Many environmental stimuli present a quasi-rhythmic structure at different timescales that the brain needs to decompose and integrate. Cortical oscillations have been proposed as instruments of sensory de-multiplexing, i.e., the parallel processing of different frequency streams in sensory signals. Yet their causal role in such a process has never been demonstrated. Here, we used a neural microcircuit model to address whether coupled theta–gamma oscillations, as observed in human auditory cortex, could underpin the multiscale sensory analysis of speech. We show that, in continuous speech, theta oscillations can flexibly track the syllabic rhythm and temporally organize the phoneme-level response of gamma neurons into a code that enables syllable identification. The tracking of slow speech fluctuations by theta oscillations, and its coupling to gamma-spiking activity both appeared as critical features for accurate speech encoding. These results demonstrate that cortical oscillations can be a key instrument of speech de-multiplexing, parsing, and encoding.
One of the key advances in genome assembly that has led to a significant improvement in contig lengths has been improved algorithms for utilization of paired reads (mate-pairs). While in most assemblers, mate-pair information is used in a post-processing step, the recently proposed Paired de Bruijn Graph (PDBG) approach incorporates the mate-pair information directly in the assembly graph structure. However, the PDBG approach faces difficulties when the variation in the insert sizes is high. To address this problem, we first transform mate-pairs into edge-pair histograms that allow one to better estimate the distance between edges in the assembly graph that represent regions linked by multiple mate-pairs. Further, we combine the ideas of mate-pair transformation and PDBGs to construct new data structures for genome assembly: pathsets and pathset graphs.
Let G be a semisimple algebraic group whose decomposition into the product of simple components does not contain simple groups of type A, and P⊆G be a parabolic subgroup. Extending the results of Popov , we enumerate all triples (G, P, n) such that (a) there exists an open G-orbit on the multiple flag variety G/P × G/P × . . . × G/P (n factors), (b) the number of G-orbits on the multiple flag variety is finite.
I give the explicit formula for the (set-theoretical) system of Resultants of m+1 homogeneous polynomials in n+1 variables