Mechanical Systems with Symmetry, Variational Principles, and Integration Algorithms

This paper studies variational principles for mechanical systems with symmetry and their applications to integration algorithms. We recall some general features of how to reduce variational principles in the presence of a symmetry group along with general features of integration algorithms for mechanical systems. Then we describe some integration algorithms based directly on variational principles using a discretization technique of Veselov. The general idea for these variational integrators is to directly discretize Hamilton’s principle rather than the equations of motion in a way that preserves the original systems invariants, notably the symplectic form and, via a discrete version of Noether’s theorem, the momentum map. The resulting mechanical integrators are second-order accurate, implicit, symplectic-momentum algorithms. We apply these integrators to the rigid body and the double spherical pendulum to show that the techniques are competitive with existing integrators

DIRK Schemes with High Weak Stage Order

Runge-Kutta time-stepping methods in general suffer from order reduction: the observed order of convergence may be less than the formal order when applied to certain stiff problems. Order reduction can be avoided by using methods with high stage order. However, diagonally-implicit Runge-Kutta (DIRK) schemes are limited to low stage order. In this paper we explore a weak stage order criterion, which for initial boundary value problems also serves to avoid order reduction, and which is compatible with a DIRK structure. We provide specific DIRK schemes of weak stage order up to 3, and demonstrate their performance in various examples.Comment: 10 pages, 5 figure

Formulation and performance of variational integrators for rotating bodies

Variational integrators are obtained for two mechanical systems whose configuration spaces are, respectively, the rotation group and the unit sphere. In the first case, an integration algorithm is presented for Euler’s equations of the free rigid body, following the ideas of Marsden et al. (Nonlinearity 12:1647–1662, 1999). In the second example, a variational time integrator is formulated for the rigid dumbbell. Both methods are formulated directly on their nonlinear configuration spaces, without using Lagrange multipliers. They are one-step, second order methods which show exact conservation of a discrete angular momentum which is identified in each case. Numerical examples illustrate their properties and compare them with existing integrators of the literature

Importance Sampling for Objetive Funtion Estimations in Neural Detector Traing Driven by Genetic Algorithms

To train Neural Networks (NNs) in a supervised way, estimations of an objective function must be carried out. The value of this function decreases as the training progresses and so, the number of test observations necessary for an accurate estimation has to be increased. Consequently, the training computational cost is unaffordable for very low objective function value estimations, and the use of Importance Sampling (IS) techniques becomes convenient. The study of three different objective functions is considered, which implies the proposal of estimators of the objective function using IS techniques: the Mean-Square error, the Cross Entropy error and the Misclassification error criteria. The values of these functions are estimated by IS techniques, and the results are used to train NNs by the application of Genetic Algorithms. Results for a binary detection in Gaussian noise are provided. These results show the evolution of the parameters during the training and the performances of the proposed detectors in terms of error probability and Receiver Operating Characteristics curves. At the end of the study, the obtained results justify the convenience of using IS in the training

The function of the alula in avian flight

The alula is a small structure located at the joint between the hand-wing and arm-wing of birds and is known to be used in slow flight with high angles of attack such as landing. It is assumed to function similarly to a leading-edge slat that increases lift and delays stall. However, in spite of its universal presence in flying birds and the wide acceptance of stall delay as its main function, how the alula delays the stall and aids the flight of birds remains unclear. Here, we investigated the function of alula on the aerodynamic performance of avian wings based on data from flight tasks and wind-tunnel experiments. With the alula, the birds performed steeper descending flights with greater changes in body orientation. Force measurements revealed that the alula increases the lift and often delays the stall. Digital particle image velocimetry showed that these effects are caused by the streamwise vortex, formed at the tip of the alula, that induces strong downwash and suppresses the flow separation over the wing surface. This is the first experimental evidence that the alula functions as a vortex generator that increases the lift force and enhances manoeuvrability in flights at high angles of attack.open1

Mathematical literacy in Plant Physiology undergraduates: results of interventions aimed at improving students' performance

The importance of mathematical literacy in any scientific career is widely recognized. However, various studies report lack of numeracy and mathematical literacy in students from various countries. In the present work we present a detailed study of the mathematical literacy of Spanish undergraduate students of Biology enrolled in a Plant Physiology course. We have performed individual analyses of results obtained during the period 2000-2011, for questions in the examinations requiring and not requiring mathematical skills. Additionally, we present the outcome of two interventions introduced with the aim of helping students improve their prospects for success in the course. Our results confirm previous research showing students' deficiencies in mathematical skills. However, the scores obtained for mathematical questions in the examinations are good predictors of the final grades attained in Plant Physiology, as there are strong correlations at the individual level between results for questions requiring and not requiring mathematical skills. The introduction of a laboratory session devoted to strengthening the application of students' previously acquired mathematical knowledge did not change significantly the results obtained for mathematical questions. Since mathematical abilities of students entering university have declined in recent years, this intervention may have helped to maintain students' performance to a level comparable to that of previous years. The outcome of self-assessment online tests indicates that though Mathematics anxiety is lower than during examinations, the poor results obtained for questions requiring mathematical skills are, at least in part, due to a lack of self-efficacy

Wandering behaviour prevents inter and intra oceanic speciation in a coastal pelagic fish

