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Using polygenic scores and clinical data for bipolar disorder patient stratification and lithium response prediction: machine learning approach – CORRIGENDUM
- Micah Cearns, Azmeraw T. Amare, Klaus Oliver Schubert, Anbupalam Thalamuthu, Joseph Frank, Fabian Streit, Mazda Adli, Nirmala Akula, Kazufumi Akiyama, Raffaella Ardau, Bárbara Arias, JeanMichel Aubry, Lena Backlund, Abesh Kumar Bhattacharjee, Frank Bellivier, Antonio Benabarre, Susanne Bengesser, Joanna M. Biernacka, Armin Birner, Clara Brichant-Petitjean, Pablo Cervantes, HsiChung Chen, Caterina Chillotti, Sven Cichon, Cristiana Cruceanu, Piotr M. Czerski, Nina Dalkner, Alexandre Dayer, Franziska Degenhardt, Maria Del Zompo, J. Raymond DePaulo, Bruno Étain, Peter Falkai, Andreas J. Forstner, Louise Frisen, Mark A. Frye, Janice M. Fullerton, Sébastien Gard, Julie S. Garnham, Fernando S. Goes, Maria Grigoroiu-Serbanescu, Paul Grof, Ryota Hashimoto, Joanna Hauser, Urs Heilbronner, Stefan Herms, Per Hoffmann, Andrea Hofmann, Liping Hou, Yi-Hsiang Hsu, Stephane Jamain, Esther Jiménez, Jean-Pierre Kahn, Layla Kassem, Po-Hsiu Kuo, Tadafumi Kato, John Kelsoe, Sarah Kittel-Schneider, Sebastian Kliwicki, Barbara König, Ichiro Kusumi, Gonzalo Laje, Mikael Landén, Catharina Lavebratt, Marion Leboyer, Susan G. Leckband, Mario Maj, the Major Depressive Disorder Working Group of the Psychiatric Genomics Consortium, Mirko Manchia, Lina Martinsson, Michael J. McCarthy, Susan McElroy, Francesc Colom, Marina Mitjans, Francis M. Mondimore, Palmiero Monteleone, Caroline M. Nievergelt, Markus M. Nöthen, Tomas Novák, Claire O'Donovan, Norio Ozaki, Vincent Millischer, Sergi Papiol, Andrea Pfennig, Claudia Pisanu, James B. Potash, Andreas Reif, Eva Reininghaus, Guy A. Rouleau, Janusz K. Rybakowski, Martin Schalling, Peter R. Schofield, Barbara W. Schweizer, Giovanni Severino, Tatyana Shekhtman, Paul D. Shilling, Katzutaka Shimoda, Christian Simhandl, Claire M. Slaney, Alessio Squassina, Thomas Stamm, Pavla Stopkova, Fasil TekolaAyele, Alfonso Tortorella, Gustavo Turecki, Julia Veeh, Eduard Vieta, Stephanie H. Witt, Gloria Roberts, Peter P. Zandi, Martin Alda, Michael Bauer, Francis J. McMahon, Philip B. Mitchell, Thomas G. Schulze, Marcella Rietschel, Scott R. Clark, Bernhard T. Baune
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- Journal:
- The British Journal of Psychiatry / Volume 221 / Issue 2 / August 2022
- Published online by Cambridge University Press:
- 04 May 2022, p. 494
- Print publication:
- August 2022
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Using polygenic scores and clinical data for bipolar disorder patient stratification and lithium response prediction: machine learning approach
- Micah Cearns, Azmeraw T. Amare, Klaus Oliver Schubert, Anbupalam Thalamuthu, Joseph Frank, Fabian Streit, Mazda Adli, Nirmala Akula, Kazufumi Akiyama, Raffaella Ardau, Bárbara Arias, Jean-Michel Aubry, Lena Backlund, Abesh Kumar Bhattacharjee, Frank Bellivier, Antonio Benabarre, Susanne Bengesser, Joanna M. Biernacka, Armin Birner, Clara Brichant-Petitjean, Pablo Cervantes, Hsi-Chung Chen, Caterina Chillotti, Sven Cichon, Cristiana Cruceanu, Piotr M. Czerski, Nina Dalkner, Alexandre Dayer, Franziska Degenhardt, Maria Del Zompo, J. Raymond DePaulo, Bruno Étain, Peter Falkai, Andreas J. Forstner, Louise Frisen, Mark A. Frye, Janice M. Fullerton, Sébastien Gard, Julie S. Garnham, Fernando S. Goes, Maria Grigoroiu-Serbanescu, Paul Grof, Ryota Hashimoto, Joanna Hauser, Urs Heilbronner, Stefan Herms, Per Hoffmann, Andrea Hofmann, Liping Hou, Yi-Hsiang Hsu, Stephane Jamain, Esther Jiménez, Jean-Pierre Kahn, Layla Kassem, Po-Hsiu Kuo, Tadafumi Kato, John Kelsoe, Sarah Kittel-Schneider, Sebastian Kliwicki, Barbara König, Ichiro Kusumi, Gonzalo Laje, Mikael Landén, Catharina Lavebratt, Marion Leboyer, Susan G. Leckband, Mario Maj, the Major Depressive Disorder Working Group of the Psychiatric Genomics Consortium, Mirko Manchia, Lina Martinsson, Michael J. McCarthy, Susan McElroy, Francesc Colom, Marina Mitjans, Francis M. Mondimore, Palmiero Monteleone, Caroline M. Nievergelt, Markus M. Nöthen, Tomas Novák, Claire O'Donovan, Norio Ozaki, Vincent Millischer, Sergi Papiol, Andrea Pfennig, Claudia Pisanu, James B. Potash, Andreas Reif, Eva Reininghaus, Guy A. Rouleau, Janusz K. Rybakowski, Martin Schalling, Peter R. Schofield, Barbara W. Schweizer, Giovanni Severino, Tatyana Shekhtman, Paul D. Shilling, Katzutaka Shimoda, Christian Simhandl, Claire M. Slaney, Alessio Squassina, Thomas Stamm, Pavla Stopkova, Fasil Tekola-Ayele, Alfonso Tortorella, Gustavo Turecki, Julia Veeh, Eduard Vieta, Stephanie H. Witt, Gloria Roberts, Peter P. Zandi, Martin Alda, Michael Bauer, Francis J. McMahon, Philip B. Mitchell, Thomas G. Schulze, Marcella Rietschel, Scott R. Clark, Bernhard T. Baune
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- Journal:
- The British Journal of Psychiatry / Volume 220 / Issue 4 / April 2022
- Published online by Cambridge University Press:
- 28 February 2022, pp. 219-228
- Print publication:
- April 2022
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Background
Response to lithium in patients with bipolar disorder is associated with clinical and transdiagnostic genetic factors. The predictive combination of these variables might help clinicians better predict which patients will respond to lithium treatment.
AimsTo use a combination of transdiagnostic genetic and clinical factors to predict lithium response in patients with bipolar disorder.
MethodThis study utilised genetic and clinical data (n = 1034) collected as part of the International Consortium on Lithium Genetics (ConLi+Gen) project. Polygenic risk scores (PRS) were computed for schizophrenia and major depressive disorder, and then combined with clinical variables using a cross-validated machine-learning regression approach. Unimodal, multimodal and genetically stratified models were trained and validated using ridge, elastic net and random forest regression on 692 patients with bipolar disorder from ten study sites using leave-site-out cross-validation. All models were then tested on an independent test set of 342 patients. The best performing models were then tested in a classification framework.
ResultsThe best performing linear model explained 5.1% (P = 0.0001) of variance in lithium response and was composed of clinical variables, PRS variables and interaction terms between them. The best performing non-linear model used only clinical variables and explained 8.1% (P = 0.0001) of variance in lithium response. A priori genomic stratification improved non-linear model performance to 13.7% (P = 0.0001) and improved the binary classification of lithium response. This model stratified patients based on their meta-polygenic loadings for major depressive disorder and schizophrenia and was then trained using clinical data.
ConclusionsUsing PRS to first stratify patients genetically and then train machine-learning models with clinical predictors led to large improvements in lithium response prediction. When used with other PRS and biological markers in the future this approach may help inform which patients are most likely to respond to lithium treatment.
