---
_id: '3651'
abstract:
- lang: eng
text: 'It is widely held that each gene typically affects many characters, and that
each character is affected by many genes. Moreover, strong stabilizing selection
cannot act on an indefinitely large number of independent traits. This makes it
likely that heritable variation in any one trait is maintained as a side effect
of polymorphisms which have nothing to do with selection on that trait. This paper
examines the idea that variation is maintained as the pleiotropic side effect
of either deleterious mutation, or balancing selection. If mutation is responsible,
it must produce alleles which are only mildly deleterious (s & 10(-3)), but
nevertheless have significant effects on the trait. Balancing selection can readily
maintain high heritabilities; however, selection must be spread over many weakly
selected polymorphisms if large responses to artificial selection are to be possible.
In both classes of pleiotropic model, extreme phenotypes are less fit, giving
the appearance of stabilizing selection on the trait. However, it is shown that
this effect is weak (of the same order as the selection on each gene): the strong
stabilizing selection which is often observed is likely to be caused by correlations
with a limited number of directly selected traits. Possible experiments for distinguishing
the alternatives are discussed.'
acknowledgement: Thanks to JERRY COYNE, BILL HILL, LINDA PARTRIDGE, MICHAEL TURELLI,
and two anonymous reviewers for their critical comments. This work was supported
by grants from the National Science Foundation (BSR-8866548) the Science and Engineering
Research Council (GR/E/08507), and by the Institute of Theoretical Dynamics, University
of California, Davis.
article_processing_charge: No
article_type: original
author:
- first_name: Nicholas H
full_name: Barton, Nicholas H
id: 4880FE40-F248-11E8-B48F-1D18A9856A87
last_name: Barton
orcid: 0000-0002-8548-5240
citation:
ama: Barton NH. Pleiotropic models of quantitative variation. Genetics. 1990;124(3):773-782.
doi:10.1093/genetics/124.3.773
apa: Barton, N. H. (1990). Pleiotropic models of quantitative variation. Genetics.
Genetics Society of America. https://doi.org/10.1093/genetics/124.3.773
chicago: Barton, Nicholas H. “Pleiotropic Models of Quantitative Variation.” Genetics.
Genetics Society of America, 1990. https://doi.org/10.1093/genetics/124.3.773 .
ieee: N. H. Barton, “Pleiotropic models of quantitative variation,” Genetics,
vol. 124, no. 3. Genetics Society of America, pp. 773–782, 1990.
ista: Barton NH. 1990. Pleiotropic models of quantitative variation. Genetics. 124(3),
773–782.
mla: Barton, Nicholas H. “Pleiotropic Models of Quantitative Variation.” Genetics,
vol. 124, no. 3, Genetics Society of America, 1990, pp. 773–82, doi:10.1093/genetics/124.3.773 .
short: N.H. Barton, Genetics 124 (1990) 773–782.
date_created: 2018-12-11T12:04:26Z
date_published: 1990-03-01T00:00:00Z
date_updated: 2022-02-23T10:41:43Z
day: '01'
doi: '10.1093/genetics/124.3.773 '
extern: '1'
external_id:
pmid:
- '2311921'
intvolume: ' 124'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://academic.oup.com/genetics/article/124/3/773/5999956?login=true
month: '03'
oa: 1
oa_version: Published Version
page: 773 - 782
pmid: 1
publication: Genetics
publication_identifier:
issn:
- 0016-6731
publication_status: published
publisher: Genetics Society of America
publist_id: '2732'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Pleiotropic models of quantitative variation
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 124
year: '1990'
...
---
_id: '4060'
abstract:
- lang: eng
text: This paper offers combinatorial results on extremum problems concerning the
number of tetrahedra in a tetrahedrization of n points in general position in
three dimensions, i.e. such that no four points are co-planar, It also presents
an algorithm that in O(n log n) time constructs a tetrahedrization of a set of
n points consisting of at most 3n-11 tetrahedra.
acknowledgement: Research of the first author is supported by Amoco Fnd. Fac. Dec.
Comput. Sci. 1-6-44862, the second author is supported by NSF Grant ECS 84-10902,
and research of the third author is supported in part by ONR Grant N00014-85K0570
and by NSF Grant DMS 8504322.
article_processing_charge: No
article_type: original
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Franco
full_name: Preparata, Franco
last_name: Preparata
- first_name: Douglas
full_name: West, Douglas
last_name: West
citation:
ama: Edelsbrunner H, Preparata F, West D. Tetrahedrizing point sets in three dimensions.
Journal of Symbolic Computation. 1990;10(3-4):335-347. doi:10.1016/S0747-7171(08)80068-5
apa: Edelsbrunner, H., Preparata, F., & West, D. (1990). Tetrahedrizing point
sets in three dimensions. Journal of Symbolic Computation. Elsevier. https://doi.org/10.1016/S0747-7171(08)80068-5
chicago: Edelsbrunner, Herbert, Franco Preparata, and Douglas West. “Tetrahedrizing
Point Sets in Three Dimensions.” Journal of Symbolic Computation. Elsevier,
1990. https://doi.org/10.1016/S0747-7171(08)80068-5.
ieee: H. Edelsbrunner, F. Preparata, and D. West, “Tetrahedrizing point sets in
three dimensions,” Journal of Symbolic Computation, vol. 10, no. 3–4. Elsevier,
pp. 335–347, 1990.
ista: Edelsbrunner H, Preparata F, West D. 1990. Tetrahedrizing point sets in three
dimensions. Journal of Symbolic Computation. 10(3–4), 335–347.
mla: Edelsbrunner, Herbert, et al. “Tetrahedrizing Point Sets in Three Dimensions.”
Journal of Symbolic Computation, vol. 10, no. 3–4, Elsevier, 1990, pp.
335–47, doi:10.1016/S0747-7171(08)80068-5.
short: H. Edelsbrunner, F. Preparata, D. West, Journal of Symbolic Computation 10
(1990) 335–347.
date_created: 2018-12-11T12:06:42Z
date_published: 1990-01-01T00:00:00Z
date_updated: 2022-02-23T10:10:35Z
day: '01'
doi: 10.1016/S0747-7171(08)80068-5
extern: '1'
intvolume: ' 10'
issue: 3-4
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://www.sciencedirect.com/science/article/pii/S0747717108800685?via%3Dihub
month: '01'
oa: 1
oa_version: Published Version
page: 335 - 347
publication: Journal of Symbolic Computation
publication_identifier:
eissn:
- 1095-855X
issn:
- 0747-7171
publication_status: published
publisher: Elsevier
publist_id: '2061'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Tetrahedrizing point sets in three dimensions
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 10
year: '1990'
...
