Solving the brachistochrone and other variational problems with soap films

We show a method to solve the problem of the brachistochrone as well as other variational problems with the help of the soap films that are formed between two suitable surfaces. We also show the interesting connection between some variational problems of dynamics, statics, optics, and elasticity.Comment: 16 pages, 11 figures. This article, except for a small correction, has been submitted to the American Journal of Physic

BRCA2 polymorphic stop codon K3326X and the risk of breast, prostate, and ovarian cancers

Background: The K3326X variant in BRCA2 (BRCA2*c.9976A>T; p.Lys3326*; rs11571833) has been found to be associated with small increased risks of breast cancer. However, it is not clear to what extent linkage disequilibrium with fully pathogenic mutations might account for this association. There is scant information about the effect of K3326X in other hormone-related cancers. Methods: Using weighted logistic regression, we analyzed data from the large iCOGS study including 76 637 cancer case patients and 83 796 control patients to estimate odds ratios (ORw) and 95% confidence intervals (CIs) for K3326X variant carriers in relation to breast, ovarian, and prostate cancer risks, with weights defined as probability of not having a pathogenic BRCA2 variant. Using Cox proportional hazards modeling, we also examined the associations of K3326X with breast and ovarian cancer risks among 7183 BRCA1 variant carriers. All statistical tests were two-sided. Results: The K3326X variant was associated with breast (ORw = 1.28, 95% CI = 1.17 to 1.40, P = 5.9x10- 6) and invasive ovarian cancer (ORw = 1.26, 95% CI = 1.10 to 1.43, P = 3.8x10-3). These associations were stronger for serous ovarian cancer and for estrogen receptor–negative breast cancer (ORw = 1.46, 95% CI = 1.2 to 1.70, P = 3.4x10-5 and ORw = 1.50, 95% CI = 1.28 to 1.76, P = 4.1x10-5, respectively). For BRCA1 mutation carriers, there was a statistically significant inverse association of the K3326X variant with risk of ovarian cancer (HR = 0.43, 95% CI = 0.22 to 0.84, P = .013) but no association with breast cancer. No association with prostate cancer was observed. Conclusions: Our study provides evidence that the K3326X variant is associated with risk of developing breast and ovarian cancers independent of other pathogenic variants in BRCA2. Further studies are needed to determine the biological mechanism of action responsible for these associations

Diagnostic Value of Lumbar Facet Joint Injection: A Prospective Triple Cross-Over Study

The diagnosis “lumbar facet syndrome” is common and often indicates severe lumbar spine surgery procedures. It is doubtful whether a painful facet joint (FJ) can be identified by a single FJ block. The aim of this study was to clarify the validity of a single and placebo controlled bilateral FJ blocks using local anesthetics. A prospective single blinded triple cross-over study was performed. 60 patients (31 f, 29 m, mean age 53.2 yrs (22–73)) with chronic low back pain (mean pain persistance 31 months, 6 months of conservative treatment without success) admitted to a local orthopaedic department for surgical or conservative therapy of chronic LBP, were included in the study. Effect on pain reduction (10 point rating scale) was measured. The 60 subjects were divided into six groups with three defined sequences of fluoroscopically guided bilateral monosegmental lumbar FJ test injections in “oblique needle” technique: verum-(local anaesthetic-), placebo-(sodium chloride-) and sham-injection. Carry-over and periodic effects were evaluated and a descriptive and statistical analysis regarding the effectiveness, difference and equality of the FJ injections and the different responses was performed. The results show a high rate of non-response, which documents the lack of reliable and valid predictors for a positive response towards FJ blocks. There was a high rate of placebo reactions noted, including subjects who previously or later reacted positively to verum injections. Equivalence was shown among verum vs. placebo and partly vs. sham also. With regard to test validity criteria, a single intraarticular FJ block with local anesthetics is not useful to detect the pain-responsible FJ and therefore is no valid and reliable diagostic tool to specify indication of lumbar spine surgery. Comparative FJ blocks with local anesthetics and placebo-controls have to be interpretated carefully also, because they solely give no proper diagnosis on FJ being main pain generator

Autobiographical memory in multiple sclerosis patients: Assessment and cognitive facilitation

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