A course in mathematical analysis.

An unabridged and unaltered republication of the Hedrick-Dunkel translation (v. 1-2); v. 3. newly translated by Howard G. Bergmann.

Anwendung der Differential- und Integralrechnung auf Geometrie: eine Revision der Principien. Vorlesung gehalten während des Sommersemesters 1901,

Available on demand as hard copy or computer file from Cornell University Library.

Lehrbuch der analysis,

Available on demand as hard copy or computer file from Cornell University Library.

Introduction to numerical analysis.

Mode of access: Internet.

A course in mathematical analysis,

Vol. II translated by Earle Raymond Hedrick and Otto Dunkel, published in 2 parts.

Investigating the Eastern Extent of the Seattle Fault Zone through Depth to Bedrock and Borehole Analysis in Bellevue, Washington

This study identifies lineaments that indicate fault activity and strengthens previous interpretations of structures within the eastern extent of the Seattle Fault zone in Bellevue, WA. My investigation has compiled geotechnical subsurface data, high-resolution LiDAR imagery, and ground-penetrating radar to produce strip log sections transecting identified lineaments and depth-to-bedrock maps exposing fault structure. My work incorporates field investigation, multiple publicly available datasets, and subsurface modeling. My results include a map showing twenty-eight identified surface lineaments, five strip-log sections, and interpolated depth-to-bedrock and minimum-depth-to-bedrock maps. Several lineaments identified in the minimum-depth-to-bedrock raster are parallel to the Seattle Fault zone and suggest the presence of small splay faults beneath east Bellevue. These results strengthen previous interpretations of seismic profile data located in the study area. Another lineament identified in the minimum-depth-to-bedrock raster suggest an unmapped tear fault accommodating differential offset along fault strike between Mercer Island and Bellevue. This work also demonstrates the utility of publicly available datasets such as geotechnical subsurface explorations and LiDAR imagery in supplementing geologic investigations in the eastern extent of the Seattle Fault zone.

Statistical Hurdle Models for Single Cell Gene Expression: Differential Expression and Graphical Modeling

Thesis (Ph.D.)--University of Washington, 2016-06

Temporal precision of interceptive action: differential effects of target size and speed

The duration of movements made to intercept moving targets decreases and movement speed increases when interception requires greater temporal precision. Changes in target size and target speed can have the same effect on required temporal precision, but the response to these changes differs: changes in target speed elicit larger changes in response speed. A possible explanation is that people attempt to strike the target in a central zone that does not vary much with variation in physical target size: the effective size of the target is relatively constant over changes in physical size. Three experiments are reported that test this idea. Participants performed two tasks: (1) strike a moving target with a bat moved perpendicular to the path of the target; (2) press on a force transducer when the target was in a location where it could be struck by the bat. Target speed was varied and target size held constant in experiment 1. Target speed and size were co-varied in experiment 2, keeping the required temporal precision constant. Target size was varied and target speed held constant in experiment 3 to give the same temporal precision as experiment 1. Duration of hitting movements decreased and maximum movement speed increased with increases in target speed and/or temporal precision requirements in all experiments. The effects were largest in experiment 1 and smallest in experiment 3. Analysis of a measure of effective target size (standard deviation of strike locations on the target) failed to support the hypothesis that performance differences could be explained in terms of effective size rather than actual physical size. In the pressing task, participants produced greater peak forces and shorter force pulses when the temporal precision required was greater, showing that the response to increasing temporal precision generalizes to different responses. It is concluded that target size and target speed have independent effects on performance.