---
_id: '2525'
abstract:
- lang: eng
text: 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.
acknowledgement: 'This work was supported in part by research grants from the Ministry
of Education, Science and Culture of Japan, the Institute of Physical and Chemical
Research, and the Science and Technology Agency of Japan. The costs of publication
of this article were defrayed in part by the payment of page charges. This article
must therefore be hereby marked “advertisement” in accordance with 18 U.S.C. Section
1734 solely to indicate this fact. '
article_processing_charge: No
article_type: original
author:
- first_name: Yoshifumi
full_name: Yokota, Yoshifumi
last_name: Yokota
- first_name: Yoshiki
full_name: Sasai, Yoshiki
last_name: Sasai
- first_name: Kohichi
full_name: Tanaka, Kohichi
last_name: Tanaka
- first_name: Tsutomu
full_name: Fujiwara, Tsutomu
last_name: Fujiwara
- first_name: Kunihiro
full_name: Tsuchida, Kunihiro
last_name: Tsuchida
- first_name: Ryuichi
full_name: Shigemoto, Ryuichi
id: 499F3ABC-F248-11E8-B48F-1D18A9856A87
last_name: Shigemoto
orcid: 0000-0001-8761-9444
- first_name: Akira
full_name: Kakizuka, Akira
last_name: Kakizuka
- first_name: Hiroaki
full_name: Ohkubo, Hiroaki
last_name: Ohkubo
- first_name: Shigetada
full_name: Nakanishi, Shigetada
last_name: Nakanishi
citation:
ama: Yokota Y, Sasai Y, Tanaka K, et al. Molecular characterization of a functional
cDNA for rat substance P receptor. Journal of Biological Chemistry. 1989;264(30):17649-17652.
doi:doi.org/10.1016/S0021-9258(19)84619-7
apa: Yokota, Y., Sasai, Y., Tanaka, K., Fujiwara, T., Tsuchida, K., Shigemoto, R.,
… Nakanishi, S. (1989). Molecular characterization of a functional cDNA for rat
substance P receptor. Journal of Biological Chemistry. American Society
for Biochemistry and Molecular Biology. https://doi.org/doi.org/10.1016/S0021-9258(19)84619-7
chicago: Yokota, Yoshifumi, Yoshiki Sasai, Kohichi Tanaka, Tsutomu Fujiwara, Kunihiro
Tsuchida, Ryuichi Shigemoto, Akira Kakizuka, Hiroaki Ohkubo, and Shigetada Nakanishi.
“Molecular Characterization of a Functional CDNA for Rat Substance P Receptor.”
Journal of Biological Chemistry. American Society for Biochemistry and
Molecular Biology, 1989. https://doi.org/doi.org/10.1016/S0021-9258(19)84619-7.
ieee: Y. Yokota et al., “Molecular characterization of a functional cDNA
for rat substance P receptor,” Journal of Biological Chemistry, vol. 264,
no. 30. American Society for Biochemistry and Molecular Biology, pp. 17649–17652,
1989.
ista: Yokota Y, Sasai Y, Tanaka K, Fujiwara T, Tsuchida K, Shigemoto R, Kakizuka
A, Ohkubo H, Nakanishi S. 1989. Molecular characterization of a functional cDNA
for rat substance P receptor. Journal of Biological Chemistry. 264(30), 17649–17652.
mla: Yokota, Yoshifumi, et al. “Molecular Characterization of a Functional CDNA
for Rat Substance P Receptor.” Journal of Biological Chemistry, vol. 264,
no. 30, American Society for Biochemistry and Molecular Biology, 1989, pp. 17649–52,
doi:doi.org/10.1016/S0021-9258(19)84619-7.
short: Y. Yokota, Y. Sasai, K. Tanaka, T. Fujiwara, K. Tsuchida, R. Shigemoto, A.
Kakizuka, H. Ohkubo, S. Nakanishi, Journal of Biological Chemistry 264 (1989)
17649–17652.
date_created: 2018-12-11T11:58:11Z
date_published: 1989-10-25T00:00:00Z
date_updated: 2022-02-15T09:29:36Z
day: '25'
doi: doi.org/10.1016/S0021-9258(19)84619-7
extern: '1'
external_id:
pmid:
- '2478537'
intvolume: ' 264'
issue: '30'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://www.sciencedirect.com/science/article/pii/S0021925819846197
month: '10'
oa: 1
oa_version: Published Version
page: 17649 - 17652
pmid: 1
publication: Journal of Biological Chemistry
publication_identifier:
eissn:
- 1083-351X
issn:
- 0021-9258
publication_status: published
publisher: American Society for Biochemistry and Molecular Biology
publist_id: '4374'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Molecular characterization of a functional cDNA for rat substance P receptor
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 264
year: '1989'
...
---
_id: '3466'
abstract:
- lang: eng
text: 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.
acknowledgement: We thank Drs. C. Baumann, D. Siemen, and W. Stuhmer for reading the
manuscript and Dr. F. Dreyer for the generous gift of DTX. The study was supported
by the Deutsche Forschungsgemeinschaft.
article_processing_charge: No
article_type: original
author:
- first_name: Peter M
full_name: Jonas, Peter M
id: 353C1B58-F248-11E8-B48F-1D18A9856A87
last_name: Jonas
orcid: 0000-0001-5001-4804
- first_name: Michael
full_name: Bräu, Michael
last_name: Bräu
- first_name: Markus
full_name: Hermsteiner, Markus
last_name: Hermsteiner
- first_name: Werner
full_name: Vogel, Werner
last_name: Vogel
citation:
ama: Jonas PM, Bräu M, Hermsteiner M, Vogel W. Single-channel recording in myelinated
nerve fibers reveals one type of Na channel but different K channels. PNAS.
1989;86(18):7238-7242. doi:10.1073/pnas.86.18.7238
apa: Jonas, P. M., Bräu, M., Hermsteiner, M., & Vogel, W. (1989). Single-channel
recording in myelinated nerve fibers reveals one type of Na channel but different
K channels. PNAS. National Academy of Sciences. https://doi.org/10.1073/pnas.86.18.7238
chicago: Jonas, Peter M, Michael Bräu, Markus Hermsteiner, and Werner Vogel. “Single-Channel
Recording in Myelinated Nerve Fibers Reveals One Type of Na Channel but Different
K Channels.” PNAS. National Academy of Sciences, 1989. https://doi.org/10.1073/pnas.86.18.7238.
ieee: P. M. Jonas, M. Bräu, M. Hermsteiner, and W. Vogel, “Single-channel recording
in myelinated nerve fibers reveals one type of Na channel but different K channels,”
PNAS, vol. 86, no. 18. National Academy of Sciences, pp. 7238–7242, 1989.
ista: Jonas PM, Bräu M, Hermsteiner M, Vogel W. 1989. Single-channel recording in
myelinated nerve fibers reveals one type of Na channel but different K channels.
PNAS. 86(18), 7238–7242.
mla: Jonas, Peter M., et al. “Single-Channel Recording in Myelinated Nerve Fibers
Reveals One Type of Na Channel but Different K Channels.” PNAS, vol. 86,
no. 18, National Academy of Sciences, 1989, pp. 7238–42, doi:10.1073/pnas.86.18.7238.
short: P.M. Jonas, M. Bräu, M. Hermsteiner, W. Vogel, PNAS 86 (1989) 7238–7242.
date_created: 2018-12-11T12:03:28Z
date_published: 1989-09-01T00:00:00Z
date_updated: 2022-02-14T16:12:33Z
day: '01'
doi: 10.1073/pnas.86.18.7238
extern: '1'
external_id:
pmid:
- '2550937 '
intvolume: ' 86'
issue: '18'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC298032/?tool=pubmed
month: '09'
oa: 1
oa_version: Published Version
page: 7238 - 7242
pmid: 1
publication: PNAS
publication_identifier:
eissn:
- 1091-6490
issn:
- 0027-8424
publication_status: published
publisher: National Academy of Sciences
publist_id: '2921'
quality_controlled: '1'
status: public
title: Single-channel recording in myelinated nerve fibers reveals one type of Na
channel but different K channels
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 86
year: '1989'
...
