Finite Element Output Bounds for a Stabilized Discretization of Incompressible Stokes Flow

We introduce a new method for computing a posteriori bounds on engineering outputs from finite element discretizations of the incompressible Stokes equations. The method results from recasting the output problem as a minimization statement without resorting to an error formulation. The minimization statement engenders a duality relationship which we solve approximately by Lagrangian relaxation. We demonstrate the method for a stabilized equal-order approximation of Stokes flow, a problem to which previous output bounding methods do not apply. The conceptual framework for the method is quite general and shows promise for application to stabilized nonlinear problems, such as Burger's equation and the incompressible Navier-Stokes equations, as well as potential for compressible flow problems.Singapore-MIT Alliance (SMA

Robust topology optimization of three-dimensional photonic-crystal band-gap structures

We perform full 3D topology optimization (in which "every voxel" of the unit cell is a degree of freedom) of photonic-crystal structures in order to find optimal omnidirectional band gaps for various symmetry groups, including fcc (including diamond), bcc, and simple-cubic lattices. Even without imposing the constraints of any fabrication process, the resulting optimal gaps are only slightly larger than previous hand designs, suggesting that current photonic crystals are nearly optimal in this respect. However, optimization can discover new structures, e.g. a new fcc structure with the same symmetry but slightly larger gap than the well known inverse opal, which may offer new degrees of freedom to future fabrication technologies. Furthermore, our band-gap optimization is an illustration of a computational approach to 3D dispersion engineering which is applicable to many other problems in optics, based on a novel semidefinite-program formulation for nonconvex eigenvalue optimization combined with other techniques such as a simple approach to impose symmetry constraints. We also demonstrate a technique for \emph{robust} topology optimization, in which some uncertainty is included in each voxel and we optimize the worst-case gap, and we show that the resulting band gaps have increased robustness to systematic fabrication errors.Comment: 17 pages, 9 figures, submitted to Optics Expres

An Empirical Interpolation and Model-Variance Reduction Method for Computing Statistical Outputs of Parametrized Stochastic Partial Differential Equations

We present an empirical interpolation and model-variance reduction method for the fast and reliable computation of statistical outputs of parametrized stochastic elliptic partial differential equations. Our method consists of three main ingredients: (1) the real-time computation of reduced basis (RB) outputs approximating high-fidelity outputs computed with the hybridizable discontinuous Galerkin (HDG) discretization; (2) the empirical interpolation for an efficient offline-online decoupling of the parametric and stochastic inuence; and (3) a multilevel variance reduction method that exploits the statistical correlation between the low-fidelity approximations and the high-fidelity HDG dis- cretization to accelerate the convergence of the Monte Carlo simulations. The multilevel variance reduction method provides efficient computation of the statistical outputs by shifting most of the computational burden from the high-fidelity HDG approximation to the RB approximations. Fur- thermore, we develop a posteriori error estimates for our approximations of the statistical outputs. Based on these error estimates, we propose an algorithm for optimally choosing both the dimensions of the RB approximations and the size of Monte Carlo samples to achieve a given error tolerance. In addition, we extend the method to compute estimates for the gradients of the statistical out- puts. The proposed method is particularly useful for stochastic optimization problems where many evaluations of the objective function and its gradient are required

Fabrication-Adaptive Optimization, with an Application to Photonic Crystal Design

It is often the case that the computed optimal solution of an optimization problem cannot be implemented directly, irrespective of data accuracy, due to either (i) technological limitations (such as physical tolerances of machines or processes), (ii) the deliberate simplification of a model to keep it tractable (by ignoring certain types of constraints that pose computational difficulties), and/or (iii) human factors (getting people to "do" the optimal solution). Motivated by this observation, we present a modeling paradigm called "fabrication-adaptive optimization" for treating issues of implementation/fabrication. We develop computationally-focused theory and algorithms, and we present computational results for incorporating considerations of implementation/fabrication into constrained optimization problems that arise in photonic crystal design. The fabrication-adaptive optimization framework stems from the robust regularization of a function. When the feasible region is not a normed space (as typically encountered in application settings), the fabrication-adaptive optimization framework typically yields a non-convex optimization problem. (In the special case where the feasible region is a finite-dimensional normed space, we show that fabrication-adaptive optimization can be re-cast as an instance of modern robust optimization.) We study a variety of problems with special structures on functions, feasible regions, and norms, for which computation is tractable, and develop an algorithmic scheme for solving these problems in spite of the challenges of non-convexity. We apply our methodology to compute fabrication-adaptive designs of two-dimensional photonic crystals with a variety of prescribed features

