@article{2426, abstract = {We introduce the adaptive neighborhood graph as a data structure for modeling a smooth manifold M embedded in some Euclidean space ℝ d. We assume that M is known to us only through a finite sample P ⊂ M, as is often the case in applications. The adaptive neighborhood graph is a geometric graph on P. Its complexity is at most min{2O(k)n, n2}, where n = P and k = dim M, as opposed to the n[d/2] complexity of the Delaunay triangulation, which is often used to model manifolds. We prove that we can correctly infer the connected components and the dimension of M from the adaptive neighborhood graph provided a certain standard sampling condition is fulfilled. The running time of the dimension detection algorithm is d20(k7 log k) for each connected component of M. If the dimension is considered constant, this is a constant-time operation, and the adaptive neighborhood graph is of linear size. Moreover, the exponential dependence of the constants is only on the intrinsic dimension k, not on the ambient dimension d. This is of particular interest if the co-dimension is high, i.e., if k is much smaller than d, as is the case in many applications. The adaptive neighborhood graph also allows us to approximate the geodesic distances between the points in P.}, author = {Giesen, Joachim and Uli Wagner}, journal = {Discrete & Computational Geometry}, number = {2}, pages = {245 -- 267}, publisher = {Springer}, title = {{Shape dimension and intrinsic metric from samples of manifolds}}, doi = {10.1007/s00454-004-1120-8}, volume = {32}, year = {2004}, } @article{2425, abstract = {A finite set N ⊂ Rd is a weak ε-net for an n-point set X ⊂ Rd (with respect to convex sets) if N intersects every convex set K with |K ∩ X| ≥ εn. We give an alternative, and arguably simpler, proof of the fact, first shown by Chazelle et al., that every point set X in Rd admits a weak ε-net of cardinality O(ε-dpolylog(1/ε)). Moreover, for a number of special point sets (e.g., for points on the moment curve), our method gives substantially better bounds. The construction yields an algorithm to construct such weak ε-nets in time O(n ln(1/ε)).}, author = {Matoušek, Jiří and Uli Wagner}, journal = {Discrete & Computational Geometry}, number = {2}, pages = {195 -- 206}, publisher = {Springer}, title = {{New constructions of weak ε-nets}}, doi = {10.1007/s00454-004-1116-4}, volume = {32}, year = {2004}, } @misc{2461, author = {Sauer, Michael and Friml, Jirí}, booktitle = {Development}, number = {23}, pages = {5774 -- 5775}, publisher = {Company of Biologists}, title = {{The Matryoshka dolls of plant polarity}}, doi = {10.1242/dev.01463}, volume = {131}, year = {2004}, } @article{2642, abstract = {In the hippocampal CA1 region, metabotropic glutamate subtype 1 (mGluR1) receptors have been implicated in a variety of physiological responses to glutamate, which include modulation of synaptic transmission and plasticity, as well as neuronal excitability and synchronization. The mGluR1α isoform is characteristically expressed only by nonprincipal cells, and it is particularly enriched in somatostatin (SS -containing interneurons in stratum oriens-alveus. Anatomical and physiological data have indicated the presence of mGluR1α in several distinct classes of interneurons with their somata located also in strata pyramidale, radiatum, and lacunosum moleculare. Each different interneuron subtype, as defined by functionally relevant criteria, including input/output characteristics and expression of selective molecular markers, subserves distinct functions in local hippocampal circuits. We have investigated which of the different CA1 interneuron classes express mGluR1α by immunofluorescent labeling, combining antibodies to mGluR1α, calcium-binding proteins, and neuropeptides, and by intracellular labeling in vitro. Several types of interneuron that are immunopositive for mGluR1α each targeted different domains of pyramidal cells and included (1) O-LM interneurons, found to coexpress both SS and parvalbumin (PV); (2) interneurons with target selectivity for other interneurons, expressing vasoactive intestinal polypeptide (VIP) and/or the calcium-binding protein calretinin; (3) procholecystokinin-immunopositive interneurons probably non-basket and dendrite-targeting; and (4) an as-yet unidentified SS-immunoreactive but PV-immunonegative interneuron class, possibly corresponding to oriensbistratified cells. Estimation of the relative proportion of mGluR1α-positive interneurons showed 43%, 46%, and 30% co-labeling with SS, VIP, or PV, respectively. The identification of the specific subclasses of CA1 interneurons expressing mGluR1α provides the network basis for assessing the contribution of this receptor to the excitability of the hippocampus.}, author = {Ferraguti, Francesco and Cobden, Philip M and Pollard, Marie and Cope, David W and Ryuichi Shigemoto and Watanabe, Masahiko and Somogyi, Péter}, journal = {Hippocampus}, number = {2}, pages = {193 -- 215}, publisher = {Wiley-Blackwell}, title = {{Immunolocalization of metabotropic glutamate receptor 1α (mGluR1α) in distinct classes of interneuron in the CA1 region of the rat hippocampus}}, doi = {10.1002/hipo.10163}, volume = {14}, year = {2004}, } @article{2639, abstract = {Vesicular glutamate transporter type 3 (VGLUT3) containing neuronal elements were characterized using antibodies to VGLUT3 and molecular cell markers. All VGLUT3-positive somata were immunoreactive for CCK, and very rarely, also for calbindin; none was positive for parvalbumin, calretinin, VIP or somatostatin. In the CA1 area, 26.8 ± 0.7% of CCK-positive interneuron somata were VGLUT3-positive, a nonoverlapping 22.8 ± 1.9% were calbindin-positive, 10.7 ± 2.5% VIP-positive and the rest were only CCK-positive. The patterns of coexpression were similar in the CA3 area, the dentate gyrus and the isocortex. Immunoreactivity for VGLUT3 was undetectable in pyramidal and dentate granule cells. Boutons colabelled for VGLUT3, CCK and GAD were most abundant in the cellular layers of the hippocampus and in layers II-III of the isocortex. Large VGLUT3-labelled boutons at the border of strata radiatum and lacunosum-moleculare in the CA1 area were negative for GAD, but were labelled for vesicular monoamine transporter type 2, plasmalemmal serotonin transporter or serotonin. No colocalization was found in terminals between VGLUT3 and parvalbumin, vesicular acetylcholine transporter and group III (mGluR7a,b; mGluR8a,b) metabotropic glutamate receptors. In stratum radiatum and the isocortex, VGLUT3-positive but GAD-negative boutons heavily innervated the soma and proximal dendrites of some VGLUT3- or calbindin-positive interneurons. The results suggest that boutons coexpressing VGLUT3, CCK and GAD originate from CCK-positive basket cells, which are VIP-immunonegative. Other VGLUT3-positive boutons immunopositive for serotonergic markers but negative for GAD probably originate from the median raphe nucleus and innervate select interneurons. The presumed amino acid substrate of VGLUT3 may act on presynaptic kainate or group II metabotropic glutamate receptors.}, author = {Somogyi, Jozsef and Baude, Agnès and Omori, Yuko and Shimizu, Hidemi and El-Mestikawy, Salah and Fukaya, Masahiro and Ryuichi Shigemoto and Watanabe, Masahiko and Somogyi, Péter}, journal = {European Journal of Neuroscience}, number = {3}, pages = {552 -- 569}, publisher = {Wiley-Blackwell}, title = {{GABAergic basket cells expressing cholecystokinin contain vesicular glutamate transporter type 3 (VGLUT3) in their synaptic terminals in hippocampus and isocortex of the rat}}, doi = {10.1111/j.0953-816X.2003.03091.x}, volume = {19}, year = {2004}, }