---
_id: '3652'
abstract:
- lang: eng
text: 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.
acknowledgement: "The publication costs of this article were partly defrayed by the
payment of page charges. This article must therefore be hereby marked “advertisment”
in accordance with 18 U.S.C. §1734 solely to indicate this fact. \r\n\r\nWe thank
the Natural Environmental Research Council for financial support, and N. SANDERSON,
M. SLATKIN and an anonymous reviewer for comments on the manuscript."
article_processing_charge: No
article_type: original
author:
- first_name: James
full_name: Mallet, James
last_name: Mallet
- first_name: Nicholas H
full_name: Barton, Nicholas H
id: 4880FE40-F248-11E8-B48F-1D18A9856A87
last_name: Barton
orcid: 0000-0002-8548-5240
citation:
ama: Mallet J, Barton NH. Inference from clines stabilized by frequency-dependent
selection. Genetics. 1989;122(4):967-976. doi:10.1093/genetics/122.4.967
apa: Mallet, J., & Barton, N. H. (1989). Inference from clines stabilized by
frequency-dependent selection. Genetics. Genetics Society of America. https://doi.org/10.1093/genetics/122.4.967
chicago: Mallet, James, and Nicholas H Barton. “Inference from Clines Stabilized
by Frequency-Dependent Selection.” Genetics. Genetics Society of America,
1989. https://doi.org/10.1093/genetics/122.4.967.
ieee: J. Mallet and N. H. Barton, “Inference from clines stabilized by frequency-dependent
selection,” Genetics, vol. 122, no. 4. Genetics Society of America, pp.
967–976, 1989.
ista: Mallet J, Barton NH. 1989. Inference from clines stabilized by frequency-dependent
selection. Genetics. 122(4), 967–976.
mla: Mallet, James, and Nicholas H. Barton. “Inference from Clines Stabilized by
Frequency-Dependent Selection.” Genetics, vol. 122, no. 4, Genetics Society
of America, 1989, pp. 967–76, doi:10.1093/genetics/122.4.967.
short: J. Mallet, N.H. Barton, Genetics 122 (1989) 967–976.
date_created: 2018-12-11T12:04:27Z
date_published: 1989-08-01T00:00:00Z
date_updated: 2022-02-14T14:07:12Z
day: '01'
doi: 10.1093/genetics/122.4.967
extern: '1'
external_id:
pmid:
- '2759433'
intvolume: ' 122'
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1203771
month: '08'
oa: 1
oa_version: None
page: 967 - 976
pmid: 1
publication: Genetics
publication_identifier:
issn:
- 0016-6731
publication_status: published
publisher: Genetics Society of America
publist_id: '2731'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Inference from clines stabilized by frequency-dependent selection
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 122
year: '1989'
...
---
_id: '4081'
abstract:
- lang: eng
text: 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.
acknowledgement: Work on this paper by the first author has been supported by Amoco
Fnd. Fac. Dev. Comput. Sci. 1-6-44862. Work by the third author has been supported
by the Office of Naval Research Grant N00014-82-K-0381, National Science Foundation
Grant No. NSF-DCR-83-20085, by grants from the Digital Equipment Corporation and
the IBM Corporation, and by a research grant from NCRD, the Israeli National Council
for Research and Development.
article_processing_charge: No
article_type: original
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Leonidas
full_name: Guibas, Leonidas
last_name: Guibas
- first_name: Micha
full_name: Sharir, Micha
last_name: Sharir
citation:
ama: 'Edelsbrunner H, Guibas L, Sharir M. The upper envelope of piecewise linear
functions: Algorithms and applications. Discrete & Computational Geometry.
1989;4(1):311-336. doi:10.1007/BF02187733'
apa: 'Edelsbrunner, H., Guibas, L., & Sharir, M. (1989). The upper envelope
of piecewise linear functions: Algorithms and applications. Discrete &
Computational Geometry. Springer. https://doi.org/10.1007/BF02187733'
chicago: 'Edelsbrunner, Herbert, Leonidas Guibas, and Micha Sharir. “The Upper Envelope
of Piecewise Linear Functions: Algorithms and Applications.” Discrete &
Computational Geometry. Springer, 1989. https://doi.org/10.1007/BF02187733.'
ieee: 'H. Edelsbrunner, L. Guibas, and M. Sharir, “The upper envelope of piecewise
linear functions: Algorithms and applications,” Discrete & Computational
Geometry, vol. 4, no. 1. Springer, pp. 311–336, 1989.'
ista: 'Edelsbrunner H, Guibas L, Sharir M. 1989. The upper envelope of piecewise
linear functions: Algorithms and applications. Discrete & Computational Geometry.
4(1), 311–336.'
mla: 'Edelsbrunner, Herbert, et al. “The Upper Envelope of Piecewise Linear Functions:
Algorithms and Applications.” Discrete & Computational Geometry, vol.
4, no. 1, Springer, 1989, pp. 311–36, doi:10.1007/BF02187733.'
short: H. Edelsbrunner, L. Guibas, M. Sharir, Discrete & Computational Geometry
4 (1989) 311–336.
date_created: 2018-12-11T12:06:50Z
date_published: 1989-12-01T00:00:00Z
date_updated: 2022-02-10T15:53:48Z
day: '01'
doi: 10.1007/BF02187733
extern: '1'
intvolume: ' 4'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://link.springer.com/article/10.1007/BF02187733
month: '12'
oa: 1
oa_version: Published Version
page: 311 - 336
publication: Discrete & Computational Geometry
publication_identifier:
eissn:
- 1432-0444
issn:
- 0179-5376
publication_status: published
publisher: Springer
publist_id: '2038'
quality_controlled: '1'
status: public
title: 'The upper envelope of piecewise linear functions: Algorithms and applications'
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 4
year: '1989'
...
---
_id: '4082'
abstract:
- lang: eng
text: 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.
acknowledgement: he authors wish to thank Raimund Seidel for suggesting the argument
that we used to prove Theorem 3.1, Harald Rosenberger who implemented the topological
sweep and compared it with a straight line sweep, the students who took the Stanford
1985 analysis of algorithms qualifying examination and suffered through a version
of this problem, and finally Lyle Ramshaw and Cynthia Hibbard for their detailed
reading and comments on the manuscript. The constructive criticism of an anonymous
referee is also appreciated.
article_processing_charge: No
article_type: original
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Leonidas
full_name: Guibas, Leonidas
last_name: Guibas
citation:
ama: Edelsbrunner H, Guibas L. Topologically sweeping an arrangement. Journal
of Computer and System Sciences. 1989;38(1):165-194. doi:10.1016/0022-0000(89)90038-X
apa: Edelsbrunner, H., & Guibas, L. (1989). Topologically sweeping an arrangement.
Journal of Computer and System Sciences. Elsevier. https://doi.org/10.1016/0022-0000(89)90038-X
chicago: Edelsbrunner, Herbert, and Leonidas Guibas. “Topologically Sweeping an
Arrangement.” Journal of Computer and System Sciences. Elsevier, 1989.
https://doi.org/10.1016/0022-0000(89)90038-X.
ieee: H. Edelsbrunner and L. Guibas, “Topologically sweeping an arrangement,” Journal
of Computer and System Sciences, vol. 38, no. 1. Elsevier, pp. 165–194, 1989.
ista: Edelsbrunner H, Guibas L. 1989. Topologically sweeping an arrangement. Journal
of Computer and System Sciences. 38(1), 165–194.
mla: Edelsbrunner, Herbert, and Leonidas Guibas. “Topologically Sweeping an Arrangement.”