Optimal Accuracy of Discontinuous Galerkin for Diffusion

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/106460/1/AIAA2013-2691.pd

Vibrationally induced fourth-order magnetic anisotropy and tunnel splittings in Mn_{12}

From density-functional-theory (DFT) based methods we calculate the vibrational spectrum of the Mn_{12}O_{12}(COOH)_{16}(H_2 O)_4 molecular magnet. Calculated infrared intensities are in accord with experimental studies. There have been no ab initio attempts at determining which interactions account for the fourth-order anisotropy. We show that vibrationally induced distortions of the molecule contribute to the fourth-order anisotropy Hamiltonian and that the magnitude and sign of the effect (-6.2 K) is in good agreement with all experiments. Vibrationally induced tunnel splittings in isotopically pure and natural samples are predicted.Comment: corres. author: [email protected] 4 pages, final version, accepted PR

Child sexual abuse and psychopathological consequences in adult life

Introducción: El abuso sexual infantil (ASI) es una forma de maltrato universal e infraestimado que constituye un problema de salud pública. Afecta a la adaptación psicológica y mental de las víctimas, a corto y largo plazo, generando problemas físicos, emocionales, sociales y conductuales. Se pretende estudiar el impacto del ASI en cuanto a psicopatología del adulto, detallando aquellas características que determinan la tipología y gravedad de la sintomatología. Metodología: Se lleva a cabo una revisión a través de bases de datos y revistas especializadas, en un intervalo temporal que abarca de enero de 2010 a septiembre de 2021, utilizando las palabras clave: ‘child sexual abuse’, ‘child sex abuse’, ‘psychopathology’, ‘psychopathological consequences’. Se preseleccionan 114 artículos, que se filtran según muestra analizada y calidad metodológica, escogiendo 21 para revisar. Resultados: Se evidencia que el ASI se asocia de forma determinante con clínica de inicio en la etapa adulta que incluye ansiedad, trastornos del estado de ánimo, quejas somáticas, abuso de sustancias e ideación suicida. La psicopatología es más grave en contexto intrafamiliar, dado que la ruptura de confianza y apego resulta traumática. Aun así, no existe una psicopatología unívoca que pueda constituir un ‘síndrome post-abuso’. Conclusiones: El abuso sexual infantil es una experiencia vital compleja que se asocia a consecuencias severas. Sería recomendable elaborar programas de prevención y detección precoz, aumentando las campañas de sensibilización y replicando ensayos longitudinales y prospectivos que contribuyan a ampliar el conocimiento sobre sus consecuencias

Lipidomics Reveals Reduced Inflammatory Lipid Species and Storage Lipids after Switching from EFV/FTC/TDF to RPV/FTC/TDF: A Randomized Open-Label Trial

