A tutorial on pseudospectral methods for computational optimal control

[English] This paper is a tutorial introduction to pseudospectral optimal control. With pseudospectral methods, a function is approximated as a linear combination of smooth basis functions, which are often chosen to be Legendre or Chebyshev polynomials. Collocation of the differential-algebraic equations is performed at orthogonal collocation points, which are selected to yield interpolation of high accuracy. Pseudospectral methods directly discretize the original optimal control problem to recast it into a nonlinear programming format. A numerical optimizer is then employed to find approximate local optimal solutions. The paper also briefly describes the functionality and implementation of PSOPT, an open source software package written in C++ that employs pseudospectral discretization methods to solve multi-phase optimal control problems. The software implements the Legendre and Chebyshev pseudospectral methods, and it has useful features such as automatic differentiation, sparsity detection, and automatic scaling. The use of pseudospectral methods is illustrated in two problems taken from the literature on computational optimal control. [Portuguese] Este artigo e um tutorial introdutorio sobre controle otimo pseudo-espectral. Em metodos pseudo-espectrais, uma funcao e aproximada como uma combinacao linear de funcoes de base suaves, tipicamente escolhidas como polinomios de Legendre ou Chebyshev. A colocacao de equacoes algebrico-diferenciais e realizada em pontos de colocacao ortogonal, que sao selecionados de modo a minimizar o erro de interpolacao. Metodos pseudoespectrais discretizam o problema de controle otimo original de modo a converte-lo em um problema de programa cao nao-linear. Um otimizador numerico e entao empregado para obter solucoes localmente otimas. Este artigo tambem descreve sucintamente a funcionalidade e a implementacao de um pacote computacional de codigo aberto escrito em C++ chamado PSOPT. Tal pacote emprega metodos de discretizacao pseudo-spectrais para resolver problemas de controle otimo com multiplas fase. O PSOPT permite a utilizacao de metodos de Legendre ou Chebyshev, e possui caractersticas uteis tais como diferenciacao automatica, deteccao de esparsidade e escalonamento automatico. O uso de metodos pseudo-espectrais e ilustrado em dois problemas retirados da literatura de controle otimo computacional.

Genetic predisposition to type 2 diabetes is associated with impaired insulin secretion but does not modify insulin resistance or secretion in response to an intervention to lower dietary saturated fat

Genome-wide association studies have identified SNPs reproducibly associated with type 2 diabetes (T2D). We examined the effect of genetic predisposition to T2D on insulin sensitivity and secretion using detailed phenotyping in overweight individuals with no diagnosis of T2D. Furthermore, we investigated whether this genetic predisposition modifies the responses in beta-cell function and insulin sensitivity to a 24-week dietary intervention. We genotyped 25 T2D-associated SNPs in 377 white participants from the RISCK study. Participants underwent an IVGTT prior to and following a dietary intervention that aimed to lower saturated fat intake by replacement with monounsaturated fat or carbohydrate. We composed a genetic predisposition score (T2D-GPS) by summing the T2D risk-increasing alleles of the 25 SNPs and tested for association with insulin secretion and sensitivity at baseline, and with the change in response to the dietary intervention. At baseline, a higher T2D-GPS was associated with lower acute insulin secretion (AIRg 4% lower/risk allele, P = 0.006) and lower insulin secretion for a given level of insulin sensitivity, assessed by the disposition index (DI 5% lower/risk allele, P = 0.002), but not with insulin sensitivity (Si). T2D-GPS did not modify changes in insulin secretion, insulin sensitivity or the disposition index in response to the dietary interventions to lower saturated fat. Participants genetically predisposed to T2D have an impaired ability to compensate for peripheral insulin resistance with insulin secretion at baseline, but this does not modify the response to a reduction in dietary saturated fat through iso-energetic replacement with carbohydrate or monounsaturated fat.

A randomised, double-blind, placebo controlled cross-over study to determine the gastrointestinal effects of consumption of arabinoxylanoligosaccharides enriched bread in healthy volunteers

BACKGROUND: Prebiotics are food ingredients, usually non-digestible oligosaccharides, that are selectively fermented by populations of beneficial gut bacteria. Endoxylanases, altering the naturally present cereal arabinoxylans, are commonly used in the bread industry to improve dough and bread characteristics. Recently, an in situ method has been developed to produce arabinoxylan-oligosaccharides (AXOS) at high levels in breads through the use of a thermophilic endoxylanase. AXOS have demonstrated potentially prebiotic properties in that they have been observed to lead to beneficial shifts in the microbiota in vitro and in murine, poultry and human studies. METHODS: A double-blind, placebo controlled human intervention study was undertaken with 40 healthy adult volunteers to assess the impact of consumption of breads with in situ produced AXOS (containing 2.2 g AXOS) compared to non-endoxylanase treated breads. Volatile fatty acid concentrations in faeces were assessed and fluorescence in situ hybridisation was used to assess changes in gut microbial groups. Secretory immunoglobulin A (sIgA) levels in saliva were also measured. RESULTS: Consumption of AXOS-enriched breads led to increased faecal butyrate and a trend for reduced iso-valerate and fatty acids associated with protein fermentation. Faecal levels of bifidobacteria increased following initial control breads and remained elevated throughout the study. Lactobacilli levels were elevated following both placebo and AXOS-breads. No changes in salivary secretory IgA levels were observed during the study. Furthermore, no adverse effects on gastrointestinal symptoms were reported during AXOS-bread intake. CONCLUSIONS: AXOS-breads led to a potentially beneficial shift in fermentation end products and are well tolerated.

