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Hospital capacities and shortages of healthcare resources among US hospitals during the coronavirus disease 2019 (COVID-19) pandemic, National Healthcare Safety Network (NHSN), March 27–July 14, 2020
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- Hsiu Wu, Minn M. Soe, Rebecca Konnor, Raymund Dantes, Kathryn Haass, Margaret A. Dudeck, Cindy Gross, Denise Leaptrot, Mathew R. P. Sapiano, Katherine Allen-Bridson, Lauren Wattenmaker, Kelly Peterson, Kent Lemoine, Sheri Chernetsky Tejedor, Jonathan R. Edwards, Daniel Pollock, Andrea L. Benin, for the National Healthcare Safety Network
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- Journal:
- Infection Control & Hospital Epidemiology / Volume 43 / Issue 10 / October 2022
- Published online by Cambridge University Press:
- 24 June 2021, pp. 1473-1476
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- October 2022
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During March 27–July 14, 2020, the Centers for Disease Control and Prevention’s National Healthcare Safety Network extended its surveillance to hospital capacities responding to COVID-19 pandemic. The data showed wide variations across hospitals in case burden, bed occupancies, ventilator usage, and healthcare personnel and supply status. These data were used to inform emergency responses.
Impact of coronavirus disease 2019 (COVID-19) on US Hospitals and Patients, April–July 2020
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- Mathew R. P. Sapiano, Margaret A. Dudeck, Minn Soe, Jonathan R. Edwards, Erin N. O’Leary, Hsiu Wu, Katherine Allen-Bridson, Agasha Amor, Rashad Arcement, Sheri Chernetsky Tejedor, Ray Dantes, Cindy Gross, Kathryn Haass, Rebecca Konnor, Seth R. Kroop, Denise Leaptrot, Kent Lemoine, Allan Nkwata, Kelly Peterson, Lauren Wattenmaker, Lindsey M. Weiner-Lastinger, Daniel Pollock, Andrea L. Benin, the NHSN Hospital COVID-19 Team
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- Journal:
- Infection Control & Hospital Epidemiology / Volume 43 / Issue 1 / January 2022
- Published online by Cambridge University Press:
- 19 February 2021, pp. 32-39
- Print publication:
- January 2022
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Objective:
The rapid spread of severe acute respiratory coronavirus virus 2 (SARS-CoV-2) throughout key regions of the United States in early 2020 placed a premium on timely, national surveillance of hospital patient censuses. To meet that need, the Centers for Disease Control and Prevention’s National Healthcare Safety Network (NHSN), the nation’s largest hospital surveillance system, launched a module for collecting hospital coronavirus disease 2019 (COVID-19) data. We present time-series estimates of the critical hospital capacity indicators from April 1 to July 14, 2020.
Design:From March 27 to July 14, 2020, the NHSN collected daily data on hospital bed occupancy, number of hospitalized patients with COVID-19, and the availability and/or use of mechanical ventilators. Time series were constructed using multiple imputation and survey weighting to allow near–real-time daily national and state estimates to be computed.
Results:During the pandemic’s April peak in the United States, among an estimated 431,000 total inpatients, 84,000 (19%) had COVID-19. Although the number of inpatients with COVID-19 decreased from April to July, the proportion of occupied inpatient beds increased steadily. COVID-19 hospitalizations increased from mid-June in the South and Southwest regions after stay-at-home restrictions were eased. The proportion of inpatients with COVID-19 on ventilators decreased from April to July.
Conclusions:The NHSN hospital capacity estimates served as important, near–real-time indicators of the pandemic’s magnitude, spread, and impact, providing quantitative guidance for the public health response. Use of the estimates detected the rise of hospitalizations in specific geographic regions in June after they declined from a peak in April. Patient outcomes appeared to improve from early April to mid-July.