Epidemiological analysis of electroconvulsive therapy in Victoria, Australia

Objective: To determine the population-based utilization rate of electroconvulsive therapy (ECT) in Victoria between 1998-1999, to examine the characteristics of the ECT treated group, and to identify patient factors independently associated with differential rates of ECT treatment. Method: Electroconvulsive therapy is reported under statute in Victoria, Australia. Crude, age-adjusted and age-sex specific utilization rates were calculated using this statutory data for the 1998-1999 financial year and estimated mid-year populations from the Australian Bureau of Statistics. Descriptive characteristics of those treated with ECT were derived from the statutory data. Patient factors associated with an increased likelihood of ECT in the public sector were explored with logistic regression analysis, using non-ECT treated mental health patients from the Victorian Psychiatric Case Register as the reference population. Results: The crude treated-person and age-adjusted rates for the State (both public and private sectors) were 39.9 and 44.0 persons per 100 000 resident population per annum, respectively. The crude and age-adjusted administration rates were 330.3 and 362.6 ECT administrations per 100 000 resident population per annum, respectively. Age-sex specific rates varied by age and sex, with rates generally increasing with age and female sex. Overall, 62.8% of the treated group were women, 32.9% aged over 64, and 75.2% had depression. Diagnosis, age and sex each independently predicted ECT in the public sector, with diagnosis the most important factor, followed by age then sex. Conclusions: Despite decades of use, the appropriate rate of ECT utilization is still unclear. Further research should be directed at exploring the factors, including provider variables, determining ECT treatment.

Tissue-specific gene expression in soybean (Glycine max) detected by cDNA microarray analysis

We have constructed cDNA microarrays for soybean (Glycine max L. Merrill), containing approximately 4,100 Unigene ESTs derived from axenic roots, to evaluate their application and utility for functional genomics of organ differentiation in legumes. We assessed microarray technology by conducting studies to evaluate the accuracy of microarray data and have found them to be both reliable and reproducible in repeat hybridisations. Several ESTs showed high levels (>50 fold) of differential expression in either root or shoot tissue of soybean. A small number of physiologically interesting, and differentially expressed sequences found by microarray analysis were verified by both quantitative real-time RT-PCR and Northern blot analysis. There was a linear correlation (r(2) = 0.99, over 5 orders of magnitude) between microarray and quantitative real-time RT-PCR data. Microarray analysis of soybean has enormous potential not only for the discovery of new genes involved in tissue differentiation and function, but also to study the expression of previously characterised genes, gene networks and gene interactions in wild-type, mutant or transgenic; plants.

Latent class and genetic analysis does not support migraine with aura and migraine without aura as separate entities

Latent class and genetic analyses were used to identify subgroups of migraine sufferers in a community sample of 6,265 Australian twins (55% female) aged 25-36 who had completed an interview based on International Headache Society UHS) criteria. Consistent with prevalence rates from other population-based studies, 703 (20%) female and 250 (9%) male twins satisfied the IHS criteria for migraine without aura (MO), and of these, 432 (13%) female and 166 (6%) male twins satisfied the criteria for migraine with aura (MA) as indicated by visual symptoms. Latent class analysis (LCA) of IHS symptoms identified three major symptomatic classes, representing 1) a mild form of recurrent nonmigrainous headache, 2) a moderately severe form of migraine, typically without visual aura symptoms (although 40% of individuals in this class were positive for aura), and 3) a severe form of migraine typically with visual aura symptoms (although 24% of individuals were negative for aura). Using the LCA classification, many more individuals were considered affected to some degree than when using IHS criteria (35% vs. 13%). Furthermore, genetic model fitting indicated a greater genetic contribution to migraine using the LCA classification (heritability, h(2) =0.40; 95% CI, 0.29-0.46) compared with the IHS classification (h(2)=0.36; 95% CI, 0.22-0.42). Exploratory latent class modeling, fitting up to 10 classes, did not identify classes corresponding to either the IHS MO or MA classification. Our data indicate the existence of a continuum of severity, with MA more severe but not etiologically distinct from MO. In searching for predisposing genes, we should therefore expect to find some genes that may underlie all major recurrent headache subtypes, with modifying genetic or environmental factors that may lead to differential expression of the liability for migraine. (C) 2004 Wiley-Liss, Inc.