Characterisation of age and polarity at onset in bipolar disorder
- Janos L. Kalman, Loes M. Olde Loohuis, Annabel Vreeker, Andrew McQuillin, Eli A. Stahl, Douglas Ruderfer, Maria Grigoroiu-Serbanescu, Georgia Panagiotaropoulou, Stephan Ripke, Tim B. Bigdeli, Frederike Stein, Tina Meller, Susanne Meinert, Helena Pelin, Fabian Streit, Sergi Papiol, Mark J. Adams, Rolf Adolfsson, Kristina Adorjan, Ingrid Agartz, Sofie R. Aminoff, Heike Anderson-Schmidt, Ole A. Andreassen, Raffaella Ardau, Jean-Michel Aubry, Ceylan Balaban, Nicholas Bass, Bernhard T. Baune, Frank Bellivier, Antoni Benabarre, Susanne Bengesser, Wade H Berrettini, Marco P. Boks, Evelyn J. Bromet, Katharina Brosch, Monika Budde, William Byerley, Pablo Cervantes, Catina Chillotti, Sven Cichon, Scott R. Clark, Ashley L. Comes, Aiden Corvin, William Coryell, Nick Craddock, David W. Craig, Paul E. Croarkin, Cristiana Cruceanu, Piotr M. Czerski, Nina Dalkner, Udo Dannlowski, Franziska Degenhardt, Maria Del Zompo, J. Raymond DePaulo, Srdjan Djurovic, Howard J. Edenberg, Mariam Al Eissa, Torbjørn Elvsåshagen, Bruno Etain, Ayman H. Fanous, Frederike Fellendorf, Alessia Fiorentino, Andreas J. Forstner, Mark A. Frye, Janice M. Fullerton, Katrin Gade, Julie Garnham, Elliot Gershon, Michael Gill, Fernando S. Goes, Katherine Gordon-Smith, Paul Grof, Jose Guzman-Parra, Tim Hahn, Roland Hasler, Maria Heilbronner, Urs Heilbronner, Stephane Jamain, Esther Jimenez, Ian Jones, Lisa Jones, Lina Jonsson, Rene S. Kahn, John R. Kelsoe, James L. Kennedy, Tilo Kircher, George Kirov, Sarah Kittel-Schneider, Farah Klöhn-Saghatolislam, James A. Knowles, Thorsten M. Kranz, Trine Vik Lagerberg, Mikael Landen, William B. Lawson, Marion Leboyer, Qingqin S. Li, Mario Maj, Dolores Malaspina, Mirko Manchia, Fermin Mayoral, Susan L. McElroy, Melvin G. McInnis, Andrew M. McIntosh, Helena Medeiros, Ingrid Melle, Vihra Milanova, Philip B. Mitchell, Palmiero Monteleone, Alessio Maria Monteleone, Markus M. Nöthen, Tomas Novak, John I. Nurnberger, Niamh O'Brien, Kevin S. O'Connell, Claire O'Donovan, Michael C. O'Donovan, Nils Opel, Abigail Ortiz, Michael J. Owen, Erik Pålsson, Carlos Pato, Michele T. Pato, Joanna Pawlak, Julia-Katharina Pfarr, Claudia Pisanu, James B. Potash, Mark H Rapaport, Daniela Reich-Erkelenz, Andreas Reif, Eva Reininghaus, Jonathan Repple, Hélène Richard-Lepouriel, Marcella Rietschel, Kai Ringwald, Gloria Roberts, Guy Rouleau, Sabrina Schaupp, William A Scheftner, Simon Schmitt, Peter R. Schofield, K. Oliver Schubert, Eva C. Schulte, Barbara Schweizer, Fanny Senner, Giovanni Severino, Sally Sharp, Claire Slaney, Olav B. Smeland, Janet L. Sobell, Alessio Squassina, Pavla Stopkova, John Strauss, Alfonso Tortorella, Gustavo Turecki, Joanna Twarowska-Hauser, Marin Veldic, Eduard Vieta, John B. Vincent, Wei Xu, Clement C. Zai, Peter P. Zandi, Psychiatric Genomics Consortium (PGC) Bipolar Disorder Working Group, International Consortium on Lithium Genetics (ConLiGen), Colombia-US Cross Disorder Collaboration in Psychiatric Genetics, Arianna Di Florio, Jordan W. Smoller, Joanna M. Biernacka, Francis J. McMahon, Martin Alda, Bertram Müller-Myhsok, Nikolaos Koutsouleris, Peter Falkai, Nelson B. Freimer, Till F.M. Andlauer, Thomas G. Schulze, Roel A. Ophoff
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- Journal:
- The British Journal of Psychiatry / Volume 219 / Issue 6 / December 2021
- Published online by Cambridge University Press:
- 25 August 2021, pp. 659-669
- Print publication:
- December 2021
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Background
Studying phenotypic and genetic characteristics of age at onset (AAO) and polarity at onset (PAO) in bipolar disorder can provide new insights into disease pathology and facilitate the development of screening tools.
AimsTo examine the genetic architecture of AAO and PAO and their association with bipolar disorder disease characteristics.
MethodGenome-wide association studies (GWASs) and polygenic score (PGS) analyses of AAO (n = 12 977) and PAO (n = 6773) were conducted in patients with bipolar disorder from 34 cohorts and a replication sample (n = 2237). The association of onset with disease characteristics was investigated in two of these cohorts.
ResultsEarlier AAO was associated with a higher probability of psychotic symptoms, suicidality, lower educational attainment, not living together and fewer episodes. Depressive onset correlated with suicidality and manic onset correlated with delusions and manic episodes. Systematic differences in AAO between cohorts and continents of origin were observed. This was also reflected in single-nucleotide variant-based heritability estimates, with higher heritabilities for stricter onset definitions. Increased PGS for autism spectrum disorder (β = −0.34 years, s.e. = 0.08), major depression (β = −0.34 years, s.e. = 0.08), schizophrenia (β = −0.39 years, s.e. = 0.08), and educational attainment (β = −0.31 years, s.e. = 0.08) were associated with an earlier AAO. The AAO GWAS identified one significant locus, but this finding did not replicate. Neither GWAS nor PGS analyses yielded significant associations with PAO.
ConclusionsAAO and PAO are associated with indicators of bipolar disorder severity. Individuals with an earlier onset show an increased polygenic liability for a broad spectrum of psychiatric traits. Systematic differences in AAO across cohorts, continents and phenotype definitions introduce significant heterogeneity, affecting analyses.
Evidence of causal effect of major depression on alcohol dependence: findings from the psychiatric genomics consortium
- Renato Polimanti, Roseann E. Peterson, Jue-Sheng Ong, Stuart MacGregor, Alexis C. Edwards, Toni-Kim Clarke, Josef Frank, Zachary Gerring, Nathan A. Gillespie, Penelope A. Lind, Hermine H. Maes, Nicholas G. Martin, Hamdi Mbarek, Sarah E. Medland, Fabian Streit, Major Depressive Disorder Working Group of the Psychiatric Genomics Consortium, Substance Use Disorder Working Group of the Psychiatric Genomics Consortium, 23andMe Research Team, Arpana Agrawal, Howard J. Edenberg, Kenneth S. Kendler, Cathryn M. Lewis, Patrick F. Sullivan, Naomi R. Wray, Joel Gelernter, Eske M. Derks
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- Journal:
- Psychological Medicine / Volume 49 / Issue 7 / May 2019
- Published online by Cambridge University Press:
- 01 April 2019, pp. 1218-1226
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Background
Despite established clinical associations among major depression (MD), alcohol dependence (AD), and alcohol consumption (AC), the nature of the causal relationship between them is not completely understood. We leveraged genome-wide data from the Psychiatric Genomics Consortium (PGC) and UK Biobank to test for the presence of shared genetic mechanisms and causal relationships among MD, AD, and AC.
MethodsLinkage disequilibrium score regression and Mendelian randomization (MR) were performed using genome-wide data from the PGC (MD: 135 458 cases and 344 901 controls; AD: 10 206 cases and 28 480 controls) and UK Biobank (AC-frequency: 438 308 individuals; AC-quantity: 307 098 individuals).
