A note on multi-dimensional Camassa-Holm type systems on the torus

We present a $2n$-component nonlinear evolutionary PDE which includes the $n$-dimensional versions of the Camassa-Holm and the Hunter-Saxton systems as well as their partially averaged variations. Our goal is to apply Arnold's [V.I. Arnold, Sur la g\'eom\'etrie diff\'erentielle des groupes de Lie de dimension infinie et ses applications \`a l'hydrodynamique des fluides parfaits. Ann. Inst. Fourier (Grenoble) 16 (1966) 319-361], [D.G. Ebin and J.E. Marsden, Groups of diffeomorphisms and the motion of an incompressible fluid. Ann. of Math. 92(2) (1970) 102-163] geometric formalism to this general equation in order to obtain results on well-posedness, conservation laws or stability of its solutions. Following the line of arguments of the paper [M. Kohlmann, The two-dimensional periodic $b$-equation on the diffeomorphism group of the torus. J. Phys. A.: Math. Theor. 44 (2011) 465205 (17 pp.)] we present geometric aspects of a two-dimensional periodic $\mu$-$b$-equation on the diffeomorphism group of the torus in this context.Comment: 14 page

Cholesterol, C-Reactive Protein, and Periodontitis: HMG-CoA-Reductase Inhibitors (Statins) as Effect Modifiers

Common risk factors of periodontitis and cardiovascular diseases fuel the debate on interrelationships between them. The aim is to prove whether statins may influence periodontal parameters by affecting either of these factors. Out of the 4,290 subjects of SHIP (Study of Health in Pomerania), we included subjects aged >30 years (219 with statins, 2937 without) and excluded edentulous. We determined periodontal measures, cholesterol fractions, and inflammation markers. Statin use and periodontal risk factors were assessed. Gingival plaque and periodontal attachment loss were associated with systemic LDL cholesterol (P < 0.001) and C-reactive protein CRP (P = 0.019) revealing interaction with statin use. When adjusted for age, sex, smoking, diabetes, education, and dental service, statins were identified as effect modifiers abolishing the relationship between attachment loss and LDL and between gingival plaque and LDL (interactions P < 0.001). No statin-related interaction was detected with increase in CRP. The interaction supports the view of inter-relationships between periodontal and systemic inflammatory mediators

The curvature of semidirect product groups associated with two-component Hunter-Saxton systems

In this paper, we study two-component versions of the periodic Hunter-Saxton equation and its $\mu$-variant. Considering both equations as a geodesic flow on the semidirect product of the circle diffeomorphism group \Diff(\S) with a space of scalar functions on $\S$ we show that both equations are locally well-posed. The main result of the paper is that the sectional curvature associated with the 2HS is constant and positive and that 2$\mu$HS allows for a large subspace of positive sectional curvature. The issues of this paper are related to some of the results for 2CH and 2DP presented in [J. Escher, M. Kohlmann, and J. Lenells, J. Geom. Phys. 61 (2011), 436-452].Comment: 19 page

Population differentiation of zander (Sander lucioperca) across native and newly colonized ranges suggests increasing admixture in the course of an invasion

In addition to ecological factors, evolutionary processes can determine the invasion success of a species. In particular, genetic admixture has the potential to induce rapid evolutionary change, which can result from natural or humanassisted secondary contact between differentiated populations. We studied the recent range expansion of zander in Germany focusing on the interplay between invasion and genetic admixture. Historically, the rivers Elbe and Danube harboured the most north-western source populations from which a north-westward range expansion occurred. This was initiated by introducing zander outside its native range into rivers and lakes, and was fostered by migration through artificial canals and stocking from various sources. We analysed zander populations of the native and invaded ranges using nuclear and mitochondrial genetic markers. Three genetic lineages were identified, which were traced to ancestral ranges. Increased genetic diversity and admixture in the invaded region highlighted asymmetric gene flow towards this area. We suppose that the adaptive potential of the invading populations was promoted by genetic admixture, whereas competitive exclusion in the native areas provided a buffer against introgression by novel genotypes. These explanations would be in line with evidence that hybridization can drive evolutionary change under conditions when new niches can be exploited

Nocturnal blood pressure fall as predictor of diabetic nephropathy in hypertensive patients with type 2 diabetes

<p>Abstract</p> <p>Background</p> <p>Hypertensive patients with reduced blood pressure fall (BPF) at night are at higher risk of cardiovascular events (CVE).</p> <p>Methods</p> <p>We evaluated in hypertensive diabetic patients, if a reduced nocturnal BPF can precedes the development of diabetic nephropathy (DN). We followed 70 patients with normal urinary albumin excretion (UAE) for two years. We performed 24-hours ambulatory BP monitoring in baseline and at the end of the study.</p> <p>Results</p> <p>Fourteen (20%) patients (GI) developed DN (N = 11) and/or CVE (n = 4). Compared to the remaining 56 patients (GII) in baseline, GI had similar diurnal systolic (SBP) and diastolic BP (DBP), but higher nocturnal SBP (138 ± 15 vs 129 ± 16 mmHg; p < 0.05) and DBP (83 ± 12 vs 75 ± 11 mmHg; p < 0,05). Basal nocturnal SBP correlated with occurrence of DN and CVE (R = 0.26; P < 0.05) and with UAE at the end of the study (r = 0.3; p < 0.05). Basal BPF (%) correlated with final UAE (r = -0.31; p < 0.05). In patients who developed DN, reductions occurred in nocturnal systolic BPF (12 ± 5 vs 3 ± 6%, p < 0,01) and diastolic BPF (15 ± 8 vs 4 ± 10%, p < 0,01) while no changes were observed in diurnal SBP (153 ± 17 vs 156 ± 16 mmHg, NS) and DBP (91 ± 9 vs 90 ± 7 mmHg, NS). Patients with final UAE < 20 μg/min, had no changes in nocturnal and diurnal BP.</p> <p>Conclusions</p> <p>Our results suggests that elevations in nocturnal BP precedes DN and increases the risk to develop CVE in hypertensive patients with T2DM.</p