[{"publisher":"Springer","article_type":"original","quality_controlled":"1","page":"277 - 289","article_processing_charge":"No","date_created":"2018-12-11T12:03:28Z","publication_status":"published","intvolume":"       112","title":"Temperature dependence of gating current in myelinated nerve fibers","scopus_import":"1","_id":"3465","pmid":1,"issue":"3","author":[{"first_name":"Peter M","last_name":"Jonas","orcid":"0000-0001-5001-4804","full_name":"Jonas, Peter M","id":"353C1B58-F248-11E8-B48F-1D18A9856A87"}],"volume":112,"extern":"1","day":"01","doi":"10.1007/BF01870958","abstract":[{"lang":"eng","text":"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."}],"year":"1989","citation":{"ama":"Jonas PM. Temperature dependence of gating current in myelinated nerve fibers. <i>Journal of Membrane Biology</i>. 1989;112(3):277-289. doi:<a href=\"https://doi.org/10.1007/BF01870958\">10.1007/BF01870958</a>","apa":"Jonas, P. M. (1989). Temperature dependence of gating current in myelinated nerve fibers. <i>Journal of Membrane Biology</i>. Springer. <a href=\"https://doi.org/10.1007/BF01870958\">https://doi.org/10.1007/BF01870958</a>","chicago":"Jonas, Peter M. “Temperature Dependence of Gating Current in Myelinated Nerve Fibers.” <i>Journal of Membrane Biology</i>. Springer, 1989. <a href=\"https://doi.org/10.1007/BF01870958\">https://doi.org/10.1007/BF01870958</a>.","ieee":"P. M. Jonas, “Temperature dependence of gating current in myelinated nerve fibers,” <i>Journal of Membrane Biology</i>, vol. 112, no. 3. Springer, pp. 277–289, 1989.","short":"P.M. Jonas, Journal of Membrane Biology 112 (1989) 277–289.","mla":"Jonas, Peter M. “Temperature Dependence of Gating Current in Myelinated Nerve Fibers.” <i>Journal of Membrane Biology</i>, vol. 112, no. 3, Springer, 1989, pp. 277–89, doi:<a href=\"https://doi.org/10.1007/BF01870958\">10.1007/BF01870958</a>.","ista":"Jonas PM. 1989. Temperature dependence of gating current in myelinated nerve fibers. Journal of Membrane Biology. 112(3), 277–289."},"date_updated":"2022-02-15T08:59:02Z","external_id":{"pmid":["2559205 "]},"language":[{"iso":"eng"}],"oa_version":"None","month":"12","publication":"Journal of Membrane Biology","main_file_link":[{"url":"https://link.springer.com/article/10.1007/BF01870958"}],"status":"public","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","publication_identifier":{"issn":["0022-2631"],"eissn":["1432-1424"]},"publist_id":"2922","type":"journal_article","date_published":"1989-12-01T00:00:00Z"},{"abstract":[{"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.","lang":"eng"}],"day":"01","doi":"10.1073/pnas.86.18.7238","external_id":{"pmid":["2550937 "]},"citation":{"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.","short":"P.M. Jonas, M. Bräu, M. Hermsteiner, W. Vogel, PNAS 86 (1989) 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.” <i>PNAS</i>, vol. 86, no. 18, National Academy of Sciences, 1989, pp. 7238–42, doi:<a href=\"https://doi.org/10.1073/pnas.86.18.7238\">10.1073/pnas.86.18.7238</a>.","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.” <i>PNAS</i>. National Academy of Sciences, 1989. <a href=\"https://doi.org/10.1073/pnas.86.18.7238\">https://doi.org/10.1073/pnas.86.18.7238</a>.","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,” <i>PNAS</i>, vol. 86, no. 18. National Academy of Sciences, pp. 7238–7242, 1989.","apa":"Jonas, P. M., Bräu, M., Hermsteiner, M., &#38; Vogel, W. (1989). Single-channel recording in myelinated nerve fibers reveals one type of Na channel but different K channels. <i>PNAS</i>. National Academy of Sciences. <a href=\"https://doi.org/10.1073/pnas.86.18.7238\">https://doi.org/10.1073/pnas.86.18.7238</a>","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. <i>PNAS</i>. 1989;86(18):7238-7242. doi:<a href=\"https://doi.org/10.1073/pnas.86.18.7238\">10.1073/pnas.86.18.7238</a>"},"year":"1989","date_updated":"2022-02-14T16:12:33Z","extern":"1","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.","volume":86,"intvolume":"        86","title":"Single-channel recording in myelinated nerve fibers reveals one type of Na channel but different K channels","date_created":"2018-12-11T12:03:28Z","article_processing_charge":"No","publication_status":"published","issue":"18","author":[{"last_name":"Jonas","first_name":"Peter M","full_name":"Jonas, Peter M","orcid":"0000-0001-5001-4804","id":"353C1B58-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Michael","last_name":"Bräu","full_name":"Bräu, Michael"},{"full_name":"Hermsteiner, Markus","first_name":"Markus","last_name":"Hermsteiner"},{"full_name":"Vogel, Werner","last_name":"Vogel","first_name":"Werner"}],"pmid":1,"_id":"3466","article_type":"original","publisher":"National Academy of Sciences","quality_controlled":"1","page":"7238 - 7242","oa":1,"publist_id":"2921","publication_identifier":{"eissn":["1091-6490"],"issn":["0027-8424"]},"type":"journal_article","date_published":"1989-09-01T00:00:00Z","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","status":"public","main_file_link":[{"url":"http://www.ncbi.nlm.nih.gov/pmc/articles/PMC298032/?tool=pubmed","open_access":"1"}],"month":"09","oa_version":"Published Version","publication":"PNAS","language":[{"iso":"eng"}]},{"extern":"1","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","status":"public","acknowledgement":"Research was supported by the National Science Foundation under grant CCR-8714565.  The author thanks Thomas Kerkhoven, Raimund Seidel, and Peter Shor for helpful discussions on the material of this paper. ","main_file_link":[{"url":"https://ipsj.ixsq.nii.ac.jp/ej/?action=pages_view_main&active_action=repository_view_main_item_detail&item_id=32670&item_no=1&page_id=13&block_id=8"}],"date_published":"1989-01-01T00:00:00Z","type":"conference","date_updated":"2022-02-14T14:34:06Z","year":"1989","citation":{"ista":"Edelsbrunner H. 1989. Spatial triangulations with dihedral angle conditions. International Workshop on Discrete Algorithms and Complexity, 83–89.","mla":"Edelsbrunner, Herbert. <i>Spatial Triangulations with Dihedral Angle Conditions</i>. Institute of the Electronics, Information and Communication Enginneers, 1989, pp. 83–89.","short":"H. Edelsbrunner, in:, Institute of the Electronics, Information and Communication Enginneers, 1989, pp. 83–89.","ieee":"H. Edelsbrunner, “Spatial triangulations with dihedral angle conditions,” presented at the International Workshop on Discrete Algorithms and Complexity, 1989, pp. 83–89.","chicago":"Edelsbrunner, Herbert. “Spatial Triangulations with Dihedral Angle Conditions,” 83–89. Institute of the Electronics, Information and Communication Enginneers, 1989.","apa":"Edelsbrunner, H. (1989). Spatial triangulations with dihedral angle conditions (pp. 83–89). Presented at the International Workshop on Discrete Algorithms and Complexity, Institute of the Electronics, Information and Communication Enginneers.","ama":"Edelsbrunner H. Spatial triangulations with dihedral angle conditions. In: Institute of the Electronics, Information and Communication Enginneers; 1989:83-89."