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Using variants of zero forcing to bound the inertia set of a graph
No full textZero forcing is a combinatorial game played on a graph with a goal of changing the color of every vertex at minimal cost. This leads to a parameter known as the zero forcing number that can be used to give an upper bound for the maximum nullity of a matrix associated with the graph. A variation on the zero forcing game is introduced that can be used to give an upper bound for the maximum nullity of such a matrix when it is constrained to have exactly q negative eigenvalues. This constrains the possible inertias that a matrix associated with a graph can achieve and gives a method to construct lower bounds on the inertia set of a graph (which is the set of all possible pairs (p,q) where p is the number of positive eigenvalues and q is the number of negative eigenvalues)
Common solutions of linear equations in a ring, with applications
No full textThis paper gives necessary and sufficient conditions for the existence of a common solution, and two expressions for the general common solution of the equation pair a_1xb_1 = c1, a_2xb_2 = c2, via a simpler equation p_1xp_2 + q_1yq_2=c, when each element belongs to an associative ring with unit. The paper also considers the same problem in the setting of a strongly â-reducing ring. Solutions of the generalized Sylvester equation are also presented. Both the solvability conditions and the expression for the general solution are given in terms of inner inverses. The paper uses the results obtained in the ring setting to give equivalent results for operators between Banach spaces, thus also recovering some of the well known matrix results
On Derivatives and Norms of Generalized Matrix Functions and Respective Symmetric Powers
No full textIn recent papers, S. Carvalho and P. J. Freitas obtained formulas for directional derivatives, of all orders, of the immanant and of the m-th -symmetric tensor power of an operator and a matrix, when is a character of the full symmetric group. The operator bound norm of these derivatives was also calculated. In this paper similar results are established for generalized matrix functions and for every symmetric tensor power
Inversion of centroskewsymmetric Toeplitz-plus-Hankel Bezoutians
No full textIn this paper, the inverse of a nonsingular, centroskewsymmetric Toeplitz-plus-Hankel Bezoutian B of (even) order n are computed, and a representation of B^(â1) as a sum of a Toeplitz and a Hankel matrix is found. Two possibilities are discussed. In the first one, the problem is reduced to the inversion of two skewsymmetric Toeplitz Bezoutians of order n. In the second one, the problem is tackled via the inversion of two Hankel Bezoutians of half the order n/2. The inversion of Toeplitz or Hankel Bezoutians is the subject of a previous paper [T. Ehrhardt and K. Rost. Resultant matrices and inversion of Bezoutians. Linear Algebra Appl., 439:621â639, 2013.]. Both approaches lead to fast O(n^2) inversion algorithms
Introduced American Bullfrog Distribution and Diets in Grand Teton National Park
No full textIntroduced American Bullfrogs (Lithobates catesbeianus) have been present in Grand Teton National Park since approximately the 1950s, but little is known about their distribution and potential impacts. In this study, we surveyed the current bullfrog distribution and spatial overlap with sympatric native amphibians in the park, and characterized post-metamorphic bullfrog diets from July â September 2015. Despite surveys in multiple large rivers and floodplain habitats, we only documented bullfrogs in a geothermal pond and 5 km of stream channel immediately downstream of this pond. In these waters, bullfrogs overlapped with native amphibians at the downstream end of their distribution, and we did not document native amphibians in bullfrog stomach contents. Larger bullfrogs (SVL ⥠96 mm) primarily consumed native rodents (especially meadow voles, Microtus pennsylvanicus), while smaller bullfrogs frequently consumed native invertebrates and less frequently consumed non-native invertebrates and fish. Taken together, these data indicate that the distribution and implications of the bullfrog invasion in Grand Teton National Park are currently localized to a small area, so these bullfrogs should therefore be vulnerable to eradication
Characterizing Biodiversity of Alpine Streams in Grand Teton National Park, Wyoming
No full textThe highest rate of climate change is occurring in alpine areas above permanent treeline. The Teton Mountains in northwestern Wyoming are one of these ecosystem and little work has been done on alpine streams in the area. We sampled 6 streams in the Teton Mountains in 2015 at both upper and lower sites. We measured environmental variables (e.g., glacierality index, basic water quality, and temperature), aquatic invertebrate assemblages and microbial diversity. The water sources for sampled streams were glacier-fed, snowmelt and icy-seep. Aquatic invertebrate density (116-11,523 ind/m2) and biomass (31-21,704 mg/m2) varied greatly among streams. Snowmelt streams had the highest biomass of invertebrates, but the density and richness did not differ among stream types. Micrbial diversity in groundwater-fed springs harbored higher diversity than glacier-fed streams. The discovery of an icy-seep stream type lead us to sample rock glacier in the Teton Mountains during 2016. We hope to continue to sample alpine streams in the Teton Mountains to understand how climate change will alter streams of different types
Jackson Energy Security Workshop: August 6-7, 2015