Contributors
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- By Francesco Acerbi, Ayca Akgoz, Matthew R. Amans, Ramsey Ashour, Mohammed Ali Aziz-Sultan, H. Hunt Batjer, Donnie Bell, Bernard R. Bendok, Giovanni Broggi, Morgan Broggi, Charles A. Bruno, Steven D. Chang, In Sup Choi, Omar Choudhri, Douglas J. Cook, William P. Dillon, Peter Dirks, Rose Du, Travis M. Dumont, Tarek Y. El Ahmadieh, Najib E. El Tecle, Mohamed Samy Elhammady, Paolo Ferroli, Alana M. Flexman, John C. Flickinger, Kai U. Frerichs, Sasikhan Geibprasert, Adrian W. Gelb, Y. Pierre Gobin, Bradley A. Gross, Seunggu J. Han, Tomoki Hashimoto, Juha Hernesniemi, Roberto C. Heros, Steven W. Hetts, Randall T. Higashida, Joshua A. Hirsch, Nikolai J. Hopf, L. Nelson Hopkins, Maziyar A. Kalani, M. Yashar S. Kalani, Hideyuki Kano, Syed Aftab Karim, Robert M. Koffie, Douglas S. Kondziolka, Timo Krings, Aki Laakso, Giuseppe Lanzino, Michael T. Lawton, Elad I. Levy, L. Dade Lunsford, Adel M. Malek, Michael P. Marks, George A. C. Mendes, Philip M. Meyers, Jacques Morcos, Nitin Mukerji, Christian Musahl, Ludmila Pawlikowska, Matthew B. Potts, Ross Puffer, James D. Rabinov, Jonathan J. Russin, Mina G. Safain, Duke Samson, Marco Schiariti, R. Michael Scott, Jason P. Sheehan, Paul Singh, Edward R. Smith, Scott G. Soltys, Robert F. Spetzler, Gary K. Steinberg, Philip E. Stieg, Hua Su, Karel terBrugge, Kiron Thomas, Tarik Tihan, Babu Welch, Jonathan White, H. Richard Winn, Chun-Po Yen, Jacky T. Yeung, Byron Yip, Samer G. Zammar
- Edited by Robert F. Spetzler, Douglas S. Kondziolka, Randall T. Higashida, University of California, San Francisco, M. Yashar S. Kalani
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- Comprehensive Management of Arteriovenous Malformations of the Brain and Spine
- Published online:
- 05 January 2015
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- 08 January 2015, pp x-xiv
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Contributors
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- By Lenard A. Adler, Pinky Agarwal, Rehan Ahmed, Jagga Rao Alluri, Fawaz Al-Mufti, Samuel Alperin, Michael Amoashiy, Michael Andary, David J. Anschel, Padmaja Aradhya, Vandana Aspen, Esther Baldinger, Jee Bang, George D. Baquis, John J. Barry, Jason J. S. Barton, Julius Bazan, Amanda R. Bedford, Marlene Behrmann, Lourdes Bello-Espinosa, Ajay Berdia, Alan R. Berger, Mark Beyer, Don C. Bienfang, Kevin M. Biglan, Thomas M. Boes, Paul W. Brazis, Jonathan L. Brisman, Jeffrey A. Brown, Scott E. Brown, Ryan R. Byrne, Rina Caprarella, Casey A. Chamberlain, Wan-Tsu W. Chang, Grace M. Charles, Jasvinder Chawla, David Clark, Todd J. Cohen, Joe Colombo, Howard Crystal, Vladimir Dadashev, Sarita B. Dave, Jean Robert Desrouleaux, Richard L. Doty, Robert Duarte, Jeffrey S. Durmer, Christyn M. Edmundson, Eric R. Eggenberger, Steven Ender, Noam Epstein, Alberto J. Espay, Alan B. Ettinger, Niloofar (Nelly) Faghani, Amtul Farheen, Edward Firouztale, Rod Foroozan, Anne L. Foundas, David Elliot Friedman, Deborah I. Friedman, Steven J. Frucht, Oded Gerber, Tal Gilboa, Martin Gizzi, Teneille G. Gofton, Louis J. Goodrich, Malcolm H. Gottesman, Varda Gross-Tsur, Deepak Grover, David A. Gudis, John J. Halperin, Maxim D. Hammer, Andrew R. Harrison, L. Anne Hayman, Galen V. Henderson, Steven Herskovitz, Caitlin Hoffman, Laryssa A. Huryn, Andres M. Kanner, Gary P. Kaplan, Bashar Katirji, Kenneth R. Kaufman, Annie Killoran, Nina Kirz, Gad E. Klein, Danielle G. Koby, Christopher P. Kogut, W. Curt LaFrance, Patrick J.M. Lavin, Susan W. Law, James L. Levenson, Richard B. Lipton, Glenn Lopate, Daniel