Invariant object recognition is maybe the most basic and fundamental property of our visual system. It is the basis of many other cognitive tasks, like motor actions and social interactions. Hence, the theoretical understanding and modeling of invariant object recognition is one of the central problems in computational neuroscience. Indeed, object recognition consists of two different tasks: classification and identification. The focus of this thesis is on object identification under the basic geometrical transformations shift, scaling, and rotation. The visual system can perform shift, size, and rotation invariant object identification. This thesis consists of two parts. In the first part, we present and investigate the VisNet model proposed by Rolls. The generalization problems of VisNet triggered our development of a new neural network model for invariant object identification. Starting point for an improved generalization behavior is the search for an operation that extracts images features that are invariant under shifts, rotations, and scalings. Extracting invariant features guarantees that an object seen once in a specific pose can be identified in any pose. We present and investigate our model in the second part of this thesis.

Thesis (M.S.)--University of Hawaii at Manoa, 2004. / Leaves 86-90 lacking. Includes bibliographical references (leaves 91-93).

Nowadays, subsalt oil and gas exploration is drawing more and more attention from the hydrocarbon industry. Hydrocarbon exploitation requires detailed geological information beneath the surface. Seismic imaging is a powerful tool employed by the hydrocarbon industry to provide subsurface characterization and monitoring information. Traditional wave-equation migration algorithms are based on the one- way-in-depth propagation using the scalar wave equation. These algorithms focus on downward continuing the upcoming waves. However, it is still really difficult for conventional seismic imaging methods, which have dip limitations, to get a correct image for the edge and shape of the salt body and the corresponding subsalt structure. The dip limitation problem in seismic imaging can be solved completely by switching to Reverse-Time Migration (RTM). Unlike old methods, which deal with the one-way wave equation, RTM propagator is two-way and, as a result, it no longer imposes dip limitations on the image. It can also handle complex waveforms, including prismatic waves. Therefore it is a powerful tool for subsalt imaging. RTM involves wave extrapolation forward and backward in time. In order to accurately and efficiently extrapolate the wavefield in heterogeneous media, I develop three novel methods for seismic wave modeling in both isotropic and tilted transversely isotropic (TTI) media. These methods overcome the space-wavenumber mixed-domain problem when solving the acoustic two-way wave equation. The first method involves cascading a Fourier Transform operator and a finite difference (FD) operator to form a chain operator: Fourier Finite Differences (FFD). The second method is lowrank finite differences (LFD), whose FD schemes are derived from the lowrank approximation of the mixed-domain operator and are represented using adapted coefficients. The third method is lowrank Fourier finite differences (LFFD), which use LFD to improve the accuracy of TTI FFD mothod. The first method, FFD, may have an advantage in efficiency, because it uses only one pair of multidimensional forward and inverse FFTs (fast Fourier transforms) per time step. The second method, LFD, as an accurate FD method, is free of FFTs and in return more suitable for massively parallel computing. It can also be applied to the FFD method to reduce the dispersion in TTI case, which results in the third method, LFFD. LFD and LFFD are based on lowrank approx- imation which is a general method to handle mixed-domain operators and can be easily applied to more complicated mixed-domain operators. I show pseudo-acoustic modeling in orthorhombic media by lowrank approximation as an example. / text