},"abstract":[{"lang":"eng","text":"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. "}],"publist_id":"2836","day":"01","language":[{"iso":"eng"}],"page":"83 - 89","quality_controlled":"1","conference":{"name":"International Workshop on Discrete Algorithms and Complexity"},"publisher":"Institute of the Electronics, Information and Communication Enginneers","author":[{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"}],"_id":"3549","title":"Spatial triangulations with dihedral angle conditions","month":"01","publication_status":"published","oa_version":"None","date_created":"2018-12-11T12:03:54Z","article_processing_charge":"No"},{"abstract":[{"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.","lang":"eng"}],"doi":"10.1093/genetics/122.4.967","day":"01","external_id":{"pmid":["2759433"]},"date_updated":"2022-02-14T14:07:12Z","year":"1989","citation":{"chicago":"Mallet, James, and Nicholas H Barton. “Inference from Clines Stabilized by Frequency-Dependent Selection.” <i>Genetics</i>. Genetics Society of America, 1989. <a href=\"https://doi.org/10.1093/genetics/122.4.967\">https://doi.org/10.1093/genetics/122.4.967</a>.","ieee":"J. Mallet and N. H. Barton, “Inference from clines stabilized by frequency-dependent selection,” <i>Genetics</i>, vol. 122, no. 4. Genetics Society of America, pp. 967–976, 1989.","ama":"Mallet J, Barton NH. Inference from clines stabilized by frequency-dependent selection. <i>Genetics</i>. 1989;122(4):967-976. doi:<a href=\"https://doi.org/10.1093/genetics/122.4.967\">10.1093/genetics/122.4.967</a>","apa":"Mallet, J., &#38; Barton, N. H. (1989). Inference from clines stabilized by frequency-dependent selection. <i>Genetics</i>. Genetics Society of America. <a href=\"https://doi.org/10.1093/genetics/122.4.967\">https://doi.org/10.1093/genetics/122.4.967</a>","ista":"Mallet J, Barton NH. 1989. Inference from clines stabilized by frequency-dependent selection. Genetics. 122(4), 967–976.","short":"J. Mallet, N.H. Barton, Genetics 122 (1989) 967–976.","mla":"Mallet, James, and Nicholas H. Barton. “Inference from Clines Stabilized by Frequency-Dependent Selection.” <i>Genetics</i>, vol. 122, no. 4, Genetics Society of America, 1989, pp. 967–76, doi:<a href=\"https://doi.org/10.1093/genetics/122.4.967\">10.1093/genetics/122.4.967</a>."},"extern":"1","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.","volume":122,"title":"Inference from clines stabilized by frequency-dependent selection","intvolume":"       122","publication_status":"published","article_processing_charge":"No","date_created":"2018-12-11T12:04:27Z","author":[{"last_name":"Mallet","first_name":"James","full_name":"Mallet, James"},{"id":"4880FE40-F248-11E8-B48F-1D18A9856A87","last_name":"Barton","first_name":"Nicholas H","full_name":"Barton, Nicholas H","orcid":"0000-0002-8548-5240"}],"issue":"4","pmid":1,"_id":"3652","scopus_import":"1","article_type":"original","publisher":"Genetics Society of America","page":"967 - 976","quality_controlled":"1","publist_id":"2731","oa":1,"publication_identifier":{"issn":["0016-6731"]},"date_published":"1989-08-01T00:00:00Z","type":"journal_article","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","status":"public","main_file_link":[{"open_access":"1","url":"http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1203771"}],"month":"08","oa_version":"None","publication":"Genetics","language":[{"iso":"eng"}]},{"abstract":[{"text":"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.","lang":"eng"}],"day":"01","doi":"10.2307/2409217 ","external_id":{"pmid":["28568556 "]},"citation":{"ieee":"J. Mallet and N. H. Barton, “Strong natural selection in a warning color hybrid zone,” <i>Evolution</i>, vol. 43, no. 2. Wiley-Blackwell, pp. 421–431, 1989.","chicago":"Mallet, James, and Nicholas H Barton. “Strong Natural Selection in a Warning Color Hybrid Zone.” <i>Evolution</i>. Wiley-Blackwell, 1989. <a href=\"https://doi.org/10.2307/2409217 \">https://doi.org/10.2307/2409217 </a>.","apa":"Mallet, J., &#38; Barton, N. H. (1989). Strong natural selection in a warning color hybrid zone. <i>Evolution</i>. Wiley-Blackwell. <a href=\"https://doi.org/10.2307/2409217 \">https://doi.org/10.2307/2409217 </a>","ama":"Mallet J, Barton NH. Strong natural selection in a warning color hybrid zone. <i>Evolution</i>. 1989;43(2):421-431. doi:<a href=\"https://doi.org/10.2307/2409217 \">10.2307/2409217 </a>","ista":"Mallet J, Barton NH. 1989. Strong natural selection in a warning color hybrid zone. Evolution. 43(2), 421–431.","mla":"Mallet, James, and Nicholas H. Barton. “Strong Natural Selection in a Warning Color Hybrid Zone.” <i>Evolution</i>, vol. 43, no. 2, Wiley-Blackwell, 1989, pp. 421–31, doi:<a href=\"https://doi.org/10.2307/2409217 \">10.2307/2409217 </a>.","short":"J. Mallet, N.H. Barton, Evolution 43 (1989) 421–431."},"year":"1989","date_updated":"2022-02-14T11:00:42Z","extern":"1","acknowledgement":"We thank G.Lamas for sharing his knowledge of the Tarapoto hybrid zone;  M.A.Arboleda, H.Eeley, S.Knapp, M.Muedas, and J.Santisteban for their help in the field;  P.Donnelly and C.Smith for statistical advice; and S.Jones, S.Knapp, G.Lamas, and the reviewers for helpful comments on the manuscript. We are grateful to the Natural Environment Research Council, the Royal Society, and the Nuffield Foundation for funding this research.","volume":43,"intvolume":"        43","title":"Strong natural selection in a warning color hybrid zone","date_created":"2018-12-11T12:04:27Z","article_processing_charge":"No","publication_status":"published","issue":"2","author":[{"full_name":"Mallet, James","first_name":"James","last_name":"Mallet"},{"last_name":"Barton","first_name":"Nicholas H","full_name":"Barton, Nicholas H","orcid":"0000-0002-8548-5240","id":"4880FE40-F248-11E8-B48F-1D18A9856A87"}],"scopus_import":"1","_id":"3653","pmid":1,"article_type":"original","publisher":"Wiley-Blackwell","quality_controlled":"1","page":"421 - 431","publist_id":"2730","publication_identifier":{"issn":["0014-3820"],"eissn":["1558-5646"]},"type":"journal_article","date_published":"1989-01-01T00:00:00Z","status":"public","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","main_file_link":[{"url":"https://www.jstor.org/stable/2409217?origin=crossref&seq=1#metadata_info_tab_contents"}],"month":"01","oa_version":"None","publication":"Evolution","language":[{"iso":"eng"}]},{"quality_controlled":"1","page":"497 - 503","publisher":"Nature Publishing Group","article_type":"original","scopus_import":"1","pmid":1,"_id":"3654","author":[{"id":"4880FE40-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8548-5240","full_name":"Barton, Nicholas H","first_name":"Nicholas H","last_name":"Barton"},{"last_name":"Hewitt","first_name":"Godfrey","full_name":"Hewitt, Godfrey"}],"date_created":"2018-12-11T12:04:27Z","article_processing_charge":"No","publication_status":"published","intvolume":"       341","title":"Adaptation, speciation and hybrid zones","volume":341,"extern":"1","citation":{"ista":"Barton NH, Hewitt G. 1989. Adaptation, speciation and hybrid zones. Nature. 341, 497–503.","mla":"Barton, Nicholas H., and Godfrey Hewitt. “Adaptation, Speciation and Hybrid Zones.” <i>Nature</i>, vol. 341, Nature Publishing Group, 1989, pp. 497–503, doi:<a href=\"https://doi.org/10.1038/341497a0\">10.1038/341497a0</a>.","short":"N.H. Barton, G. Hewitt, Nature 341 (1989) 497–503.","ieee":"N. H. Barton and G. Hewitt, “Adaptation, speciation and hybrid zones,” <i>Nature</i>, vol. 341. Nature Publishing Group, pp. 497–503, 1989.","chicago":"Barton, Nicholas H, and Godfrey Hewitt. “Adaptation, Speciation and Hybrid Zones.” <i>Nature</i>. Nature Publishing Group, 1989. <a href=\"https://doi.org/10.1038/341497a0\">https://doi.org/10.1038/341497a0</a>.","ama":"Barton NH, Hewitt G. Adaptation, speciation and hybrid zones. <i>Nature</i>. 