Journal of Computer and System Sciences, vol. 38, no. 1, Elsevier, 1989,
pp. 165–94, doi:10.1016/0022-0000(89)90038-X.
short: H. Edelsbrunner, L. Guibas, Journal of Computer and System Sciences 38 (1989)
165–194.
date_created: 2018-12-11T12:06:50Z
date_published: 1989-02-01T00:00:00Z
date_updated: 2022-02-10T16:06:05Z
day: '01'
doi: 10.1016/0022-0000(89)90038-X
extern: '1'
intvolume: ' 38'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://www.sciencedirect.com/science/article/pii/002200008990038X?via%3Dihub
month: '02'
oa: 1
oa_version: Published Version
page: 165 - 194
publication: Journal of Computer and System Sciences
publication_identifier:
eissn:
- 1090-2724
issn:
- 0022-0000
publication_status: published
publisher: Elsevier
publist_id: '2039'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Topologically sweeping an arrangement
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 38
year: '1989'
...
---
_id: '4083'
abstract:
- lang: eng
text: '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.'
article_processing_charge: No
article_type: original
author:
- first_name: F.
full_name: Yao, F.
last_name: Yao
- first_name: David
full_name: Dobkin, David
last_name: Dobkin
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Michael
full_name: Paterson, Michael
last_name: Paterson
citation:
ama: Yao F, Dobkin D, Edelsbrunner H, Paterson M. Partitioning space for range queries.
SIAM Journal on Computing. 1989;18(2):371-384. doi:10.1137/0218025
apa: Yao, F., Dobkin, D., Edelsbrunner, H., & Paterson, M. (1989). Partitioning
space for range queries. SIAM Journal on Computing. SIAM. https://doi.org/10.1137/0218025
chicago: Yao, F., David Dobkin, Herbert Edelsbrunner, and Michael Paterson. “Partitioning
Space for Range Queries.” SIAM Journal on Computing. SIAM, 1989. https://doi.org/10.1137/0218025.
ieee: F. Yao, D. Dobkin, H. Edelsbrunner, and M. Paterson, “Partitioning space for
range queries,” SIAM Journal on Computing, vol. 18, no. 2. SIAM, pp. 371–384,
1989.
ista: Yao F, Dobkin D, Edelsbrunner H, Paterson M. 1989. Partitioning space for
range queries. SIAM Journal on Computing. 18(2), 371–384.
mla: Yao, F., et al. “Partitioning Space for Range Queries.” SIAM Journal on
Computing, vol. 18, no. 2, SIAM, 1989, pp. 371–84, doi:10.1137/0218025.
short: F. Yao, D. Dobkin, H. Edelsbrunner, M. Paterson, SIAM Journal on Computing
18 (1989) 371–384.
date_created: 2018-12-11T12:06:50Z
date_published: 1989-04-01T00:00:00Z
date_updated: 2022-02-11T07:55:48Z
day: '01'
doi: 10.1137/0218025
extern: '1'
intvolume: ' 18'
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://epubs.siam.org/doi/10.1137/0218025
month: '04'
oa: 1
oa_version: Published Version
page: 371 - 384
publication: SIAM Journal on Computing
publication_identifier:
eissn:
- 1095-7111
issn:
- 0097-5397
publication_status: published
publisher: SIAM
publist_id: '2040'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Partitioning space for range queries
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 18
year: '1989'
...
---
_id: '4084'
abstract:
- lang: eng
text: "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.\r\n\r\nIn 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."
article_processing_charge: No
article_type: original
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Günter
full_name: Rote, Günter
last_name: Rote
- first_name: Emo
full_name: Welzl, Emo
last_name: Welzl
citation:
ama: Edelsbrunner H, Rote G, Welzl E. Testing the necklace condition for shortest
tours and optimal factors in the plane. Theoretical Computer Science. 1989;66(2):157-180.
doi:10.1016/0304-3975(89)90133-3
apa: Edelsbrunner, H., Rote, G., & Welzl, E. (1989). Testing the necklace condition
for shortest tours and optimal factors in the plane. Theoretical Computer Science.
Elsevier. https://doi.org/10.1016/0304-3975(89)90133-3
chicago: Edelsbrunner, Herbert, Günter Rote, and Emo Welzl. “Testing the Necklace
Condition for Shortest Tours and Optimal Factors in the Plane.” Theoretical
Computer Science. Elsevier, 1989. https://doi.org/10.1016/0304-3975(89)90133-3.
ieee: H. Edelsbrunner, G. Rote, and E. Welzl, “Testing the necklace condition for
shortest tours and optimal factors in the plane,” Theoretical Computer Science,
vol. 66, no. 2. Elsevier, pp. 157–180, 1989.
ista: Edelsbrunner H, Rote G, Welzl E. 1989. Testing the necklace condition for
shortest tours and optimal factors in the plane. Theoretical Computer Science.
66(2), 157–180.
mla: Edelsbrunner, Herbert, et al. “Testing the Necklace Condition for Shortest
Tours and Optimal Factors in the Plane.” Theoretical Computer Science,
vol. 66, no. 2, Elsevier, 1989, pp. 157–80, doi:10.1016/0304-3975(89)90133-3.
short: H. Edelsbrunner, G. Rote, E. Welzl, Theoretical Computer Science 66 (1989)
157–180.
date_created: 2018-12-11T12:06:51Z
date_published: 1989-08-01T00:00:00Z
date_updated: 2022-02-11T11:15:43Z
day: '01'
doi: 10.1016/0304-3975(89)90133-3
extern: '1'
intvolume: ' 66'
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://www.sciencedirect.com/science/article/pii/0304397589901333?via%3Dihub
month: '08'
oa: 1
oa_version: Published Version
page: 157 - 180
publication: Theoretical Computer Science
publication_identifier:
eissn:
- 1879-2294
issn:
- 0304-3975
publication_status: published
publisher: Elsevier
publist_id: '2041'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Testing the necklace condition for shortest tours and optimal factors in the
plane
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 66
year: '1989'
...
---
_id: '4086'
abstract:
- lang: eng
text: 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.
acknowledgement: "This work was supported by Amoco Fnd. Fac. Dev. Comput. Sci. 1-6-44862
and by the National Science Foundation under Grant CCR-8714565. Research on the
presented result was partially carried out while the author worked for the IBM T.
J. Watson Research Center at Yorktown Height, New York, USA. \r\n"
article_processing_charge: No
article_type: original
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
citation:
ama: 'Edelsbrunner H. The upper envelope of piecewise linear functions: Tight bounds
on the number of faces . Discrete & Computational Geometry. 1989;4(4):337-343.
doi:10.1007/BF02187734'
apa: 'Edelsbrunner, H. (1989). The upper envelope of piecewise linear functions:
Tight bounds on the number of faces . Discrete & Computational Geometry.
Springer. https://doi.org/10.1007/BF02187734'
chicago: 'Edelsbrunner, Herbert. “The Upper Envelope of Piecewise Linear Functions:
Tight Bounds on the Number of Faces .” Discrete & Computational Geometry.
Springer, 1989. https://doi.org/10.1007/BF02187734.'
ieee: 'H. Edelsbrunner, “The upper envelope of piecewise linear functions: Tight
bounds on the number of faces ,” Discrete & Computational Geometry,
vol. 4, no. 4. Springer, pp. 337–343, 1989.'
ista: 'Edelsbrunner H. 1989. The upper envelope of piecewise linear functions: Tight
bounds on the number of faces . Discrete & Computational Geometry. 4(4), 337–343.'
mla: 'Edelsbrunner, Herbert. “The Upper Envelope of Piecewise Linear Functions:
Tight Bounds on the Number of Faces .” Discrete & Computational Geometry,
vol. 4, no. 4, Springer, 1989, pp. 337–43, doi:10.1007/BF02187734.'
short: H. Edelsbrunner, Discrete & Computational Geometry 4 (1989) 337–343.
date_created: 2018-12-11T12:06:51Z
date_published: 1989-11-01T00:00:00Z
date_updated: 2022-02-10T11:08:12Z
day: '01'
doi: 10.1007/BF02187734
extern: '1'
intvolume: ' 4'
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://link.springer.com/article/10.1007/BF02187734
month: '11'
oa: 1
oa_version: Published Version
page: 337 - 343
publication: Discrete & Computational Geometry
publication_identifier:
eissn:
- 1432-0444
issn:
- 0179-5376
publication_status: published
publisher: Springer
publist_id: '2034'
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'The upper envelope of piecewise linear functions: Tight bounds on the number
of faces '
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 4
year: '1989'
...