J. Luciano, Reema Maindiratta, Robert M. Mallery, Georgios Manousakis, Alan Mazurek, Luis J. Mejico, Dragana Micic, Ali Mokhtarzadeh, Walter J. Molofsky, Heather E. Moss, Mark L. Moster, Manpreet Multani, Siddhartha Nadkarni, George C. Newman, Rolla Nuoman, Paul A. Nyquist, Gaia Donata Oggioni, Odi Oguh, Denis Ostrovskiy, Kristina Y. Pao, Juwen Park, Anastas F. Pass, Victoria S. Pelak, Jeffrey Peterson, John Pile-Spellman, Misha L. Pless, Gregory M. Pontone, Aparna M. Prabhu, Michael T. Pulley, Philip Ragone, Prajwal Rajappa, Venkat Ramani, Sindhu Ramchandren, Ritesh A. Ramdhani, Ramses Ribot, Heidi D. Riney, Diana Rojas-Soto, Michael Ronthal, Daniel M. Rosenbaum, David B. Rosenfield, Durga Roy, Michael J. Ruckenstein, Max C. Rudansky, Eva Sahay, Friedhelm Sandbrink, Jade S. Schiffman, Angela Scicutella, Maroun T. Semaan, Robert C. Sergott, Aashit K. Shah, David M. Shaw, Amit M. Shelat, Claire A. Sheldon, Anant M. Shenoy, Yelizaveta Sher, Jessica A. Shields, Tanya Simuni, Rajpaul Singh, Eric E. Smouha, David Solomon, Mehri Songhorian, Steven A. Sparr, Egilius L. H. Spierings, Eve G. Spratt, Beth Stein, S.H. Subramony, Rosa Ana Tang, Cara Tannenbaum, Hakan Tekeli, Amanda J. Thompson, Michael J. Thorpy, Matthew J. Thurtell, Pedro J. Torrico, Ira M. Turner, Scott Uretsky, Ruth H. Walker, Deborah M. Weisbrot, Michael A. Williams, Jacques Winter, Randall J. Wright, Jay Elliot Yasen, Shicong Ye, G. Bryan Young, Huiying Yu, Ryan J. Zehnder
- Edited by Alan B. Ettinger, Albert Einstein College of Medicine, New York, Deborah M. Weisbrot, State University of New York, Stony Brook
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- Neurologic Differential Diagnosis
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- 05 June 2014
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- 17 April 2014, pp xi-xx
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- By J. William Allwood, Eleni T. Bairaktari, Jean-Pierre Bellocq, Malika A. Benahmed, Hanne Christine Bertram, Zaver M. Bhujwalla, Ulrich Braumann, Juan Casado-Vela, Marta Cascante, Arancha Cebrián, Albert Chen, Man Ho Choi, Bong Chul Chung, Yuen-Li Chung, Morten Rahr Clausen, Patrick J. Cozzone, Ralph J. DeBerardinis, Julien Detour, Santiago Díaz-Moralli, Warwick B. Dunn, Karim Elbayed, Udo Engelke, Teresa W.-M. Fan, Ana M. Gil, Kristine Glunde, Markus Godejohann, Teresa Gómez del Pulgar, Royston Goodacre, Angelina Goudswaard, Gonçalo Graça, Richard W. Gross, Herbert H. Hill, Ralph E. Hurd, Alessio Imperiale, Kimberly A. Kaplan, Neil L. Kelleher, Michael A. Kiebish, Ann M. Knolhoff, Christina E. Kostara, Juan Carlos Lacal, Andrew N. Lane, Martin O. Leach, Norbert W. Lutz, Elizabeth Maher, Craig R. Malloy, Isaac Marin-Valencia, Laura Menchén, Bruce Mickey, Fanny Mochel, Éva Morava, François-Marie Moussallieh, Izzie J. Namer, Peter Nemes, Ioanna Ntai, Geoffrey S. Payne, Marie-France Penet, Martial Piotto, Stanislav S. Rubakhin, Elsa Sánchez-López, A. Dean Sherry, Bindesh Shrestha, Jonathan V. Sweedler, Akos Vertes, Mark R. Viant, Ralf J. M. Weber, Ron Wehrens, Ron A. Wevers, Catherine L. Winder, David S. Wishart, Kui Yang, Yi-Fen Yen
- Edited by Norbert W. Lutz, Jonathan V. Sweedler, University of Illinois, Urbana-Champaign, Ron A. Wevers
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- Methodologies for Metabolomics
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- 05 January 2013
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- 21 January 2013, pp viii-xii