This thesis develops a generic framework based on the Fourier transform for pricing and hedging of various options in equity, commodity, currency, and insurance markets. The pricing problem can be reduced to solving a partial integro-differential equation (PIDE). The Fourier Space Time-stepping (FST) framework developed in this thesis circumvents the problems associated with the existing finite difference methods by utilizing the Fourier transform to solve the PIDE. The FST framework-based methods are generic, highly efficient and rapidly convergent. The Fourier transform can be applied to the pricing PIDE to obtain a linear system of ordinary differential equations that can be solved explicitly. Solving the PIDE in Fourier space allows for the integral term to be handled efficiently and avoids the asymmetrical treatment of diffusion and integral terms, common in the finite difference schemes found in the literature. For path-independent options, prices can be obtained for a range of stock prices in one iteration of the algorithm. For exotic, path-dependent options, a time-stepping methodology is developed to handle barriers, free boundaries, and exercise policies. The thesis includes applications of the FST framework-based methods to a wide range of option pricing problems. Pricing of single- and multi-asset, European and path-dependent options under independent-increment exponential Levy stock price models, common in equity and insurance markets, can be done efficiently via the cornerstone FST method. Mean-reverting Levy spot price models, common in commodity markets, are handled by introducing a frequency transformation, which can be readily computed via scaling of the option value function. Generating stochastic volatility, to match the long-term equity options market data, and stochastic skew, observed in currency markets, is addressed by introducing a non-stationary extension of multi-dimensional Levy processes using regime-switching. Finally, codependent jumps in multi-asset models are introduced through copulas. The FST methods are computationally efficient, running in O(MN^d log_2 N) time with M time steps and N space points in each dimension on a d-dimensional grid. The methods achieve second-order convergence in space; for American options, a penalty method is used to attain second-order convergence in time. Furthermore, graphics processing units are utilized to further reduce the computational time of FST methods.

Over the last several years, a submillimetre astronomical polarizing Fourier Transform Spectrometer (FTS) has been developed for use at the James Clerk Maxwell Telescope (JCMT) located atop Mauna Kea, Hawaii. A new liquid3 He cooled dual polarization detector system has been carefully designed for use with this FTS to eliminate noise problems encountered with UKT14, the JCMT facility bolometric detector. The objective of this thesis is to evaluate and optimize the performance of the new detector system. The design of the detector system is discussed, and the noise performance of the system is evaluated. The system performance is determined from photmetric, classical B-I, and spectroscopic measurements. Compared to UKT14, the intrinsic bolometer noise is reduced by a factor of - 2. More importantly, the spectral signal to noise ratio is improved by a factor of - 10 due to the elimination of electrical pickup and microphone noise in the detector signal. / xiv, 156 leaves : ill. ; 28 cm.

The Herschel Space Observatory (Herschel), a flagship mission of the European Space Agency (ESA), is comprised of three cryogenically cooled instruments commissioned to explore the far-infrared/submillimetre universe. Herschel's remote orbit at the second Lagrangian point (L2) of the Sun-Earth system, and its cryogenic payload, impose a need for thorough instrument characterization and rigorous testing as there will be no possibility for any servicing after launch. The Spectral and Photometric Imaging Receiver (SPIRE) is one of the instrument payloads aboard Herschel and consists of a three band imaging photometer and a two band imaging spectrometer. The imaging spectrometer on SPIRE consists of a Mach-Zehnder (MZ)-Fourier transform spectrometer (FTS) coupled with bolometric detector arrays to form an imaging FTS (IFTS). This thesis presents experiments conducted to verify the performance of an IFTS system from a space based platform, i.e. the use of the SPIRE IFTS within the Herschel space observatory. Prior to launch, the SPIRE instrument has undergone a series of performance verification tests conducted at the Rutherford Appleton Laboratory (RAL) near Oxford, UK. Canada is involved in the SPIRE project through provision of instrument development hardware and software, mission flight software, and support personnel. Through this thesis project I have been stationed at RAL for a period spanning fifteen months to participate in the development, performance verification, and characterization of both the SPIRE FTS and photometer instruments. This thesis discusses Fourier transform spectroscopy and related FTS data process ing (Chapter 2). Detailed discussions are included on the spectral phase related to the FTS beamsplitter (Chapter 3), the imaging aspects of the SPIRE IFTS instrument (Chapter 4), and the noise characteristics of the SPIRE bolometer detector arrays as measured using the SPIRE IFTS (Chapter 5). This thesis presents results from experiments performed both on site at the RAL Space Science and Technology Department (SSTD) Assembly Integration Verification (AIV) instrument test facility as well as from the Astronomical Instrumentation Group (AIG) research laboratories within the Department of Physics & Astronomy at the University of Lethbridge. / xxiii, 243 leaves : ill. (some col.) ; 29 cm

The Spectral and Photometric Imaging Receiver (SPIRE) is one of three scientific instruments on the European Space Agency's (ESA's) Herschel Space Observatory (HSO). The medium resolution spectroscopic capabilities of SPIRE are provided by an imaging Fourier transform spectrometer (IFTS). A software simulator of the SPIRE IFTS was written to generate realistic data products, making use of available qualification and test data. We present the design and implementation of the simulator. Component and end-to-end simulations were compared to results from the first SPIRE instrument proto-flight model (PFMI) test campaign conducted at the Rutherford Appleton Laboratory (RAL) in Oxford, England in 2005. Final characterization of the simulator involved the determination of astronomical quantities from the synthetic data products of a simple molecular cloud. / xix, 213 leaves : ill. (some col.) ; 29 cm.

