TY - JOUR
AB - It is shown that a triangulation of a set of n points in the plane that minimizes the maximum edge length can be computed in time 0(n2). The algorithm is reasonably easy to implement and is based on the theorem that there is a triangulation with minmax edge length that contains the relative neighborhood graph of the points as a subgraph. With minor modifications the algorithm works for arbitrary normed metrics.
AU - Herbert Edelsbrunner
AU - Tan, Tiow Seng
ID - 4042
IS - 3
JF - SIAM Journal on Computing
TI - A quadratic time algorithm for the minmax length triangulation
VL - 22
ER -
TY - JOUR
AB - Edge insertion iteratively improves a triangulation of a finite point set in ℜ2 by adding a new edge, deleting old edges crossing the new edge, and retriangulating the polygonal regions on either side of the new edge. This paper presents an abstract view of the edge insertion paradigm, and then shows that it gives polynomial-time algorithms for several types of optimal triangulations, including minimizing the maximum slope of a piecewise-linear interpolating surface.
AU - Bern, Marshall
AU - Herbert Edelsbrunner
AU - Eppstein, David
AU - Mitchell, Stephen
AU - Tan, Tiow Seng
ID - 4044
IS - 1
JF - Discrete & Computational Geometry
TI - Edge insertion for optimal triangulations
VL - 10
ER -
TY - JOUR
AB - We apply Megiddo's parametric searching technique to several geometric optimization problems and derive significantly improved solutions for them. We obtain, for any fixed ε>0, an O(n1+ε) algorithm for computing the diameter of a point set in 3-space, an O(8/5+ε) algorithm for computing the width of such a set, and on O(n8/5+ε) algorithm for computing the closest pair in a set of n lines in space. All these algorithms are deterministic.
AU - Chazelle, Bernard
AU - Herbert Edelsbrunner
AU - Guibas, Leonidas
AU - Sharir, Micha
ID - 4045
IS - 1
JF - Discrete & Computational Geometry
TI - Diameter, width, closest line pair, and parametric searching
VL - 10
ER -
TY - JOUR
AB - We have studied the effects of different neurotrophins on the survival and proliferation of rat cerebellar granule cells in culture. These neurons express trkB and trkC, the putative neuronal receptors for brain-derived neurotrophic factor (BDNF) and neurotrophin-3 (NT-3) respectively. Binding studies using iodinated BDNF and NT-3 demonstrated that both BDNF and NT-3 bind to the cerebellar granule neurons with a similar affinity of approximately 2 x 10(-9) M. The number of receptors per granule cell was surprisingly high, approximately 30 x 10(-4) and 2 x 10(5) for BDNF and NT-3, respectively. Both NT-3 and BDNF elevated c-fos mRNA in the granule neurons, but only BDNF up-regulated the mRNA encoding the low-affinity neurotrophin receptor (p75). In contrast to NT-3, BDNF acted as a survival factor for the granule neurons. BDNF also induced sprouting of the granule neurons and significantly protected them against neurotoxicity induced by high (1 mM) glutamate concentrations. Cultured granule neurons also expressed low levels of BDNF mRNA which were increased by kainic acid, a glutamate receptor agonist. Thus, BDNF, but not NT-3, is a survival factor for cultured cerebellar granule neurons and activation of glutamate receptor(s) up-regulates BDNF expression in these cells.
AU - Lindholm, Dan
AU - Dechant, Georg
AU - Heisenberg, Carl-Philipp
AU - Thoenen, Hans
ID - 4175
IS - 11
JF - European Journal of Neuroscience
TI - Brain-derived neurotrophic factor is a survival factor for cultured rat cerebellar granule neurons and protects them against glutamate-induced neurotoxicity
VL - 5
ER -
TY - JOUR
AB - Thyroid hormones play an important role in brain development, but the mechanism(s) by which triiodothyronine (T3) mediates neuronal differentiation is poorly understood. Here we demonstrate that T3 regulates the neurotrophic factor, neurotrophin-3 (NT-3), in developing rat cerebellar granule cells both in cell culture and in vivo. In situ hybridization experiments showed that developing Purkinje cells do not express NT-3 mRNA but do express trkC, the putative neuronal receptor for NT-3. Addition of recombinant NT-3 to cerebellar cultures from embryonic rat brain induces hypertrophy and neurite sprouting of Purkinje cells, and upregulates the mRNA encoding the calcium-binding protein, calbindin-28 kD. The present study demonstrates a novel interaction between cerebellar granule neurons and developing Purkinje cells in which NT-3 induced by T3 in the granule cells promotes Purkinje cell differentiation.
AU - Lindholm, Dan
AU - Castrén, Eero
AU - Tsoulfas, Pantelis
AU - Kolbeck, Roland
AU - Berzaghi, Maria da Penha
AU - Leingärtner, Axel
AU - Heisenberg, Carl-Philipp
AU - Tesarollo, Lino
AU - Parada, Luis F
AU - Thoenen, Hans
ID - 4177
IS - 2
JF - Journal of Cell Biology
TI - Neurotrophin-3 induced by tri-iodothyronine in cerebellar granule cells promotes Purkinje cell differentiation
VL - 122
ER -