Adaptive Refinements in BEM

Accuracy estimates and adaptive refinements is nowadays one of the main research topics in finite element computations [6,7,8, 9,11].Its extension to Boundary Elements has been tried as a means to better understand its capabilities as well as to impro ve its efficiency and its obvious advantages. The possibility of implementing adaptive techniques was shown [1,2] for h-conver gence and p-convergence respectively. Some posterior works [3,4 5,10] have shown the promising results that can be expected from those techniques. The main difficulty is associated to the reasonable establishment of “estimation” and “indication” factors related to the global and local errors in each refinement. Although some global measures have been used it is clear that the reduction in dimension intrinsic to boundary elements (3D→2D: 2D→1D) could allow a direct comparison among residuals using the graphic possibilities of modern computers and allowing a point-to-point comparison in place of the classical global approaches. Nevertheless an indicator generalizing the well known Peano’s one has been produced

Molecular analysis of the vaginal response to estrogens in the ovariectomized rat and postmenopausal woman

<p>Abstract</p> <p>Background</p> <p>Vaginal atrophy (VA) is the thinning of the vaginal epithelial lining, typically the result of lowered estrogen levels during menopause. Some of the consequences of VA include increased susceptibility to bacterial infection, pain during sexual intercourse, and vaginal burning or itching. Although estrogen treatment is highly effective, alternative therapies are also desired for women who are not candidates for post-menopausal hormone therapy (HT). The ovariectomized (OVX) rat is widely accepted as an appropriate animal model for many estrogen-dependent responses in humans; however, since reproductive biology can vary significantly between mammalian systems, this study examined how well the OVX rat recapitulates human biology.</p> <p>Methods</p> <p>We analyzed 19 vaginal biopsies from human subjects pre and post 3-month 17β-estradiol treated by expression profiling. Data were compared to transcriptional profiling generated from vaginal samples obtained from ovariectomized rats treated with 17β-estradiol for 6 hrs, 3 days or 5 days. The level of differential expression between pre- vs. post- estrogen treatment was calculated for each of the human and OVX rat datasets. Probe sets corresponding to orthologous rat and human genes were mapped to each other using NCBI Homologene.</p> <p>Results</p> <p>A positive correlation was observed between the rat and human responses to estrogen. Genes belonging to several biological pathways and GO categories were similarly differentially expressed in rat and human. A large number of the coordinately regulated biological processes are already known to be involved in human VA, such as inflammation, epithelial development, and EGF pathway activation.</p> <p>Conclusion</p> <p>At the transcriptional level, there is evidence of significant overlap of the effects of estrogen treatment between the OVX rat and human VA samples.</p

The Mechanization of Mathematics

Summary. The mechanization of mathematics refers to the use of computers to find, or to help find, mathematical proofs. Turing showed that a complete reduction of mathematics to computation is not possible, but nevertheless the art and science of automated deduction has made progress. This paper describes some of the history and surveys the state of the art.