Principal component and second generation wavelet analysis of Treasury yield curve evolution

Prices of U.S. Treasury securities vary over time and across maturities. When the market in Treasurys is sufficiently complete and frictionless, these prices may be modeled by a function time and maturity. A cross-section of this function for time held fixed is called the yield curve; the aggregate of these sections is the evolution of the yield curve. This dissertation studies aspects of this evolution. ^ There are two complementary approaches to the study of yield curve evolution here. The first is principal components analysis; the second is wavelet analysis. In both approaches both the time and maturity variables are discretized. In principal components analysis the vectors of yield curve shifts are viewed as observations of a multivariate normal distribution. The resulting covariance matrix is diagonalized; the resulting eigenvalues and eigenvectors (the principal components) are used to draw inferences about the yield curve evolution. ^ In wavelet analysis, the vectors of shifts are resolved into hierarchies of localized fundamental shifts (wavelets) that leave specified global properties invariant (average change and duration change). The hierarchies relate to the degree of localization with movements restricted to a single maturity at the base and general movements at the apex. Second generation wavelet techniques allow better adaptation of the model to economic observables. Statistically, the wavelet approach is inherently nonparametric while the wavelets themselves are better adapted to describing a complete market. ^ Principal components analysis provides information on the dimension of the yield curve process. While there is no clear demarkation between operative factors and noise, the top six principal components pick up 99% of total interest rate variation 95% of the time. An economically justified basis of this process is hard to find; for example a simple linear model will not suffice for the first principal component and the shape of this component is nonstationary. ^ Wavelet analysis works more directly with yield curve observations than principal components analysis. In fact the complete process from bond data to multiresolution is presented, including the dedicated Perl programs and the details of the portfolio metrics and specially adapted wavelet construction. The result is more robust statistics which provide balance to the more fragile principal components analysis. ^

Broadband RF current detector

The problems to be solved in this thesis were 1) development of a broadband RF preamplifier to be used with non-ferrous current probes so that the amplified signal exceeds the errors due to cable pickup, no detection is needed in this application, and 2) development of a self-contained device that amplifies and detects the output from a nonferrous current probe, providing a digital readout of the current. These instruments have been completed and are being tested for use by the National Institutes of Occupational Safety and Health (NIOSH). The self-contained current meter operates at frequencies up to 600 MHz, and detects currents as low as 8 mA . At these current magnitudes, the probe (pick-up coil) will output a voltage of 500μV (-53 dBm on 50Ω) which will have to be raised above 0 dBm. The final circuit uses a RF mixer as a variable attenuator in order to increase the dynamic range, two Monolithic Microwave Integrated Circuits (MMIC) for preamplification, a final broadband amplifier to raise the output compression point, a Schottky diode detector, a sample and hold circuit, and a liquid crystal digital panel meter.

Fluorescence-enhanced optical imaging on three-dimensional phantoms using a hand-held probe based frequency-domain intensified charge coupled device (ICCD) optical imager

Fluorescence-enhanced optical imaging is an emerging non-invasive and non-ionizing modality towards breast cancer diagnosis. Various optical imaging systems are currently available, although most of them are limited by bulky instrumentation, or their inability to flexibly image different tissue volumes and shapes. Hand-held based optical imaging systems are a recent development for its improved portability, but are currently limited only to surface mapping. Herein, a novel optical imager, consisting primarily of a hand-held probe and a gain-modulated intensified charge coupled device (ICCD) detector, is developed towards both surface and tomographic breast imaging. The unique features of this hand-held probe based optical imager are its ability to; (i) image large tissue areas (5×10 sq. cm) in a single scan, (ii) reduce overall imaging time using a unique measurement geometry, and (iii) perform tomographic imaging for tumor three-dimensional (3-D) localization. Frequency-domain based experimental phantom studies have been performed on slab geometries (650 ml) under different target depths (1-2.5 cm), target volumes (0.45, 0.23 and 0.10 cc), fluorescence absorption contrast ratios (1:0, 1000:1 to 5:1), and number of targets (up to 3), using Indocyanine Green (ICG) as fluorescence contrast agents. An approximate extended Kalman filter based inverse algorithm has been adapted towards 3-D tomographic reconstructions. Single fluorescence target(s) was reconstructed when located: (i) up to 2.5 cm deep (at 1:0 contrast ratio) and 1.5 cm deep (up to 10:1 contrast ratio) for 0.45 cc-target; and (ii) 1.5 cm deep for target as small as 0.10 cc at 1:0 contrast ratio. In the case of multiple targets, two targets as close as 0.7 cm were tomographically resolved when located 1.5 cm deep. It was observed that performing multi-projection (here dual) based tomographic imaging using a priori target information from surface images, improved the target depth recovery over using single projection based imaging. From a total of 98 experimental phantom studies, the sensitivity and specificity of the imager was estimated as 81-86% and 43-50%, respectively. With 3-D tomographic imaging successfully demonstrated for the first time using a hand-held based optical imager, the clinical translation of this technology is promising upon further experimental validation from in-vitro and in-vivo studies.

