Learning with classroom videos: conception and first results of an online teacher-training program

Within the framework of a yearlong teacher education program we examined the conditions and effectiveness of learning with classroom videos. In online phases and face-to-face sessions (blended learning), 20 teachers from two different countries. (Germany and Switzerland) analyzed videos of their own mathlessons and math-lessons of other teachers. Using different instruments, the training program was evaluated from a scientific perspective. The evaluation aimed to obtain information about processes within the training, about the acceptance of the training by the teachers and the patterns of perception of teaching processes of the teachers.     

Folding of the Tau Protein on Microtubules

Microtubules are regulated by microtubule‐associated proteins. However, little is known about the structure of microtubule‐associated proteins in complex with microtubules. Herein we show that the microtubule‐associated protein Tau, which is intrinsically disordered in solution, locally folds into a stable structure upon binding to microtubules. While Tau is highly flexible in solution and adopts a β‐sheet structure in amyloid fibrils, in complex with microtubules the conserved hexapeptides at the beginning of the Tau repeats two and three convert into a hairpin conformation. Thus, binding to microtubules stabilizes a unique conformation in Tau.     

Petersen Cores and the Oddness of Cubic Graphs

Let G be a bridgeless cubic graph. Consider a list of k 1‐factors of G. Let be the set of edges contained in precisely i members of the k 1‐factors. Let be the smallest over all lists of k 1‐factors of G. We study lists by three 1‐factors, and call with a ‐core of G. If G is not 3‐edge‐colorable, then . In Steffen (J Graph Theory 78 (2015), 195–206) it is shown that if , then is an upper bound for the girth of G. We show that bounds the oddness of G as well. We prove that . If , then every ‐core has a very specific structure. We call these cores Petersen cores. We show that for any given oddness there is a cyclically 4‐edge‐connected cubic graph G with . On the other hand, the difference between and can be arbitrarily big. This is true even if we additionally fix the oddness. Furthermore, for every integer , there exists a bridgeless cubic graph G such that .     

Nowhere‐Zero 5‐Flows On Cubic Graphs with Oddness 4

Tutte's 5‐flow conjecture from 1954 states that every bridgeless graph has a nowhere‐zero 5‐flow. It suffices to prove the conjecture for cyclically 6‐edge‐connected cubic graphs. We prove that every cyclically 6‐edge‐connected cubic graph with oddness at most 4 has a nowhere‐zero 5‐flow. This implies that every minimum counterexample to the 5‐flow conjecture has oddness at least 6.     

Structural impact of proline-directed pseudophosphorylation at AT8, AT100, and PHF1 epitopes on 441-residue tau

The intrinsically disordered protein tau becomes excessively phosphorylated and aggregates into neurofibrillary tangles in Alzheimer's disease. To obtain insight into the structural consequences of phosphorylation, we characterized a mutant protein of tau in which epitopes recognized by Alzheimer diagnostic antibodies were mimicked by mutation to glutamic acid [AT8 (S199E, S202E, T205E), AT100 (T212E and S214E), and PHF1 (S396E and S404E)]. A large number of distance restraints obtained from NMR paramagnetic relaxation enhancement in combination with ensemble conformer calculations demonstrate that pseudophosphorylation causes an opening of the transient folding of tau. Together with previous studies on the Parkinson-related protein α-synuclein, our data indicate that networks of transient long-range interactions are common properties of intrinsically disordered proteins and that their modulation is important for aggregation.     

Ab initio virial equation of state for argon using a new nonadditive three-body potential

An ab initio nonadditive three-body potential for argon has been developed using quantum-chemical calculations at the CCSD(T) and CCSDT levels of theory. Applying this potential together with a recent ab initio pair potential from the literature, the third and fourth to seventh pressure virial coefficients of argon were computed by standard numerical integration and the Mayer-sampling Monte Carlo method, respectively, for a wide temperature range. All calculated virial coefficients were fitted separately as polynomials in temperature. The results for the third virial coefficient agree with values evaluated directly from experimental data and with those computed for other nonadditive three-body potentials. We also redetermined the second and third virial coefficients from the best experimental pρT data utilizing the computed higher virial coefficients as constraints. Thus, a significantly closer agreement of the calculated third virial coefficients with the experimental data was achieved. For different orders of the virial expansion, pρT data have been calculated and compared with results from high quality measurements in the gaseous and supercritical region. The theoretically predicted pressures are within the very small experimental errors of ±0.02% for p ≤ 12 MPa in the supercritical region near room temperature, whereas for subcritical temperatures the deviations increase up to +0.3%. The computed pressure at the critical density and temperature is about 1.3% below the experimental value. At pressures between 200 MPa and 1000 MPa and at 373 K, the calculated values deviate by 1% to 9% from the experimental results.