Direct QR factorizations for tall-and-skinny matrices in MapReduce architectures

The QR factorization and the SVD are two fundamental matrix decompositions with applications throughout scientific computing and data analysis. For matrices with many more rows than columns, so-called "tall-and-skinny matrices," there is a numerically stable, efficient, communication-avoiding algorithm for computing the QR factorization. It has been used in traditional high performance computing and grid computing environments. For MapReduce environments, existing methods to compute the QR decomposition use a numerically unstable approach that relies on indirectly computing the Q factor. In the best case, these methods require only two passes over the data. In this paper, we describe how to compute a stable tall-and-skinny QR factorization on a MapReduce architecture in only slightly more than 2 passes over the data. We can compute the SVD with only a small change and no difference in performance. We present a performance comparison between our new direct TSQR method, a standard unstable implementation for MapReduce (Cholesky QR), and the classic stable algorithm implemented for MapReduce (Householder QR). We find that our new stable method has a large performance advantage over the Householder QR method. This holds both in a theoretical performance model as well as in an actual implementation

What we can freeze from the body and why : a historical, physical, and mathematical introduction [abstract]

This presentation was made during the session "After the Body: Is It Still Human?"Abstract of a presentation given at the 2008 Body Project conference at the University of Missouri-Columbia.The public often links cryobiology, the study of biological materials at low temperatures, with the science fiction of whole body and head freezing, but in reality successful cryopreservation of biological materials is limited to isolated cells, some tissues, and in some instances organs. Few scientific fields encompass as many diverse disciplines as cryobiology, where chemistry, physics, plant and animal biology, economics, agriculture, oncology, ethics, and management all play pivotal roles. Cryobiology even poses questions such as: are cryopreserved cells alive? In this presentation I will provide a brief history of the field, an overview of the scope of research and applications of cryobiology, and briefly introduce my mathematical research into optimizing freezing protocols

A surface-potential-based compact model for partially-depleted silicon-on-insulator MOSFETs

With the continuous scaling of CMOS technologies, Silicon-on-Insulator (SOI) technologies have become more competitive compared to bulk, due to their lower parasitic capacitances and leakage currents. The shift towards high frequency, low power circuitry, coupled with the increased maturity of SOI process technologies, have made SOI a genuinely costeffective solution for leading edge applications. The original STAG2 model, developed at the University of Southampton, UK, was among the first compact circuit simulation models to specifically model the behaviour of Partially-Depleted (PD) SOI devices. STAG2 was a robust, surface-potential based compact model, employing closed-form equations to minimise simulation times for large circuits. It was able to simulate circuits in DC, small signal, and transient modes, and particular care was taken to ensure that convergence problems were kept to a minimum. In this thesis, the ongoing development of the STAG model, culminating in the release of a new version, STAG3, is described. STAG3 is intended to make the STAG model applicable to process technologies down to 100nm. To this end, a number of major model improvements were undertaken, including: a new core surface potential model, new vertical and lateral field mobility models, quantum mechanical models, the ability to model non-uniform vertical doping profiles, and other miscellaneous effects relevant to deep submicron devices such as polysilicon depletion, velocity overshoot, and the reverse short channel effect.As with the previous versions of STAG, emphasis has been placed on ensuring that model equations are numerically robust, as well as closed-form wherever possible, in order to minimise convergence problems and circuit simulation times. The STAG3 model has been evaluated with devices manufactured in PD-SOI technologies down to 0.25?m, and was found to give good matching to experimental data across a range of device sizes and biases, whilst requiring only a single set of model parameters

