@article{2358, abstract = {A study was conducted on the one-dimensional (1D) bosons in three-dimensional (3D) traps. A rigorous analysis was carried out on the parameter regions in which various types of 1D or 3D behavior occurred in the ground state. The four parameter regions include density, transverse, longitudinal dimensions and scattering length.}, author = {Lieb, Élliott H and Robert Seiringer and Yngvason, Jakob}, journal = {Physical Review Letters}, number = {15}, pages = {1504011 -- 1504014}, publisher = {American Physical Society}, title = {{One-dimensional Bosons in three-dimensional traps}}, doi = {10.1103/PhysRevLett.91.150401}, volume = {91}, year = {2003}, } @phdthesis{2414, author = {Uli Wagner}, publisher = {ETH Zurich}, title = {{On k-Sets and Their Applications}}, doi = {10.3929/ethz-a-004708408}, year = {2003}, } @inproceedings{2424, abstract = {We introduce the adaptive neighborhood graph as a data structure for modeling a smooth manifold M embedded in some (potentially very high-dimensional) Euclidean space ℝd. We assume that M is known to us only through a finite sample P ⊂ M, as it 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 show that we can provably correctly infer the connectivity of M 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 d2O(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}, pages = {329 -- 337}, publisher = {ACM}, title = {{Shape dimension and intrinsic metric from samples of manifolds with high co-dimension}}, doi = {10.1145/777792.777841}, year = {2003}, } @inproceedings{2423, 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. [7], that every point set X in Rd admits a weak ε-net of cardinality O(ε-d polylog(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)). We also prove, by a different method, a near-linear upper bound for points uniformly distributed on the (d - 1)-dimensional sphere.}, author = {Matoušek, Jiří and Uli Wagner}, pages = {129 -- 135}, publisher = {ACM}, title = {{New constructions of weak epsilon-nets}}, doi = {10.1145/777792.777813}, year = {2003}, } @inproceedings{2422, abstract = {We prove a lower bound of 0.3288(4 n) for the rectilinear crossing number cr̄(Kn) of a complete graph on n vertices, or in other words, for the minimum number of convex quadrilaterals in any set of n points in general position in the Euclidean plane. As we see it, the main contribution of this paper is not so much the concrete numerical improvement over earlier bounds, as the novel method of proof, which is not based on bounding cr̄(Kn) for some small n.}, author = {Uli Wagner}, pages = {583 -- 588}, publisher = {SIAM}, title = {{On the rectilinear crossing number of complete graphs}}, year = {2003}, } @article{2623, abstract = {Patients with Hodgkin's disease can develop paraneoplastic cerebellar ataxia because of the generation of autoantibodies against mGluR1 (mGluR1-Abs). Yet, the pathophysiological mechanisms underlying their motor coordination deficits remain to be elucidated. Here, we show that application of IgG purified from the patients' serum to cerebellar slices of mice acutely reduces the basal activity of Purkinje cells, whereas application to the flocculus of mice in vivo evokes acute disturbances in the performance of their compensatory eye movements. In addition, the mGluR1-Abs block induction of long-term depression in cultured mouse Purkinje cells, whereas the cerebellar motor learning behavior of the patients is affected in that they show impaired adaptation of their saccadic eye movements. Finally, postmortem analysis of the cerebellum of a paraneoplastic cerebellar ataxia patient showed that the number of Purkinje cells was significantly reduced by approximately two thirds compared with three controls. We conclude that autoantibodies against mGluR1 can cause cerebellar motor coordination deficits caused by a combination of rapid effects on both acute and plastic responses of Purkinje cells and chronic degenerative effects.}, author = {Coesmans, Michiel P and Sillevis-Smitt, Peter A and Linden, David J and Ryuichi Shigemoto and Hirano, Tomoo and Yamakawa, Yoshinori and Van Alphen, Adriaan M and Luo, Chongde and Van Der Geest, Jos N and Kros, Johan M and Gaillard, Carlo A and Frens, Maarten A and De Zeeuw, Chris I}, journal = {Annals of Neurology}, number = {3}, pages = {325 -- 336}, publisher = {Wiley-Blackwell}, title = {{Mechanisms underlying cerebellar motor deficits due to mGluR1-autoantibodies}}, doi = {10.1002/ana.10451}, volume = {53}, year = {2003}, } @article{2625, abstract = {Metabotropic glutamate receptor 1 (mGluR1) plays a crucial role in synaptic plasticity and motor learning in the cerebellum. We have studied activity-dependent changes in mGluR1 function in mouse cultured Purkinje neurons. Depolarizing stimulation potentiated Ca2+ and current responses to an mGluR1 agonist for several hours in the cultured Purkinje neurons. It also blocked internalization of mGluR1 and increased the number of mGluR1s on the cell membrane. We found that depolarization simultaneously increased transcription of Homer1a in Purkinje neurons. Homer1a inhibited internalization and increased cell-surface expression of mGluR1 when coexpressed in human embryonic kidney (HEK)-293 cells. Depolarization-induced Homer1a expression in Purkinje neurons was blocked by a mitogen-activated protein kinase (MAPK) inhibitor. Changes in internalization and mGluR1-mediated Ca2+ response were also blocked by inhibition of MAPK activity, suggesting that localization and activity of mGluR1 were regulated in the same signalling pathway as Homer1a expression. It is thus suggested that depolarization of the Purkinje neuron leads to the increment in mGluR1 responsiveness through MAPK activity and induction of Homer1a expression, which increases active mGluR1 on the cell surface by blocking internalization of mGluR1.