21 results
Education in Twins and Their Parents Across Birth Cohorts Over 100 years: An Individual-Level Pooled Analysis of 42-Twin Cohorts
- Karri Silventoinen, Aline Jelenkovic, Antti Latvala, Reijo Sund, Yoshie Yokoyama, Vilhelmina Ullemar, Catarina Almqvist, Catherine A. Derom, Robert F. Vlietinck, Ruth J. F. Loos, Christian Kandler, Chika Honda, Fujio Inui, Yoshinori Iwatani, Mikio Watanabe, Esther Rebato, Maria A. Stazi, Corrado Fagnani, Sonia Brescianini, Yoon-Mi Hur, Hoe-Uk Jeong, Tessa L. Cutler, John L. Hopper, Andreas Busjahn, Kimberly J. Saudino, Fuling Ji, Feng Ning, Zengchang Pang, Richard J. Rose, Markku Koskenvuo, Kauko Heikkilä, Wendy Cozen, Amie E. Hwang, Thomas M. Mack, Sisira H. Siribaddana, Matthew Hotopf, Athula Sumathipala, Fruhling Rijsdijk, Joohon Sung, Jina Kim, Jooyeon Lee, Sooji Lee, Tracy L. Nelson, Keith E. Whitfield, Qihua Tan, Dongfeng Zhang, Clare H. Llewellyn, Abigail Fisher, S. Alexandra Burt, Kelly L. Klump, Ariel Knafo-Noam, David Mankuta, Lior Abramson, Sarah E. Medland, Nicholas G. Martin, Grant W. Montgomery, Patrik K. E. Magnusson, Nancy L. Pedersen, Anna K. Dahl Aslan, Robin P. Corley, Brooke M. Huibregtse, Sevgi Y. Öncel, Fazil Aliev, Robert F. Krueger, Matt McGue, Shandell Pahlen, Gonneke Willemsen, Meike Bartels, Catharina E. M. van Beijsterveldt, Judy L. Silberg, Lindon J. Eaves, Hermine H. Maes, Jennifer R. Harris, Ingunn Brandt, Thomas S. Nilsen, Finn Rasmussen, Per Tynelius, Laura A. Baker, Catherine Tuvblad, Juan R. Ordoñana, Juan F. Sánchez-Romera, Lucia Colodro-Conde, Margaret Gatz, David A. Butler, Paul Lichtenstein, Jack H. Goldberg, K. Paige Harden, Elliot M. Tucker-Drob, Glen E. Duncan, Dedra Buchwald, Adam D. Tarnoki, David L. Tarnoki, Carol E. Franz, William S. Kremen, Michael J. Lyons, José A. Maia, Duarte L. Freitas, Eric Turkheimer, Thorkild I. A. Sørensen, Dorret I. Boomsma, Jaakko Kaprio
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- Journal:
- Twin Research and Human Genetics / Volume 20 / Issue 5 / October 2017
- Published online by Cambridge University Press:
- 04 October 2017, pp. 395-405
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Whether monozygotic (MZ) and dizygotic (DZ) twins differ from each other in a variety of phenotypes is important for genetic twin modeling and for inferences made from twin studies in general. We analyzed whether there were differences in individual, maternal and paternal education between MZ and DZ twins in a large pooled dataset. Information was gathered on individual education for 218,362 adult twins from 27 twin cohorts (53% females; 39% MZ twins), and on maternal and paternal education for 147,315 and 143,056 twins respectively, from 28 twin cohorts (52% females; 38% MZ twins). Together, we had information on individual or parental education from 42 twin cohorts representing 19 countries. The original education classifications were transformed to education years and analyzed using linear regression models. Overall, MZ males had 0.26 (95% CI [0.21, 0.31]) years and MZ females 0.17 (95% CI [0.12, 0.21]) years longer education than DZ twins. The zygosity difference became smaller in more recent birth cohorts for both males and females. Parental education was somewhat longer for fathers of DZ twins in cohorts born in 1990–1999 (0.16 years, 95% CI [0.08, 0.25]) and 2000 or later (0.11 years, 95% CI [0.00, 0.22]), compared with fathers of MZ twins. The results show that the years of both individual and parental education are largely similar in MZ and DZ twins. We suggest that the socio-economic differences between MZ and DZ twins are so small that inferences based upon genetic modeling of twin data are not affected.
Paraquat Soil Bonding and Plant Response
- B. V. Tucker, D. E. Pack, J. N. Ospenson, A. Omid, W. D. Thomas, Jr.
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- Weed Science / Volume 17 / Issue 4 / October 1969
- Published online by Cambridge University Press:
- 12 June 2017, pp. 448-451
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The toxicity of 1,1'-dimethyl-4,4'-bipyridinium ion (paraquat) in soil can be related to the degree of bonding strength to the soil aggregates. Tightly bound material is unavailable to plants, while loosely bound material can be potentially available to plants. On the basis of growth of corn (Zea mays L., var. Golden Cross Bantam) and beans (Phaseolus vulgaris L., var. Idaho 1-11) in sand, loamy sand, loam, and muck treated with paraquat, it is concluded that planned and careful application would not lead to accumulation of lethal dosages in medium to heavy soils.