---
_id: '4088'
abstract:
- lang: eng
text: '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.'
acknowledgement: The first author is pleased to acknowledge the support of Amoco Fnd.
Fac. Dev. Comput. Sci. 1-6-44862 and National Science Foundation Grant CCR-8714565.
Work on this paper by the fifth author has been supported by Office of Naval Research
Grant N00014-87-K-0129, by National Science Foundation Grant NSF-DCR-83-20085, by
grants from the Digital Equipment Corporation, and the IBM Corporation, and by a
research grant from the NCRD—the Israeli National Council for Research and Development.
The sixth author was supported in part by a National Science Foundation Graduate
Fellowship. This work was begun while the non-DEC authors were visiting at the DEC
Systems Research Center.
article_processing_charge: No
article_type: original
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Leonidas
full_name: Guibas, Leonidas
last_name: Guibas
- first_name: John
full_name: Hershberger, John
last_name: Hershberger
- first_name: Raimund
full_name: Seidel, Raimund
last_name: Seidel
- first_name: Micha
full_name: Sharir, Micha
last_name: Sharir
- first_name: Jack
full_name: Snoeyink, Jack
last_name: Snoeyink
- first_name: Emo
full_name: Welzl, Emo
last_name: Welzl
citation:
ama: Edelsbrunner H, Guibas L, Hershberger J, et al. Implicitly representing arrangements
of lines or segments. Discrete & Computational Geometry. 1989;4(1):433-466.
doi:10.1007/BF02187742
apa: Edelsbrunner, H., Guibas, L., Hershberger, J., Seidel, R., Sharir, M., Snoeyink,
J., & Welzl, E. (1989). Implicitly representing arrangements of lines or segments.
Discrete & Computational Geometry. Springer. https://doi.org/10.1007/BF02187742
chicago: Edelsbrunner, Herbert, Leonidas Guibas, John Hershberger, Raimund Seidel,
Micha Sharir, Jack Snoeyink, and Emo Welzl. “Implicitly Representing Arrangements
of Lines or Segments.” Discrete & Computational Geometry. Springer,
1989. https://doi.org/10.1007/BF02187742.
ieee: H. Edelsbrunner et al., “Implicitly representing arrangements of lines
or segments,” Discrete & Computational Geometry, vol. 4, no. 1. Springer,
pp. 433–466, 1989.
ista: Edelsbrunner H, Guibas L, Hershberger J, Seidel R, Sharir M, Snoeyink J, Welzl
E. 1989. Implicitly representing arrangements of lines or segments. Discrete &
Computational Geometry. 4(1), 433–466.
mla: Edelsbrunner, Herbert, et al. “Implicitly Representing Arrangements of Lines
or Segments.” Discrete & Computational Geometry, vol. 4, no. 1, Springer,
1989, pp. 433–66, doi:10.1007/BF02187742.
short: H. Edelsbrunner, L. Guibas, J. Hershberger, R. Seidel, M. Sharir, J. Snoeyink,
E. Welzl, Discrete & Computational Geometry 4 (1989) 433–466.
date_created: 2018-12-11T12:06:52Z
date_published: 1989-12-01T00:00:00Z
date_updated: 2022-02-10T15:03:48Z
day: '01'
doi: 10.1007/BF02187742
extern: '1'
intvolume: ' 4'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://link.springer.com/article/10.1007/BF02187742
month: '12'
oa: 1
oa_version: Published Version
page: 433 - 466
publication: Discrete & Computational Geometry
publication_identifier:
eissn:
- 1432-0444
issn:
- 0179-5376
publication_status: published
publisher: Springer
publist_id: '2036'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Implicitly representing arrangements of lines or segments
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 4
year: '1989'
...
---
_id: '4089'
abstract:
- lang: eng
text: 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.
acknowledgement: The first author is pleased to acknowledge the support of Amoco Fnd.
Fac. Dev. Comput. Sci. 1-6-44862 and National Science Foundation Grant CCR-8714565.
Work on this paper by the fourth and seventh authors has been supported by Office
of Naval Research Grant N00014-87-K-0129, by National Science Foundation Grant NSF-DCR-83-20085,
and by grants from the Digital Equipment Corporation and the IBM Corporation. The
seventh author in addition wishes to acknowledge support by a research grant from
the NCRD—the Israeli National Council for Research and Development. The fifth author
would like to acknowledge support in part by NSF grant DMS-8501947. Finally, the
eighth author was supported in part by a National Science Foundation Graduate Fellowship.
article_processing_charge: No
article_type: original
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Leonidas
full_name: Guibas, Leonidas
last_name: Guibas
- first_name: John
full_name: Hershberger, John
last_name: Hershberger
- first_name: János
full_name: Pach, János
last_name: Pach
- first_name: Richard
full_name: Pollack, Richard
last_name: Pollack
- first_name: Raimund
full_name: Seidel, Raimund
last_name: Seidel
- first_name: Micha
full_name: Sharir, Micha
last_name: Sharir
- first_name: Jack
full_name: Snoeyink, Jack
last_name: Snoeyink
citation:
ama: Edelsbrunner H, Guibas L, Hershberger J, et al. On arrangements of Jordan arcs
with three intersections per pair. Discrete & Computational Geometry.
1989;4(1):523-539. doi:10.1007/BF02187745
apa: Edelsbrunner, H., Guibas, L., Hershberger, J., Pach, J., Pollack, R., Seidel,
R., … Snoeyink, J. (1989). On arrangements of Jordan arcs with three intersections
per pair. Discrete & Computational Geometry. Springer. https://doi.org/10.1007/BF02187745
chicago: Edelsbrunner, Herbert, Leonidas Guibas, John Hershberger, János Pach, Richard
Pollack, Raimund Seidel, Micha Sharir, and Jack Snoeyink. “On Arrangements of
Jordan Arcs with Three Intersections per Pair.” Discrete & Computational
Geometry. Springer, 1989. https://doi.org/10.1007/BF02187745.
ieee: H. Edelsbrunner et al., “On arrangements of Jordan arcs with three
intersections per pair,” Discrete & Computational Geometry, vol. 4,
no. 1. Springer, pp. 523–539, 1989.
ista: Edelsbrunner H, Guibas L, Hershberger J, Pach J, Pollack R, Seidel R, Sharir
M, Snoeyink J. 1989. On arrangements of Jordan arcs with three intersections per
pair. Discrete & Computational Geometry. 4(1), 523–539.
mla: Edelsbrunner, Herbert, et al. “On Arrangements of Jordan Arcs with Three Intersections
per Pair.” Discrete & Computational Geometry, vol. 4, no. 1, Springer,
1989, pp. 523–39, doi:10.1007/BF02187745.
short: H. Edelsbrunner, L. Guibas, J. Hershberger, J. Pach, R. Pollack, R. Seidel,
M. Sharir, J. Snoeyink, Discrete & Computational Geometry 4 (1989) 523–539.
date_created: 2018-12-11T12:06:52Z
date_published: 1989-12-01T00:00:00Z
date_updated: 2022-02-10T15:40:04Z
day: '01'
doi: 10.1007/BF02187745
extern: '1'
intvolume: ' 4'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://link.springer.com/article/10.1007/BF02187745
month: '12'
oa: 1
oa_version: Published Version
page: 523 - 539
publication: Discrete & Computational Geometry
publication_identifier:
eissn:
- 1432-0444
issn:
- 0179-5376
publication_status: published
publisher: Springer
publist_id: '2037'
quality_controlled: '1'
scopus_import: '1'
status: public
title: On arrangements of Jordan arcs with three intersections per pair
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 4
year: '1989'
...
