Convergence of restarted Krylov subspaces to invariant subspaces

The performance of Krylov subspace eigenvalue algorithms for large matrices can be measured by the angle between a desired invariant subspace and the Krylov subspace. We develop general bounds for this convergence that include the effects of polynomial restarting and impose no restrictions concerning the diagonalizability of the matrix or its degree of non-normality. Associated with a desired set of eigenvalues is a maximum ``reachable invariant subspace'' that can be developed from the given starting vector. Convergence for this distinguished subspace is bounded in terms involving a polynomial approximation problem. Elementary results from potential theory lead to convergence rate estimates and suggest restarting strategies based on optimal approximation points (e.g., Leja or Chebyshev points); exact shifts are evaluated within this framework. Computational examples illustrate the utility of these results. Origins of superlinear effects are also described

Bacterial wilt symptoms are impacted by host age and involve net downward movement of Erwinia tracheiphila in muskmelon

Cucurbit bacterial wilt, caused by Erwinia tracheiphila, is a damaging disease of cucurbit crops in the Midwest and Northeast U.S. Current management of bacterial wilt relies primarily on insecticide applications to control striped and spotted cucumber beetles (Acalymma vittatum and Diabrotica undecimpunctata howardi, respectively), which vector E. tracheiphila. Development of alternative management strategies is constrained by a lack of understanding of bacterial wilt etiology. The impact of host age on rate on symptom development and extent of bacterial movement in the xylem of muskmelon (Cucumis melo cv. Athena) was evaluated following wound inoculation of 2- to 8-week-old plants in growth chamber experiments. Wilting occurred more rapidly in plants after inoculating E. tracheiphila into 2- or 4-week-old plants than 6- or 8-week-old plants. Recovery of viable cells from stem segments revealed that vascular spread of E. tracheiphila was more extensive below than above the inoculation point. These findings provide experimental evidence that host age impacts the rate of symptom development in cucurbit bacterial wilt and that movement of the xylem-inhabiting pathogen E. tracheiphila within muskmelon plants occurs primarily in the downward direction

A Preliminary Evaluation of the Ability of Keratotic Tissue to Act as a Prognostic Indicator of Hip Fracture Risk

Studies have shown that Raman spectroscopic analysis of fingernail clippings can help differentiate between post-menopausal women who have and who have not suffered a fracture. However, all studies to date have been retrospective in nature, comparing the proteins in nails sourced from women, post-fracture. The objective of this study was to investigate the potential of a prospective test for hip fracture based on spectroscopic analysis of nail tissue. Archived toenail samples from post-menopausal women aged 50 to 63 years in the Nurses\u27 Health Study were obtained and analysed by Raman spectroscopy. Nails were matched case-controls sourced from 161 women; 82 who underwent a hip fracture up to 20 years after nail collection and 81 age-matched controls. A number of clinical risk factors (CRFs) from the Fracture Risk Assessment (FRAX) tool had been assessed at toenail collection. Using 80% of the spectra, models were developed for increasing time periods between nail collection and fracture. Scores were calculated from these models for the other 20% of the sample and the ability of the score to predict hip fracture was tested in model with and without the CRFs by comparing the odds ratios (ORs) per 1 SD increase in standardised predictive values. The Raman score successfully distinguished between hip fracture cases and controls. With only the score as a predictor, a statistically significant OR of 2.2 (95% confidence interval [CI]: 1.5-3.1) was found for hip fracture for up to 20 years after collection. The OR increased to 3.8 (2.6-5.4) when the CRFs were added to the model. For fractures limited to 13 years after collection, the OR was 6.3 (3.0-13.1) for the score alone. The test based on Raman spectroscopy has potential for identifying individuals who may suffer hip fractures several years in advance. Higher powered studies are required to evaluate the predictive capability of this test

A DigitalCAT: A Fusion of Creativity Assessment Theory and HCI

As a ‘gold standard’ creativity assessment method, it is important to reflect on the digital future of Amabile’s Consensual Assessment Technique (CAT). Over the past three decades, the CAT has given creativity researchers a formal tool on which to build a true science out of the subjective phenomenon of creativity in a vast range of domains. Research practice, however, has relied on primitive paper-based tools or only rudimentary digital technology. As a result, it is high time a more sophisticated, standardized research tool is developed to greatly facilitate future creativity research and assessment - a DigitalCAT - building on expertise from the design research, psychology and human-computer interaction (HCI) disciplines

