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The 2015 Table Mountain Ice Patch Project: Grand Teton National Park, Teton County, WY
No full textIce patches are permanent snow and ice fields that survive through the summer months but are not massive enough to become glaciers. Prehistorically, people used ice patches for hunting, and organic hunting-related artifacts have been recovered from them. As a result of global warming, the ice patches are melting and exposing artifacts and other material that were preserved under the ice for millennia. Once exposed, the organic artifacts deteriorate. Recovery of these artifacts before they are lost is critical to understanding the paleoecology of and the prehistoric people who used the Teton high elevations (Lee 2009, 2015). In 2015, I surveyed ice patches on Table Mountain pursuant to Section 110 of the National Historic Preservation Act. The work was conducted under OWSA permits 15-GRTE-01 and GRTE-2015-SCI-0040 and was partially funded by the UW-NPS Research Station. One historic archaeological site (48TE1983) was documented and four paleobiological specimens were collected
Graph energy change due to any single edge deletion
No full textThe energy of a graph is the sum of the absolute values of its eigenvalues. We propose a new problem on graph energy change due to any single edge deletion. Then we survey the literature for existing partial solution of the problem, and mention a conjecture based on numerical evidence. Moreover, we prove in three different ways that the energy of a cycle graph decreases when an arbitrary edge is deleted except for the order of 4
Almost Definite Matrices Revisited
No full textA real matrix A is called as an almost definite matrix if â¨x, Axâ© = 0 â Ax = 0. This notion is revisited. Many basic properties of such matrices are established. Several characterizations for a matrix to be an almost definite matrix are presented. Comparisons of certain properties of almost definite matrices with similar properties for positive definite or positive semidefinite matrices are brought to the fore. Interconnections with matrix classes arising in the theory of linear complementarity problems are discussed briefly
Extremal graph on normalized Laplacian spectral radius and energy
No full textLet be a simple graph of order and the normalized Laplacian eigenvalues . The normalized Laplacian energy (or Randi\'c energy) of without any isolated vertex is defined as In this paper, a lower bound on of connected graph ( is not isomorphic to complete graph) is given and the extremal graphs (that is, the second minimal normalized Laplacian spectral radius of connected graphs) are characterized. Moreover, Nordhaus-Gaddum type results for are obtained. Recently, Gutman et al.~gave a conjecture on Randi\'c energy of connected graph [I. Gutman, B. Furtula, \c{S}. B. Bozkurt, On Randi\'c energy, Linear Algebra Appl. 442 (2014) 50--57]. Here this conjecture for starlike trees is proven
Further results on generalized inverses in rings with involution
No full textLet R be a unital ring with an involution. Necessary and sufficient conditions for the existence of the Bott-Duffin inverse of a in R relative to a pair of self-adjoint idempotents (e, f) are derived. The existence of a {1, 3}-inverse, {1, 4}-inverse, and the Moore-Penrose inverse of a matrix product is characterized, and explicit formulas for their computations are obtained. Some applications to block matrices over a ring are given
An Iterative algorithm for -(anti)-Hermitian least-squares solutions of quaternion matrix equations
No full textRecently, some research has been devoted to finding the explicit forms of the η-Hermitian and η-anti-Hermitian solutions of several kinds of quaternion matrix equations and their associated least-squares problems in the literature. Although exploiting iterative algorithms is superior than utilizing the explicit forms in application, hitherto, an iterative approach has not been offered for finding η-(anti)-Hermitian solutions of quaternion matrix equations. The current paper deals with applying an efficient iterative manner for determining η-Hermitian and η-anti-Hermitian least-squares solutions corresponding to the quaternion matrix equation AXB + CY D = E. More precisely, first, this paper establishes some properties of the η-Hermitian and η-anti-Hermitian matrices. These properties allow for the demonstration of how the well-known conjugate gradient least- squares (CGLS) method can be developed for solving the mentioned problem over the η-Hermitian and η-anti-Hermitian matrices. In addition, the convergence properties of the proposed algorithm are discussed with details. In the circumstance that the coefficient matrices are ill-conditioned, it is suggested to use a preconditioner for accelerating the convergence behavior of the algorithm. Numerical experiments are reported to reveal the validity of the elaborated results and feasibility of the proposed iterative algorithm and its preconditioned version
