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Bounds for the Completely Positive Rank of a Symmetric Matrix over a Tropical Semiring
No full textIn this paper, an upper bound for the CP-rank of a matrix over a tropical semiring is obtained, according to the vertex clique cover of the graph prescribed by the positions of zero entries in the matrix. The graphs that beget the matrices with the lowest possible CP-ranks are studied, and it is proved that any such graph must have its diameter equal to
On the Largest Distance (Signless Laplacian) Eigenvalue of Non-transmission-regular Graphs
No full textLet be a -connected graph with vertices and edges. Let be the distance matrix of . Suppose are the -eigenvalues of . The transmission of , denoted by is defined to be the sum of distances from to all other vertices of , i.e., the row sum of indexed by vertex and suppose that . The of denoted by is given by . Let be the diagonal matrix with its -entry equal to . The distance signless Laplacian matrix of is defined as and its spectral radius is denoted by or . A connected graph is said to be -transmission-regular if for every vertex , otherwise, non-transmission-regular. In this paper, we respectively estimate and for a -connected non-transmission-regular graph in different ways and compare these obtained results. And we conjecture that D_1(G)-\lambda_1(G)>\frac{1}{n+1}. Moreover, we show that the conjecture is valid for trees
On the Condition Number Theory of the Equality Constrained Indefinite Least Squares Problem
No full textIn this paper, within a unified framework of the condition number theory, the explicit expression of the projectedcondition number of the equality constrained indefinite least squares problem is presented. By setting specific norms and parameters, some widely used condition numbers, like the normwise, mixed and componentwise condition numbers follow as its special cases. Considering practical applications and computation, some new compact forms or upper bounds of the projected condition numbers are given to improve the computational efficiency. The new compact forms are of particular interest in calculating the exact value of the 2-norm projected condition numbers. When the equality constrained indefinite least squares problem degenerates into some specific least squares problems, our results give some new findings on the condition number theory of these specific least squares problems. Numerical experiments are given to illustrate our theoretical results
An inventory and assessment of glaciers, rock glaciers, perennial snowfields, and permafrost landforms in the Teton Range, WY, USA
No full textGlaciers, rock glaciers, and permafrost landforms store water within ice reserves in alpine and periglacial zones. In the Greater Yellowstone Ecosystem of northwestern Wyoming, U.S.A., these landforms charge the hydrological system through meltwater, which raises questions about the ecological impacts of these limited water reserves in a regime trending toward warmer and drier conditions. Here, I investigate the impact of glacier and rock glacier meltwater on the ecological systems within the Grand Teton, Wind River, and Gros Ventre mountain watersheds. This investigation relies on remotely sensed satellite imagery, aerial photography, and Lidar, as well as in situ field data. With these data, I provide a high-resolution inventory of glacial, rock glacial, and permafrost landforms in the GYE.
Featured photo by Grand Teton on Flickr. https://flic.kr/p/2hwtrR
Understanding the influence of climate, genetic variation, and herbivory on aspen (Populus tremuloides) growth in Yellowstone National Park
No full textPredation is commonly cited as a top-down effect that structures food webs, with the reintroduction of wolves to Yellowstone as perhaps the most famous example. However, despite two decades of research, there is still debate as to whether wolves (Canis lupus) have indirectly benefited aspen (Populus tremuloides) by reducing herbivory from elk (Cervus canadensis). As such, the purpose of this study was to investigate the role of top-down and bottom-up forces on aspen recruitment in northern Yellowstone. The UW-NPS grant funds were used to conduct a genetic analysis of 59 aspen stands in an effort to determine whether genetic variation is one control of aspen recruitment. During summer 2018, 122 leaves were collected and sent to the Mock Lab at Utah State University. The samples will undergo DNA extractions at 12 microsatellite loci, which will provide us with genotype and ploidy level, with the genotype at a resolution to distinguish clones. Concurrently, we measured aspen heights and browse rates, as well as soil moisture. The median aspen height in 2018 was 110 cm (SD=135), and the browse rate was 0.45. Stands varied in volumetric water content (VWC), ranging from a mean VWC of 2.7% to 45.2%.
Featured photo by Yellowstone National Park on Flickr. https://flic.kr/p/efXLV
Catte, Elizabeth (2018) What You’re Getting Wrong about Appalachia, Belt Publishing, Cleveland, OH. Stoll, Steven (2017) Ramp Hollow: The Ordeal of Appalachia, Hill and Wang, New York, NY.
No full textDiPaolo, Marc, ed. (2018) Working-Class Comic Book Heroes: Class Conflict and Populist Politics in Comics, University Press of Mississippi, Jackson, MS.
No full textOptimal dual fusion frames for probabilistic erasures
No full textFor any fixed fusion frame, its optimal dual fusion frames for reconstruction is studied in case of erasures of subspaces. It is considered that a probability distribution of erasure of subspaces is given and that a blind reconstruction procedure is used, where the erased data are set to zero. It is proved that there are always optimal duals. Sufficient conditions for the canonical dual fusion frame being either the unique optimal dual, a non-unique optimal dual, or a non optimal dual, are obtained. The reconstruction error is analyzed, using the optimal duals in the probability model considered here and using the optimal duals in a non-probability model
Decomposition of approaches of a general linear model with fixed parameters
No full textThe well-known ordinary least-squares estimators (OLSEs) and the best linear unbiased estimators (BLUEs) under linear regression models can be represented by certain closed-form formulas composed by the given matrices and their generalized inverses in the models. This paper provides a general algebraic approach to relationships between OLSEs and BLUEs of the whole and partial mean parameter vectors in a constrained general linear model (CGLM) with fixed parameters by using a variety of matrix analysis tools on generalized inverses of matrices and matrix rank formulas. In particular, it establishes a variety of necessary and sufficient conditions for OLSEs to be BLUEs under a CGLM, which include many reasonable statistical interpretations on the equalities of OLSEs and BLUEs of parameter space in the CGLM. The whole work shows how to effectively establish matrix equalities composed by matrices and their generalized inverses and how to use them when characterizing performances of estimators of parameter spaces in linear models under most general assumptions
The common invariant subspace problem and Tarskiâs theorem
No full textThis article presents a computable criterion for the existence of a common invariant subspace of complex matrices of a fixed dimension . The approach taken in the paper is model-theoretic. Namely, the criterion is based on a constructive proof of the renowned Tarski's theorem on quantifier elimination in the theory \ACF of algebraically closed fields. This means that for an arbitrary formula of the language of fields, a quantifier-free formula such that \varphi\lra\varphi' in \ACF is given explicitly. The construction of is elementary and based on the effective Nullstellensatz. The existence of a common invariant subspace of of dimension can be expressed in the first-order language of fields, and hence, the constructive version of Tarski's theorem yields the criterion. In addition, some applications of this criterion in quantum information theory are discussed