CHARACTERIZATION OF PIEDMONT PRAIRIE SITES IN NORTH AND SOUTH CAROLINA

Grassland habitats have essentially disappeared from the Piedmont. This study was conducted to determine which site characteristics in remnant Piedmont prairie sites could be used as indicators of suitable sites. Eight prairie remnant sites located in the Piedmont of North and South Carolina were evaluated based on soil series, slope, aspect, landform index, temperature, and precipitation. Geographic Information System technology was used to create layers of these characteristics to predict potential restoration sites throughout the North and South Carolina Piedmont. It was found that southern aspects, slopes generally less than 15%, upper slope positions, and occurrence on Enon (Fine, mixed, active, thermic Ultic Hapludalfs), Iredell (Fine, montmorillonitic, thermic, Oxyaquic Vertic Hapludalfs), Mecklenburg (Fine, mixed, active, thermic Ultic Hapludalfs), Wilkes (Loamy, mixed, active, thermic, shallow Typic Hapludalfs and Wynott (Fine, mixed, active, thermic Typic Hapludalfs) soil series were common to all sites. All sites had been disturbed in some manner. Analysis of soil chemical and physical properties showed no significant differences for C, N, and Zn among locations. Significant site differences were found for P, K, Ca, Mg, B, Cu, Mn, Na, Zn, acidity, pH, buffer pH, C/N ratio, K base saturation, Ca base saturation, Mg base saturation, Na base saturation, total base saturation, CEC, and percent sand, silt, and clay. When soil nutrients were rated for growth sufficiency, N, P, and K were found deficient, and other nutrients were sufficient or greater. Base saturation ranged from 29-70%, but averaged 52% for all sites. Soil texture to a 15 cm depth was loamy with sand comprising the greatest volume (mean 45%), followed by silt (33%) then clay (21%). Ordination of five prairie remnants indicated that the sites group based on moisture. Winter bentgrass (Agrostis hyemalis (Walt.) B.S.P.), yellowfruit sedge (Carex annectens (Bickn.) Bickn.), scarlet Indian paintbrush (Castilleja coccinea (L.) Spreng.), spotted water hemlock (Cicuta maculata L.), chickasaw plum (Prunus angustifolia Marsh.), needletip blue-eyed grass (Sisyrinchium mucronatum Michx.), and spring lady\u27s tresses (Spiranthes vernalis Engelm. & Gray) are preferential to the most mesic site. Remaining locations were divided based on the occurrence of Indian hemp (Apocynum cannabinum L.). One location contained this species while four did not. Thirty-eight species did not show a preference to site with twenty-two having an association with prairies. Qualification of landscape position, soil chemical and physical characteristics, and species occurrence will assist restorationists and land managers by aiding them in choosing better sites thus increasing restoration success. Results may also give insight into whether present management and selection methods are suitable

Abundance, distribution, and habitat of leatherback turtles (Dermochelys coriacea) off California, 1990−2003

Leatherback turtles (Dermochelys coriacea) are regularly seen off the U.S. West Coast, where they forage on jellyfish (Scyphomedusae) during summer and fall. Aerial line-transect surveys were conducted in neritic waters (<92 m depth) off central and northern California during 1990−2003, providing the first foraging population estimates for Pacific leatherback turtles. Males and females of about 1.1 to 2.1 m length were observed. Estimated abundance was linked to the Northern Oscillation Index and ranged from 12 (coefficient of variation [CV] =0.75) in 1995 to 379 (CV= 0.23) in 1990, averaging 178 (CV= 0.15). Greatest densities were found off central California, where oceanographic retention areas or upwelling shadows created favorable habitat for leatherback turtle prey. Results from independent telemetry studies have linked leatherback turtles off the U.S. West Coast to one of the two largest remaining Pacific breeding populations, at Jamursba Medi, Indonesia. Nearshore waters off California thus represent an important foraging region for the critically endangered Pacific leatherback turtle

Investigation of the effects of porcine reproductive and respiratory syndrome virus (PRRSV) exposure dose on pregnant swine, the effect of PRRSV on the ovary, and methods for detection of PRRSV in the fetus