Spiders Revisited: Retracing the Steps of Herbert and Lorna Levi's Historic Invertebrate Surveys of the Jackson Hole Region of Wyoming
No full textIn 1950, Herbert and Lorna Levi collected invertebrates in Yellowstone and Grand Teton National Parks and other localities in the region. Sixty-five years later and looking towards the centennial of the National Park Service, a preliminary reassessment of the biodiversity of spiders was conducted in a subset of localities that were collected by the Levis. Specimens have been collected and are in the process of being identified. Comparison of this new collection with the historical records is currently underway. As the arts have played a crucial role in the history of national parks, we are exploring how to partner art and science to share the beauty and wonder of spiders based on our fieldwork in celebration of the upcoming National Park Service centennial
Small Mammal Movements and Fire History: Testing the Long-Term Effects of the 1988 Huckleberry Mountain Fire
No full textFires are an important ecological force shaping biological communities in western North America. Fires change landscapes in ways which influence the relative abundance and activities of the organisms occurring in those habitats. Preliminary results from previous work suggest the stage of fire succession may influence individual movements on the landscape. As part of a long-term study of the 1988 Yellowstone fires along the John D. Rockefeller, Jr. Memorial Parkway, we set out to examine these patterns in more detail to (1) test whether the two dominant small mammal species were moving different distances based upon the stage of succession in a particular habitat, and (2) determine the role of habitat complexity, resource types, and species abundance in driving these patterns. Using movement distances from capture-recapture data and fluorescent powder tracking of individuals we compared movement distances and habitat usage between mid-succession and late-succession trapping grids for red-backed voles (Myodes gapperi) and deer mice (Peromyscus maniculatus). The results suggest deer mice, some of the first colonizers to burned habitat, are moving farther than red-backed voles, and move farther in burned habitats than in unburned habitats. Red-backed voles exhibit slightly, but not significantly, longer movements in burned habitats. Powder tracking results suggest habitat complexity, in particular the quantity of coarse woody debris, may partially explain the differences in movement patterns by burn history. These results are important for understanding the long-lasting impacts of fire history on population and community patterns
Exploring Vertical Wilderness in the Acoustic Environment
No full textHearing sounds of nature is an important motivation for visitors to National Parks, such as Grand Teton National Park (GRTE; Newman et al. 2015). Furthermore, managers are required to provide park visitors with an enjoyable soundscape experience. In 2006, Pilcher and Newman conducted a study on visitor perceptions of soundscapes in highly trafficked locations in GRTE, the Jenny Lake boat dock and Inspiration Point. While this study used similar methods, it aimed to better understand the influence of soundscapes to a unique visitor group -- climbers on the Grand Teton. This iconic climbing destination is located in an area that is potentially susceptible to anthropogenic or human caused noise interruptions because of its proximity to an airport and heavily used highways. In the summer of 2015 researchers from Penn State University used a combination of qualitative interviews and listening exercises with climbers to identify sounds that were being heard during their climbing experience and their emotions related to those sounds. These data provide managers with information about sounds that could be prioritized when managing for an optimal soundscape experience
An improved estimate for the condition number anomaly of univariate Gaussian correlation matrices
No full textIn this short note, it is proved that the derivatives of the parametrized univariate Gaussian correlation matrix R_g (θ) = (exp(âθ(x_i â x_j )^2_{i,j} â R^{nÃn} are rank-deficient in the limit θ = 0 up to any order m < (n â 1)/2. This result generalizes the rank deficiency theorem for Euclidean distance matrices, which appear as the first-order derivatives of the Gaussian correlation matrices in the limit θ = 0. As a consequence, it is shown that the condition number of R_g(θ) grows at least as fast as 1(/θ^(mË +1) for θ â 0, where mË is the largest integer such that mË < (n â 1)/2. This considerably improves the previously known growth rate estimate of 1/θ^22 for the so-called Gaussian condition number anomaly