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.

Differential effect of beetroot bread on postprandial DBP according to Glu298Asp polymorphism in the eNOS gene: a pilot study.

Our objective was to investigate whether the presence of Glu298Asp polymorphism in the endothelial NO synthase (eNOS) gene differentially affects the postprandial blood pressure response to dietary nitrate-rich beetroot bread. A randomised, single-blind, controlled, crossover acute pilot study was performed in 14 healthy men (mean age: 34±9 years) who were retrospectively genotyped for Glu298Asp polymorphism (7GG; T carriers 7). Volunteers were randomised to receive 200 g beetroot-enriched bread (1.1 mmol nitrate) or control bread (no beetroot; 0.01 mmol nitrate) on two separate occasions 10 days apart. Baseline and incremental area under the curve of blood pressure and NOx (nitrate/nitrite) were measured for a 6-h postprandial period. A treatment × genotype interaction was observed for diastolic blood pressure (P<0.02), which was significantly lower in T carriers (P<0.01) after consumption of beetroot bread compared with control bread. No significant differences were observed in the GG group. The beneficial diastolic blood pressure reduction was observed only in the T carriers of the Glu298Asp polymorphism in the eNOS gene after consumption of nitrate-rich beetroot bread. These data require confirmation in a larger population group.

Applying robust control theory to solve problems in bio-medical sciences: study of an apoptotic model

Biological models of an apoptotic process are studied using models describing a system of differential equations derived from reaction kinetics information. The mathematical model is re-formulated in a state-space robust control theory framework where parametric and dynamic uncertainty can be modelled to account for variations naturally occurring in biological processes. We propose to handle the nonlinearities using neural networks.

Insulin resistance determines a differential response to changes in dietary fat modification on metabolic syndrome risk factors: the LIPGENE study

Background: Previous data support the benefits of reducing dietary saturated fatty acids (SFAs) on insulin resistance (IR) and other metabolic risk factors. However, whether the IR status of those suffering from metabolic syndrome (MetS) affects this response is not established. OBJECTIVE: Our objective was to determine whether the degree of IR influences the effect of substituting high-saturated fatty acid (HSFA) diets by isoenergetic alterations in the quality and quantity of dietary fat on MetS risk factors. DESIGN: In this single-blind, parallel, controlled, dietary intervention study, MetS subjects (n = 472) from 8 European countries classified by different IR levels according to homeostasis model assessment of insulin resistance (HOMA-IR) were randomly assigned to 4 diets: an HSFA diet; a high-monounsaturated fatty acid (HMUFA) diet; a low-fat, high-complex carbohydrate (LFHCC) diet supplemented with long-chain n-3 polyunsaturated fatty acids (1.2 g/d); or an LFHCC diet supplemented with placebo for 12 wk (control). Anthropometric, lipid, inflammatory, and IR markers were determined. RESULTS: Insulin-resistant MetS subjects with the highest HOMA-IR improved IR, with reduced insulin and HOMA-IR concentrations after consumption of the HMUFA and LFHCC n-3 diets (P < 0.05). In contrast, subjects with lower HOMA-IR showed reduced body mass index and waist circumference after consumption of the LFHCC control and LFHCC n-3 diets and increased HDL cholesterol concentrations after consumption of the HMUFA and HSFA diets (P < 0.05). MetS subjects with a low to medium HOMA-IR exhibited reduced blood pressure, triglyceride, and LDL cholesterol levels after the LFHCC n-3 diet and increased apolipoprotein A-I concentrations after consumption of the HMUFA and HSFA diets (all P < 0.05). CONCLUSIONS: Insulin-resistant MetS subjects with more metabolic complications responded differently to dietary fat modification, being more susceptible to a health effect from the substitution of SFAs in the HMUFA and LFHCC n-3 diets. Conversely, MetS subjects without IR may be more sensitive to the detrimental effects of HSFA intake. The metabolic phenotype of subjects clearly determines response to the quantity and quality of dietary fat on MetS risk factors, which suggests that targeted and personalized dietary therapies may be of value for its different metabolic features.