ResultsPositive genetic correlation was observed between MD and AD (rgMD−AD = + 0.47, P = 6.6 × 10−10). AC-quantity showed positive genetic correlation with both AD (rgAD−AC quantity = + 0.75, P = 1.8 × 10−14) and MD (rgMD−AC quantity = + 0.14, P = 2.9 × 10−7), while there was negative correlation of AC-frequency with MD (rgMD−AC frequency = −0.17, P = 1.5 × 10−10) and a non-significant result with AD. MR analyses confirmed the presence of pleiotropy among these four traits. However, the MD-AD results reflect a mediated-pleiotropy mechanism (i.e. causal relationship) with an effect of MD on AD (beta = 0.28, P = 1.29 × 10−6). There was no evidence for reverse causation.
ConclusionThis study supports a causal role for genetic liability of MD on AD based on genetic datasets including thousands of individuals. Understanding mechanisms underlying MD-AD comorbidity addresses important public health concerns and has the potential to facilitate prevention and intervention efforts.
Contributors
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- By Mitchell Aboulafia, Frederick Adams, Marilyn McCord Adams, Robert M. Adams, Laird Addis, James W. Allard, David Allison, William P. Alston, Karl Ameriks, C. Anthony Anderson, David Leech Anderson, Lanier Anderson, Roger Ariew, David Armstrong, Denis G. Arnold, E. J. Ashworth, Margaret Atherton, Robin Attfield, Bruce Aune, Edward Wilson Averill, Jody Azzouni, Kent Bach, Andrew Bailey, Lynne Rudder Baker, Thomas R. Baldwin, Jon Barwise, George Bealer, William Bechtel, Lawrence C. Becker, Mark A. Bedau, Ernst Behler, José A. Benardete, Ermanno Bencivenga, Jan Berg, Michael Bergmann, Robert L. Bernasconi, Sven Bernecker, Bernard Berofsky, Rod Bertolet, Charles J. Beyer, Christian Beyer, Joseph Bien, Joseph Bien, Peg Birmingham, Ivan Boh, James Bohman, Daniel Bonevac, Laurence BonJour, William J. Bouwsma, Raymond D. Bradley, Myles Brand, Richard B. Brandt, Michael E. Bratman, Stephen E. Braude, Daniel Breazeale, Angela Breitenbach, Jason Bridges, David O. Brink, Gordon G. Brittan, Justin Broackes, Dan W. Brock, Aaron Bronfman, Jeffrey E. Brower, Bartosz Brozek, Anthony Brueckner, Jeffrey Bub, Lara Buchak, Otavio Bueno, Ann E. Bumpus, Robert W. Burch, John Burgess, Arthur W. Burks, Panayot Butchvarov, Robert E. Butts, Marina Bykova, Patrick Byrne, David Carr, Noël Carroll, Edward S. Casey, Victor Caston, Victor Caston, Albert Casullo, Robert L. Causey, Alan K. L. Chan, Ruth Chang, Deen K. Chatterjee, Andrew Chignell, Roderick M. Chisholm, Kelly J. Clark, E. J. Coffman, Robin Collins, Brian P. Copenhaver, John Corcoran, John Cottingham, Roger Crisp, Frederick J. Crosson, Antonio S. Cua, Phillip D. Cummins, Martin Curd, Adam Cureton, Andrew Cutrofello, Stephen Darwall, Paul Sheldon Davies, Wayne A. Davis, Timothy Joseph Day, Claudio de Almeida, Mario De Caro, Mario De Caro, John Deigh, C. F. Delaney, Daniel C. Dennett, Michael R. DePaul, Michael Detlefsen, Daniel Trent Devereux, Philip E. Devine, John M. Dillon, Martin C. Dillon, Robert DiSalle, Mary Domski, Alan Donagan, Paul Draper, Fred Dretske, Mircea Dumitru, Wilhelm Dupré, Gerald Dworkin, John Earman, Ellery Eells, Catherine Z. Elgin, Berent Enç, Ronald P. Endicott, Edward Erwin, John Etchemendy, C. Stephen Evans, Susan L. Feagin, Solomon Feferman, Richard Feldman, Arthur Fine, Maurice A. Finocchiaro, William FitzPatrick, Richard E. Flathman, Gvozden Flego, Richard Foley, Graeme Forbes, Rainer Forst, Malcolm R. Forster, Daniel Fouke, Patrick Francken, Samuel Freeman, Elizabeth Fricker, Miranda Fricker, Michael Friedman, Michael Fuerstein, Richard A. Fumerton, Alan Gabbey, Pieranna Garavaso, Daniel Garber, Jorge L. A. Garcia, Robert K. Garcia, Don Garrett, Philip Gasper, Gerald Gaus, Berys Gaut, Bernard Gert, Roger F. Gibson, Cody Gilmore, Carl Ginet, Alan H. Goldman, Alvin I. Goldman, Alfonso Gömez-Lobo, Lenn E. Goodman, Robert M. Gordon, Stefan Gosepath, Jorge J. E. Gracia, Daniel W. Graham, George A. Graham, Peter J. Graham, Richard E. Grandy, I. Grattan-Guinness, John Greco, Philip T. Grier, Nicholas Griffin, Nicholas Griffin, David A. Griffiths, Paul J. Griffiths, Stephen R. Grimm, Charles L. Griswold, Charles B. Guignon, Pete A. Y. Gunter, Dimitri Gutas, Gary Gutting, Paul Guyer, Kwame Gyekye, Oscar A. Haac, Raul Hakli, Raul Hakli, Michael Hallett, Edward C. Halper, Jean Hampton, R. James Hankinson, K. R. Hanley, Russell Hardin, Robert M. Harnish, William Harper, David Harrah, Kevin Hart, Ali Hasan, William Hasker, John Haugeland, Roger Hausheer, William Heald, Peter Heath, Richard Heck, John F. Heil, Vincent F. Hendricks, Stephen Hetherington, Francis Heylighen, Kathleen Marie Higgins, Risto Hilpinen, Harold T. Hodes, Joshua Hoffman, Alan Holland, Robert L. Holmes, Richard Holton, Brad W. Hooker, Terence E. Horgan, Tamara Horowitz, Paul Horwich, Vittorio Hösle, Paul Hoβfeld, Daniel Howard-Snyder, Frances Howard-Snyder, Anne Hudson, Deal W. Hudson, Carl A. Huffman, David L. Hull, Patricia Huntington, Thomas Hurka, Paul Hurley, Rosalind Hursthouse, Guillermo Hurtado, Ronald E. Hustwit, Sarah Hutton, Jonathan Jenkins Ichikawa, Harry A. Ide, David Ingram, Philip J. Ivanhoe, Alfred L. Ivry, Frank Jackson, Dale Jacquette, Joseph Jedwab, Richard Jeffrey, David Alan Johnson, Edward Johnson, Mark D. Jordan, Richard Joyce, Hwa Yol Jung, Robert Hillary Kane, Tomis Kapitan, Jacquelyn Ann K. Kegley, James A. Keller, Ralph Kennedy, Sergei Khoruzhii, Jaegwon Kim, Yersu Kim, Nathan L. King, Patricia Kitcher, Peter D. Klein, E. D. Klemke, Virginia