@inproceedings{4073,
abstract = {A number of rendering algorithms in computer graphics sort three-dimensional objects by depth and assume that there is no cycle that makes the sorting impossible. One way to resolve the problem caused by cycles is to cut the objects into smaller pieces. The problem of estimating how many such cuts are always sufficient is addressed. A few related algorithmic and combinatorial geometry problems are considered.},
author = {Chazelle, Bernard and Edelsbrunner, Herbert and Guibas, Leonidas and Pollack, Richard and Seidel, Raimund and Sharir, Micha and Snoeyink, Jack},
booktitle = {31st Annual Symposium on Foundations of Computer Science},
isbn = {0-8186-2082-X},
location = {St. Louis, MO, United States of America},
pages = {242 -- 251},
publisher = {IEEE},
title = {{Counting and cutting cycles of lines and rods in space}},
doi = {10.1109/FSCS.1990.89543},
year = {1990},
}
@article{4074,
abstract = {We present upper and lower bounds for extremal problems defined for arrangements of lines, circles, spheres, and alike. For example, we prove that the maximum number of edges boundingm cells in an arrangement ofn lines is Θ(m 2/3 n 2/3 +n), and that it isO(m 2/3 n 2/3 β(n) +n) forn unit-circles, whereβ(n) (and laterβ(m, n)) is a function that depends on the inverse of Ackermann's function and grows extremely slowly. If we replace unit-circles by circles of arbitrary radii the upper bound goes up toO(m 3/5 n 4/5 β(n) +n). The same bounds (without theβ(n)-terms) hold for the maximum sum of degrees ofm vertices. In the case of vertex degrees in arrangements of lines and of unit-circles our bounds match previous results, but our proofs are considerably simpler than the previous ones. The maximum sum of degrees ofm vertices in an arrangement ofn spheres in three dimensions isO(m 4/7 n 9/7 β(m, n) +n 2), in general, andO(m 3/4 n 3/4 β(m, n) +n) if no three spheres intersect in a common circle. The latter bound implies that the maximum number of unit-distances amongm points in three dimensions isO(m 3/2 β(m)) which improves the best previous upper bound on this problem. Applications of our results to other distance problems are also given.},
author = {Clarkson, Kenneth and Edelsbrunner, Herbert and Guibas, Leonidas and Sharir, Micha and Welzl, Emo},
issn = {1432-0444},
journal = {Discrete & Computational Geometry},
number = {1},
pages = {99 -- 160},
publisher = {Springer},
title = {{Combinatorial complexity bounds for arrangements of curves and spheres}},
doi = {10.1007/BF02187783},
volume = {5},
year = {1990},
}
@article{4075,
abstract = {A key problem in computational geometry is the identification of subsets of a point set having particular properties. We study this problem for the properties of convexity and emptiness. We show that finding empty triangles is related to the problem of determining pairs of vertices that see each other in a star-shaped polygon. A linear-time algorithm for this problem which is of independent interest yields an optimal algorithm for finding all empty triangles. This result is then extended to an algorithm for finding empty convex r-gons (r> 3) and for determining a largest empty convex subset. Finally, extensions to higher dimensions are mentioned.},
author = {Dobkin, David and Edelsbrunner, Herbert and Overmars, Mark},
issn = {1432-0541},
journal = {Algorithmica},
number = {4},
pages = {561 -- 571},
publisher = {Springer},
title = {{Searching for empty convex polygons}},
doi = {10.1007/BF01840404},
volume = {5},
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 and Edelsbrunner, Herbert and Schwarzkopf, Otfried and Welzl, Emo},
booktitle = {Proceedings of the 6th annual symposium on Computational geometry},
isbn = {978-0-89791-362-1},
location = {Berkeley, CA, United States},
pages = {203 -- 210},
publisher = {ACM},
title = {{ Euclidean minimum spanning trees and bichromatic closest pairs}},
doi = {10.1145/98524.98567},
year = {1990},
}
@inproceedings{4077,
abstract = {We prove that for any set S of n points in the plane and n3-α triangles spanned by the points of S there exists a point (not necessarily of S) contained in at least n3-3α/(512 log25 n) of the triangles. This implies that any set of n points in three - dimensional space defines at most 6.4n8/3 log5/3 n halving planes.},
author = {Aronov, Boris and Chazelle, Bernard and Edelsbrunner, Herbert and Guibas, Leonidas and Sharir, Micha and Wenger, Rephael},
booktitle = {Proceedings of the 6th annual symposium on Computational geometry},
isbn = {978-0-89791-362-1},
location = {Berkley, CA, United States},
pages = {112 -- 115},
publisher = {ACM},
title = {{Points and triangles in the plane and halving planes in space}},
doi = {10.1145/98524.98548},
year = {1990},
}
@inproceedings{4078,
abstract = {In this paper we derived combinatorial point selection results for geometric objects defined by pairs of points. In a nutshell, the results say that if many pairs of a set of n points in some fixed dimension each define a geometric object of some type, then there is a point covered by many of these objects. Based on such a result for three-dimensional spheres we show that the combinatorial size of the Delaunay triangulation of a point set in space can be reduced by adding new points. We believe that from a practical point of view this is the most important result of this paper.},
author = {Chazelle, Bernard and Edelsbrunner, Herbert and Guibas, Leonidas and Hershberger, John and Seidel, Raimund and Sharir, Micha},
booktitle = {Proceedings of the 6th annual symposium on computational geometry},
isbn = {978-0-89791-362-1},
location = {Berkley, CA, United States},
pages = {116 -- 127},
publisher = {ACM},
title = {{Slimming down by adding; selecting heavily covered points}},
doi = {10.1145/98524.98551},
year = {1990},
}
@article{4310,
author = {Barton, Nicholas H and Jones, Steve},
issn = {1476-4687},
journal = {Nature},
pages = {415 -- 416},
publisher = {Nature Publishing Group},
title = {{The language of the genes}},
doi = {10.1038/346415a0},
volume = {346},
year = {1990},
}
@inbook{4311,
author = {Barton, Nicholas H and Clark, A.},
booktitle = {Population biology: Ecological and evolutionary viewpoints},
editor = {Wöhrmann, Klaus and Jain, Subodh},
isbn = { 978-3642744761},
pages = {115 -- 174},
publisher = {Springer},
title = {{Population structure and processes in evolution}},
doi = {10.1007/978-3-642-74474-7_5},
year = {1990},
}
@inproceedings{4596,
abstract = {A real-time temporal logic for the specification of reactive systems is introduced. The novel feature of the logic, TPTL, is the adoption of temporal operators as quantifiers over time variables; every modality binds a variable to the time(s) it refers to. TPTL is demonstrated to be both a natural specification language and a suitable formalism for verification and synthesis. A tableau-based decision procedure and model-checking algorithm for TPTL are presented. Several generalizations of TPTL are shown to be highly undecidable.},
author = {Alur, Rajeev and Henzinger, Thomas A},
booktitle = {30th Annual Symposium on Foundations of Computer Science},
isbn = {0-8186-1982-1},
issn = {1558-0814},
location = {Research Triangle Park, NC, USA},
pages = {164 -- 169},
publisher = {IEEE},
title = {{A really temporal logic}},
doi = {10.1109/SFCS.1989.63473},
year = {1989},
}
@article{2479,
abstract = {Distribution of putative glutamatergic neurons in the lower brainstem and cerebellum of the rat was examined immunocytochemically by using a monoclonal antibody against phosphate-activated glutaminase, which has been proposed to be a major synthetic enzyme of transmitter glutamate and so may serve as a marker for glutamatergic neurons in the central nervous system. Intensely-immunolabeled neuronal cell bodies were densely distributed in the main precerebellar nuclei sending mossy fibers to the cerebellum; in the pontine nuclei, pontine tegmental reticular nucleus of Bechterew, external cuneate nucleus, and lateral reticular nucleus of the medulla oblongata. Phosphate-activated glutaminase-immunoreactive granular deposits were densely seen in the brachium pontis and restiform body, suggesting the immunolabeling of mossy fibers of passage. In the cerebellum, neuropil within the granule cell layer of the cerebellar cortex displayed intense phosphate-activated glutaminase-immunoreactivity, and that within the deep cerebellar nuclei showed moderate immunoreactivity. These results indicate that many mossy fiber terminals originate from phosphate-activated glutaminase-containing neurons and utilize phosphate-activated glutaminase for the synthesis of transmitter glutamate. Intensely-immunostained neuronal cell bodies were further observed in other regions which have been reported to contain neurons sending mossy fibers to the cerebellum; in the dorsal part of the principal sensory trigeminal nucleus, dorsomedial part of the oral subnucleus of the spinal trigeminal nucleus, interpolar subnucleus of the spinal trigeminal nucleus, paratrigeminal nucleus, supragenual nucleus, regions dorsal to the abducens nucleus and genu of the facial nerve, superior and medial vestibular nuclei, cell groups f, x and y, hypoglossal prepositus nucleus, intercalated nucleus, nucleus of Roller, reticular regions intercalated between the motor trigeminal and principal sensory trigeminal nuclei, linear nucleus, and gigantocellular and paramedian reticular formation. Neuronal cell bodies with intense phosphate-activated glutaminase-immunoreactivity were also found in other brainstem regions, such as the paracochlear glial substance, posterior ventral cochlear nucleus, and cell group e. Although it is still controversial whether all glutamatergic neurons use phosphate-activated glutaminase in a transmitter-related process and whether phosphate-activated glutaminase is involved in other metabolism-related processes, the neurons showing intense phosphate-activated glutaminase-immuno-reactivity in the present study were suggested to be putative glutamatergic neurons.},
