@article{794, abstract = {We show that c-planarity is solvable in quadratic time for flat clustered graphs with three clusters if the combinatorial embedding of the underlying graph is fixed. In simpler graph-theoretical terms our result can be viewed as follows. Given a graph G with the vertex set partitioned into three parts embedded on a 2-sphere, our algorithm decides if we can augment G by adding edges without creating an edge-crossing so that in the resulting spherical graph the vertices of each part induce a connected sub-graph. We proceed by a reduction to the problem of testing the existence of a perfect matching in planar bipartite graphs. We formulate our result in a slightly more general setting of cyclic clustered graphs, i.e., the simple graph obtained by contracting each cluster, where we disregard loops and multi-edges, is a cycle.}, author = {Fulek, Radoslav}, journal = {Computational Geometry: Theory and Applications}, pages = {1 -- 13}, publisher = {Elsevier}, title = {{C-planarity of embedded cyclic c-graphs}}, doi = {10.1016/j.comgeo.2017.06.016}, volume = {66}, year = {2017}, } @article{736, abstract = {The neurotransmitter receptor subtype, number, density, and distribution relative to the location of transmitter release sites are key determinants of signal transmission. AMPA-type ionotropic glutamate receptors (AMPARs) containing GluA3 and GluA4 subunits are prominently expressed in subsets of neurons capable of firing action potentials at high frequencies, such as auditory relay neurons. The auditory nerve (AN) forms glutamatergic synapses on two types of relay neurons, bushy cells (BCs) and fusiform cells (FCs) of the cochlear nucleus. AN-BC and AN-FC synapses have distinct kinetics; thus, we investigated whether the number, density, and localization of GluA3 and GluA4 subunits in these synapses are differentially organized using quantitative freeze-fracture replica immunogold labeling. We identify a positive correlation between the number of AMPARs and the size of AN-BC and AN-FC synapses. Both types of AN synapses have similar numbers of AMPARs; however, the AN-BC have a higher density of AMPARs than AN-FC synapses, because the AN-BC synapses are smaller. A higher number and density of GluA3 subunits are observed at AN-BC synapses, whereas a higher number and density of GluA4 subunits are observed at AN-FC synapses. The intrasynaptic distribution of immunogold labeling revealed that AMPAR subunits, particularly GluA3, are concentrated at the center of the AN-BC synapses. The central distribution of AMPARs is absent in GluA3-knockout mice, and gold particles are evenly distributed along the postsynaptic density. GluA4 gold labeling was homogenously distributed along both synapse types. Thus, GluA3 and GluA4 subunits are distributed at AN synapses in a target-cell-dependent manner.}, author = {Rubio, María and Matsui, Ko and Fukazawa, Yugo and Kamasawa, Naomi and Harada, Harumi and Itakura, Makoto and Molnár, Elek and Abe, Manabu and Sakimura, Kenji and Shigemoto, Ryuichi}, issn = {18632653}, journal = {Brain Structure and Function}, number = {8}, pages = {3375 -- 3393}, publisher = {Springer}, title = {{The number and distribution of AMPA receptor channels containing fast kinetic GluA3 and GluA4 subunits at auditory nerve synapses depend on the target cells}}, doi = {10.1007/s00429-017-1408-0}, volume = {222}, year = {2017}, } @article{740, abstract = {Developments in bioengineering and molecular biology have introduced a palette of genetically encoded probes for identification of specific cell populations in electron microscopy. These probes can be targeted to distinct cellular compartments, rendering them electron dense through a subsequent chemical reaction. These electron densities strongly increase the local contrast in samples prepared for electron microscopy, allowing three major advances in ultrastructural mapping of circuits: genetic identification of circuit components, targeted imaging of regions of interest and automated analysis of the tagged circuits. Together, the gains from these advances can decrease the time required for the analysis of targeted circuit motifs by over two orders of magnitude. These genetic encoded tags for electron microscopy promise to simplify the analysis of circuit motifs and become a central tool for structure‐function studies of synaptic connections in the brain. We review the current state‐of‐the‐art with an emphasis on connectomics, the quantitative analysis of neuronal structures and motifs.}, author = {Shigemoto, Ryuichi and Jösch, Maximilian A}, issn = {17597684}, journal = {WIREs Developmental Biology}, number = {6}, publisher = {Wiley-Blackwell}, title = {{The genetic encoded toolbox for electron microscopy and connectomics}}, doi = {10.1002/wdev.288}, volume = {6}, year = {2017}, } @article{741, abstract = {We prove that a system of N fermions interacting with an additional particle via point interactions is stable if the ratio of the mass of the additional particle to the one of the fermions is larger than some critical m*. The value of m* is independent of N and turns out to be less than 1. This fact has important implications for the stability of the unitary Fermi gas. We also characterize the domain of the Hamiltonian of this model, and establish the validity of the Tan relations for all wave functions in the domain.}, author = {Moser, Thomas and Seiringer, Robert}, issn = {00103616}, journal = {Communications in Mathematical Physics}, number = {1}, pages = {329 -- 355}, publisher = {Springer}, title = {{Stability of a fermionic N+1 particle system with point interactions}}, doi = {10.1007/s00220-017-2980-0}, volume = {356}, year = {2017}, } @article{739, abstract = {We study the norm approximation to the Schrödinger dynamics of N bosons in with an interaction potential of the form . Assuming that in the initial state the particles outside of the condensate form a quasi-free state with finite kinetic energy, we show that in the large N limit, the fluctuations around the condensate can be effectively described using Bogoliubov approximation for all . The range of β is expected to be optimal for this large class of initial states.}, author = {Nam, Phan and Napiórkowski, Marcin M}, issn = {00217824}, journal = {Journal de Mathématiques Pures et Appliquées}, number = {5}, pages = {662 -- 688}, publisher = {Elsevier}, title = {{A note on the validity of Bogoliubov correction to mean field dynamics}}, doi = {10.1016/j.matpur.2017.05.013}, volume = {108}, year = {2017}, }