---
_id: '3655'
abstract:
- lang: eng
text: "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
\r\ndivergence may contribute to hybrid inviability. "
acknowledgement: 'We thank Dr. W. Kunz for providing the clones pLm6F4 and pLm4Bll
and Dr. D. Glover for the clone pDm238. We thank Brian Curtis for his photographic
assistance. '
article_processing_charge: No
article_type: original
author:
- first_name: John
full_name: Dallas, John
last_name: Dallas
- first_name: Nicholas H
full_name: Barton, Nicholas H
id: 4880FE40-F248-11E8-B48F-1D18A9856A87
last_name: Barton
orcid: 0000-0002-8548-5240
- first_name: Gabriel
full_name: Dover, Gabriel
last_name: Dover
citation:
ama: Dallas J, Barton NH, Dover G. Interracial rDNA variation in the grasshopper
Podisma Pedestris. Molecular Biology and Evolution. 1988;5(6):660-674.
doi:10.1093/oxfordjournals.molbev.a040528
apa: Dallas, J., Barton, N. H., & Dover, G. (1988). Interracial rDNA variation
in the grasshopper Podisma Pedestris. Molecular Biology and Evolution.
Oxford University Press. https://doi.org/10.1093/oxfordjournals.molbev.a040528
chicago: Dallas, John, Nicholas H Barton, and Gabriel Dover. “Interracial RDNA Variation
in the Grasshopper Podisma Pedestris.” Molecular Biology and Evolution.
Oxford University Press, 1988. https://doi.org/10.1093/oxfordjournals.molbev.a040528.
ieee: J. Dallas, N. H. Barton, and G. Dover, “Interracial rDNA variation in the
grasshopper Podisma Pedestris,” Molecular Biology and Evolution, vol. 5,
no. 6. Oxford University Press, pp. 660–674, 1988.
ista: Dallas J, Barton NH, Dover G. 1988. Interracial rDNA variation in the grasshopper
Podisma Pedestris. Molecular Biology and Evolution. 5(6), 660–674.
mla: Dallas, John, et al. “Interracial RDNA Variation in the Grasshopper Podisma
Pedestris.” Molecular Biology and Evolution, vol. 5, no. 6, Oxford University
Press, 1988, pp. 660–74, doi:10.1093/oxfordjournals.molbev.a040528.
short: J. Dallas, N.H. Barton, G. Dover, Molecular Biology and Evolution 5 (1988)
660–674.
date_created: 2018-12-11T12:04:28Z
date_published: 1988-07-01T00:00:00Z
date_updated: 2022-02-08T13:20:51Z
day: '01'
doi: 10.1093/oxfordjournals.molbev.a040528
extern: '1'
intvolume: ' 5'
issue: '6'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://academic.oup.com/mbe/article/5/6/660/1044340
month: '07'
oa: 1
oa_version: None
page: 660 - 674
publication: Molecular Biology and Evolution
publication_identifier:
eissn:
- 1537-1719
issn:
- 0737-4038
publication_status: published
publisher: Oxford University Press
publist_id: '2728'
quality_controlled: '1'
status: public
title: Interracial rDNA variation in the grasshopper Podisma Pedestris
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 5
year: '1988'
...
---
_id: '4090'
abstract:
- lang: eng
text: 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.
acknowledgement: Research of the first author is supported by Amoco Fnd. Fat. Dev.
Comput. Sci. l-6-44862; research of the second author is supported by NSF Grant
ECS 84-10902.
article_processing_charge: No
article_type: original
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Franco
full_name: Preparata, Franco
last_name: Preparata
citation:
ama: Edelsbrunner H, Preparata F. Minimum polygonal separation. Information and
Computation. 1988;77(3):218-232. doi:10.1016/0890-5401(88)90049-1
apa: Edelsbrunner, H., & Preparata, F. (1988). Minimum polygonal separation.
Information and Computation. Elsevier. https://doi.org/10.1016/0890-5401(88)90049-1
chicago: Edelsbrunner, Herbert, and Franco Preparata. “Minimum Polygonal Separation.”
Information and Computation. Elsevier, 1988. https://doi.org/10.1016/0890-5401(88)90049-1.
ieee: H. Edelsbrunner and F. Preparata, “Minimum polygonal separation,” Information
and Computation, vol. 77, no. 3. Elsevier, pp. 218–232, 1988.
ista: Edelsbrunner H, Preparata F. 1988. Minimum polygonal separation. Information
and Computation. 77(3), 218–232.
mla: Edelsbrunner, Herbert, and Franco Preparata. “Minimum Polygonal Separation.”
Information and Computation, vol. 77, no. 3, Elsevier, 1988, pp. 218–32,
doi:10.1016/0890-5401(88)90049-1.
short: H. Edelsbrunner, F. Preparata, Information and Computation 77 (1988) 218–232.
date_created: 2018-12-11T12:06:53Z
date_published: 1988-06-01T00:00:00Z
date_updated: 2022-02-08T10:36:30Z
day: '01'
doi: 10.1016/0890-5401(88)90049-1
extern: '1'
intvolume: ' 77'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://www.sciencedirect.com/science/article/pii/0890540188900491?via%3Dihub
month: '06'
oa: 1
oa_version: None
page: 218 - 232
publication: Information and Computation
publication_identifier:
eissn:
- 0890-5401
publication_status: published
publisher: Elsevier
publist_id: '2029'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Minimum polygonal separation
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 77
year: '1988'
...
---
_id: '3658'
abstract:
- lang: eng
text: 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.
acknowledgement: "We are most grateful to Manse East for excellent technical assistance,
to Dr Michael Shaw and Martin Dransfield for statistical advice and to Dr Roger
Butlin for critical reading of the manuscript. It is a pleasure to thank M. and
Mme. Aviotti and family at Casterino for their help and hospitality over several
years of field work. The authorities of Le Parc National de Mercantour kindly gave
permission for the collections. This work was financed by grants from the N.E.R.C.
and S.E.R.C.\r\n"
article_processing_charge: No
article_type: original
author:
- first_name: Godfrey
full_name: Hewitt, Godfrey
last_name: Hewitt
- first_name: R.
full_name: Nichols, R.
last_name: Nichols
- first_name: Nicholas H
full_name: Barton, Nicholas H
id: 4880FE40-F248-11E8-B48F-1D18A9856A87
last_name: Barton
orcid: 0000-0002-8548-5240
citation:
ama: Hewitt G, Nichols R, Barton NH. Homogamy in a hybrid zone in the alpine grasshopper
Podisma pedestris. Heredity. 1987;59(3):457-466. doi:10.1038/hdy.1987.156
apa: Hewitt, G., Nichols, R., & Barton, N. H. (1987). Homogamy in a hybrid zone
in the alpine grasshopper Podisma pedestris. Heredity. Nature Publishing
Group. https://doi.org/10.1038/hdy.1987.156
chicago: Hewitt, Godfrey, R. Nichols, and Nicholas H Barton. “Homogamy in a Hybrid
Zone in the Alpine Grasshopper Podisma Pedestris.” Heredity. Nature Publishing
Group, 1987. https://doi.org/10.1038/hdy.1987.156.