1989;341:497-503. doi:<a href=\"https://doi.org/10.1038/341497a0\">10.1038/341497a0</a>","apa":"Barton, N. H., &#38; Hewitt, G. (1989). Adaptation, speciation and hybrid zones. <i>Nature</i>. Nature Publishing Group. <a href=\"https://doi.org/10.1038/341497a0\">https://doi.org/10.1038/341497a0</a>"},"year":"1989","date_updated":"2022-02-14T10:13:44Z","external_id":{"pmid":["2677747 "]},"day":"12","doi":"10.1038/341497a0","abstract":[{"text":"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.","lang":"eng"}],"language":[{"iso":"eng"}],"publication":"Nature","oa_version":"None","month":"10","main_file_link":[{"url":"https://www.nature.com/articles/341497a0"}],"status":"public","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","type":"journal_article","date_published":"1989-10-12T00:00:00Z","publication_identifier":{"issn":["0028-0836"],"eissn":["1476-4687"]},"publist_id":"2729"},{"doi":"10.1080/00029890.1989.11972250","day":"01","date_updated":"2022-02-11T12:59:01Z","year":"1989","citation":{"ama":"Edelsbrunner H, Skiena S. On the number of furthest neighbor pairs in a point set. <i>American Mathematical Monthly</i>. 1989;96(7):614-618. doi:<a href=\"https://doi.org/10.1080/00029890.1989.11972250\">10.1080/00029890.1989.11972250</a>","apa":"Edelsbrunner, H., &#38; Skiena, S. (1989). On the number of furthest neighbor pairs in a point set. <i>American Mathematical Monthly</i>. Mathematical Association of America. <a href=\"https://doi.org/10.1080/00029890.1989.11972250\">https://doi.org/10.1080/00029890.1989.11972250</a>","chicago":"Edelsbrunner, Herbert, and Steven Skiena. “On the Number of Furthest Neighbor Pairs in a Point Set.” <i>American Mathematical Monthly</i>. Mathematical Association of America, 1989. <a href=\"https://doi.org/10.1080/00029890.1989.11972250\">https://doi.org/10.1080/00029890.1989.11972250</a>.","ieee":"H. Edelsbrunner and S. Skiena, “On the number of furthest neighbor pairs in a point set,” <i>American Mathematical Monthly</i>, vol. 96, no. 7. Mathematical Association of America, pp. 614–618, 1989.","short":"H. Edelsbrunner, S. Skiena, American Mathematical Monthly 96 (1989) 614–618.","mla":"Edelsbrunner, Herbert, and Steven Skiena. “On the Number of Furthest Neighbor Pairs in a Point Set.” <i>American Mathematical Monthly</i>, vol. 96, no. 7, Mathematical Association of America, 1989, pp. 614–18, doi:<a href=\"https://doi.org/10.1080/00029890.1989.11972250\">10.1080/00029890.1989.11972250</a>.","ista":"Edelsbrunner H, Skiena S. 1989. On the number of furthest neighbor pairs in a point set. American Mathematical Monthly. 96(7), 614–618."},"acknowledgement":"Research supported by Amoco Fnd. Fac. Dev. Comput. Sci. 1-6-44862","volume":96,"extern":"1","publication_status":"published","article_processing_charge":"No","date_created":"2018-12-11T12:06:49Z","title":"On the number of furthest neighbor pairs in a point set","intvolume":"        96","_id":"4079","author":[{"orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Skiena","first_name":"Steven","full_name":"Skiena, Steven"}],"issue":"7","publisher":"Mathematical Association of America","article_type":"original","page":"614 - 618","quality_controlled":"1","publication_identifier":{"issn":["0002-9890"],"eissn":["1930-0972"]},"publist_id":"2042","date_published":"1989-01-01T00:00:00Z","type":"journal_article","main_file_link":[{"url":"http://www.jstor.org/stable/2325182 "}],"user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","status":"public","oa_version":"None","month":"01","publication":"American Mathematical Monthly","language":[{"iso":"eng"}]},{"abstract":[{"lang":"eng","text":"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."}],"doi":"10.1007/BF00181432","day":"01","date_updated":"2022-02-14T09:55:28Z","year":"1989","citation":{"ama":"Edelsbrunner H, Hasan N, Seidel R, Shen X. Circles through two points that always enclose many points. <i>Geometriae Dedicata</i>. 1989;32(1):1-12. doi:<a href=\"https://doi.org/10.1007/BF00181432\">10.1007/BF00181432</a>","apa":"Edelsbrunner, H., Hasan, N., Seidel, R., &#38; Shen, X. (1989). Circles through two points that always enclose many points. <i>Geometriae Dedicata</i>. Springer. <a href=\"https://doi.org/10.1007/BF00181432\">https://doi.org/10.1007/BF00181432</a>","chicago":"Edelsbrunner, Herbert, Nany Hasan, Raimund Seidel, and Xiao Shen. “Circles through Two Points That Always Enclose Many Points.” <i>Geometriae Dedicata</i>. Springer, 1989. <a href=\"https://doi.org/10.1007/BF00181432\">https://doi.org/10.1007/BF00181432</a>.","ieee":"H. Edelsbrunner, N. Hasan, R. Seidel, and X. Shen, “Circles through two points that always enclose many points,” <i>Geometriae Dedicata</i>, vol. 32, no. 1. Springer, pp. 1–12, 1989.","mla":"Edelsbrunner, Herbert, et al. “Circles through Two Points That Always Enclose Many Points.” <i>Geometriae Dedicata</i>, vol. 32, no. 1, Springer, 1989, pp. 1–12, doi:<a href=\"https://doi.org/10.1007/BF00181432\">10.1007/BF00181432</a>.","short":"H. Edelsbrunner, N. Hasan, R. Seidel, X. Shen, Geometriae Dedicata 32 (1989) 1–12.","ista":"Edelsbrunner H, Hasan N, Seidel R, Shen X. 1989. Circles through two points that always enclose many points. Geometriae Dedicata. 32(1), 1–12."},"extern":"1","volume":32,"acknowledgement":"Work on this paper by the first author has been supported by Amoco Fnd. Fac. Dev. Comput. Sci. 1-6-44862 and by the National Science Foundation under Grant CCR-8714565, by the second author has been partially supported by the Digital Equipment Corporation, by the fourth author has been partially supported by the Office of Naval Research under Grant N00014-86K-0416.","title":"Circles through two points that always enclose many points","intvolume":"        32","publication_status":"published","article_processing_charge":"No","date_created":"2018-12-11T12:06:49Z","author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","first_name":"Herbert"},{"full_name":"Hasan, Nany","first_name":"Nany","last_name":"Hasan"},{"first_name":"Raimund","last_name":"Seidel","full_name":"Seidel, Raimund"},{"first_name":"Xiao","last_name":"Shen","full_name":"Shen, Xiao"}],"issue":"1","_id":"4080","scopus_import":"1","article_type":"original","publisher":"Springer","page":"1 - 12","quality_controlled":"1","publist_id":"2043","publication_identifier":{"eissn":["1572-9168"],"issn":["0046-5755"]},"date_published":"1989-10-01T00:00:00Z","type":"journal_article","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","status":"public","main_file_link":[{"url":"https://link.springer.com/article/10.1007/BF00181432"}],"month":"10","oa_version":"None","publication":"Geometriae Dedicata","language":[{"iso":"eng"}]},{"quality_controlled":"1","page":"311 - 336","article_type":"original","publisher":"Springer","issue":"1","author":[{"orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Guibas, Leonidas","last_name":"Guibas","first_name":"Leonidas"},{"last_name":"Sharir","first_name":"Micha","full_name":"Sharir, Micha"}],"_id":"4081","intvolume":"         4","title":"The upper envelope of piecewise linear functions: Algorithms and applications","article_processing_charge":"No","date_created":"2018-12-11T12:06:50Z","publication_status":"published","extern":"1","volume":4,"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.","citation":{"ista":"Edelsbrunner H, Guibas L, Sharir M. 1989. The upper envelope of piecewise linear functions: Algorithms and applications. Discrete &#38; Computational Geometry. 