Estimating root–soil contact from 3D X-ray microtomographs

Adequate contact with the soil is essential for water and nutrient adsorption by plant roots, but the determination of root–soil contact is a challenging task because it is difficult to visualize roots in situ and quantify their interactions with the soil at the scale of micrometres. A method to determine root–soil contact using X-ray microtomography was developed. Contact areas were determined from 3D volumetric images using segmentation and iso-surface determination tools. The accuracy of the method was tested with physical model systems of contact between two objects (phantoms). Volumes, surface areas and contact areas calculated from the measured phantoms were compared with those estimated from image analysis. The volume was accurate to within 0.3%, the surface area to within 2–4%, and the contact area to within 2.5%. Maize and lupin roots were grown in soil (<2 mm) and vermiculite at matric potentials of −0.03 and −1.6 MPa and in aggregate fractions of 4–2, 2–1, 1–0.5 and < 0.5 mm at a matric potential of −0.03 MPa. The contact of the roots with their growth medium was determined from 3D volumetric images. Macroporosity (>70 µm) of the soil sieved to different aggregate fractions was calculated from binarized data. Root-soil contact was greater in soil than in vermiculite and increased with decreasing aggregate or particle size. The differences in root–soil contact could not be explained solely by the decrease in porosity with decreasing aggregate size but may also result from changes in particle and aggregate packing around the root.

Effect of "Pollutants" on the functionality of breathable roofing membranes in a bat roost

The performance of breathable roofing membranes (BRM’s) in buildings where bats roost have been investigated using experimental measurements and numerical simulations. Measurement techniques as outlined in BS EN ISO 12572 of membranes from manufacturers in its pure state and those that have been contaminated with bat urine, faeces and natural oils transmitted via fur because they were found in bat roost have been tested for their permeability functions. The findings from this shows that there are significant differences between the functionality of the pure samples compared to the contaminated samples, with an average of about 20-30% reduction in functionality. This paper integrates modelling techniques using a heat, air and mass software with a simulink interface on a Matlab platform to investigate the moisture transfer properties of the BRMs. The simulation results demonstrate high level of condensation formation when the BRM is contaminated as compared to when it is not.

Regulation of KCa2.3 andendothelium-dependent hyperpolarization (EDH) in the rat middle cerebral artery: the role of lipoxygenase metabolites and isoprostanes

Background and Purpose. In rat middle cerebral arteries, endothelium-dependent hyperpolarization (EDH) is mediated by activation of calcium-activated potassium(KCa) channels specifically KCa2.3 and KCa3.1. Lipoxygenase (LOX) products function as endothelium-derived hyperpolarizing factors (EDHFs) in rabbit arteries by stimulating KCa2.3. We investigated if LOX products contribute to EDH in rat cerebral arteries. Methods. Arachidonic acid (AA) metabolites produced in middle cerebral arteries were measured using HPLC and LC/MS. Vascular tension and membrane potential responses to SLIGRL were simultaneously recorded using wire myography and intracellular microelectrodes. Results. SLIGRL, an agonist at PAR2 receptors, caused EDH that was inhibited by a combination of KCa2.3 and KCa3.1 blockade. Non-selective LOX-inhibition reduced EDH, whereas inhibition of 12-LOX had no effect. Soluble epoxide hydrolase (sEH) inhibition enhanced the KCa2.3 component of EDH. Following NO synthase (NOS) inhibition, the KCa2.3 component of EDH was absent. Using HPLC, middle cerebral arteries metabolized 14C-AA to 15- and 12-LOX products under control conditions. With NOS inhibition, there was little change in LOX metabolites, but increased F-type isoprostanes. 8-iso-PGF2α inhibited the KCa2.3 component of EDH. Conclusions. LOX metabolites mediate EDH in rat middle cerebral arteries. Inhibition of sEH increases the KCa2.3 component of EDH. Following NOS inhibition,loss of KCa2.3 function is independent of changes in LOX production or sEH inhibition but due to increased isoprostane production and subsequent stimulation of TP receptors. These findings have important implications in diseases associated with loss of NO signaling such as stroke; where inhibition of sEH and/or isoprostane formation may of benefit.