ieee: G. Hewitt, R. Nichols, and N. H. Barton, “Homogamy in a hybrid zone in the
alpine grasshopper Podisma pedestris,” Heredity, vol. 59, no. 3. Nature
Publishing Group, pp. 457–466, 1987.
ista: Hewitt G, Nichols R, Barton NH. 1987. Homogamy in a hybrid zone in the alpine
grasshopper Podisma pedestris. Heredity. 59(3), 457–466.
mla: Hewitt, Godfrey, et al. “Homogamy in a Hybrid Zone in the Alpine Grasshopper
Podisma Pedestris.” Heredity, vol. 59, no. 3, Nature Publishing Group,
1987, pp. 457–66, doi:10.1038/hdy.1987.156.
short: G. Hewitt, R. Nichols, N.H. Barton, Heredity 59 (1987) 457–466.
date_created: 2018-12-11T12:04:28Z
date_published: 1987-12-01T00:00:00Z
date_updated: 2022-02-04T12:20:46Z
day: '01'
doi: 10.1038/hdy.1987.156
extern: '1'
intvolume: ' 59'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://www.nature.com/articles/hdy1987156
month: '12'
oa: 1
oa_version: Published Version
page: 457 - 466
publication: Heredity
publication_identifier:
eissn:
- 1365-2540
issn:
- 0018-067X
publication_status: published
publisher: Nature Publishing Group
publist_id: '2725'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Homogamy in a hybrid zone in the alpine grasshopper Podisma pedestris
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 59
year: '1987'
...
---
_id: '4319'
abstract:
- lang: eng
text: 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.
acknowledgement: "s We would like to thank Manse East for technical assistance and
M. et Mme Aviotti for their hospitality in France. We are grateful to Dr Michael
Rennet, Dr Donald Fox, Professor Hubert Rees, and an anonymous referee for their
helpful comments on earlier manuscripts. This work was supported by an S.E.R.C.
grant to G.M.H., and by an S.E.R.C. postdoctoral fellowship to N.H.B. MW. worked
at UEA under an Outside Studies Program.\r\n"
article_processing_charge: No
article_type: original
author:
- first_name: Michael
full_name: Westerman, Michael
last_name: Westerman
- first_name: Nicholas H
full_name: Barton, Nicholas H
id: 4880FE40-F248-11E8-B48F-1D18A9856A87
last_name: Barton
orcid: 0000-0002-8548-5240
- first_name: Godfrey
full_name: Hewitt, Godfrey
last_name: Hewitt
citation:
ama: Westerman M, Barton NH, Hewitt G. Differences in DNA content between two chromosomal
races of the grasshopper Podisma pedestris. Heredity. 1987;58:221-228.
doi:10.1038/hdy.1987.36
apa: Westerman, M., Barton, N. H., & Hewitt, G. (1987). Differences in DNA content
between two chromosomal races of the grasshopper Podisma pedestris. Heredity.
Nature Publishing Group. https://doi.org/10.1038/hdy.1987.36
chicago: Westerman, Michael, Nicholas H Barton, and Godfrey Hewitt. “Differences
in DNA Content between Two Chromosomal Races of the Grasshopper Podisma Pedestris.”
Heredity. Nature Publishing Group, 1987. https://doi.org/10.1038/hdy.1987.36.
ieee: M. Westerman, N. H. Barton, and G. Hewitt, “Differences in DNA content between
two chromosomal races of the grasshopper Podisma pedestris,” Heredity,
vol. 58. Nature Publishing Group, pp. 221–228, 1987.
ista: Westerman M, Barton NH, Hewitt G. 1987. Differences in DNA content between
two chromosomal races of the grasshopper Podisma pedestris. Heredity. 58, 221–228.
mla: Westerman, Michael, et al. “Differences in DNA Content between Two Chromosomal
Races of the Grasshopper Podisma Pedestris.” Heredity, vol. 58, Nature
Publishing Group, 1987, pp. 221–28, doi:10.1038/hdy.1987.36.
short: M. Westerman, N.H. Barton, G. Hewitt, Heredity 58 (1987) 221–228.
date_created: 2018-12-11T12:08:14Z
date_published: 1987-01-01T00:00:00Z
date_updated: 2022-02-03T10:48:40Z
day: '01'
doi: 10.1038/hdy.1987.36
extern: '1'
intvolume: ' 58'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://www.nature.com/articles/hdy198736
month: '01'
oa: 1
oa_version: Published Version
page: 221 - 228
publication: Heredity
publication_identifier:
eissn:
- 1365-2540
issn:
- 0018-067X
publication_status: published
publisher: Nature Publishing Group
publist_id: '1733'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Differences in DNA content between two chromosomal races of the grasshopper
Podisma pedestris
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 58
year: '1987'
...
---
_id: '3663'
abstract:
- lang: eng
text: 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.
acknowledgement: This research has been supported in part by grants from the Royal
Society of London, S.E.R.C., and the National Science Foundation. We thank J. Felsenstein
for helpful discussions of this problem.
article_processing_charge: No
article_type: original
author:
- first_name: Nicholas H
full_name: Barton, Nicholas H
id: 4880FE40-F248-11E8-B48F-1D18A9856A87
last_name: Barton
orcid: 0000-0002-8548-5240
- first_name: Montgomery
full_name: Slatkin, Montgomery
last_name: Slatkin
citation:
ama: Barton NH, Slatkin M. A quasi-equilibrium theory of the distribution of rare
alleles in a subdivided population. Heredity. 1986;56(3):409-416. doi:10.1038/hdy.1986.63
apa: Barton, N. H., & Slatkin, M. (1986). A quasi-equilibrium theory of the
distribution of rare alleles in a subdivided population. Heredity. Nature
Publishing Group. https://doi.org/10.1038/hdy.1986.63
chicago: Barton, Nicholas H, and Montgomery Slatkin. “A Quasi-Equilibrium Theory
of the Distribution of Rare Alleles in a Subdivided Population.” Heredity.
Nature Publishing Group, 1986. https://doi.org/10.1038/hdy.1986.63.
ieee: N. H. Barton and M. Slatkin, “A quasi-equilibrium theory of the distribution
of rare alleles in a subdivided population,” Heredity, vol. 56, no. 3.
Nature Publishing Group, pp. 409–416, 1986.
ista: Barton NH, Slatkin M. 1986. A quasi-equilibrium theory of the distribution
of rare alleles in a subdivided population. Heredity. 56(3), 409–416.
mla: Barton, Nicholas H., and Montgomery Slatkin. “A Quasi-Equilibrium Theory of
the Distribution of Rare Alleles in a Subdivided Population.” Heredity,
vol. 56, no. 3, Nature Publishing Group, 1986, pp. 409–16, doi:10.1038/hdy.1986.63.
short: N.H. Barton, M. Slatkin, Heredity 56 (1986) 409–416.
date_created: 2018-12-11T12:04:30Z
date_published: 1986-06-01T00:00:00Z
date_updated: 2022-02-01T15:04:01Z
day: '01'
doi: 10.1038/hdy.1986.63
extern: '1'
external_id:
pmid:
- '3733460 '
intvolume: ' 56'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://www.nature.com/articles/hdy198663
month: '06'
oa: 1
oa_version: None
page: 409 - 416
pmid: 1
publication: Heredity
publication_identifier:
eissn:
- 1365-2540
issn:
- 0018-067X
publication_status: published
publisher: Nature Publishing Group
publist_id: '2720'
quality_controlled: '1'
scopus_import: '1'
status: public
title: A quasi-equilibrium theory of the distribution of rare alleles in a subdivided
population
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 56
year: '1986'
...