4(1), 311–336.","mla":"Edelsbrunner, Herbert, et al. “The Upper Envelope of Piecewise Linear Functions: Algorithms and Applications.” <i>Discrete &#38; Computational Geometry</i>, vol. 4, no. 1, Springer, 1989, pp. 311–36, doi:<a href=\"https://doi.org/10.1007/BF02187733\">10.1007/BF02187733</a>.","short":"H. Edelsbrunner, L. Guibas, M. Sharir, Discrete &#38; Computational Geometry 4 (1989) 311–336.","ieee":"H. Edelsbrunner, L. Guibas, and M. Sharir, “The upper envelope of piecewise linear functions: Algorithms and applications,” <i>Discrete &#38; Computational Geometry</i>, vol. 4, no. 1. Springer, pp. 311–336, 1989.","chicago":"Edelsbrunner, Herbert, Leonidas Guibas, and Micha Sharir. “The Upper Envelope of Piecewise Linear Functions: Algorithms and Applications.” <i>Discrete &#38; Computational Geometry</i>. Springer, 1989. <a href=\"https://doi.org/10.1007/BF02187733\">https://doi.org/10.1007/BF02187733</a>.","ama":"Edelsbrunner H, Guibas L, Sharir M. The upper envelope of piecewise linear functions: Algorithms and applications. <i>Discrete &#38; Computational Geometry</i>. 1989;4(1):311-336. doi:<a href=\"https://doi.org/10.1007/BF02187733\">10.1007/BF02187733</a>","apa":"Edelsbrunner, H., Guibas, L., &#38; Sharir, M. (1989). The upper envelope of piecewise linear functions: Algorithms and applications. <i>Discrete &#38; Computational Geometry</i>. Springer. <a href=\"https://doi.org/10.1007/BF02187733\">https://doi.org/10.1007/BF02187733</a>"},"year":"1989","date_updated":"2022-02-10T15:53:48Z","abstract":[{"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.","lang":"eng"}],"day":"01","doi":"10.1007/BF02187733","language":[{"iso":"eng"}],"publication":"Discrete & Computational Geometry","month":"12","oa_version":"Published Version","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","status":"public","main_file_link":[{"open_access":"1","url":"https://link.springer.com/article/10.1007/BF02187733"}],"type":"journal_article","date_published":"1989-12-01T00:00:00Z","publist_id":"2038","oa":1,"publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]}},{"intvolume":"        38","title":"Topologically sweeping an arrangement","article_processing_charge":"No","date_created":"2018-12-11T12:06:50Z","publication_status":"published","issue":"1","author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833"},{"full_name":"Guibas, Leonidas","first_name":"Leonidas","last_name":"Guibas"}],"scopus_import":"1","_id":"4082","article_type":"original","publisher":"Elsevier","quality_controlled":"1","page":"165 - 194","abstract":[{"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.","lang":"eng"}],"day":"01","doi":"10.1016/0022-0000(89)90038-X","year":"1989","citation":{"mla":"Edelsbrunner, Herbert, and Leonidas Guibas. “Topologically Sweeping an Arrangement.” <i>Journal of Computer and System Sciences</i>, vol. 38, no. 1, Elsevier, 1989, pp. 165–94, doi:<a href=\"https://doi.org/10.1016/0022-0000(89)90038-X\">10.1016/0022-0000(89)90038-X</a>.","short":"H. Edelsbrunner, L. Guibas, Journal of Computer and System Sciences 38 (1989) 165–194.","ista":"Edelsbrunner H, Guibas L. 1989. Topologically sweeping an arrangement. Journal of Computer and System Sciences. 38(1), 165–194.","apa":"Edelsbrunner, H., &#38; Guibas, L. (1989). Topologically sweeping an arrangement. <i>Journal of Computer and System Sciences</i>. Elsevier. <a href=\"https://doi.org/10.1016/0022-0000(89)90038-X\">https://doi.org/10.1016/0022-0000(89)90038-X</a>","ama":"Edelsbrunner H, Guibas L. Topologically sweeping an arrangement. <i>Journal of Computer and System Sciences</i>. 1989;38(1):165-194. doi:<a href=\"https://doi.org/10.1016/0022-0000(89)90038-X\">10.1016/0022-0000(89)90038-X</a>","chicago":"Edelsbrunner, Herbert, and Leonidas Guibas. “Topologically Sweeping an Arrangement.” <i>Journal of Computer and System Sciences</i>. Elsevier, 1989. <a href=\"https://doi.org/10.1016/0022-0000(89)90038-X\">https://doi.org/10.1016/0022-0000(89)90038-X</a>.","ieee":"H. Edelsbrunner and L. Guibas, “Topologically sweeping an arrangement,” <i>Journal of Computer and System Sciences</i>, vol. 38, no. 1. Elsevier, pp. 165–194, 1989."},"date_updated":"2022-02-10T16:06:05Z","extern":"1","volume":38,"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.","month":"02","oa_version":"Published Version","publication":"Journal of Computer and System Sciences","language":[{"iso":"eng"}],"oa":1,"publist_id":"2039","publication_identifier":{"issn":["0022-0000"],"eissn":["1090-2724"]},"type":"journal_article","date_published":"1989-02-01T00:00:00Z","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","status":"public","main_file_link":[{"open_access":"1","url":"https://www.sciencedirect.com/science/article/pii/002200008990038X?via%3Dihub"}]},{"language":[{"iso":"eng"}],"oa_version":"Published Version","month":"04","publication":"SIAM Journal on Computing","main_file_link":[{"url":"https://epubs.siam.org/doi/10.1137/0218025","open_access":"1"}],"status":"public","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","publication_identifier":{"eissn":["1095-7111"],"issn":["0097-5397"]},"oa":1,"publist_id":"2040","type":"journal_article","date_published":"1989-04-01T00:00:00Z","publisher":"SIAM","article_type":"original","quality_controlled":"1","page":"371 - 384","date_created":"2018-12-11T12:06:50Z","article_processing_charge":"No","publication_status":"published","intvolume":"        18","title":"Partitioning space for range queries","scopus_import":"1","_id":"4083","issue":"2","author":[{"full_name":"Yao, F.","last_name":"Yao","first_name":"F."},{"full_name":"Dobkin, David","first_name":"David","last_name":"Dobkin"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","first_name":"Herbert","last_name":"Edelsbrunner"},{"full_name":"Paterson, Michael","first_name":"Michael","last_name":"Paterson"}],"volume":18,"extern":"1","day":"01","doi":"10.1137/0218025","abstract":[{"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.","lang":"eng"}],"citation":{"ista":"Yao F, Dobkin D, Edelsbrunner H, Paterson M. 1989. Partitioning space for range queries. SIAM Journal on Computing. 18(2), 371–384.","short":"F. Yao, D. Dobkin, H. Edelsbrunner, M. Paterson, SIAM Journal on Computing 18 (1989) 371–384.","mla":"Yao, F., et al. “Partitioning Space for Range Queries.” <i>SIAM Journal on Computing</i>, vol. 18, no. 2, SIAM, 1989, pp. 371–84, doi:<a href=\"https://doi.org/10.1137/0218025\">10.1137/0218025</a>.","ieee":"F. Yao, D. Dobkin, H. Edelsbrunner, and M. Paterson, “Partitioning space for range queries,” <i>SIAM Journal on Computing</i>, vol. 18, no. 2. SIAM, pp. 371–384, 1989.","chicago":"Yao, F., David Dobkin, Herbert Edelsbrunner, and Michael Paterson. “Partitioning Space for Range Queries.” <i>SIAM Journal on Computing</i>. SIAM, 1989. <a href=\"https://doi.org/10.1137/0218025\">https://doi.org/10.1137/0218025</a>.","ama":"Yao F, Dobkin D, Edelsbrunner H, Paterson M. Partitioning space for range queries. <i>SIAM Journal on Computing</i>. 