Klenk, George L. Kline, Christian Klotz, Simo Knuuttila, Joseph J. Kockelmans, Konstantin Kolenda, Sebastian Tomasz Kołodziejczyk, Isaac Kramnick, Richard Kraut, Fred Kroon, Manfred Kuehn, Steven T. Kuhn, Henry E. Kyburg, John Lachs, Jennifer Lackey, Stephen E. Lahey, Andrea Lavazza, Thomas H. Leahey, Joo Heung Lee, Keith Lehrer, Dorothy Leland, Noah M. Lemos, Ernest LePore, Sarah-Jane Leslie, Isaac Levi, Andrew Levine, Alan E. Lewis, Daniel E. Little, Shu-hsien Liu, Shu-hsien Liu, Alan K. L. Chan, Brian Loar, Lawrence B. Lombard, John Longeway, Dominic McIver Lopes, Michael J. Loux, E. J. Lowe, Steven Luper, Eugene C. Luschei, William G. Lycan, David Lyons, David Macarthur, Danielle Macbeth, Scott MacDonald, Jacob L. Mackey, Louis H. Mackey, Penelope Mackie, Edward H. Madden, Penelope Maddy, G. B. Madison, Bernd Magnus, Pekka Mäkelä, Rudolf A. Makkreel, David Manley, William E. Mann (W.E.M.), Vladimir Marchenkov, Peter Markie, Jean-Pierre Marquis, Ausonio Marras, Mike W. Martin, A. P. Martinich, William L. McBride, David McCabe, Storrs McCall, Hugh J. McCann, Robert N. McCauley, John J. McDermott, Sarah McGrath, Ralph McInerny, Daniel J. McKaughan, Thomas McKay, Michael McKinsey, Brian P. McLaughlin, Ernan McMullin, Anthonie Meijers, Jack W. Meiland, William Jason Melanson, Alfred R. Mele, Joseph R. Mendola, Christopher Menzel, Michael J. Meyer, Christian B. Miller, David W. Miller, Peter Millican, Robert N. Minor, Phillip Mitsis, James A. Montmarquet, Michael S. Moore, Tim Moore, Benjamin Morison, Donald R. Morrison, Stephen J. Morse, Paul K. Moser, Alexander P. D. Mourelatos, Ian Mueller, James Bernard Murphy, Mark C. Murphy, Steven Nadler, Jan Narveson, Alan Nelson, Jerome Neu, Samuel Newlands, Kai Nielsen, Ilkka Niiniluoto, Carlos G. Noreña, Calvin G. Normore, David Fate Norton, Nikolaj Nottelmann, Donald Nute, David S. Oderberg, Steve Odin, Michael O’Rourke, Willard G. Oxtoby, Heinz Paetzold, George S. Pappas, Anthony J. Parel, Lydia Patton, R. P. Peerenboom, Francis Jeffry Pelletier, Adriaan T. Peperzak, Derk Pereboom, Jaroslav Peregrin, Glen Pettigrove, Philip Pettit, Edmund L. Pincoffs, Andrew Pinsent, Robert B. Pippin, Alvin Plantinga, Louis P. Pojman, Richard H. Popkin, John F. Post, Carl J. Posy, William J. Prior, Richard Purtill, Michael Quante, Philip L. Quinn, Philip L. Quinn, Elizabeth S. Radcliffe, Diana Raffman, Gerard Raulet, Stephen L. Read, Andrews Reath, Andrew Reisner, Nicholas Rescher, Henry S. Richardson, Robert C. Richardson, Thomas Ricketts, Wayne D. Riggs, Mark Roberts, Robert C. Roberts, Luke Robinson, Alexander Rosenberg, Gary Rosenkranz, Bernice Glatzer Rosenthal, Adina L. Roskies, William L. Rowe, T. M. Rudavsky, Michael Ruse, Bruce Russell, Lilly-Marlene Russow, Dan Ryder, R. M. Sainsbury, Joseph Salerno, Nathan Salmon, Wesley C. Salmon, Constantine Sandis, David H. Sanford, Marco Santambrogio, David Sapire, Ruth A. Saunders, Geoffrey Sayre-McCord, Charles Sayward, James P. Scanlan, Richard Schacht, Tamar Schapiro, Frederick F. Schmitt, Jerome B. Schneewind, Calvin O. Schrag, Alan D. Schrift, George F. Schumm, Jean-Loup Seban, David N. Sedley, Kenneth Seeskin, Krister Segerberg, Charlene Haddock Seigfried, Dennis M. Senchuk, James F. Sennett, William Lad Sessions, Stewart Shapiro, Tommie Shelby, Donald W. Sherburne, Christopher Shields, Roger A. Shiner, Sydney Shoemaker, Robert K. Shope, Kwong-loi Shun, Wilfried Sieg, A. John Simmons, Robert L. Simon, Marcus G. Singer, Georgette Sinkler, Walter Sinnott-Armstrong, Matti T. Sintonen, Lawrence Sklar, Brian Skyrms, Robert C. Sleigh, Michael Anthony Slote, Hans Sluga, Barry Smith, Michael Smith, Robin Smith, Robert Sokolowski, Robert C. Solomon, Marta Soniewicka, Philip Soper, Ernest Sosa, Nicholas Southwood, Paul Vincent Spade, T. L. S. Sprigge, Eric O. Springsted, George J. Stack, Rebecca Stangl, Jason Stanley, Florian Steinberger, Sören Stenlund, Christopher Stephens, James P. Sterba, Josef Stern, Matthias Steup, M. A. Stewart, Leopold Stubenberg, Edith Dudley Sulla, Frederick Suppe, Jere Paul Surber, David George Sussman, Sigrún Svavarsdóttir, Zeno G. Swijtink, Richard Swinburne, Charles C. Taliaferro, Robert B. Talisse, John Tasioulas, Paul Teller, Larry S. Temkin, Mark Textor, H. S. Thayer, Peter Thielke, Alan Thomas, Amie L. Thomasson, Katherine Thomson-Jones, Joshua C. Thurow, Vzalerie Tiberius, Terrence N. Tice, Paul Tidman, Mark C. Timmons, William Tolhurst, James E. Tomberlin, Rosemarie Tong, Lawrence Torcello, Kelly Trogdon, J. D. Trout, Robert E. Tully, Raimo Tuomela, John Turri, Martin M. Tweedale, Thomas Uebel, Jennifer Uleman, James Van Cleve, Harry van der Linden, Peter van Inwagen, Bryan W. Van Norden, René van Woudenberg, Donald Phillip Verene, Samantha Vice, Thomas Vinci, Donald Wayne Viney, Barbara Von Eckardt, Peter B. M. Vranas, Steven J. Wagner, William J. Wainwright, Paul E. Walker, Robert E. Wall, Craig Walton, Douglas Walton, Eric Watkins, Richard A. Watson, Michael V. Wedin, Rudolph H. Weingartner, Paul Weirich, Paul J. Weithman, Carl Wellman, Howard Wettstein, Samuel C. Wheeler, Stephen A. White, Jennifer Whiting, Edward R. Wierenga, Michael Williams, Fred Wilson, W. Kent Wilson, Kenneth P. Winkler, John F. Wippel, Jan Woleński, Allan B. Wolter, Nicholas P. Wolterstorff, Rega Wood, W. Jay Wood, Paul Woodruff, Alison Wylie, Gideon Yaffe, Takashi Yagisawa, Yutaka Yamamoto, Keith E. Yandell, Xiaomei Yang, Dean Zimmerman, Günter Zoller, Catherine Zuckert, Michael Zuckert, Jack A. Zupko (J.A.Z.)
