An ODE Model of the Motion of Pelagic Fish

A system of ordinary differential equations (ODEs) is derived from a discrete system of Vicsek, Czirók et al. [Phys. Rev. Lett. 75(6):1226–1229, 1995], describing the motion of a school of fish. Classes of linear and stationary solutions of the ODEs are found and their stability explored using equivariant bifurcation theory. The existence of periodic and toroidal solutions is also proven under deterministic perturbations and structurally stable heteroclinic connections are found. Applications of the model to the migration of the capelin, a pelagic fish that undertakes an extensive migration in the North Atlantic, are discussed and simulation of the ODEs presented.     

Future teachers’ professional knowledge on argumentation and proof: a case study from universities in three countries

In this paper, qualitative results of a case study about the professional knowledge in the area of argumentation and proof of future teachers from universities in three countries are described. Based on results of open questionnaires, data about the competencies these future teachers have in the areas of mathematical knowledge and knowledge of mathematics pedagogy are presented. The study shows that the majority of the future teachers at the participating universities situated in Germany, Hong Kong and Australia, were not able to execute formal proofs, requiring only lower secondary mathematical content, in an adequate and mathematically correct way. In contrast, in all samples there was evidence of at least average competencies of pedagogical content reflection about formal and pre-formal proving in mathematics teaching. However, it appears that possessing a mathematical background as mandated for teaching and having a high affinity with proving in mathematics teaching at the lower secondary level are not a sufficient preparation for teaching proof.     

Selective pressurized liquid extraction of polychlorinated biphenyls in sediment.

A selective pressurized liquid extraction procedure (SPLE) was developed for a fast determination of polychlorinated biphenyls in sediment. The final method was performed at 100 degrees C with heptane/dichloromethane (90:10, v/v) as extraction solvent for 2x5 min. Sulfuric acid impregnated silica was placed downstream of the sample in the extraction cell to remove interfering components. This simultaneous extraction/clean-up was performed in 20 min, with an average congener recovery of 92% compared to a classical 24 h Soxhlet methodology and 2 h of external manual clean-up.     

ADLOC: An Aptamer‐Displacement Assay Based on Luminescent Oxygen Channeling

Functional nucleic acids, such as aptamers and allosteric ribozymes, can sense their ligands specifically, thereby undergoing structural alterations that can be converted into a detectable signal. The direct coupling of molecular recognition to signal generation enables the production of versatile reporters that can be applied as molecular probes for various purposes, including high‐throughput screening. Here we describe an unprecedented type of a nucleic acid‐based sensor system and show that it is amenable to high‐throughput screening (HTS) applications. The approach detects the displacement of an aptamer from its bound protein partner by means of luminescent oxygen channeling. In a proof‐of‐principle study we demonstrate that the format is feasible for efficient identification of small drug‐like molecules that bind to a protein target, in this case to the Sec7 domain of cytohesin. We extended the approach to a new cytohesin‐specific single chain DNA aptamer, C10.41, which exhibits a similar binding behavior to cytohesins but has the advantage of being more stable and easier to synthesize and to modify than the RNA‐aptamer M69. The results obtained with both aptamers indicate the general suitability of the aptamer‐displacement assay based on luminescent oxygen channelling (ADLOC) for HTS. We also analyzed the potential for false positive hits and identified from a library of 18 000 drug‐like small molecules two compounds as strong singlet‐oxygen quenchers. With full automation and the use of commercially available plate readers, we estimate that the ADLOC‐based assay described here could be used to screen at least 100 000 compounds per day.     

Charge transport in columnar mesophases of carbazole macrocycles

Charge transport properties of a columnar mesophase of carbazole macrocycles are analyzed. Realistic morphologies are sampled using all-atom molecular dynamics simulations while charge transport is simulated using the kinetic Monte Carlo method with transfer rates obtained from the high temperature nonadiabatic limit of Marcus theory. It is shown that the molecular design with side chains pointing inside the macrocycle allows close approach between molecules of neighboring columns, thus enabling three-dimensional transport and helping to circumvent charge trapping on structural defects.