[{"day":"01","month":"01","language":[{"iso":"eng"}],"publication_status":"published","main_file_link":[{"url":"https://www.nature.com/articles/hdy198736","open_access":"1"}],"intvolume":"        58","article_processing_charge":"No","doi":"10.1038/hdy.1987.36","date_updated":"2022-02-03T10:48:40Z","date_published":"1987-01-01T00:00:00Z","author":[{"full_name":"Westerman, Michael","last_name":"Westerman","first_name":"Michael"},{"full_name":"Barton, Nicholas H","id":"4880FE40-F248-11E8-B48F-1D18A9856A87","first_name":"Nicholas H","orcid":"0000-0002-8548-5240","last_name":"Barton"},{"last_name":"Hewitt","first_name":"Godfrey","full_name":"Hewitt, Godfrey"}],"quality_controlled":"1","scopus_import":"1","article_type":"original","oa":1,"status":"public","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","publication_identifier":{"issn":["0018-067X"],"eissn":["1365-2540"]},"citation":{"apa":"Westerman, M., Barton, N. H., &#38; Hewitt, G. (1987). Differences in DNA content between two chromosomal races of the grasshopper Podisma pedestris. <i>Heredity</i>. Nature Publishing Group. <a href=\"https://doi.org/10.1038/hdy.1987.36\">https://doi.org/10.1038/hdy.1987.36</a>","ieee":"M. Westerman, N. H. Barton, and G. Hewitt, “Differences in DNA content between two chromosomal races of the grasshopper Podisma pedestris,” <i>Heredity</i>, vol. 58. Nature Publishing Group, pp. 221–228, 1987.","chicago":"Westerman, Michael, Nicholas H Barton, and Godfrey Hewitt. “Differences in DNA Content between Two Chromosomal Races of the Grasshopper Podisma Pedestris.” <i>Heredity</i>. Nature Publishing Group, 1987. <a href=\"https://doi.org/10.1038/hdy.1987.36\">https://doi.org/10.1038/hdy.1987.36</a>.","short":"M. Westerman, N.H. Barton, G. Hewitt, Heredity 58 (1987) 221–228.","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.” <i>Heredity</i>, vol. 58, Nature Publishing Group, 1987, pp. 221–28, doi:<a href=\"https://doi.org/10.1038/hdy.1987.36\">10.1038/hdy.1987.36</a>.","ama":"Westerman M, Barton NH, Hewitt G. Differences in DNA content between two chromosomal races of the grasshopper Podisma pedestris. <i>Heredity</i>. 1987;58:221-228. doi:<a href=\"https://doi.org/10.1038/hdy.1987.36\">10.1038/hdy.1987.36</a>"},"user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","type":"journal_article","volume":58,"page":"221 - 228","year":"1987","_id":"4319","extern":"1","abstract":[{"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.","lang":"eng"}],"publisher":"Nature Publishing Group","publication":"Heredity","title":"Differences in DNA content between two chromosomal races of the grasshopper Podisma pedestris","publist_id":"1733","date_created":"2018-12-11T12:08:14Z","oa_version":"Published Version"},{"abstract":[{"lang":"eng","text":"Bosonic field theories may be formulated in terms of stochastic differential equations. The characteristic long term behaviour of these systems is a decay into the global minimum of their Hamiltonian. If local minima exist, the rate of this decay is determined by instanton effects. We calculate the decay rate and perform computer simulations on a 1 + 1 dimensional model to test the instanton approximation. We find the instanton approximations to be in very good agreement with the simulation results."}],"extern":"1","oa_version":"None","date_created":"2018-12-11T12:08:14Z","publist_id":"1730","title":"Instantons in stochastic quantization","publication":"Physica A: Statistical Mechanics and its Applications","publisher":"Elsevier","citation":{"ama":"Rouhani S, Barton NH. Instantons in stochastic quantization. <i>Physica A: Statistical Mechanics and its Applications</i>. 1987;143(1-2):220-226. doi:<a href=\"https://doi.org/10.1016/0378-4371(87)90064-1\">10.1016/0378-4371(87)90064-1</a>","short":"S. Rouhani, N.H. Barton, Physica A: Statistical Mechanics and Its Applications 143 (1987) 220–226.","ista":"Rouhani S, Barton NH. 1987. Instantons in stochastic quantization. Physica A: Statistical Mechanics and its Applications. 143(1–2), 220–226.","mla":"Rouhani, Shahin, and Nicholas H. Barton. “Instantons in Stochastic Quantization.” <i>Physica A: Statistical Mechanics and Its Applications</i>, vol. 143, no. 1–2, Elsevier, 1987, pp. 220–26, doi:<a href=\"https://doi.org/10.1016/0378-4371(87)90064-1\">10.1016/0378-4371(87)90064-1</a>.","ieee":"S. Rouhani and N. H. Barton, “Instantons in stochastic quantization,” <i>Physica A: Statistical Mechanics and its Applications</i>, vol. 143, no. 1–2. Elsevier, pp. 220–226, 1987.","chicago":"Rouhani, Shahin, and Nicholas H Barton. “Instantons in Stochastic Quantization.” <i>Physica A: Statistical Mechanics and Its Applications</i>. Elsevier, 1987. <a href=\"https://doi.org/10.1016/0378-4371(87)90064-1\">https://doi.org/10.1016/0378-4371(87)90064-1</a>.","apa":"Rouhani, S., &#38; Barton, N. H. (1987). Instantons in stochastic quantization. <i>Physica A: Statistical Mechanics and Its Applications</i>. Elsevier. <a href=\"https://doi.org/10.1016/0378-4371(87)90064-1\">https://doi.org/10.1016/0378-4371(87)90064-1</a>"},"publication_identifier":{"issn":["0378-4371"],"eissn":["1873-2119"]},"status":"public","article_type":"original","issue":"1-2","_id":"4320","year":"1987","page":"220 - 226","volume":143,"type":"journal_article","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","scopus_import":"1","quality_controlled":"1","date_published":"1987-01-01T00:00:00Z","author":[{"full_name":"Rouhani, Shahin","last_name":"Rouhani","first_name":"Shahin"},{"first_name":"Nicholas H","last_name":"Barton","orcid":"0000-0002-8548-5240","full_name":"Barton, Nicholas H","id":"4880FE40-F248-11E8-B48F-1D18A9856A87"}],"date_updated":"2022-02-03T10:33:03Z","doi":"10.1016/0378-4371(87)90064-1","article_processing_charge":"No","language":[{"iso":"eng"}],"month":"01","day":"01","intvolume":"       143","publication_status":"published"},{"language":[{"iso":"eng"}],"month":"01","pmid":1,"day":"01","intvolume":"        50","publication_status":"published","scopus_import":"1","quality_controlled":"1","author":[{"id":"4880FE40-F248-11E8-B48F-1D18A9856A87","full_name":"Barton, Nicholas H","last_name":"Barton","orcid":"0000-0002-8548-5240","first_name":"Nicholas H"}],"date_published":"1987-01-01T00:00:00Z","date_updated":"2022-02-03T10:16:16Z","doi":"10.1017/S0016672300023314","article_processing_charge":"No","citation":{"short":"N.H. Barton, Genetical Research 50 (1987) 35–40.","mla":"Barton, Nicholas H. “The Probability of Establishment of an Advantageous Mutation in a Subdivided Population.” <i>Genetical Research</i>, vol. 50, no. 1, Cambridge University Press, 1987, pp. 35–40, doi:<a href=\"https://doi.org/10.1017/S0016672300023314\">10.1017/S0016672300023314</a>.","ista":"Barton NH. 1987. The probability of establishment of an advantageous mutation in a subdivided population. Genetical Research. 50(1), 35–40.","ama":"Barton NH. The probability of establishment of an advantageous mutation in a subdivided population. <i>Genetical Research</i>. 1987;50(1):35-40. doi:<a href=\"https://doi.org/10.1017/S0016672300023314\">10.1017/S0016672300023314</a>","apa":"Barton, N. H. (1987). The probability of establishment of an advantageous mutation in a subdivided population. <i>Genetical Research</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/S0016672300023314\">https://doi.org/10.1017/S0016672300023314</a>","chicago":"Barton, Nicholas H. “The Probability of Establishment of an Advantageous Mutation in a Subdivided Population.” <i>Genetical Research</i>. Cambridge University Press, 1987. <a href=\"https://doi.org/10.1017/S0016672300023314\">https://doi.org/10.1017/S0016672300023314</a>.","ieee":"N. H. Barton, “The probability of establishment of an advantageous mutation in a subdivided population,” <i>Genetical Research</i>, vol. 50, no. 1. Cambridge University Press, pp. 35–40, 1987."