author = {Kaneko, Takeshi and Itoh, Kazuo and Shigemoto, Ryuichi and Mizuno, Noboru},
issn = {1873-7544},
journal = {Neuroscience},
number = {1},
pages = {79 -- 98},
publisher = {Elsevier},
title = {{Glutaminase-like immunoreactivity in the lower brainstem and cerebellum of the adult rat}},
doi = {10.1016/0306-4522(89)90109-7},
volume = {32},
year = {1989},
}
@article{2525,
abstract = {This paper describes the amino acid sequence of the rat substance P receptor and its comparison with that of the rat substance K receptor on the basis of molecular cloning and sequence analysis. From a rat brain cDNA library constructed with an RNA expression vector, we identified a cDNA mixture containing a functional substance P receptor cDNA by examining electrophysiologically a receptor expression following injection of the mRNAs synthesized in vitro into Xenopus oocytes. A receptor cDNA clone was then isolated by cross-hybridization with the bovine substance K receptor DNA. The clone was confirmed by selective binding of substance P to the cloned receptor expressed in mammalian COS cells. The deduced amino acid sequence (407 amino acid residues) possesses seven putative membrane spanning domains and shows a sequence similarity to the members of G-protein-coupled receptors. The rat substance P and substance K receptor are very similar in both size and amino acid sequences, particularly in the putative transmembrane similarity is in marked contrast to the sequence divergence in the amino- and carboxyl-terminal regions and the third cytoplasmic loop. The observed sequence similarytity and divergence would thus contribute to the expression of similar but pharmacological regions and the first and second cytoplasmic loops. This distinguishable activities of the two tachykinin receptors.},
author = {Yokota, Yoshifumi and Sasai, Yoshiki and Tanaka, Kohichi and Fujiwara, Tsutomu and Tsuchida, Kunihiro and Shigemoto, Ryuichi and Kakizuka, Akira and Ohkubo, Hiroaki and Nakanishi, Shigetada},
issn = {1083-351X},
journal = {Journal of Biological Chemistry},
number = {30},
pages = {17649 -- 17652},
publisher = {American Society for Biochemistry and Molecular Biology},
title = {{Molecular characterization of a functional cDNA for rat substance P receptor}},
doi = {doi.org/10.1016/S0021-9258(19)84619-7},
volume = {264},
year = {1989},
}
@article{2526,
abstract = {When WGA-HRP (wheat germ agglutinin-horseradish peroxidase conjugate) or HRP was injected into the regions around the superior central and/or the dorsal raphe nuclei in the cat, cell bodies of a number of non-pyramidal neurons were labeled in Ammon's horn. Thus the existence of direct projections from non-pyramidal neurons in Ammon's horn to the rostral raphe regions in the brainstem was suggested in the cat.},
author = {Ino, Tadashi and Itoh, Kazuo and Kamiya, Hiroto and Kaneko, Takeshi and Shigemoto, Ryuichi and Akiguchi, Ichiro and Mizuno, Noboru},
issn = {1872-6240},
journal = {Brain Research},
number = {1},
pages = {157 -- 161},
publisher = {Elsevier},
title = {{Direct projections from Ammon's horn to the rostral raphe regions in the brainstem of the cat}},
doi = {10.1016/0006-8993(89)91346-2},
volume = {479},
year = {1989},
}
@article{2527,
author = {Akimoto, Masumi and Shigemoto, Ryuichi and Kawamura, Makiko and Yamagata, Hideharu and Kurihara, Takeshi and Takata, S and Miwa, Yoko and Akagami, N and Katsu, Kenichi and Yamauchi, D},
journal = {Japanese Journal of Gastroenterology},
number = {11},
pages = {2627},
publisher = {Japanese Society of Gastroenterology},
title = {{Effect of endothelin on gastric mucosal blood flow in rat}},
doi = {10.11405/nisshoshi1964.86.2627},
volume = {86},
year = {1989},
}
@article{3465,
abstract = {Asymmetrical displacement currents and Na currents of single myelinated nerve fibers of Xenopus laevis were studied in the temperature range from 5 to 24 degrees C. The time constant of the on-response at E = 4 mV, tau on, was strongly temperature dependent, whereas the amount of displaced charge at E = 39 mV, Qon, was only slightly temperature dependent. The mean Q10 for tau on-1 was 2.54, the mean Q10 for Qon was 1.07. The time constant of charge immobilization, tau i, at E = 4 mV varied significantly (alpha = 0.001) with temperature. The mean Q10 for tau i-1 was 2.71 +/- 0.38. The time constants of immobilization of gating charge and of fast inactivation of Na permeability were similar in the temperature range from 6 to 22 degrees C. The Qoff/Qon ratio for E = 4 mV pulses of 0.5 msec duration decreased with increasing temperature. The temperature dependence of the time constant of the off-response could not be described by a single Q10 value, since the Q10 depended on the duration of the test pulse. Increasing temperature shifted Qon (E) curves to more negative potentials by 0.51 mV K-1, but shifted PNa (E) curves and h infinity (E) curves to more positive potentials by 0.43 and 0.57 mV K-1, respectively. h infinity (E = -70 mV) increased monotonously with increasing temperature. The present data indicate that considerable entropy changes may occur when the Na channel molecule passes from closed through open to inactivated states.},
author = {Jonas, Peter M},
issn = {1432-1424},
journal = {Journal of Membrane Biology},
number = {3},
pages = {277 -- 289},
publisher = {Springer},
title = {{Temperature dependence of gating current in myelinated nerve fibers}},
doi = {10.1007/BF01870958},
volume = {112},
year = {1989},
}
@article{3466,
abstract = {Amphibian myelinated nerve fibers were treated with collagenase and protease. Axons with retraction of the myelin sheath were patch-clamped in the nodal and paranodal region. One type of Na channel was found. It has a single-channel conductance of 11 pS (15 degrees C) and is blocked by tetrodotoxin. Averaged events show the typical activation and inactivation kinetics of macroscopic Na current. Three potential-dependent K channels were identified (I, F, and S channel). The I channel, being the most frequent type, has a single-channel conductance of 23 pS (inward current, 105 mM K on both sides of the membrane), activates between -60 and -30 mV, deactivates with intermediate kinetics, and is sensitive to dendrotoxin. The F channel has a conductance of 30 pS, activates between -40 and 60 mV, and deactivates with fast kinetics. The former inactivates within tens of seconds; the latter inactivates within seconds. The third type, the S channel, has a conductance of 7 pS and deactivates slowly. All three channels can be blocked by external tetraethylammonium chloride. We suggest that these distinct K channel types form the basis for the different components of macroscopic K current described previously.},
author = {Jonas, Peter M and Bräu, Michael and Hermsteiner, Markus and Vogel, Werner},
issn = {1091-6490},
journal = {PNAS},
number = {18},
pages = {7238 -- 7242},
publisher = {National Academy of Sciences},
title = {{Single-channel recording in myelinated nerve fibers reveals one type of Na channel but different K channels}},
doi = {10.1073/pnas.86.18.7238},
volume = {86},
year = {1989},
}
@inproceedings{3549,
abstract = {We study three types of spatial triangulations: Delaunay triangulations, triangulations with non-obtuse dihedral angles, and KJ-triangulations. The latter satisfy a certain angle condition useful for finite element approximation. We show that the condition for Delaunay triangulations is incomparable with the other two conditions, and that triangulations with non-obtuse dihedral angles are necessarily also KJ-triangulations. These relationships are in sharp contrast to the ones in the planar case. },
author = {Edelsbrunner, Herbert},
pages = {83 -- 89},
publisher = {Institute of the Electronics, Information and Communication Enginneers},
title = {{Spatial triangulations with dihedral angle conditions}},
year = {1989},
}
@article{3652,
abstract = {Frequency-dependent selection against rare forms can maintain clines. For weak selection, s, in simple linear models of frequency-dependence, single locus clines are stabilized with a maximum slope of between square root of s/square root of 8 sigma and square root of s/square root of 12 delta, where sigma is the dispersal distance. These clines are similar to those maintained by heterozygote disadvantage. Using computer simulations, the weak-selection analytical results are extended to higher selection pressures with up to three unlinked genes. Graphs are used to display the effect of selection, migration, dominance, and number of loci on cline widths, speeds of cline movements, two-way gametic correlations ("linkage disequilibria"), and heterozygote deficits. The effects of changing the order of reproduction, migration, and selection, are also briefly explored. Epistasis can also maintain tension zones. We show that epistatic selection is similar in its effects to frequency-dependent selection, except that the disequilibria produced in the zone will be higher for a given level of selection. If selection consists of a mixture of frequency-dependence and epistasis, as is likely in nature, the error made in estimating selection is usually less than twofold. From the graphs, selection and migration can be estimated using knowledge of the dominance and number of genes, of gene frequencies and of gametic correlations from a hybrid zone.},
author = {Mallet, James and Barton, Nicholas H},
issn = {0016-6731},
journal = {Genetics},
number = {4},
pages = {967 -- 976},
publisher = {Genetics Society of America},
title = {{Inference from clines stabilized by frequency-dependent selection}},
doi = {10.1093/genetics/122.4.967},
volume = {122},
year = {1989},
}
@article{3653,