1989;18(2):371-384. doi:<a href=\"https://doi.org/10.1137/0218025\">10.1137/0218025</a>","apa":"Yao, F., Dobkin, D., Edelsbrunner, H., &#38; Paterson, M. (1989). Partitioning space for range queries. <i>SIAM Journal on Computing</i>. SIAM. <a href=\"https://doi.org/10.1137/0218025\">https://doi.org/10.1137/0218025</a>"},"year":"1989","date_updated":"2022-02-11T07:55:48Z"},{"month":"08","oa_version":"Published Version","publication":"Theoretical Computer Science","language":[{"iso":"eng"}],"publist_id":"2041","oa":1,"publication_identifier":{"eissn":["1879-2294"],"issn":["0304-3975"]},"date_published":"1989-08-01T00:00:00Z","type":"journal_article","status":"public","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","main_file_link":[{"open_access":"1","url":"https://www.sciencedirect.com/science/article/pii/0304397589901333?via%3Dihub"}],"title":"Testing the necklace condition for shortest tours and optimal factors in the plane","intvolume":"        66","publication_status":"published","date_created":"2018-12-11T12:06:51Z","article_processing_charge":"No","author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","first_name":"Herbert"},{"full_name":"Rote, Günter","last_name":"Rote","first_name":"Günter"},{"last_name":"Welzl","first_name":"Emo","full_name":"Welzl, Emo"}],"issue":"2","_id":"4084","scopus_import":"1","article_type":"original","publisher":"Elsevier","page":"157 - 180","quality_controlled":"1","abstract":[{"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.","lang":"eng"}],"doi":"10.1016/0304-3975(89)90133-3","day":"01","date_updated":"2022-02-11T11:15:43Z","year":"1989","citation":{"chicago":"Edelsbrunner, Herbert, Günter Rote, and Emo Welzl. “Testing the Necklace Condition for Shortest Tours and Optimal Factors in the Plane.” <i>Theoretical Computer Science</i>. Elsevier, 1989. <a href=\"https://doi.org/10.1016/0304-3975(89)90133-3\">https://doi.org/10.1016/0304-3975(89)90133-3</a>.","ieee":"H. Edelsbrunner, G. Rote, and E. Welzl, “Testing the necklace condition for shortest tours and optimal factors in the plane,” <i>Theoretical Computer Science</i>, vol. 66, no. 2. Elsevier, pp. 157–180, 1989.","apa":"Edelsbrunner, H., Rote, G., &#38; Welzl, E. (1989). Testing the necklace condition for shortest tours and optimal factors in the plane. <i>Theoretical Computer Science</i>. Elsevier. <a href=\"https://doi.org/10.1016/0304-3975(89)90133-3\">https://doi.org/10.1016/0304-3975(89)90133-3</a>","ama":"Edelsbrunner H, Rote G, Welzl E. Testing the necklace condition for shortest tours and optimal factors in the plane. <i>Theoretical Computer Science</i>. 1989;66(2):157-180. doi:<a href=\"https://doi.org/10.1016/0304-3975(89)90133-3\">10.1016/0304-3975(89)90133-3</a>","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.","short":"H. Edelsbrunner, G. Rote, E. Welzl, Theoretical Computer Science 66 (1989) 157–180.","mla":"Edelsbrunner, Herbert, et al. “Testing the Necklace Condition for Shortest Tours and Optimal Factors in the Plane.” <i>Theoretical Computer Science</i>, vol. 66, no. 2, Elsevier, 1989, pp. 157–80, doi:<a href=\"https://doi.org/10.1016/0304-3975(89)90133-3\">10.1016/0304-3975(89)90133-3</a>."},"extern":"1","volume":66},{"article_processing_charge":"No","date_created":"2018-12-11T12:06:51Z","publication_status":"published","oa_version":"None","title":"An acyclicity theorem for cell complexes in d dimension","month":"06","scopus_import":"1","publication":"Proceedings of the 5th annual symposium on Computational geometry","_id":"4085","author":[{"first_name":"Herbert","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"}],"publisher":"ACM","conference":{"location":"Saarbruchen, Germany","end_date":"1989-06-07","start_date":"1989-06-05","name":"SCG: Symposium on Computational Geometry"},"quality_controlled":"1","page":"145 - 151","language":[{"iso":"eng"}],"publication_identifier":{"isbn":["978-0-89791-318-8"]},"day":"01","doi":"10.1145/73833.73850","publist_id":"2033","abstract":[{"lang":"eng","text":"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."}],"year":"1989","citation":{"ista":"Edelsbrunner H. 1989. An acyclicity theorem for cell complexes in d dimension. Proceedings of the 5th annual symposium on Computational geometry. SCG: Symposium on Computational Geometry, 145–151.","short":"H. Edelsbrunner, in:, Proceedings of the 5th Annual Symposium on Computational Geometry, ACM, 1989, pp. 145–151.","mla":"Edelsbrunner, Herbert. “An Acyclicity Theorem for Cell Complexes in d Dimension.” <i>Proceedings of the 5th Annual Symposium on Computational Geometry</i>, ACM, 1989, pp. 145–51, doi:<a href=\"https://doi.org/10.1145/73833.73850\">10.1145/73833.73850</a>.","ieee":"H. Edelsbrunner, “An acyclicity theorem for cell complexes in d dimension,” in <i>Proceedings of the 5th annual symposium on Computational geometry</i>, Saarbruchen, Germany, 1989, pp. 145–151.","chicago":"Edelsbrunner, Herbert. “An Acyclicity Theorem for Cell Complexes in d Dimension.” In <i>Proceedings of the 5th Annual Symposium on Computational Geometry</i>, 145–51. ACM, 1989. <a href=\"https://doi.org/10.1145/73833.73850\">https://doi.org/10.1145/73833.73850</a>.","ama":"Edelsbrunner H. An acyclicity theorem for cell complexes in d dimension. In: <i>Proceedings of the 5th Annual Symposium on Computational Geometry</i>. ACM; 1989:145-151. doi:<a href=\"https://doi.org/10.1145/73833.73850\">10.1145/73833.73850</a>","apa":"Edelsbrunner, H. (1989). An acyclicity theorem for cell complexes in d dimension. In <i>Proceedings of the 5th annual symposium on Computational geometry</i> (pp. 145–151). Saarbruchen, Germany: ACM. <a href=\"https://doi.org/10.1145/73833.73850\">https://doi.org/10.1145/73833.73850</a>"},"date_updated":"2022-02-10T10:56:49Z","type":"conference","date_published":"1989-06-01T00:00:00Z","main_file_link":[{"url":"https://dl.acm.org/doi/10.1145/73833.73850"}],"status":"public","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","extern":"1"},{"extern":"1","volume":4,"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","date_updated":"2022-02-10T11:08:12Z","citation":{"ista":"Edelsbrunner H. 1989. The upper envelope of piecewise linear functions: Tight bounds on the number of faces . Discrete &#38; Computational Geometry. 4(4), 337–343.","short":"H. Edelsbrunner, Discrete &#38; Computational Geometry 4 (1989) 337–343.","mla":"Edelsbrunner, Herbert. “The Upper Envelope of Piecewise Linear Functions: Tight Bounds on the Number of Faces .” <i>Discrete &#38; Computational Geometry</i>, vol. 4, no. 4, Springer, 1989, pp. 337–43, doi:<a href=\"https://doi.org/10.1007/BF02187734\">10.1007/BF02187734</a>.","chicago":"Edelsbrunner, Herbert. “The Upper Envelope of Piecewise Linear Functions: Tight Bounds on the Number of Faces .” <i>Discrete &#38; Computational Geometry</i>. Springer, 1989. <a href=\"https://doi.org/10.1007/BF02187734\">https://doi.org/10.1007/BF02187734</a>.","ieee":"H. Edelsbrunner, “The upper envelope of piecewise linear functions: Tight bounds on the number of faces ,” <i>Discrete &#38; Computational Geometry</i>, vol. 4, no. 4. Springer, pp. 337–343, 1989.","ama":"Edelsbrunner H. The upper envelope of piecewise linear functions: Tight bounds on the number of faces . <i>Discrete &#38; Computational Geometry</i>. 