},"publication_identifier":{"eissn":["1469-5073"],"issn":["0016-6723"]},"acknowledgement":"This work was supported by a grant from the Science and Engineering Research Council (GR/D/91529). Shahin\r\nRouhani supplied the proof that no positive solution to (6) exists when all eigenvalues are negative (Appendix);\r\nM. Slatkin, M. Turelli, T. Nagylaki and he also gave helpful comments on the manuscript.","status":"public","external_id":{"pmid":["3653687 "]},"article_type":"original","issue":"1","_id":"4322","year":"1987","page":"35 - 40","volume":50,"type":"journal_article","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","abstract":[{"text":"A method is developed for calculating the probability of establishment of an allele which is favoured in some places, but not others, in a large subdivided population. This method is quite general, and could be used to calculate the chance that any system which is linear near an absorbing boundary will move away from that boundary. The results are applied to a population distributed along one dimension. Only mutants which arise within a distance  σ/ √2s of the region in which they are favoured stand an appreciable chance of establishment. The net chance of establishment of mutations distributed randomly across the habitat will be decreased by gene flow if selection against them is sufficiently strong. However, if the mutations are only weakly deleterious outside some limited region, gene flow may increase the net chance of establishment.","lang":"eng"}],"extern":"1","oa_version":"None","date_created":"2018-12-11T12:08:15Z","publist_id":"1725","title":"The probability of establishment of an advantageous mutation in a subdivided population","publication":"Genetical Research","publisher":"Cambridge University Press"},{"publication_status":"published","intvolume":"       407","day":"01","pmid":1,"language":[{"iso":"eng"}],"month":"07","date_updated":"2022-02-03T09:46:42Z","doi":"10.1007/BF00580727","article_processing_charge":"No","date_published":"1986-07-01T00:00:00Z","author":[{"orcid":"0000-0001-5001-4804","last_name":"Jonas","first_name":"Peter M","id":"353C1B58-F248-11E8-B48F-1D18A9856A87","full_name":"Jonas, Peter M"},{"last_name":"Vogel","first_name":"Werner","full_name":"Vogel, Werner"},{"first_name":"Eliane","last_name":"Arantes","full_name":"Arantes, Eliane"},{"full_name":"Giglio, Jose","first_name":"Jose","last_name":"Giglio"}],"quality_controlled":"1","type":"journal_article","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","page":"92 - 99","volume":407,"year":"1986","_id":"3464","article_type":"original","external_id":{"pmid":["2426654 "]},"issue":"1","status":"public","publication_identifier":{"issn":["0031-6768"],"eissn":["1432-2013"]},"citation":{"ama":"Jonas PM, Vogel W, Arantes E, Giglio J. Toxin γ of the scorpion Tityus serrulatus modifies both activation and inactivation of sodium permeability of nerve membrane. <i>Pflugers Archiv : European Journal of Physiology</i>. 1986;407(1):92-99. doi:<a href=\"https://doi.org/10.1007/BF00580727\">10.1007/BF00580727</a>","ista":"Jonas PM, Vogel W, Arantes E, Giglio J. 1986. Toxin γ of the scorpion Tityus serrulatus modifies both activation and inactivation of sodium permeability of nerve membrane. Pflugers Archiv : European Journal of Physiology. 407(1), 92–99.","mla":"Jonas, Peter M., et al. “Toxin γ of the Scorpion Tityus Serrulatus Modifies Both Activation and Inactivation of Sodium Permeability of Nerve Membrane.” <i>Pflugers Archiv : European Journal of Physiology</i>, vol. 407, no. 1, Springer, 1986, pp. 92–99, doi:<a href=\"https://doi.org/10.1007/BF00580727\">10.1007/BF00580727</a>.","short":"P.M. Jonas, W. Vogel, E. Arantes, J. Giglio, Pflugers Archiv : European Journal of Physiology 407 (1986) 92–99.","ieee":"P. M. Jonas, W. Vogel, E. Arantes, and J. Giglio, “Toxin γ of the scorpion Tityus serrulatus modifies both activation and inactivation of sodium permeability of nerve membrane,” <i>Pflugers Archiv : European Journal of Physiology</i>, vol. 407, no. 1. Springer, pp. 92–99, 1986.","chicago":"Jonas, Peter M, Werner Vogel, Eliane Arantes, and Jose Giglio. “Toxin γ of the Scorpion Tityus Serrulatus Modifies Both Activation and Inactivation of Sodium Permeability of Nerve Membrane.” <i>Pflugers Archiv : European Journal of Physiology</i>. Springer, 1986. <a href=\"https://doi.org/10.1007/BF00580727\">https://doi.org/10.1007/BF00580727</a>.","apa":"Jonas, P. M., Vogel, W., Arantes, E., &#38; Giglio, J. (1986). Toxin γ of the scorpion Tityus serrulatus modifies both activation and inactivation of sodium permeability of nerve membrane. <i>Pflugers Archiv : European Journal of Physiology</i>. Springer. <a href=\"https://doi.org/10.1007/BF00580727\">https://doi.org/10.1007/BF00580727</a>"},"publisher":"Springer","title":"Toxin γ of the scorpion Tityus serrulatus modifies both activation and inactivation of sodium permeability of nerve membrane","publication":"Pflugers Archiv : European Journal of Physiology","publist_id":"2923","oa_version":"None","date_created":"2018-12-11T12:03:28Z","extern":"1","abstract":[{"text":"The effects of the major neurotoxic fraction isolated from scorpion venom of Tityus serrulatus, TiTx gamma, on peripheral nerve membrane of Xenopus laevis were studied under current- and voltage-clamp conditions. 700 nmol/l TiTx gamma depolarized the membrane and induced spontaneous activity (150 s-1, maximum value), which ceased within a few minutes. It reduced the amplitude of the action potentials from 109 mV to 52 mV and increased their duration from 1.25 ms to 4.5 ms. 440 nmol/l TiTx gamma induced inward Na current flow at resting potential. The descending branch of the Na current-voltage curve was flattened and shifted approximately 10 mV to more negative potentials. Maximum Na permeability was reduced to about 20%. Both development of and recovery from inactivation of Na permeability were slowed. The steepness of the steady-state inactivation curve was decreased, but the mid-potential changed only insignificantly. No prepulse was necessary to elicit either a shift of activation or an inward current at resting potential. Expressing the toxin effect either in terms of the decrease of Na peak current or of the slowing of inactivation, half-maximum effects were found with 0.3 +/- 0.1 and 3.7 +/- 0.7 mumol/l TiTx gamma, respectively.","lang":"eng"}]},{"_id":"3579","intvolume":"        53","year":"1986","publication_status":"published","volume":53,"page":"193 - 200","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","type":"journal_article","citation":{"apa":"Edelsbrunner, H., &#38; Jaromczyk, J. (1986). How often can you see yourself in a convex configuration of mirrors? <i>Congressus Numerantium</i>. Utilitas Mathemtica Publ. Inc.","chicago":"Edelsbrunner, Herbert, and Jerzy Jaromczyk. “How Often Can You See Yourself in a Convex Configuration of Mirrors?” <i>Congressus Numerantium</i>. Utilitas Mathemtica Publ. Inc., 1986.","ieee":"H. Edelsbrunner and J. Jaromczyk, “How often can you see yourself in a convex configuration of mirrors?,” <i>Congressus Numerantium</i>, vol. 53. Utilitas Mathemtica Publ. Inc., pp. 193–200, 1986.","mla":"Edelsbrunner, Herbert, and Jerzy Jaromczyk. “How Often Can You See Yourself in a Convex Configuration of Mirrors?” <i>Congressus Numerantium</i>, vol. 53, Utilitas Mathemtica Publ. Inc., 1986, pp. 193–200.","short":"H. Edelsbrunner, J. Jaromczyk, Congressus Numerantium 53 (1986) 193–200.","ista":"Edelsbrunner H, Jaromczyk J. 1986. How often can you see yourself in a convex configuration of mirrors? Congressus Numerantium. 