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On the Laplacian characteristic polynomials of mixed graphs
No full textLet G be a mixed graph and L(G) be the Laplacian matrix of G. In this paper, the coefficients of the Laplacian characteristic polynomial of G are studied. The first derivative of the characteristic polynomial of L(G) is explicitly expressed by means of Laplacian characteristic polynomials of its edge deleted subgraphs. As a consequence, it is shown that the Laplacian characteristic polynomial of a mixed graph is reconstructible from the collection of the Laplacian characteristic polynomials of its edge deleted subgraphs. Then, it is investigated how graph modifications affect the mixed Laplacian characteristic polynomial. Also, a connection between the Laplacian characteristic polynomial of a non-singular connected mixed graph and the signless Laplacian characteristic polynomial is provided, and it is used to establish a lower bound for the spectral radius of L(G). Finally, using Coates digraphs, the perturbation of the mixed Laplacian spectral radius under some graph transformations is discussed
The Dirichlet spectral radius of trees
No full textIn this paper, the trees with the largest Dirichlet spectral radius among all trees with a given degree sequence are characterized. Moreover, the extremal graphs having the largest Dirichlet spectral radius are obtained in the sets ofall trees of order n with a given number of pendant vertices
Note on the Jordan form of an irreducible eventually nonnegative matrix
No full textA square complex matrix A is eventually nonnegative if there exists a positive integer k_0 such that for all k ⥠k_0, A^k ⥠0; A is strongly eventually nonnegative if it is eventually nonnegative and has an irreducible nonnegative power. It is proved that a collection of elementary Jordan blocks is a Frobenius Jordan multiset with cyclic index r if and only if it is the multiset of elementary Jordan blocks of a strongly eventually nonnegative matrix with cyclic index r. A positive answer to an open question and a counterexample to a conjecture raised by Zaslavsky and Tam are given. It is also shown that for a square complex matrix A with index at most one, A is irreducible and eventually nonnegative if and only if A is strongly eventually nonnegative
Some Properties of the Exchange Operator with respect to Structured Matrices defined by Indefinite Scalar Product Spaces
No full textThe properties of the exchange operator on some types of matrices are explored in this paper. In particular, the properties of exc(A,p,q), where A is a given structured matrix of size (p+q)Ã(p+q) and exc : M ÃNÃN â M is the exchange operator are studied. This paper is a generalization of one of the results in [N.J. Higham. J-orthogonal matrices: Properties and generation. SIAM Review, 45:504â519, 2003.]
Conjugacy classes of torsion in GL_n(Z)
No full textThe problem of integral similarity of block-triangular matrices over the ring of integers is connected to that of finding representatives of the classes of an equivalence relation on general integer matrices. A complete list of representatives of conjugacy classes of torsion in the 4 Ã 4 general linear group over ring of integers is given. There are 45 distinct such classes and each torsion element has order of 1, 2, 3, 4, 5, 6, 8, 10 or 12
Extremal graphs for the sum of the two largest signless Laplacian eigenvalues
No full textLet G be a simple graph on n vertices and e(G) edges. Consider the signless Laplacian, Q(G) = D + A, where A is the adjacency matrix and D is the diagonal matrix of the vertices degree of G. Let q_1(G) and q_2(G) be the first and the second largest eigenvalues of Q(G), respectively, and denote by S_n^+ the star graph with an additional edge. It is proved that inequality q_1(G)+q_2(G) \leq e(G)+3 is tighter for the graph S_n^+ among all firefly graphs and also tighter to S_n^+ than to the graphs K_k \vee K_{nâk} recently presented by Ashraf, Omidi and Tayfeh-Rezaie. Also, it is conjectured that S_n^+ minimizes f(G) = e(G) â q_1(G) â q_2(G) among all graphs G on n vertices
Using twins and scaling to construct cospectral graphs for the normalized Laplacian
No full textThe spectrum of the normalized Laplacian matrix cannot determine the number of edges in a graph, however finding constructions of cospectral graphs with differing number of edges has been elusive. In this paper we use basic properties of twins and scaling to show how to construct such graphs. We also give examples of families of graphs which are cospectral with a subgraph for the normalized Laplacian matrix
The State-Dependent Resource Allocation Hypothesis: Implications for the Foraging Ecology and Life History of Migratory Ungulates in the GYE
No full textUnderstanding the behavioral and physiological responses of animals to environmental stressors is vital to our comprehension of their ecology and life history. The life-history strategy of ungulates is for females to prioritize survival over reproductive effort to maximize life-long fitness (Stearns 1992, Eberhardt 2002, BÃ¥rdsen et al. 2008). Consequently, an individualâs reproductive decisions are expected to be dependent on nutritional state (BÃ¥rdsen et al. 2008). Researchers have long assumed that individuals reduce their metabolism and energy expenditure to conserve nutritional reserves (i.e., fat and protein) during winter because winter has been demonstrated to be a period of energetic loss for temperate ungulates. Recent research, however, has shown that mule deer (Odocoileus hemionus) in a poor nutritional state are capable of increasing their nutritional reserves over winter (Monteith et al. 2013), and hormone analysis of moose (Alces alces; Jesmer et al. in review) indicates that animals with low nutritional reserves have high energy expenditure and energy intake. Therefore, regulation of nutritional state through plasticity in foraging behavior may allow animals to cope with resource shortages. We refer to this notion, wherein animals alter their energy intake and expenditure via foraging behavior as the State-Dependent Resource Allocation Hypothesis (Figure 1). In 2014 we proposed to apply state-of-the-art nutritional, isotopic, and hormone analyses to test the State-Dependent Resource Allocation Hypothesis (SRAH) in migratory mule deer within the Greater Yellowstone Ecosystem
Summary of an Ongoing Population Study of Parnassius Clodius Butterflies
No full textClimate change presents unique challenges to high-altitude, high-latitude flying insects such as butterflies, bees, and flies. Models predict that climate change will cause general range shifts toward the poles and high elevations (Parmesan and Yohe 2003, Root et al. 2003) and empirical studies confirm that these range shifts are occurring (Parmesan et al. 1999, Kerr et al. 2015). As the earth warms, animals already living at high elevations and/or high latitudes may have nowhere to go. Furthermore, the body temperature of insects is dependent on ambient temperatures, and therefore many aspects of their ecology and general biology (development, growth, survival, dispersal, mating) may be stressed by or incompatible with a changing climate. Finally, animal flight at altitude involves substantial aerodynamic and physiological challenges, and significant reductions in air density and oxygen constrain flight at higher elevations (Dillon and Dudley 2015). Moving up in elevation therefore may not be an option for some high-altitude fliers
In Situ Performance Assessment and Evaluation of Hydrophobic and Ultraviolet Protective Treatments for Historic Log Structures
No full textBeginning in the summer of 2015, research was conducted on protective wood coatings and accelerated weathering testing methods for architectural log and timber. A rack for supplementary natural weathering testing of hydrophobic and ultraviolet protective surface treatments for logs was also erected as a subsequent phase at Grand Teton National Park. This laboratory and field research is part of an ongoing project to develop an appropriate treatment for historic log structures in the region that will preserve their original fabric while maintaining the intended historic appearance of the buildings, i.e., unpainted. The weathering rack will be in place for upwards of five years to verify the lab-based results from Phase I and to determine the long-term durability of the chosen treatments on already aged materials in situ. This report addresses the methods and materials for preparation of the weathering rack and samples as well as the methods being used to monitor their progress and initial results. Readings will be taken yearly to monitor the effects of weathering on each treatment