DESAlert: Enabling Real-Time Transient Follow-Up with Dark Energy Survey Data
- A. Poci, K. Kuehn, T. Abbott, F. B. Abdalla, S. Allam, A.H. Bauer, A. Benoit-Lévy, E. Bertin, D. Brooks, P. J. Brown, E. Buckley-Geer, D. L. Burke, A. Carnero Rosell, M. Carrasco Kind, R. Covarrubias, L. N. da Costa, C. B. D’Andrea, D. L. DePoy, S. Desai, J. P. Dietrich, C. E Cunha, T. F. Eifler, J. Estrada, A. E. Evrard, A. Fausti Neto, D. A. Finley, B. Flaugher, P. Fosalba, J. Frieman, D. Gerdes, D. Gruen, R. A. Gruendl, K. Honscheid, D. James, N. Kuropatkin, O. Lahav, T. S. Li, M. March, J. Marshall, K. W. Merritt, C.J. Miller, R. C. Nichol, B. Nord, R. Ogando, A. A. Plazas, A. K. Romer, A. Roodman, E. S. Rykoff, M. Sako, E. Sanchez, V. Scarpine, M. Schubnell, I. Sevilla, C. Smith, M. Soares-Santos, F. Sobreira, E. Suchyta, M. E. C. Swanson, G. Tarle, J. Thaler, R. C. Thomas, D. Tucker, A. R. Walker, W. Wester, (The DES Collaboration)
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- Journal:
- Publications of the Astronomical Society of Australia / Volume 33 / 2016
- Published online by Cambridge University Press:
- 30 September 2016, e049
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The Dark Energy Survey is undertaking an observational programme imaging 1/4 of the southern hemisphere sky with unprecedented photometric accuracy. In the process of observing millions of faint stars and galaxies to constrain the parameters of the dark energy equation of state, the Dark Energy Survey will obtain pre-discovery images of the regions surrounding an estimated 100 gamma-ray bursts over 5 yr. Once gamma-ray bursts are detected by, e.g., the Swift satellite, the DES data will be extremely useful for follow-up observations by the transient astronomy community. We describe a recently-commissioned suite of software that listens continuously for automated notices of gamma-ray burst activity, collates information from archival DES data, and disseminates relevant data products back to the community in near-real-time. Of particular importance are the opportunities that non-public DES data provide for relative photometry of the optical counterparts of gamma-ray bursts, as well as for identifying key characteristics (e.g., photometric redshifts) of potential gamma-ray burst host galaxies. We provide the functional details of the DESAlert software, and its data products, and we show sample results from the application of DESAlert to numerous previously detected gamma-ray bursts, including the possible identification of several heretofore unknown gamma-ray burst hosts.
Zygosity Differences in Height and Body Mass Index of Twins From Infancy to Old Age: A Study of the CODATwins Project
- Aline Jelenkovic, Yoshie Yokoyama, Reijo Sund, Chika Honda, Leonie H Bogl, Sari Aaltonen, Fuling Ji, Feng Ning, Zengchang Pang, Juan R. Ordoñana, Juan F. Sánchez-Romera, Lucia Colodro-Conde, S. Alexandra Burt, Kelly L. Klump, Sarah E. Medland, Grant W. Montgomery, Christian Kandler, Tom A. McAdams, Thalia C. Eley, Alice M. Gregory, Kimberly J. Saudino, Lise Dubois, Michel Boivin, Adam D. Tarnoki, David L. Tarnoki, Claire M. A. Haworth, Robert Plomin, Sevgi Y. Öncel, Fazil Aliev, Maria A. Stazi, Corrado Fagnani, Cristina D’Ippolito, Jeffrey M. Craig, Richard Saffery, Sisira H. Siribaddana, Matthew Hotopf, Athula Sumathipala, Fruhling Rijsdijk, Timothy Spector, Massimo Mangino, Genevieve Lachance, Margaret Gatz, David A. Butler, Gombojav Bayasgalan, Danshiitsoodol Narandalai, Duarte L Freitas, José Antonio Maia, K. Paige Harden, Elliot M. Tucker-Drob, Bia Kim, Youngsook Chong, Changhee Hong, Hyun Jung Shin, Kaare Christensen, Axel Skytthe, Kirsten O. Kyvik, Catherine A. Derom, Robert F. Vlietinck, Ruth J. F. Loos, Wendy Cozen, Amie E. Hwang, Thomas M. Mack, Mingguang He, Xiaohu Ding, Billy Chang, Judy L. Silberg, Lindon J. Eaves, Hermine H. Maes, Tessa L. Cutler, John L. Hopper, Kelly Aujard, Patrik K. E. Magnusson, Nancy L. Pedersen, Anna K. Dahl Aslan, Yun-Mi Song, Sarah Yang, Kayoung Lee, Laura A. Baker, Catherine Tuvblad, Morten Bjerregaard-Andersen, Henning Beck-Nielsen, Morten Sodemann, Kauko Heikkilä, Qihua Tan, Dongfeng