- Edited by Robert Audi, University of Notre Dame, Indiana
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- The Cambridge Dictionary of Philosophy
- Published online:
- 05 August 2015
- Print publication:
- 27 April 2015, pp ix-xxx
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- By Rony A. Adam, Gloria Bachmann, Nichole M. Barker, Randall B. Barnes, John Bennett, Inbar Ben-Shachar, Jonathan S. Berek, Sarah L. Berga, Monica W. Best, Eric J. Bieber, Frank M. Biro, Shan Biscette, Anita K. Blanchard, Candace Brown, Ronald T. Burkman, Joseph Buscema, John E. Buster, Michael Byas-Smith, Sandra Ann Carson, Judy C. Chang, Annie N. Y. Cheung, Mindy S. Christianson, Karishma Circelli, Daniel L. Clarke-Pearson, Larry J. Copeland, Bryan D. Cowan, Navneet Dhillon, Michael P. Diamond, Conception Diaz-Arrastia, Nicole M. Donnellan, Michael L. Eisenberg, Eric Eisenhauer, Sebastian Faro, J. Stuart Ferriss, Lisa C. Flowers, Susan J. Freeman, Leda Gattoc, Claudine Marie Gayle, Timothy M. Geiger, Jennifer S. Gell, Alan N. Gordon, Victoria L. Green, Jon K. Hathaway, Enrique Hernandez, S. Paige Hertweck, Randall S. Hines, Ira R. Horowitz, Fred M. Howard, William W. Hurd, Fidan Israfilbayli, Denise J. Jamieson, Carolyn R. Jaslow, Erika B. Johnston-MacAnanny, Rohna M. Kearney, Namita Khanna, Caroline C. King, Jeremy A. King, Ira J. Kodner, Tamara Kolev, Athena P. Kourtis, S. Robert Kovac, Ertug Kovanci, William H. Kutteh, Eduardo Lara-Torre, Pallavi Latthe, Herschel W. Lawson, Ronald L. Levine, Frank W. Ling, Larry I. Lipshultz, Steven D. McCarus, Robert McLellan, Shruti Malik, Suketu M. Mansuria, Mohamed K. Mehasseb, Pamela J. Murray, Saloney Nazeer, Farr R. Nezhat, Hextan Y. S. Ngan, Gina M. Northington, Peggy A. Norton, Ruth M. O'Regan, Kristiina Parviainen, Resad P. Pasic, Tanja Pejovic, K. Ulrich Petry, Nancy A. Phillips, Ashish Pradhan, Elizabeth E. Puscheck, Suneetha Rachaneni, Devon M. Ramaeker, David B. Redwine, Robert L. Reid, Carla P. Roberts, Walter Romano, Peter G. Rose, Robert L. Rosenfield, Shon P. Rowan, Mack T. Ruffin, Janice M. Rymer, Evis Sala, Ritu Salani, Joseph S. Sanfilippo, Mahmood I. Shafi, Roger P. Smith, Meredith L. Snook, Thomas E. Snyder, Mary D. Stephenson, Thomas G. Stovall, Richard L. Sweet, Philip M. Toozs-Hobson, Togas Tulandi, Elizabeth R. Unger, Denise S. Uyar, Marion S. Verp, Rahi Victory, Tamara J. Vokes, Michelle J. Washington, Katharine O'Connell White, Paul E. Wise, Frank M. Wittmaack, Miya P. Yamamoto, Christine Yu, Howard A. Zacur
- Edited by Eric J. Bieber, Joseph S. Sanfilippo, University of Pittsburgh, Ira R. Horowitz, Emory University, Atlanta, Mahmood I. Shafi
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- Clinical Gynecology
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- 05 April 2015
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- 23 April 2015, pp viii-xiv
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- By Frank Andrasik, Melissa R. Andrews, Ana Inés Ansaldo, Evangelos G. Antzoulatos, Lianhua Bai, Ellen Barrett, Linamara Battistella, Nicolas Bayle, Michael S. Beattie, Peter J. Beek, Serafin Beer, Heinrich Binder, Claire Bindschaedler, Sarah Blanton, Tasia Bobish, Michael L. Boninger, Joseph F. Bonner, Chadwick B. Boulay, Vanessa S. Boyce, Anna-Katharine Brem, Jacqueline C. Bresnahan, Floor E. Buma, Mary Bartlett Bunge, John H. Byrne, Jeffrey R. Capadona, Stefano F. Cappa, Diana D. Cardenas, Leeanne M. Carey, S. Thomas Carmichael, Glauco A. P. Caurin, Pablo Celnik, Kimberly M. Christian, Stephanie Clarke, Leonardo G. Cohen, Adriana B. Conforto, Rory A. Cooper, Rosemarie Cooper, Steven C. Cramer, Armin Curt, Mark D’Esposito, Matthew B. Dalva, Gavriel David, Brandon Delia, Wenbin Deng, Volker Dietz, Bruce H. Dobkin, Marco Domeniconi, Edith Durand, Tracey Vause Earland, Georg Ebersbach, Jonathan J. Evans, James W. Fawcett, Uri Feintuch, Toby A. Ferguson, Marie T. Filbin, Diasinou Fioravante, Itzhak Fischer, Agnes Floel, Herta Flor, Karim Fouad, Richard S. J. Frackowiak, Peter H. Gorman, Thomas W. Gould, Jean-Michel Gracies, Amparo Gutierrez, Kurt Haas, C.D. Hall, Hans-Peter Hartung, Zhigang He, Jordan Hecker, Susan J. Herdman, Seth Herman, Leigh R. Hochberg, Ahmet Höke, Fay B. Horak, Jared C. Horvath, Richard L. Huganir, Friedhelm C. Hummel, Beata Jarosiewicz, Frances E. Jensen, Michael Jöbges, Larry M. Jordan, Jon H. Kaas, Andres M. Kanner, Noomi Katz, Matthew S. Kayser, Annmarie Kelleher, Gerd Kempermann, Timothy E. Kennedy, Jürg Kesselring, Fary Khan, Rachel Kizony, Jeffery D. Kocsis, Boudewijn J. Kollen, Hubertus Köller, John W. Krakauer, Hermano I. Krebs, Gert Kwakkel, Bradley Lang, Catherine E. Lang, Helmar C. Lehmann, Angelo C. Lepore, Glenn S. Le Prell, Mindy F. Levin, Joel M. Levine, David A. Low, Marilyn MacKay-Lyons, Jeffrey D. Macklis, Margaret Mak, Francine Malouin, William C. Mann, Paul D. Marasco, Christopher J. Mathias, Laura McClure, Jan Mehrholz, Lorne M. Mendell, Robert H. Miller, Carol Milligan, Beth Mineo, Simon W. Moore, Jennifer Morgan, Charbel E-H. Moussa, Martin Munz, Randolph J. Nudo, Joseph J. Pancrazio, Theresa Pape, Alvaro Pascual-Leone, Kristin M. Pearson-Fuhrhop, P. Hunter Peckham, Tamara L. Pelleshi, Catherine Verrier Piersol, Thomas Platz, Marcus Pohl, Dejan B. Popović, Andrew M. Poulos, Maulik Purohit, Hui-Xin Qi, Debbie Rand, Mahendra S. Rao, Josef P. Rauschecker, Aimee Reiss, Carol L. Richards, Keith M. Robinson, Melvyn Roerdink, John C. Rosenbek, Serge Rossignol, Edward S. Ruthazer, Arash Sahraie, Krishnankutty Sathian, Marc H. Schieber, Brian J. Schmidt, Michael E. Selzer, Mijail D. Serruya, Himanshu Sharma, Michael Shifman, Jerry Silver, Thomas Sinkjær, George M. Smith, Young-Jin Son, Tim Spencer, John D. Steeves, Oswald Steward, Sheela Stuart, Austin J. Sumner, Chin Lik Tan, Robert W. Teasell, Gareth Thomas, Aiko K. Thompson, Richard F. Thompson, Wesley J. Thompson, Erika Timar, Ceri T. Trevethan, Christopher Trimby, Gary R. Turner, Mark H. Tuszynski, Erna A. van Niekerk, Ricardo Viana, Difei Wang, Anthony B. Ward, Nick S. Ward, Stephen G. Waxman, Patrice L. Weiss, Jörg Wissel, Steven L. Wolf, Jonathan R. Wolpaw, Sharon Wood-Dauphinee, Ross D. Zafonte, Binhai Zheng, Richard D. Zorowitz
- Edited by Michael Selzer, Stephanie Clarke, Leonardo Cohen, Gert Kwakkel, Robert Miller, Case Western Reserve University, Ohio
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- Textbook of Neural Repair and Rehabilitation
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- 05 May 2014
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- 24 April 2014, pp ix-xvi
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- By Frank Andrasik, Melissa R. Andrews, Ana Inés Ansaldo, Evangelos G. Antzoulatos, Lianhua Bai, Ellen Barrett, Linamara Battistella, Nicolas Bayle, Michael S. Beattie, Peter J. Beek, Serafin Beer, Heinrich Binder, Claire Bindschaedler, Sarah Blanton, Tasia Bobish, Michael L. Boninger, Joseph F. Bonner, Chadwick B. Boulay, Vanessa S. Boyce, Anna-Katharine Brem, Jacqueline C. Bresnahan, Floor E. Buma, Mary Bartlett Bunge, John H. Byrne, Jeffrey R. Capadona, Stefano F. Cappa, Diana D. Cardenas, Leeanne M. Carey, S. Thomas Carmichael, Glauco A. P. Caurin, Pablo Celnik, Kimberly M. Christian, Stephanie Clarke, Leonardo G. Cohen, Adriana B. Conforto, Rory A. Cooper, Rosemarie Cooper, Steven C. Cramer, Armin Curt, Mark D’Esposito, Matthew B. Dalva, Gavriel David, Brandon Delia, Wenbin Deng, Volker Dietz, Bruce H. Dobkin, Marco Domeniconi, Edith Durand, Tracey Vause Earland, Georg Ebersbach, Jonathan J. Evans, James W. Fawcett, Uri Feintuch, Toby A. Ferguson, Marie T. Filbin, Diasinou Fioravante, Itzhak Fischer, Agnes Floel, Herta Flor, Karim Fouad, Richard S. J. Frackowiak, Peter H. Gorman, Thomas W. Gould, Jean-Michel Gracies, Amparo Gutierrez, Kurt Haas, C.D. Hall, Hans-Peter