53, 193–200.","ama":"Edelsbrunner H, Jaromczyk J. How often can you see yourself in a convex configuration of mirrors? <i>Congressus Numerantium</i>. 1986;53:193-200."},"month":"01","publication_identifier":{"issn":["0384-9864"]},"language":[{"iso":"eng"}],"status":"public","day":"01","article_type":"original","date_created":"2018-12-11T12:04:04Z","oa_version":"None","publist_id":"2806","publication":"Congressus Numerantium","title":"How often can you see yourself in a convex configuration of mirrors?","publisher":"Utilitas Mathemtica Publ. Inc.","extern":"1","quality_controlled":"1","author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","first_name":"Herbert"},{"first_name":"Jerzy","last_name":"Jaromczyk","full_name":"Jaromczyk, Jerzy"}],"date_published":"1986-01-01T00:00:00Z","article_processing_charge":"No","date_updated":"2022-02-02T15:58:04Z"},{"intvolume":"         1","publication_status":"published","language":[{"iso":"eng"}],"month":"11","day":"01","scopus_import":"1","quality_controlled":"1","author":[{"full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833"}],"date_published":"1986-11-01T00:00:00Z","doi":"10.1007/BF01840438","date_updated":"2022-02-02T09:36:32Z","article_processing_charge":"No","_id":"3580","year":"1986","page":"93 - 109","volume":1,"type":"journal_article","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","citation":{"ista":"Edelsbrunner H. 1986. Edge-skeletons in arrangements with applications. Algorithmica. 1(1–4), 93–109.","mla":"Edelsbrunner, Herbert. “Edge-Skeletons in Arrangements with Applications.” <i>Algorithmica</i>, vol. 1, no. 1–4, Springer, 1986, pp. 93–109, doi:<a href=\"https://doi.org/10.1007/BF01840438\">10.1007/BF01840438</a>.","short":"H. Edelsbrunner, Algorithmica 1 (1986) 93–109.","ama":"Edelsbrunner H. Edge-skeletons in arrangements with applications. <i>Algorithmica</i>. 1986;1(1-4):93-109. doi:<a href=\"https://doi.org/10.1007/BF01840438\">10.1007/BF01840438</a>","apa":"Edelsbrunner, H. (1986). Edge-skeletons in arrangements with applications. <i>Algorithmica</i>. Springer. <a href=\"https://doi.org/10.1007/BF01840438\">https://doi.org/10.1007/BF01840438</a>","ieee":"H. Edelsbrunner, “Edge-skeletons in arrangements with applications,” <i>Algorithmica</i>, vol. 1, no. 1–4. Springer, pp. 93–109, 1986.","chicago":"Edelsbrunner, Herbert. “Edge-Skeletons in Arrangements with Applications.” <i>Algorithmica</i>. Springer, 1986. <a href=\"https://doi.org/10.1007/BF01840438\">https://doi.org/10.1007/BF01840438</a>."},"publication_identifier":{"eissn":["1432-0541"],"issn":["0178-4617"]},"status":"public","article_type":"original","issue":"1-4","oa_version":"None","date_created":"2018-12-11T12:04:04Z","publist_id":"2805","title":"Edge-skeletons in arrangements with applications","publication":"Algorithmica","publisher":"Springer","abstract":[{"lang":"eng","text":"An edge-skeleton in an arrangementA(H) of a finite set of planes inE 3 is a connected collection of edges inA(H). We give a method that constructs a skeleton inO(√n logn) time per edge. This method implies new and more efficient algorithms for a number of structures in computational geometry including order-k power diagrams inE 2 and space cutting trees inE 3.\r\nWe also give a novel method for handling special cases which has the potential to substantially decrease the amount of effort needed to implement geometric algorithms."}],"extern":"1"},{"title":"Intrachromosomal gene conversion, linkage, and the evolution of multigene families","publication":"Theoretical Population Biology","publisher":"Academic Press","oa_version":"None","date_created":"2018-12-11T12:04:30Z","publist_id":"2721","abstract":[{"text":"The evolution of the probabilities of genetic identity within and between tandemly repeated loci of a multigene family is investigated analytically and numerically. Unbiased intrachromosomal gene conversion, equal crossing over, random genetic drift, and mutation to new alleles are incorporated. Generations are discrete and nonoverlapping; the diploid, monoecious population mates at random. Under the restriction that there is at most one crossover in the multigene family per individual per generation, the dependence on location of the probabilities of identity is treated exactly. In the “homogeneous” approximation to this “exact” model, end effects are disregarded; in the “exchangeable” approximation, to which all previous work was confined, all position dependence is neglected. Numerical results indicate that (i) the exchangeable and homogeneous models are both qualitatively correct, (ii) the exchangeable model is sometimes too inaccurate for quantitative conclusions, and (iii) the homogeneous model is always more accurate than the exchangeable one and is always sufficiently accurate for quantitative conclusions.","lang":"eng"}],"extern":"1","page":"407 - 437","volume":29,"type":"journal_article","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","_id":"3662","year":"1986","status":"public","acknowledgement":"Supported by National Science Foundation Grant DEB81-03530","article_type":"original","issue":"3","citation":{"short":"T. Nagylaki, N.H. Barton, Theoretical Population Biology 29 (1986) 407–437.","ista":"Nagylaki T, Barton NH. 1986. Intrachromosomal gene conversion, linkage, and the evolution of multigene families. Theoretical Population Biology. 29(3), 407–437.","mla":"Nagylaki, Thomas, and Nicholas H. Barton. “Intrachromosomal Gene Conversion, Linkage, and the Evolution of Multigene Families.” <i>Theoretical Population Biology</i>, vol. 29, no. 3, Academic Press, 1986, pp. 407–37, doi:<a href=\"https://doi.org/10.1016/0040-5809(86)90017-1\">10.1016/0040-5809(86)90017-1</a>.","ama":"Nagylaki T, Barton NH. Intrachromosomal gene conversion, linkage, and the evolution of multigene families. <i>Theoretical Population Biology</i>. 1986;29(3):407-437. doi:<a href=\"https://doi.org/10.1016/0040-5809(86)90017-1\">10.1016/0040-5809(86)90017-1</a>","apa":"Nagylaki, T., &#38; Barton, N. H. (1986). Intrachromosomal gene conversion, linkage, and the evolution of multigene families. <i>Theoretical Population Biology</i>. Academic Press. <a href=\"https://doi.org/10.1016/0040-5809(86)90017-1\">https://doi.org/10.1016/0040-5809(86)90017-1</a>","chicago":"Nagylaki, Thomas, and Nicholas H Barton. “Intrachromosomal Gene Conversion, Linkage, and the Evolution of Multigene Families.” <i>Theoretical Population Biology</i>. Academic Press, 1986. <a href=\"https://doi.org/10.1016/0040-5809(86)90017-1\">https://doi.org/10.1016/0040-5809(86)90017-1</a>.","ieee":"T. Nagylaki and N. H. Barton, “Intrachromosomal gene conversion, linkage, and the evolution of multigene families,” <i>Theoretical Population Biology</i>, vol. 29, no. 3. Academic Press, pp. 407–437, 1986."},"publication_identifier":{"eissn":["1096-0325"],"issn":["0040-5809"]},"author":[{"full_name":"Nagylaki, Thomas","first_name":"Thomas","last_name":"Nagylaki"},{"full_name":"Barton, Nicholas H","id":"4880FE40-F248-11E8-B48F-1D18A9856A87","first_name":"Nicholas H","last_name":"Barton","orcid":"0000-0002-8548-5240"}],"date_published":"1986-06-01T00:00:00Z","doi":"10.1016/0040-5809(86)90017-1","date_updated":"2022-02-01T15:50:10Z","article_processing_charge":"No","scopus_import":"1","quality_controlled":"1","intvolume":"        29","publication_status":"published","day":"01","language":[{"iso":"eng"}],"month":"06"},{"type":"journal_article","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","page":"409 - 416","volume":56,"year":"1986","_id":"3663","article_type":"original","external_id":{"pmid":["3733460 "]},"issue":"3","oa":1,"status":"public","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.","publication_identifier":{"eissn":["1365-2540"],"issn":["0018-067X"]},"citation":{"ama":"Barton NH, Slatkin M. A quasi-equilibrium theory of the distribution of rare alleles in a subdivided population. <i>Heredity</i>. 