Zhang, Gary E. Swan, Ruth Krasnow, Kerry L. Jang, Ariel Knafo-Noam, David Mankuta, Lior Abramson, Paul Lichtenstein, Robert F. Krueger, Matt McGue, Shandell Pahlen, Per Tynelius, Glen E. Duncan, Dedra Buchwald, Robin P. Corley, Brooke M. Huibregtse, Tracy L. Nelson, Keith E. Whitfield, Carol E. Franz, William S. Kremen, Michael J. Lyons, Syuichi Ooki, Ingunn Brandt, Thomas Sevenius Nilsen, Fujio Inui, Mikio Watanabe, Meike Bartels, Toos C. E. M. van Beijsterveldt, Jane Wardle, Clare H. Llewellyn, Abigail Fisher, Esther Rebato, Nicholas G. Martin, Yoshinori Iwatani, Kazuo Hayakawa, Joohon Sung, Jennifer R. Harris, Gonneke Willemsen, Andreas Busjahn, Jack H. Goldberg, Finn Rasmussen, Yoon-Mi Hur, Dorret I. Boomsma, Thorkild I. A. Sørensen, Jaakko Kaprio, Karri Silventoinen
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- Journal:
- Twin Research and Human Genetics / Volume 18 / Issue 5 / October 2015
- Published online by Cambridge University Press:
- 04 September 2015, pp. 557-570
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A trend toward greater body size in dizygotic (DZ) than in monozygotic (MZ) twins has been suggested by some but not all studies, and this difference may also vary by age. We analyzed zygosity differences in mean values and variances of height and body mass index (BMI) among male and female twins from infancy to old age. Data were derived from an international database of 54 twin cohorts participating in the COllaborative project of Development of Anthropometrical measures in Twins (CODATwins), and included 842,951 height and BMI measurements from twins aged 1 to 102 years. The results showed that DZ twins were consistently taller than MZ twins, with differences of up to 2.0 cm in childhood and adolescence and up to 0.9 cm in adulthood. Similarly, a greater mean BMI of up to 0.3 kg/m2 in childhood and adolescence and up to 0.2 kg/m2 in adulthood was observed in DZ twins, although the pattern was less consistent. DZ twins presented up to 1.7% greater height and 1.9% greater BMI than MZ twins; these percentage differences were largest in middle and late childhood and decreased with age in both sexes. The variance of height was similar in MZ and DZ twins at most ages. In contrast, the variance of BMI was significantly higher in DZ than in MZ twins, particularly in childhood. In conclusion, DZ twins were generally taller and had greater BMI than MZ twins, but the differences decreased with age in both sexes.
The CODATwins Project: The Cohort Description of Collaborative Project of Development of Anthropometrical Measures in Twins to Study Macro-Environmental Variation in Genetic and Environmental Effects on Anthropometric Traits
- Karri Silventoinen, Aline Jelenkovic, Reijo Sund, Chika Honda, Sari Aaltonen, Yoshie Yokoyama, Adam D. Tarnoki, David L. Tarnoki, Feng Ning, Fuling Ji, Zengchang Pang, Juan R. Ordoñana, Juan F. Sánchez-Romera, Lucia Colodro-Conde, S. Alexandra Burt, Kelly L. Klump, Sarah E. Medland, Grant W. Montgomery, Christian Kandler, Tom A. McAdams, Thalia C. Eley, Alice M. Gregory, Kimberly J. Saudino, Lise Dubois, Michel Boivin, Claire M. A. Haworth, Robert Plomin, Sevgi Y. Öncel, Fazil Aliev, Maria A. Stazi, Corrado Fagnani, Cristina D’Ippolito, Jeffrey M. Craig, Richard Saffery, Sisira H. Siribaddana, Matthew Hotopf, Athula Sumathipala, Timothy Spector, Massimo Mangino, Genevieve Lachance, Margaret Gatz, David A. Butler, Gombojav Bayasgalan, Danshiitsoodol Narandalai, Duarte L. Freitas, José Antonio Maia, K. Paige Harden, Elliot M. Tucker-Drob, Kaare Christensen, Axel Skytthe, Kirsten O. Kyvik, Changhee Hong, Youngsook Chong, Catherine A. Derom, Robert F. Vlietinck, Ruth J. F. Loos, Wendy Cozen, Amie E. Hwang, Thomas M. Mack, Mingguang He, Xiaohu Ding, Billy Chang, Judy L. Silberg, Lindon J. Eaves, Hermine H. Maes, Tessa L. Cutler, John L. Hopper, Kelly Aujard, Patrik K. E. Magnusson, Nancy L. Pedersen, Anna K. Dahl Aslan, Yun-Mi Song, Sarah Yang, Kayoung Lee, Laura A. Baker, Catherine Tuvblad, Morten Bjerregaard-Andersen, Henning Beck-Nielsen, Morten Sodemann, Kauko Heikkilä, Qihua Tan, Dongfeng Zhang, Gary E. Swan, Ruth Krasnow, Kerry