Optimal Control of Fractional Elliptic PDEs with State Constraints and Characterization of the Dual of Fractional-Order Sobolev Spaces

Journal of Optimization Theory and Applications - This paper introduces the notion of state constraints for optimal control problems governed by fractional elliptic partial differential equations....     

TTRISK: Tensor train decomposition algorithm for risk averse optimization

This article develops a new algorithm named TTRISK to solve high-dimensional risk-averse optimization problems governed by differential equations (ODEs and/or partial differential equations [PDEs]) under uncertainty. As an example, we focus on the so-called Conditional Value at Risk (CVaR), but the approach is equally applicable to other coherent risk measures. Both the full and reduced space formulations are considered. The algorithm is based on low rank tensor approximations of random fields discretized using stochastic collocation. To avoid nonsmoothness of the objective function underpinning the CVaR, we propose an adaptive strategy to select the width parameter of the smoothed CVaR to balance the smoothing and tensor approximation errors. Moreover, unbiased Monte Carlo CVaR estimate can be computed by using the smoothed CVaR as a control variate. To accelerate the computations, we introduce an efficient preconditioner for the Karush–Kuhn–Tucker (KKT) system in the full space formulation.The numerical experiments demonstrate that the proposed method enables accurate CVaR optimization constrained by large-scale discretized systems. In particular, the first example consists of an elliptic PDE with random coefficients as constraints. The second example is motivated by a realistic application to devise a lockdown plan for United Kingdom under COVID-19. The results indicate that the risk-averse framework is feasible with the tensor approximations under tens of random variables.     

MODELING,SIMULATION,AND OPTIMIZATION OF SURFACE ACOUSTIC WAVE DRIVEN MICROFLUIDIC BIOCHIPS

We will be concerned with the mathematical modeling, numerical simulation, and shape optimization of micro fluidic biochips that are used for various biomedical applications. A particular feature is that the fluid flow in the fluidic network on top of the biochips is in- duced by surface acoustic waves generated by interdigital transducers. We are thus faced with a multiphysics problem that will be modeled by coupling the equations of piezoelectricity with the compressible Navier-Stokes equations. Moreover, the fluid flow exhibits a multiscale character that will be taken care of by a homogenization approach. We will discuss and analyze the mathematical models and deal with their numerical solution by space-time discretizations featuring appropriate finite element approximations with respect to hierarchies of simplicial triangulations of the underlying computational domains. Simulation results will be given for the propagation of the surface acoustic waves on top of the piezoelectric substrate and for the induced fluid flow in the microchannels of the fluidic network. The performance of the operational behavior of the biochips can be significantly improved by shape optimization. In particular, for such purposes we present a multilevel interior point method relying on a predictor-corrector strategy with an adaptive choice of the continuation steplength along the barrier path. As a specific example, we will consider the shape optimization of pressure driven capillary barriers between microchannels and reservoirs.     

Captopril Electrochemical Oxidation on Fluorine‐Doped SnO2 Electrodes and Their Determination in Pharmaceutical Preparations

A novel application of fluorine‐doped tin oxide (FTO) electrodes is reported in the present work. To this end, the captopril electrochemical oxidation mechanism on FTO electrodes at various pH and its determination in pharmaceutical preparations was investigated. Captopril oxidation on FTO proceeds at pH between 2.0 and 4.0. The study revealed that interferences for captopril determination in pharmaceutical samples was totally suppressed using these electrode materials. Voltammetric survey showed an anodic peak at about 0.375 V (Ag|AgCl) for captopril oxidation, that takes place through an EC process at pH interval 2.0–4.0. The investigation demonstrated that captopril oxidation occurs through protonated species and these electroactive species interact by adsorption on FTO electrodes, with a large heterogeneous rate constant and a mechanism involving 1H⁺/1e^? in the global reaction. Moreover, a captopril sensor based upon FTO electrodes, with a linear range miliMolar, is proposed. These electrodes are promising candidates for the efficient electrochemical determination of captopril in pharmaceutical preparations.     

Analytical parameters of the microplate-based ORAC-pyrogallol red assay

The analytical parameters of the microplate-based oxygen radicals absorbance capacity (ORAC) method using pyrogallol red (PGR) as probe (ORAC-PGR) are presented. In addition, the antioxidant capacity of commercial beverages, such as wines, fruit juices, and iced teas, is estimated. A good linearity of the area under the curve (AUC) versus Trolox concentration plots was obtained [AUC = (845 +/- 110) + (23 +/- 2) [Trolox, microM], R = 0.9961, n = 19]. QC experiments showed better precision and accuracy at the highest Trolox concentration (40 microM) with RSD and REC (recuperation) values of 1.7 and 101.0%, respectively. When red wine was used as sample, the method also showed good linearity [AUC = (787 +/- 77) + (690 +/- 60) [red wine, microL/mL]; R = 0.9926, n = 17], precision and accuracy with RSD values from 1.4 to 8.3%, and REC values that ranged from 89.7 to 103.8%. Additivity assays using solutions containing gallic acid and Trolox (or red wine) showed an additive protection of PGR given by the samples. Red wines showed higher ORAC-PGR values than white wines, while the ORAC-PGR index of fruit juices and iced teas presented a great variability, ranging from 0.6 to 21.6 mM of Trolox equivalents. This variability was also observed for juices of the same fruit, showing the influence of the brand on the ORAC-PGR index. The ORAC-PGR methodology can be applied in a microplate reader with good linearity, precision, and accuracy.     

Decrypting the Potential of Nanotechnology-Based Approaches as Cutting-Edge for Management of Hyperpigmentation Disorder

The abundant synthesis and accretion of melanin inside skin can be caused by activation of melanogenic enzymes or increase in number of melanocytes. Melasma is defined as hyperpigmented bright or dark brown spots which are symmetrically distributed and have serrated and irregular borders. The three general categories of pigmentation pattern include centro facial pattern, malar pattern, and mandibular pattern. Exposure to UV rays, heat, use of cosmetics and photosensitizing drugs, female sex hormonal therapies, aberrant production of melanocyte stimulating hormone, and increasing aesthetic demands are factors which cause the development of melasma disease. This review gives a brief overview regarding the Fitzpatrick skin phototype classification system, life cycle of melanin, mechanism of action of anti-hyperpigmenting drugs, and existing pharmacotherapy strategies for the treatment of melasma. The objectives of this review are focused on role of cutting-edge nanotechnology-based strategies, such as lipid-based nanocarriers, i.e., lipid nanoparticles, microemulsions, nanoemulsions, liposomes, ethosomes, niosomes, transfersomes, aspasomes, invasomes penetration-enhancing vesicles; inorganic nanocarriers, i.e., gold nanoparticles and fullerenes; and polymer-based nanocarriers i.e., polymeric nanoparticles, polymerosomes, and polymeric micelles for the management of hyperpigmentation.