@article{2521, author = {Nishimura, Masaki and Shigemoto, Ryuichi and Matsubayashi, K and Mimori, Y and Kameyama, Masakuni}, journal = {Clinical Neurology}, number = {11}, pages = {1441 -- 1444}, publisher = {Societas Neurologica Japonica}, title = {{Meningoencephalitis during the pre-icteric phase of hepatitis A - a case report}}, volume = {27}, year = {1987}, } @inproceedings{3514, abstract = {We consider the problem of obtaining sharp (nearly quadratic) bounds for the combinatorial complexity of the lower envelope (i.e. pointwise minimum) of a collection of n bivariate (or generally multi-variate) continuous and "simple" functions, and of designing efficient algorithms for the calculation of this envelope. This problem generalizes the well-studied univariate case (whose analysis is based on the theory of Davenport-Schinzel sequences), but appears to be much more difficult and still largely unsolved. It is a central problem that arises in many areas in computational and combinatorial geometry, and has numerous applications including generalized planar Voronoi diagrams, hidden surface elimination for intersecting surfaces, purely translational motion planning, finding common transversals of polyhedra, and more. In this abstract we provide several partial solutions and generalizations of this problem, and apply them to the problems mentioned above. The most significant of our results is that the lower envelope of n triangles in three dimensions has combinatorial complexity at most O(n2α(n)) (where α(n) is the extremely slowly growing inverse of Ackermann's function), that this bound is tight in the worst case, and that this envelope can be calculated in time O(n2α(n)).}, author = {Edelsbrunner, Herbert and Pach, János and Schwartz, Jacob and Sharir, Micha}, booktitle = {28th Annual Symposium on Foundations of Computer Science }, isbn = {0-8186-0807-2}, issn = {0272-5428}, location = {Los Angeles, CA, USA}, pages = {27 -- 37}, publisher = {IEEE}, title = {{On the lower envelope of bivariate functions and its applications}}, doi = {10.1109/SFCS.1987.44}, year = {1987}, } @article{3656, abstract = {We have analysed the role of sampling drift in inducing shifts between alternative adaptive peaks, in small and rapidly growing populations. Using a simple model of disruptive selection on a polygenic character, we calculate the net probabilityofapeakshift. If the growth rate is high, theprobabilityofashiftina growing population is insensitive to selection on the character. Assuming that the character is effectively neutral during the brief initial increase, we find that theprobabilityofapeakshift is given by theprobabilityof finding a standard normal variate greater than √2ΔV where ΔV is the reduction in additive genetic variance during the growth period. This result holds for arbitrary pattern of increase in size, provided that the rate of increase is high enough for selection to be negligible, and the character depends on a large number of loci. Comparing theprobabilityofpeakshiftsin founding populations with the rate ofshiftsin static and allopatric populations it appears that although strongly selected shifts are only likely to occur ina growing population, a static population is a more congenial setting for adaptive shifts.}, author = {Rouhani, Shahin and Barton, Nicholas H}, issn = {1095-8541}, journal = {Journal of Theoretical Biology}, number = {1}, pages = {51 -- 62}, publisher = {Elsevier}, title = {{The probability of peak shifts in a founder population}}, doi = {10.1016/S0022-5193(87)80100-5}, volume = {126}, year = {1987}, } @article{3657, abstract = {Shifts between adaptive peaks, caused by sampling drift, are involved in both speciation and adaptation via Wright's “shiftingbalance.” We use techniques from statistical mechanics to calculate the rate of such transitions for apopulation in a single panmictic deme and for apopulation which is continuously distributed over one- and two-dimensional regions. This calculation applies in the limit where transitions are rare. Our results indicate that stochastic divergence is feasible despite free gene flow, provided that neighbourhood size is low enough. In two dimensions, the rate of transition depends primarily on neighbourhood size N and only weakly on selection pressure (≈sk exp(− cN)), where k is a number determined by the local population structure, in contrast with the exponential dependence on selection pressure in one dimension (≈exp(− cN √s)) or in a single deme (≈exp(− cNs)). Our calculations agree with simulations of a single deme and a one-dimensional population.}, author = {Rouhani, Shahin and Barton, Nicholas H}, issn = {1096-0325}, journal = {Theoretical Population Biology}, number = {3}, pages = {465 -- 492}, publisher = {Elsevier}, title = {{Speciation and the "shifting balance" in a continuous population}}, doi = {10.1016/0040-5809(87)90016-5}, volume = {31}, year = {1987}, } @article{3658, abstract = {Females of the grasshopper Podisima pedestris were collected from the middle of a hybrid zone between two chromosomal races in the Alpes Maritimes. They had already mated in the field, and could therefore lay fertilised eggs in the laboratory. The embryos were karyotyped, and found to contain an excess of chromosomal homozygotes. No evidence of assortative mating was found from copulating pairs taken in the field. The excess appears to have been caused by a combination of multiple insemination and assortative fertilisation. The genetics of the assortment, and the implications for the evolution of reproductive isolation are discussed.