L. Jang, Ariel Knafo-Noam, David Mankuta, Lior Abramson, Paul Lichtenstein, Robert F. Krueger, Matt McGue, Shandell Pahlen, Per Tynelius, Glen E. Duncan, Dedra Buchwald, Robin P. Corley, Brooke M. Huibregtse, Tracy L. Nelson, Keith E. Whitfield, Carol E. Franz, William S. Kremen, Michael J. Lyons, Syuichi Ooki, Ingunn Brandt, Thomas Sevenius Nilsen, Fujio Inui, Mikio Watanabe, Meike Bartels, Toos C. E. M. van Beijsterveldt, Jane Wardle, Clare H. Llewellyn, Abigail Fisher, Esther Rebato, Nicholas G. Martin, Yoshinori Iwatani, Kazuo Hayakawa, Finn Rasmussen, Joohon Sung, Jennifer R. Harris, Gonneke Willemsen, Andreas Busjahn, Jack H. Goldberg, Dorret I. Boomsma, Yoon-Mi Hur, Thorkild I. A. Sørensen, Jaakko Kaprio
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- Journal:
- Twin Research and Human Genetics / Volume 18 / Issue 4 / August 2015
- Published online by Cambridge University Press:
- 27 May 2015, pp. 348-360
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For over 100 years, the genetics of human anthropometric traits has attracted scientific interest. In particular, height and body mass index (BMI, calculated as kg/m2) have been under intensive genetic research. However, it is still largely unknown whether and how heritability estimates vary between human populations. Opportunities to address this question have increased recently because of the establishment of many new twin cohorts and the increasing accumulation of data in established twin cohorts. We started a new research project to analyze systematically (1) the variation of heritability estimates of height, BMI and their trajectories over the life course between birth cohorts, ethnicities and countries, and (2) to study the effects of birth-related factors, education and smoking on these anthropometric traits and whether these effects vary between twin cohorts. We identified 67 twin projects, including both monozygotic (MZ) and dizygotic (DZ) twins, using various sources. We asked for individual level data on height and weight including repeated measurements, birth related traits, background variables, education and smoking. By the end of 2014, 48 projects participated. Together, we have 893,458 height and weight measures (52% females) from 434,723 twin individuals, including 201,192 complete twin pairs (40% monozygotic, 40% same-sex dizygotic and 20% opposite-sex dizygotic) representing 22 countries. This project demonstrates that large-scale international twin studies are feasible and can promote the use of existing data for novel research purposes.
Contributors
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- By Magdalena Anitescu, Charles E. Argoff, Arash Asher, Nyla Azam, Nomen Azeem, Sachin K. Bansal, Jose E. Barreto, Rodrigo A Benavides, Niteesh Bharara, Justin B. Boge, Robert B. Bolash, Thomas K. Bond, Christopher Centeno, Zachariah W. Chambers, Jonathan Chang, Grace Chen, Hamilton Chen, Jeffry Chen, Jianguo Cheng, Natalia Covarrubias, Claire J. Creutzfeldt, Gulshan Doulatram, Amirpasha Ehsan, Ike Eriator, Jeff Ericksen, Mark Etscheidt, Frank J. E. Falco, Jack Fu, Timothy Furnish, Annemarie E. Gallagher, Kingsuk Ganguly, Eugene Garvin, Cliff Gevirtz, Scott E. Glaser, Brandon J. Goff, Harry J. Gould, Christine Greco, Jay S. Grider, Maged Guirguis, Qiao Guo, Justin Hata, John Hau, Garett J. Helber, Eric R. Helm, Lori Hill Marshall, Dean Hommer, Jeffrey Hopcian, Eric S. Hsu, Jakun Ing, Tracy P. Jackson, Gaurav Jain, Chrystina Jeter, Alan David Kaye, James Kelly, Soorena Khojasteh, Ankur Khosla, Daniel Krashin, Monika A. Krzyzek, Prasad Lakshminarasimhiah, Steven Michael Lampert, Garrett LaSalle, Quan D. Le, Ankit Maheshwari, Edward R. Mariano, Joaquin Maury, John P. McCallin, John Michels, Natalia Murinova, Narendren Narayanasamy, Rebekah L. Nilson, Elliot Palmer, Vikram B. Patel, Devin Peck, Donald B. Penzien, Danielle Perret Karimi, Tilak Raj, Michael R. Rasmussen, Mohit Rastogi, Rahul Rastogi, Nashaat N. Rizk, Rinoo V. Shah, Paul A. Sloan, Julian Sosner, A. Raj Swain, Minyi Tan, Natacha Telusca, Santhosh A. Thomas, Andrea Trescot, Michael Truong, Jason Tucker, Richard D. Urman, Brandon A. Van Noord, Nihir Waghela, Irene Wu, Jiang Wu, Jijun Xu, Jinghui Xie, William Yancey