1986;56(3):409-416. doi:<a href=\"https://doi.org/10.1038/hdy.1986.63\">10.1038/hdy.1986.63</a>","mla":"Barton, Nicholas H., and Montgomery Slatkin. “A Quasi-Equilibrium Theory of the Distribution of Rare Alleles in a Subdivided Population.” <i>Heredity</i>, vol. 56, no. 3, Nature Publishing Group, 1986, pp. 409–16, doi:<a href=\"https://doi.org/10.1038/hdy.1986.63\">10.1038/hdy.1986.63</a>.","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.","short":"N.H. Barton, M. Slatkin, Heredity 56 (1986) 409–416.","ieee":"N. H. Barton and M. Slatkin, “A quasi-equilibrium theory of the distribution of rare alleles in a subdivided population,” <i>Heredity</i>, vol. 56, no. 3. Nature Publishing Group, pp. 409–416, 1986.","chicago":"Barton, Nicholas H, and Montgomery Slatkin. “A Quasi-Equilibrium Theory of the Distribution of Rare Alleles in a Subdivided Population.” <i>Heredity</i>. Nature Publishing Group, 1986. <a href=\"https://doi.org/10.1038/hdy.1986.63\">https://doi.org/10.1038/hdy.1986.63</a>.","apa":"Barton, N. H., &#38; Slatkin, M. (1986). A quasi-equilibrium theory of the distribution of rare alleles in a subdivided population. <i>Heredity</i>. Nature Publishing Group. <a href=\"https://doi.org/10.1038/hdy.1986.63\">https://doi.org/10.1038/hdy.1986.63</a>"},"publisher":"Nature Publishing Group","title":"A quasi-equilibrium theory of the distribution of rare alleles in a subdivided population","publication":"Heredity","publist_id":"2720","oa_version":"None","date_created":"2018-12-11T12:04:30Z","extern":"1","abstract":[{"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 &quot;quasi-equilibrium&quot; 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.","lang":"eng"}],"publication_status":"published","intvolume":"        56","main_file_link":[{"url":"https://www.nature.com/articles/hdy198663","open_access":"1"}],"day":"01","pmid":1,"language":[{"iso":"eng"}],"month":"06","doi":"10.1038/hdy.1986.63","date_updated":"2022-02-01T15:04:01Z","article_processing_charge":"No","author":[{"full_name":"Barton, Nicholas H","id":"4880FE40-F248-11E8-B48F-1D18A9856A87","first_name":"Nicholas H","orcid":"0000-0002-8548-5240","last_name":"Barton"},{"last_name":"Slatkin","first_name":"Montgomery","full_name":"Slatkin, Montgomery"}],"date_published":"1986-06-01T00:00:00Z","quality_controlled":"1","scopus_import":"1"},{"year":"1986","_id":"3664","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","type":"journal_article","volume":57,"page":"357 - 376","publication_identifier":{"issn":["0018-067X"],"eissn":["1365-2540"]},"citation":{"ama":"Barton NH, Bengtsson B. The barrier to genetic exchange between hybridising populations. <i>Heredity</i>. 1986;57:357-376.","ista":"Barton NH, Bengtsson B. 1986. The barrier to genetic exchange between hybridising populations. Heredity. 57, 357–376.","short":"N.H. Barton, B. Bengtsson, Heredity 57 (1986) 357–376.","mla":"Barton, Nicholas H., and Bengt Bengtsson. “The Barrier to Genetic Exchange between Hybridising Populations.” <i>Heredity</i>, vol. 57, Nature Publishing Group, 1986, pp. 357–76.","chicago":"Barton, Nicholas H, and Bengt Bengtsson. “The Barrier to Genetic Exchange between Hybridising Populations.” <i>Heredity</i>. Nature Publishing Group, 1986.","ieee":"N. H. Barton and B. Bengtsson, “The barrier to genetic exchange between hybridising populations,” <i>Heredity</i>, vol. 57. Nature Publishing Group, pp. 357–376, 1986.","apa":"Barton, N. H., &#38; Bengtsson, B. (1986). The barrier to genetic exchange between hybridising populations. <i>Heredity</i>. Nature Publishing Group."},"article_type":"original","oa":1,"status":"public","publist_id":"2719","date_created":"2018-12-11T12:04:30Z","oa_version":"Published Version","publisher":"Nature Publishing Group","publication":"Heredity","title":"The barrier to genetic exchange between hybridising populations","extern":"1","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."}],"publication_status":"published","main_file_link":[{"url":"https://www.nature.com/articles/hdy1986135","open_access":"1"}],"intvolume":"        57","month":"01","language":[{"iso":"eng"}],"day":"01","quality_controlled":"1","scopus_import":"1","article_processing_charge":"No","date_updated":"2022-02-01T14:49:02Z","date_published":"1986-01-01T00:00:00Z","author":[{"id":"4880FE40-F248-11E8-B48F-1D18A9856A87","full_name":"Barton, Nicholas H","orcid":"0000-0002-8548-5240","last_name":"Barton","first_name":"Nicholas H"},{"full_name":"Bengtsson, Bengt","last_name":"Bengtsson","first_name":"Bengt"}]},{"article_type":"original","oa":1,"status":"public","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).","publication_identifier":{"eissn":["1365-2540"],"issn":["0018-067X"]},"citation":{"short":"N.H. Barton, Heredity 57 (1986) 415–426.","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.” <i>Heredity</i>, vol. 57, Nature Publishing Group, 1986, pp. 415–26.","ama":"Barton NH. The effects of linkage and density-dependent regulation on gene flow. <i>Heredity</i>. 1986;57:415-426.","apa":"Barton, N. H. (1986). The effects of linkage and density-dependent regulation on gene flow. <i>Heredity</i>. Nature Publishing Group.","chicago":"Barton, Nicholas H. “The Effects of Linkage and Density-Dependent Regulation on Gene Flow.” <i>Heredity</i>. Nature Publishing Group, 1986.","ieee":"N. H. Barton, “The effects of linkage and density-dependent regulation on gene flow,” <i>Heredity</i>, vol. 57. Nature Publishing Group, pp. 415–426, 1986."},"user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","type":"journal_article","volume":57,"page":"415 - 426","year":"1986","_id":"3665","extern":"1","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."}],"publisher":"Nature Publishing Group","publication":"Heredity","title":"The effects of linkage and density-dependent regulation on gene flow","publist_id":"2718","date_created":"2018-12-11T12:04:30Z","oa_version":"Published Version","day":"01","month":"01","language":[{"iso":"eng"}],"publication_status":"published","intvolume":"        57","main_file_link":[{"url":"https://www.nature.com/articles/hdy1986142","open_access":"1"}],"article_processing_charge":"No","date_updated":"2022-02-01T14:31:29Z","author":[{"last_name":"Barton","orcid":"0000-0002-8548-5240","first_name":"Nicholas H","id":"4880FE40-F248-11E8-B48F-1D18A9856A87","full_name":"Barton, Nicholas H"}],"date_published":"1986-01-01T00:00:00Z","quality_controlled":"1","scopus_import":"1"},{"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."