@article{3467, abstract = {The effects of mast cell degranulating peptide (MCDP), a toxin from the honey bee, and of dendrotoxin (DTX), a toxin from the green mamba snake, were studied in voltage-clamped experiments with myelinated nerve fibres of Xenopus. MCDP and DTX blocked part of the K+ current. About 20% of the K+ current, however, was resistant to the toxins even in high concentrations. In Ringer solution half-maximal block was reached with concentrations of 33 nM MCDP and 11 nM DTX. In high-K+ solution the potency of both toxins was lower. β-Bungarotoxin (β-BuTX), another snake toxin, also blocked part of the K+ current, but was less potent than MCDP and DTX. Tail currents in high-K+ solution were analysed and three K+ current components were separated according to Dubois (1981b). Both MCDP and DTX selectively blocked a fast deactivating, slowly inactivating K+ current component which steeply activates between E = -60 mV and E = -40 mV (component f1). In concentrations around 100 nM, MCDP and DTX blocked neither the slow K+ current (component s) nor the fast deactivating, rapidly inactivating K+ current which activates between E = -40 mV and E = 20 mV (component f2). Similar results could be derived from K+ outward currents in Ringer solution. In high-K+, IC50 of MCDP for component f1 was 99 nM, whereas it was 7.6 μM for f2. Corresponding values for DTX are 68 nM and 1.8 μM. Binding studies with nerve fibre membranes of Xenopus reveal high-affinity binding sites for 125I-labelled DTX )K(D) = 22 pM in Ringer solution and 81 pM in high-K+ solution). 125I-labelled DTX can be displaced from its sites completely by unlabelled DTX, toxin I (black mamba toxin), MCDP, and partially by β-BuTX. Immunocytochemical staining demonstrates that binding sites for DTX are present in nodal and paranodal regions of the axonal membrane. The axonal membrane of motor and sensory nerve fibres is equipped with three types of well-characterized K+ channels and constitutes so far the best preparation to study MCDP- and DTX-sensitive K+ channels with electrophysiological and biochemical methods.}, author = {Bräu, Michael and Dreyer, Florian and Jonas, Peter M and Repp, Holger and Vogel, Werner}, issn = {1469-7793}, journal = {Journal of Physiology}, pages = {365 -- 385}, publisher = {Wiley-Blackwell}, title = {{A K+ channel in Xenopus nerve fibres selectively blocked by bee and snake toxins: binding and voltage-clamp experiments}}, doi = {10.1113/jphysiol.1990.sp017918}, volume = {420}, year = {1990}, } @inbook{3565, abstract = {We investigate the complexity of determining the shape and presentation (i.e. position with orientation) of convex polytopes in multi-dimensional Euclidean space using a variety of probe models.}, author = {Dobkin, David and Edelsbrunner, Herbert and Yap, Chee}, booktitle = {Autonomous Robot Vehicles}, editor = {Cox, Ingemar and Wilfong, Gordon}, isbn = {978-1-4613-8997-2}, pages = {328 -- 341}, publisher = {Springer}, title = {{Probing convex polytopes}}, doi = {10.1007/978-1-4613-8997-2_25}, year = {1990}, } @article{4064, abstract = {Given a set of data points pi = (xi, yi ) for 1 ≤ i ≤ n, the least median of squares regression line is a line y = ax + b for which the median of the squared residuals is a minimum over all choices of a and b. An algorithm is described that computes such a line in O(n 2) time and O(n) memory space, thus improving previous upper bounds on the problem. This algorithm is an application of a general method built on top of the topological sweep of line arrangements.}, author = {Edelsbrunner, Herbert and Souvaine, Diane}, issn = {1537-274X}, journal = {Journal of the American Statistical Association}, number = {409}, pages = {115 -- 119}, publisher = {American Statistical Association}, title = {{Computing least median of squares regression lines and guided topological sweep}}, doi = {10.1080/01621459.1990.10475313}, volume = {85}, year = {1990}, } @article{4063, abstract = {This paper describes a general-purpose programming technique, called Simulation of Simplicity, that can be used to cope with degenerate input data for geometric algorithms. It relieves the programmer from the task of providing a consistent treatment for every single special case that can occur. The programs that use the technique tend to be considerably smaller and more robust than those that do not use it. We believe that this technique will become a standard tool in writing geometric software.}, author = {Edelsbrunner, Herbert and Mücke, Ernst}, issn = {1557-7368}, journal = {ACM Transactions on Graphics}, number = {1}, pages = {66 -- 104}, publisher = {ACM}, title = {{Simulation of simplicity: A technique to cope with degenerate cases in geometric algorithms}}, doi = {10.1145/77635.77639}, volume = {9}, year = {1990}, } @article{4060, abstract = {This paper offers combinatorial results on extremum problems concerning the number of tetrahedra in a tetrahedrization of n points in general position in three dimensions, i.e. such that no four points are co-planar, It also presents an algorithm that in O(n log n) time constructs a tetrahedrization of a set of n points consisting of at most 3n-11 tetrahedra.}, author = {Edelsbrunner, Herbert and Preparata, Franco and West, Douglas}, issn = {1095-855X}, journal = {Journal of Symbolic Computation}, number = {3-4}, pages = {335 -- 347}, publisher = {Elsevier}, title = {{Tetrahedrizing point sets in three dimensions}}, doi = {10.1016/S0747-7171(08)80068-5}, volume = {10}, year = {1990}, }