Hartung, Zhigang He, Jordan Hecker, Susan J. Herdman, Seth Herman, Leigh R. Hochberg, Ahmet Höke, Fay B. Horak, Jared C. Horvath, Richard L. Huganir, Friedhelm C. Hummel, Beata Jarosiewicz, Frances E. Jensen, Michael Jöbges, Larry M. Jordan, Jon H. Kaas, Andres M. Kanner, Noomi Katz, Matthew S. Kayser, Annmarie Kelleher, Gerd Kempermann, Timothy E. Kennedy, Jürg Kesselring, Fary Khan, Rachel Kizony, Jeffery D. Kocsis, Boudewijn J. Kollen, Hubertus Köller, John W. Krakauer, Hermano I. Krebs, Gert Kwakkel, Bradley Lang, Catherine E. Lang, Helmar C. Lehmann, Angelo C. Lepore, Glenn S. Le Prell, Mindy F. Levin, Joel M. Levine, David A. Low, Marilyn MacKay-Lyons, Jeffrey D. Macklis, Margaret Mak, Francine Malouin, William C. Mann, Paul D. Marasco, Christopher J. Mathias, Laura McClure, Jan Mehrholz, Lorne M. Mendell, Robert H. Miller, Carol Milligan, Beth Mineo, Simon W. Moore, Jennifer Morgan, Charbel E-H. Moussa, Martin Munz, Randolph J. Nudo, Joseph J. Pancrazio, Theresa Pape, Alvaro Pascual-Leone, Kristin M. Pearson-Fuhrhop, P. Hunter Peckham, Tamara L. Pelleshi, Catherine Verrier Piersol, Thomas Platz, Marcus Pohl, Dejan B. Popović, Andrew M. Poulos, Maulik Purohit, Hui-Xin Qi, Debbie Rand, Mahendra S. Rao, Josef P. Rauschecker, Aimee Reiss, Carol L. Richards, Keith M. Robinson, Melvyn Roerdink, John C. Rosenbek, Serge Rossignol, Edward S. Ruthazer, Arash Sahraie, Krishnankutty Sathian, Marc H. Schieber, Brian J. Schmidt, Michael E. Selzer, Mijail D. Serruya, Himanshu Sharma, Michael Shifman, Jerry Silver, Thomas Sinkjær, George M. Smith, Young-Jin Son, Tim Spencer, John D. Steeves, Oswald Steward, Sheela Stuart, Austin J. Sumner, Chin Lik Tan, Robert W. Teasell, Gareth Thomas, Aiko K. Thompson, Richard F. Thompson, Wesley J. Thompson, Erika Timar, Ceri T. Trevethan, Christopher Trimby, Gary R. Turner, Mark H. Tuszynski, Erna A. van Niekerk, Ricardo Viana, Difei Wang, Anthony B. Ward, Nick S. Ward, Stephen G. Waxman, Patrice L. Weiss, Jörg Wissel, Steven L. Wolf, Jonathan R. Wolpaw, Sharon Wood-Dauphinee, Ross D. Zafonte, Binhai Zheng, Richard D. Zorowitz
- Edited by Michael E. Selzer, Stephanie Clarke, Leonardo G. Cohen, Gert Kwakkel, Robert H. Miller, Case Western Reserve University, Ohio
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- Textbook of Neural Repair and Rehabilitation
- Published online:
- 05 June 2014
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- 24 April 2014, pp ix-xvi
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- By Victoria M. Allen, Frederic Amant, Sarah Armstrong, Thomas F. Baskett, Michael A. Belfort, Meredith Birsner, Renee D. Boss, Leanne Bricker, Josaphat K. Byamugisha, Giorgio Capogna, Michael P. Casaer, Frank A. Chervenak, Vicki Clark, Filip Claus, Malachy O. Columb, Charles Cox, Jean T. Cox, Vegard Dahl, John Davison, Jan Deprest, Clifford S. Deutschman, Roland Devlieger, Karim Djekidel, Steven Dymarkowski, Roshan Fernando, Clare Fitzpatrick, Sreedhar Gaddipati, Thierry Girard, Emily Gordon, Ian A. Greer, David Grooms, Sina Haeri, Katy Harrison, Edward J. Hayes, Michelle Hladunewich, Andra H. James, Tracey Johnston, Bellal Joseph, Erin Keely, Ruth Landau, Stephen E. Lapinsky, Susanna I. Lee, Larry Leeman, Hennie Lombaard, Stephen Lu, Alison MacArthur, Laura A. Magee, Paul E. Marik, Laurence B. McCullough, Alexandre Mignon, Carlo Missant, Jack Moodley, Lisa E. Moore, Kate Morse, Warwick D. Ngan Kee, Catherine Nelson-Piercy, Clemens M. Ortner, Geraldine O’Sullivan, Luis D. Pacheco, Fathima Paruk, Melina Pectasides, Nigel Pereira, Patricia Peticca, Sharon T. Phelan, Felicity Plaat, Lauren A. Plante, Michael P. Plevyak, Dianne Plews, Wendy Pollock, Laura C. Price, Peter Rhee, Leiv Arne Rosseland, Kathryn M. Rowan, Helen Ryan, Helen Scholefield, Neil S. Seligman, Nadir Sharawi, Alex Sia, Bob Silver, Mieke Soens, Ulrich J. Spreng, Silvia Stirparo, Nova Szoka, Andrew Tang, Kha M. Tran, Els Troost, Lawrence C. Tsen, Derek Tuffnell, Kristel Van Calsteren, Marc Van de Velde, Marcel Vercauteren, Chris Verslype, Peter von Dadelszen, Carl Waldman, Michelle Walters, Linda Watkins, Paul Westhead, Cynthia A. Wong, Gerda G. Zeeman, Joost J. Zwart
- Edited by Marc van de Velde, Helen Scholefield, Lauren A. Plante
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- Book:
- Maternal Critical Care
- Published online:
- 05 July 2013
- Print publication:
- 04 July 2013, pp ix-xiv
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- By Blair C. Armstrong, David A. Balota, Lawrence W. Barsalou, Jos J. A. Van Berkum, Lera Boroditsky, Gregory A. Bryant, Cristina Cacciari, Joana Cholin, Morten H. Christiansen, Stella Christie, Eve V. Clark, Herbert H. Clark, Eliana Colunga, John F. Connolly, Michael J. Cortese, Seana Coulson, George S. Cree, Christopher M. Crew, Gary S. Dell, Kevin Diependaele, Judit Druks, Thomas A. Farmer, Anne Fernald, Kelly Forbes, Carol A. Fowler, Michael Frank, Stephen J. Frost, Dedre Gentner, Raymond W. Gibbs, Monica Gonzalez-Marquez, Arthur C. Graesser, Jonathan Grainger, Zenzi M. Griffin, Mary Hare, Harlan D. Harris, Marc F. Joanisse, Leonard Katz, Albert Kim, Gina R. Kuperberg, Nicole Landi, Birte Loenneker-Rodman, Danielle S. MacNamara, James S. Magnuson, Ken McRae, W. Einar Mencl, Daniel Mirman, Jennifer B. Misyak, Srini Narayanan, Kate Nation, Randy L. Newman, Lee Osterhout, Roberto Padovani, Karalyn Patterson, Kenneth R. Pugh, Terry Regier, Douglas Roland, Jay G. Rueckl, Vasile Rus, Jenny R. Saffran, Sarah D. Sahni, Arthur G. Samuel, Rebecca Sandak, Dominiek Sandra, Sophie Scott, Mark S. Seidenberg, Linda B. Smith, Michael J. Spivey, Meghan Sumner, Daniel Tranel, Gabriella Vigliocco, Nicole L. Wilson, Anna Woollams
- Edited by Michael Spivey, Ken McRae, University of Western Ontario, Marc Joanisse, University of Western Ontario
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- Book:
- The Cambridge Handbook of Psycholinguistics
- Published online:
- 05 November 2012
- Print publication:
- 20 August 2012, pp xi-xiv
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The Hispanic Paradox in Twin Pregnancies
- Barbara Luke, Morton B. Brown, Ruta B. Misiunas, Victor H. Gonzalez-Quintero, Clark Nugent, Cosmas van de Ven, Frank R. Witter, Roger B. Newman, Mary D'Alton, Gary D. V. Hankins, David A. Grainger, George A. Macones
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- Journal:
- Twin Research and Human Genetics / Volume 8 / Issue 5 / 01 October 2005
- Published online by Cambridge University Press:
- 21 February 2012, pp. 532-537
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The objective of this study was to compare length of gestation, fetal growth, and birthweight by race/ethnicity and pregravid weight groups in twin pregnancies. Three thousand and thirty-six twin pregnancies of 28 weeks or more gestation were divided by race/ethnicity (White, Black and Hispanic), and pregravid body mass index (BMI) groups (less than 25.0 vs. 25.0 or more). Outcomes were modeled using multiple regression, controlling for confounders, with White non-Hispanic women as the reference group. Hispanic women had the highest average birthweight and the longest gestation, as well as the lowest proportions of low birthweight, very low birthweight, preterm and early preterm births of the 3 race/ethnicity groups. In the multivariate analyses, Hispanic women had significantly longer gestations (by 7.8 days) and faster rates of fetal growth midgestation (20 to 28 weeks, by 17.4 g/week) and late gestation (after 28 weeks, by 5.3 g/week), whereas Black women had significantly slower rates of fetal growth (by 5.7 g/week and by 4.5 g/week, respectively). These findings in twins reflect the racial and ethnic disparities previously shown in singletons, including the Hispanic paradox of longer gestations and higher rates of fetal growth.
