@inproceedings{688, abstract = {We show that the framework of topological data analysis can be extended from metrics to general Bregman divergences, widening the scope of possible applications. Examples are the Kullback - Leibler divergence, which is commonly used for comparing text and images, and the Itakura - Saito divergence, popular for speech and sound. In particular, we prove that appropriately generalized čech and Delaunay (alpha) complexes capture the correct homotopy type, namely that of the corresponding union of Bregman balls. Consequently, their filtrations give the correct persistence diagram, namely the one generated by the uniformly growing Bregman balls. Moreover, we show that unlike the metric setting, the filtration of Vietoris-Rips complexes may fail to approximate the persistence diagram. We propose algorithms to compute the thus generalized čech, Vietoris-Rips and Delaunay complexes and experimentally test their efficiency. Lastly, we explain their surprisingly good performance by making a connection with discrete Morse theory. }, author = {Edelsbrunner, Herbert and Wagner, Hubert}, issn = {18688969}, location = {Brisbane, Australia}, pages = {391--3916}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Topological data analysis with Bregman divergences}}, doi = {10.4230/LIPIcs.SoCG.2017.39}, volume = {77}, year = {2017}, } @article{687, abstract = {Pursuing the similarity between the Kontsevich-Soibelman construction of the cohomological Hall algebra (CoHA) of BPS states and Lusztig's construction of canonical bases for quantum enveloping algebras, and the similarity between the integrality conjecture for motivic Donaldson-Thomas invariants and the PBW theorem for quantum enveloping algebras, we build a coproduct on the CoHA associated to a quiver with potential. We also prove a cohomological dimensional reduction theorem, further linking a special class of CoHAs with Yangians, and explaining how to connect the study of character varieties with the study of CoHAs.}, author = {Davison, Ben}, issn = {00335606}, journal = {Quarterly Journal of Mathematics}, number = {2}, pages = {635 -- 703}, publisher = {Oxford University Press}, title = {{The critical CoHA of a quiver with potential}}, doi = {10.1093/qmath/haw053}, volume = {68}, year = {2017}, } @article{686, abstract = {Tissues are thought to behave like fluids with a given surface tension. Differences in tissue surface tension (TST) have been proposed to trigger cell sorting and tissue envelopment. D'Arcy Thompson in his seminal book ‘On Growth and Form’ has introduced this concept of differential TST as a key physical mechanism dictating tissue formation and organization within the developing organism. Over the past century, many studies have picked up the concept of differential TST and analyzed the role and cell biological basis of TST in development, underlining the importance and influence of this concept in developmental biology.}, author = {Heisenberg, Carl-Philipp J}, issn = {09254773}, journal = {Mechanisms of Development}, pages = {32 -- 37}, publisher = {Elsevier}, title = {{D'Arcy Thompson's ‘on growth and form’: From soap bubbles to tissue self organization}}, doi = {10.1016/j.mod.2017.03.006}, volume = {145}, year = {2017}, } @article{689, abstract = {Rett syndrome modeling in monkey mirrors the human disorder.}, author = {Novarino, Gaia}, issn = {19466234}, journal = {Science Translational Medicine}, number = {393}, publisher = {American Association for the Advancement of Science}, title = {{Rett syndrome modeling goes simian}}, doi = {10.1126/scitranslmed.aan8196}, volume = {9}, year = {2017}, } @article{693, abstract = {Many central synapses contain a single presynaptic active zone and a single postsynaptic density. Vesicular release statistics at such “simple synapses” indicate that they contain a small complement of docking sites where vesicles repetitively dock and fuse. In this work, we investigate functional and morphological aspects of docking sites at simple synapses made between cerebellar parallel fibers and molecular layer interneurons. Using immunogold labeling of SDS-treated freeze-fracture replicas, we find that Cav2.1 channels form several clusters per active zone with about nine channels per cluster. The mean value and range of intersynaptic variation are similar for Cav2.1 cluster numbers and for functional estimates of docking-site numbers obtained from the maximum numbers of released vesicles per action potential. Both numbers grow in relation with synaptic size and decrease by a similar extent with age between 2 wk and 4 wk postnatal. Thus, the mean docking-site numbers were 3.15 at 2 wk (range: 1–10) and 2.03 at 4 wk (range: 1–4), whereas the mean numbers of Cav2.1 clusters were 2.84 at 2 wk (range: 1–8) and 2.37 at 4 wk (range: 1–5). These changes were accompanied by decreases of miniature current amplitude (from 93 pA to 56 pA), active-zone surface area (from 0.0427 μm2 to 0.0234 μm2), and initial success rate (from 0.609 to 0.353), indicating a tightening of synaptic transmission with development. Altogether, these results suggest a close correspondence between the number of functionally defined vesicular docking sites and that of clusters of voltage-gated calcium channels. }, author = {Miki, Takafumi and Kaufmann, Walter and Malagon, Gerardo and Gomez, Laura and Tabuchi, Katsuhiko and Watanabe, Masahiko and Shigemoto, Ryuichi and Marty, Alain}, issn = {00278424}, journal = {PNAS}, number = {26}, pages = {E5246 -- E5255}, publisher = {National Academy of Sciences}, title = {{Numbers of presynaptic Ca2+ channel clusters match those of functionally defined vesicular docking sites in single central synapses}}, doi = {10.1073/pnas.1704470114}, volume = {114}, year = {2017}, }