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- By Aakash Agarwala, Linda S. Aglio, Rae M. Allain, Paul D. Allen, Houman Amirfarzan, Yasodananda Kumar Areti, Amit Asopa, Edwin G. Avery, Patricia R. Bachiller, Angela M. Bader, Rana Badr, Sibinka Bajic, David J. Baker, Sheila R. Barnett, Rena Beckerly, Lorenzo Berra, Walter Bethune, Sascha S. Beutler, Tarun Bhalla, Edward A. Bittner, Jonathan D. Bloom, Alina V. Bodas, Lina M. Bolanos-Diaz, Ruma R. Bose, Jan Boublik, John P. Broadnax, Jason C. Brookman, Meredith R. Brooks, Roland Brusseau, Ethan O. Bryson, Linda A. Bulich, Kenji Butterfield, William R. Camann, Denise M. Chan, Theresa S. Chang, Jonathan E. Charnin, Mark Chrostowski, Fred Cobey, Adam B. Collins, Mercedes A. Concepcion, Christopher W. Connor, Bronwyn Cooper, Jeffrey B. Cooper, Martha Cordoba-Amorocho, Stephen B. Corn, Darin J. Correll, Gregory J. Crosby, Lisa J. Crossley, Deborah J. Culley, Tomas Cvrk, Michael N. D'Ambra, Michael Decker, Daniel F. Dedrick, Mark Dershwitz, Francis X. Dillon, Pradeep Dinakar, Alimorad G. Djalali, D. John Doyle, Lambertus Drop, Ian F. Dunn, Theodore E. Dushane, Sunil Eappen, Thomas Edrich, Jesse M. Ehrenfeld, Jason M. Erlich, Lucinda L. Everett, Elliott S. Farber, Khaldoun Faris, Eddy M. Feliz, Massimo Ferrigno, Richard S. Field, Michael G. Fitzsimons, Hugh L. Flanagan Jr., Vladimir Formanek, Amanda A. Fox, John A. Fox, Gyorgy Frendl, Tanja S. Frey, Samuel M. Galvagno Jr., Edward R. Garcia, Jonathan D. Gates, Cosmin Gauran, Brian J. Gelfand, Simon Gelman, Alexander C. Gerhart, Peter Gerner, Omid Ghalambor, Christopher J. Gilligan, Christian D. Gonzalez, Noah E. Gordon, William B. Gormley, Thomas J. Graetz, Wendy L. Gross, Amit Gupta, James P. Hardy, Seetharaman Hariharan, Miriam Harnett, Philip M. Hartigan, Joaquim M. Havens, Bishr Haydar, Stephen O. Heard, James L. Helstrom, David L. Hepner, McCallum R. Hoyt, Robert N. Jamison, Karinne Jervis, Stephanie B. Jones, Swaminathan Karthik, Richard M. Kaufman, Shubjeet Kaur, Lee A. Kearse Jr., John C. Keel, Scott D. Kelley, Albert H. Kim, Amy L. Kim, Grace Y. Kim, Robert J. Klickovich, Robert M. Knapp, Bhavani S. Kodali, Rahul Koka, Alina Lazar, Laura H. Leduc, Stanley Leeson, Lisa R. Leffert, Scott A. LeGrand, Patricio Leyton, J. Lance Lichtor, John Lin, Alvaro A. Macias, Karan Madan, Sohail K. Mahboobi, Devi Mahendran, Christine Mai, Sayeed Malek, S. Rao Mallampati, Thomas J. Mancuso, Ramon Martin, Matthew C. Martinez, J. A. Jeevendra Martyn, Kai Matthes, Tommaso Mauri, Mary Ellen McCann, Shannon S. McKenna, Dennis J. McNicholl, Abdel-Kader Mehio, Thor C. Milland, Tonya L. K. Miller, John D. Mitchell, K. Annette Mizuguchi, Naila Moghul, David R. Moss, Ross J. Musumeci, Naveen Nathan, Ju-Mei Ng, Liem C. Nguyen, Ervant Nishanian, Martina Nowak, Ala Nozari, Michael Nurok, Arti Ori, Rafael A. Ortega, Amy J. Ortman, David Oxman, Arvind Palanisamy, Carlo Pancaro, Lisbeth Lopez Pappas, Benjamin Parish, Samuel Park, Deborah S. Pederson, Beverly K. Philip, James H. Philip, Silvia Pivi, Stephen D. Pratt, Douglas E. Raines, Stephen L. Ratcliff, James P. Rathmell, J. Taylor Reed, Elizabeth M. Rickerson, Selwyn O. Rogers Jr., Thomas M. Romanelli, William H. Rosenblatt, Carl E. Rosow, Edgar L. Ross, J. Victor Ryckman, Mônica M. Sá Rêgo, Nicholas Sadovnikoff, Warren S. Sandberg, Annette Y. Schure, B. Scott Segal, Navil F. Sethna, Swapneel K. Shah, Shaheen F. Shaikh, Fred E. Shapiro, Torin D. Shear, Prem S. Shekar, Stanton K. Shernan, Naomi Shimizu, Douglas C. Shook, Kamal K. Sikka, Pankaj K. Sikka, David A. Silver, Jeffrey H. Silverstein, Emily A. Singer, Ken Solt, Spiro G. Spanakis, Wolfgang Steudel, Matthias Stopfkuchen-Evans, Michael P. Storey, Gary R. Strichartz, Balachundhar Subramaniam, Wariya