Bacterial wilt symptoms are impacted by host age and involve net downward movement of Erwinia tracheiphila in muskmelon

Cucurbit bacterial wilt, caused by Erwinia tracheiphila, is a damaging disease of cucurbit crops in the Midwest and Northeast U.S. Current management of bacterial wilt relies primarily on insecticide applications to control striped and spotted cucumber beetles (Acalymma vittatum and Diabrotica undecimpunctata howardi, respectively), which vector E. tracheiphila. Development of alternative management strategies is constrained by a lack of understanding of bacterial wilt etiology. The impact of host age on rate on symptom development and extent of bacterial movement in the xylem of muskmelon (Cucumis melo cv. Athena) was evaluated following wound inoculation of 2- to 8-week-old plants in growth chamber experiments. Wilting occurred more rapidly in plants after inoculating E. tracheiphila into 2- or 4-week-old plants than 6- or 8-week-old plants. Recovery of viable cells from stem segments revealed that vascular spread of E. tracheiphila was more extensive below than above the inoculation point. These findings provide experimental evidence that host age impacts the rate of symptom development in cucurbit bacterial wilt and that movement of the xylem-inhabiting pathogen E. tracheiphila within muskmelon plants occurs primarily in the downward direction.This is a manuscript of an article published as Liu, Q., G.A. Beattie, E. Saalau Rojas and M.L. Gleason. 2018. Bacterial wilt symptoms are impacted by host age and involve net downward movement of Erwinia tracheiphila in muskmelon. European Journal of Plant Pathology 151:803-810. doi: 10.1007/s10658-018- 1418-7. Posted with permission.</p

Lessons from the Field: Teaching a Completely Online Global Business Course to African Refugees in Northern Kenya and Malawi

The six authors of this paper taught a completely online “Global Business” course to African refugees in the Kakuma refugee camp in Northern Kenya and the Dzaleka refugee camp in Malawi. The paper summarizes twelve lessons learned by the instructors while teaching the course and offers suggestions for adaptations in future courses delivered in the “Jesuit Commons: Higher Education at the Margins” diploma program

Fundamental MHD scales -- II: the kinematic phase of the supersonic small-scale dynamo

The small-scale dynamo (SSD) amplifies weak magnetic fields exponentially fast via kinetic motions. While there exist well-established theories for SSDs in incompressible flows, many astrophysical SSDs operate in supersonic turbulence. To understand the impact of compressibility on amplified magnetic fields, we perform an extensive set of visco-resistive SSD simulations, covering a wide range of sonic Mach number $\mathcal{M}$, hydrodynamic Reynolds number Re, and magnetic Prandtl number Pm. We develop robust methods for measuring kinetic and magnetic energy dissipation scales $\ell_\nu$ and $\ell_\eta$, as well as the scale at which magnetic fields are strongest $\ell_p$ during the kinematic phase of these simulations. We show that $\ell_\nu/\ell_\eta \sim$ Pm$^{1/2}$ is a universal feature in the kinematic phase of Pm $\geq 1$ SSDs, regardless of $\mathcal{M}$ or Re, and we confirm earlier predictions that SSDs operating in incompressible plasmas (either $\mathcal{M} \leq 1$ or Re $<$ Re$_{\rm crit} \approx 100$) concentrate magnetic energy at the smallest scales allowed by magnetic dissipation, $\ell_p \sim \ell_\eta$, and produce fields organised with field strength and field-line curvature inversely correlated. However, we show that these predictions fail for compressible SSDs ($\mathcal{M} > 1$ and Re $>$ Re$_{\rm crit}$), where shocks concentrate magnetic energy in large-scale, over-dense, coherent structures, with size $\ell_p \sim (\ell_{\rm turb} / \ell_{\rm shock})^{1/3} \ell_\eta \gg \ell_\eta$, where $\ell_{\rm shock} \sim \mathcal{M}^2 / [$Re $(\mathcal{M} - 1)^2]$ is shock width, and $\ell_{\rm turb}$ is the turbulent outer scale; magnetic field-line curvature becomes almost independent of the field strength. We discuss the implications for galaxy mergers and for cosmic-ray transport models in the interstellar medium that are sensitive to field-line curvature statistics.Comment: 25 pages, 15 figures, submitted to MNRAS, json-file w/ dat