- Edited by Alan David Kaye, Louisiana State University, Rinoo V. Shah
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- Book:
- Case Studies in Pain Management
- Published online:
- 05 October 2014
- Print publication:
- 16 October 2014, pp xi-xv
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Contributors
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- By Jennifer Alvarez, Ananda B. Amstadter, Metin Başoğlu, David M. Benedek, Charles C. Benight, George A. Bonanno, Evelyn J. Bromet, Richard A. Bryant, Barbara Lopes Cardozo, M. L. Somchai Chakkraband, Claude Chemtob, Roman Cieslak, Lauren M. Conoscenti, Joan M. Cook, Judith Cukor, Carla Kmett Danielson, JoAnn Difede, Charles DiMaggio, Anja J.E. Dirkzwager, Cristiane S. Duarte, Jon D. Elhai, Diane L. Elmore, Yael L.E. Errera, Julian D. Ford, Carol S. Fullerton, Sandro Galea, Freya Goodhew, Neil Greenberg, Lindsay Greene, Linda Grievink, Michael J. Gruber, Sumati Gupta, Johan M. Havenaar, Alesia O. Hawkins, Clare Henn-Haase, Kimberly Eaton Hoagwood, Christina W. Hoven, Sabra S. Inslicht, Krzysztof Kaniasty, Ronald C. Kessler, Rachel Kimerling, Richard V. King, Rolf J. Kleber, Jessica Mass Levitt, Brett T. Litz, Maria Livanou, Katelyn P. Mack, Paula Madrid, Shira Maguen, Paul Maguire, Donald J. Mandell, Charles R. Marmar, Andrea R. Maxwell, Shannon E. McCaslin, Alexander C. McFarlane, Thomas J. Metzler, Summer Nelson, Yuval Neria, Elana Newman, Thomas C. Neylan, Fran H. Norris, Carol S. North, Lawrence A. Palinkas, Benjaporn Panyayong, Maria Petukhova, Betty Pfefferbaum, Marleen Radigan, Beverley Raphael, James Rodriguez, G. James Rubin, Kenneth J. Ruggiero, Ebru Şalcıoğlu, Nancy A. Sampson, Arieh Y. Shalev, Bruce Shapiro, Laura M. Stough, Prawate Tantipiwatanaskul, Warunee Thienkrua, Phebe Tucker, J. Blake Turner, Robert J. Ursano, Bellis van den Berg, Peter G. van der Velden, Frits van Griensven, Miranda Van Hooff, Edward Waldrep, Philip S. Wang, Simon Wessely, Leslie H. Wind, C. Joris Yzermans, Heidi M. Zinzow
- Edited by Yuval Neria, Columbia University, New York, Sandro Galea, University of Michigan, Ann Arbor, Fran H. Norris
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- Book:
- Mental Health and Disasters
- Published online:
- 07 May 2010
- Print publication:
- 20 July 2009, pp xi-xvi
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Contents
- Edited by Lowell W. Beineke, Purdue University, Indiana, Robin J. Wilson, The Open University, Milton Keynes
- Edited in consultation with Jonathan L. Gross, Columbia University, New York, Thomas W. Tucker, Colgate University, New York
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- Topics in Topological Graph Theory
- Published online:
- 05 June 2012
- Print publication:
- 09 July 2009, pp ix-xiv
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Foreword
- Edited by Lowell W. Beineke, Purdue University, Indiana, Robin J. Wilson, The Open University, Milton Keynes
- Edited in consultation with Jonathan L. Gross, Columbia University, New York, Thomas W. Tucker, Colgate University, New York
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- Topics in Topological Graph Theory
- Published online:
- 05 June 2012
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- 09 July 2009, pp xv-xvi
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Summary
The origins of topological graph theory lie in the 19th century, largely with the four colour problem and its extension to higher-order surfaces – the Heawood map problem. With the explosive growth of topology in the early 20th century, mathematicians like Veblen, Rado and Papakyriakopoulos provided foundational results for understanding surfaces combinatorially and algebraically. Kuratowski, MacLane and Whitney in the 1930s approached the four colour problem as a question about the structure of graphs that can be drawn without edge-crossings in the plane. Kuratowski's theorem characterizing planarity by two obstructions is the most famous, and its generalization to the higher-order surfaces became an influential unsolved problem.