Clinical translation of a hand-held optical imager for breast cancer diagnostics: In vitro and in vivo tomography studies

Optical imaging is an emerging technology towards non-invasive breast cancer diagnostics. In recent years, portable and patient comfortable hand-held optical imagers are developed towards two-dimensional (2D) tumor detections. However, these imagers are not capable of three-dimensional (3D) tomography because they cannot register the positional information of the hand-held probe onto the imaged tissue. A hand-held optical imager has been developed in our Optical Imaging Laboratory with 3D tomography capabilities, as demonstrated from tissue phantom studies. The overall goal of my dissertation is towards the translation of our imager to the clinical setting for 3D tomographic imaging in human breast tissues. A systematic experimental approach was designed and executed as follows: (i) fast 2D imaging, (ii) coregistered imaging, and (iii) 3D tomographic imaging studies. (i) Fast 2D imaging was initially demonstrated in tissue phantoms (1% Liposyn solution) and in vitro (minced chicken breast and 1% Liposyn). A 0.45 cm3 fluorescent target at 1:0 contrast ratio was detectable up to 2.5 cm deep. Fast 2D imaging experiments performed in vivo with healthy female subjects also detected a 0.45 cm3 fluorescent target superficially placed ∼2.5 cm under the breast tissue. (ii) Coregistered imaging was automated and validated in phantoms with ∼0.19 cm error in the probe’s positional information. Coregistration also improved the target depth detection to 3.5 cm, from multi-location imaging approach. Coregistered imaging was further validated in-vivo , although the error in probe’s positional information increased to ∼0.9 cm (subject to soft tissue deformation and movement). (iii) Three-dimensional tomography studies were successfully demonstrated in vitro using 0.45 cm3 fluorescence targets. The feasibility of 3D tomography was demonstrated for the first time in breast tissues using the hand-held optical imager, wherein a 0.45 cm3 fluorescent target (superficially placed) was recovered along with artifacts. Diffuse optical imaging studies were performed in two breast cancer patients with invasive ductal carcinoma. The images showed greater absorption at the tumor cites (as observed from x-ray mammography, ultrasound, and/or MRI). In summary, my dissertation demonstrated the potential of a hand-held optical imager towards 2D breast tumor detection and 3D breast tomography, holding a promise for extensive clinical translational efforts.

Using Optical Properties to Quantify Fringe Mangrove Inputs to the Dissolved Organic Matter (DOM) Pool in a Subtropical Estuary

Dissolved organic carbon (DOC) concentration and dissolved organic matter (DOM) optical properties were analyzed along two estuarine river transects during the wet and dry seasons to better understand DOM dynamics and quantify mangrove inputs. A tidal study was performed to assess the impacts of tidal pumping on DOM transport. DOM in the estuaries showed non-conservative mixing indicative of mangrove-derived inputs. Similarly, fluorescence data suggest that some terrestrial humic-like components showed non-conservative behavior. An Everglades freshwater-derived fluorescent component, which is associated with soil inputs from the Northern Everglades, behaved conservatively. During the dry season, a protein-like component behaved conservatively until the mid-salinity range when non-conservative behavior due to degradation and/or loss was observed. The tidal study data suggests mangrove porewater inputs to the rivers following low tide. The differences in quantity of DOM exported by the Shark and Harney Rivers imply that geomorphology and tidal hydrology may be a dominant factor controlling the amount of DOM exported from the mangrove ecotone, where up to 21 % of the DOC is mangrove-derived. Additionally, nutrient concentrations and other temporal factors may control DOM export from the mangroves, particularly for the microbially derived fluorescent components, contributing to the seasonal differences. The wet and dry season fluxes of mangrove DOM from the Shark River is estimated as 0.27 × 109 mg C d−1 and 0.075 × 109 mg C d−1, respectively, and the Harney River is estimated as 1.9 × 109 mg C d−1 and 0.20 × 109 mg C d−1.