---
_id: '3664'
abstract:
- lang: eng
text: 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.
article_processing_charge: No
article_type: original
author:
- first_name: Nicholas H
full_name: Barton, Nicholas H
id: 4880FE40-F248-11E8-B48F-1D18A9856A87
last_name: Barton
orcid: 0000-0002-8548-5240
- first_name: Bengt
full_name: Bengtsson, Bengt
last_name: Bengtsson
citation:
ama: Barton NH, Bengtsson B. The barrier to genetic exchange between hybridising
populations. Heredity. 1986;57:357-376.
apa: Barton, N. H., & Bengtsson, B. (1986). The barrier to genetic exchange
between hybridising populations. Heredity. Nature Publishing Group.
chicago: Barton, Nicholas H, and Bengt Bengtsson. “The Barrier to Genetic Exchange
between Hybridising Populations.” Heredity. Nature Publishing Group, 1986.
ieee: N. H. Barton and B. Bengtsson, “The barrier to genetic exchange between hybridising
populations,” Heredity, vol. 57. Nature Publishing Group, pp. 357–376,
1986.
ista: Barton NH, Bengtsson B. 1986. The barrier to genetic exchange between hybridising
populations. Heredity. 57, 357–376.
mla: Barton, Nicholas H., and Bengt Bengtsson. “The Barrier to Genetic Exchange
between Hybridising Populations.” Heredity, vol. 57, Nature Publishing
Group, 1986, pp. 357–76.
short: N.H. Barton, B. Bengtsson, Heredity 57 (1986) 357–376.
date_created: 2018-12-11T12:04:30Z
date_published: 1986-01-01T00:00:00Z
date_updated: 2022-02-01T14:49:02Z
day: '01'
extern: '1'
intvolume: ' 57'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://www.nature.com/articles/hdy1986135
month: '01'
oa: 1
oa_version: Published Version
page: 357 - 376
publication: Heredity
publication_identifier:
eissn:
- 1365-2540
issn:
- 0018-067X
publication_status: published
publisher: Nature Publishing Group
publist_id: '2719'
quality_controlled: '1'
scopus_import: '1'
status: public
title: The barrier to genetic exchange between hybridising populations
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 57
year: '1986'
...
---
_id: '3665'
abstract:
- lang: eng
text: 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.
acknowledgement: I would like to thank Shahin Rouhani and Richard Nichols for their
helpful comments on the manuscript, and the latter for providing the data used in
fig. 3. This work was supported by a grant from the Science and Engineering Research
Council (GR/C/91529).
article_processing_charge: No
article_type: original
author:
- first_name: Nicholas H
full_name: Barton, Nicholas H
id: 4880FE40-F248-11E8-B48F-1D18A9856A87
last_name: Barton
orcid: 0000-0002-8548-5240
citation:
ama: Barton NH. The effects of linkage and density-dependent regulation on gene
flow. Heredity. 1986;57:415-426.
apa: Barton, N. H. (1986). The effects of linkage and density-dependent regulation
on gene flow. Heredity. Nature Publishing Group.
chicago: Barton, Nicholas H. “The Effects of Linkage and Density-Dependent Regulation
on Gene Flow.” Heredity. Nature Publishing Group, 1986.
ieee: N. H. Barton, “The effects of linkage and density-dependent regulation on
gene flow,” Heredity, vol. 57. Nature Publishing Group, pp. 415–426, 1986.
ista: Barton NH. 1986. The effects of linkage and density-dependent regulation on
gene flow. Heredity. 57, 415–426.
mla: Barton, Nicholas H. “The Effects of Linkage and Density-Dependent Regulation
on Gene Flow.” Heredity, vol. 57, Nature Publishing Group, 1986, pp. 415–26.
short: N.H. Barton, Heredity 57 (1986) 415–426.
date_created: 2018-12-11T12:04:30Z
date_published: 1986-01-01T00:00:00Z
date_updated: 2022-02-01T14:31:29Z
day: '01'
extern: '1'
intvolume: ' 57'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://www.nature.com/articles/hdy1986142
month: '01'
oa: 1
oa_version: Published Version
page: 415 - 426
publication: Heredity
publication_identifier:
eissn:
- 1365-2540
issn:
- 0018-067X
publication_status: published
publisher: Nature Publishing Group
publist_id: '2718'
quality_controlled: '1'
scopus_import: '1'
status: public
title: The effects of linkage and density-dependent regulation on gene flow
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 57
year: '1986'
...
---
_id: '4098'
abstract:
- lang: eng
text: 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.
article_processing_charge: No
article_type: original
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Gerd
full_name: Stöckl, Gerd
last_name: Stöckl
citation:
ama: Edelsbrunner H, Stöckl G. The number of extreme pairs of finite point-sets
in Euclidean spaces. Journal of Combinatorial Theory Series A. 1986;43(2):344-349.
doi:10.1016/0097-3165(86)90075-0
apa: Edelsbrunner, H., & Stöckl, G. (1986). The number of extreme pairs of finite
point-sets in Euclidean spaces. Journal of Combinatorial Theory Series A.
Elsevier. https://doi.org/10.1016/0097-3165(86)90075-0
chicago: Edelsbrunner, Herbert, and Gerd Stöckl. “The Number of Extreme Pairs of
Finite Point-Sets in Euclidean Spaces.” Journal of Combinatorial Theory Series
A. Elsevier, 1986. https://doi.org/10.1016/0097-3165(86)90075-0.
ieee: H. Edelsbrunner and G. Stöckl, “The number of extreme pairs of finite point-sets
in Euclidean spaces,” Journal of Combinatorial Theory Series A, vol. 43,
no. 2. Elsevier, pp. 344–349, 1986.
ista: Edelsbrunner H, Stöckl G. 1986. The number of extreme pairs of finite point-sets
in Euclidean spaces. Journal of Combinatorial Theory Series A. 43(2), 344–349.
mla: Edelsbrunner, Herbert, and Gerd Stöckl. “The Number of Extreme Pairs of Finite
Point-Sets in Euclidean Spaces.” Journal of Combinatorial Theory Series A,
vol. 43, no. 2, Elsevier, 1986, pp. 344–49, doi:10.1016/0097-3165(86)90075-0.
short: H. Edelsbrunner, G. Stöckl, Journal of Combinatorial Theory Series A 43 (1986)
344–349.
date_created: 2018-12-11T12:06:56Z
date_published: 1986-11-01T00:00:00Z
date_updated: 2022-02-01T14:02:41Z
day: '01'
doi: 10.1016/0097-3165(86)90075-0
extern: '1'
intvolume: ' 43'
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://www.sciencedirect.com/science/article/pii/0097316586900750?via%3Dihub
month: '11'
oa: 1
oa_version: None
page: 344 - 349
publication: Journal of Combinatorial Theory Series A
publication_identifier:
eissn:
- 1096-0899
issn:
- 0097-3165
publication_status: published
publisher: Elsevier
publist_id: '2020'
quality_controlled: '1'
scopus_import: '1'
status: public
title: The number of extreme pairs of finite point-sets in Euclidean spaces
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 43
year: '1986'
...