The second half of the 20th century saw the solutions of all three problems: the Heawood map problem by Ringel, Youngs et al. by 1968, the four colour problem by Appel and Haken in 1976, and finally the generalized Kuratowski problem by Robertson and Seymour in the mid-1990s. Each is a landmark of 20th-century mathematics. The Ringel–Youngs work led to an alliance between combinatorics and the algebraic topology of branched coverings. The Appel–Haken work was the first time that a mathematical theorem relied on exhaustive computer calculations. And the Robertson–Seymour work led to their solution of Wagner's conjecture, which provides a breathtaking structure for the collection of all finite graphs, a collection that would seem to have no structure at all.
Each of these problems centres on the question of which graphs can be embedded in which surfaces, with two complementary perspectives – fixing the graph or fixing the surface.
10 - Symmetric maps
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- By Jozef Širáň, University of Technology, Slovakia, Thomas W. Tucker, Colgate University
- Edited by Lowell W. Beineke, Purdue University, Indiana, Robin J. Wilson, The Open University, Milton Keynes
- Edited in consultation with Jonathan L. Gross, Columbia University, New York, Thomas W. Tucker, Colgate University, New York
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- Topics in Topological Graph Theory
- Published online:
- 05 June 2012
- Print publication:
- 09 July 2009, pp 199-224
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Summary
A map is a graph embedding in which the focus is on the vertex-edge-face incidence relation together with its morphisms. This chapter concentrates on maps that are highly symmetric: regular maps, Cayley maps, regular Cayley maps and edge-transitive maps. In each case, we show how to construct a map using only information about the automorphism group. As a consequence, the viewpoint and methods are almost entirely group-theoretic.
Introduction
Symmetric maps – graphs embedded on surfaces with a sufficient ‘level of symmetry’ – have been extensively studied over the last 100 years. Their roots, however, go much deeper, to the Platonic solids of the ancient Greeks and (much later) to Kepler's stellated polyhedra.
The theme of this chapter is how maps can be treated as purely algebraic structures. This is not just an exercise in abstract nonsense: such a viewpoint has historical origins, not only in Coxeter and Moser [11] but also in Edmonds' original rotation schemes [13] and Tutte's flags [42], both of which view maps as permutation groups. Moreover, this algebraicization has a number of important consequences. It allows the simple description and construction of complicated maps – a group presentation is a remarkably efficient data structure. This in turn makes it possible to list all symmetric maps of moderate size, using computer software for group-theoretic calculations. For example, Conder [5] has determined all regular maps of genus at most 100, and Orbanič [34] has found all edge-transitive maps with at most 1000 edges; such lists have been extraordinarily helpful for detecting general phenomena.
Topics in Topological Graph Theory
- Edited by Lowell W. Beineke, Robin J. Wilson
- Edited in consultation with Jonathan L. Gross, Thomas W. Tucker
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- Published online:
- 05 June 2012
- Print publication:
- 09 July 2009
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The use of topological ideas to explore various aspects of graph theory, and vice versa, is a fruitful area of research. There are links with other areas of mathematics, such as design theory and geometry, and increasingly with such areas as computer networks where symmetry is an important feature. Other books cover portions of the material here, but there are no other books with such a wide scope. This book contains fifteen expository chapters written by acknowledged international experts in the field. Their well-written contributions have been carefully edited to enhance readability and to standardize the chapter structure, terminology and notation throughout the book. To help the reader, there is an extensive introductory chapter that covers the basic background material in graph theory and the topology of surfaces. Each chapter concludes with an extensive list of references.
11 - The genus of a group
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- By Thomas W. Tucker, Colgate University
- Edited by Lowell W. Beineke, Purdue University, Indiana, Robin J. Wilson, The Open University, Milton Keynes
- Edited in consultation with Jonathan L. Gross, Columbia University, New York, Thomas W. Tucker, Colgate University, New York
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- Topics in Topological Graph Theory
- Published online:
- 05 June 2012
- Print publication:
- 09 July 2009, pp 225-244
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Summary
This chapter surveys the genus of a finite group. Various symmetric embeddings of Cayley graphs are discussed, together with their associated genus parameters and their relationship to group actions on surfaces. Computations for low genus and certain families of groups are given. Particular attention is paid to general results relating the various genus parameters to each other.
Introduction
The (orientable) genus γ (A) of a finite group A is the smallest integer h such that some Cayley graph for A can be embedded in the orientable surface Sh. (Recall that the Cayley graph C(A, X) for a group A with generating set X has vertex-set A and edges between a and ax, for all a ∈ A and x ∈ X.) The term was first introduced by White [50], but similar ideas appear as far back as the late 19th century. Burnside [6] has two chapters on the ‘graphical representation of a group’ that include the determination of all groups of ‘genus’ 0 and 1 (really the strong symmetric genus, in the language of the next section). The early history is mostly in the context of finite groups of conformal automorphisms of Riemann surfaces, and this context continues to play an important role. On the other hand, Burnside also viewed an embedding of a Cayley graph, or more explicitly the faces of such an embedding, as a way of understanding the relations in a group presentation, in the spirit of Dehn [14] a few years later.
