Synthesis and characterization of a tris(2-hydroxyphenyl)methane-based cryptand and its triiron(III) complex

Reaction of tris(5-amino-2-ethoxy-3-isopropylphenyl)methane and pyridine-2,6-dicarbonyl-dichloride affords a multi-dentate cryptand in 48% yield. Metallation with iron(III) chloride results in a substantial conformational change of this ligand to give a trianionic triiron(III) complex. Ferric cations line the periphery of the internal cavity with each adopting a square pyramidal N(3)Cl(2) coordination environment.     

Über einen zusammenhang zwischen gewissen linearen differential- und differenzengleichungen

Ohne Zusammenfassung     

On sublattices of the hexagonal lattice

How many sublattices of index N are there in the planar hexagonal lattice? Which of them are the best from the point of view of packing density, signal-to-noise ratio, or energy? We answer the first question completely and give partial answers to the other questions.     

Subsampling effects in neuronal avalanche distributions recorded in vivo

Background  

Many systems in nature are characterized by complex behaviour where large cascades of events, or avalanches, unpredictably alternate with periods of little activity. Snow avalanches are an example. Often the size distribution f(s) of a system's avalanches follows a power law, and the branching parameter sigma, the average number of events triggered by a single preceding event, is unity. A power law for f(s), and sigma = 1, are hallmark features of self-organized critical (SOC) systems, and both have been found for neuronal activity in vitro. Therefore, and since SOC systems and neuronal activity both show large variability, long-term stability and memory capabilities, SOC has been proposed to govern neuronal dynamics in vivo. Testing this hypothesis is difficult because neuronal activity is spatially or temporally subsampled, while theories of SOC systems assume full sampling. To close this gap, we investigated how subsampling affects f(s) and sigma by imposing subsampling on three different SOC models. We then compared f(s) and sigma of the subsampled models with those of multielectrode local field potential (LFP) activity recorded in three macaque monkeys performing a short term memory task.