Validated Numerical Approximation of Stable Manifolds for Parabolic Partial Differential Equations

This paper develops validated computational methods for studying infinite dimensional stable manifolds at equilibrium solutions of parabolic PDEs, synthesizing disparate errors resulting from numerical approximation. To construct our approximation, we decompose the stable manifold into three components: a finite dimensional slow component, a fast-but-finite dimensional component, and a strongly contracting infinite dimensional “tail”. We employ the parameterization method in a finite dimensional projection to approximate the slow-stable manifold, as well as the attached finite dimensional invariant vector bundles. This approximation provides a change of coordinates which largely removes the nonlinear terms in the slow stable directions. In this adapted coordinate system we apply the Lyapunov-Perron method, resulting in mathematically rigorous bounds on the approximation errors. As a result, we obtain significantly sharper bounds than would be obtained using only the linear approximation given by the eigendirections. As a concrete example we illustrate the technique for a 1D Swift-Hohenberg equation.</p

Pathogen detection, testing, and control in fresh broccoli sprouts

BACKGROUND: The recent increased interest in consuming green vegetable sprouts has been tempered by the fact that fresh sprouts can in some cases be vehicles for food-borne illnesses. They must be grown according to proper conditions of sanitation and handled as a food product rather than as an agricultural commodity. When sprouts are grown in accordance with the criteria proposed from within the sprout industry, developed by regulatory agencies, and adhered to by many sprouters, green sprouts can be produced with very low risk. Contamination may occur when these guidelines are not followed. METHODS: A one year program of microbial hold-and-release testing, conducted in concert with strict seed and facility cleaning procedures by 13 U.S. broccoli sprout growers was evaluated. Microbial contamination tests were performed on 6839 drums of sprouts, equivalent to about 5 million consumer packages of fresh green sprouts. RESULTS: Only 24 (0.75%) of the 3191 sprout samples gave an initial positive test for Escherichia coli O157:H7 or Salmonella spp., and when re-tested, 3 drums again tested positive. Composite testing (e.g., pooling up to 7 drums for pathogen testing) was equally sensitive to single drum testing. CONCLUSION: By using a "test-and-re-test" protocol, growers were able to minimize crop destruction. By pooling drums for testing, they were also able to reduce testing costs which now represent a substantial portion of the costs associated with sprout growing. The test-and-hold scheme described herein allowed those few batches of contaminated sprouts to be found prior to packaging and shipping. These events were isolated, and only safe sprouts entered the food supply

Reproductive rights approach to reproductive health in developing countries

Research on reproductive health in developing countries focuses mostly on the role of economic development on various components of reproductive health. Cross-sectional and empirical research studies in particular on the effects of non-economic factors such as reproductive rights remain few and far between.This study investigates the influence of two components of an empowerment strategy, gender equality, and reproductive rights on women&#x0027;s reproductive health in developing countries. The empowerment strategy for improving reproductive health is theoretically situated on a number of background factors such as economic and social development.Cross-national socioeconomic and demographic data from a number of international organizations on 142 developing countries are used to test a model of reproductive rights and reproductive health.The findings suggest that both economic and democratic development have significant positive effects on levels of gender equality. The level of social development plays a prominent role in promoting reproductive rights. It is found that reproductive rights channel the influences of social structural factors and gender equality on reproductive health

Border Insecurity: Reading Transnational Environments in Jim Lynch’s Border Songs

This article applies an eco-critical approach to contemporary American fiction about the Canada-US border, examining Jim Lynch’s portrayal of the British Columbia-Washington borderlands in his 2009 novel Border Songs. It argues that studying transnational environmental actors in border texts—in this case, marijuana, human migrants, and migratory birds—helps illuminate the contingency of political boundaries, problems of scale, and discourses of risk and security in cross-border regions after 9/11. Further, it suggests that widening the analysis of trans-border activity to include environmental phenomena productively troubles concepts of nature and regional belonging in an era of climate change and economic globalization. Cet article propose une lecture écocritique de la fiction étatsunienne contemporaine portant sur la frontière entre le Canada et les États-Unis, en étudiant le portrait donné par Jim Lynch de la région frontalière entre la Colombie-Britannique et Washington dans son roman Border Songs, paru en 2009. L’article soutient que l’étude, dans les textes sur la frontière, des acteurs environnementaux transnationaux – dans ce cas-ci, la marijuana, les migrants humains et les oiseaux migratoires – jette un jour nouveau sur la contingence des limites territoriales politiques, des problèmes d’échelle et des discours sur le risque et la sécurité des régions transfrontalières après les évènements du 11 septembre 2001. Il suggère également qu’en élargissant l’analyse de l’activité transfrontalière pour y inclure les phénomènes environnementaux, on brouille de façon productive les concepts de nature et d’appartenance régionale d’une époque marquée par les changements climatiques et la mondialisation de l’économie

Aβ-CT Affective Touch: Touch Pleasantness Ratings for Gentle Stroking and Deep Pressure Exhibit Dependence on A-Fibers

Gentle stroking of the skin is a common social touch behavior with positive affective consequences. A preference for slow versus fast stroking of hairy skin has been closely linked to the firing of unmyelinated C-tactile (CT) somatosensory afferents. Because the firing of CT afferents strongly correlates with touch pleasantness, the CT pathway has been considered a social-affective sensory pathway. Recently, ablation of the spinothalamic pathway- thought to convey all C-fiber sensations- in patients with cancer pain impaired pain, temperature, and itch, but not ratings of pleasant touch. This suggested integration of afferent A and CT fiber input in the spinal cord, or mechanoreceptive A-fiber contributions to computations of touch pleasantness in the brain. However, contribution of mechanoreceptive A-fibers to touch pleasantness, in humans without pain, remains unknown. In the current, single-blinded study, we performed two types of peripheral nerve blocks in healthy adults to temporarily eliminate the contribution of A-fibers to touch perception. Our findings show that when mechanoreceptive A-fiber function is greatly diminished, the perceived intensity and pleasantness of both gentle stroking and deep pressure are nearly abolished. These findings demonstrate that explicit perception of the pleasantness of CT-targeted brushing and pressure both critically depend on afferent A-fibers