Frontmatter
- Edited by Lowell W. Beineke, Purdue University, Indiana, Robin J. Wilson, The Open University, Milton Keynes
- Edited in consultation with Jonathan L. Gross, Columbia University, New York, Thomas W. Tucker, Colgate University, New York
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- Topics in Topological Graph Theory
- Published online:
- 05 June 2012
- Print publication:
- 09 July 2009, pp i-viii
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3 - Distribution of embeddings
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- By Jonathan L. Gross, Columbia University, Thomas W. Tucker, Colgate University
- Edited by Lowell W. Beineke, Purdue University, Indiana, Robin J. Wilson, The Open University, Milton Keynes
- Edited in consultation with Jonathan L. Gross, Columbia University, New York, Thomas W. Tucker, Colgate University, New York
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- Topics in Topological Graph Theory
- Published online:
- 05 June 2012
- Print publication:
- 09 July 2009, pp 45-61
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Summary
The principal genus distribution problem is to count the number of cellular embeddings of a given graph. Complete distributions have been obtained for a few basic families of graphs. Various properties of genus distributions and of related invariants are examined, especially the properties of the average genus.
Introduction
A ubiquitous question in topological graph theory is whether a given graph can be embedded in a given surface, a question that readily extends to the problem of counting the number of different embeddings of that graph into that surface. (A contrasting classical problem with its origins in geometry asks, for a fixed surface, how many different maps there are onto that surface, where what varies is the graph that serves as the 1-skeleton.) This chapter explores the programme introduced by Gross and Furst [11] of constructing surface-by-surface inventories of the embeddings of a fixed graph into not just one surface, but every surface, and gives the related theory.
All embeddings are taken to be cellular, except where it is clear from context that non-cellular embeddings are under consideration. Two cellular embeddings are considered to be the same if their rotation systems are combinatorially equivalent (see Chapter 1).
Given a graph G and an orientable surface Sh, the number of embeddings of G in Sh is the number gh(G) of rotation systems for G that induce a cellular embedding in Sh. The orientable genus range of a graph G is the set of integers h for which gh(G) > 0.
Notes on contributors
- Edited by Lowell W. Beineke, Purdue University, Indiana, Robin J. Wilson, The Open University, Milton Keynes
- Edited in consultation with Jonathan L. Gross, Columbia University, New York, Thomas W. Tucker, Colgate University, New York
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- Topics in Topological Graph Theory
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- 05 June 2012
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- 09 July 2009, pp 337-340
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Index
- Edited by Lowell W. Beineke, Purdue University, Indiana, Robin J. Wilson, The Open University, Milton Keynes
- Edited in consultation with Jonathan L. Gross, Columbia University, New York, Thomas W. Tucker, Colgate University, New York
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- Topics in Topological Graph Theory
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- 05 June 2012
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- 09 July 2009, pp 341-347
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1 - Embedding graphs on surfaces
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- By Jonathan L. Gross, Columbia University, Thomas W. Tucker, Colgate University
- Edited by Lowell W. Beineke, Purdue University, Indiana, Robin J. Wilson, The Open University, Milton Keynes
- Edited in consultation with Jonathan L. Gross, Columbia University, New York, Thomas W. Tucker, Colgate University, New York
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- Topics in Topological Graph Theory
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- 05 June 2012
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- 09 July 2009, pp 18-33
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Summary
In this first chapter, we review the basic ideas of topological graph theory. We describe the principal early theme of constructing embeddings, and we then survey the launching of the dominant programmatic themes of the present era, which are presented in greater detail individually in subsequent chapters.
Introduction
By the late 19th century, the work of Heawood [16] and Heffter [17] had expanded the study of graph drawings beyond the confines of the plane to surfaces of higher order. Over the next hundred years or so, the solution of several long-standing problems attracted many researchers and the present-day programmatic themes were set into place. Of course, some of the methods used in the solutions led to new problems. Topological graph theory is now one of the largest branches of graph theory.
This chapter gives a brief overview of some of the principal concepts, terminology and notation of topological graph theory. As general resources, we recommend [13], Chapter 7 of [14], [22] and [44].
Graphs and surfaces
We start by recalling some definitions from the Introduction. A graph G is formally defined to be a combinatorial incidence structure with a vertex-set V and an edgeset E, where each edge e is incident with at most two vertices; we may write VG and EG, respectively, when there is more than one graph under consideration. A graph may have multiple adjacencies and loops and is usually taken to be finite unless the immediate context implies otherwise.
