Inequalities Between Pythagoras Numbers and Algebraic Ranks in Witt Rings of Fields.

This dissertation establishes new lower bounds for the algebraic ranks of certain Witt classes of quadratic forms. Let K denote a field of characteristic different from 2 and let q be a quadratic form over K. The form q is said to be algebraic when q is Witt equivalent to the trace form qL∣K of some finite algebraic field extension L∣K . When q is algebraic, the algebraic rank of q is defined to be the degree of the minimal extension L∣K whose trace form is Witt equivalent to q. It is an important, unsolved problem to find reasonable bounds on the algebraic rank of a given algebraic form. This dissertation makes a beginning contribution to this problem of bounding the algebraic rank by investigating a simple, special case. Let sigma denote a totally positive square-class in a field K (characteristic different from 2, as always). Assuming that the 1-dimensional quadratic form sigma X2 is algebraic, what can be said about the algebraic rank? Even in this simple case, little was known prior to this dissertation. Let pyKs denote the pythagoras number of sigma relative to K. This is the smallest natural number, j, such that or can be written as a sum of j squares of elements in K. Let n be the algebraic rank of sigma X2. In general, n is unknown, and a reasonable lower bound is sought. The main result is: pyKs ≤2n-dn+1 where d(n + 1) is the sum of the coefficients of the 2-adic expansion of n + 1. Thus, if sigma is chosen with a large pythagoras number, then the algebraic rank n must be correspondingly large as well. This dissertation also considers a slightly more general case

Rumen and Urine Amine/Phenol-Metabolome of Beef Steers with Divergent Residual Feed Intake

Cattle production is one of the most important agricultural industries in the United States. Despite its overall production efficiency, the industry is facing considerable adversities to its long-term sustainability due to population growth, decreased land availability, and the increase in global warming. Since feed efficiency imposes an immense influence on the cost of production for animals and is a major cost determinant for profitability, the improvement of feed utilization through the understanding of animal-to-animal variation in feed efficiency is pertinent to increase farm productivity and profitability. Residual feed intake (RFI) is a measure of feed efficiency and is defined as the difference between the actual and predicted feed intake of an animal, with consideration of variation in body size and growth performance. The objective of this study was to analyze rumen and urine metabolome to identify metabolite biomarkers and biochemical pathways associated with divergent RFI phenotype in crossbred beef steers. A group of 56 crossbred growing beef steers (average BW= 261± 18.5 kg) were adapted to a high-forage total mixed ration in a confinement dry lot equipped with GrowSafe intake nodes for a period of 49 d to determine their residual feed intake classification (RFI). After RFI determination, weekly urine samples were collected three times from beef steers with negative RFI (most efficient (HFE); RFI = - 1.93 kg/d, n = 8) and positive RFI (least efficient (LFE); RFI = + 2.01 kg/d, n = 8). Urine samples collected were then composited for each steer. Rumen fluid samples were collected weekly for three weeks from beef steers with negative RFI (most efficient (HFE; RFI=-1.93 kg/d, n=7) and positive RFI (least efficient (LFE); RFI= +2.01 kg/d, n=7). Metabolome analysis was conducted using a chemical isotope labeling/liquid chromatography-mass spectrometry, specifically analyzing metabolites containing anime/phenol-chemical groups, which are metabolites involved in the metabolism of amino acids. A total number of 443 amine/phenol-containing metabolites were detected and identified in rumen fluid, while a total number of 557 amine/phenol-containing metabolites were detected and identified in urine. Biomarker analysis of the rumen amine/phenol-metabolome identified isomer of cadaverine, baeocystin, 6-methyladenine, N(6)-methyllysine as candidate biomarkers of RFI (false discovery rate ≤ 0.05; Area Under the Curve ≥ 0.70). Biomarker analysis of the urinary amine/phenol-metabolome identified N-acetyl-L-tyrosine, O-methyl-L-threonine, uridine, and threoninyl-hydroxyproline as candidate biomarkers of RFI (false discovery rate ≤ 0.05; Area Under the Curve ≥ 0.85). In conclusion, the results of our study revealed that alterations in rumen fluid and urine amine/phenol-metabolome are associated with divergent RFI phenotype and both rumen fluid and urine are potential sources of candidate metabolite biomarkers associated with RFI in beef cattle

MassMine: Collecting and Archiving Big Data for Social Media Humanities Researchers

The MassMine project team representing participants from the Department of English, George A. Smathers Libraries (Libraries), and Research Computing at the University of Florida (UF) requests $60,000 to finish the version 1.0 release, develop a robust training program, and promote the MassMine open source software. MassMine enables researchers to collect their own social media data archives and supports data mining, thus providing free access to big data for academic inquiry. MassMine further supports researchers in creating and defining methods and measures for analyzing cultural and localized trends, and developing humanities research questions and data mining practices. The primary aims of this project are to: 1) refine the MassMine tools to support collection, acquisition, and use of available social media and web data; and, 2) develop a training program and corresponding online resources for supporting the broad use of MassMine by humanities researchers, regardless of experience

