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Structured eigenvalue/eigenvector backward errors of matrix pencils arising in optimal control
No full textEigenvalue and eigenpair backward errors are computed for matrix pencils arising in optimal control. In particular, formulas for backward errors are developed that are obtained under block-structure-preserving and symmetry-structure-preserving perturbations. It is shown that these eigenvalue and eigenpair backward errors are sometimes significantly larger than the corresponding backward errors that are obtained under perturbations that ignore the special structure of the pencil
For everything there was a season: phenological shifts in the Tetons
No full textAround the world, phenology — the timing of ecological events — is shifting as the climate warms. This can lead to a variety of consequences for individual species and entire ecological communities. Grand Teton National Park biologists have identified this topic (“effect of earlier plant flowering on pollinators and wildlife”) as one of their priority research needs. We assembled phenological observations of first flowering dates for 49 species collected by Frank Craighead, Jr. in the 1970s, before significant warming occurred. In 2016 we began standardized phenological observations of these same species, plus an additional 61 for a total of 110 species, in the same locations. First flowering date for 65% of the species with historic records correlated significantly with mean spring temperature; these species are therefore expected to flower earlier now than in the 1970s. Early spring flowers had the largest shifts in phenology, emerging an average of 21 days earlier now relative to the 1970s. Yet not all species are emerging earlier. In particular, phenology of late summer/early fall flowering plants was largely unchanged. In 2017, we initiated pollinator collections at our key phenology sites. Additional years of observations will allow us to better understand plant-pollinator interactions and identify potential phenological mismatches.
Featured photo by Shawna Wolf, taken from the AMK Ranch photo collection
Unlocking the biogeochemical role of beaver in state-transition of landscapes in Yellowstone's northern range
No full textExtirpation of wolves from the Greater Yellowstone Ecosystem in the 1920s hypothetically triggered a trophic cascade in which browsers, released from wolf (Canis lupus) predation, over-browsed riparian zones. 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 investigated 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 show that beaver streams trend toward higher nutrient levels and higher variances than the LTREB sites. The data tentatively support the role of beaver as keystone species in state transitions, although more data are needed. The unexpected and late May notice from the NPS to obtain an independent research permit—approved late August—curtailed my 2018 research to a brief field bout in September. Analysis of 2018 samples is underway.
Featured photo from Figure 1 in report
Lights, bats, and buildings: investigating the factors influencing roosting sites and habitat use by bats in Grand Teton National Park
No full textBats are often useful bioindicators for ecosystem health and are disproportionately affected by sources of night light. Changes in bat behavior may manifest in two different ways: 1) some bats are light-exploiting and therefore attracted to areas with light sources, and 2) some are light-shy, traveling far out of their way to avoid lit areas. Grand Teton National Park provides an excellent natural system to study the effects of lights on bat behavior, as the park supports a large community of over a dozen species, as well as sizeable human infrastructure that generates night light. From June to August 2018 we used passive acoustic monitoring and radiotelemetry to study the activity and space use of bats in Colter Bay Village, specifically in the large parking lot at the center of the village and the adjacent naturally dark areas. We recorded 98,238 echolocation call sequences from 11 species, with the vast majority (~69,000) occurring in lit areas. Further, we recorded 4,665 location fixes from 32 tagged individuals from three species and, similarly, most location fixes (2,970) were in lit areas. All day roosts were found within buildings. We discuss the importance of these results and our work moving forward.
Featured photo by Shawna Wolf, taken from the AMK Ranch photo collection
Environmental noise influences song frequency of Yellow Warblers (Dendroica petechia) in Grand Teton National Park
No full textWe explored how Yellow Warblers (Dendroica petechia) alter their songs when encountering noise in Grand Teton National Park. Different strategies for avoiding signal masking are used by other species of birds, yet there is a lack of information of birds’ responses to higher noise levels -- above 65 dB; such levels are often found in National Parks that have many visitors. In this study, we investigated singing behavior of Yellow Warblers when facing noise that ranged from 30 dB to 80 dB. In these preliminary results, we found that some features of Yellow Warblers did not appear to change with background noise level, including mean minimum frequency, bandwidth and song length. Other song features we studied did show small but statistically significant changes with higher background noise, including the peak frequency and the mean minimum frequency, both of which were significantly negatively correlated with the level of background noise. This result is different from the positive correlations that are typically observed. We speculate that this difference is due to the very high dB levels of background noise that we observed.
Featured photo by wagon16 on Flickr. https://flic.kr/p/G2W6B
Regularity radius: properties, approximation, and a not a priori exponential algorithm
No full textThe radius of regularity, sometimes spelled as the radius of nonsingularity, is a measure providing the distance of a given matrix to the nearest singular one. Despite its possible application strength this measure is still far from being handled in an efficient way also due to findings of Poljak and Rohn providing proof that checking this property is NP-hard for a general matrix. There are basically two approaches to handle this situation. Firstly, approximation algorithms are applied and secondly, tighter bounds for radius of regularity are considered. Improvements of both approaches have been recently shown by Hartman and Hlad\'{i}k (doi:10.1007/978-3-319-31769-4\_9) utilizing relaxation of the radius computation to semidefinite programming. An estimation of the regularity radius using any of the above mentioned approaches is usually applied to general matrices considering none or just weak assumptions about the original matrix. Surprisingly less explored area is represented by utilization of properties of special classes of matrices as well as utilization of classical algorithms extended to be used to compute the considered radius. This work explores a process of regularity radius analysis and identifies useful properties enabling easier estimation of the corresponding radius values. At first, checking finiteness of this characteristic is shown to be a polynomial problem along with determining a sharp upper bound on the number of nonzero elements of the matrix to obtain infinite radius. Further, relationship between maximum (Chebyshev) norm and spectral norm is used to construct new bounds for the radius of regularity. Considering situations where the known bounds are not tight enough, a new method based on Jansson-Rohn algorithm for testing regularity of an interval matrix is presented which is not a priory exponential along with numerical experiments. For a situation where an input matrix has a special form, several corresponding results are provided such as exact formulas for several special classes of matrices, e.g., for totally positive and inverse non-negative, or approximation algorithms, e.g., rank-one radius matrices. For tridiagonal matrices, an algorithm by Bar-On, Codenotti and Leoncini is utilized to design a polynomial algorithm to compute the radius of regularity
New perturbation bounds in unitarily invariant norms for subunitary polar factors
No full textLet have generalized polar decomposition with subunitary and positive semidefinite. Absolute and relative perturbation bounds are derived for the subunitary polar factor in unitarily invariant norms and in -norms, that extend and improve existing bounds
Positive solutions of the system of operator equations in Hilbert -modules
No full textNecessary and sufficient conditions are given for the operator system , , , and to have a common positive solution, where 's and 's are adjointable operators on Hilbert -modules. This corrects a published result by removing some gaps in its proof. Finally, a technical example is given to show that the proposed investigation in the setting of Hilbert -modules is different from that of Hilbert spaces
Two linear preserver problems on graphs
No full textLet n, t, k be integers such that 3 ≤ t, k ≤ n. Denote by Gn the set of graphs with vertex set {1, 2, . . . , n}. In this paper, the complete linear transformations on Gn mapping Kt-free graphs to Kt-free graphs are characterized. The complete linear transformations on Gn mapping Ck-free graphs to Ck-free graphs are also characterized when n ≥ 6