1989;4(4):337-343. doi:<a href=\"https://doi.org/10.1007/BF02187734\">10.1007/BF02187734</a>","apa":"Edelsbrunner, H. (1989). The upper envelope of piecewise linear functions: Tight bounds on the number of faces . <i>Discrete &#38; Computational Geometry</i>. Springer. <a href=\"https://doi.org/10.1007/BF02187734\">https://doi.org/10.1007/BF02187734</a>"},"year":"1989","abstract":[{"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.","lang":"eng"}],"doi":"10.1007/BF02187734","day":"01","page":"337 - 343","quality_controlled":"1","article_type":"original","publisher":"Springer","author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"}],"issue":"4","_id":"4086","scopus_import":"1","title":"The upper envelope of piecewise linear functions: Tight bounds on the number of faces ","intvolume":"         4","publication_status":"published","article_processing_charge":"No","date_created":"2018-12-11T12:06:51Z","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","status":"public","main_file_link":[{"open_access":"1","url":"https://link.springer.com/article/10.1007/BF02187734"}],"date_published":"1989-11-01T00:00:00Z","type":"journal_article","publist_id":"2034","oa":1,"publication_identifier":{"eissn":["1432-0444"],"issn":["0179-5376"]},"language":[{"iso":"eng"}],"publication":"Discrete & Computational Geometry","month":"11","oa_version":"Published Version"},{"alternative_title":["LNCS"],"title":"Tetrahedrizing point sets in three dimensions","intvolume":"       358","publication_status":"published","date_created":"2018-12-11T12:06:52Z","article_processing_charge":"No","author":[{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Preparata, Franco","last_name":"Preparata","first_name":"Franco"},{"full_name":"West, Douglas","last_name":"West","first_name":"Douglas"}],"_id":"4087","scopus_import":"1","publisher":"Springer","page":"315 - 331","quality_controlled":"1","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 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."}],"doi":"10.1007/3-540-51084-2_31","day":"20","date_updated":"2022-02-10T13:27:41Z","citation":{"ista":"Edelsbrunner H, Preparata F, West D. 1989. Tetrahedrizing point sets in three dimensions.  International Symposium on Symbolic and Algebraic Computation. ISSAC: International Symposium on Symbolic and Algebraic Computation, LNCS, vol. 358, 315–331.","short":"H. Edelsbrunner, F. Preparata, D. West, in:,  International Symposium on Symbolic and Algebraic Computation, Springer, 1989, pp. 315–331.","mla":"Edelsbrunner, Herbert, et al. “Tetrahedrizing Point Sets in Three Dimensions.” <i> International Symposium on Symbolic and Algebraic Computation</i>, vol. 358, Springer, 1989, pp. 315–31, doi:<a href=\"https://doi.org/10.1007/3-540-51084-2_31\">10.1007/3-540-51084-2_31</a>.","chicago":"Edelsbrunner, Herbert, Franco Preparata, and Douglas West. “Tetrahedrizing Point Sets in Three Dimensions.” In <i> International Symposium on Symbolic and Algebraic Computation</i>, 358:315–31. Springer, 1989. <a href=\"https://doi.org/10.1007/3-540-51084-2_31\">https://doi.org/10.1007/3-540-51084-2_31</a>.","ieee":"H. Edelsbrunner, F. Preparata, and D. West, “Tetrahedrizing point sets in three dimensions,” in <i> International Symposium on Symbolic and Algebraic Computation</i>, Rome, Italy, 1989, vol. 358, pp. 315–331.","ama":"Edelsbrunner H, Preparata F, West D. Tetrahedrizing point sets in three dimensions. In: <i> International Symposium on Symbolic and Algebraic Computation</i>. Vol 358. Springer; 1989:315-331. doi:<a href=\"https://doi.org/10.1007/3-540-51084-2_31\">10.1007/3-540-51084-2_31</a>","apa":"Edelsbrunner, H., Preparata, F., &#38; West, D. (1989). Tetrahedrizing point sets in three dimensions. In <i> International Symposium on Symbolic and Algebraic Computation</i> (Vol. 358, pp. 315–331). Rome, Italy: Springer. <a href=\"https://doi.org/10.1007/3-540-51084-2_31\">https://doi.org/10.1007/3-540-51084-2_31</a>"},"year":"1989","extern":"1","acknowledgement":"Research of the first author is supported by Amoco Fnd. Fac. Dev. 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 8504","volume":358,"month":"09","oa_version":"None","publication":" International Symposium on Symbolic and Algebraic Computation","conference":{"start_date":"1988-07-04","name":"ISSAC: International Symposium on Symbolic and Algebraic Computation","end_date":"1988-07-08","location":"Rome, Italy"},"language":[{"iso":"eng"}],"publist_id":"2035","date_published":"1989-09-20T00:00:00Z","type":"conference","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","status":"public","main_file_link":[{"url":"https://link.springer.com/chapter/10.1007/3-540-51084-2_31"}]},{"author":[{"first_name":"Herbert","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Guibas","first_name":"Leonidas","full_name":"Guibas, Leonidas"},{"first_name":"John","last_name":"Hershberger","full_name":"Hershberger, John"},{"first_name":"Raimund","last_name":"Seidel","full_name":"Seidel, Raimund"},{"full_name":"Sharir, Micha","first_name":"Micha","last_name":"Sharir"},{"full_name":"Snoeyink, Jack","first_name":"Jack","last_name":"Snoeyink"},{"first_name":"Emo","last_name":"Welzl","full_name":"Welzl, Emo"}],"issue":"1","_id":"4088","scopus_import":"1","title":"Implicitly representing arrangements of lines or segments","intvolume":"         4","publication_status":"published","article_processing_charge":"No","date_created":"2018-12-11T12:06:52Z","page":"433 - 466","quality_controlled":"1","article_type":"original","publisher":"Springer","date_updated":"2022-02-10T15:03:48Z","citation":{"mla":"Edelsbrunner, Herbert, et al. “Implicitly Representing Arrangements of Lines or Segments.” <i>Discrete &#38; Computational Geometry</i>, vol. 4, no. 1, Springer, 1989, pp. 433–66, doi:<a href=\"https://doi.org/10.1007/BF02187742\">10.1007/BF02187742</a>.","short":"H. Edelsbrunner, L. Guibas, J. Hershberger, R. Seidel, M. Sharir, J. Snoeyink, E. Welzl, Discrete &#38; Computational Geometry 4 (1989) 433–466.","ista":"Edelsbrunner H, Guibas L, Hershberger J, Seidel R, Sharir M, Snoeyink J, Welzl E. 1989. Implicitly representing arrangements of lines or segments. Discrete &#38; Computational Geometry. 4(1), 433–466.","apa":"Edelsbrunner, H., Guibas, L., Hershberger, J., Seidel, R., Sharir, M., Snoeyink, J., &#38; Welzl, E. (1989). Implicitly representing arrangements of lines or segments. <i>Discrete &#38; Computational Geometry</i>. Springer. <a href=\"https://doi.org/10.1007/BF02187742\">https://doi.org/10.1007/BF02187742</a>","ama":"Edelsbrunner H, Guibas L, Hershberger J, et al. Implicitly representing arrangements of lines or segments. <i>Discrete &#38; Computational Geometry</i>. 1989;4(1):433-466. doi:<a href=\"https://doi.org/10.1007/BF02187742\">10.1007/BF02187742</a>","ieee":"H. Edelsbrunner <i>et al.</i>, “Implicitly representing arrangements of lines or segments,” <i>Discrete &#38; Computational Geometry</i>, vol. 4, no. 1. Springer, pp. 433–466, 1989.","chicago":"Edelsbrunner, Herbert, Leonidas Guibas, John Hershberger, Raimund Seidel, Micha Sharir, Jack Snoeyink, and Emo Welzl. “Implicitly Representing Arrangements of Lines or Segments.” <i>Discrete &#38; Computational Geometry</i>. Springer, 1989. <a href=\"https://doi.org/10.1007/BF02187742\">https://doi.org/10.1007/BF02187742</a>."