Kyzylkumite, Ti2V3+O5(OH): new structure type, modularity and revised formula

The crystal structure of kyzylkumite, ideally Ti2V3+O5(OH), from the Sludyanka complex in South Baikal, Russia was solved and refined (including the hydrogen atom position) to an agreement index, R1, of 2.34 using X-ray diffraction data collected on a twinned crystal. Kyzylkumite crystallizes in space group P21/c, with a = 8.4787(1), b = 4.5624(1), c = 10.0330(1) Å, β = 93.174(1)°, V = 387.51(1) Å3 and Z = 4. Tivanite, TiV3+O3OH, and kyzylkumite have modular structures based on hexagonal close packing of oxygen, which are made up of rutile TiO2 and montroseite V3+O(OH) slices. In tivanite the rutile:montroseite ratio is 1:1, in kyzylkumite the ratio is 2:1. The montroseite module may be replaced by the isotypic paramontroseite V4+O2 module, which produces a phase with the formula Ti2V4+O6. In the metamorphic rocks of the Sludyanka complex, vanadium can be present as V4+ and V3+ within the same mineral (e.g. in batisivite, schreyerite and berdesinskiite). Kyzylkumite has a flexible composition with respect to the M4+/M3+ ratio. The relationship between kyzylkumite and a closely related Be-bearing kyzylkumite-like mineral with an orthorhombic norbergite-type structure from Byrud mine, Norway is discussed. Both minerals have similar X-ray powder diffraction patterns.

Random Sampling with Interspike-Intervals of the Exponential Integrate and Fire Neuron: A Computational Interpretation of UP-States

Oscillations between high and low values of the membrane potential (UP and DOWN states respectively) are an ubiquitous feature of cortical neurons during slow wave sleep and anesthesia. Nevertheless, a surprisingly small number of quantitative studies have been conducted only that deal with this phenomenon’s implications for computation. Here we present a novel theory that explains on a detailed mathematical level the computational benefits of UP states. The theory is based on random sampling by means of interspike intervals (ISIs) of the exponential integrate and fire (EIF) model neuron, such that each spike is considered a sample, whose analog value corresponds to the spike’s preceding ISI. As we show, the EIF’s exponential sodium current, that kicks in when balancing a noisy membrane potential around values close to the firing threshold, leads to a particularly simple, approximative relationship between the neuron’s ISI distribution and input current. Approximation quality depends on the frequency spectrum of the current and is improved upon increasing the voltage baseline towards threshold. Thus, the conceptually simpler leaky integrate and fire neuron that is missing such an additional current boost performs consistently worse than the EIF and does not improve when voltage baseline is increased. For the EIF in contrast, the presented mechanism is particularly effective in the high-conductance regime, which is a hallmark feature of UP-states. Our theoretical results are confirmed by accompanying simulations, which were conducted for input currents of varying spectral composition. Moreover, we provide analytical estimations of the range of ISI distributions the EIF neuron can sample from at a given approximation level. Such samples may be considered by any algorithmic procedure that is based on random sampling, such as Markov Chain Monte Carlo or message-passing methods. Finally, we explain how spike-based random sampling relates to existing computational theories about UP states during slow wave sleep and present possible extensions of the model in the context of spike-frequency adaptation.