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Proof of a Conjecture of Graham and Lovász concerning Unimodality of Coefficients of the Distance Characteristic Polynomial of a Tree
No full textThe conjecture of Graham and Lovász that the (normalized) coefficients of the distance characteristic polynomial of a tree are unimodal is proved; it is also shown that the (normalized) coefficients are log-concave. Upper and lower bounds on the location of the peak are established
Spectral Bounds for the Connectivity of Regular Graphs with Given Order
No full textThe second-largest eigenvalue and second-smallest Laplacian eigenvalue of a graph are measures of its connectivity. These eigenvalues can be used to analyze the robustness, resilience, and synchronizability of networks, and are related to connectivity attributes such as the vertex- and edge-connectivity, isoperimetric number, and characteristic path length. In this paper, two upper bounds are presented for the second-largest eigenvalues of regular graphs and multigraphs of a given order which guarantee a desired vertex- or edge-connectivity. The given bounds are in terms of the order and degree of the graphs, and hold with equality for infinite families of graphs. These results answer a question of Mohar
Working-Class Culture as Political Participation: Reading Trump as Revolt Against a Middle-Class Public Sphere
No full textThe 2016 election cycle and ensuing presidency of Donald Trump has been attributed in large part to his support among working-class whites (Gest 2016, p. 193; Tyson and Maniam 2016). Their reasons for support, however, are open to interpretation. This article will suggest that elements of Donald Trump’s public communication style and ethos align with elements of working-class culture, language use, and knowledge construction. Trump’s anti-institutional, anti-government rhetoric reifies these components of working-class culture because of institutions’ and government’s deep foundations in middle-class culture, language use, and knowledge construction—and the working-class’s, especially the white working-class’s, alienation from these institutions, with the result being anger or apathy (Lareau 2003; Jensen 2012; Gest 2016). These values are often embedded in a master narrative that defines white working-class life as one of victimization (Hochschild 2016; Gest 2016; Cramer 2016). The article next suggests that Trump’s oft-used rhetorical framework of not just immigrants as threat, but of immigrants as protected and valued by institutions that overlook white workingclass concerns (Gest 2016), opens up one possible persuasive framework to legitimate Trump’s xenophobia and racism through white working-class attitudes
Gorman, Thomas J. (2017) Growing up Working Class: Hidden Injuries and the Development of Angry White Men and Women, Palgrave Macmillan, Cham, Switzerland
No full textSemipositivity of linear maps relative to proper cones in finite dimensional real Hilbert spaces
No full textFor a proper cone in a finite dimensional real Hilbert space , a linear map is said to be -semipositive if there exists , the interior of , such that . The aim of this manuscript is to characterize -semipositivity of linear maps relative to a proper cone. Among several results obtained, -semipositivity is characterized in terms of products of the form for -positive linear maps () with invertible, semipositivity of matrices relative to the -dimensional Lorentz cone is characterized, semipositivity of the following three linear maps relative to the cone : (denoted by ), (denoted by ), where , and (denoted by , known as the Stein transformation) is characterized. It is also proved that is semipositive if and only if for some \alpha > 0, the map is semipositive if and only if is positive stable. A particular case of the new result generalizes Lyapunov's theorem. Decompositions of the above maps (when they are semipositive) in the form , where and are both positive and invertible (assuming is invertible in the case of ) are presented. Moreover, a question on invariance of the semipositive cone of a matrix under is partially answered
Identifying combinatorially symmetric Hidden Markov Models
No full textA sufficient criterion for the unique parameter identification of combinatorially symmetric Hidden Markov Models, based on the structure of their transition matrix, is provided. If the observed states of the chain form a zero forcing set of the graph of the Markov model, then it is uniquely identifiable and an explicit reconstruction method is given
Bounds on the sum of minimum semidefinite rank of a graph and its complement
No full textThe minimum semi-definite rank (msr) of a graph is the minimum rank among all positive semi-definite matrices associated to the graph. The graph complement conjecture gives an upper bound for the sum of the msr of a graph and the msr of its complement. It is shown that when the msr of a graph is equal to its independence number, the graph complement conjecture holds with a better upper bound. Several sufficient conditions are provided for the msr of different classes of graphs to equal to its independence number
A note on linear preservers of semipositive and minimally semipositive matrices
No full textSemipositive matrices (matrices that map at least one nonnegative vector to a positive vector) and minimally semipositive matrices (semipositive matrices whose no column-deleted submatrix is semipositive) are well studied in matrix theory. In this short note, the structure of linear maps which preserve the set of all semipositive/minimally semipositive matrices is studied. An open problem is solved, and some ambiguities in the article [J. Dorsey, T. Gannon, N. Jacobson, C.R. Johnson and M. Turnansky. Linear preservers of semi-positive matrices. {\em Linear and Multilinear Algebra}, 64:1853--1862, 2016.] are clarified
Factors influencing amphibian distributions in Grand Teton National Park and western Wyoming
No full textPredicting the distribution of amphibians can be difficult because habitat suitability may depend on a variety of environmental and anthropogenic factors, including water quality of wetlands, geology of watersheds, and presence of invasive pathogens. Previous studies hypothesized that water chemistry may influence the rate of chytrid infection in amphibians where higher conductivity sites may have less infection. We sampled two watersheds in Grand Teton National Park and 3 watersheds adjacent to the park, and measured amphibian presence, chytrid infection, basic water quality, major ion concentrations and geology of the wetland. This is part of a larger project where we are comparing amphibian presence and infection rate among wetlands in the Gros Ventre, Wind River, and Teton Ranges. We sampled watersheds that were predominately limestone, granite or a mixture. Water quality varied among sites with higher conductivity and ion concentrations for limestone watersheds compared to granite watersheds. This report includes preliminary results of amphibian surveys and water quality analyses. Future analyses will relate occupancy rates of amphibians to environmental factors, including water chemistry, geology, and presence of chytrid fungus, as well as comparing detection rates of amphibians with environmental DNA (eDNA) and visual observation surveys.
Featured photo by Neal Herbert on Flickr. https://flic.kr/p/2gv9PJ