Non-linear analysis of the thermo-electro-mechanical behaviour of shear deformable FGM plates with piezoelectric actuators

This paper investigates the non-linear bending behaviour of functionally graded plates that are bonded with piezoelectric actuator layers and subjected to transverse loads and a temperature gradient based on Reddy's higher-order shear deformation plate theory. The von Karman-type geometric non-linearity, piezoelectric and thermal effects are included in mathematical formulations. The temperature change is due to a steady-state heat conduction through the plate thickness. The material properties are assumed to be graded in the thickness direction according to a power-law distribution in terms of the volume fractions of the constituents. The plate is clamped at two opposite edges, while the remaining edges can be free, simply supported or clamped. Differential quadrature approximation in the X-axis is employed to convert the partial differential governing equations and the associated boundary conditions into a set of ordinary differential equations. By choosing the appropriate functions as the displacement and stress functions on each nodal line and then applying the Galerkin procedure, a system of non-linear algebraic equations is obtained, from which the non-linear bending response of the plate is determined through a Picard iteration scheme. Numerical results for zirconia/aluminium rectangular plates are given in dimensionless graphical form. The effects of the applied actuator voltage, the volume fraction exponent, the temperature gradient, as well as the characteristics of the boundary conditions are also studied in detail. Copyright (C) 2004 John Wiley Sons, Ltd.

Differential expression of N-methyl-D-aspartate receptor NR2 isoforms in Alzheimer's disease

We have previously shown that the expression of NMDA receptor NR1 subunit mRNA splice variants in Alzheimer's disease (AD) brain varies according to regional susceptibility to pathological damage. Here we investigated the expression of the modulatory NR2 subunits of the NMDA receptor using quantitative RT-PCR to assay all NR2 isoforms. Significantly lower expression of NR2A and NR2B transcripts was found in susceptible regions of AD brain, whereas expression of NR2C and NR2D transcripts did not differ from that in controls. Western blot analysis confirmed a lower expression of the NR2A and NR2B isoforms at the protein level. The results suggest that NR2 subunit composition may modulate NMDA receptor-mediated excitotoxicity. NMDA receptor dysfunction might give rise to the regionally selective pattern of neuronal loss that is characteristic of AD.

Adaptive stepsize based on control theory for stochastic differential equations

The numerical solution of stochastic differential equations (SDEs) has been focussed recently on the development of numerical methods with good stability and order properties. These numerical implementations have been made with fixed stepsize, but there are many situations when a fixed stepsize is not appropriate. In the numerical solution of ordinary differential equations, much work has been carried out on developing robust implementation techniques using variable stepsize. It has been necessary, in the deterministic case, to consider the best choice for an initial stepsize, as well as developing effective strategies for stepsize control-the same, of course, must be carried out in the stochastic case. In this paper, proportional integral (PI) control is applied to a variable stepsize implementation of an embedded pair of stochastic Runge-Kutta methods used to obtain numerical solutions of nonstiff SDEs. For stiff SDEs, the embedded pair of the balanced Milstein and balanced implicit method is implemented in variable stepsize mode using a predictive controller for the stepsize change. The extension of these stepsize controllers from a digital filter theory point of view via PI with derivative (PID) control will also be implemented. The implementations show the improvement in efficiency that can be attained when using these control theory approaches compared with the regular stepsize change strategy. (C) 2004 Elsevier B.V. All rights reserved.

Numerical simulation of stochastic ordinary differential equations in biomathematical modelling

In this work we discuss the effects of white and coloured noise perturbations on the parameters of a mathematical model of bacteriophage infection introduced by Beretta and Kuang in [Math. Biosc. 149 (1998) 57]. We numerically simulate the strong solutions of the resulting systems of stochastic ordinary differential equations (SDEs), with respect to the global error, by means of numerical methods of both Euler-Taylor expansion and stochastic Runge-Kutta type. (C) 2003 IMACS. Published by Elsevier B.V. All rights reserved.