Abstract: Two metallacyclic complexes of general formula Na-8[(M2L3)-L-II]center dot xH(2)O [M = Ni (4) and Co (5) with x = 15 (4) and 17 (5)] have been self-assembled in aqueous solution from N,N'-1,3-phenylenebis(oxamic acid) (H4L) and M2+ ions in a ligand/metal molar ratio of 3 : 2 in the presence of NaOH acting as base. X-Ray structural analyses of 4 and 5 show triple-stranded, dinuclear anions of the meso-helicate-type (so-called mesocates) with C-3h molecular symmetry. The two octahedral metal-tris(oxamate) moieties of opposite chiralities (Delta, Lambda form) are connected by three m-phenylene spacers at intermetallic distances of 6.822(2) (4) and 6.868(2) angstrom (5) to give a metallacryptand core. In the crystal lattice, the binding of these heterochiral dinickel(II) and dicobalt(II) triple mesocates to sodium(I) ions leads to oxamato-bridged heterobimetallic three-dimensional open-frameworks with a hexagonal diamond architecture having small pores of 17.566(4) (4) and 17.640(2) angstrom (5) in diameter where the crystallization water molecules and the sodium(I) countercations are hosted. Variable temperature (2.0-300 K) magnetic susceptibility measurements reveal relatively anisotropic S = 2 Ni-2(II) (4) and S = 3 Co-2(II) (5) ground states resulting from the moderate to weak intramolecular ferromagnetic coupling between the two high-spin Ni-II (S-Ni = 1) or Co-II (S-Co = 3/2) ions across the m-phenylenediamidate bridges [J = +3.6 (4) and +1.1 cm(-1) (5); H = -JS(1)center dot S-2]. A simple molecular orbital analysis of the electron exchange interaction identifies the p-type pathways of the meta-substituted phenylene spacers involving the d(z2) and d(x2-y2) pairs of magnetic orbitals of the two trigonally distorted octahedral high-spin M-II ions (M = Ni and Co) as responsible for the overall ferromagnetic coupling observed in 4 and 5 in agreement with a spin polarization mechanism. The decrease of the overall ferromagnetic coupling from 4 to 5 is in turn explained by the additional antiferromagnetic exchange contribution involving the d(xy) pair of magnetic orbitals of the two trigonally distorted octahedral high-spin Co-II ions across the sigma-type pathway of the meta-substituted phenylene spacers.

Abstract: Slow waves constitute the main signature of sleep in the electroencephalogram (EEG). They reflect alternating periods of neuronal hyperpolarization and depolarization in cortical networks. While recent findings have demonstrated their functional role in shaping and strengthening neuronal networks, a large-scale characterization of these two processes remains elusive in the human brain. In this study, by using simultaneous scalp EEG and intracranial recordings in 10 epileptic subjects, we examined the dynamics of hyperpolarization and depolarization waves over a large extent of the human cortex. We report that both hyperpolarization and depolarization processes can occur with two different characteristic time durations which are consistent across all subjects. For both hyperpolarization and depolarization waves, their average speed over the cortex was estimated to be approximately 1 m/s. Finally, we characterized their propagation pathways by studying the preferential trajectories between most involved intracranial contacts. For both waves, although single events could begin in almost all investigated sites across the entire cortex, we found that the majority of the preferential starting locations were located in frontal regions of the brain while they had a tendency to end in posterior and temporal regions.

Abstract: A particular type of order-to-chaos transition mediated by an infinite set of coexisting neutrally stable limit cycles of different periods is studied in the Varley-Gradwell-Hassell population model. We prove by an algebraic method that this kind of transition can only happen for a particular bifurcation parameter value. Previous results on the structure of the attractor at the transition point are here simplified and extended.