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- By Jean-Noël Aletti, Ian Breward, James P. Byrd, Noriel Capulong, Elizabeth A. Clark, Valentin Dedji, Beatriz de Vasconcellos Dias, Ramathate T. H. Dolamo, Noel Leo Erskine, George Thomas Kurian, Armando Lampe, Marjorie Lewis, Frank D. Macchia, Fortunato Mallimaci, Bonnie J. Miller-McLemore, Nektarios Morrow, Gerald O'Collins, Muriel Orevillo-Montenegro, Peter Paris, Keith F. Pecklers, Bishop Yeznik Petrossian, María Alicia Puente Lutteroth, Fernando F. Segovia, Karel Steenbrink, Elsa Tamez, Archbishop Demetrios, Justin Ukpong, Andrew Walls, Patricia A. Ward, Paul Zamora
- Edited by Daniel Patte, Vanderbilt University, Tennessee
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- The Cambridge Dictionary of Christianity
- Published online:
- 05 August 2012
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- 20 September 2010, pp ix-x
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- By Rose Teteki Abbey, K. C. Abraham, David Tuesday Adamo, LeRoy H. Aden, Efrain Agosto, Victor Aguilan, Gillian T. W. Ahlgren, Charanjit Kaur AjitSingh, Dorothy B E A Akoto, Giuseppe Alberigo, Daniel E. Albrecht, Ruth Albrecht, Daniel O. Aleshire, Urs Altermatt, Anand Amaladass, Michael Amaladoss, James N. Amanze, Lesley G. Anderson, Thomas C. Anderson, Victor Anderson, Hope S. Antone, María Pilar Aquino, Paula Arai, Victorio Araya Guillén, S. Wesley Ariarajah, Ellen T. Armour, Brett Gregory Armstrong, Atsuhiro Asano, Naim Stifan Ateek, Mahmoud Ayoub, John Alembillah Azumah, Mercedes L. García Bachmann, Irena Backus, J. Wayne Baker, Mieke Bal, Lewis V. Baldwin, William Barbieri, António Barbosa da Silva, David Basinger, Bolaji Olukemi Bateye, Oswald Bayer, Daniel H. Bays, Rosalie Beck, Nancy Elizabeth Bedford, Guy-Thomas Bedouelle, Chorbishop Seely Beggiani, Wolfgang Behringer, Christopher M. Bellitto, Byard Bennett, Harold V. Bennett, Teresa Berger, Miguel A. Bernad, Henley Bernard, Alan E. Bernstein, Jon L. Berquist, Johannes Beutler, Ana María Bidegain, Matthew P. Binkewicz, Jennifer Bird, Joseph Blenkinsopp, Dmytro Bondarenko, Paulo Bonfatti, Riet en Pim Bons-Storm, Jessica A. Boon, Marcus J. Borg, Mark Bosco, Peter C. Bouteneff, François Bovon, William D. Bowman, Paul S. Boyer, David Brakke, Richard E. Brantley, Marcus Braybrooke, Ian Breward, Ênio José da Costa Brito, Jewel Spears Brooker, Johannes Brosseder, Nicholas Canfield Read Brown, Robert F. Brown, Pamela K. Brubaker, Walter Brueggemann, Bishop Colin O. Buchanan, Stanley M. Burgess, Amy Nelson Burnett, J. Patout Burns, David B. Burrell, David Buttrick, James P. Byrd, Lavinia Byrne, Gerado Caetano, Marcos Caldas, Alkiviadis Calivas, William J. Callahan, Salvatore Calomino, Euan K. Cameron, William S. Campbell, Marcelo Ayres Camurça, Daniel F. Caner, Paul E. Capetz, Carlos F. Cardoza-Orlandi, Patrick W. Carey, Barbara Carvill, Hal Cauthron, Subhadra Mitra Channa, Mark D. Chapman, James H. Charlesworth, Kenneth R. Chase, Chen Zemin, Luciano Chianeque, Philip Chia Phin Yin, Francisca H. Chimhanda, Daniel Chiquete, John T. Chirban, Soobin Choi, Robert Choquette, Mita Choudhury, Gerald Christianson, John Chryssavgis, Sejong Chun, Esther Chung-Kim, Charles M. A. Clark, Elizabeth A. Clark, Sathianathan Clarke, Fred Cloud, John B. Cobb, W. Owen Cole, John A Coleman, John J. Collins, Sylvia Collins-Mayo, Paul K. Conkin, Beth A. Conklin, Sean Connolly, Demetrios J. Constantelos, Michael A. Conway, Paula M. Cooey, Austin Cooper, Michael L. Cooper-White, Pamela Cooper-White, L. William Countryman, Sérgio Coutinho, Pamela Couture, Shannon Craigo-Snell, James L. Crenshaw, David Crowner, Humberto Horacio Cucchetti, Lawrence S. Cunningham, Elizabeth Mason Currier, Emmanuel Cutrone, Mary L. Daniel, David D. Daniels, Robert Darden, Rolf Darge, Isaiah Dau, Jeffry C. Davis, Jane Dawson, Valentin Dedji, John W. de Gruchy, Paul DeHart, Wendy J. Deichmann Edwards, Miguel A. De La Torre, George E. Demacopoulos, Thomas de Mayo, Leah DeVun, Beatriz de Vasconcellos Dias, Dennis C. Dickerson, John M. Dillon, Luis Miguel Donatello, Igor Dorfmann-Lazarev, Susanna Drake, Jonathan A. Draper, N. Dreher Martin, Otto Dreydoppel, Angelyn Dries, A. J. Droge, Francis X. D'Sa, Marilyn Dunn, Nicole Wilkinson Duran, Rifaat Ebied, Mark J. Edwards, William H. Edwards, Leonard H. Ehrlich, Nancy L. Eiesland, Martin Elbel, J. Harold Ellens, Stephen Ellingson, Marvin M. Ellison, Robert Ellsberg, Jean Bethke Elshtain, Eldon Jay Epp, Peter C. Erb, Tassilo Erhardt, Maria Erling, Noel Leo Erskine, Gillian R. Evans, Virginia Fabella, Michael A. Fahey, Edward Farley, Margaret A. Farley, Wendy Farley, Robert Fastiggi, Seena Fazel, Duncan S. Ferguson, Helwar Figueroa, Paul Corby Finney, Kyriaki Karidoyanes FitzGerald, Thomas E. FitzGerald, John R. Fitzmier, Marie Therese Flanagan, Sabina Flanagan, Claude Flipo, Ronald B. Flowers, Carole Fontaine, David Ford, Mary Ford, Stephanie A. Ford, Jim Forest, William Franke, Robert M. Franklin, Ruth Franzén, Edward H. Friedman, Samuel Frouisou, Lorelei F. Fuchs, Jojo M. Fung, Inger Furseth, Richard R. Gaillardetz, Brandon Gallaher, China Galland, Mark Galli, Ismael García, Tharscisse Gatwa, Jean-Marie Gaudeul, Luis María Gavilanes del Castillo, Pavel L. Gavrilyuk, Volney P. Gay, Metropolitan Athanasios Geevargis, Kondothra M. George, Mary Gerhart, Simon Gikandi, Maurice Gilbert, Michael J. Gillgannon, Verónica Giménez Beliveau, Terryl Givens, Beth Glazier-McDonald, Philip Gleason, Menghun Goh, Brian Golding, Bishop Hilario M. Gomez, Michelle A. Gonzalez, Donald K. Gorrell, Roy Gottfried, Tamara Grdzelidze, Joel B. Green, Niels Henrik Gregersen, Cristina Grenholm, Herbert Griffiths, Eric W. Gritsch, Erich S. Gruen, Christoffer H. Grundmann, Paul H. Gundani, Jon P. Gunnemann, Petre Guran, Vidar L. Haanes, Jeremiah M. Hackett, Getatchew Haile, Douglas John Hall, Nicholas Hammond, Daphne Hampson, Jehu J. Hanciles, Barry Hankins, Jennifer Haraguchi, Stanley S. Harakas, Anthony John Harding, Conrad L. Harkins, J. William Harmless, Marjory Harper, Amir Harrak, Joel