}, author = {Hewitt, Godfrey and Nichols, R. and Barton, Nicholas H}, issn = {1365-2540}, journal = {Heredity}, number = {3}, pages = {457 -- 466}, publisher = {Nature Publishing Group}, title = {{Homogamy in a hybrid zone in the alpine grasshopper Podisma pedestris}}, doi = {10.1038/hdy.1987.156}, volume = {59}, year = {1987}, } @article{3659, abstract = {We develop models of the rates of evolution at sex-linked and autosomal loci and of the rates of fixation of chromosomal rearrangements involving sex chromosomes and autosomes. We show that the substitution of selectively favorable mutations often proceeds more rapidly for X- or Y-linked loci than for the autosomes, provided that mutations are recessive or partially recessive on the average. Selection acting on a quantitative character is expected to result in similar long-term rates of gene substitution for X-linked and autosomal loci, unless there is strong directional dominance. Short-term responses to such selection often preferentially fix alleles at autosomal loci. The fixation of slightly deleterious alleles by random drift and the stochastic turnover of alleles at loci controlling quantitative characters under stabilizing selection usually proceed somewhat more slowly at sex-linked loci. In contrast, the fixation of underdominant chromosomal rearrangements by random genetic drift is faster with sex linkage. Sex-specific selection may also differentially favor the fixation of sex-linked rearrangements. These results are discussed in relation to genetic and cytological data on species differences. We show that the frequently disproportionate effects of the sex chromosomes on interspecific inviability or sterility are consistent with the hypothesis that the gene differences concerned involve recessive or partially recessive alleles fixed by selection. Haldane's rule is readily interpreted in this light. There is little evidence for strong effects of the sex chromosomes on quantitative characters in interspecific crosses, in accordance with our theoretical results. Thus, the evolution of reproductive isolation may not be the byproduct of selective change in additively inherited, polygenic traits. Rather, it may be due mainly to the fixation of favorable mutations whose effects on fitness reflect locus-specific effects on the phenotype. These mutations behave as major genes in the sense of contributing the bulk of the genetic variance in the characters that they control during the course of the mutations' substitution. The data on the genetics of short-term responses to selection in Drosophila are hard to interpret, but, in accordance with theory, these responses do not usually seem to involve the X chromosome disproportionately. In some groups, there is evidence for a disproportionate role of the sex chromosomes in chromosomal changes, but others show no clear pattern. Factors that may distort the expectations of the simple models of chromosomal evolution are discussed.}, author = {Charlesworth, Brian and Coyne, Jerry and Barton, Nicholas H}, issn = {1537-5323}, journal = {American Naturalist}, number = {1}, pages = {113 -- 146}, publisher = {University of Chicago Press}, title = {{The relative rates of evolution of sex chromosomes and autosomes}}, doi = {10.1086/284701}, volume = {130}, year = {1987}, } @article{3660, abstract = {The maintenance of polygenic variability by a balance between mutation and stabilizing selection has been analysed using two approximations: the ‘Gaussian’ and the ‘house of cards’. These lead to qualitatively different relationships between the equilibrium genetic variance and the parameters describing selection and mutation. Here we generalize these approximations to describe the dynamics of genetic means and variances under arbitrary patterns of selection and mutation. We incorporate genetic drift into the same mathematical framework. The effects of frequency-independent selection and genetic drift can be determined from the gradient of log mean fitness and a covariance matrix that depends on genotype frequencies. These equations describe an ‘adaptive landscape’, with a natural metric of genetic distance set by the covariance matrix. From this representation we can change coordinates to derive equations describing the dynamics of an additive polygenic character in terms of the moments (means, variances, …) of allelic effects at individual loci. Only under certain simplifying conditions, such as those derived from the Gaussian and house-of-cards approximations, do these general recursions lead to tractable equations for the first few phenotypic moments. The alternative approximations differ in the constraints they impose on the distributions of allelic effects at individual loci. The Gaussian-based prediction that evolution of the phenotypic mean does not change the genetic variance is shown to be a consequence of the assumption that the allelic distributions are never skewed. We present both analytical and numerical results delimiting the parameter values consistent with our approximations.