abstract = {Frequency-dependent selection on warning color can maintain narrow hybrid zones between unpalatable prey taxa. To measure such selection, we transferred marked Heliconius erato (Lepidoptera: Nymphalidae) in both directions across a 10-km-wide hybrid zone between Peruvian races differing in color pattern. These experimental H. erato were released at four sites, along with control H. erato of the phenotype native to each site. Survival of experimental butterflies was significantly lower than that of controls at two sites and overall. Most selection, measured as differences in survival, occurred soon after release. Selection against foreign morphs was 52% (confidence limits: 25-71%) and was probably due to bird attacks on unusual warning-color morphs (more than 10% of the recaptures had beak marks). Since only three major loci determine the color-pattern differences, this suggests an average selection coefficient of 0.17 per locus, sufficient to maintain the narrow clines in H. erato.},
author = {Mallet, James and Barton, Nicholas H},
issn = {1558-5646},
journal = {Evolution},
number = {2},
pages = {421 -- 431},
publisher = {Wiley-Blackwell},
title = {{Strong natural selection in a warning color hybrid zone}},
doi = {10.2307/2409217 },
volume = {43},
year = {1989},
}
@article{3654,
abstract = {Many species are divided into a mosaic of genetically distinct populations, separated by narrow zones of hybridization. Studies of hybrid zones allow us to quantify the genetic differences responsible for speciation, to measure the diffusion of genes between diverging taxa, and to understand the spread of alternative adaptations.},
author = {Barton, Nicholas H and Hewitt, Godfrey},
issn = {1476-4687},
journal = {Nature},
pages = {497 -- 503},
publisher = {Nature Publishing Group},
title = {{Adaptation, speciation and hybrid zones}},
doi = {10.1038/341497a0},
volume = {341},
year = {1989},
}
@article{4079,
author = {Edelsbrunner, Herbert and Skiena, Steven},
issn = {1930-0972},
journal = {American Mathematical Monthly},
number = {7},
pages = {614 -- 618},
publisher = {Mathematical Association of America},
title = {{On the number of furthest neighbor pairs in a point set}},
doi = {10.1080/00029890.1989.11972250},
volume = {96},
year = {1989},
}
@article{4080,
abstract = {This paper proves that any set of n points in the plane contains two points such that any circle through those two points encloses at least n12−112+O(1)n47 points of the set. The main ingredients used in the proof of this result are edge counting formulas for k-order Voronoi diagrams and a lower bound on the minimum number of semispaces of size at most k.},
author = {Edelsbrunner, Herbert and Hasan, Nany and Seidel, Raimund and Shen, Xiao},
issn = {1572-9168},
journal = {Geometriae Dedicata},
number = {1},
pages = {1 -- 12},
publisher = {Springer},
title = {{Circles through two points that always enclose many points}},
doi = {10.1007/BF00181432},
volume = {32},
year = {1989},
}
@article{4081,
abstract = {This paper studies applications of envelopes of piecewise linear functions to problems in computational geometry. Among these applications we find problems involving hidden line/surface elimination, motion planning, transversals of polytopes, and a new type of Voronoi diagram for clusters of points. All results are either combinatorial or computational in nature. They are based on the combinatorial analysis in two companion papers [PS] and [E2] and a divide-and-conquer algorithm for computing envelopes described in this paper.},
author = {Edelsbrunner, Herbert and Guibas, Leonidas and Sharir, Micha},
issn = {1432-0444},
journal = {Discrete & Computational Geometry},
number = {1},
pages = {311 -- 336},
publisher = {Springer},
title = {{The upper envelope of piecewise linear functions: Algorithms and applications}},
doi = {10.1007/BF02187733},
volume = {4},
year = {1989},
}
@article{4082,
abstract = {Sweeping a collection of figures in the Euclidean plane with a straight line is one of the novel algorithmic paradigms that have emerged in the field of computational geometry. In this paper we demonstrate the advantages of sweeping with a topological line that is not necessarily straight. We show how an arrangement of n lines in the plane can be swept over in O(n2) time and O(n) space by a such a line. In the process each element, i.e., vertex, edge, or region, is visited once in a consistent ordering. Our technique makes use of novel data structures which exhibit interesting amortized complexity behavior; the result is an algorithm that improves upon all its predecessors either in the space or the time bounds, as well as being eminently practical. Numerous applications of the technique to problems in computational geometry are given—many through the use of duality transforms. Examples include solving visibility problems, detecting degeneracies in configurations, computing the extremal shadows of convex polytopes, and others. Even though our basic technique solves a planar problem, its applications include several problems in higher dimensions.},
author = {Edelsbrunner, Herbert and Guibas, Leonidas},
issn = {1090-2724},
journal = {Journal of Computer and System Sciences},
number = {1},
pages = {165 -- 194},
publisher = {Elsevier},
title = {{Topologically sweeping an arrangement}},
doi = {10.1016/0022-0000(89)90038-X},
volume = {38},
year = {1989},
}
@article{4083,
abstract = {It is shown that, given a set S of n points in $R^3 $, one can always find three planes that form an eight-partition of S, that is, a partition where at most ${n / 8}$ points of S lie in each of the eight open regions. This theorem is used to define a data structure, called an octant tree, for representing any point set in $R^3 $. An octant tree for n points occupies $O(n)$ space and can be constructed in polynomial time. With this data structure and its refinements, efficient solutions to various range query problems in two and three dimensions can be obtained, including (1) half-space queries: find all points of S that lie to one side of any given plane; (2) polyhedron queries: find all points that lie inside (outside) any given polyhedron; and (3) circle queries in $R^2 $: for a planar set S, find all points that lie inside (outside) any given circle. The retrieval time for all these queries is $T(n) = O(n^\alpha + m)$, where $\alpha = 0.8988$ (or 0.8471 in case (3)), and m is the size of the output. This performance is the best currently known for linear-space data structures that can be deterministically constructed in polynomial time.},
author = {Yao, F. and Dobkin, David and Edelsbrunner, Herbert and Paterson, Michael},
issn = {1095-7111},
journal = {SIAM Journal on Computing},
number = {2},
pages = {371 -- 384},
publisher = {SIAM},
title = {{Partitioning space for range queries}},
doi = {10.1137/0218025},
volume = {18},
year = {1989},
}
@article{4084,
abstract = {A tour of a finite set P of points is a necklace-tour if there are disks with the points in P as centers such that two disks intersect if and only if their centers are adjacent in . It has been observed by Sanders that a necklace-tour is an optimal traveling salesman tour.
In this paper, we present an algorithm that either reports that no necklace-tour exists or outputs a necklace-tour of a given set of n points in O(n2 log n) time. If a tour is given, then we can test in O(n2) time whether or not this tour is a necklace-tour. Both algorithms can be generalized to ƒ-factors of point sets in the plane. The complexity results rely on a combinatorial analysis of certain intersection graphs of disks defined for finite sets of points in the plane.},
author = {Edelsbrunner, Herbert and Rote, Günter and Welzl, Emo},
issn = {1879-2294},
journal = {Theoretical Computer Science},
number = {2},
pages = {157 -- 180},
publisher = {Elsevier},
title = {{Testing the necklace condition for shortest tours and optimal factors in the plane}},
doi = {10.1016/0304-3975(89)90133-3},
volume = {66},
year = {1989},
}
@inproceedings{4085,
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 = {Edelsbrunner, Herbert},
booktitle = {Proceedings of the 5th annual symposium on Computational geometry},
isbn = {978-0-89791-318-8},
location = {Saarbruchen, Germany},
pages = {145 -- 151},
publisher = {ACM},
title = {{An acyclicity theorem for cell complexes in d dimension}},
doi = {10.1145/73833.73850},
year = {1989},
}
@article{4086,
abstract = {This note proves that the maximum number of faces (of any dimension) of the upper envelope of a set ofn possibly intersectingd-simplices ind+1 dimensions is (n d (n)). This is an extension of a result of Pach and Sharir [PS] who prove the same bound for the number ofd-dimensional faces of the upper envelope.},
author = {Edelsbrunner, Herbert},
issn = {1432-0444},
journal = {Discrete & Computational Geometry},
number = {4},
pages = {337 -- 343},
publisher = {Springer},
title = {{The upper envelope of piecewise linear functions: Tight bounds on the number of faces }},
doi = {10.1007/BF02187734},
volume = {4},
year = {1989},
}
@inproceedings{4087,
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 coplanar. It also presents an algorithm that in O(nlog 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},
booktitle = { International Symposium on Symbolic and Algebraic Computation},
location = {Rome, Italy},
pages = {315 -- 331},
publisher = {Springer},
title = {{Tetrahedrizing point sets in three dimensions}},
doi = {10.1007/3-540-51084-2_31},
volume = {358},
year = {1989},
}
@article{4088,
abstract = {Anarrangement ofn lines (or line segments) in the plane is the partition of the plane defined by these objects. Such an arrangement consists ofO(n 2) regions, calledfaces. In this paper we study the problem of calculating and storing arrangementsimplicitly, using subquadratic space and preprocessing, so that, given any query pointp, we can calculate efficiently the face containingp. First, we consider the case of lines and show that with (n) space1 and (n 3/2) preprocessing time, we can answer face queries in (n)+O(K) time, whereK is the output size. (The query time is achieved with high probability.) In the process, we solve three interesting subproblems: (1) given a set ofn points, find a straight-edge spanning tree of these points such that any line intersects only a few edges of the tree, (2) given a simple polygonal path , form a data structure from which we can find the convex hull of any subpath of quickly, and (3) given a set of points, organize them so that the convex hull of their subset lying above a query line can be found quickly. Second, using random sampling, we give a tradeoff between increasing space and decreasing query time. Third, we extend our structure to report faces in an arrangement of line segments in (n 1/3)+O(K) time, given(n 4/3) space and (n 5/3) preprocessing time. Lastly, we note that our techniques allow us to computem faces in an arrangement ofn lines in time (m 2/3 n 2/3+n), which is nearly optimal.},
