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A note on simultaneous block diagonally stable matrices
No full textConsider a set of square real matrices of the same size A={A1, A2,...,AN}, where each matrix is partitioned, in the same way, into blocks such that the diagonal ones are square matrices. Under the assumption that the diagonal blocks in the same position have a common Lyapunov solution, sufficient conditions for the existence of a common Lyapunov solution with block diagonal structure for A are presented. Furthermore, as a by-product, an algorithm for the construction of such a common Lyapunov solution is proposed. 
Using Field Data to Validate Satellite Models of Elk Forage in the Upper Yellowstone River Basin
No full textSpatial and temporal variations in grassland phenology are thought to play a critical role in migration patterns of large herbivores in the Greater Yellowstone Ecosystem. Phenology, referring to the timing of green-up in this study, is directly related to biomass and forage quality. Migratory elk (Cervus elaphus), therefore, are believed to follow phenology across an elevation gradient during the growing season to maximize their access to high quality and quantity of forage. Concern that climate change and human land use alterations of phenology may impact the benefits of elk migration highlights the need for landscape-scale vegetation phenology monitoring. Satellite-derived Normalized Difference Vegetation Index (NDVI) shows potential as a remote sensing tool to predict landscape-level shifts in grassland phenology, but is limited by a lack of validation at varying scales, seasons, and in human land use areas. This study is focused on validating the accuracy of satellite-derived NDVI in estimating grassland phenology, biomass, and forage quality throughout the summer growing season within elk migratory ranges in the Upper Yellowstone River Basin. Results from this study will provide managers and researchers with information on the accuracy of NDVI as a tool for monitoring the effects of climate change and human land use on grassland dynamics relevant to migratory elk
Field Research and Conservation
No full textThe Field Research & Conservation class emphasizes long-term field research experiences, examines ecosystem processes, and investigates the evolution of American perspectives about nature. Our time spent at the UW-NPS research station was divided between pursuing behavioral ecology research and exploring Grand Teton National Park and the surrounding area to gain understanding of how the region was shaped, both by geological and biological process as well as political processes that have been shaped by Americaâs ever-changing conservation ethic
The Role of Dendrochronology in Understanding the Modern Decline of Whitebark Pine in Grand Teton National Park, Wyoming
No full textWhitebark pine (Pinus albicaulis) is the only pine keystone species found in North America. Although it is considered a keystone species in high elevation ecosystems in the northern Rockies, it occupies a relatively restricted range and its future is uncertain. In modern times, it has experienced a significant decline in population due to pine beetle infestations, blister rust infections, fire suppression, and climate change. Despite the knowledge that the species is severely threatened, little is known about its paleoecology. More specifically, much remains unknown about how the distribution and stability of whitebark pine were affected by past climate change. The purpose of this study is to determine in great temporal and spatial detail the demographics of the current stand of whitebark pine trees in the watershed surrounding an unnamed, high-altitude pond (known informally as Whitebark Pine Moraine Pond) located approximately 3.06 miles NW of Jenny Lake in Grand Teton National Park (GTNP). The main objectives of this study are: 1.) To obtain the precise GPS locations of the current stand of whitebark pine trees in the watershed to generate a GIS map detailing their locations. 2.) To obtain increment cores of a subset of the trees in the watershed to estimate age and date of establishment for the current stand of whitebark pines, with particular attention to fire history. 3.) To analyze ring widths from core samples to identify climatic indicators that may influence the regeneration and survival of whitebark pine
Exploring the Physiological mechanisms and Ecological Consequences of Energetic Tradeoffs: An Integative Study of the Influences of Avian Malarial Infection on Thermogenic Performance
No full textSurvival in variable environments often requires careful allocation of resources to competing physiological and behavioral functions. Because these competing processes often have additive energetic costs (Hawley et al. 2012), a limited resource pool forces individuals to make difficult trade-off decisions regarding energetic investments (Lochmiller and Deerenberg 2000). These trade-offs are a cornerstone of life-history theory that is aimed at determining the optimal allocation strategies in variable environments (Ricklefs and Wikelski 2002), and understanding their physiological and ecological consequences has renewed poignancy in the face of the unprecedented rate of anthropogenic environmental change occurring across the planet
Effects of Climate and Biotic Factors on Life History Characteristics and Vital Rates of Yellowstone Cutthroat Trout in Spread Creek, Wyoming
No full textThe Upper Snake River represents one of the largest remaining strongholds of Yellowstone cutthroat across its native range. Understanding the effects of restoration activities and the diversity of life-history patterns and factors influencing such patterns remains paramount for long-term conservation strategies. In 2011, we initiated a project to quantify the success of the removal of a historic barrier on Spread Creek and to evaluate the relative influence of different climate attributes on native Yellowstone cutthroat trout and non-native brook trout behavior and fitness. Our results to date have demonstrated the partial success of the dam removal with large, fluvial Yellowstone cutthroat trout migrating up Spread Creek to spawn, thus reconnecting this population to the greater Snake River metapopulation. Early indications from mark-recapture data demonstrate considerable differences in life-history and demographic patterns across tributaries within the Spread Creek drainage. Our results highlight the diversity of life-history patterns of resident and fluvial Yellowstone cutthroat trout with considerable differences in seasonal and annual growth rates and behavior across populations. Continuing to understand the factors influencing such patterns will provide a template for prioritizing restoration activities in the context of future challenges to conservation (e.g., climate change)
Techniques for identifying inertially arbitrary patterns
No full textTwo techniques used to show a matrix pattern is spectrally arbitrary are the nilpotent-Jacobian method and more recently the nilpotent-centralizer method. This paper presents generalizations of both techniques, which are then used to show that certain non-spectrally-arbitrary patterns are inertially arbitrary. A flaw in a method used in three previous publications of inertially arbitrary patterns is discussed. By using the techniques developed here, it is shown that all of the patterns in the three papers affected by the flaw are neverthless inertially arbitrary. 
3-by-3 matrices with elliptical numerical range revisited
No full textAccording to Kippenhahn's classification, numerical ranges W(A) of unitarily irreducible 3x3 matrices A come in three possible shapes, an elliptical disk being one of them. The known criterion for the ellipticity of W(A) consists of several equations, involving the eigenvalues of A. It is shown herein that the set of 3x3 matrices satisfying these conditions is nowhere dense, i.e., one of the necessary conditions can be violated by an arbitratily small perturbation of the matrix and therefore by an insufficiently good numberical approximation of the eigenvalues.
Moreover, necessary and sufficient conditions for a real A to have an elliptical W(A) are derived involving only the matrix coefficients and not requiring the knowledge of the eigenvalues. A particular case of real companion matrices is considered in detail.