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SPN Graphs
No full textA simple graph G is an SPN graph if every copositive matrix having graph G is the sum of a positive semidefinite and nonnegative matrix. SPN graphs were introduced in [N. Shaked-Monderer. SPN graphs: When copositive = SPN. Linear Algebra Appl., 509:82{113, 2016.], where it was conjectured that the complete subdivision graph of K4 is an SPN graph. This conjecture is disproved, which in conjunction with results in the Shaked-Monderer paper show that a subdivision of K4 is a SPN graph if and only if at most one edge is subdivided. It is conjectured that a graph is an SPN graph if and only if it does not have an F5 minor, where F5 is the fan on five vertices. To establish that the complete subdivision graph of K4 is not an SPN graph, rank-1 completions are introduced and graphs that are rank-1 completable are characterized
Tridiagonal pairs of type III with height one
No full textLet K denote an algebraically closed field with characteristic 0. Let V denote a vector space over K with finite positive dimension, and let A, A∗ denote a tridiagonal pair on V of diameter d. Let V0, . . . , Vd denote a standard ordering of the eigenspaces of A on V , and let θ0, . . . , θd denote the corresponding eigenvalues of A. It is assumed that d ≥ 3. Let ρi denote the dimension of Vi. The sequence ρ0, ρ1, . . . , ρd is called the shape of the tridiagonal pair. It is known that ρ0 = 1 and there exists a unique integer h (0 ≤ h ≤ d/2) such that ρi−1 < ρi for 1 ≤ i ≤ h, ρi−1 = ρi for h < i ≤ d − h, and ρi−1 > ρi for d − h < i ≤ d. The integer h is known as the height of the tridiagonal pair. In this paper, it is showed that the shape of a tridiagonal pair of type III with height one is either 1, 2, 2, . . ., 2, 1 or 1, 3, 3, 1. In each case, an interesting basis is found for V and the actions of A, A∗ on this basis are described
Unlocking the biogeochemical role of beaver in state-transition of landscapes in Yellowstone's northern range: Tantalizing insights, initial results, and evolving research design
No full textExtirpation of wolves from the Greater Yellowstone Ecosystem in the 1920s hypothetically triggered a trophic cascade in which herbivores over-browsed riparian zones once released from the fear of wolf (Canis lupus) predation. Eventually, vast meadow-wetland complexes transitioned to grass-lodgepole systems. By 1954, beaver (Castor canadensis) virtually abandoned the Greater Yellowstone Ecosystem. In 2000, Colorado State University established experimental dams with browsing exclosures for Long Term Environmental Research in Biology (LTREB) on three streams in Lamar Valley to compare hydrologic effects of pseudo-beaver dams and browsing on willow (Salix spp.) productivity and state transitions. In 2015, beaver began recolonizing the region. I investigate how the biogeochemical role of beaver versus their hydrologic influence affects the underlying mechanisms of state transition: nutrient cycling, productivity, and stream respiration. Analyses of the 2017 field samples showed that beaver streams trend toward higher nutrient levels and higher variances than the LTREB sites. These trends continued in 2018 and 2019. The data tentatively support the role of beaver as keystone species in state transitions. Interannual modeling of nutrient dynamics, comparisons of stream metabolism, and genetic identification of microbial communities are underway. Similarly, analyses of the repeated measures collected across the month of July 2019 are underway.
Featured photo from figure 1 in report
Forecasting eco-evolutionary dynamics in the Northern Blue butterfly (2019 field season)
No full textNatural selection can drive rapid evolutionary change, particularly in human-altered habitats. Rapid adaptation to global change requires standing genetic variation for ecologically important traits, but at present little is known about how much relevant genetic variation most populations possess. With this in mind, we began a long term study of genome-wide molecular evolution in a series of natural butterfly populations in the Greater Yellowstone Area in 2012 to quantify the contribution of environment-dependent natural selection to evolution in these butterfly populations, and determine whether selection varies enough across space and time to maintain variation that could facilitate adaptation to global change. In 2019, we visited 11 focal populations to collect samples for DNA and plant chemistry, estimate population sizes (mark-release-recapture methods), and survey arthropod communities at the sites. Our analyses are ongoing, and this is a preliminary report, but thus far we have found that census population sizes are much higher than contemporary effective population sizes (though these metrics are highly correlated), and that both are independent of genetic diversity levels. These results are consistent with the hypothesis that selection plays a central role in eco-evolutionary dynamics in this system.
Featured photo from figure 1 in report. 
Smarsh, Sarah (2018) Heartland: A Memoir of Working Hard and Being Broke in the Richest Country on Earth, Scribner, New York, NY.
No full text"Clark, Ben and Hubble, Nick, eds. (2018) Working-Class Writing: Theory and Practice, Palgrave MacMillan, New York, NY."
No full textTesting Hypotheses Of Covariance Structure In Multivariate Data
No full textIn this paper there is given a new approach for testing hypotheses on the structure of covariance matrices in double multivariate data. It is proved that ratio of positive and negative parts of best unbiased estimators (BUE) provide an F-test for independence of blocks variables in double multivariate models
Estimators Comparison of Separable Covariance Structure with One Component as Compound Symmetry Matrix
No full textThe maximum likelihood estimation (MLE) of separable covariance structure with one component as compound symmetry matrix has been widely studied in the literature. Nevertheless, the proposed estimates are not given in explicit form and can be determined only numerically. In this paper we give an alternative form of MLE and we show that this new algorithm is much quicker than the algorithms given in the literature. Another estimator of covariance structure can be found by minimizing the entropy loss function. In this paper we give three methods of finding the best approximation of separable covariance structure with one component as compound symmetry matrix and we compare the quickness of proposed algorithms. We conduct simulation studies to compare statistical properties of MLEs and entropy loss estimators (ELEs), such us biasedness, variability and loss. Another estimator of covariance structure can be found by minimizing the entropy loss function. In this paper we give three methods of finding the best approximation of separable covariance structure with one component as compound symmetry matrix and we compare the quickness of proposed algorithms. We conduct simulation studies to compare statistical properties of MLEs and entropy loss estimators (ELEs), such us biasedness and variability
Algebraic Methods for the Construction of Algebraic-Difference Equations With Desired Behavior
No full textFor a given system of algebraic and difference equations, written as an Auto-Regressive (AR) representation , where denotes the shift forward operator and a regular polynomial matrix, the forward-backward behavior of this system can be constructed by using the finite and infinite elementary divisor structure of . This work studies the inverse problem: Given a specific forward-backward behavior, find a family of regular or non-regular polynomial matrices , such that the constructed system has exactly the prescribed behavior. It is proved that this problem can be reduced either to a linear system of equations problem or to an interpolation problem and an algorithm is proposed for constructing a system satisfying a given forward and/or backward behavior
Range-compatible homomorphisms over the field with two elements
No full textLet U and V be finite-dimensional vector spaces over a field K, and S be a linear subspace of the space L(U, V ) of all linear operators from U to V . A map F : S → V is called range-compatible when F (s) ∈ Im s for all s ∈ S.Previous work has classified all the range-compatible group homomorphisms provided that codimL(U,V )S ≤ 2 dim V − 3, except in the special case when K has only two elements and codimL(U,V )S = 2 dim V − 3. This article gives a thorough treatment of that special case. The results are partly based upon the recent classification of vector spaces of matrices with rank at most 2 over F2.As an application, the 2-dimensional non-reflexive operator spaces are classified over any field, and so do the affine subspaces of Mn,p(K) with lower-rank at least 2 and codimension 3