author = {Edelsbrunner, Herbert and Guibas, Leonidas and Hershberger, John and Seidel, Raimund and Sharir, Micha and Snoeyink, Jack and Welzl, Emo},
issn = {1432-0444},
journal = {Discrete & Computational Geometry},
number = {1},
pages = {433 -- 466},
publisher = {Springer},
title = {{Implicitly representing arrangements of lines or segments}},
doi = {10.1007/BF02187742},
volume = {4},
year = {1989},
}
@article{4089,
abstract = {Motivated by a number of motion-planning questions, we investigate in this paper some general topological and combinatorial properties of the boundary of the union ofn regions bounded by Jordan curves in the plane. We show that, under some fairly weak conditions, a simply connected surface can be constructed that exactly covers this union and whose boundary has combinatorial complexity that is nearly linear, even though the covered region can have quadratic complexity. In the case where our regions are delimited by Jordan acrs in the upper halfplane starting and ending on thex-axis such that any pair of arcs intersect in at most three points, we prove that the total number of subarcs that appear on the boundary of the union is only (n(n)), where(n) is the extremely slowly growing functional inverse of Ackermann's function.},
author = {Edelsbrunner, Herbert and Guibas, Leonidas and Hershberger, John and Pach, János and Pollack, Richard and Seidel, Raimund and Sharir, Micha and Snoeyink, Jack},
issn = {1432-0444},
journal = {Discrete & Computational Geometry},
number = {1},
pages = {523 -- 539},
publisher = {Springer},
title = {{On arrangements of Jordan arcs with three intersections per pair}},
doi = {10.1007/BF02187745},
volume = {4},
year = {1989},
}
@inproceedings{4092,
author = {Chazelle, Bernard and Edelsbrunner, Herbert and Guibas, Leonidas and Sharir, Micha},
booktitle = {16th International Colloquium on Automata, Languages, and Programming},
location = {Stresa, Italy},
pages = {179 -- 193},
publisher = {Springer},
title = {{A singly exponential stratification scheme for real semi-algebraic varieties and its applications}},
doi = {10.1007/BFb0035760},
volume = {372},
year = {1989},
}
@article{4093,
abstract = {This paper investigates the combinatorial and computational aspects of certain extremal geometric problems in two and three dimensions. Specifically, we examine the problem of intersecting a convex subdivision with a line in order to maximize the number of intersections. A similar problem is to maximize the number of intersected facets in a cross-section of a three-dimensional convex polytope. Related problems concern maximum chains in certain families of posets defined over the regions of a convex subdivision. In most cases we are able to prove sharp bounds on the asymptotic behavior of the corresponding extremal functions. We also describe polynomial algorithms for all the problems discussed.},
author = {Chazelle, Bernard and Edelsbrunner, Herbert and Guibas, Leonidas},
issn = {1432-0444},
journal = {Discrete & Computational Geometry},
number = {1},
pages = {139 -- 181},
publisher = {Springer},
title = {{The complexity of cutting complexes}},
doi = {10.1007/BF02187720},
volume = {4},
year = {1989},
}
@article{4309,
abstract = {Three methods for estimating the average level of gene flow in natural population are discussed and compared. The three methods are FST, rare alleles, and maximum likelihood. All three methods yield estimates of the combination of parameters (the number of migrants [Nm] in a demic model or the neighborhood size [4πDσ2] in a continuum model) that determines the relative importance of gene flow and genetic drift. We review the theory underlying these methods and derive new analytic results for the expectation of FST in stepping-stone and continuum models when small sets of samples are taken. We also compare the effectiveness of the different methods using a variety of simulated data. We found that the FST and rare-alleles methods yield comparable estimates under a wide variety of conditions when the population being sampled is demographically stable. They are roughly equally sensitive to selection and to variation in population structure, and they approach their equilibrium values at approximately the same rate. We found that two different maximum-likelihood methods tend to yield biased estimates when relatively small numbers of locations are sampled but more accurate estimates when larger numbers are sampled. Our conclusion is that, although FST and rare-alleles methods are expected to be equally effective in analyzing ideal data, practical problems in estimating the frequencies of rare alleles in electrophoretic studies suggest that FST is likely to be more useful under realistic conditions.},
author = {Slatkin, Montgomery and Barton, Nicholas H},
issn = {1558-5646},
journal = {Evolution; International Journal of Organic Evolution},
number = {7},
pages = {1349 -- 1368},
publisher = {Wiley-Blackwell},
title = {{A comparison of three methods for estimating average levels of gene flow}},
doi = {10.1111/j.1558-5646.1989.tb02587.x },
volume = {43},
year = {1989},
}
@article{4312,
author = {Barton, Nicholas H and Turelli, Michael},
issn = {1545-2948},
journal = {Annual Review of Genetics},
pages = {337 -- 370},
publisher = {Annual Reviews},
title = {{Evolutionary quantitative genetics: how little do we know?}},
doi = {10.1146/annurev.ge.23.120189.002005},
volume = {23},
year = {1989},
}
@inbook{4313,
author = {Barton, Nicholas H},
booktitle = {Speciation and its consequences},
editor = {Otte, Daniel and Endler, John},
isbn = { 978-0878936571},
publisher = {Sinauer Press},
title = {{Founder effect speciation}},
year = {1989},
}
@article{4314,
abstract = {Polygenic variation can be maintained by a balance between mutation and stabilizing selection. When the alleles responsible for variation are rare, many classes of equilibria may be stable. The rate at which drift causes shifts between equilibria is investigated by integrating the gene frequency distribution W2N II (pq)4N mu-1. This integral can be found exactly, by numerical integration, or can be approximated by assuming that the full distribution of allele frequencies is approximately Gaussian. These methods are checked against simulations. Over a wide range of population sizes, drift will keep the population near an equilibrium which minimizes the genetic variance and the deviation from the selective optimum. Shifts between equilibria in this class occur at an appreciable rate if the product of population size and selection on each locus is small (Ns alpha 2 less than 10). The Gaussian approximation is accurate even when the underlying distribution is strongly skewed. Reproductive isolation evolves as populations shift to new combinations of alleles: however, this process is slow, approaching the neutral rate (approximately mu) in small populations.},
author = {Barton, Nicholas H},
issn = {1469-5073},
journal = {Genetical Research},
number = {1},
pages = {59 -- 78},
publisher = {Cambridge University Press},
title = {{The divergence of a polygenic system under stabilising selection, mutation and drift}},
doi = {10.1017/S0016672300028378},
volume = {54},
year = {1989},
}
@article{1941,
author = {Sazanov, Leonid A and Karavaev, V A and Kukushkin, A K},
issn = {1990-7923},
journal = {Russian Journal of Physical Chemistry B},
pages = {3351 -- 3354},
publisher = {Elsevier},
title = {{Mathematical model of photosynthesis regulation accounts for the effects of changes in external conditions and observed oscillations}},
volume = {52},
year = {1988},
}
@article{2522,
abstract = {Non-pyramidal neurons in cat Ammon's horn were shown to send their axons to the supramammillary regions (SMR), i.e. the supramammillary nucleus and its vicinities including the supramammillary nucleus and the lateral, posterior and dorsal hypothalamic areas: wheat germ agglutinin-horseradish peroxidase (WGA-HRP) injection into Ammon's horn resulted in labeling of presumed axon terminals in the SMR; and after injecting HRP into the SMR, retrogradely labeled non-pyramidal neurons were seen in Ammon's horn.},
author = {Ino, Tadashi and Itoh, Kazuo and Kamiya, Hiroto and Shigemoto, Ryuichi and Akiguchi, Ichiro and Mizuno, Noboru},
issn = {1872-6240},
journal = {Brain Research},
number = {1},
pages = {173 -- 177},
publisher = {Elsevier},
title = {{Direct projections of non-pyramidal neurons of Ammon's horn to the supramammillary region in the cat}},
doi = {10.1016/0006-8993(88)91219-X},
volume = {460},
year = {1988},
}
@article{2523,
abstract = {Injection of large amounts of a mixture of horseradish peroxidase and wheat germ agglutinin-horseradish peroxidase conjugate into the upper cervical segments of the spinal cord in the Japanese monkey (Macaca fuscata) led to the retrograde labeling of a small number of neuronal cell bodies within the rostral part of the subthalamic nucleus of Luys. Direct projection from the subthalamic nucleus to the spinal cord appeared to be much less prominent in the Japanese monkey than in the cat and rat.},
author = {Mizuno, Noboru and Ueyama, Teizo and Itoh, Kazuo and Satoda, Takahiro and Tashiro, Takashi and Shigemoto, Ryuichi},
issn = {1872-7972},
journal = {Neuroscience Letters},
number = {1},
pages = {13 -- 18},
publisher = {Elsevier},
