Not all simplicial polytopes are weakly vertex-decomposable

In 1980 Provan and Billera defined the notion of weak $k$-decomposability for pure simplicial complexes. They showed the diameter of a weakly $k$-decomposable simplicial complex $\Delta$ is bounded above by a polynomial function of the number of $k$-faces in $\Delta$ and its dimension. For weakly 0-decomposable complexes, this bound is linear in the number of vertices and the dimension. In this paper we exhibit the first examples of non-weakly 0-decomposable simplicial polytopes

Localizable invariants of combinatorial manifolds and Euler characteristic

It is shown that if a real value PL-invariant of closed combinatorial manifolds admits a local formula that depends only on the f-vector of the link of each vertex, then the invariant must be a constant times the Euler characteristic.Comment: 14 pages, 5 figures. Some arguments are improved and one picture is adde

TVET Capacity Development in Afghanistan: Introducing Self-Reliant Internship in In-Service Technical Teacher Training at the Technical Teacher Training Institute (TTTI)

This paper describes the approach applied to the introduction of self-reliant internship into the in-service TVET (Technical Vocational Education and Training) teacher training at the Technical Teacher Training Institute (TTTI) in Afghanistan. As data show in 2014, Afghan TVET teachers neither meet the legal requirements set by the government (Bachelor degree) nor have contacts to or work experiences in private or public sector companies. They have no knowledge of the working requirements they are preparing their students for. Consequently, in-service teacher training at the TTTI has to provide it\u27s learners with knowledge and skills in accordance with the market requirements. Thus, at the TTTI Capacity Building is focusing among others on the multifaceted interdependent relationship between teacher-student-company in order to empower teachers to be able to contribute to the employability of their students. In this respect TTTI\u27s in-service teacher training foresees the teacher\u27s participation in a private or public sector self-reliant internship to benefit from the expertise of companies\u27 work force and employers and actualize their understanding for the world of work. Afghan TVET teachers completing successful the TTTI in-service training are able to train many cohorts of students for the labor market or self-employment with the gained competences. Two subsequent cohorts of TTTI trainees - government employed TVET teachers undergoing in-service teacher training - have been participating for their first time in self-reliant internship in 2013 and 2014. According to the findings, recommendations are given for using the approach of introducing internship in in-service training for TVET teacher capacity building

Model of Low-pass Filtering of Local Field Potentials in Brain Tissue

Local field potentials (LFPs) are routinely measured experimentally in brain tissue, and exhibit strong low-pass frequency filtering properties, with high frequencies (such as action potentials) being visible only at very short distances ($\approx$10~$\mu m$) from the recording electrode. Understanding this filtering is crucial to relate LFP signals with neuronal activity, but not much is known about the exact mechanisms underlying this low-pass filtering. In this paper, we investigate a possible biophysical mechanism for the low-pass filtering properties of LFPs. We investigate the propagation of electric fields and its frequency dependence close to the current source, i.e. at length scales in the order of average interneuronal distance. We take into account the presence of a high density of cellular membranes around current sources, such as glial cells. By considering them as passive cells, we show that under the influence of the electric source field, they respond by polarisation, i.e., creation of an induced field. Because of the finite velocity of ionic charge movement, this polarization will not be instantaneous. Consequently, the induced electric field will be frequency-dependent, and much reduced for high frequencies. Our model establishes that with respect to frequency attenuation properties, this situation is analogous to an equivalent RC-circuit, or better a system of coupled RC-circuits. We present a number of numerical simulations of induced electric field for biologically realistic values of parameters, and show this frequency filtering effect as well as the attenuation of extracellular potentials with distance. We suggest that induced electric fields in passive cells surrounding neurons is the physical origin of frequency filtering properties of LFPs.Comment: 10 figs, revised tex file and revised fig