}],"extern":"1","publication":"Journal of Combinatorial Theory Series A","title":"The number of extreme pairs of finite point-sets in Euclidean spaces","publisher":"Elsevier","date_created":"2018-12-11T12:06:56Z","oa_version":"None","publist_id":"2020","status":"public","oa":1,"issue":"2","article_type":"original","citation":{"apa":"Edelsbrunner, H., &#38; Stöckl, G. (1986). The number of extreme pairs of finite point-sets in Euclidean spaces. <i>Journal of Combinatorial Theory Series A</i>. Elsevier. <a href=\"https://doi.org/10.1016/0097-3165(86)90075-0\">https://doi.org/10.1016/0097-3165(86)90075-0</a>","ieee":"H. Edelsbrunner and G. Stöckl, “The number of extreme pairs of finite point-sets in Euclidean spaces,” <i>Journal of Combinatorial Theory Series A</i>, vol. 43, no. 2. Elsevier, pp. 344–349, 1986.","chicago":"Edelsbrunner, Herbert, and Gerd Stöckl. “The Number of Extreme Pairs of Finite Point-Sets in Euclidean Spaces.” <i>Journal of Combinatorial Theory Series A</i>. Elsevier, 1986. <a href=\"https://doi.org/10.1016/0097-3165(86)90075-0\">https://doi.org/10.1016/0097-3165(86)90075-0</a>.","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.","short":"H. Edelsbrunner, G. Stöckl, Journal of Combinatorial Theory Series A 43 (1986) 344–349.","mla":"Edelsbrunner, Herbert, and Gerd Stöckl. “The Number of Extreme Pairs of Finite Point-Sets in Euclidean Spaces.” <i>Journal of Combinatorial Theory Series A</i>, vol. 43, no. 2, Elsevier, 1986, pp. 344–49, doi:<a href=\"https://doi.org/10.1016/0097-3165(86)90075-0\">10.1016/0097-3165(86)90075-0</a>.","ama":"Edelsbrunner H, Stöckl G. The number of extreme pairs of finite point-sets in Euclidean spaces. <i>Journal of Combinatorial Theory Series A</i>. 1986;43(2):344-349. doi:<a href=\"https://doi.org/10.1016/0097-3165(86)90075-0\">10.1016/0097-3165(86)90075-0</a>"},"publication_identifier":{"eissn":["1096-0899"],"issn":["0097-3165"]},"volume":43,"page":"344 - 349","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","type":"journal_article","_id":"4098","year":"1986","author":[{"full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner"},{"last_name":"Stöckl","first_name":"Gerd","full_name":"Stöckl, Gerd"}],"date_published":"1986-11-01T00:00:00Z","article_processing_charge":"No","date_updated":"2022-02-01T14:02:41Z","doi":"10.1016/0097-3165(86)90075-0","scopus_import":"1","quality_controlled":"1","day":"01","month":"11","language":[{"iso":"eng"}],"main_file_link":[{"url":"https://www.sciencedirect.com/science/article/pii/0097316586900750?via%3Dihub","open_access":"1"}],"intvolume":"        43","publication_status":"published"},{"year":"1986","_id":"4099","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","type":"journal_article","volume":23,"page":"289 - 293","publication_identifier":{"eissn":["1872-6119"],"issn":["0020-0190"]},"citation":{"apa":"Edelsbrunner, H., &#38; Welzl, E. (1986). Halfplanar range search in linear space and O(n0.695) query time. <i>Information Processing Letters</i>. Elsevier. <a href=\"https://doi.org/10.1016/0020-0190(86)90088-8\">https://doi.org/10.1016/0020-0190(86)90088-8</a>","ieee":"H. Edelsbrunner and E. Welzl, “Halfplanar range search in linear space and O(n0.695) query time,” <i>Information Processing Letters</i>, vol. 23, no. 5. Elsevier, pp. 289–293, 1986.","chicago":"Edelsbrunner, Herbert, and Emo Welzl. “Halfplanar Range Search in Linear Space and O(N0.695) Query Time.” <i>Information Processing Letters</i>. Elsevier, 1986. <a href=\"https://doi.org/10.1016/0020-0190(86)90088-8\">https://doi.org/10.1016/0020-0190(86)90088-8</a>.","mla":"Edelsbrunner, Herbert, and Emo Welzl. “Halfplanar Range Search in Linear Space and O(N0.695) Query Time.” <i>Information Processing Letters</i>, vol. 23, no. 5, Elsevier, 1986, pp. 289–93, doi:<a href=\"https://doi.org/10.1016/0020-0190(86)90088-8\">10.1016/0020-0190(86)90088-8</a>.","ista":"Edelsbrunner H, Welzl E. 1986. Halfplanar range search in linear space and O(n0.695) query time. Information Processing Letters. 23(5), 289–293.","short":"H. Edelsbrunner, E. Welzl, Information Processing Letters 23 (1986) 289–293.","ama":"Edelsbrunner H, Welzl E. Halfplanar range search in linear space and O(n0.695) query time. <i>Information Processing Letters</i>. 1986;23(5):289-293. doi:<a href=\"https://doi.org/10.1016/0020-0190(86)90088-8\">10.1016/0020-0190(86)90088-8</a>"},"issue":"5","article_type":"original","status":"public","acknowledgement":"We thank W. Bucher for help in the analysis of the time complexity of the query algorithm. ","publist_id":"2021","date_created":"2018-12-11T12:06:56Z","oa_version":"None","publisher":"Elsevier","publication":"Information Processing Letters","title":"Halfplanar range search in linear space and O(n0.695) query time","extern":"1","abstract":[{"lang":"eng","text":"Let S denote a set of n points in the Euclidean plane. A halfplanar range query specifies a halfplane h and requires the determination of the number of points in S which are contained in h. A new data structure is described which stores S in O(n) space and allows us to answer a halfplanar range query in O(nlog2(1+√5)−1) time in the worst case, thus improving the best result known before. The structure can be built in O(n log n) time."}],"publication_status":"published","intvolume":"        23","month":"11","language":[{"iso":"eng"}],"day":"24","quality_controlled":"1","article_processing_charge":"No","doi":"10.1016/0020-0190(86)90088-8","date_updated":"2022-02-01T14:17:10Z","author":[{"full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner"},{"full_name":"Welzl, Emo","last_name":"Welzl","first_name":"Emo"}],"date_published":"1986-11-24T00:00:00Z"},{"extern":"1","abstract":[{"lang":"eng","text":"Let A be an arrangement of n lines in the plane. Suppose F1,…, Fk are faces in the dissection induced by A and that Fi is a t(Fi)-gon. We give asymptotic bounds on the maximal sum ∑i=1kt(Fi) which can be realized by k different faces in an arrangement of n lines. The results improve known bounds for k of higher order than n(1/2)."}],"publist_id":"2015","date_created":"2018-12-11T12:06:57Z","oa_version":"Published Version","publisher":"Elsevier","publication":"Journal of Combinatorial Theory Series A","title":"On the maximal number of edges of many faces in an arrangement","publication_identifier":{"issn":["0097-3165"],"eissn":["1096-0899"]},"citation":{"ama":"Edelsbrunner H, Welzl E. On the maximal number of edges of many faces in an arrangement. <i>Journal of Combinatorial Theory Series A</i>. 1986;41(2):159-166. doi:<a href=\"https://doi.org/10.1016/0097-3165(86)90078-6\">10.1016/0097-3165(86)90078-6</a>","mla":"Edelsbrunner, Herbert, and Emo Welzl. “On the Maximal Number of Edges of Many Faces in an Arrangement.” <i>Journal of Combinatorial Theory Series A</i>, vol. 41, no. 2, Elsevier, 1986, pp. 159–66, doi:<a href=\"https://doi.org/10.1016/0097-3165(86)90078-6\">10.1016/0097-3165(86)90078-6</a>.","short":"H. Edelsbrunner, E. Welzl, Journal of Combinatorial Theory Series A 41 (1986) 159–166.","ista":"Edelsbrunner H, Welzl E. 1986. On the maximal number of edges of many faces in an arrangement. Journal of Combinatorial Theory Series A. 41(2), 159–166.","ieee":"H. Edelsbrunner and E. Welzl, “On the maximal number of edges of many faces in an arrangement,” <i>Journal of Combinatorial Theory Series A</i>, vol. 41, no. 2. Elsevier, pp. 159–166, 1986.","chicago":"Edelsbrunner, Herbert, and Emo Welzl. “On the Maximal Number of Edges of Many Faces in an Arrangement.” <i>Journal of Combinatorial Theory Series A</i>. Elsevier, 1986. <a href=\"https://doi.org/10.1016/0097-3165(86)90078-6\">https://doi.org/10.1016/0097-3165(86)90078-6</a>.","apa":"Edelsbrunner, H., &#38; Welzl, E. (1986). On the maximal number of edges of many faces in an arrangement. <i>Journal of Combinatorial Theory Series A</i>. Elsevier. <a href=\"https://doi.org/10.1016/0097-3165(86)90078-6\">https://doi.org/10.1016/0097-3165(86)90078-6</a>"},"issue":"2","oa":1,"status":"public","acknowledgement":"The second author thanks Gan Gusfield for useful discussion.","year":"1986","_id":"4103","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","type":"journal_article","volume":41,"page":"159 - 166","quality_controlled":"1","scopus_import":"1","article_processing_charge":"No","doi":"10.1016/0097-3165(86)90078-6","date_updated":"2022-02-01T09:46:55Z","date_published":"1986-11-01T00:00:00Z","author":[{"full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner"},{"full_name":"Welzl, Emo","last_name":"Welzl","first_name":"Emo"}],"month":"11","language":[{"iso":"eng"}],"day":"01","publication_status":"published","main_file_link":[{"open_access":"1","url":"https://www.sciencedirect.com/science/article/pii/0097316586900786?via%3Dihub"}],"intvolume":"        41"},{"month":"01","language":[{"iso":"eng"}],"day":"01","intvolume":"        15","publication_status":"published","scopus_import":"1","quality_controlled":"1","date_published":"1986-01-01T00:00:00Z","author":[{"full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833"},{"last_name":"Guibas","first_name":"Leonidas","full_name":"Guibas, Leonidas"},{"full_name":"Stolfi, Jorge","last_name":"Stolfi","first_name":"Jorge"}],"article_processing_charge":"No","date_updated":"2022-02-01T10:05:55Z","doi":"10.1137/0215023","citation":{"ama":"Edelsbrunner H, Guibas L, Stolfi J. Optimal point location in a monotone subdivision. <i>SIAM Journal on Computing</i>. 1986;15(2):317-340. doi:<a href=\"https://doi.org/10.1137/0215023\">10.1137/0215023</a>","short":"H. Edelsbrunner, L. Guibas, J. Stolfi, SIAM Journal on Computing 15 (1986) 317–340.","ista":"Edelsbrunner H, Guibas L, Stolfi J. 1986. Optimal point location in a monotone subdivision. SIAM Journal on Computing. 15(2), 317–340.","mla":"Edelsbrunner, Herbert, et al. “Optimal Point Location in a Monotone Subdivision.” <i>SIAM Journal on Computing</i>, vol. 15, no. 2, SIAM, 1986, pp. 317–40, doi:<a href=\"https://doi.org/10.1137/0215023\">10.1137/0215023</a>.","chicago":"Edelsbrunner, Herbert, Leonidas Guibas, and Jorge Stolfi. “Optimal Point Location in a Monotone Subdivision.” <i>SIAM Journal on Computing</i>. SIAM, 1986. <a href=\"https://doi.org/10.1137/0215023\">https://doi.org/10.1137/0215023</a>.","ieee":"H. Edelsbrunner, L. Guibas, and J. Stolfi, “Optimal point location in a monotone subdivision,” <i>SIAM Journal on Computing</i>, vol. 15, no. 2. SIAM, pp. 317–340, 1986.","apa":"Edelsbrunner, H., Guibas, L., &#38; Stolfi, J. (1986). Optimal point location in a monotone subdivision. <i>SIAM Journal on Computing</i>. SIAM. <a href=\"https://doi.org/10.1137/0215023\">https://doi.org/10.1137/0215023</a>"},"publication_identifier":{"issn":["0097-5397"],"eissn":["1095-7111"]},"status":"public","acknowledgement":"We would like to thank Andrei Broder, Dan Greene, Mary Claire van Leunen, Greg Nelson, Lyle Ramshaw, and F. Frances Yao, whose comments and suggestions have greatly improved the readability of this paper.","issue":"2","article_type":"original","_id":"4104","year":"1986","volume":15,"page":"317 - 340","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","type":"journal_article","abstract":[{"text":"Point location, often known in graphics as “hit detection,” is one of the fundamental problems of computational geometry. In a point location query we want to identify which of a given collection of geometric objects contains a particular point. Let $\\mathcal{S}$ denote a subdivision of the Euclidean plane into monotone regions by a straight-line graph of $m$ edges. In this paper we exhibit a substantial refinement of the technique of Lee and Preparata [SIAM J. Comput., 6 (1977), pp. 594–606] for locating a point in $\\mathcal{S}$ based on separating chains. The new data structure, called a layered dag, can be built in $O(m)$ time, uses $O(m)$ storage, and makes possible point location in $O(\\log m)$ time. Unlike previous structures that attain these optimal bounds, the layered dag can be implemented in a simple and practical way, and is extensible to subdivisions with edges more general than straight-line segments.\r\n© 1986 Society for Industrial and Applied Mathematics","lang":"eng"}],"extern":"1","date_created":"2018-12-11T12:06:58Z","oa_version":"None","publist_id":"2016","publication":"SIAM Journal on Computing","title":"Optimal point location in a monotone subdivision","publisher":"SIAM"},{"author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","first_name":"Herbert"},{"last_name":"O'Rourke","first_name":"Joseph","full_name":"O'Rourke, Joseph"},{"first_name":"Raimund","last_name":"Seidel","full_name":"Seidel, Raimund"}],"date_published":"1986-01-01T00:00:00Z","article_processing_charge":"No","doi":"10.1137/0215024","date_updated":"2022-02-01T11:03:07Z","scopus_import":"1","quality_controlled":"1","day":"01","month":"01","language":[{"iso":"eng"}],"intvolume":"        15","publication_status":"published","abstract":[{"text":"A finite set of lines partitions the Euclidean plane into a cell complex. Similarly, a finite set of $(d - 1)$-dimensional hyperplanes partitions $d$-dimensional Euclidean space. An algorithm is presented that constructs a representation for the cell complex defined by $n$ hyperplanes in optimal $O(n^d )$ time in $d$ dimensions. It relies on a combinatorial result that is of interest in its own right. The algorithm is shown to lead to new methods for computing $\\lambda $-matrices, constructing all higher-order Voronoi diagrams, halfspatial range estimation, degeneracy testing, and finding minimum measure simplices. In all five applications, the new algorithms are asymptotically faster than previous results, and in several cases are the only known methods that generalize to arbitrary dimensions. The algorithm also implies an upper bound of $2^{cn^d } $, $c$ a positive constant, for the number of combinatorially distinct arrangements of $n$ hyperplanes in $E^d $.\r\n© 1986 Society for Industrial and Applied Mathematics","lang":"eng"}],"extern":"1","publication":"SIAM Journal on Computing","title":"Constructing arrangements of lines and hyperplanes with applications","publisher":"SIAM","date_created":"2018-12-11T12:06:58Z","oa_version":"None","publist_id":"2017","acknowledgement":"We thank Emmerich Welzl for discussions on Theorem 2.7. We also thank Friedrich Huber for implementing the \r\nconstruction of arrangements in arbitrary dimensions, and Gerd Stoeckl for implementing the algorithms presented in §§\r\n4.1 and 4.3. The third author wishes to thank Jack Edmonds for the many enlightening discussions.\r\n","status":"public","issue":"2","article_type":"original","citation":{"mla":"Edelsbrunner, Herbert, et al. “Constructing Arrangements of Lines and Hyperplanes with Applications.” <i>SIAM Journal on Computing</i>, vol. 15, no. 2, SIAM, 1986, pp. 341–63, doi:<a href=\"https://doi.org/10.1137/0215024\">10.1137/0215024</a>.","ista":"Edelsbrunner H, O’Rourke J, Seidel R. 1986. Constructing arrangements of lines and hyperplanes with applications. SIAM Journal on Computing. 15(2), 341–363.","short":"H. Edelsbrunner, J. O’Rourke, R. Seidel, SIAM Journal on Computing 15 (1986) 341–363.","ama":"Edelsbrunner H, O’Rourke J, Seidel R. Constructing arrangements of lines and hyperplanes with applications. <i>SIAM Journal on Computing</i>. 1986;15(2):341-363. doi:<a href=\"https://doi.org/10.1137/0215024\">10.1137/0215024</a>","apa":"Edelsbrunner, H., O’Rourke, J., &#38; Seidel, R. (1986). Constructing arrangements of lines and hyperplanes with applications. <i>SIAM Journal on Computing</i>. SIAM. <a href=\"https://doi.org/10.1137/0215024\">https://doi.org/10.1137/0215024</a>","ieee":"H. Edelsbrunner, J. O’Rourke, and R. Seidel, “Constructing arrangements of lines and hyperplanes with applications,” <i>SIAM Journal on Computing</i>, vol. 15, no. 2. SIAM, pp. 341–363, 1986.","chicago":"Edelsbrunner, Herbert, Joseph O’Rourke, and Raimund Seidel. “Constructing Arrangements of Lines and Hyperplanes with Applications.” <i>SIAM Journal on Computing</i>. SIAM, 1986. <a href=\"https://doi.org/10.1137/0215024\">https://doi.org/10.1137/0215024</a>."