Small pelagic fishes have the ability to disperse over long distances and may present complex evolutionary histories. Here, Old World Anchovies (OWA) were used as a model system to understand genetic patterns and connectivity of fish between the Atlantic and Pacific basins. We surveyed 16 locations worldwide using mtDNA and 8 microsatellite loci for genetic parameters, and mtDNA (cyt b; 16S) and nuclear (RAG1; RAG2) regions for dating major lineage-splitting events within Engraulidae family. The OWA genetic divergences (0-0.4%) are compatible with intra-specific divergence, showing evidence of both ancient and contemporary admixture between the Pacific and Atlantic populations, enhanced by high asymmetrical migration from the Pacific to the Atlantic. The estimated divergence between Atlantic and Pacific anchovies (0.67 [0.53-0.80] Ma) matches a severe drop of sea temperature during the Gunz glacial stage of the Pleistocene. Our results support an alternative evolutionary scenario for the OWA, suggesting a coastal migration along south Asia, Middle East and eastern Africa continental platforms, followed by the colonization of the Atlantic via the Cape of the Good Hope.Portuguese Foundation for Science & Technology (FCT) [SFRH/BD/36600/2007]; FCT [UID/MAR/04292/2013, SFRH/BPD/65830/2009]; FCT strategic plan [UID/Multi/04326/2013]info:eu-repo/semantics/publishedVersio

Cross-cultural adaptation of children´s environmental health questionnaires for English nursing students

Objectives: Children are among the most vulnerable population groups with regard to environmental risks. Nursing students must be fully educated on children’s environmental health as they are in a key position to prevent and reduce the effects of environmental hazards. The main objective of this study was to adapt and validate an English language version of two questionnaires about children’s health and the environment, to assess the knowledge and skills of student nurses in England. Design: Observational cross-sectional study. Setting: A university in Southern England. Method: The study involves translating, adapting and validating the Children’s Environmental Health Knowledge Questionnaire (ChEHK-Q) and the Children’s Environmental Health Skills Questionnaire (ChEHS-Q) with nursing students in England (N = 232). Results: The psychometric characteristics of both questionnaires were strong. Infit and outfit values were close to 1. The reliability values for the items and people were 0.96 and 0.79 for ChEHK-Q and 0.98 and 0.89 for ChEHS-Q, respectively. Only 52 (22.41%) and 77 (33.62%) participants had at least good knowledge and skills, respectively. Higher knowledge and skills were found with respect to the vulnerability of children and identification of environmental risks in the home. Lower levels of knowledge and skills were found with respect to the effects of pesticides and the assessment of neoplastic pollutants. Conclusion: Findings demonstrate deficiencies in nursing competencies related to children’s environmental health. The use of these questionnaires will facilitate improvement in both knowledge and skills related to children’s environmental health among future nurses

Adrenal Dysfunction in Hemodynamically Unstable Patients in the Emergency Department

Objective: Adrenal failure, a treatable condition, can have catastrophic consequences if unrecognized in critically ill ED patients. The authors' objective was to prospectively study adrenal function in a case series of hemodynamically unstable (high-risk) patients from a large, urban ED over a 12-month period. Methods: In a prospective manner, critically ill adult patients presenting to the ED were enrolled when presenting with a mean arterial blood pressure ≤60 mm Hg requiring vasopressor therapy for more than one hour after receiving fluid resuscitation (central venous pressure of 12-15 mm Hg or a minimum of 40 mL/kg of crystalloid). Patients were excluded if presenting with hemorrhage, trauma, or AIDS, or if steroids were used within the previous six months. An adrenocorticotropic hormone (ACTH) stimulation test was performed and serum cortisol was measured. Treatment for adrenal insufficiency was not instituted. Results: A total of 57 consecutive patients were studied. Of these, eight (14%) had baseline serum cortisol concentrations of <20 Μg/dL (<552 nmol/L), which was considered adrenal insufficiency (AI). Three additional patients (5%) had subnormal 60-minute post-ACTH-stimulation cortisol responses (<30 Μg/dL) and a delta cortisol ≤9 Μg/dL, which is the difference between the baseline and 60-minute levels. This is functional hypoadrenalism (FH). There were no laboratory abnormalities that distinguished patients with AI or FH from those with preserved adrenal function (PAF). Rates of survival to discharge did not differ between the AI group (7 of 8) and PAF patients (21 of 46; p = 0.052). Conclusions: Adrenal dysfunction is common in high-risk ED patients. Overall, it has a frequency of 19% among a homogeneous population of hemodynamically unstable vasopressor-dependent patients. The effect of physiologic glucocorticoid replacement in this setting remains to be determined.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/71956/1/j.1553-2712.1999.tb00417.x.pd

Development of the preterm gut microbiome in twins at risk of necrotising enterocolitis and sepsis

The preterm gut microbiome is a complex dynamic community influenced by genetic and environmental factors and is implicated in the pathogenesis of necrotising enterocolitis (NEC) and sepsis. We aimed to explore the longitudinal development of the gut microbiome in preterm twins to determine how shared environmental and genetic factors may influence temporal changes and compared this to the expressed breast milk (EBM) microbiome. Stool samples (n = 173) from 27 infants (12 twin pairs and 1 triplet set) and EBM (n = 18) from 4 mothers were collected longitudinally. All samples underwent PCR-DGGE (denaturing gradient gel electrophoresis) analysis and a selected subset underwent 454 pyrosequencing. Stool and EBM shared a core microbiome dominated by Enterobacteriaceae, Enterococcaceae, and Staphylococcaceae. The gut microbiome showed greater similarity between siblings compared to unrelated individuals. Pyrosequencing revealed a reduction in diversity and increasing dominance of Escherichia sp. preceding NEC that was not observed in the healthy twin. Antibiotic treatment had a substantial effect on the gut microbiome, reducing Escherichia sp. and increasing other Enterobacteriaceae. This study demonstrates related preterm twins share similar gut microbiome development, even within the complex environment of neonatal intensive care. This is likely a result of shared genetic and immunomodulatory factors as well as exposure to the same maternal microbiome during birth, skin contact and exposure to EBM. Environmental factors including antibiotic exposure and feeding are additional significant determinants of community structure, regardless of host genetics