title = {{Direct projections from the subthalamic nucleus of Luys to the spinal cord in the Japanese monkey}},
doi = {10.1016/0304-3940(88)90473-9},
volume = {89},
year = {1988},
}
@article{2524,
abstract = {Alpha-ketoglutamate (α-KG) reductive amination activity in rat brain was found to be mostly absorbed with an antibody against liver glutamate dehydrogenase. With this and anti-glutamine synthetase antibodies, α-KG reductive amination activity was immunocytochemically shown to coexist with glutamine synthetase activity in astrocytes. The results suggest that astrocytes de novo synthesize glutamate from α-KG and ammonia, and metabolize it to glutamine.},
author = {Kaneko, Takeshi and Shigemoto, Ryuichi and Mizuno, Noboru},
issn = {1872-6240},
journal = {Brain Research},
number = {1},
pages = {160 -- 164},
publisher = {Elsevier},
title = {{Metabolism of glutamate and ammonia in astrocyte an immunocytochemical study}},
doi = {10.1016/0006-8993(88)90069-8},
volume = {457},
year = {1988},
}
@article{3655,
abstract = {The structural basis and distribution of variation in the ribosomal RNA multigene family ( rDNA) was studied in the X0 and neo-XY races of the Alpine grasshopper Podisma pedestris. Restriction-enzyme sites in the gene region of the rDNA repeat were identical in both races and homogeneous in the rDNA family. In contrast, sites for Hind111 and PvuII in the intergenic spacer (IGS) region showed racial divergence and variation within the rDNA family and within populations. A short insertion in the 28s gene region was present in a minority of repeats in both races. The distributions of four polymorphic IGS Hind111 fragments were surveyed at 43 locations in and around the hybrid zone. Two of these fragments appear to be distributed as clines, one of which is strongly associated with the neo-X chromosome. The other two fragments show considerable variation in both races and show negative association. It is proposed that the clinally distributed variants arise from processes of amplification and divergence of IGS sequence variants and that such
divergence may contribute to hybrid inviability. },
author = {Dallas, John and Barton, Nicholas H and Dover, Gabriel},
issn = {1537-1719},
journal = {Molecular Biology and Evolution},
number = {6},
pages = {660 -- 674},
publisher = {Oxford University Press},
title = {{Interracial rDNA variation in the grasshopper Podisma Pedestris}},
doi = {10.1093/oxfordjournals.molbev.a040528},
volume = {5},
year = {1988},
}
@article{4090,
abstract = {In this paper we study the problem of polygonal separation in the plane, i.e., finding a convex polygon with minimum number k of sides separating two given finite point sets (k-separator), if it exists. We show that for k = Θ(n), is a lower bound to the running time of any algorithm for this problem, and exhibit two algorithms of distinctly different flavors. The first relies on an O(n log n)-time preprocessing task, which constructs the convex hull of the internal set and a nested star-shaped polygon determined by the external set; the k-separator is contained in the annulus between the boundaries of these two polygons and is constructed in additional linear time. The second algorithm adapts the prune-and-search approach, and constructs, in each iteration, one side of the separator; its running time is O(kn), but the separator may have one more side than the minimum.},
author = {Edelsbrunner, Herbert and Preparata, Franco},
issn = {0890-5401},
journal = {Information and Computation},
number = {3},
pages = {218 -- 232},
publisher = {Elsevier},
title = {{Minimum polygonal separation}},
doi = {10.1016/0890-5401(88)90049-1},
volume = {77},
year = {1988},
}
@article{4091,
abstract = {An X-ray probe through a polygon measures the length of intersection between a line and the polygon. This paper considers the properties of various classes of X-ray probes, and shows how they interact to give finite strategies for completely describing convex n-gons. It is shown that (3n/2)+6 probes are sufficient to verify a specified n-gon, while for determining convex polygons (3n-1)/2 X-ray probes are necesssary and 5n+O(1) sufficient, with 3n+O(1) sufficient given that a lower bound on the size of the smallest edge of P is known.},
author = {Edelsbrunner, Herbert and Skiena, Steven},
issn = {1095-7111},
journal = {SIAM Journal on Computing},
number = {5},
pages = {870 -- 882},
publisher = {SIAM},
title = {{Probing convex polygons with X-Rays}},
doi = {10.1137/0217054 },
volume = {17},
year = {1988},
}
@inproceedings{4096,
author = {Edelsbrunner, Herbert},
booktitle = {15th International Colloquium on Automata, Languages and Programming},
isbn = {978-3-540-19488-0},
location = {Tampere, Finland},
pages = {201 -- 213},
publisher = {Springer},
title = {{Geometric structures in computational geometry}},
doi = {10.1007/3-540-19488-6_117},
volume = {317},
year = {1988},
}
@inproceedings{4097,
abstract = {Arrangements of curves in the plane are of fundamental significance in many problems of computational and combinatorial geometry (e.g. motion planning, algebraic cell decomposition, etc.). In this paper we study various topological and combinatorial properties of such arrangements under some mild assumptions on the shape of the curves, and develop basic tools for the construction, manipulation, and analysis of these arrangements. Our main results include a generalization of the zone theorem of [EOS], [CGL] to arrangements of curves (in which we show that the combinatorial complexity of the zone of a curve is nearly linear in the number of curves), and an application of (some weaker variant of) that theorem to obtain a nearly quadratic incremental algorithm for the construction of such arrangements.},
author = {Edelsbrunner, Herbert and Guibas, Leonidas and Pach, János and Pollack, Richard and Seidel, Raimund and Sharir, Micha},
booktitle = {15th International Colloquium on Automata, Languages and Programming},
isbn = {978-3-540-19488-0},
keywords = {line segment, computational geometry, Jordan curve, cell decomposition, vertical tangency},
location = {Tampere, Finland},
pages = {214 -- 229},
publisher = {Springer},
title = {{Arrangements of curves in the plane - topology, combinatorics, and algorithms}},
doi = {10.1007/3-540-19488-6_118},
volume = {317},
year = {1988},
}
@misc{4315,
author = {Coyne, Jerry and Barton, Nicholas H},
booktitle = {Nature},
issn = {1476-4687},
pages = {485 -- 486},
publisher = {Nature Publishing Group},
title = {{What do we know about speciation?}},
doi = {10.1038/331485a0},
volume = {331},
year = {1988},
}
@misc{4316,
author = {Barton, Nicholas H and Jones, Steve},
booktitle = {Nature},
issn = {1476-4687},
pages = {597 -- 597},
publisher = {Springer Nature},
title = {{Molecular evolutionary genetics}},
doi = {10.1038/332597a0},
volume = {332},
year = {1988},
}
@inbook{4317,
author = {Barton, Nicholas H},
booktitle = {Analytical biogeography: An integrated approach to the study of animal and plant distributions},
editor = {Myers, Alan and Giller, Paul},
isbn = {978-0-412-40050-6},
issn = {978-94-009-0435-4},
keywords = {biogeography, biology, complexity, distribution, evolution, geology},
pages = {185 -- 218},
publisher = {Springer},
title = {{Speciation}},
doi = {10.1007/978-94-009-0435-4},
year = {1988},
}
@misc{4318,
author = {Barton, Nicholas H and Jones, Steve and Mallet, James},
booktitle = {Nature},
issn = {1476-4687},
pages = {13 -- 14},
publisher = {Springer Nature},
title = {{No barriers to speciation}},
doi = {10.1038/336013a0},
volume = {336},
year = {1988},
}
@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},
}
@article{3464,
abstract = {The effects of the major neurotoxic fraction isolated from scorpion venom of Tityus serrulatus, TiTx gamma, on peripheral nerve membrane of Xenopus laevis were studied under current- and voltage-clamp conditions. 700 nmol/l TiTx gamma depolarized the membrane and induced spontaneous activity (150 s-1, maximum value), which ceased within a few minutes. It reduced the amplitude of the action potentials from 109 mV to 52 mV and increased their duration from 1.25 ms to 4.5 ms. 440 nmol/l TiTx gamma induced inward Na current flow at resting potential. The descending branch of the Na current-voltage curve was flattened and shifted approximately 10 mV to more negative potentials. Maximum Na permeability was reduced to about 20%. Both development of and recovery from inactivation of Na permeability were slowed. The steepness of the steady-state inactivation curve was decreased, but the mid-potential changed only insignificantly. No prepulse was necessary to elicit either a shift of activation or an inward current at resting potential. Expressing the toxin effect either in terms of the decrease of Na peak current or of the slowing of inactivation, half-maximum effects were found with 0.3 +/- 0.1 and 3.7 +/- 0.7 mumol/l TiTx gamma, respectively.},
author = {Jonas, Peter M and Vogel, Werner and Arantes, Eliane and Giglio, Jose},
issn = {1432-2013},
journal = {Pflugers Archiv : European Journal of Physiology},
number = {1},
pages = {92 -- 99},
publisher = {Springer},
title = {{Toxin γ of the scorpion Tityus serrulatus modifies both activation and inactivation of sodium permeability of nerve membrane}},
doi = {10.1007/BF00580727},
volume = {407},
year = {1986},
}
@article{3579,
author = {Edelsbrunner, Herbert and Jaromczyk, Jerzy},
issn = {0384-9864},
journal = {Congressus Numerantium},
pages = {193 -- 200},
publisher = {Utilitas Mathemtica Publ. Inc.},
title = {{How often can you see yourself in a convex configuration of mirrors?}},
volume = {53},
year = {1986},
}
@article{3580,
abstract = {An edge-skeleton in an arrangementA(H) of a finite set of planes inE 3 is a connected collection of edges inA(H). We give a method that constructs a skeleton inO(√n logn) time per edge. This method implies new and more efficient algorithms for a number of structures in computational geometry including order-k power diagrams inE 2 and space cutting trees inE 3.
