Discrete Approximations of a Controlled Sweeping Process

The paper is devoted to the study of a new class of optimal control problems governed by the classical Moreau sweeping process with the new feature that the polyhe- dral moving set is not fixed while controlled by time-dependent functions. The dynamics of such problems is described by dissipative non-Lipschitzian differential inclusions with state constraints of equality and inequality types. It makes challenging and difficult their anal- ysis and optimization. In this paper we establish some existence results for the sweeping process under consideration and develop the method of discrete approximations that allows us to strongly approximate, in the W^{1,2} topology, optimal solutions of the continuous-type sweeping process by their discrete counterparts

Dynamic probabilistic constraints under continuous random distributions

The paper investigates analytical properties of dynamic probabilistic constraints (chance constraints). The underlying random distribution is supposed to be continuous. In the first part, a general multistage model with decision rules depending on past observations of the random process is analyzed. Basic properties like (weak sequential) (semi-) continuity of the probability function or existence of solutions are studied. It turns out that the results differ significantly according to whether decision rules are embedded into Lebesgue or Sobolev spaces. In the second part, the simplest meaningful two-stage model with decision rules from L2 is investigated. More specific properties like Lipschitz continuity and differentiability of the probability function are considered. Explicitly verifiable conditions for these properties are provided along with explicit gradient formulae in the Gaussian case. The application of such formulae in the context of necessary optimality conditions is discussed and a concrete identification of solutions presented. © 2020, The Author(s)

A mixed-integer stochastic nonlinear optimization problem with joint probabilistic constraints

We illustrate the solution of a mixed-integer stochastic nonlinear optimization problem in an application of power management. In this application, a coupled system consisting of a hydro power station and a wind farm is considered. The objective is to satisfy the local energy demand and sell any surplus energy on a spot market for a short time horizon. Generation of wind energy is assumed to be random, so that demand satisfaction is modeled by a joint probabilistic constraint taking into accountthe multivariate distribution. The turbine is forced to either operate between given positive limits or to be shut down. This introduces additional binary decisions. The numerical solution procedure is presented and results are illustrated

Author's personal copy Discrete Optimization A model for dynamic chance constraints in hydro power reservoir management

a b s t r a c t In this paper, a model for (joint) dynamic chance constraints is proposed and applied to an optimization problem in water reservoir management. The model relies on discretization of the decision variables but keeps the probability distribution continuous. Our approach relies on calculating probabilities of rectangles which is particularly useful in the presence of independent random variables but works equally well in the case of correlated variables. Numerical results are provided for two and three stages

Calculus of Tangent Sets and Derivatives of Set Valued Maps under Metric Subregularity Conditions

In this paper we intend to give some calculus rules for tangent sets in the sense of Bouligand and Ursescu, as well as for corresponding derivatives of set-valued maps. Both first and second order objects are envisaged and the assumptions we impose in order to get the calculus are in terms of metric subregularity of the assembly of the initial data. This approach is different from those used in alternative recent papers in literature and allows us to avoid compactness conditions. A special attention is paid for the case of perturbation set-valued maps which appear naturally in optimization problems.Comment: 17 page

In Vitro Effects of the Endocrine Disruptor p,p’-DDT on Human Follitropin Receptor