}, author = {Barton, Nicholas H and Turelli, Michael}, issn = {1469-5073}, journal = {Genetical Research}, number = {2}, pages = {157 -- 174}, publisher = {Cambridge University Press}, title = {{Adaptive landscapes, genetic distance, and the evolution of quantitative characters}}, doi = {10.1017/S0016672300026951}, volume = {49}, year = {1987}, } @article{3661, abstract = {We derive a formula giving thefrequency with which random drift shifts a population betweenalternativeequilibria. This formula is valid when such shifts are rare (Ns >> 1), and applies over a wide range of mutation rates. When the number of mutations entering the population is low (4Nμ << 1), the rate of stochastic shifts reduces to the product ofthe mutation rate and the probability of fixation of a single mutation. However, when many mutations enter the population in each generation (4Nμ >> 1), the rate is higher than would be expected if mutations were established independently, and converges to that given by a gaussian approximation. We apply recent results on bistable systems to extend this formula to the general multidimensional case. This gives an explicit expression for thefrequencyof stochastic shifts, which depends only on theequilibrium probability distribution near the saddle point separating thealternative stable states. The plausibility of theories of speciation through random drift are discussed in the light of these results.}, author = {Barton, Nicholas H and Rouhani, Shahin}, issn = {1095-8541}, journal = {Journal of Theoretical Biology}, number = {4}, pages = {397 -- 418}, publisher = {Elsevier}, title = {{The frequency of shifts between alternative equilibria}}, doi = {10.1016/S0022-5193(87)80210-2}, volume = {125}, year = {1987}, } @book{3900, abstract = {Computational geometry as an area of research in its own right emerged in the early seventies of this century. Right from the beginning, it was obvious that strong connections of various kinds exist to questions studied in the considerably older field of combinatorial geometry. For example, the combinatorial structure of a geometric problem usually decides which algorithmic method solves the problem most efficiently. Furthermore, the analysis of an algorithm often requires a great deal of combinatorial knowledge. As it turns out, however, the connection between the two research areas commonly referred to as computa­ tional geometry and combinatorial geometry is not as lop-sided as it appears. Indeed, the interest in computational issues in geometry gives a new and con­ structive direction to the combinatorial study of geometry. It is the intention of this book to demonstrate that computational and com­ binatorial investigations in geometry are doomed to profit from each other. To reach this goal, I designed this book to consist of three parts, acorn binatorial part, a computational part, and one that presents applications of the results of the first two parts. The choice of the topics covered in this book was guided by my attempt to describe the most fundamental algorithms in computational geometry that have an interesting combinatorial structure. In this early stage geometric transforms played an important role as they reveal connections between seemingly unrelated problems and thus help to structure the field.}, author = {Edelsbrunner, Herbert}, isbn = {978-3-540-13722-1}, issn = {1431-2654}, pages = {XV, 423}, publisher = {Springer}, title = {{Algorithms in Combinatorial Geometry}}, doi = {10.1007/978-3-642-61568-9}, volume = {10}, year = {1987}, } @article{4094, abstract = {The visibility graph of a finite set of line segments in the plane connects two endpoints u and v if and only if the straight line connection between u and v does not cross any line segment of the set. This article proves that 5n - 4 is a lower bound on the number of edges in the visibility graph of n nonintersecting line segments in the plane. This bound is tight.}, author = {Edelsbrunner, Herbert and Shen, Xiaojun}, issn = {1872-6119}, journal = {Information Processing Letters}, number = {2}, pages = {61 -- 64}, publisher = {Elsevier}, title = {{A tight lower bound on the size of visibility graphs}}, doi = {10.1016/0020-0190(87)90038-X}, volume = {26}, year = {1987}, } @article{4095, abstract = {he kth-order Voronoi diagram of a finite set of sites in the Euclidean plane E2 subdivides E2 into maximal regions such that all points within a given region have the same k nearest sites. Two versions of an algorithm are developed for constructing the kth-order Voronoi diagram of a set of n sites in O(n2 log n + k(n - k) log2 n) time, O(k(n - k)) storage, and in O(n2 + k(n - k) log2 n) time, O(n2) storage, respectively.}, author = {Chazelle, Bernard and Edelsbrunner, Herbert}, issn = {1557-9956}, journal = {IEEE Transactions on Computers}, number = {11}, pages = {1349 -- 1354}, publisher = {IEEE}, title = {{An improved algorithm for constructing kth-order Voronoi diagrams}}, doi = {10.1109/TC.1987.5009474}, volume = {36}, year = {1987}, } @article{4100, abstract = {This paper investigates the existence of linear space data structures for range searching. We examine thehomothetic range search problem, where a setS ofn points in the plane is to be preprocessed so that for any triangleT with sides parallel to three fixed directions the points ofS that lie inT can be computed efficiently. We also look atdomination searching in three dimensions. In this problem,S is a set ofn points inE 3 and the question is to retrieve all points ofS that are dominated by some query point. We describe linear space data structures for both problems. The query time is optimal in the first case and nearly optimal in the second. }, author = {Chazelle, Bernard and Edelsbrunner, Herbert}, issn = {1432-0444}, journal = {Discrete & Computational Geometry}, number = {1}, pages = {113 -- 126}, publisher = {Springer}, title = {{Linear space data structures for two types of range search}}, doi = {10.1007/BF02187875}, volume = {2}, year = {1987}, } @article{4101, abstract = {In a number of recent papers, techniques from computational geometry (the field of algorithm design that deals with objects in multi-dimensional space) have been applied to some problems in the area of computer graphics. In this way, efficient solutions were obtained for the windowing problem that asks for those line segments in a planar set that lie in given window (range) and the moving problem that asks for the first line segment that comes into the window when moving the window in some direction. In this paper we show that also the zooming problem, which asks for the first line segment that comes into the window when we enlarge it, can be solved efficiently. This is done by repeatedly performing range queries with ranges of varying sizes. The obtained structure is dynamic and yields a query time of O(log2n) and an insertion and deletion time of O(log2n), where n is the number of line segments in the set. The amount of storage required is O(n log n). It is also shown that the technique of repeated range search can be used to solve several other problems efficiently.}, author = {Edelsbrunner, Herbert and Overmars, Mark}, issn = {1872-6119}, journal = {Information Processing Letters}, number = {6}, pages = {413 -- 417}, publisher = {Elsevier}, title = {{Zooming by repeated range detection}}, doi = {10.1016/0020-0190(87)90120-7}, volume = {24}, year = {1987}, } @article{4102, abstract = {Determining or counting geometric objects that intersect another geometric query object is at the core of algorithmic problems in a number of applied areas of computer science. This article presents a family of space-efficient data structures that realize sublinear query time for points, line segments, lines and polygons in the plane, and points, line segments, planes, and polyhedra in three dimensions.}, author = {Dobkin, David and Edelsbrunner, Herbert}, issn = {1090-2678}, journal = {Journal of Algorithms}, number = {3}, pages = {348 -- 361}, publisher = {Academic Press}, title = {{Space searching for intersecting objects}}, doi = {10.1016/0196-6774(87)90015-0}, volume = {8}, year = {1987}, } @article{4319, abstract = {The grasshopper Podisma pedestris contains two chromosomal races, which differ by a Robertsonian fusion between the sex chromosome and an autosome, and which meet in a narrow hybrid zone in the Alpes Maritimes. DNA content variation across this hybrid zone was investigated by optical densitometry of Feulgen stained spermatids. Spermatids from males with the unfused sex chromosome stain more strongly than those from males with the fused chromosome. The difference between the karyotypes is greater in the centre of the hybrid zone, suggesting that it is not a pleiotropic effect of the fusion itself, but is due instead to differences at closely linked loci.}, author = {Westerman, Michael and Barton, Nicholas H and Hewitt, Godfrey}, issn = {1365-2540}, journal = {Heredity}, pages = {221 -- 228}, publisher = {Nature Publishing Group}, title = {{Differences in DNA content between two chromosomal races of the grasshopper Podisma pedestris}}, doi = {10.1038/hdy.1987.36}, volume = {58}, year = {1987}, } @article{4320, abstract = {Bosonic field theories may be formulated in terms of stochastic differential equations. The characteristic long term behaviour of these systems is a decay into the global minimum of their Hamiltonian. If local minima exist, the rate of this decay is determined by instanton effects. We calculate the decay rate and perform computer simulations on a 1 + 1 dimensional model to test the instanton approximation. We find the instanton approximations to be in very good agreement with the simulation results.}, author = {Rouhani, Shahin and Barton, Nicholas H}, issn = {1873-2119}, journal = {Physica A: Statistical Mechanics and its Applications}, number = {1-2}, pages = {220 -- 226}, publisher = {Elsevier}, title = {{Instantons in stochastic quantization}}, doi = {10.1016/0378-4371(87)90064-1}, volume = {143}, year = {1987}, } @article{4322, abstract = {A method is developed for calculating the probability of establishment of an allele which is favoured in some places, but not others, in a large subdivided population. This method is quite general, and could be used to calculate the chance that any system which is linear near an absorbing boundary will move away from that boundary. The results are applied to a population distributed along one dimension. Only mutants which arise within a distance σ/ √2s of the region in which they are favoured stand an appreciable chance of establishment. The net chance of establishment of mutations distributed randomly across the habitat will be decreased by gene flow if selection against them is sufficiently strong. However, if the mutations are only weakly deleterious outside some limited region, gene flow may increase the net chance of establishment.}, author = {Barton, Nicholas H}, issn = {1469-5073}, journal = {Genetical Research}, number = {1}, pages = {35 -- 40}, publisher = {Cambridge University Press}, title = {{The probability of establishment of an advantageous mutation in a subdivided population}}, doi = {10.1017/S0016672300023314}, volume = {50}, year = {1987}, }