TY - CONF AB - We present a randomized incremental algorithm for computing a single face in an arrangement of n line segments in the plane that is fairly simple to implement. The expected running time of the algorithm is O (nα(n) log n). The analysis of the algorithm uses a novel approach that generalizes and extends the Clarkson-Shor analysis technique. AU - Chazelle, Bernard AU - Edelsbrunner, Herbert AU - Guibas, Leonidas AU - Sharir, Micha AU - Snoeyink, Jack ID - 4058 SN - 978-0-89791-376-8 T2 - Proceedings of the 2nd annual ACM-SIAM symposium on Discrete algorithms TI - Computing a face in an arrangement of line segments ER - TY - CONF 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 O(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 - Edelsbrunner, Herbert AU - Tan, Tiow ID - 4055 T2 - 32nd Annual Symposium of Foundations of Computer Science TI - A quadratic time algorithm for the minmax length triangulation ER - TY - JOUR AB - An algorithm is presented that constructs the convex hull of a set of n points in three dimensions in worst-case time O(n log2h) and storage O(n), where h is the number of extreme points. This is an improvement of the O(nh) time gift-wrapping algorithm and, for certain values of h, of the O(n log n) time divide-and-conquer algorithm. AU - Edelsbrunner, Herbert AU - Shi, Weiping ID - 4051 IS - 2 JF - SIAM Journal on Computing SN - 0097-5397 TI - An O(n log^2 h) time algorithm for the three-dimensional convex hull problem VL - 20 ER - TY - JOUR AU - Edelsbrunner, Herbert ID - 4057 IS - 2 JF - Journal of Computer and System Sciences SN - 0022-0000 TI - Corrigendum VL - 42 ER - TY - JOUR AB - Two types of metabolically regulated K channels have been identified for the first time in enzymatically demyelinated fibres of amphibian sciatic nerve using the patch-clamp technique. A maxi K channel with a single-channel conductance of 132 pS (105 mM K on both sides of the membrane, 15°C) is activated both by micromolar concentrations of internal Ca and by depolarization. A second type of K channel with a conductance of 44 pS is inhibited by intracellular adenosine 5'-triphosphate (ATP) with a half-maximal inhibitory concentration (IC50) of 35 μM. It is blocked by submicromolar concentrations of external glibenclamide. Both channels are sensitive to external tetraethylammonium chloride (IC50 = 0.2 mM for the maxi K channel and 4.2 mM for the ATP-sensitive channel). They may be part of a complex feedback system regulating axonal excitability under various metabolic conditions. AU - Jonas, Peter M AU - Koh, Duk AU - Kampe, Knut AU - Hermsteiner, Markus AU - Vogel, Werner ID - 3468 IS - 1-2 JF - Pflügers Archiv : European Journal of Physiology SN - 0031-6768 TI - ATP-sensitive and Ca-activated K channels in vertebrate axons: novel links between metabolism and excitability VL - 418 ER - TY - JOUR AB - We compare the pattern of morphological and electrophoretic variation in the hybrid zone between Bombina bombina and B. variegata across two transects: one near Cracow and one 200 km away, near Przemysl in southeastern Poland. Morphological variation across the Przemysl transect had been surveyed more than 50 years ago; though we found a significant shift at one site, there is no evidence for gross movement over this period. Morphological and electrophoretic changes coincide, and the average shape of the clines is the same across both transects. At the center, most of the change in frequency of six diagnostic allozymes occurs within w = 6.05 km (2-unit support limits 5.56-6.54 km). These steep gradients are generated not by selection on the allozymes themselves, but by associations with other loci: though these markers are unlinked, they are in strong linkage disequilibrium with each other [R = D/ = 0.22 (0.15-0.29) at the center]. Disequilibria are broken up as alleles diffuse away from the zone and flow into the new genetic background. The net barrier to the flow of genes from bombina into variegata, which is generated by these disequilibria, is B = 51 (22-81) km. The fitness of hybrids must be substantially reduced to produce such a barrier [W̄H/W̄P = 0.58 (0.54-0.68)], and this selection must be spread over many loci [N = 55 (26-88)]. Alleles introgress significantly less far than would be expected from the age of the zone and the estimated dispersal rate [σ = 0.99 (0.82-1.14) km gen.