},"year":"1989","abstract":[{"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.","lang":"eng"}],"doi":"10.1007/BF02187742","day":"01","extern":"1","volume":4,"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.","publication":"Discrete & Computational Geometry","month":"12","oa_version":"Published Version","language":[{"iso":"eng"}],"date_published":"1989-12-01T00:00:00Z","type":"journal_article","oa":1,"publist_id":"2036","publication_identifier":{"eissn":["1432-0444"],"issn":["0179-5376"]},"status":"public","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","main_file_link":[{"url":"https://link.springer.com/article/10.1007/BF02187742","open_access":"1"}]},{"publication":"Discrete & Computational Geometry","month":"12","oa_version":"Published Version","language":[{"iso":"eng"}],"date_published":"1989-12-01T00:00:00Z","type":"journal_article","oa":1,"publist_id":"2037","publication_identifier":{"eissn":["1432-0444"],"issn":["0179-5376"]},"status":"public","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","main_file_link":[{"url":"https://link.springer.com/article/10.1007/BF02187745","open_access":"1"}],"author":[{"orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Leonidas","last_name":"Guibas","full_name":"Guibas, Leonidas"},{"first_name":"John","last_name":"Hershberger","full_name":"Hershberger, John"},{"full_name":"Pach, János","first_name":"János","last_name":"Pach"},{"full_name":"Pollack, Richard","first_name":"Richard","last_name":"Pollack"},{"first_name":"Raimund","last_name":"Seidel","full_name":"Seidel, Raimund"},{"full_name":"Sharir, Micha","first_name":"Micha","last_name":"Sharir"},{"full_name":"Snoeyink, Jack","first_name":"Jack","last_name":"Snoeyink"}],"issue":"1","_id":"4089","scopus_import":"1","title":"On arrangements of Jordan arcs with three intersections per pair","intvolume":"         4","publication_status":"published","date_created":"2018-12-11T12:06:52Z","article_processing_charge":"No","page":"523 - 539","quality_controlled":"1","article_type":"original","publisher":"Springer","date_updated":"2022-02-10T15:40:04Z","year":"1989","citation":{"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 &#38; Computational Geometry. 4(1), 523–539.","mla":"Edelsbrunner, Herbert, et al. “On Arrangements of Jordan Arcs with Three Intersections per Pair.” <i>Discrete &#38; Computational Geometry</i>, vol. 4, no. 1, Springer, 1989, pp. 523–39, doi:<a href=\"https://doi.org/10.1007/BF02187745\">10.1007/BF02187745</a>.","short":"H. Edelsbrunner, L. Guibas, J. Hershberger, J. Pach, R. Pollack, R. Seidel, M. Sharir, J. Snoeyink, Discrete &#38; Computational Geometry 4 (1989) 523–539.","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.” <i>Discrete &#38; Computational Geometry</i>. Springer, 1989. <a href=\"https://doi.org/10.1007/BF02187745\">https://doi.org/10.1007/BF02187745</a>.","ieee":"H. Edelsbrunner <i>et al.</i>, “On arrangements of Jordan arcs with three intersections per pair,” <i>Discrete &#38; Computational Geometry</i>, vol. 4, no. 1. Springer, pp. 523–539, 1989.","ama":"Edelsbrunner H, Guibas L, Hershberger J, et al. On arrangements of Jordan arcs with three intersections per pair. <i>Discrete &#38; Computational Geometry</i>. 1989;4(1):523-539. doi:<a href=\"https://doi.org/10.1007/BF02187745\">10.1007/BF02187745</a>","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. <i>Discrete &#38; Computational Geometry</i>. Springer. <a href=\"https://doi.org/10.1007/BF02187745\">https://doi.org/10.1007/BF02187745</a>"},"abstract":[{"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.","lang":"eng"}],"doi":"10.1007/BF02187745","day":"01","extern":"1","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.","volume":4},{"publication":"16th International Colloquium on Automata, Languages, and Programming","month":"07","oa_version":"None","language":[{"iso":"eng"}],"conference":{"location":"Stresa, Italy","end_date":"1989-07-15","name":"ICALP: International Colloquium on Automata, Languages, and Programming","start_date":"1989-07-11"},"date_published":"1989-07-24T00:00:00Z","type":"conference","publist_id":"2031","status":"public","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","main_file_link":[{"url":"https://link.springer.com/chapter/10.1007/BFb0035760"}],"author":[{"full_name":"Chazelle, Bernard","last_name":"Chazelle","first_name":"Bernard"},{"first_name":"Herbert","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Guibas","first_name":"Leonidas","full_name":"Guibas, Leonidas"},{"full_name":"Sharir, Micha","last_name":"Sharir","first_name":"Micha"}],"_id":"4092","scopus_import":"1","title":"A singly exponential stratification scheme for real semi-algebraic varieties and its applications","alternative_title":["LNCS"],"intvolume":"       372","publication_status":"published","date_created":"2018-12-11T12:06:53Z","article_processing_charge":"No","page":"179 - 193","quality_controlled":"1","publisher":"Springer","date_updated":"2022-02-10T10:06:23Z","year":"1989","citation":{"short":"B. Chazelle, H. Edelsbrunner, L. Guibas, M. Sharir, in:, 16th International Colloquium on Automata, Languages, and Programming, Springer, 1989, pp. 179–193.","mla":"Chazelle, Bernard, et al. “A Singly Exponential Stratification Scheme for Real Semi-Algebraic Varieties and Its Applications.” <i>16th International Colloquium on Automata, Languages, and Programming</i>, vol. 372, Springer, 1989, pp. 179–93, doi:<a href=\"https://doi.org/10.1007/BFb0035760\">10.1007/BFb0035760</a>.","ista":"Chazelle B, Edelsbrunner H, Guibas L, Sharir M. 1989. A singly exponential stratification scheme for real semi-algebraic varieties and its applications. 16th International Colloquium on Automata, Languages, and Programming. ICALP: International Colloquium on Automata, Languages, and Programming, LNCS, vol. 372, 179–193.","ama":"Chazelle B, Edelsbrunner H, Guibas L, Sharir M. A singly exponential stratification scheme for real semi-algebraic varieties and its applications. In: <i>16th International Colloquium on Automata, Languages, and Programming</i>. Vol 372. Springer; 1989:179-193. doi:<a href=\"https://doi.org/10.1007/BFb0035760\">10.1007/BFb0035760</a>","apa":"Chazelle, B., Edelsbrunner, H., Guibas, L., &#38; Sharir, M. (1989). A singly exponential stratification scheme for real semi-algebraic varieties and its applications. In <i>16th International Colloquium on Automata, Languages, and Programming</i> (Vol. 372, pp. 179–193). Stresa, Italy: Springer. <a href=\"https://doi.org/10.1007/BFb0035760\">https://doi.org/10.1007/BFb0035760</a>","ieee":"B. Chazelle, H. Edelsbrunner, L. Guibas, and M. Sharir, “A singly exponential stratification scheme for real semi-algebraic varieties and its applications,” in <i>16th International Colloquium on Automata, Languages, and Programming</i>, Stresa, Italy, 1989, vol. 372, pp. 179–193.","chicago":"Chazelle, Bernard, Herbert Edelsbrunner, Leonidas Guibas, and Micha Sharir. “A Singly Exponential Stratification Scheme for Real Semi-Algebraic Varieties and Its Applications.” In <i>16th International Colloquium on Automata, Languages, and Programming</i>, 372:179–93. Springer, 1989. <a href=\"https://doi.org/10.1007/BFb0035760\">https://doi.org/10.1007/BFb0035760</a>."