Scalar and vector Slepian functions, spherical signal estimation and spectral analysis

It is a well-known fact that mathematical functions that are timelimited (or spacelimited) cannot be simultaneously bandlimited (in frequency). Yet the finite precision of measurement and computation unavoidably bandlimits our observation and modeling scientific data, and we often only have access to, or are only interested in, a study area that is temporally or spatially bounded. In the geosciences we may be interested in spectrally modeling a time series defined only on a certain interval, or we may want to characterize a specific geographical area observed using an effectively bandlimited measurement device. It is clear that analyzing and representing scientific data of this kind will be facilitated if a basis of functions can be found that are "spatiospectrally" concentrated, i.e. "localized" in both domains at the same time. Here, we give a theoretical overview of one particular approach to this "concentration" problem, as originally proposed for time series by Slepian and coworkers, in the 1960s. We show how this framework leads to practical algorithms and statistically performant methods for the analysis of signals and their power spectra in one and two dimensions, and, particularly for applications in the geosciences, for scalar and vectorial signals defined on the surface of a unit sphere.Comment: Submitted to the 2nd Edition of the Handbook of Geomathematics, edited by Willi Freeden, Zuhair M. Nashed and Thomas Sonar, and to be published by Springer Verlag. This is a slightly modified but expanded version of the paper arxiv:0909.5368 that appeared in the 1st Edition of the Handbook, when it was called: Slepian functions and their use in signal estimation and spectral analysi

A fast Bayesian approach to discrete object detection in astronomical datasets - PowellSnakes I

A new fast Bayesian approach is introduced for the detection of discrete objects immersed in a diffuse background. This new method, called PowellSnakes, speeds up traditional Bayesian techniques by: i) replacing the standard form of the likelihood for the parameters characterizing the discrete objects by an alternative exact form that is much quicker to evaluate; ii) using a simultaneous multiple minimization code based on Powell's direction set algorithm to locate rapidly the local maxima in the posterior; and iii) deciding whether each located posterior peak corresponds to a real object by performing a Bayesian model selection using an approximate evidence value based on a local Gaussian approximation to the peak. The construction of this Gaussian approximation also provides the covariance matrix of the uncertainties in the derived parameter values for the object in question. This new approach provides a speed up in performance by a factor of `hundreds' as compared to existing Bayesian source extraction methods that use MCMC to explore the parameter space, such as that presented by Hobson & McLachlan. We illustrate the capabilities of the method by applying to some simplified toy models. Furthermore PowellSnakes has the advantage of consistently defining the threshold for acceptance/rejection based on priors which cannot be said of the frequentist methods. We present here the first implementation of this technique (Version-I). Further improvements to this implementation are currently under investigation and will be published shortly. The application of the method to realistic simulated Planck observations will be presented in a forthcoming publication.Comment: 30 pages, 15 figures, revised version with minor changes, accepted for publication in MNRA

Identification of dynamic characteristics of linear systems.

Structures, built in active earthquake zones, can be subjected to damaging dynamic loading. The health monitoring process for these structures is essential. When a structure is submitted to repetitive moderate earthquake events, it is expected to accumulate certain damage. The variation of the dynamic characteristics can be an indicator of the damage extension in a structure. The procedure of evaluating the dynamic characteristics of a structure is referred to as system identification. This investigation focuses on the analysis of different techniques for identifying linear structures with available recorded responses during earthquake events. These approaches are: (i) Fourier transform approach; (ii) Discrete-time filter method with Least Squares solver; and (iii) Discrete-time filter method with Instrumental Variables solver. A critical assessment of these methods is presented. The analysis of these methods was conducted considering four examples: (i) water tower subjected to blast loading; (ii) cantilever steel beam subjected to earthquake (1995 Kobe, Japan); (iii) ten-story residential reinforced-concrete building; and (iv) six-story commercial steel building. The dynamic responses of the first two examples are obtained numerically and therefore they are free of noise. For the real building examples the acceleration response recoded during the 1994 Northridge earthquake is used to identify the dynamic characteristics. The vibration data of the two buildings are obtained from the California Strong Motion Instrumentation Program (CSMIP).Dept. of Civil and Environmental Engineering. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis2003 .R345. Source: Masters Abstracts International, Volume: 42-03, page: 1001. Adviser: Faouzi Ghrib. Thesis (M.A.Sc.)--University of Windsor (Canada), 2003

How do we think : Modeling Interactions of Perception and Memory

A model of artificial perception based on self-organizing data into hierarchical structures is generalized to abstract thinking. This approach is illustrated using a two-level perception model, which is justified theoretically and tested empirically. The model can be extended to an arbitrary number of levels, with abstract concepts being understood as patterns of stable relationships between data aggregates of high representation levels

Quantitative Endothelial Cell Monolayer Impedance Sensing and Analysis

The electrical analysis of the biological material has been in existence since the turn of last century. A novel application of this technology to cellular monolayers was implemented by Giaever and Keese 20 years ago with their Electrical Cell-Substrate Impedance Sensing (ECIS) system. The capabilities of a real-time system for endothelial impedance measurement are of immense importance. The endothelium is typically the body’s first contact with stimuli and its reaction to medical conditions of inflammation, disease, and body response are of great significance to understanding the physiology of numerous conditions ranging from heart, lung, and renal disease, to intestinal diseases. It is the purpose of this Master’s thesis to analyze and optimize the ECIS system for making quantitative measurements of endothelial monolayer impedance, and accurately applying the results to a thoroughly reviewed analysis package in order to produce accurate cellular resistance parameters. The optimization of data acquisition (DAQ) is accomplished by systematic noise recognition, examination, and minimization; a task that has previously been unexplored in any studies using the ECIS system. Harmonic, 60 Hz, and Gaussian noise sources were well documented in unfiltered data and successfully minimized in the DAQ. Analog to digital (A/D) noise was found to be the lower limit of reducible noise and was properly documented and considered in analysis. Contamination of the electrode arrays from manufacturing processes and proper electrical connection were also found to be of concern to the proper functioning of the system. Analysis of the optimized acquired data was performed in the LabVIEW programming environment, as it offered a more flexible software package than that provided by the current commercially available ECIS system. The optimized system was applied to a further look into hand arm-vibration syndrome (HAVS) and it was concluded that the acceleration exposure dose, incorrectly calculated from the international standards, did not elicit an acute endothelial inflammation response by our measurements. The cumulative result of this study is that the ECIS system has been optimized and various unresolved sources of error were corrected for a more accurate real-time measurement of the endothelial monolayer barrier function in response to stimuli

Nonparametric Bayesian methods for one-dimensional diffusion models

In this paper we review recently developed methods for nonparametric Bayesian inference for one-dimensional diffusion models. We discuss different possible prior distributions, computational issues, and asymptotic results