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    Kirshner, J.A. (2019). Broke: Hardship and Resilience in a City of Broken Promises. St. Martin’s Press.

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    Winslow, C. (2020). Radical Seattle: The General Strike of 1919. New York University Press.

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    Developing a baseline understanding of gill lice distribution, prevalence, and infestation intensity in the Upper Snake River Watershed

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    Climate change is altering temperature, precipitation, and snowpack dynamics, which will affect aquatic ecosystem thermal and flow regimes. Pathogens are an emerging threat that also has the potential to interact with climate change to affect fish population dynamics. Our research addresses: 1) What species of gill lice are present within the USR, 2) What is their distribution, prevalence, and infection intensity, and 3) Does gill lice infestation negatively affect metrics of fish condition? During 2020 and 2021, our team observed gill lice on 307 out of 7,255 fish inspected. Of twelve species inspected, gill lice were only observed on Snake River Cutthroat Trout and Mountain Whitefish. Our preliminary results suggest that the current distributions of gill lice within USR is primarily limited to the Snake River and immediately adjacent tributaries and infection prevalence and intensity remain low. While conditions in the USR have not reached the level of concern observed in other locations, a greater understanding of what factors could increase the extent and intensity of gill lice is needed to develop management strategies to improve the resilience of fish populations and communities to multiple stressors, including climate change, non-native species, and emerging pathogens.   Featured photo by Yellowstone National Park on Flickr (https://flic.kr/p/2h6Zmfw)

    Understanding food web structure in high-elevation streams of the Teton Range

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    Climate change is dramatically altering high-elevation streams around the world through the recession of glaciers and other meltwater sources. Rapidly changing hydrological regimes imperil entire communities of mountain stream biodiversity. We have monitored high-elevation streams in the Teton Range since 2015, with a specific focus on understanding how hydrological source variation affects the susceptibility of downstream communities, and the stoneflies Zapada glacier and Lednia tetonica, to climate-induced impacts. We monitor streams fed by three sources – glaciers, snowfields, and subterranean ice (primarily rock glaciers). Streams fed by subterranean ice – “icy seeps” – are predicted to persist on the landscape longer than their surface counterparts due to the inherent thermal buffering of their source ice provided by debris cover. We hypothesize that icy seep communities will be buffered against climate-induced environmental changes and will act as key refugia for cold-adapted communities. In late 2019, the conservation implications of our work were escalated by the listing of one of the key species we study, the stonefly Zapada glacier, under the US Endangered Species Act due to climate-induced habitat loss. In 2020, our first objective was to collect a 6th year of continuous data for core sites and continue investigating longer term signals in the data. For our second objective, we addressed another large gap in contemporary knowledge of high-elevation stream ecology: food web structure. Despite imminent threats to biodiversity in headwater streams, little is known of the basic quantity and quality of basal resources in mountain streams, how these resources vary with stream type, and linkages between feeding groups. Additionally, little is known about the diet or trophic position of Zapada glacier. We will use an array of modern approaches, including stable isotopes and nutrient content analyses, to generate a high-resolution view of food web structure in the high Teton Range. Our results will inform management in the Teton Range while also shedding new light on a standing challenge in mountain stream ecology worldwide.   Featured photo by Bonnie Robinson, taken from the UW-NPS photo collection

    The Energy Change of the Complete Multipartite Graph

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    The energy of a graph is defined as the sum of the absolute values of all eigenvalues of the graph. Akbari et al. [S. Akbari, E. Ghorbani, and M. Oboudi. Edge addition, singular values, and energy of graphs and matrices. {\em Linear Algebra Appl.}, 430:2192--2199, 2009.] proved that for a complete multipartite graph Kt1,,tkK_{t_1 ,\ldots,t_k}, if ti2 (i=1,,k)t_i\geq 2 \ (i=1,\ldots,k), then deleting any edge will increase the energy. A natural question is how the energy changes when min{t1,,tk}=1\min\{t_1 ,\ldots,t_k\}=1. In this paper, a new method to study the energy of graph is explored. As an application of this new method, the above natural question is answered and it is completely determined how the energy of a complete multipartite graph changes when one edge is removed

    Volume of Hypercubes Clipped by Hyperplanes and Combinatorial Identities

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    There is an elegant expression for the volume of hypercube [0,1]n[0,1]^n clipped by a single hyperplane. In the article, the formula is generalized to the case of more than one hyperplane. An important foundation for the result is Lawrence's formula and a way to weaken two restrictions of simplicity and non-parallelness in his formula is also considered. Several concrete volume formulas of clipped hypercubes are derived explicitly and the corresponding combinatorial identities are obtained as an application

    Bounds on the AαA_{\alpha}-spread of a graph

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    Let GG be a simple undirected graph. For any real number α[0,1]\alpha \in[0,1], Nikiforov defined the AαA_{\alpha}-matrix of GG as Aα(G)=αD(G)+(1α)A(G)A_{\alpha}(G)=\alpha D(G)+(1-\alpha)A(G), where A(G)A(G) and D(G)D(G) are the adjacency matrix and the degree diagonal matrix of GG, respectively. The AαA_{\alpha}-spread of a graph is defined as the difference between the largest eigenvalue and the smallest eigenvalue of the associated AαA_{\alpha}-matrix. In this paper, some lower and upper bounds on AαA_{\alpha}-spread are obtained, which extend the results of AA-spread and QQ-spread. Moreover, the trees with the minimum and the maximum AαA_{\alpha}-spread are determined, respectively

    Linearizations for Interpolatory Bases - a Comparison: New Families of Linearizations

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    One strategy to solve a nonlinear eigenvalue problem T(λ)x=0T(\lambda)x=0 is to solve a polynomial eigenvalue problem (PEP) P(λ)x=0P(\lambda)x=0 that approximates the original problem through interpolation. Then, this PEP is usually solved by linearization. Because of the polynomial approximation techniques, in this context, P(λ)P(\lambda) is expressed in a non-monomial basis. The bases used with most frequency are the Chebyshev basis, the Newton basis and the Lagrange basis. Although, there exist already a number of linearizations available in the literature for matrix polynomials expressed in these bases, new families of linearizations are introduced because they present the following advantages: 1) they are easy to construct from the matrix coefficients of P(λ)P(\lambda) when this polynomial is expressed in any of those three bases; 2) their block-structure is given explicitly; 3) it is possible to provide equivalent formulations for all three bases which allows a natural framework for comparison. Also, recovery formulas of eigenvectors (when P(λ)P(\lambda) is regular) and recovery formulas of minimal bases and minimal indices (when P(λ)P(\lambda) is singular) are provided. The ultimate goal is to use these families to compare the numerical behavior of the linearizations associated to the same basis (to select the best one) and with the linearizations associated to the other two bases, to provide recommendations on what basis to use in each context. This comparison will appear in a subsequent paper

    Complete characterisation of Kronecker invariants of a matrix pencil with a prescribed quasi-regular subpencil

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    In this paper, the possible Kronecker invariants of a matrix pencil with a prescribed quasi-regular subpencil are determined.&nbsp

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