},"publication_identifier":{"issn":["0097-5397"],"eissn":["1095-7111"]},"volume":15,"page":"341 - 363","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","type":"journal_article","_id":"4105","year":"1986"},{"publication_status":"published","intvolume":"         2","language":[{"iso":"eng"}],"month":"01","day":"01","quality_controlled":"1","scopus_import":"1","doi":"10.1016/S0747-7171(86)80020-7","date_updated":"2022-02-01T11:22:59Z","article_processing_charge":"No","date_published":"1986-01-01T00:00:00Z","author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","first_name":"Herbert"},{"last_name":"Waupotitsch","first_name":"Roman","full_name":"Waupotitsch, Roman"}],"year":"1986","_id":"4106","type":"journal_article","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","page":"171 - 178","volume":2,"publication_identifier":{"issn":["0747-7171"],"eissn":["1095-855X"]},"citation":{"ista":"Edelsbrunner H, Waupotitsch R. 1986. Computing a ham-sandwich cut in two dimensions. Journal of Symbolic Computation. 2(2), 171–178.","mla":"Edelsbrunner, Herbert, and Roman Waupotitsch. “Computing a Ham-Sandwich Cut in Two Dimensions.” <i>Journal of Symbolic Computation</i>, vol. 2, no. 2, Elsevier, 1986, pp. 171–78, doi:<a href=\"https://doi.org/10.1016/S0747-7171(86)80020-7\">10.1016/S0747-7171(86)80020-7</a>.","short":"H. Edelsbrunner, R. Waupotitsch, Journal of Symbolic Computation 2 (1986) 171–178.","ama":"Edelsbrunner H, Waupotitsch R. Computing a ham-sandwich cut in two dimensions. <i>Journal of Symbolic Computation</i>. 1986;2(2):171-178. doi:<a href=\"https://doi.org/10.1016/S0747-7171(86)80020-7\">10.1016/S0747-7171(86)80020-7</a>","apa":"Edelsbrunner, H., &#38; Waupotitsch, R. (1986). Computing a ham-sandwich cut in two dimensions. <i>Journal of Symbolic Computation</i>. Elsevier. <a href=\"https://doi.org/10.1016/S0747-7171(86)80020-7\">https://doi.org/10.1016/S0747-7171(86)80020-7</a>","chicago":"Edelsbrunner, Herbert, and Roman Waupotitsch. “Computing a Ham-Sandwich Cut in Two Dimensions.” <i>Journal of Symbolic Computation</i>. Elsevier, 1986. <a href=\"https://doi.org/10.1016/S0747-7171(86)80020-7\">https://doi.org/10.1016/S0747-7171(86)80020-7</a>.","ieee":"H. Edelsbrunner and R. Waupotitsch, “Computing a ham-sandwich cut in two dimensions,” <i>Journal of Symbolic Computation</i>, vol. 2, no. 2. Elsevier, pp. 171–178, 1986."},"article_type":"original","issue":"2","status":"public","publist_id":"2018","oa_version":"None","date_created":"2018-12-11T12:06:58Z","publisher":"Elsevier","title":"Computing a ham-sandwich cut in two dimensions","publication":"Journal of Symbolic Computation","extern":"1","abstract":[{"lang":"eng","text":"Let B be a set of nb black points and W a set of nw, white points in the Euclidean plane. A line h is said to bisect B (or W) if, at most, half of the points of B (or W) lie on any one side of h. A line that bisects both B and W is called a ham-sandwich cut of B and W. We give an algorithm that computes a ham-sandwich cut of B and W in 0((nh+nw) log (min {nb, nw}+ 1)) time. The algorithm is considerably simpler than the previous most efficient one which takes 0((nb + nw) log (nb + nw)) time."}]},{"extern":"1","abstract":[{"text":"A set of m planes dissects E3 into cells, facets, edges and vertices. Letting deg(c) be the number of facets that bound a cellc, we give exact and asymptotic bounds on the maximum of ∈cinCdeg(c), if C is a family of cells of the arrangement with fixed cardinality.","lang":"eng"}],"publisher":"Elsevier","title":"The complexity of cells in 3-dimensional arrangements","publication":"Discrete Mathematics","publist_id":"2019","oa_version":"None","date_created":"2018-12-11T12:06:59Z","article_type":"original","issue":"C","acknowledgement":"Research reported in the paper was conducted while the second author was visiting the Technical University of Graz. Support provided by the Technical University for this visit is gratefully acknowledged. ","status":"public","publication_identifier":{"issn":["0012-365X"],"eissn":["1872-681X"]},"citation":{"mla":"Edelsbrunner, Herbert, and David Haussler. “The Complexity of Cells in 3-Dimensional Arrangements.” <i>Discrete Mathematics</i>, vol. 60, no. C, Elsevier, 1986, pp. 139–46, doi:<a href=\"https://doi.org/10.1016/0012-365X(86)90008-7\">10.1016/0012-365X(86)90008-7</a>.","short":"H. Edelsbrunner, D. Haussler, Discrete Mathematics 60 (1986) 139–146.","ista":"Edelsbrunner H, Haussler D. 1986. The complexity of cells in 3-dimensional arrangements. Discrete Mathematics. 60(C), 139–146.","ama":"Edelsbrunner H, Haussler D. The complexity of cells in 3-dimensional arrangements. <i>Discrete Mathematics</i>. 1986;60(C):139-146. doi:<a href=\"https://doi.org/10.1016/0012-365X(86)90008-7\">10.1016/0012-365X(86)90008-7</a>","apa":"Edelsbrunner, H., &#38; Haussler, D. (1986). The complexity of cells in 3-dimensional arrangements. <i>Discrete Mathematics</i>. Elsevier. <a href=\"https://doi.org/10.1016/0012-365X(86)90008-7\">https://doi.org/10.1016/0012-365X(86)90008-7</a>","ieee":"H. Edelsbrunner and D. Haussler, “The complexity of cells in 3-dimensional arrangements,” <i>Discrete Mathematics</i>, vol. 60, no. C. Elsevier, pp. 139–146, 1986.","chicago":"Edelsbrunner, Herbert, and David Haussler. “The Complexity of Cells in 3-Dimensional Arrangements.” <i>Discrete Mathematics</i>. Elsevier, 1986. <a href=\"https://doi.org/10.1016/0012-365X(86)90008-7\">https://doi.org/10.1016/0012-365X(86)90008-7</a>."},"type":"journal_article","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","page":"139 - 146","volume":60,"year":"1986","_id":"4107","date_updated":"2022-02-01T12:44:50Z","doi":"10.1016/0012-365X(86)90008-7","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"},{"last_name":"Haussler","first_name":"David","full_name":"Haussler, David"}],"date_published":"1986-06-01T00:00:00Z","quality_controlled":"1","day":"01","language":[{"iso":"eng"}],"month":"06","publication_status":"published","intvolume":"        60"},{"issue":"1","article_type":"original","acknowledgement":"We would like to thank John Gilbert for his careful reading of the manuscript and his many suggestions for improvement. We also want to thank Bennett Battaile, Gianfranco Bilardi, Joseph O'Rourke, and Chee Yap for their comments. ","status":"public","publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"citation":{"apa":"Edelsbrunner, H., &#38; Seidel, R. (1986). Voronoi diagrams and arrangements. <i>Discrete &#38; Computational Geometry</i>. Springer. <a href=\"https://doi.org/10.1007/BF02187681\">https://doi.org/10.1007/BF02187681</a>","ieee":"H. Edelsbrunner and R. Seidel, “Voronoi diagrams and arrangements,” <i>Discrete &#38; Computational Geometry</i>, vol. 1, no. 1. Springer, pp. 25–44, 1986.","chicago":"Edelsbrunner, Herbert, and Raimund Seidel. “Voronoi Diagrams and Arrangements.” <i>Discrete &#38; Computational Geometry</i>. Springer, 1986. <a href=\"https://doi.org/10.1007/BF02187681\">https://doi.org/10.1007/BF02187681</a>.","short":"H. Edelsbrunner, R. Seidel, Discrete &#38; Computational Geometry 1 (1986) 25–44.","ista":"Edelsbrunner H, Seidel R. 1986. Voronoi diagrams and arrangements. Discrete &#38; Computational Geometry. 