We also give a novel method for handling special cases which has the potential to substantially decrease the amount of effort needed to implement geometric algorithms.},
author = {Edelsbrunner, Herbert},
issn = {1432-0541},
journal = {Algorithmica},
number = {1-4},
pages = {93 -- 109},
publisher = {Springer},
title = {{Edge-skeletons in arrangements with applications}},
doi = {10.1007/BF01840438},
volume = {1},
year = {1986},
}
@article{3662,
abstract = {The evolution of the probabilities of genetic identity within and between tandemly repeated loci of a multigene family is investigated analytically and numerically. Unbiased intrachromosomal gene conversion, equal crossing over, random genetic drift, and mutation to new alleles are incorporated. Generations are discrete and nonoverlapping; the diploid, monoecious population mates at random. Under the restriction that there is at most one crossover in the multigene family per individual per generation, the dependence on location of the probabilities of identity is treated exactly. In the “homogeneous” approximation to this “exact” model, end effects are disregarded; in the “exchangeable” approximation, to which all previous work was confined, all position dependence is neglected. Numerical results indicate that (i) the exchangeable and homogeneous models are both qualitatively correct, (ii) the exchangeable model is sometimes too inaccurate for quantitative conclusions, and (iii) the homogeneous model is always more accurate than the exchangeable one and is always sufficiently accurate for quantitative conclusions.},
author = {Nagylaki, Thomas and Barton, Nicholas H},
issn = {1096-0325},
journal = {Theoretical Population Biology},
number = {3},
pages = {407 -- 437},
publisher = {Academic Press},
title = {{Intrachromosomal gene conversion, linkage, and the evolution of multigene families}},
doi = {10.1016/0040-5809(86)90017-1},
volume = {29},
year = {1986},
}
@article{3663,
abstract = {The conditional average frequency of rare alleles has been shown in simulations to provide a simple and robust estimator of the number of individuals exchanged between local populations in an island model (Nm). This statistic is defined as the average frequency of an allele in those samples in which the allele is present. Here, we show that the conditional average frequency can be calculated from the distribution of allele frequencies. It is a measure of the spread of this distribution, and so is analogous to the standardised variance, FST. Analytic predictions for the island model of migration agree well with the corresponding simulation results. These predictions are based on the assumption that the rare alleles found in samples have reached a "quasi-equilibrium" distribution. As well as relating the conditional average frequency to the underlying allele frequency distribution, our results provide a more accurate method of estimating Nm from the conditional average frequency of private alleles in samples of different sizes.},
author = {Barton, Nicholas H and Slatkin, Montgomery},
issn = {1365-2540},
journal = {Heredity},
number = {3},
pages = {409 -- 416},
publisher = {Nature Publishing Group},
title = {{A quasi-equilibrium theory of the distribution of rare alleles in a subdivided population}},
doi = {10.1038/hdy.1986.63},
volume = {56},
year = {1986},
}
@article{3664,
abstract = {Suppose that selection acts at one or more loci to maintain genetic differences between hybridising populations. Then, the flow of alleles at a neutral marker locus which is linked to these selected loci will be impeded. We define and calculate measures of the barrier to gene flow between two distinct demes, and across a continuous habitat. In both cases, we find that in order for gene flow to be significantly reduced over much of the genome, hybrids must be substantially less fit, and the number of genes involved in building the barrier must be so large that the majority of other genes become closely linked to some locus which is under selection. This conclusion is not greatly affected by the pattern of epistasis, or the position of the marker locus along the chromosome.},
author = {Barton, Nicholas H and Bengtsson, Bengt},
issn = {1365-2540},
journal = {Heredity},
pages = {357 -- 376},
publisher = {Nature Publishing Group},
title = {{The barrier to genetic exchange between hybridising populations}},
volume = {57},
year = {1986},
}
@article{3665,
abstract = {The rate of gene flow across a hybrid zone may be reduced by the presence of a physical barrier, by a reduction of population density caused by reduced fitness of hybrids (the “hybrid sink” effect), and by linkage. If the reduction in hybrid fitness is not extreme, the strength of the barrier to gene flow caused by these effects is. Here, w is the width of the cline; ρ* is the carrying capacity; W̄* is the mean fitness of the population, excluding effects of density; R is the strength of density-dependent regulation; and r̄ is the harmonic mean recombination rate between the locus whose flow is being calculated, and loci under selection. +, 0 denote populations outside the hybrid zone, and at its centre, respectively. This relation is illustrated using data from hybrid ones in Bombina and Podisma, and its implications for interpretation of data from nature are discussed.},
author = {Barton, Nicholas H},
issn = {1365-2540},
journal = {Heredity},
pages = {415 -- 426},
publisher = {Nature Publishing Group},
title = {{The effects of linkage and density-dependent regulation on gene flow}},
volume = {57},
year = {1986},
}
@article{4098,
abstract = {To points p and q of a finite set S in d-dimensional Euclidean space Ed are extreme if {p, q} = S ∩ h, for some open halfspace h. Let e2(d)(n) be the maximum number of extreme pairs realized by any n points in Ed. We give geometric proofs of , if n⩾4, and e2(3)(n) = 3n−6, if n⩾6. These results settle the question since all other cases are trivial.},
author = {Edelsbrunner, Herbert and Stöckl, Gerd},
issn = {1096-0899},
journal = {Journal of Combinatorial Theory Series A},
number = {2},
pages = {344 -- 349},
publisher = {Elsevier},
title = {{The number of extreme pairs of finite point-sets in Euclidean spaces}},
doi = {10.1016/0097-3165(86)90075-0},
volume = {43},
year = {1986},
}
@article{4099,
abstract = {Let S denote a set of n points in the Euclidean plane. A halfplanar range query specifies a halfplane h and requires the determination of the number of points in S which are contained in h. A new data structure is described which stores S in O(n) space and allows us to answer a halfplanar range query in O(nlog2(1+√5)−1) time in the worst case, thus improving the best result known before. The structure can be built in O(n log n) time.},
author = {Edelsbrunner, Herbert and Welzl, Emo},
issn = {1872-6119},
journal = {Information Processing Letters},
number = {5},
pages = {289 -- 293},
publisher = {Elsevier},
title = {{Halfplanar range search in linear space and O(n0.695) query time}},
doi = {10.1016/0020-0190(86)90088-8},
volume = {23},
year = {1986},
}
@article{4103,
abstract = {Let A be an arrangement of n lines in the plane. Suppose F1,…, Fk are faces in the dissection induced by A and that Fi is a t(Fi)-gon. We give asymptotic bounds on the maximal sum ∑i=1kt(Fi) which can be realized by k different faces in an arrangement of n lines. The results improve known bounds for k of higher order than n(1/2).},
author = {Edelsbrunner, Herbert and Welzl, Emo},
issn = {1096-0899},
journal = {Journal of Combinatorial Theory Series A},
number = {2},
pages = {159 -- 166},
publisher = {Elsevier},
title = {{On the maximal number of edges of many faces in an arrangement}},
doi = {10.1016/0097-3165(86)90078-6},
volume = {41},
year = {1986},
}
@article{4104,
abstract = {Point location, often known in graphics as “hit detection,” is one of the fundamental problems of computational geometry. In a point location query we want to identify which of a given collection of geometric objects contains a particular point. Let $\mathcal{S}$ denote a subdivision of the Euclidean plane into monotone regions by a straight-line graph of $m$ edges. In this paper we exhibit a substantial refinement of the technique of Lee and Preparata [SIAM J. Comput., 6 (1977), pp. 594–606] for locating a point in $\mathcal{S}$ based on separating chains. The new data structure, called a layered dag, can be built in $O(m)$ time, uses $O(m)$ storage, and makes possible point location in $O(\log m)$ time. Unlike previous structures that attain these optimal bounds, the layered dag can be implemented in a simple and practical way, and is extensible to subdivisions with edges more general than straight-line segments.
© 1986 Society for Industrial and Applied Mathematics},
author = {Edelsbrunner, Herbert and Guibas, Leonidas and Stolfi, Jorge},
issn = {1095-7111},
journal = {SIAM Journal on Computing},
number = {2},
pages = {317 -- 340},
publisher = {SIAM},
title = {{Optimal point location in a monotone subdivision}},
doi = {10.1137/0215023},
volume = {15},
year = {1986},
}
@article{4105,
abstract = {A finite set of lines partitions the Euclidean plane into a cell complex. Similarly, a finite set of $(d - 1)$-dimensional hyperplanes partitions $d$-dimensional Euclidean space. An algorithm is presented that constructs a representation for the cell complex defined by $n$ hyperplanes in optimal $O(n^d )$ time in $d$ dimensions. It relies on a combinatorial result that is of interest in its own right. The algorithm is shown to lead to new methods for computing $\lambda $-matrices, constructing all higher-order Voronoi diagrams, halfspatial range estimation, degeneracy testing, and finding minimum measure simplices. In all five applications, the new algorithms are asymptotically faster than previous results, and in several cases are the only known methods that generalize to arbitrary dimensions. The algorithm also implies an upper bound of $2^{cn^d } $, $c$ a positive constant, for the number of combinatorially distinct arrangements of $n$ hyperplanes in $E^d $.