Contributors
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- By Nalini Vadivelu, Christian J. Whitney, Raymond S. Sinatra, M. Khurram Ghori, Yu-Fan (Robert) Zhang, Raymond S. Sinatra, Joshua Wellington, Yuan-Yi Chia, Francis J. Keefe, Jon McCormack, Ian Power, John Butterworth, P. M. Lavand’homme, M. F. De Kock, Bradley Urie, Oscar A. de Leon-Casasola, Frederick M. Perkins, Larry F. Chu, David Clark, Martin S. Angst, Cynthia M. Welchek, Lisa Mastrangelo, Raymond S. Sinatra, Richard Martinez, Scott S. Reuben, Asokumar Buvanendran, Raymond S. Sinatra, Pamela E Macintyre, Julia Coldrey, Daniel B. Maalouf, Spencer S. Liu, Susan Dabu-Bondoc, Samantha A. Franco, Raymond S. Sinatra, James Benonis, Jennifer Fortney, David Hardman, Gavin Martin, Holly Evans, Karen C. Nielsen, Marcy S. Tucker, Stephen M. Klein, Benjamin Sherman, Ikay Enu, Raymond S. Sinatra, James W. Heitz, Eugene R. Viscusi, Jonathan S. Jahr, Kofi N. Donkor, Raymond S. Sinatra, Manzo Suzuki, Johan Raeder, Vegard Dahl, Stefan Erceg, Keun Sam Chung, Kok-Yuen Ho, Tong J. Gan, Dermot R. Fitzgibbon, Paul Willoughby, Brian E. Harrington, Joseph Marino, Tariq M. Malik, Raymond S. Sinatra, Giorgio Ivani, Valeria Mossetti, Simona Italiano, Thomas M. Halaszynski, Nousheh Saidi, Javier Lopez, Kate Miller, Ferne Braveman, Jaya L. Varadarajan, Steven J. Weisman, Sukanya Mitra, Raymond S. Sinatra, Theodore J. Saclarides, Knox H. Todd, James R. Miner, Chris Pasero, Nancy Eksterowicz, Margo McCaffery, Leslie N. Schechter, Amr E. Abouleish, Govindaraj Ranganathan, Tee Yong Tan, Stephan A. Schug, Marie N. Hanna, Spencer S. Liu, Christopher L. Wu, Craig T. Hartrick, Garen Manvelian, Christine Miaskowski, Brian Durkin, Peter S. A. Glass
- Edited by Raymond S. Sinatra, Oscar A. de Leon-Cassasola, University of Rochester Medical Center, New York, Eugene R. Viscusi, Brian Ginsberg
- Foreword by Henry McQuay
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- Acute Pain Management
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- 26 October 2009
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- 27 April 2009, pp vii-xii
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Hindgut fermentation in dogs
- I Singh, W Hendriks, L Tucker, D G Thomas, G Fahey
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- Proceedings of the British Society of Animal Science / Volume 2009 / April 2009
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- 22 November 2017, p. 65
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- April 2009
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There is a large body of research investigating the nutritional needs of the dog at different life-stages and the use of different feed ingredients in commercial diets (Clapper et al, 2001; Schroeder & Smith, 2008). Despite this, though there has been relatively little published work looking at the role the large intestine plays in nutrient digestion in the dog. The dog’s gastro-intestinal tract has been compared to the cat’s in terms of relative length. However the cat is a true carnivore and has little need to ferment fibre from the diet, whereas the dog is a scavenger and will consume a much wider range of food, and therefore may need to ferment fibrous material from the diet. The dog may therefore require a more developed large intestine to harbour a microbial population to aid in the digestion of this fibrous material. This study was performed to determine differences in digestion of nutrients in this segment of the canine gastrointestinal tract.
Investigation of indigestible markers in dogs
- I Singh, W Hendriks, L Tucker, D G Thomas
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- Proceedings of the British Society of Animal Science / Volume 2009 / April 2009
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- 22 November 2017, p. 67
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- April 2009
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Digestibility trials enable researchers to determine the amount of nutrients an animal absorbs and utilises from feed. There are a number of methods available, with the most common being the measurement of total feed intake and total collection of faeces. However, in situations where it is not practical to conduct a total collection trial, indigestible markers are used in conjunction with grab-sampling or sub-sampling techniques. To date, the most common marker used in dog studies has been chromium oxide (Cr2O3; Hill et al., 1996), with little data available on the suitability of other markers such as titanium dioxide (TiO2). A major problem in using Cr2O3 as an indigestible marker is poor repeatability and agreement between laboratories in the determination of Cr2O3. This has led to variable results due to incomplete and inconsistent recovery in excreta (Sales and Janssens, 2003). However work on other species comparing the use of TiO2 and Cr2O3, has demonstrated that TiO2 was a more accurate marker (Jagger et al., 1992). This study was performed to determine the digestibility of two diets, a low (LN) and a high nutrient (HN) diet using TiO2 or Cr2O3 as indigestible markers. The two different quality diets were used to investigate if digestibility affected marker recovery.