}, author = {Minami, Itsunari and Kengaku, Mineko and Smitt, Sillevis P and Ryuichi Shigemoto and Hirano, Tomoo}, journal = {European Journal of Neuroscience}, number = {5}, pages = {1023 -- 1032}, publisher = {Wiley-Blackwell}, title = {{Long-term potentiation of mGluR1 activity by depolarization-induced Homer1a in mouse cerebellar Purkinje neurons}}, doi = {10.1046/j.1460-9568.2003.02499.x}, volume = {17}, year = {2003}, } @article{2626, abstract = {The expression pattern of metabotropic glutamate receptor Iα (mGluR1α) was immunohistochemically investigated in substantia nigra dopaminergic neurons of the macaque monkey. In normal monkeys, mGluR1α immunoreactivity was weakly observed in the dorsal tier of the substantia nigra pars compacta (SNc-d) where calbindin-D28k-containing dopaminergic neurons invulnerable to parkinsonian degeneration are specifically located. On the other hand, mGluR1α was strongly expressed in the ventral tier of the substantia nigra pars cornpacta (SNc-v). In monkeys treated with the parkinsonism-inducing drug, I-methyl-4-phenyl-1,2,3,6-tetrahydropyridine (MPTP), mGluR1α expression was decreased in dopaminergic neurons in the SNc-v that were spared its toxic action. These results suggest that mGluR1α expression may be involved at least partly in the vulnerability of dopaminergic neurons to parkinsonian insults.}, author = {Kaneda, Katsuyuki and Imanishi, Michiko and Nambu, Atsushi and Ryuichi Shigemoto and Takada, Masahiko}, journal = {Neuroreport}, number = {7}, pages = {947 -- 950}, publisher = {Lippincott, Williams & Wilkins}, title = {{Differential expression patterns of mGluR1α in monkey nigral dopamine neurons}}, doi = {10.1097/01.wnr.0000074344.81633.e4}, volume = {14}, year = {2003}, } @article{2627, abstract = {Despite its implications for higher order functions of the brain, little is currently known about the molecular basis of left-right asymmetry of the brain. Here we report that synaptic distribution of N-methyl-D-aspartate (NMDA) receptor GluRε2 (NR2B) subunits in the adult mouse hippocampus is asymmetrical between the left and right and between the apical and basal dendrites of single neurons. These asymmetrical allocations of ε2 subunits differentiate the properties of NMDA receptors and synaptic plasticity between the left and right hippocampus. These results provide a molecular basis for the structural and functional asymmetry of the mature brain.}, author = {Kawakami, Ryosuke and Shinohara, Yoshiaki and Kato, Yuichiro and Sugiyama, Hiroyuki and Ryuichi Shigemoto and Ito, Isao}, journal = {Science}, number = {5621}, pages = {990 -- 994}, publisher = {American Association for the Advancement of Science}, title = {{Asymmetrical allocation of NMDA receptor ε2 subunits in hippocampal circuitry}}, doi = {10.1126/science.1082609}, volume = {300}, year = {2003}, } @article{2629, abstract = {The release of neurotransmitters is modulated by presynaptic metabotropic glutamate receptors (mGluRs), which show a highly selective expression and subcellular location in glutamatergic terminals in the hippocampus. Using immunocytochemistry, we investigated whether one of the receptors, mGluR7, whose level of expression is governed by the postsynaptic target, was present in GABAergic terminals and whether such terminals targeted particular cells. A total of 165 interneuron dendritic profiles receiving 466 synapses (82% mGluR7a-positive) were analysed. The presynaptic active zones of most GAD-(77%) or GABA-positive (94%) synaptic boutons on interneurons innervated by mGluR7a-enriched glutamatergic terminals (mGluR7a-decorated) were immunopositive for mGluR7a. GABAergic terminals on pyramidal cells and most other interneurons in str. oriens were mGluR7a-immunonegative. The mGluR7a-decorated cells were mostly somatostatin- and mGluR1α-immunopositive neurons in str. oriens and the alveus. Their GABAergic input mainly originated from VIP-positive terminals, 90% of which expressed high levels of mGluR7a in the presynaptic active zone. Parvalbumin-positive synaptic terminals were rare on mGluR7a-decorated cells, but on these neurons 73% of them were mGluR7a-immunopositive. Some type II synapses innervating interneurons were immunopositive for mGluR7b, as were some type I synapses. Because not all target cells of VIP-positive neurons are known it has not been possible to determine whether mGluR7 is expressed in a target-cell-specific manner in the terminals of single GABAergic cells. The activation of mGluR7 may decrease GABA release to mGluR7-decorated cells at times of high pyramidal cell activity, which elevates extracellular glutamate levels. Alternatively, the presynaptic receptor may be activated by as yet unidentified endogenous ligands released by the GABAergic terminals or the postsynaptic dendrites.}, author = {Somogyi, Péter and Dalezios, Yannis and Luján, Rafael and Roberts, John D and Watanabe, Masahiko and Ryuichi Shigemoto}, journal = {European Journal of Neuroscience}, number = {12}, pages = {2503 -- 2520}, publisher = {Wiley-Blackwell}, title = {{High level of mGluR7 in the presynaptic active zones of select populations of GABAergic terminals innervating interneurons in the rat hippocampus}}, doi = {10.1046/j.1460-9568.2003.02697.x}, volume = {17}, year = {2003}, }