Crosstalk between oestrogen receptors and thyroid hormone receptor isoforms results in differential regulation of the preproenkephalin gene

Nuclear receptors are ligand-activated transcription factors, which have the potential to integrate internal metabolic events in an organism, with consequences for control of behaviour. Previous studies from this laboratory have shown that thyroid hormone receptor (TR) isoforms can inhibit oestrogen receptor (ER)alpha-mediated induction of preproenkephalin (PPE) gene expression in the hypothalamus. Also, thyroid hormone administration inhibits lordosis, a behaviour facilitated by PPE expression. We have examined the effect of multiple ligand-binding TR isoforms on the ER-mediated induction of the PPE gene in transient transfection assays in CV-1 cells. On a natural PPE gene promoter fragment containing two putative oestrogen response elements (EREs), both ER alpha and beta isoforms mediate a four to five-fold induction by oestrogen. Cotransfection of TR alpha 1 along with ER alpha inhibited the ER alpha transactivation of PPE by approximately 50%. However, cotransfection with either TR beta 1 or TR beta 2 expression plasmids produced no effect on the ER alpha or ER beta mediated induction of PPE. Therefore, under these experimental conditions, interactions with a single ER isoform are specific to an individual TR isoform. Transfection with a TR alpha 1 DNA-binding mutant could also inhibit ER alpha transactivation, suggesting that competition for binding on the ERE may not be the exclusive mechanism for inhibition. Data with the coactivator, SRC-1, suggested that coactivator squelching may participate in the inhibition. In dramatic contrast, when ER beta is cotransfected, TR alpha 1 stimulated ER beta-mediated transactivation of PPE by approximately eight-fold over control levels. This is the first study revealing specific interactions among nuclear receptor isoforms on a neuroendocrine promoter. These data also suggest that the combinatorics of ER and TR isoforms allow multiple forms of flexible gene regulations in the service of neuroendocrine integration.

Differential proteome analysis of mature and germinated embryos of Araucaria angustifolia

Araucaria angustifolia is an endangered Brazilian native conifer tree. The aim of the present work was to identify differentially expressed proteins between mature and germinated embryos of A. angustifolia, using one and two dimensional gel electrophoresis approaches followed by protein identification by tandem mass spectrometry. The identities of 32 differentially expressed protein spots from two dimensional gel maps were successfully determined, including proteins and enzymes involved in storage mobilization such as the vicilin-like storage protein and proteases. A label free approach, based on spectral counts, resulted in detection of 10 and 14 mature and germinated enriched proteins, respectively. Identified proteins were mainly related to energetic metabolism pathways, translational processes. oxidative stress regulation and cellular signaling. The integrated use of both strategies permitted a comprehensive protein expression overview of changes in germinated embryos in relation to matures, providing insights into the this process in a recalcitrant seed species. Applications of the data generated on the monitoring and control of in vitro somatic embryos were discussed. Published by Elsevier Ltd.

Differential regulation of the renin-angiotensin system by nicotine in WKY and SHR glia

Given that (1) the renin-angiotensin system (RAS) is compartmentalized within the central nervous system in neurons and glia (2) the major source of brain angiotensinogen is the glial cells, (3) the importance of RAS in the central control of blood pressure, and (4) nicotine increases the probability of development of hypertension associated to genetic predisposition; the objective of the present study was to evaluate the effects of nicotine on the RAS in cultured glial cells from the brainstem and hypothalamus of Wistar Kyoto (WKY) and spontaneously hypertensive (SHR) rats. Ligand binding, real-time PCR and western blotting assays were used to compare the expression of angiotensinogen, angiotensin converting enzyme, angiotensin converting enzyme 2 and angiotensin II type1 receptors. We demonstrate, for the first time, that there are significant differences in the basal levels of RAS components between WKY and SHR rats in glia from 1-day-old rats. We also observed that nicotine is able to modulate the renin-angiotensin system in glial cells from the brainstem and hypothalamus and that the SHR responses were more pronounced than WKY ones. The present data suggest that nicotine effects on the RAS might collaborate to the development of neurogenic hypertension in SHR through modulation of glial cells.

