An approach for robust PDE-constrained optimization with application to shape optimization of electrical engines and of dynamic elastic structures under uncertainty

We present a robust optimization framework that is applicable to general nonlinear programs (NLP) with uncertain parameters. We focus on design problems with partial differential equations (PDE), which involve high computational cost. Our framework addresses the uncertainty with a deterministic worst-case approach. Since the resulting min–max problem is computationally intractable, we propose an approximate robust formulation that employs quadratic models of the involved functions that can be handled efficiently with standard NLP solvers. We outline numerical methods to build the quadratic models, compute their derivatives, and deal with high-dimensional uncertainties. We apply the presented approach to the parametrized shape optimization of systems that are governed by different kinds of PDE and present numerical results.     

Surface energy-mediated fibronectin adsorption and osteoblast responses on nanostructured diamond

Nanostructured diamond have potential applications in many biomedical related fields and demonstrated extraordinary capacity to influence cellular responses. Studying the surface property of nanodiamond and its influence to protein adsorption and subsequent cellular responses along with the mechanism behind such capacity becomes more important. Here the role of surface energy associated with nanostructured diamond in modulating fibronectin and osteoblast(OB, bone forming cells) responses was investigated. Nanocrystalline diamond(NCD) and submicron crystalline diamond(SMCD) films with controllable surface energy were prepared by microwave-enhanced plasma chemical vapor deposition(MPCVD) techniques. Fibronectin adsorption on the diamond films with varied surface energy values was measured via the enzyme-linked immunosorbent assay(ELISA) and the relationship between the surface energy and fibronectin adsorption was studied. The result indicated that fibronectin adsorption on nanostructured surfaces was closely related to both surface energy and material microstructures. The spreading and migration of OB aggregates(each containing 30–50 cells) on the NCD with varied surface energy values were also studied. The result indicates a correlation between the cell spreading and migration on nanodiamond and the surface energy of nanostructured surface.     

Psychosexual development of women with congenital adrenal hyperplasia

Women with congenital adrenal hyperplasia (CAH) (N = 31) and their unaffected sisters or female cousins (N = 15) participated in a study of psychosexual development. All participants were > or = 18 years of age (mean age, 25 years; range, 18-40). Comparisons were also made between the CAH women with the salt-wasting (SW) form of the disorder and those with simple virilization (SV). A psychosexual assessment protocol examined six variables: (1) sex assignment at birth (probands only); (2) recalled sex-typed behavior during childhood; (3) gender identity and gender role identification in adulthood; (4) relationship status; (5) sexual orientation in fantasy; and (6) sexual orientation in behavior. Salt-wasting status and sex assignment at birth were also ascertained for the CAH women who either refused to participate in the study (N = 10) or could not be traced (N = 13). Compared to the controls, the women with CAH recalled more cross-gender role behavior and less comfort with their sense of "femininity" during childhood. The two groups did not differ in degree of gender dysphoria in adulthood, although the probands showed more cross-gender role identification. Three of the nonparticipant probands were living, as adults, in the male social role (2 reared from birth as boys and 1 who changed from the female to the male social role during adolescence). The CAH women and the controls did not differ in relationship status (married/cohabiting vs. single). The CAH women had lower rates of exclusive heterosexual fantasy and fewer sexual experiences with men than the controls; however, the CAH women did not have more sexual experiences with women than the controls. Comparisons between the SW and SV revealed several differences: the SW were less likely to be assigned to the female sex at birth, recalled more cross-gender role behavior during childhood, were less likely to be married or cohabiting, and had lower rates of sexual experiences with men. The results were discussed in relation to the effects of prenatal androgens on psychosexual differentiation.     

Branching and circular features in high dimensional data

Large observations and simulations in scientific research give rise to high-dimensional data sets that present many challenges and opportunities in data analysis and visualization. Researchers in application domains such as engineering, computational biology, climate study, imaging and motion capture are faced with the problem of how to discover compact representations of high-dimensional data while preserving their intrinsic structure. In many applications, the original data is projected onto low-dimensional space via dimensionality reduction techniques prior to modeling. One problem with this approach is that the projection step in the process can fail to preserve structure in the data that is only apparent in high dimensions. Conversely, such techniques may create structural illusions in the projection, implying structure not present in the original high-dimensional data. Our solution is to utilize topological techniques to recover important structures in high-dimensional data that contains non-trivial topology. Specifically, we are interested in high-dimensional branching structures. We construct local circle-valued coordinate functions to represent such features. Subsequently, we perform dimensionality reduction on the data while ensuring such structures are visually preserved. Additionally, we study the effects of global circular structures on visualizations. Our results reveal never-before-seen structures on real-world data sets from a variety of applications.