University of Wyoming Open Journals
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Kemeny's Constant And An Analogue Of Braess' Paradox For Trees
No full textGiven an irreducible stochastic matrix M, Kemenyâs constant K(M) measures the expected time for the corresponding Markov chain to transition from any given initial state to a randomly chosen final state. A combinatorially based expression for K(M) is provided in terms of the weights of certain directed forests in a directed graph associated with M, yielding a particularly simple expression in the special case that M is the transition matrix for a random walk on a tree. An analogue of Braessâ paradox is investigated, whereby inserting an edge into an undirected graph can increase the value of Kemenyâs constant for the corresponding random walk. It is shown in particular that for almost all trees, there is an edge whose insertion increases the corresponding value of Kemenyâs constant. Finally, it is proven that for any m â N, almost every tree T has the property that there are at least m trees, none of which are isomorphic to T , such that the values of Kemenyâs constant for the corresponding random walks coincide with the value of Kemenyâs constant for the random walk on T . Several illustrative examples are included
Numerical Range for the Matrix Exponential Function
No full textFor a given square matrix A, the numerical range for the exponential function e^(At), t in C, is considered. Some geometrical and topological properties of the numerical range are presented
Zero-dilation Index of S_n-matrix and Companion Matrix
No full textThe zero-dilation index of a square matrix is the largest for which is unitarily similar to a matrix of the form , where denotes the -by- zero matrix. In this paper, it is shown that if is an -matrix or an -by- companion matrix, then is at most , the smallest integer greater than or equal to . Those 's for which the upper bound is attained are also characterized. Among other things, it is shown that, for an odd , the -matrix is such that if and only if is unitarily similar to , and, for an even , every -by- companion matrix has equal to $n/2
A note on the real nonnegative inverse eigenvalue problem
No full textThe Real Nonnegative Inverse Eigenvalue Problem (RNIEP) asks when is a list consisting of real numbers the spectrum of an nonnegative matrix . In that case, is said to be realizable and is a realizing matrix. In a recent paper dealing with RNIEP, P.~Paparella considered cases of realizable spectra where a realizing matrix can be taken to have a special form, more precisely such that the entries of each row are obtained by permuting the entries of the first row. A matrix of this form is called permutative. Paparella raised the question whether any realizable list can be realized by a permutative matrix or a direct sum of permutative matrices. In this paper, it is shown that in general the answer is no
Paleoseismic investigation of the Teton fault at Leigh Lake, Grand Teton National Park, Wyoming
No full textTo improve knowledge of the Teton fault’s ground-rupturing earthquake history, we excavated trenches across two fault scarps near the southwest shore of Leigh Lake. Detailed stratigraphic and sedimentologic analyses allow preliminary inferences regarding the fault history. The trenches exposed faulted glacial sediments and overlying hillslope colluvium sediments, documenting at least two fault ruptures since deglaciation of the range front at ~15 ka. Samples are currently being analyzed using radiocarbon and luminescence dating techniques to determine the ages of the sediments and constrain the timing of fault rupture.
Featured photo from Figure 3 in report
Tracing the cultural history of upper Snake River guides in Grand Teton National Park
No full textThis study traces the development and evolution of Snake River use and management through an in-depth exploration of historic commercial scenic river guiding and concessions on the upper Snake River in Grand Teton National Park (GRTE) from 1950 to the present day. The research is based on a combination of methods including archival research, oral history analysis, historical landscape analysis, and fieldwork. I suggest that a distinct cultural community of river runners and outdoor recreationalists developed in Grand Teton National Park after World War II. In GRTE, a combination of physical, cultural, and technical forces shaped this community’s evolution including the specific geomorphology and dynamic channel patterns of the upper Snake River, the individuals and groups that worked on this river, and changes in boat and gear technology over time. The following paper presents the early results from the first year of this project in 2016 including the work of a graduate student and myself. This study offers connections between the upper Snake River and Grand Teton National Park to broader national trends in the evolution of outdoor recreation and concessions in national parks, the impact of World War II on technological developments for boating, and the cultural history of adventure outdoor recreation and tourism in the United States.
Featured photo by Elton Menefee on Unsplash. https://unsplash.com/photos/AHgCFeg-gX
Rejecting Respectability: On Being Unapologetically Working Class
No full textMany working-class people have aspired to respectability – maintaining cleanliness in the home, presenting an image of ‘niceness’ through neat modes of dress, or speaking ‘proper’. This respectability is intended to show those in power that working-class people are worthy of their attention and assistance. But what happens when workingclass people refuse to be respectable? When they choose to use strong language and won’t speak in soft tones? What happens when working-class people do not defer to their ‘betters’ and instead articulate their anger loudly and assertively? Critiques of class systems and calls for social justice are arguably more threatening when presented in a loud and direct manner. This article considers how the politics of respectability are used against working-class activists
Understanding and managing wildlife jams in national parks: An evaluation in Grand Teton National Park
No full textAs recreation and tourism in parks and protected areas continues to increase, managers face rising concerns of degradation of natural resources and the visitor experience. Many park visitors are seeking opportunities to view or photograph wildlife. Visitor behavior in prime wildlife-viewing areas often involves visitors parking along roadways and exiting their cars to view wildlife. This creates a phenomenon known as a “wildlife jam”, as visitors park informally along a roadway, often becoming pedestrians as they view wildlife, while other motorists attempt to drive through. To date, no studies have comprehensively investigated this phenomenon. Our study characterizes the nature of wildlife jams on the Moose-Wilson Road in Grand Teton National Park. Global Positioning System (GPS) technology was used to collect high-accuracy data on location and duration of the jams. Observations during jams characterize size (how many visitors and cars were involved) and visitor behaviors during jams. Preliminary results suggest that jam characteristics including presence of park staff, species involved, and location, can affect the duration, extent, and visitor behaviors that occur. Understanding the nature of these jams will enable park managers to minimize the potential negative effects of jams on wildlife and the visitor experience.
Featured photo by letdown102 on Flickr. https://flic.kr/p/57jUo
Realizing Suleimanova-type Spectra via Permutative Matrices
No full textA permutative matrix is a square matrix such that every row is a permutation of the first row. A constructive version of a result attributed to Sule耱manova is given via permutative matrices. A well-known result is strenghthened by showing that all realizable spectra containing at most four elements can be realized by a permutative matrix or by a direct sum of permutative matrices. The paper concludes by posing a problem
Potentially eventually positive star sign patterns
No full textAn -by- real matrix is eventually positive if there exists a positive integer such that for all . An -by- sign pattern is potentially eventually positive (PEP) if there exists an eventually positive real matrix with the same sign pattern as . An -by- sign pattern is a minimal potentially eventually positive sign pattern (MPEP sign pattern) if is PEP and no proper subpattern of is PEP. Berman, Catral, Dealba, et al. [Sign patterns that allow eventual positivity, {\it ELA}, 19(2010): 108-120] established some sufficient and some necessary conditions for an -by- sign pattern to allow eventual positivity and classified the potentially eventually positive sign patterns of order . However, the identification and classification of PEP signpatterns of order remain open. In this paper, all the -by- PEP star sign patterns are classified by identifying all the MPEP star sign patterns