1(1), 25–44.","mla":"Edelsbrunner, Herbert, and Raimund Seidel. “Voronoi Diagrams and Arrangements.” <i>Discrete &#38; Computational Geometry</i>, vol. 1, no. 1, Springer, 1986, pp. 25–44, doi:<a href=\"https://doi.org/10.1007/BF02187681\">10.1007/BF02187681</a>.","ama":"Edelsbrunner H, Seidel R. Voronoi diagrams and arrangements. <i>Discrete &#38; Computational Geometry</i>. 1986;1(1):25-44. doi:<a href=\"https://doi.org/10.1007/BF02187681\">10.1007/BF02187681</a>"},"user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","type":"journal_article","volume":1,"page":"25 - 44","year":"1986","_id":"4108","extern":"1","abstract":[{"text":"We propose a uniform and general framework for defining and dealing with Voronoi diagrams. In this framework a Voronoi diagram is a partition of a domainD induced by a finite number of real valued functions onD. Valuable insight can be gained when one considers how these real valued functions partitionD ×R. With this view it turns out that the standard Euclidean Voronoi diagram of point sets inR d along with its order-k generalizations are intimately related to certain arrangements of hyperplanes. This fact can be used to obtain new Voronoi diagram algorithms. We also discuss how the formalism of arrangements can be used to solve certain intersection and union problems.","lang":"eng"}],"publisher":"Springer","publication":"Discrete & Computational Geometry","title":"Voronoi diagrams and arrangements","publist_id":"2012","date_created":"2018-12-11T12:06:59Z","oa_version":"None","day":"01","month":"01","language":[{"iso":"eng"}],"publication_status":"published","intvolume":"         1","article_processing_charge":"No","doi":"10.1007/BF02187681","date_updated":"2022-02-01T08:53:39Z","author":[{"first_name":"Herbert","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Seidel, Raimund","last_name":"Seidel","first_name":"Raimund"}],"date_published":"1986-01-01T00:00:00Z","quality_controlled":"1"},{"year":"1986","publication_status":"published","intvolume":"        29","_id":"4109","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","type":"journal_article","volume":29,"page":"76 - 82","month":"01","publication_identifier":{"issn":["0010-4620"],"eissn":["1460-2067"]},"language":[{"iso":"eng"}],"citation":{"short":"H. Edelsbrunner, G. Haring, D. Hilbert, Computer Journal 29 (1986) 76–82.","mla":"Edelsbrunner, Herbert, et al. “Rectangular Point Location in D-Dimensions with Applications.” <i>Computer Journal</i>, vol. 29, no. 1, Oxford University Press, 1986, pp. 76–82, doi:<a href=\"https://doi.org/10.1093/comjnl/29.1.76\">10.1093/comjnl/29.1.76</a>.","ista":"Edelsbrunner H, Haring G, Hilbert D. 1986. Rectangular point location in d-dimensions with applications. Computer Journal. 29(1), 76–82.","ama":"Edelsbrunner H, Haring G, Hilbert D. Rectangular point location in d-dimensions with applications. <i>Computer Journal</i>. 1986;29(1):76-82. doi:<a href=\"https://doi.org/10.1093/comjnl/29.1.76\">10.1093/comjnl/29.1.76</a>","apa":"Edelsbrunner, H., Haring, G., &#38; Hilbert, D. (1986). Rectangular point location in d-dimensions with applications. <i>Computer Journal</i>. Oxford University Press. <a href=\"https://doi.org/10.1093/comjnl/29.1.76\">https://doi.org/10.1093/comjnl/29.1.76</a>","chicago":"Edelsbrunner, Herbert, Günter Haring, and D Hilbert. “Rectangular Point Location in D-Dimensions with Applications.” <i>Computer Journal</i>. Oxford University Press, 1986. <a href=\"https://doi.org/10.1093/comjnl/29.1.76\">https://doi.org/10.1093/comjnl/29.1.76</a>.","ieee":"H. Edelsbrunner, G. Haring, and D. Hilbert, “Rectangular point location in d-dimensions with applications,” <i>Computer Journal</i>, vol. 29, no. 1. Oxford University Press, pp. 76–82, 1986."},"issue":"1","article_type":"original","day":"01","status":"public","publist_id":"2013","date_created":"2018-12-11T12:06:59Z","oa_version":"None","publisher":"Oxford University Press","publication":"Computer Journal","title":"Rectangular point location in d-dimensions with applications","quality_controlled":"1","extern":"1","abstract":[{"lang":"eng","text":"Rectangle location search in d dimensions is finding the d-dimensional axis-parallel box of a non-overlapping collection C that contains a query point. A new data structure is proposed that requires optimal space and 0(logd|C|) time for a search. The significance of this data structure in practical applications is substantiated by empirical examinations of its behaviour."}],"article_processing_charge":"No","date_updated":"2022-02-01T09:17:51Z","doi":"10.1093/comjnl/29.1.76","date_published":"1986-01-01T00:00:00Z","author":[{"full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner"},{"full_name":"Haring, Günter","last_name":"Haring","first_name":"Günter"},{"full_name":"Hilbert, D","first_name":"D","last_name":"Hilbert"}]},{"page":"271 - 284","volume":15,"type":"journal_article","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","_id":"4110","year":"1986","status":"public","article_type":"original","issue":"1","citation":{"short":"H. Edelsbrunner, E. Welzl, SIAM Journal on Computing 15 (1986) 271–284.","ista":"Edelsbrunner H, Welzl E. 1986. Constructing belts in two-dimensional arrangements with applications. SIAM Journal on Computing. 15(1), 271–284.","mla":"Edelsbrunner, Herbert, and Emo Welzl. “Constructing Belts in Two-Dimensional Arrangements with Applications.” <i>SIAM Journal on Computing</i>, vol. 15, no. 1, SIAM, 1986, pp. 271–84, doi:<a href=\"https://doi.org/10.1137/0215019\">10.1137/0215019</a>.","ama":"Edelsbrunner H, Welzl E. Constructing belts in two-dimensional arrangements with applications. <i>SIAM Journal on Computing</i>. 1986;15(1):271-284. doi:<a href=\"https://doi.org/10.1137/0215019\">10.1137/0215019</a>","apa":"Edelsbrunner, H., &#38; Welzl, E. (1986). Constructing belts in two-dimensional arrangements with applications. <i>SIAM Journal on Computing</i>. SIAM. <a href=\"https://doi.org/10.1137/0215019\">https://doi.org/10.1137/0215019</a>","ieee":"H. Edelsbrunner and E. Welzl, “Constructing belts in two-dimensional arrangements with applications,” <i>SIAM Journal on Computing</i>, vol. 15, no. 1. SIAM, pp. 271–284, 1986.","chicago":"Edelsbrunner, Herbert, and Emo Welzl. “Constructing Belts in Two-Dimensional Arrangements with Applications.” <i>SIAM Journal on Computing</i>. SIAM, 1986. <a href=\"https://doi.org/10.1137/0215019\">https://doi.org/10.1137/0215019</a>."},"publication_identifier":{"eissn":["1095-7111"],"issn":["0097-5397"]},"title":"Constructing belts in two-dimensional arrangements with applications","publication":"SIAM Journal on Computing","publisher":"SIAM","oa_version":"None","date_created":"2018-12-11T12:07:00Z","publist_id":"2014","abstract":[{"lang":"eng","text":"For H a set of lines in the Euclidean plane, $A(H)$ denotes the induced dissection, called the arrangement of H. We define the notion of a belt in $A(H)$, which is bounded by a subset of the edges in $A(H)$, and describe two algorithms for constructing belts. All this is motivated by applications to a host of seemingly unrelated problems including a type of range search and finding the minimum area triangle with the vertices taken from some finite set of points."}],"extern":"1","intvolume":"        15","publication_status":"published","day":"01","language":[{"iso":"eng"}],"month":"01","author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","first_name":"Herbert"},{"full_name":"Welzl, Emo","last_name":"Welzl","first_name":"Emo"}],"date_published":"1986-01-01T00:00:00Z","date_updated":"2022-02-01T09:34:20Z","doi":"10.1137/0215019","article_processing_charge":"No","scopus_import":"1","quality_controlled":"1"}]