© 1986 Society for Industrial and Applied Mathematics},
author = {Edelsbrunner, Herbert and O'Rourke, Joseph and Seidel, Raimund},
issn = {1095-7111},
journal = {SIAM Journal on Computing},
number = {2},
pages = {341 -- 363},
publisher = {SIAM},
title = {{Constructing arrangements of lines and hyperplanes with applications}},
doi = {10.1137/0215024},
volume = {15},
year = {1986},
}
@article{4106,
abstract = {Let B be a set of nb black points and W a set of nw, white points in the Euclidean plane. A line h is said to bisect B (or W) if, at most, half of the points of B (or W) lie on any one side of h. A line that bisects both B and W is called a ham-sandwich cut of B and W. We give an algorithm that computes a ham-sandwich cut of B and W in 0((nh+nw) log (min {nb, nw}+ 1)) time. The algorithm is considerably simpler than the previous most efficient one which takes 0((nb + nw) log (nb + nw)) time.},
author = {Edelsbrunner, Herbert and Waupotitsch, Roman},
issn = {1095-855X},
journal = {Journal of Symbolic Computation},
number = {2},
pages = {171 -- 178},
publisher = {Elsevier},
title = {{Computing a ham-sandwich cut in two dimensions}},
doi = {10.1016/S0747-7171(86)80020-7},
volume = {2},
year = {1986},
}
@article{4107,
abstract = {A set of m planes dissects E3 into cells, facets, edges and vertices. Letting deg(c) be the number of facets that bound a cellc, we give exact and asymptotic bounds on the maximum of ∈cinCdeg(c), if C is a family of cells of the arrangement with fixed cardinality.},
author = {Edelsbrunner, Herbert and Haussler, David},
issn = {1872-681X},
journal = {Discrete Mathematics},
number = {C},
pages = {139 -- 146},
publisher = {Elsevier},
title = {{The complexity of cells in 3-dimensional arrangements}},
doi = {10.1016/0012-365X(86)90008-7},
volume = {60},
year = {1986},
}
@article{4108,
abstract = {We propose a uniform and general framework for defining and dealing with Voronoi diagrams. In this framework a Voronoi diagram is a partition of a domainD induced by a finite number of real valued functions onD. Valuable insight can be gained when one considers how these real valued functions partitionD ×R. With this view it turns out that the standard Euclidean Voronoi diagram of point sets inR d along with its order-k generalizations are intimately related to certain arrangements of hyperplanes. This fact can be used to obtain new Voronoi diagram algorithms. We also discuss how the formalism of arrangements can be used to solve certain intersection and union problems.},
author = {Edelsbrunner, Herbert and Seidel, Raimund},
issn = {1432-0444},
journal = {Discrete & Computational Geometry},
number = {1},
pages = {25 -- 44},
publisher = {Springer},
title = {{Voronoi diagrams and arrangements}},
doi = {10.1007/BF02187681},
volume = {1},
year = {1986},
}
@article{4109,
abstract = {Rectangle location search in d dimensions is finding the d-dimensional axis-parallel box of a non-overlapping collection C that contains a query point. A new data structure is proposed that requires optimal space and 0(logd|C|) time for a search. The significance of this data structure in practical applications is substantiated by empirical examinations of its behaviour.},
author = {Edelsbrunner, Herbert and Haring, Günter and Hilbert, D},
issn = {1460-2067},
journal = {Computer Journal},
number = {1},
pages = {76 -- 82},
publisher = {Oxford University Press},
title = {{Rectangular point location in d-dimensions with applications}},
doi = {10.1093/comjnl/29.1.76},
volume = {29},
year = {1986},
}
@article{4110,
abstract = {For H a set of lines in the Euclidean plane, $A(H)$ denotes the induced dissection, called the arrangement of H. We define the notion of a belt in $A(H)$, which is bounded by a subset of the edges in $A(H)$, and describe two algorithms for constructing belts. All this is motivated by applications to a host of seemingly unrelated problems including a type of range search and finding the minimum area triangle with the vertices taken from some finite set of points.},
author = {Edelsbrunner, Herbert and Welzl, Emo},
issn = {1095-7111},
journal = {SIAM Journal on Computing},
number = {1},
pages = {271 -- 284},
publisher = {SIAM},
title = {{Constructing belts in two-dimensional arrangements with applications}},
doi = {10.1137/0215019},
volume = {15},
year = {1986},
}
@article{4321,
abstract = {The fire-bellied toads Bombina bombina and B. variegata differ extensively in biochemistry, morphology, and behavior. We use a survey of five diagnostic enzyme loci across the hybrid zone near Cracow in Southern Poland to estimate the dispersal rate, selection pressures, and numbers of loci which maintain this zone. The enzyme clines coincide closely with each other and with morphological and mitochondrial DNA clines. Although the zone lies on a broad transition between environments suitable for bombina and variegata, the close concordance of diverse characters, together with increased aberrations and mortality in hybrids, suggest that the zone is maintained largely by selection against hybrids. There are strong “linkage disequilibria” between each pair of (unlinked) enzyme loci (R̄ = 0.129 [2-unit support limits: 0.119–0.139]). These are probably caused by gene flow into the zone, and they give an estimate of dispersal (σ = 890 [790–940] m gen−½). The clines are sharply stepped, with most of the change occurring within 6.15 (5.45–6.45) km, but with long tails of introgression on either side. This implies that the effective selection pressure on each enzyme marker (due largely to disequilibrium with other loci) is s* = 0.17 (0.159–0.181) at the center but that the selection acting directly on the enzyme loci is weak or zero (se < 0.0038). The stepped pattern implies a barrier to gene flow of 220 (48–415) km. This would substantially delay neutral introgression but would have little effect on advantageous alleles; the two taxa need not evolve independently. Strong selection is needed to maintain such a barrier: hybrid populations must have their mean fitness reduced by a factor of 0.65 (0.60–0.77). This selection must be spread over a large number of loci to account for the concordant patterns and the observed cline widths (N = 300 [80–2,000]).},
author = {Szymura, Jacek and Barton, Nicholas H},
issn = {1558-5646},
journal = {Evolution; International Journal of Organic Evolution},
pages = {1141 -- 1159},
publisher = {Society for the Study of Evolution},
title = {{Genetic analysis of a hybrid zone between the fire-bellied toads Bombina bombina and B. variegata, near Cracow in Southern Poland}},
doi = {10.1111/j.1558-5646.1986.tb05740.x},
volume = {40},
year = {1986},
}
@article{4323,
abstract = {It is noted that the sibling competition model for the evolution of sex and recombination, as it has been developed so far, involves truncation selection. After briefly reviewing aspects of the development and behaviour of such models an analytical treatment is presented which involves additive selection. Additive selection, as compared with truncation selection, decreases the advantage of sex to such an extent that it is unlikely that sibling competition could overcome its intrinsic two-fold cost, although it could still be important in promoting family variability produced by other mechanisms, such as polyandry.},
author = {Barton, Nicholas H and Post, R.J.},
issn = {1095-8541},
journal = {Journal of Theoretical Biology},
number = {4},
pages = {381 -- 387},
publisher = {Elsevier},
title = {{Sibling competition and the advantage of mixed families}},
doi = {10.1016/S0022-5193(86)80033-9},
volume = {120},
year = {1986},
}
@article{4324,
abstract = {The maintenance of polygenic variation through a balance between mutation and stabilizing selection can be approximated in two ways. In the ‘Gaussian’ approximation, a normal distribution of allelic effects is assumed at each locus. In the ‘House of Cards’ approximation, the effect of new mutations is assumed to be large compared with the spread of the existing distribution. These approximations were developed to describe models where alleles may have a continuous range of effects. However, previous analyses of models with only two alleles have predicted an equilibrium variance equal to that given by the ‘House of Cards’ approximation. These analyses of biallelic models have assumed that, at equilibrium, the population mean is at the optimum. Here, it is shown that many stable equilibria may coexist, each giving a slight deviation from the optimum. Though the variance is given by the ‘House of Cards’ approximation when the mean is at the optimum, it increases towards a value of the same order as that given by the ‘Gaussian’ approximation when the mean deviates from the optimum. Thus, the equilibrium variance cannot be predicted by any simple model, but depends on the previous history of the population.},
author = {Barton, Nicholas H},
issn = {1469-5073},
journal = {Genetical Research},
number = {3},
pages = {209 -- 216},
publisher = {Cambridge University Press},
title = {{The maintenance of polygenic variation through a balance between mutation and stabilising selection}},
doi = {10.1017/S0016672300023156},
volume = {47},
year = {1986},
}
@article{4111,
abstract = {This paper describes an optimal solution for the following geometric search problem defined for a set P of n points in three dimensions: Given a plane h with all points of P on one side and a line ℓ in h, determine a point of P that is hit first when h is rotated around ℓ. The solution takes O(n) space and O(log n) time for a query. By use of geometric transforms, the post-office problem for a finite set of points in two dimensions and certain two-dimensional point location problems are reduced to the former problem and thus also optimally solved.},
author = {Edelsbrunner, Herbert and Maurer, Hermann},
issn = {1872-6119},
journal = {Information Processing Letters},
number = {1},
pages = {39 -- 47},
publisher = {Elsevier},
title = {{Finding extreme-points in 3-dimensions and solving the post-office problem in the plane}},
