University of Wyoming Open Journals
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A smooth version of Sylvester's law of inertia and its numerical realization
No full textA smooth version of Sylvester's law of inertia is presented for symmetric matrix functions of constant rank. The techniques used in the proof are constructive but the resulting numerical approaches are unstable, and therefore require stabilization. Two different stabilization techniques are suggested, one based on a descent method and one based on Newton's method. Some numerical tests are included to demonstrate the applicability of the obtained numerical methods
An elementary proof of Mirsky's low rank approximation theorem
No full textAn elementary proof is given for Mirsky's result on best low rank approximations of a given matrix with respect to all unitarily invariant norms
Predictability and stability of sagebrush-steppe restoration in a changing climate
No full textThe sagebrush steppe is now one of the most imperiled ecosystems in North America, prompting the need for successful restoration. However, restoration efforts often fall short of expectations due to poorly-understood ecological factors and variable outcomes. When, where, and how restoration is initiated could play a large role in community composition in the long-term, but the potential impacts of these contingencies is poorly understood. Plant traits are expected to respond more predictably to restoration treatments than species, but few studies have compared the responses of species and traits in the context of contingencies. In this study, we conducted a preliminary analysis of long-term monitoring data from 13 restored sites in Grand Teton National Park paired with measurements of five traits to understand spatial and temporal community dynamics at two levels of biodiversity. Results show species composition became more similar (converged) across restored sites over time and trajected towards but did not meet reference conditions. Trait composition converged quickly with the reference in early years but diverged among sites. Communities transitioned from volunteer annuals with more resource acquisitive traits to sown species with conservative traits. Future work will use ecological modeling to test whether trends are contingent upon establishment conditions.
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Brim, M. (2020). Poor Queer Studies: Confronting Elitism in the University. Duke University Press.
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Hurst, Allison L. (2020) Amplified Advantage: Going to a ‘Good’ College in an Era of Inequality, Lexington Books, Lanham, MD.
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Relations between classes of potentially stable sign patterns
No full textTwo subsets of the potentially stable sign patterns of order have recently been defined, namely, those that allow sets of (refined) inertias and . For and , it is proved that a sign pattern is potentially stable if and only if it is sign stable, allows , or allows . This result is also true for sign patterns of order with associated graph that is a tree, remains open for non-tree potentially stable sign patterns of order , and is false for potentially stable sign patterns of orders greater than or equal to .