No full textThe UW Center for Global Studies hosted a two-day workshop focusing on energy security involving interdisciplinary faculty from UW, faculty from the Free University of Berlin, and participants from the non-profit and business sectors. This two day event included presentation of six papers (see agenda below) in three panel sessions addressing a variety of issues including traditional and new approaches to energy security, governance and management issues, and community development and agency. A final roundtable session focused on engaging industry, practitioners, and activists in emerging solutions. The workshop was funded by the School of Energy Resources, the Center for Global Studies, and through a European Union grant through the Colorado European Union Center for Excellence at CU-Boulder. This report proceeds in three parts: 1) rationale and agenda, 2) participant list with bios, 3) a discussion of outcomes to date of the workshop
Testing Field Methods to Assess Interactions Between Native Caddisflies and the Invasive New Zealand Mudsnail (Potamopyrgus Antipodarum)
No full textIn Polecat Creek, WY, located in the Greater Yellowstone Ecosystem, the invasive New Zealand mudsnail (Potamopyrgus antipodarum) has been found to reach densities exceeding 500,000 individuals/m². At this extremely high density, P. antipodarum has been observed to consume most of the gross primary production and have a negative impact on native macroinvertebrates such as the Hydropsyche caddisfly. The current population of P. antipodarum in Polecat Creek has declined suggesting the population âboomed and bustedâ; the population was booming in 2000-2001, but in 2011 the population had decreased substantially suggesting a âbustâ period for P. antipodarum. Native Hydropsyche caddisflies have increased dramatically in biomass during the 10-year span of data, which may indicate that some native macroinvertebrates have increased in biomass due to release of suppression by P. antipodarum. Consequently, during my research this summer I assessed several possible methods to test suppression of Hydropsyche by P. antipodarum. I devised a method to collect Hydropsyche and determined whether Hydropsyche can survive in experimental chambers for use in a future field experiment. I built wooden tiles to colonize Hydropsyche out of 4x4x2 inch wood blocks with 1/2 inch grooves along the length of the tile. Colonization was successful with approximately two Hydropsyche collected per tile in a 24-hour period. Based on low survival of Hydropsyche within experimental chambers, the use of different experimental chambers will be necessary. Specifically, chambers that are open on the upstream side should be used to better allow a fast flow of water, which is a requirement for Hydropsyche to collect food
Influence of the River Otter (Lontra Canadensis) on the Formation of Pro-Conservation Intentions in the Greater Yellowstone Ecosystem
No full textThe potential to increase participation in support and fundraising, as well as affect pro-conservation intentions and behaviors makes the flagship approach valuable to conservation. Flagships are charismatic species that engender public interest and promote broader ecological and economic values of conservation. Advocates for wildlife tourism suggest that viewing flagships can increase touristsâ awareness and participation in conservation behaviors such as philanthropy, volunteering and activism. However, empirical support for behavioral outcomes associated with flagship exposure is lacking. Exposure to a flagship can vary, such as exposure to marketing materials (i.e., websites, guide books, environmental organizations) or direct viewing experience (i.e., wild, captive). The specific goal of this study was to: (a) determine if direct exposure to the river otter, or marketing material about the species and/or (b) a personâs level of environmental concern influences behavioral intentions to conserve the river otter and its habitat. On-site self-administered questionnaires (n =523) were conducted at 6 locations throughout the Greater Yellowstone Ecosystem (GYE) from 5 June 2015 to 24 August 2015. The results of this study suggests that exposure to the river otter heightens concern and can lead to the formation of specific environmental intentions such as keeping local waterways unpolluted and planting trees along local waterways
On The Inverse Of A Class Of Bipartite Graphs With Unique Perfect Matchings
No full textLet G be a simple, undirected graph and Gw be the weighted graph obtained from G by giving weights to its edges using a positive weight function w. A weighted graph Gw is said to be nonsingular if its adjacency matrix A(Gw) is nonsingular. In [9], Godsil has given a class of connected, unweighted, bipartite, nonsingular graphs G with a unique perfect matching, such that A(G)â1 is signature similar to a nonnegative matrix, that is, there exists a diagonal matrix D with diagonal entries ±1 such that DA(G)â1D is nonnegative. The graph associated to the matrix DA(G)â1D is called the inverse of G and it is denoted by G+. The graph G+ is an undirected, weighted, connected, bipartite graph with a unique perfect matching. Nonsingular, unweighted trees are contained inside the class G. We first give a constructive characterization of the class of weighted graphs Hw that can occur as the inverse of some graph Gâ\mathcal{ G}. This generalizes Theorem 2.6 of Neumann and Pati[13], where the authors have characterized graphs that occur as inverses of nonsingular, unweighted trees. A weighted graph Gw is said to have the property (R) if for each eigenvalue λ of A(Gw), 1âλ is also an eigenvalue of A(Gw). If further, the multiplicity of λ and 1âλ are the same, then Gw is said to have property (SR). A characterization of the class of nonsingular, weighted trees Tw with at least 8 vertices that have property (R) was given in [13] under some restriction on the weights. It is natural to ask for such a characterization for the whole of G, possibly with some weaker restrictions on the weights. We supply such a characterization. In particular, for trees it settles an open problem raised in [13]