-1/2]: this implies selection of se = 0.37 (0.15-0.58)% on the enzymes themselves. There is weak but significant linkage disequilibrium well away from the center of the zone; this, together with the presence of parental and F1 genotypes, suggests some long-range migration. However, such migration is not likely to cause significant introgression. AU - Szymura, Jacek AU - Barton, Nicholas H ID - 3646 IS - 2 JF - Evolution SN - 0014-3820 TI - The genetic structure of the hybrid zone between the fire-bellied toads Bombina bombina and B. variegata: comparisons between transects and between loci VL - 45 ER - TY - JOUR AB - A method is developed that describes the effects on an arbitrary number of autosomal loci of selection on haploid and diploid stages, of nonrandom mating between haploid individuals, and of recombination. We provide exact recursions for the dynamics of allele frequencies and linkage disequilibria (nonrandom associations of alleles across loci). When selection is weak relative to recombination, our recursions provide simple approximations for the linkage disequilibria among arbitrary combinations of loci. We show how previous models of sex-independent natural selection on diploids, assortative mating between haploids, and sexual selection on haploids can be analyzed in this framework. Using our weak-selection approximations, we derive new results concerning the coevolution of male traits and female preferences under natural and sexual selection. In particular, we provide general expressions for the intensity of linkage-disequilibrium induced selection experienced by loci that contribute to female preferences for specific male traits. Our general results support the previous observation that these indirect selection forces are so weak that they are unlikely to dominate the evolution of preference-producing loci. AU - Barton, Nicholas H AU - Turelli, Michael ID - 3647 IS - 1 JF - Genetics SN - 0016-6731 TI - Natural and sexual selection on many loci VL - 127 ER - TY - JOUR AB - We investigate the probability of fixation of a chromosome rearrangement in a subdivided population, concentrating on the limit where migration is so large relative to selection (m ≫ s) that the population can be thought of as being continuously distributed. We study two demes, and one- and two-dimensional populations. For two demes, the probability of fixation in the limit of high migration approximates that of a population with twice the size of a single deme: migration therefore greatly reduces the fixation probability. However, this behavior does not extend to a large array of demes. Then, the fixation probability depends primarily on neighborhood size (Nb), and may be appreciable even with strong selection and free gene flow (≈exp(-B·Nb) in one dimension, ≈exp(-B\cdotNb) in two dimensions). Our results are close to those for the more tractable case of a polygenic character under disruptive selection. AU - Barton, Nicholas H AU - Rouhani, Shahin ID - 3648 IS - 3 JF - Evolution SN - 0014-3820 TI - The probability of fixation of a new karyotype in a continuous population VL - 45 ER - TY - CONF AB - Let P be a simple polygon with n vertices. We present a simple decomposition scheme that partitions the interior of P into O(n) so-called geodesic triangles, so that any line segment interior to P crosses at most 2 log n of these triangles. This decomposition can be used to preprocess P in time O(n log n) and storage O(n), so that any ray-shooting query can be answered in time O(log n).The algorithms are fairly simple and easy to implement. We also extend this technique to the case of ray-shooting amidst k polygonal obstacles with a total of n edges, so that a query can be answered in O(radicklog n) time. AU - Chazelle, Bernard AU - Edelsbrunner, Herbert AU - Grigni, Michelangelo AU - Guibas, Leonidas AU - Hershberger, John AU - Sharir, Micha AU - Snoeyink, Jack ID - 4059 T2 - 18th International Colloquium on Automata, Languages and Programming TI - Ray shooting in polygons using geodesic triangulations VL - 510 ER - TY - JOUR AB - We present an algorithm to compute a Euclidean minimum spanning tree of a given set S of N points in Ed in time O(Fd (N,N) logd N), where Fd (n,m) is the time required to compute a bichromatic closest pair among n red and m green points in Ed . If Fd (N,N)=Ω(N1+ε), for some fixed e{open}>0, then the running time improves to O(Fd (N,N)). Furthermore, we describe a randomized algorithm to compute a bichromatic closest pair in expected time O((nm log n log m)2/3+m log2 n+n log2 m) in E3, which yields an O(N4/3 log4/3 N) expected time, algorithm for computing a Euclidean minimum spanning tree of N points in E3. In d≥4 dimensions we obtain expected time O((nm)1-1/([d/2]+1)+ε+m log n+n log m) for the bichromatic closest pair problem and O(N2-2/([d/2]+1)ε) for the Euclidean minimum spanning tree problem, for any positive e{open}. AU - Agarwal, Pankaj AU - Edelsbrunner, Herbert AU - Schwarzkopf, Otfried AU - Welzl, Emo ID - 4061 IS - 1 JF - Discrete & Computational Geometry SN - 0179-5376 TI - Euclidean minimum spanning trees and bichromatic closest pairs VL - 6 ER -