},"doi":"10.1007/BFb0035760","day":"24","extern":"1","acknowledgement":"The support of the Digital Systems Research center and the Digital Paris Research laboratory, where much of this research was carried out, are gratefully acknowledged. Work on this paper by Bernard Chazelle has been supported by NSF Grant CCI~-87-00917. Work on this paper by Herbert Edelsbrunner has been supported by NSF Grant CCR-87-14565. Work on this paper by Micha Sharir has been supported by ONR Grant N00014-87-K-0129, by NSF Grant DCP~-83-20085, and by grants from the U.S.-Israeli Binational Science Foundation, the NCRD - the Israeli National Council for Research and Development, and the EMET Fund of the Israeli Academy of Sciences. ","volume":372},{"publisher":"Springer","quality_controlled":"1","page":"139 - 181","date_created":"2018-12-11T12:06:54Z","article_processing_charge":"No","publication_status":"published","intvolume":"         4","title":"The complexity of cutting complexes","_id":"4093","issue":"1","author":[{"full_name":"Chazelle, Bernard","first_name":"Bernard","last_name":"Chazelle"},{"first_name":"Herbert","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Guibas, Leonidas","last_name":"Guibas","first_name":"Leonidas"}],"acknowledgement":"Bernard Chazelle wishes to acknowledge the National Science Foundation for supporting this research in part under Grant No. MCS83-03925. Herbert Edelsbrunner is pleased to acknowledge the support of Amoco Fnd. Fac. Dev. Comput. Sci. 1-6-44862. We wish to thank J. Pach and E. Szemeredi for valuable discussions on several\r\nof the problems studied in this paper.","volume":4,"extern":"1","day":"01","doi":"10.1007/BF02187720","abstract":[{"lang":"eng","text":"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."}],"year":"1989","citation":{"ieee":"B. Chazelle, H. Edelsbrunner, and L. Guibas, “The complexity of cutting complexes,” <i>Discrete &#38; Computational Geometry</i>, vol. 4, no. 1. Springer, pp. 139–181, 1989.","chicago":"Chazelle, Bernard, Herbert Edelsbrunner, and Leonidas Guibas. “The Complexity of Cutting Complexes.” <i>Discrete &#38; Computational Geometry</i>. Springer, 1989. <a href=\"https://doi.org/10.1007/BF02187720\">https://doi.org/10.1007/BF02187720</a>.","ama":"Chazelle B, Edelsbrunner H, Guibas L. The complexity of cutting complexes. <i>Discrete &#38; Computational Geometry</i>. 1989;4(1):139-181. doi:<a href=\"https://doi.org/10.1007/BF02187720\">10.1007/BF02187720</a>","apa":"Chazelle, B., Edelsbrunner, H., &#38; Guibas, L. (1989). The complexity of cutting complexes. <i>Discrete &#38; Computational Geometry</i>. Springer. <a href=\"https://doi.org/10.1007/BF02187720\">https://doi.org/10.1007/BF02187720</a>","ista":"Chazelle B, Edelsbrunner H, Guibas L. 1989. The complexity of cutting complexes. Discrete &#38; Computational Geometry. 4(1), 139–181.","mla":"Chazelle, Bernard, et al. “The Complexity of Cutting Complexes.” <i>Discrete &#38; Computational Geometry</i>, vol. 4, no. 1, Springer, 1989, pp. 139–81, doi:<a href=\"https://doi.org/10.1007/BF02187720\">10.1007/BF02187720</a>.","short":"B. Chazelle, H. Edelsbrunner, L. Guibas, Discrete &#38; Computational Geometry 4 (1989) 139–181."},"date_updated":"2022-02-10T10:25:57Z","language":[{"iso":"eng"}],"oa_version":"None","month":"03","publication":"Discrete & Computational Geometry","main_file_link":[{"url":"https://link.springer.com/article/10.1007/BF02187720"}],"user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","status":"public","publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"publist_id":"2032","type":"journal_article","date_published":"1989-03-01T00:00:00Z"},{"language":[{"iso":"eng"}],"publication":"Evolution; International Journal of Organic Evolution","oa_version":"None","month":"11","main_file_link":[{"url":"http://www.jstor.org/stable/2409452"}],"status":"public","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","type":"journal_article","date_published":"1989-11-01T00:00:00Z","publication_identifier":{"issn":["0014-3820"],"eissn":["1558-5646"]},"publist_id":"1751","quality_controlled":"1","page":"1349 - 1368","publisher":"Wiley-Blackwell","article_type":"original","pmid":1,"_id":"4309","issue":"7","author":[{"full_name":"Slatkin, Montgomery","last_name":"Slatkin","first_name":"Montgomery"},{"first_name":"Nicholas H","last_name":"Barton","orcid":"0000-0002-8548-5240","full_name":"Barton, Nicholas H","id":"4880FE40-F248-11E8-B48F-1D18A9856A87"}],"date_created":"2018-12-11T12:08:10Z","article_processing_charge":"No","publication_status":"published","intvolume":"        43","title":"A comparison of three methods for estimating average levels of gene flow","acknowledgement":"This research has been supported in partv by grant 85-00258 from the National Science Foundation and by grants GR/C/9 1529 and GR/E/08507 from the Science and Engineering Research Council. We thank C. C. Cockerham and B. S. Weir for helpful discussions of this topic, C. Wehrhahn for bringing his method to our attention and for providing us with a copy of his program for estimating Nm, and J. Coyne, M. Nei, B. S. Weir, and an anonymous referee for comments on an earlier draft of this paper.","volume":43,"extern":"1","citation":{"ama":"Slatkin M, Barton NH. A comparison of three methods for estimating average levels of gene flow. <i>Evolution; International Journal of Organic Evolution</i>. 1989;43(7):1349-1368. doi:<a href=\"https://doi.org/10.1111/j.1558-5646.1989.tb02587.x \">10.1111/j.1558-5646.1989.tb02587.x </a>","apa":"Slatkin, M., &#38; Barton, N. H. (1989). A comparison of three methods for estimating average levels of gene flow. <i>Evolution; International Journal of Organic Evolution</i>. Wiley-Blackwell. <a href=\"https://doi.org/10.1111/j.1558-5646.1989.tb02587.x \">https://doi.org/10.1111/j.1558-5646.1989.tb02587.x </a>","ieee":"M. Slatkin and N. H. Barton, “A comparison of three methods for estimating average levels of gene flow,” <i>Evolution; International Journal of Organic Evolution</i>, vol. 43, no. 7. Wiley-Blackwell, pp. 1349–1368, 1989.","chicago":"Slatkin, Montgomery, and Nicholas H Barton. “A Comparison of Three Methods for Estimating Average Levels of Gene Flow.” <i>Evolution; International Journal of Organic Evolution</i>. Wiley-Blackwell, 1989. <a href=\"https://doi.org/10.1111/j.1558-5646.1989.tb02587.x \">https://doi.org/10.1111/j.1558-5646.1989.tb02587.x </a>.","short":"M. Slatkin, N.H. Barton, Evolution; International Journal of Organic Evolution 43 (1989) 1349–1368.","mla":"Slatkin, Montgomery, and Nicholas H. Barton. “A Comparison of Three Methods for Estimating Average Levels of Gene Flow.” <i>Evolution; International Journal of Organic Evolution</i>, vol. 43, no. 7, Wiley-Blackwell, 1989, pp. 1349–68, doi:<a href=\"https://doi.org/10.1111/j.1558-5646.1989.tb02587.x \">10.1111/j.1558-5646.1989.tb02587.x </a>.","ista":"Slatkin M, Barton NH. 1989. A comparison of three methods for estimating average levels of gene flow. Evolution; International Journal of Organic Evolution. 43(7), 1349–1368."},"year":"1989","date_updated":"2022-02-10T09:44:53Z","external_id":{"pmid":["28564250 "]},"day":"01","doi":"10.1111/j.1558-5646.1989.tb02587.x ","abstract":[{"lang":"eng","text":"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."}]}]