discarded since they do not lend themselves to general design when the intention is to up-rate circular clarifiers. In stead a unique type of conical lamella settler was designed which comprises of one cone stacked on top of the other. The cones can be installed within an existing settler, and in so doing up-rate it. A conventional upward flow tank and tne up-rated version in the form of the rriniral lamella settler were tested in the laboratory. It was found that the conical lamella settler produces considerably better effluent qualities in comparison with the conventional cifirifior, especially at high overflow rates. In addition, the conical lameliti settler is comparatively insensitive to changes in hydraulic loading and influent s us pended solids concentrations making it ideal in absorbing shock loads. A conical lamella settler is modelled mathematically and it is shown that theoretically conical plates are a much more efficient form of settling than conventional rectangular lamella plates. The conical lamella settler can result in substantial savings in cost and space and therefore more research is needed to perfect it and to make it as generally applicable as possible

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Origin and Functional Evolution of the Cdc48/p97/VCP AAA+ Protein Unfolding and Remodeling Machine

The AAA + Cdc48 ATPase (alias p97 or VCP) is a key player in multiple ubiquitin-dependent cell signaling, degradation, and quality control pathways. Central to these broad biological functions is the ability of Cdc48 to interact with a large number of adaptor proteins and to remodel macromolecular proteins and their complexes. Different models have been proposed to explain how Cdc48 might couple ATP hydrolysis to forcible unfolding, dissociation, or remodeling of cellular clients. In this review, we provide an overview of possible mechanisms for substrate unfolding/remodeling by this conserved and essential AAA + protein machine and their adaption and possible biological function throughout evolution. Keywords: AAA + machine; protein remodeling; human diseaseNational Institutes of Health (U.S.) (Grant AI-16892