@article{4069,
abstract = {Let C be a cell complex in d-dimensional Euclidean space whose faces are obtained by orthogonal projection of the faces of a convex polytope in d + 1 dimensions. For example, the Delaunay triangulation of a finite point set is such a cell complex. This paper shows that the in front/behind relation defined for the faces of C with respect to any fixed viewpoint x is acyclic. This result has applications to hidden line/surface removal and other problems in computational geometry.},
author = {Herbert Edelsbrunner},
journal = {Combinatorica},
number = {3},
pages = {251 -- 260},
publisher = {Springer},
title = {{An acyclicity theorem for cell complexes in d dimension}},
doi = {10.1007/BF02122779},
volume = {10},
year = {1990},
}
@inproceedings{4071,
abstract = {We show that a triangulation of a set of n points in the plane that minimizes the maximum angle can be computed in time O(n2 log n) and space O(n). In the same amount of time and space we can also handle the constrained case where edges are prescribed. The algorithm iteratively improves an arbitrary initial triangulation and is fairly easy to implement.},
author = {Herbert Edelsbrunner and Tan, Tiow Seng and Waupotitsch, Roman},
pages = {44 -- 52},
publisher = {ACM},
title = {{An O(n^2log n) time algorithm for the MinMax angle triangulation}},
doi = {10.1145/98524.98535},
year = {1990},
}
@inproceedings{4076,
abstract = {We present an algorithm to compute a Euclidean minimum spanning tree of a given set S of n points in Ed in time O(Td(N, N) logd N), where Td(n, m) is the time required to compute a bichromatic closest pair among n red and m blue points in Ed. If Td(N, N) = Ω(N1+ε), for some fixed ε > 0, then the running time improves to O(Td(N, N)). Furthermore, we describe a randomized algorithm to compute a bichromatic closets pair in expected time O((nm log n log m)2/3+m log2 n + n log2 m) in E3, which yields an O(N4/3log4/3 N) expected time algorithm for computing a Euclidean minimum spanning tree of N points in E3.},
author = {Agarwal, Pankaj K and Herbert Edelsbrunner and Schwarzkopf, Otfried and Welzl, Emo},
pages = {203 -- 210},
publisher = {ACM},
title = {{ Euclidean minimum spanning trees and bichromatic closest pairs}},
doi = {10.1145/98524.98567},
year = {1990},
}
@article{3649,
abstract = {Selection on polygenic characters is generally analyzed by statistical methods that assume a Gaussian (normal) distribution of breeding values. We present an alternative analysis based on multilocus population genetics. We use a general representation of selection, recombination, and drift to analyze an idealized polygenic system in which all genetic effects are additive (i.e., both dominance and epistasis are absent), but no assumptions are made about the distribution of breeding values or the numbers of loci or alleles. Our analysis produces three results. First, our equations reproduce the standard recursions for the mean and additive variance if breeding values are Gaussian; but they also reveal how non-Gaussian distributions of breeding values will alter these dynamics. Second, an approximation valid for weak selection shows that even if genetic variance is attributable to an effectively infinite number of loci with only additive effects, selection will generally drive the distribution of breeding values away from a Gaussian distribution by creating multilocus linkage disequilibria. Long-term dynamics of means can depart substantially from the predictions of the standard selection recursions, but the discrepancy may often be negligible for short-term selection. Third, by including mutation, we show that, for realistic parameter values, linkage disequilibrium has little effect on the amount of additive variance maintained at an equilibrium between stabilizing selection and mutation. Each of these analytical results is supported by numerical calculations.},
author = {Turelli, Michael and Nicholas Barton},
journal = {Theoretical Population Biology},
number = {1},
pages = {1 -- 57},
publisher = {Academic Press},
title = {{Dynamics of polygenic characters under selection}},
doi = {10.1016/0040-5809(90)90002-D},
volume = {38},
year = {1990},
}
@article{3651,
abstract = {It is widely held that each gene typically affects many characters, and that each character is affected by many genes. Moreover, strong stabilizing selection cannot act on an indefinitely large number of independent traits. This makes it likely that heritable variation in any one trait is maintained as a side effect of polymorphisms which have nothing to do with selection on that trait. This paper examines the idea that variation is maintained as the pleiotropic side effect of either deleterious mutation, or balancing selection. If mutation is responsible, it must produce alleles which are only mildly deleterious (s & 10(-3)), but nevertheless have significant effects on the trait. Balancing selection can readily maintain high heritabilities; however, selection must be spread over many weakly selected polymorphisms if large responses to artificial selection are to be possible. In both classes of pleiotropic model, extreme phenotypes are less fit, giving the appearance of stabilizing selection on the trait. However, it is shown that this effect is weak (of the same order as the selection on each gene): the strong stabilizing selection which is often observed is likely to be caused by correlations with a limited number of directly selected traits. Possible experiments for distinguishing the alternatives are discussed.},
author = {Nicholas Barton},
journal = {Genetics},
number = {3},
pages = {773 -- 782},
publisher = {Genetics Society of America},
title = {{Pleiotropic models of quantitative variation}},
volume = {124},
year = {1990},
}