BACKGROUND: 1-chloro-4-[2,2,2-trichloro-1-(4-chlorophenyl)ethyl]benzene (p,p\u27-DDT) is a persistent environmental endocrine disruptor (ED). Several studies have shown an association between p,p\u27-DDT exposure and reproductive abnormalities. OBJECTIVES: To investigate the putative effects of p,p\u27-DDT on the human follitropin receptor (FSHR) function. METHODS AND RESULTS: We used Chinese hamster ovary (CHO) cells stably expressing human FSHR to investigate the impact of p,p\u27-DDT on FSHR activity and its interaction with the receptor. At a concentration of 5 μM p,p\u27-DDT increased the maximum response of the FSHR to follitropin by 32 ± 7.45%. However, 5 μM p,p\u27-DDT decreased the basal activity and did not influence the maximal response of the closely related LH/hCG receptor to human chorionic gonadotropin (hCG). The potentiating effect of p,p\u27-DDT was specific for the FSHR. Moreover, in cells that did not express FSHR, p,p\u27-DDT had no effect on cAMP response. Thus, the potentiating effect of p,p\u27-DDT was dependent on the FSHR. In addition, p,p\u27-DDT increased the sensitivity of FSHR to hCG and to a low molecular weight agonist of the FSHR, 3-((5methyl)-2-(4-benzyloxy-phenyl)-5-{[2-[3-ethoxy-4-methoxy-phenyl)-ethylcarbamoyl]-methyl}-4-oxo-thiazolidin-3-yl)-benzamide (16a). Basal activity in response to p,p\u27-DDT and potentiation of the FSHR response to FSH by p,p\u27-DDT varied among FSHR mutants with altered transmembrane domains (TMDs), consistent with an effect of p,p\u27-DDT via TMD binding. This finding was corroborated by the results of simultaneously docking p,p\u27-DDT and 16a into the FSHR transmembrane bundle. CONCLUSION:p,p\u27-DDT acted as a positive allosteric modulator of the FSHR in our experimental model. These findings suggest that G protein-coupled receptors are additional targets of endocrine disruptor

Recombinant human activated protein C improves endotoxemia-induced endothelial dysfunction: a blood-free model in isolated mouse arteries

Recombinant human activated protein C (rhAPC) is one of the treatment panels for improving vascular dysfunction in septic patients. In a previous study, we reported that rhAPC treatment in rat endotoxemia improved vascular reactivity, although the mechanisms involved are still under debate. In the present study, we hypothesized that rhAPC may improve arterial dysfunction through its nonanticoagulant properties. Ten hours after injection of LPS in mice (50 mg/kg ip), aortic rings and mesenteric arteries were isolated and incubated with or without rhAPC for 12 h. Aortic rings were mounted in a myograph, after which arterial contractility and endothelium-dependent relaxation were measured in the presence or absence of nitric oxide synthase or cyclooxygenase inhibitors. Flow (shear stress)-mediated dilation with or without the above inhibitors was also measured in mesenteric resistance arteries. Protein expression was assessed by Western blotting. Lipopolysaccharide (LPS) reduced aortic contractility to KCl and phenylephrine as well as dilation to acetylcholine. LPS also reduced flow-mediated dilation in mesenteric arteries. In rhAPC-treated aorta and mesenteric arteries, contractility and endothelial responsiveness to vasodilator drug and shear stress were improved. rhAPC treatment also improved LPS-induced endothelial dysfunction; this effect was associated with an increase in the phosphorylated form of endothelial nitric oxide synthase and protein kinase B as well as cyclooxygenase vasodilatory pathways, thus suggesting that these pathways, together with the decrease in nuclear factor-κB activation and inducible nitric oxide synthase expression in the vascular wall, are implicated in the endothelial effect of rhAPC. In conclusion, ex vivo application of rhAPC improves arterial contractility and endothelial dysfunction resulting from endotoxemia in mice. This finding provides important insights into the mechanism underlying rhAPC-induced improvements on arterial dysfunction during septic shock

Influence of the scattering potential model on low energy electron diffraction from Cu(001)−c(2 × 2)-Pb

A dynamical LEED intensity analysis is reported for Cu(001)−c(2 × 2)-Pb. The adsorbate layer distance from the substrate is determined as 2.29 Å, and the topmost interlayer spacing for the substrate is the same as in bulk Cu, in contrast to a contraction for clean Cu(001). This structural result is, within the accuracy reached, insensitive to changes in the assumed scattering potential models. The r-factors suggest a weak preference for an energy-dependent exchange correlation and a moderate one for adding a localized adsorption part inside the muffin-tin spheres. The sensitivity of spectra and r-factors to changes in the assumed isotropic Debye temperature for Pb suggests that vibrational anisotropy should be taken into account in order to improve the accuracy of the analysis. Calculated spin polarization spectra are very sensitive to the exchange approximation, the localized absorption and the Debye temperature. Together with experimental data, they should be useful in particular for determining the vibrational anisotropy