Differential expression of cytokines, chemokines and chemokine receptors in patients with coronary artery disease

Monocytes/macrophages and lymphocytes have a key role in the pathogenesis of atherosclerosis through the production of inflammatory and anti-inflammatory cytokines. We evaluated mRNA expression and protein production of CCL2, CXCL8, CXCL9, CXCL10, IFN-gamma and IL-10 in vitro as well as the expression of the CCR2 and CXCR3 receptors in peripheral blood mononuclear cells (PBMCs) of patients with coronary artery disease (CAD) and healthy controls in the presence or absence of oxidized LDL (oxLDL). Patients with CAD showed higher constitutive expression of CCL2, CXCL8, CXCL9, CXCL10 and IFN-gamma mRNA and, after stimulation with oxLDL, higher expression of CCL2 and CXCL8 mRNA than the control group. We also detected higher levels of CCL2 and CXCL8 in supernatants of oxLDL-stimulated PBMCs from CAD patients than in corresponding supernatants from controls. Patients with CAD had a higher percentage of constitutive CCR2(+) and CXCR3(+) cells after stimulation with oxLDL. Among CAD patients, the main differences between the stable (SA) and unstable angina (UA) groups were lower IL-10 mRNA production in the latter group. Altogether, our data suggest that PBMCs from CAD patients are able to produce higher concentrations of chemokines and cytokines involved in the regulation of monocyte and lymphocyte migration and retention in atherosclerotic lesions. (C) 2008 Elsevier Ireland Ltd. All rights reserved.

Fonsecaea pedrosoi infection induces differential modulation of costimulatory molecules and cytokines in monocytes from patients with severe and mild forms of chromoblastomycosis

The host defense mechanism in chromoblastomycosis has not been thoroughly investigated. It has been suggested that cell- mediated immunity in patients with long- standing chromoblastomycosis is somehow impaired. As a result, these individuals became unable to develop an efficient immune reaction. Many studies have shown that monocyte- derived macrophages exhibit critical activities in immunity to microorganisms. Moreover, the ability of cells from the monocytic lineage to process and present antigens, to produce cytokines, and to provide costimulatory signals confirms their pivotal role in the initiation of specific immune responses. In the present study, it was observed that monocytes from patients with a severe form of disease had a higher production of IL- 10 and a lower expression of HLA- DR and costimulatory molecules when stimulated with specific antigen or LPS. Immune modulation with recombinant IL- 12 or anti- IL- 10 can restore the antigen- specific Th1- type immune response in chromoblastomycosis patients by up- regulating HLA- DR and costimulatory molecules in monocytes. Therefore, our data show that monocytes from patients with different clinical forms of chromoblastomycosis present distinct phenotypic and functional profiles. This observation suggests possible mechanisms that control the T cell response and influence their role in the development of pathology.

Differential effects of female sex hormones on cellular recruitment and tracheal reactivity after formaldehyde exposure

Female sex hormones (FSHs) exert profound regulatory effects on the course of lung inflammation due to allergic and non-allergic immune responses. As pollution is one of the pivotal factors to induce lung dysfunction, in this study we investigated the modulatory role of FSHs on lung inflammation after a formaldehyde (FA) exposure. For this purpose, lung and systemic inflammatory responses were evaluated in terms of leukocytes countings in bronchoalveolar lavage (BAL), peripheral blood and bone marrow lavage from 7-day ovariectomized (OVx) and Sham-OVx rats subjected to FA inhalation for 3 consecutive days. The hypothesized link between effects of FSHs on expression of adhesion molecules and mast cells degranulation was also studied. Once exposed to FA, Sham-OVx rats increased the number of total cells recovered in BAL and of leukocytes in peripheral blood, and decreased the counts in bone marrow. By contrast, in OVx rats upon FA exposure there was a reduction of the total cells counts in BAL and of blood leukocytes: lung expressions of ICAM-1 and Mac-1 were depressed, but the number of bone marrow cells did not vary. Estradiol treatment of OVx rats increased the total cells in BAL and decreased the number of blood leukocytes, whereas the number of bone marrow cell remained unaltered. Progesterone treatment, in turn increased the total cells in BAL and blood leukocytes, but decreased the number of bone marrow cells. OVx rats exposed to FA developed tracheal hyperresponsiveness to methacholine (MCh). A similarly altered response was found between the tracheal segments of Sham-OVx rats after FA exposure and that found in tracheae of naive rats. Estradiol treatment prevented FA-induced tracheal hyperresponsiveness to MCh whereas progesterone was ineffective in this regard. In addition, OVx rats upon FA exposure significantly increased both, the ability of mast cell degranulation and serum corticosterone levels. In conclusion, it was found that FSHs act by distinct control mechanisms on FA-induced lung inflammation and tracheal hyperresponsiveness, since at low circulating levels of FSHs (such as those after OVx) there is some resistance to the development of a lung inflammatory response, but the cholinergic tracheal responsiveness is exacerbated. Our data also help to understand the involvement of FSHs on mast cells activity after pollutants exposure and add information regarding the role of FSHs on the mechanisms related to endothelium-leukocyte interactions. (C) 2011 Elsevier Ireland Ltd. All rights reserved.