doi = {10.1016/0020-0190(85)90107-3},
volume = {21},
year = {1985},
}
@article{4112,
abstract = {The batched static version of a searching problem asks for performing a given set of queries on a given set of objects. All queries are known in advance. The batched dynamic version of a searching problem is the following: given a sequence of insertions, deletions, and queries, perform them on an initially empty set. We will develop methods for solving batched static and batched dynamic versions of searching problems which are in particular applicable to decomposable searching problems. The techniques show that batched static (dynamic) versions of searching problems can often be solved more efficiently than by using known static (dynamic) data structures. In particular, a technique called “streaming” is described that reduces the space requirements considerably. The methods have also a number of applications on set problems. E.g., the k intersecting pairs in a set of n axis-parallel hyper-rectangles in d dimensions can be reported in O (nlogd−1n + k) time using only O(n) space.},
author = {Edelsbrunner, Herbert and Overmars, Mark},
issn = {1090-2678},
journal = {Journal of Algorithms},
number = {4},
pages = {515 -- 542},
publisher = {Elsevier},
title = {{Batched dynamic solutions to decomposable searching problems}},
doi = {10.1016/0196-6774(85)90030-6},
volume = {6},
year = {1985},
}
@article{4113,
abstract = {Let S denote a set of n points in the Euclidean plane. A subset S′ of S is termed a k-set of S if it contains k points and there exists a straight line which has no point of S on it and separates S′ from S−S′. We let fk(n) denote the maximum number of k-sets which can be realized by a set of n points. This paper studies the asymptotic behaviour of fk(n) as this function has applications to a number of problems in computational geometry. A lower and an upper bound on fk(n) is established. Both are nontrivial and improve bounds known before. In particular, is shown by exhibiting special point-sets which realize that many k-sets. In addition, is proved by the study of a combinatorial problem which is of interest in its own right.},
author = {Edelsbrunner, Herbert and Welzl, Emo},
issn = {1096-0899},
journal = {Journal of Combinatorial Theory Series A},
number = {1},
pages = {15 -- 29},
publisher = {Elsevier},
title = {{On the number of line separations of a finite set in the plane}},
doi = {10.1016/0097-3165(85)90017-2},
volume = {38},
year = {1985},
}
@article{4114,
abstract = {Proportional link linkage (PLL) clustering methods are a parametric family of monotone invariant agglomerative hierarchical clustering methods. This family includes the single, minimedian, and complete linkage clustering methods as special cases; its members are used in psychological and ecological applications. Since the literature on clustering space distortion is oriented to quantitative input data, we adapt its basic concepts to input data with only ordinal significance and analyze the space distortion properties of PLL methods. To enable PLL methods to be used when the numbern of objects being clustered is large, we describe an efficient PLL algorithm that operates inO(n 2 logn) time andO(n 2) space},
author = {Day, William and Edelsbrunner, Herbert},
issn = {1432-1343},
journal = {Journal of Classification},
number = {2-3},
pages = {239 -- 254},
publisher = {Springer},
title = {{Investigation of Proportional Link Linkage Clustering Methods}},
doi = {10.1007/BF01908077},
volume = {2},
year = {1985},
}
@article{4115,
abstract = {A polygon in the plane is convex if it contains all line segments connecting any two of its points. Let P and Q denote two convex polygons. The computational complexity of finding the minimum and maximum distance possible between two points p in P and q in Q is studied. An algorithm is described that determines the minimum distance (together with points p and q that realize it) in O(logm + logn) time, where m and n denote the number of vertices of P and Q, respectively. This is optimal in the worst case. For computing the maximum distance, a lower bound Ω(m + n) is proved. This bound is also shown to be best possible by establishing an upper bound of O(m + n).},
author = {Edelsbrunner, Herbert},
issn = {1090-2678},
journal = {Journal of Algorithms},
number = {2},
pages = {213 -- 224},
publisher = {Academic Press},
title = {{Computing the extreme distances between two convex polygons}},
doi = {10.1016/0196-6774(85)90039-2},
volume = {6},
year = {1985},
}
@article{4116,
abstract = {A straight line that intersects all members of a set S of objects in the real plane is called a transversal of S. Geometric transforms are described that reduce transversal problems for various types of objects to convex hull problems for points. These reductions lead to efficient algorithms for finding transversals which are also described. Applications of the algorithms are found in computer graphics: “Reproduce the line displayed by a collection of pixels”, and in statistics: “Find the line that minimizes the maximum distance from a collection of (weighted) points in the plane”.},
author = {Edelsbrunner, Herbert},
issn = {0304-3975},
journal = {Theoretical Computer Science},
number = {1},
pages = {55 -- 69},
publisher = {Elsevier},
title = {{Finding Transversals for Sets of Simple Geometric-Figures}},
doi = {10.1016/0304-3975(85)90005-2},
volume = {35},
year = {1985},
}
@article{4120,
abstract = {Let P be a set of n points in the Euclidean plane and let C be a convex figure. We study the problem of preprocessing P so that for any query point q, the points of P in C+q can be retrieved efficiently. If constant time sumces for deciding the inclusion of a point in C, we then demonstrate the existence of an optimal solution: the algorithm requires O(n) space and O(k + log n) time for a query with output size k. If C is a disk, the problem becomes the wellknown fixed-radius neighbour problem, to which we thus provide the first known optimal solution.},
author = {Chazelle, Bernard and Edelsbrunner, Herbert},
issn = {1095-855X},
journal = {Journal of Symbolic Computation},
number = {1},
pages = {47 -- 56},
publisher = {Elsevier},
title = {{Optimal solutions for a class of point retrieval problems}},
doi = {10.1016/S0747-7171(85)80028-6},
volume = {1},
year = {1985},
}
@inbook{4241,
author = {Curtis, C. and Curtis, J. and Barton, Nicholas H},
booktitle = {Genetic Control of Host Resistance to Infection and Malignancy},
editor = {Skamene, Emil},
isbn = {9780845141021},
publisher = {Liss},
title = {{Methodology for testing the hypothesis of single locus control of host resistance to infection and malignancy}},
volume = {3},
year = {1985},
}
@article{4325,
author = {Jones, Steve and Barton, Nicholas H},
journal = {Nature},
pages = {668 -- 668},
publisher = {Nature Publishing Group},
title = {{Haldane's Rule OK}},
doi = {10.1038/314668a0},
volume = {314},
year = {1985},
}
@article{4326,
author = {Barton, Nicholas H and Hewitt, Godfrey},
issn = {1545-2069},
journal = {Annual Review of Ecology and Systematics},
pages = {113 -- 148},
publisher = {Annual Reviews},
title = {{Analysis of hybrid zones}},
doi = {10.1146/annurev.es.16.110185.000553},
volume = {16},
year = {1985},
}
@inproceedings{3513,
author = {Dobkin, David and Edelsbrunner, Herbert},
booktitle = {9th International Workshop on Graph Theoretic Concepts in Computer Science},
isbn = {3-853-20311-6},
location = {Haus Ohrbeck, Germany},
pages = {88 -- 99},
publisher = {Teubner},
title = {{Ham-sandwich theorems applied to intersection problems}},
year = {1984},
}
@article{4117,
abstract = {Two or more geometrical objects (solids) are said to be connected whenever their union is a connected point set in the usual sense. Sets of geometrical objects are naturally divided into connected components, which are maximal connected subsets. We show that the connected components of a given collection of n horizontal and vertical line segments in the plane can be computed in O (n log n) time and O (n) space and prove that this is essentially optimal. The result is generalized to compute the connected components of a set of n rectilinearly-oriented rectangles
in the plane with the same time and space bounds. Several extensions of the results to higher dimensions and to dynamic sets of objects are discussed.},
author = {Edelsbrunner, Herbert and Van Leeuwen, Jan and Ottmann, Thomas and Wood, Derick},
issn = {1290-385X},
journal = {Rairo-Informatique Theorique Et Applications-Theoretical Informatics and Applications},
number = {2},
pages = {171 -- 183},
publisher = {EDP Sciences},
title = {{Computing the connected components of simple rectilinear geometrical objects in D-Space}},
doi = {10.1051/ita/1984180201711},
volume = {18},
year = {1984},
}
@article{4118,
abstract = {A rectilinear polygon can be viewed as an art gallery room whose walls meet at right angles. An algorithm is presented that stations guards in such a room so that every interior point is visible to some guard. The algorithm partitions the polygon into L-shaped pieces, a subclass of star-shaped pieces, and locates one guard within each kernel. The algorithm runs in O(n log n) time in the worst case for a polygon of n vertices.},
author = {Edelsbrunner, Herbert and O'Rourke, Joseph and Welzl, Emo},
issn = {0734-189X},
journal = {Computer Vision, Graphics, and Image Processing},
number = {2},
pages = {167 -- 176},
publisher = {Elsevier},
title = {{Stationing guards in rectilinear art galleries}},
doi = {10.1016/S0734-189X(84)80041-9},
volume = {27},
year = {1984},
}
@inproceedings{4119,
author = {Edelsbrunner, Herbert and Welzl, Emo},
booktitle = {11th International Symposium on Mathematical Foundations of Computer Science},
isbn = {3-540-13372-0},
location = {Praha, Czechoslovakia},
pages = {265 -- 272},
publisher = {Springer},
title = {{Monotone edge sequences in line arrangements and applications}},
doi = {10.1007/BFb0030307},
volume = {176},
year = {1984},
}