Adsorption und phase equilibria: completely without diffusion?

In this work, we will present experimental and theoretical results concerning adsorption und phase equilibria being influenced by kinetic effects

Continuation Sheaves in Dynamics: Sheaf Cohomology and Bifurcation

Continuation of algebraic structures in families of dynamical systems is described using category theory, sheaves, and lattice algebras. Well-known concepts in dynamics, such as attractors or invariant sets, are formulated as functors on appropriate categories of dynamical systems mapping to categories of lattices, posets, rings or abelian groups. Sheaves are constructed from such functors, which encode data about the continuation of structure as system parameters vary. Similarly, morphisms for the sheaves in question arise from natural transformations. This framework is applied to a variety of lattice algebras and ring structures associated to dynamical systems, whose algebraic properties carry over to their respective sheaves. Furthermore, the cohomology of these sheaves are algebraic invariants which contain information about bifurcations of the parametrized systems

Varicella vaccination coverage of children under two years of age in Germany

Background: Since July 2004, routine varicella vaccination is recommended by the German Standing Vaccination Committee in Germany. Health Insurance Funds started to cover vaccination costs at different time points between 2004 and 2006 in the Federal States. Nationwide representative data on vaccination coverage against varicella of children under two years of age are not available. We aimed to determine varicella vaccination coverage in statutory health insured children under two years of age in twelve German Federal States using data from associations of statutory health insurance physicians (ASHIPs), in order to investigate the acceptance of the recommended routine varicella vaccination programme. Methods: We analysed data on varicella vaccination from 13 of 17 ASHIPs of the years 2004 to 2007. The study population consisted of all statutory health insured children under two years of age born in 2004 (cohort 2004) or 2005 (cohort 2005) in one of the studied regions. Vaccination coverage was determined by the number of children vaccinated under 2 years of age within the study population. Results: Varicella vaccination coverage of children under two years of age with either one dose of the monovalent varicella vaccine or two doses of the measles, mumps, rubella, and varicella vaccine increased from 34% (cohort 2004) to 51% (cohort 2005) in the studied regions (p < 0.001). More than half of the vaccinated children of cohort 2004 and two third of cohort 2005 were immunised at the recommended age 11 to 14 months. The level of vaccination coverage of cohort 2004 was significantly associated with the delay in introduction of cost coverage since the recommendation of varicella vaccination (p < 0.001). Conclusions: Our study shows increasing varicella vaccination coverage of young children, indicating a growing acceptance of the routine varicella vaccination programme by the parents and physicians. We recommend further monitoring of vaccination coverage using data from ASHIPs to investigate acceptance of the routine vaccination programmes over time

CD14 and ALPK1 Affect Expression of Tight Junction Components and Proinflammatory Mediators upon Bacterial Stimulation in a Colonic 3D Organoid Model

Cd14 and Alpk1 both encode pathogen recognition receptors and are known candidate genes for affecting severity in inflammatory bowel diseases. CD14 acts as a coreceptor for bacterial lipopolysaccharide (LPS), while ALPK1 senses ADP-D-glycero-beta-D-manno-heptose, a metabolic intermediate of LPS biosynthesis. Intestinal barrier integrity can be influenced by CD14, whereas to date, the role of ALPK1 in maintaining barrier function remains unknown. We used colon-derived 3D organoids, first characterised for growth, proliferation, stem cell markers, and expression of tight junction (TJ) components using qPCR and immunohistochemistry. They showed characteristic crypt stem cells, apical shedding of dead cells, and TJ formation. Afterwards, organoids of different genotypes (WT, Il10-/-, Cd14-/-, and Alpk1-/-) were then stimulated with either LPS or Escherichia coli Nissle 1917 (EcN). Gene expression and protein levels of cytokines and TJ components were analysed. WT organoids increased expression of Tnfα and tight junction components. Cd14-/- organoids expressed significantly less Tnfα and Ocln after LPS stimulation than WT organoids but reacted similarly to WT organoids after EcN stimulation. In contrast, compared to WT, Alpk1-/- organoids showed decreased expression of different TJ and cytokine genes in response to EcN but not LPS. However, Western blotting revealed an effect of ALPK1 on TJ protein levels. These findings demonstrate that Cd14, but not Alpk1, alters the response to LPS stimulation in colonic epithelial cells, whereas Alpk1 is involved in the response upon bacterial challenge. © 2020 Pascal Brooks et al

One-dimensional symmetry and Liouville type results for the fourth order Allen-Cahn equation in RN^N

In this paper, we prove an analogue of Gibbons' conjecture for the extended fourth order Allen-Cahn equation in R N , as well as Liouville type results for some solutions converging to the same value at infinity in a given direction. We also prove a priori bounds and further one-dimensional symmetry and rigidity results for semilinear fourth order elliptic equations with more general nonlinearities

Computational approach for complete Lyapunov functions

Ordinary differential equations arise in a variety of applications, including climate modeling, electronics, predator-prey modeling, etc., and they can exhibit highly complicated dynamical behaviour. Complete Lyapunov functions capture this behaviour by dividing the phase space into two disjoint sets: the chain-recurrent part and the transient part. If a complete Lyapunov function is known for a dynamical system the qualitative behaviour of the system’s solutions is transparent to a large degree. The computation of a complete Lyapunov function for a given system is, however, a very hard task. We present significant improvements of an algorithm recently suggested by the authors to compute complete Lyapunov functions. Previously this methodology was incapable to fully detect chain-recurrent sets in dynamical systems with high differences in speed. In the new approach we replace the system under consideration with another one having the same solution trajectories but such that they are traversed at a more uniform speed. The qualitative properties of the new system such as attractors and repellers are the same as for the original one. This approach gives a better approximation to the chain-recurrent set of the system under study

Computation of Lyapunov functions for systems with multiple attractors

We present a novel method to compute Lyapunov functions for continuous-time systems with multiple local attractors. In the proposed method one first computes an outer approximation of the local attractors using a graphtheoretic approach. Then a candidate Lyapunov function is computed using a Massera-like construction adapted to multiple local attractors. In the final step this candidate Lyapunov function is interpolated over the simplices of a simplicial complex and, by checking certain inequalities at the vertices of the complex, we can identify the region in which the Lyapunov function is decreasing along system trajectories. The resulting Lyapunov function gives information on the qualitative behavior of the dynamics, including lower bounds on the basins of attraction of the individual local attractors. We develop the theory in detail and present numerical examples demonstrating the applicability of our method