GAF: Mechanical Paint Line Test Stand

The roofing manufacturer GAF located in Shafter, CA is in pursuit of a mechanism with the ability to improve the quality of paint lining applied on a dynamic roll of roofing shingles. The mechanism must consist of an alignment system along which a paint line applicator can be adjusted in the vertical direction and operate at a certain range of speeds. Other requirements for the mechanism demand that it is feasibly portable, reasonably durable, capable of accurate alignment, mountable to the ground, and within a budget of $15,000. With the customer\u27s design requirements established and understood, a one-year project has been outlined with details on how the objectives assigned to the Cal Poly 2018 senior project team will be satisfied. The first quarter was spent researching, brainstorming ideas, drafting a Quality Functional Deployment chart and producing different design concepts from which a final design would be made. After finalizing the design concept, it was presented to GAF for evaluation where approval and feedback were provided. After evaluating the feedback from GAF, the team proceeded with the project doing an Interim Design review to finalize the design by deciding which parts of the design concept can remain in use, and identifying parts that needed to be changed or added to. Some of the original structural components were modified in an effort to help improve the quality of paint application. Additionally, the Pac-Man device is driven by a belt and pulley coupled to a motor while maintaining the use of a mill table and hydraulic scissor link table for horizontal and vertical position adjustability respectfully. Throughout the second quarter the team was tasked with conducting a critical design review which involved calculations needed for design verification. Also the majority of the quarter was spent on planning for the manufacturing and testing part of the following quarter. The third and final quarter was spent doing a final design review where the team concludes the project with the last round of design modifications, followed by a hardware and safety demo. From there the project was assembled and tested after all parts were ordered, manufactured, and assembled. This was then followed by the project exposition where it has been presented and shown to viewers what it was designed for and how it operates

Aspects of anisotropic harmonic analysis beyond Calderón-Zygmund Theory

We consider three major parts of Fourier analysis and their role in Fefferman-Stein inequalities. The three areas can be considered as three separate topics in their own right, or as three steps to proving certain $L$$^p$-$L$$^q$ inequalities via the Fefferman-Stein inequalities of the form \begin{align*} \int_{\R^n} |T f|^2 w \lesssim \int_{\R^n}|f|^2 \mathcal{M}w. \end{align*} The first area discussed is that of maximal functions, specifically obtaining $L$$^p$-$L$$^q$ inequalities on large classes of maximal functions. We then use a simple duality argument to transfer these to operators where we have a Fefferman-Stein inequality via \begin{align*} \|T\|_{p \to q} \lesssim \|\mathcal{M}\|^{1/2}_{(q/2)' \to (p/2)'}. \end{align*} The second area aims to control operators defined via multipliers by the previous section's geometrically defined maximal functions. In particular, we build up to a schema that can be used to prove Fefferman-Stein inequalities via the so called $g$-functions, originating in work of E. M. Stein* but having historic roots that can be easily seen by viewing $g$-functions as speciality square functions. In the final section we consider some classes of operators with oscillatory kernels and obtain estimates on their multipliers, and by application of the previous two sections obtain some $L$$^p$-$L$$^q$ inequalities. [*Elias M Stein. Singular integrals and differentiability properties of functions (PMS-30), volume 30. Princeton University Press, 1970.

Effective Temperatures of a Driven System Near Jamming

Fluctuations in a model of a sheared, zero-temperature foam are studied numerically. Five different quantities that reduce to the true temperature in an equilibrium thermal system are calculated. All five have the same shear-rate dependence, and three have the same value. Near the onset of jamming, the relaxation time is the same function of these three temperatures in the sheared system as of the true temperature in an unsheared system. These results imply that statistical mechanics is useful for the system and provide strong support for the concept of jamming.Comment: 4 pages, 4 postscript figure

Early modern intertextuality: post structuralism, narrative systems, and 'A midsummer night's dream'

Central to both early modern critical study and the theory of intertextuality are concepts such as the plurality of discourse, the mutually informing relationship between cultural ideologies and texts, and the instability of texts. Following revised critical approaches, this essay argues that there is potential in the direct application and exploration of the theory of intertextuality in early modern literature, particularly in the sense of engagement with and the extensive refiguring of elements from available narrative systems including classical mythology, folklore, and contemporary continental writing through allegory, allusion and translation. Critical consideration of reading, creative imitation, and interpretative variety are central to both fields. This essay argues that these central aspects of early modern creative writing constitute a valid application of intertextual theory, which can be used to generate detailed and multilayered critical readings. It outlines an understanding of intertextuality, demonstrates how the theory is illustrated both in the period and in inherited classical textual theory, and offers a brief applied case study, reading Shakespeare’s A Midsummer Night’s Dream (1595) as an overtly intertextual text

A critical evaluation of network and pathway based classifiers for outcome prediction in breast cancer

Recently, several classifiers that combine primary tumor data, like gene expression data, and secondary data sources, such as protein-protein interaction networks, have been proposed for predicting outcome in breast cancer. In these approaches, new composite features are typically constructed by aggregating the expression levels of several genes. The secondary data sources are employed to guide this aggregation. Although many studies claim that these approaches improve classification performance over single gene classifiers, the gain in performance is difficult to assess. This stems mainly from the fact that different breast cancer data sets and validation procedures are employed to assess the performance. Here we address these issues by employing a large cohort of six breast cancer data sets as benchmark set and by performing an unbiased evaluation of the classification accuracies of the different approaches. Contrary to previous claims, we find that composite feature classifiers do not outperform simple single gene classifiers. We investigate the effect of (1) the number of selected features; (2) the specific gene set from which features are selected; (3) the size of the training set and (4) the heterogeneity of the data set on the performance of composite feature and single gene classifiers. Strikingly, we find that randomization of secondary data sources, which destroys all biological information in these sources, does not result in a deterioration in performance of composite feature classifiers. Finally, we show that when a proper correction for gene set size is performed, the stability of single gene sets is similar to the stability of composite feature sets. Based on these results there is currently no reason to prefer prognostic classifiers based on composite features over single gene classifiers for predicting outcome in breast cancer