HIV and antiretroviral therapy affect lipid metabolism. Lipidomics quantifies several individual species that are overlooked using conventional biochemical analyses, outperforming traditional risk equations. We aimed to compare the plasma lipidomic profile of HIV patients taking efavirenz (EFV) or rilpivirine (RPV). Patients >/= 18 years old on EFV co-formulated with emtricitabine and tenofovir disoproxil fumarate (FTC/TDF) with HIV-RNA /=6 months were randomized to continue EFV/FTC/TDF (n = 14) or switch to RPV/FTC/TDF (n =15). Lipidomic analyses conducted by mass spectrometry (MS) were performed at baseline and after 12 and 24 weeks. OWLiver((R)) Care and OWLiver((R)) tests were performed to estimate the presence of fatty liver disease (NAFLD). No significant differences (83% male, median age 44 years, 6 years receiving EFV/FTC/TDF, CD4(+) count 740 cells/mm(3), TC 207 [57 HDL-C/133 LDL-C] mg/dL, TG 117 mg/dL) were observed between the groups at baseline. Significant reductions in plasma lipids and lipoproteins but increased circulating bilirubin concentrations were observed in patients who switched to RPV/FTC/TDF. Patients on RPV/FTC/TDF showed a decrease in the global amount of storage lipids (-0.137 log2 [fold-change] EFV vs. 0.059 log2 [fold-change] RPV) but an increase in lysophosphatidylcholines (LPCs) and total steroids. Compared with EFV, RPV increased metabolites with anti-inflammatory properties and reduced the repository of specific lipotoxic lipids

DBP rs7041 and DHCR7 rs3829251 are Linked to CD4+ Recovery in HIV Patients on Antiretroviral Therapy

Background: The lack of the recovery of CD4+ T-cells (CD4+ recovery) among immunodeficiency virus (HIV)-infected patients on antiretroviral therapy (ART) is not well known. We aimed to analyze the association between single nucleotide polymorphisms (SNPs) underlying vitamin D metabolism and the CD4+ recovery in naïve HIV-infected patients who started ART with low baseline CD4+. Methods: We conducted a retrospective study in 411 naïve individuals with plasma HIV load >200 copies/mL and CD4+ <200 cells/mm3. During 24 months of follow-up, all patients had plasma HIV load <50 copies/mL. DNA genotyping was performed using the Sequenom MassARRAY platform. The outcome variable was the change in CD4+ during the study. Results: CD4+ recovery was higher in patients carrying DBP rs7041 AA genotype (AA versus CC/AC) and DHCR7 rs3829251 AA genotype (AA versus GG/AG) (p-value < 0.05). DBP rs7041 AA genotype was linked to increase in CD4+ (adjusted arithmetic mean ratio (aAMR) = 1.22; q-value = 0.011), increase in CD4+ ≥P75th [adjusted odds ratio (aOR) = 2.31; q-value = 0.005], slope of CD4+ recovery (aAMR = 1.25; q-value = 0.008), slope of CD4+ recovery ≥ P75th (aOR = 2.55; q-value = 0.005) and achievement of CD4+ ≥500 cells/mm3 (aOR = 1.89; q-value = 0.023). Besides, DHCR7 rs3829251 AA genotype was related to increase in CD4+ (aAMR = 1.43; q-value = 0.031), increase in CD4+ ≥P75th (aOR = 3.92; q-value = 0.030), slope of CD4+ recovery (aAMR = 1.40; q-value = 0.036), slope of CD4+ recovery ≥ P75th (aOR = 3.42; q-value = 0.031) and achievement of CD4+ ≥500 cells/mm3 (aOR = 5.68; q-value = 0.015). Conclusion: In summary, DHCR7 rs3829251 and DBP rs7041 polymorphisms were associated with CD4+ recovery in HIV-infected patients who started cART with low CD4+ T-cell counts.This study has been (partially) funded by grants from Instituto de Salud Carlos III (RD16/0025/0013 to JMB and RD16CIII/0002/0002 to SR) as part of the Health Research and Development Strategy, State Plan for Scientific and Technical Research and Innovation (2008–2011; 2013–2016) and co-financed by Institute of Health Carlos III, ISCIII – Sub-Directorate General for Research Assessment and Promotion and European Regional Development Fund (ERDF). The study was also funded by the Centro de Investigación Biomédica en Red (CIBER) de Enfermedades Infecciosas (CB21/13/00044, CB21/13/00020, and CB21/13/00063). MAJ-S is supported and funded by ISCIII (grant number CP17CIII/00007). NR is a Miguel Servet researcher from the ISCIII (grant number CPII19/00025).S