Invariants of binary differential equations

In this paper, we study binary differential equations a(x, y)dy (2) + 2b(x, y) dx dy + c(x, y)dx (2) = 0, where a, b, and c are real analytic functions. Following the geometric approach of Bruce and Tari in their work on multiplicity of implicit differential equations, we introduce a definition of the index for this class of equations that coincides with the classical Hopf`s definition for positive binary differential equations. Our results also apply to implicit differential equations F(x, y, p) = 0, where F is an analytic function, p = dy/dx, F (p) = 0, and F (pp) not equal aEuro parts per thousand 0 at the singular point. For these equations, we relate the index of the equation at the singular point with the index of the gradient of F and index of the 1-form omega = dy -aEuro parts per thousand pdx defined on the singular surface F = 0.

Dynamic hedging with stocastic differential utility

In this paper we study the dynamic hedging problem using three different utility specifications: stochastic differential utility, terminal wealth utility, and we propose a particular utility transformation connecting both previous approaches. In all cases, we assume Markovian prices. Stochastic differential utility, SDU, impacts the pure hedging demand ambiguously, but decreases the pure speculative demand, because risk aversion increases. We also show that consumption decision is, in some sense, independent of hedging decision. With terminal wealth utility, we derive a general and compact hedging formula, which nests as special all cases studied in Duffie and Jackson (1990). We then show how to obtain their formulas. With the third approach we find a compact formula for hedging, which makes the second-type utility framework a particular case, and show that the pure hedging demand is not impacted by this specification. In addition, with CRRA- and CARA-type utilities, the risk aversion increases and, consequently the pure speculative demand decreases. If futures price are martingales, then the transformation plays no role in determining the hedging allocation. We also derive the relevant Bellman equation for each case, using semigroup techniques.

Determinants of differential pricing of equity classes in the Brazilian equity market

We examine the differential pricing of equity classes between voting and non-voting shares in Brazilian listed companies with particular emphasis on privatized companies, and we discuss the role of majority control, liquidity, and governance issues that may influence these differentials over time. We include a brief discussion on the Brazilian corporate law system, its impact on controlling and minority shareholders, and the characteristics of the Brazilian privatization process, before proceeding to the econometric analysis. We find empirical evidence to support that liquidity is a major component for determining this differential pricing over time. Other variables, such as the ratio of non-voting equity to total equity, type of majority control, and changes in regulation signal the high level of agency costs between majority controllers and minority shareholders in explaining the differential pricing of equity classes.

Optimum contribution selection using differential evolution

Um programa baseado na técnica de evolução diferencial foi desenvolvido para a definição da contribuição genética ótima na seleção de candidatos a reprodução. A função- objetivo a ser otimizada foi composta pelo mérito genético esperado da futura progênie e pela coascendência média dos animais em reprodução. Conjuntos de dados reais e simulados de populações com gerações sobrepostas foram usados para validar e testar o desempenho do programa desenvolvido. O programa se mostrou computacionalmente eficiente e viável para ser aplicado na prática e as consequências esperadas de sua aplicação, em comparação a procedimentos empíricos de controle da endogamia e/ou com a seleção baseada apenas no valor genético esperado, seriam a melhora da resposta genética futura e limitação mais efetiva da taxa de endogamia.