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

Stellar-to-halo mass relation of cluster galaxies

In the hierarchical formation model, galaxy clusters grow by accretion of smaller groups or isolated galaxies. During the infall into the centre of a cluster, the properties of accreted galaxies change. In particular, both observations and numerical simulations suggest that its dark matter halo is stripped by the tidal forces of the host. We use galaxy-galaxy weak lensing to measure the average mass of dark matter haloes of satellite galaxies as a function of projected distance to the centre of the host, for different stellar mass bins. Assuming that the stellar component of the galaxy is less disrupted by tidal stripping, stellar mass can be used as a proxy of the infall mass. We study the stellar to halo mass relation of satellites as a function of the cluster-centric distance to measure tidal stripping. We use the shear catalogues of the DES science verification archive, the CFHTLenS and the CFHT Stripe 82 (CS82) surveys, and we select satellites from the redMaPPer catalogue of clusters. For galaxies located in the outskirts of clusters, we find a stellar to halo mass relation in good agreement with the theoretical expectations from \citet{moster2013} for central galaxies. In the centre of the cluster, we find that this relation is shifted to smaller halo mass for a given stellar mass. We interpret this finding as further evidence for tidal stripping of dark matter haloes in high density environments.Comment: 15 pages, 14 figure

The continuity of the inversion and the structure of maximal subgroups in countably compact topological semigroups

In this paper we search for conditions on a countably compact (pseudo-compact) topological semigroup under which: (i) each maximal subgroup $H(e)$ in $S$ is a (closed) topological subgroup in $S$; (ii) the Clifford part $H(S)$(i.e. the union of all maximal subgroups) of the semigroup $S$ is a closed subset in $S$; (iii) the inversion $\operatorname{inv}\colon H(S)\to H(S)$ is continuous; and (iv) the projection $\pi\colon H(S)\to E(S)$, $\pi\colon x\longmapsto xx^{-1}$, onto the subset of idempotents $E(S)$ of $S$, is continuous

Drinking Water Salinity and Raised Blood Pressure: Evidence from a Cohort Study in Coastal Bangladesh.

BACKGROUND: Millions of coastal inhabitants in Southeast Asia have been experiencing increasing sodium concentrations in their drinking-water sources, likely partially due to climate change. High (dietary) sodium intake has convincingly been proven to increase risk of hypertension; it remains unknown, however, whether consumption of sodium in drinking water could have similar effects on health. OBJECTIVES: We present the results of a cohort study in which we assessed the effects of drinking-water sodium (DWS) on blood pressure (BP) in coastal populations in Bangladesh. METHODS: DWS, BP, and information on personal, lifestyle, and environmental factors were collected from 581 participants. We used generalized linear latent and mixed methods to model the effects of DWS on BP and assessed the associations between changes in DWS and BP when participants experienced changing sodium levels in water, switched from "conventional" ponds or tube wells to alternatives [managed aquifer recharge (MAR) and rainwater harvesting] that aimed to reduce sodium levels, or experienced a combination of these changes. RESULTS: DWS concentrations were highly associated with BP after adjustments for confounding factors. Furthermore, for each 100 mg/L reduction in sodium in drinking water, systolic/diastolic BP was lower on average by 0.95/0.57 mmHg, and odds of hypertension were lower by 14%. However, MAR did not consistently lower sodium levels. CONCLUSIONS: DWS is an important source of daily sodium intake in salinity-affected areas and is a risk factor for hypertension. Considering the likely increasing trend in coastal salinity, prompt action is required. Because MAR showed variable effects, alternative technologies for providing reliable, safe, low-sodium fresh water should be developed alongside improvements in MAR and evaluated in "real-life" salinity-affected settings. https://doi.org/10.1289/EHP659

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

Lek dynamics and range-wide morphometric patterns of lesser prairie-chickens

Doctor of PhilosophyDivision of BiologyDavid A. HaukosThe lesser prairie-chicken (Tympanuchus pallidicinctus) is a lek-breeding prairie-grouse of the Southern Great Plains. The lesser prairie-chicken range spans four ecoregions with an east-west precipitation gradient and is subject to severe droughts on a 5-10 year cycle. The influence of the range-wide precipitation gradient and severe drought cycle on lesser prairie-chicken morphology is unknown and a range-wide morphometric compilation has never been assembled. The lesser prairie-chicken population booms and busts in response to drought and estimates of population trends are made from counts of displaying males on leks. Despite the conservation importance of leks, there are many untested assumptions about how leks form on the landscape and what factors determine their persistence into subsequent breeding seasons. My dissertation seeks to fill these knowledge gaps, by (1) assembling a range-wide synthesis of lesser prairie-chicken morphometrics data, (2) determining severe weather influences on morphometric traits, (3) test the hotspot hypothesis as an explanation for lek formation, (4) determine factors that influence lek persistence and (5) evaluate lek formation and persistence findings in translocated population that has no existing lek complex. I assembled a range-wide data set of (n = 2,048) lesser prairie-chicken morphometrics from the period of 1986 to 2019 and compared among ecoregions and weather conditions based on the Palmer Drought Severity Index. Lesser prairie-chicken morphometric traits are largest in the Short-Grass and Sand Shinnery Oak Prairies and smaller in in the Mixed-Grass and Sand Sagebrush Prairies. Morphometric changes following years of extreme weather are universal across ecoregions, where adult female traits remain unaffected and male sexually selected traits increase in size after extreme weather. Incredibly, lesser prairie-chicken body fat during spring lekking is tightly constrained by sex with males exhibiting 2-3% body fat, whereas females exhibited 4-8% across all weather conditions. I tested the hotspot hypothesis, which posits that leks should form in areas where males are most likely to encounter females, and anthropogenic and female movement data as determinants of lek persistence in the Short-Grass Prairie/CRP Mosaic and Mixed-Grass Prairie ecoregions of Kansas with 143 GSP-backpacked females from 2013-2016 and 53 individual leks. As a lek-breeding species, lesser prairie-chicken females are solely responsible for incubating their nest and raising broods, which creates a sexually driven difference in space and habitat use that is reflected in both the formation and persistence of leks on the landscape. I found that lesser prairie-chicken lek dynamics are driven by female habitat constraints, where increased female space use and number of nest sites starting at a 5 km scale (F₅,₇₈ = 2.50, P = 0.04) determines the number of males displaying at leks and concentrations of female spatial use determines where new leks form on the landscape. I then compared patterns of established lek complexes to the dynamics of lek formation and persistence in the translocation of lesser prairie-chickens (n = 411) to the Sand Sagebrush Prairie Ecoregion in 2016-2019. The formation and persistence of leks by translocated birds is also driven by female space utilization, where the location of newly formed leks comprised of translocated birds can be explained by female nesting attempts and space use and the persistence and stability of translocation leks can be explained by multiyear nesting efforts by females starting at a 5 km buffer (F₄,₂₁ = 6.57, P = 0.01). My research offers an explanation for the spatial-temporal dynamics of lek formation and persistence on the landscape and provides means to use morphometrics to evaluate weather stressors and resource allocation in lesser prairie-chickens