The purpose of this study was to investigate the feasibility of using Fourier transform mid-infrared (FT-IR) microspectroscopy, with attenuated total reflectance (ATR), to detect the presence of Fusarium spp., classify differences in ability to detect Fusarium spp. among the Canadian soil zones, determine whether Fusarium spp. can serve as an indicator for the concentration of deoxynivalenol (DON), and develop an equation that can predict DON within wheat kernels. Canadian Western Red Spring wheat kernels were pressed against an ATR crystal to obtain spectra. Five chemical functional groups were investigated. The ability of FT-IR-ATR microspectroscopy to detect the presence of Fusarium spp. was confirmed. The chemical composition, and the ability to identify Fusarium spp., differed in kernels grown among the soil zones. Several methods to use Fusarium spp. as an indicator for the concentration of DON content within the wheat kernels were attempted and found to be unsuccessful.

This thesis develops a generic framework based on the Fourier transform for pricing and hedging of various options in equity, commodity, currency, and insurance markets. The pricing problem can be reduced to solving a partial integro-differential equation (PIDE). The Fourier Space Time-stepping (FST) framework developed in this thesis circumvents the problems associated with the existing finite difference methods by utilizing the Fourier transform to solve the PIDE. The FST framework-based methods are generic, highly efficient and rapidly convergent. The Fourier transform can be applied to the pricing PIDE to obtain a linear system of ordinary differential equations that can be solved explicitly. Solving the PIDE in Fourier space allows for the integral term to be handled efficiently and avoids the asymmetrical treatment of diffusion and integral terms, common in the finite difference schemes found in the literature. For path-independent options, prices can be obtained for a range of stock prices in one iteration of the algorithm. For exotic, path-dependent options, a time-stepping methodology is developed to handle barriers, free boundaries, and exercise policies. The thesis includes applications of the FST framework-based methods to a wide range of option pricing problems. Pricing of single- and multi-asset, European and path-dependent options under independent-increment exponential Levy stock price models, common in equity and insurance markets, can be done efficiently via the cornerstone FST method. Mean-reverting Levy spot price models, common in commodity markets, are handled by introducing a frequency transformation, which can be readily computed via scaling of the option value function. Generating stochastic volatility, to match the long-term equity options market data, and stochastic skew, observed in currency markets, is addressed by introducing a non-stationary extension of multi-dimensional Levy processes using regime-switching. Finally, codependent jumps in multi-asset models are introduced through copulas. The FST methods are computationally efficient, running in O(MN^d log_2 N) time with M time steps and N space points in each dimension on a d-dimensional grid. The methods achieve second-order convergence in space; for American options, a penalty method is used to attain second-order convergence in time. Furthermore, graphics processing units are utilized to further reduce the computational time of FST methods.

The purpose of this study was to investigate the feasibility of using Fourier transform mid-infrared (FT-IR) microspectroscopy, with attenuated total reflectance (ATR), to detect the presence of Fusarium spp., classify differences in ability to detect Fusarium spp. among the Canadian soil zones, determine whether Fusarium spp. can serve as an indicator for the concentration of deoxynivalenol (DON), and develop an equation that can predict DON within wheat kernels. Canadian Western Red Spring wheat kernels were pressed against an ATR crystal to obtain spectra. Five chemical functional groups were investigated. The ability of FT-IR-ATR microspectroscopy to detect the presence of Fusarium spp. was confirmed. The chemical composition, and the ability to identify Fusarium spp., differed in kernels grown among the soil zones. Several methods to use Fusarium spp. as an indicator for the concentration of DON content within the wheat kernels were attempted and found to be unsuccessful.