Porcine reproductive and respiratory syndrome virus (PRRSV) was inoculated into multiple PRRSV-vaccinated and nonvaccinated late term pregnant sows for investigation of the effect of varied exposure dose on vaccine-induced protection, the effect of PRRSV infection on progesterone levels and ovary, and the relative suitability of virus isolation, immunohistochemistry, fetal serology, and reverse transcription polymerase chain reaction for the detection of transplacental fetal infection. In phase 1, dead and virus infected fetuses were identified at necropsy on postinoculation day 21 in 4 of 4, 3 of 3, and 3 of 4 litters from nonvaccinated sows and 0 of 4, 1 of 2, and 1 of 4 litters from PRRSV-vaccinated sows inoculated with 102, 104, or 10 6 CCID50 of PRRSV strain NADC-8 respectively. The rate of infection was significantly different (P \u3c .001) between the vaccinated and nonvaccinated 102 CCID50 groups. Litter infection rates were lower in the higher dose vaccinated groups but not significantly different from nonvaccinates. No difference in the rate of infection of fetuses within transplacentally infected litters was identified regardless of dose or vaccination status. In phase 2, plasma progesterone levels were not different from controls regardless of vaccination status or dose group, no ovarian lesions were detected on light microscopy, and no PRRSV was detected in ovarian tissues by immunchistochernistry or by in situ hybridization. In phase 3, virus isolation, immunohistochemical staining, and fetal serology identified PRRSV infection in 48.6, 23.4, and 14.9% of 107 fetuses respectively, and identified at least one infected fetus in 10, 10, and 5 of 10 litters respectively. In-utero death with autolysis reduced the test efficacy of all three methods. Fetal thoracic fluid and tissues proved equally suitable for rtPCR detection of PRRSV. Pooling of fetal tissues or fluids from VI-positive animals with comparable material from negative controls had no detrimental effect on rtPCR results when evaluated at dilutions of 1:1, 1:2, 1:4, and 1:8. The results of rtPCR testing were positive in 100, 94.4, and 83.3% of VI-positive specimens allowed to autolyze at 4, 21 or 37°C respectively. Compared to the other testing modalities, rtPCR appeared to be impacted the least by autolysis

Love Your Neighbor: An Educational Strategy to Cultivate Compassion in Adolescent Males

When challenged to identify the greatest commandment in the Law, Jesus Christ famously included “love your neighbor” in his response, making love foundational for all followers of Christ. Compassion is a key element that serves to demonstrate biblical love; sadly, today’s culture often minimizes or discourages compassion. In ten years of chaplaincy at the secondary school level, this author has seen too many Christian young men finish their high school journey without a foundation in love through compassion. This thesis project will utilize existing resources for academic and biblical research, as well as interviews of 25 high school males, to identify factors contributing to successful development of compassion in young males. As a result, this thesis project will develop a strategy, through intentional ministry and educational planning and methodology, to instill or reinforce compassion in adolescent males. This strategy will enable young men to better express love which is foundational for all followers of Christ

Mathematical problems from cryobiology

The entire thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file; a non-technical public abstract appears in the public.pdf file.Title from PDF of title page (University of Missouri--Columbia, viewed on January 25, 2011).Thesis advisors: Professor Carmen Chicone and Professor John Critser.Vita.Ph. D. University of Missouri--Columbia 2009.Cryobiology is the study of life anddeath at low temperatures and provides a fascinating setting for applied mathematics. The interdisciplinary nature of cryobiology mirrors the diversity of applications ranging from animal agriculture to laboratory cell and species preservation to critical human clinical applications for the preservation of life and for the killing of cells during cryosurgery. The work comprising this thesis develops approaches for optimization of cryobiological protocols, and defines a new model for common cryobiological procedures. The first step is to advance an understanding of the optimal control of a classical ODE system describing the mass transport that occurs during cryopreservation. This investigation leads to the description of exact solutions to this 70-year-old nonlinear system, a global stability result for the generalized system with n-solutes, controllability and existence of optimal controls in the n-solute case, and a complete synthesis of optimal controls in the 2- solute case. After defining optimal controls, the question arises whether the predicted continuous optimal control of the extracellular environment affects the hypotheses of the ODE model, namely, perfect stirring inside and outside of the cell/tissue-media boundary. We constructed a new model coupling the ODE mass transport at the cell/tissue boundary of changing radius with convection-diffusion and potential flow models and a numerical integration scheme to explore the effects of advection on the cell-media interface.Includes bibliographical reference