Sukhupragarn, John Summers, Shine Sun, Eswar Sundar, Sugantha Sundar, Neelakantan Sunder, Faraz Syed, Usha B. Tedrow, Nelson L. Thaemert, George P. Topulos, Lawrence C. Tsen, Richard D. Urman, Charles A. Vacanti, Francis X. Vacanti, Joshua C. Vacanti, Assia Valovska, Ivan T. Valovski, Mary Ann Vann, Susan Vassallo, Anasuya Vasudevan, Kamen V. Vlassakov, Gian Paolo Volpato, Essi M. Vulli, J. Matthias Walz, Jingping Wang, James F. Watkins, Maxwell Weinmann, Sharon L. Wetherall, Mallory Williams, Sarah H. Wiser, Zhiling Xiong, Warren M. Zapol, Jie Zhou
- Edited by Charles Vacanti, Scott Segal, Pankaj Sikka, Richard Urman
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- Essential Clinical Anesthesia
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- 05 January 2012
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- 11 July 2011, pp xv-xxviii
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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
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- 05 June 2012
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- 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
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- 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.
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.
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
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- 05 June 2012
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- 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
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- 05 June 2012
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- 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.
5 - The newly dead
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- By Kenneth V. Iserson, University of Arizona College of Medicine, Michael L. Gross, University of Haifa, Jonathan Wyatt, Royal Cornwall Hospital
- Edited by Thomasine K. Kushner, University of California, Berkeley, David C. Thomasma
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- Ward Ethics
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- 05 February 2015
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- 07 June 2001, pp 56-65
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Summary
CASE
“Patient or cadaver?”
One evening during my first year of medical school I was observing a preceptor in the Emergency Department. A paramedic-staffed ambulance brought in a man who had been in cardiac arrest for some time. In the Emergency Department it was clear from the start that the situation looked very grim. The doctor asked if I was CPR certified and if I wanted to do cardiopulmonary resuscitation on this patient. I told him that I was certified, but I wasn't ready to take on this situation. He brushed aside my reluctance and said, “Don't worry about it. Go ahead and try. I'll be here next to you.” I administered effective CPR. Yet nothing worked, and eventually the patient was declared dead.
At that point, the curtain was pulled around the bed and the doctor told me he was going to practice intubation using the corpse that, only moments ago, had been his patient. He explained that since all the paramedics were now trained to intubate patients in the field, he seldom had the opportunity to practice this important skill. Since he didn't want to lose his proficiency, he felt this was a good way to maintain it. Later, I heard that there was also a group of training paramedic students who needed intubation experience and were invited to make use of this “practice opportunity.”