F. Harrington, Mark W. Harris, Susan Ashbrook Harvey, Van A. Harvey, R. Chris Hassel, Jione Havea, Daniel Hawk, Diana L. Hayes, Leslie Hayes, Priscilla Hayner, S. Mark Heim, Simo Heininen, Richard P. Heitzenrater, Eila Helander, David Hempton, Scott H. Hendrix, Jan-Olav Henriksen, Gina Hens-Piazza, Carter Heyward, Nicholas J. Higham, David Hilliard, Norman A. Hjelm, Peter C. Hodgson, Arthur Holder, M. Jan Holton, Dwight N. Hopkins, Ronnie Po-chia Hsia, Po-Ho Huang, James Hudnut-Beumler, Jennifer S. Hughes, Leonard M. Hummel, Mary E. Hunt, Laennec Hurbon, Mark Hutchinson, Susan E. Hylen, Mary Beth Ingham, H. Larry Ingle, Dale T. Irvin, Jon Isaak, Paul John Isaak, Ada María Isasi-Díaz, Hans Raun Iversen, Margaret C. Jacob, Arthur James, Maria Jansdotter-Samuelsson, David Jasper, Werner G. Jeanrond, Renée Jeffery, David Lyle Jeffrey, Theodore W. Jennings, David H. Jensen, Robin Margaret Jensen, David Jobling, Dale A. Johnson, Elizabeth A. Johnson, Maxwell E. Johnson, Sarah Johnson, Mark D. Johnston, F. Stanley Jones, James William Jones, John R. Jones, Alissa Jones Nelson, Inge Jonsson, Jan Joosten, Elizabeth Judd, Mulambya Peggy Kabonde, Robert Kaggwa, Sylvester Kahakwa, Isaac Kalimi, Ogbu U. Kalu, Eunice Kamaara, Wayne C. Kannaday, Musimbi Kanyoro, Veli-Matti Kärkkäinen, Frank Kaufmann, Léon Nguapitshi Kayongo, Richard Kearney, Alice A. Keefe, Ralph Keen, Catherine Keller, Anthony J. Kelly, Karen Kennelly, Kathi Lynn Kern, Fergus Kerr, Edward Kessler, George Kilcourse, Heup Young Kim, Kim Sung-Hae, Kim Yong-Bock, Kim Yung Suk, Richard King, Thomas M. King, Robert M. Kingdon, Ross Kinsler, Hans G. Kippenberg, Cheryl A. Kirk-Duggan, Clifton Kirkpatrick, Leonid Kishkovsky, Nadieszda Kizenko, Jeffrey Klaiber, Hans-Josef Klauck, Sidney Knight, Samuel Kobia, Robert Kolb, Karla Ann Koll, Heikki Kotila, Donald Kraybill, Philip D. W. Krey, Yves Krumenacker, Jeffrey Kah-Jin Kuan, Simanga R. Kumalo, Peter Kuzmic, Simon Shui-Man Kwan, Kwok Pui-lan, André LaCocque, Stephen E. Lahey, John Tsz Pang Lai, Emiel Lamberts, Armando Lampe, Craig Lampe, Beverly J. Lanzetta, Eve LaPlante, Lizette Larson-Miller, Ariel Bybee Laughton, Leonard Lawlor, Bentley Layton, Robin A. Leaver, Karen Lebacqz, Archie Chi Chung Lee, Marilyn J. Legge, Hervé LeGrand, D. L. LeMahieu, Raymond Lemieux, Bill J. Leonard, Ellen M. Leonard, Outi Leppä, Jean Lesaulnier, Nantawan Boonprasat Lewis, Henrietta Leyser, Alexei Lidov, Bernard Lightman, Paul Chang-Ha Lim, Carter Lindberg, Mark R. Lindsay, James R. Linville, James C. Livingston, Ann Loades, David Loades, Jean-Claude Loba-Mkole, Lo Lung Kwong, Wati Longchar, Eleazar López, David W. Lotz, Andrew Louth, Robin W. Lovin, William Luis, Frank D. Macchia, Diarmaid N. J. MacCulloch, Kirk R. MacGregor, Marjory A. MacLean, Donald MacLeod, Tomas S. Maddela, Inge Mager, Laurenti Magesa, David G. Maillu, Fortunato Mallimaci, Philip Mamalakis, Kä Mana, Ukachukwu Chris Manus, Herbert Robinson Marbury, Reuel Norman Marigza, Jacqueline Mariña, Antti Marjanen, Luiz C. L. Marques, Madipoane Masenya (ngwan'a Mphahlele), Caleb J. D. Maskell, Steve Mason, Thomas Massaro, Fernando Matamoros Ponce, András Máté-Tóth, Odair Pedroso Mateus, Dinis Matsolo, Fumitaka Matsuoka, John D'Arcy May, Yelena Mazour-Matusevich, Theodore Mbazumutima, John S. McClure, Christian McConnell, Lee Martin McDonald, Gary B. McGee, Thomas McGowan, Alister E. McGrath, Richard J. McGregor, John A. McGuckin, Maud Burnett McInerney, Elsie Anne McKee, Mary B. McKinley, James F. McMillan, Ernan McMullin, Kathleen E. McVey, M. 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Yee, Viktor Yelensky, Yeo Khiok-Khng, Gustav K. K. Yeung, Angela Yiu, Amos Yong, Yong Ting Jin, You Bin, Youhanna Nessim Youssef, Eliana Yunes, Robert Michael Zaller, Valarie H. Ziegler, Barbara Brown Zikmund, Joyce Ann Zimmerman, Aurora Zlotnik, Zhuo Xinping
- Edited by Daniel Patte, Vanderbilt University, Tennessee
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- The Cambridge Dictionary of Christianity
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- 05 August 2012
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- 20 September 2010, pp xi-xliv
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Unrestricted whey for fattening pigs
- R. Braude, P. M. Clarke, K. G. Mitchell, A. S. Cray, A. Franke, P. H. Sedgwick
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- The Journal of Agricultural Science / Volume 49 / Issue 3 / October 1957
- Published online by Cambridge University Press:
- 27 March 2009, pp. 347-356
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1. Results are reported from two experiments in a series to determine the optimal amount of meal to be fed in conjunction with unrestricted whey for fattening pigs.
2. In both experiments, one carried out during the summer and the other during the winter season, the same four treatments were given. The control pigs received meal ad. lib up to a maximum of 6½ lb./ head daily. Pigs on the other three treatments received whey ad lib., and either 3 lb., or 3 lb. reduced at two different stages to 2 lb. of meal per head daily. There were ten pens of nine pigs on each treatment, involving a total of 360 pigs. Comprehensive carcass measurements were made on all pigs.
3. The data obtained showed that satisfactory results could be obtained by feeding a daily allowance of 3 lb./pig of a proprietary sow and weaner meal throughout the fattening period, in conjunction with unrestricted whey. Where the utilization of as much whey and as little meal as possible was required, it was shown that a reduction from 3 to 2 lb. meal/pig/day by the 13th week of life could be made without adverse effects, apart from an increase of approximately 12 days in the time taken to reach bacon weights.
4. Carcass grading results of all whey-fed pigs were reasonably satisfactory, but both the carcass grading and general performance of the control animals was not good. Possible reasons for this were discussed.
5. Data concerning the pattern of food consumption over 14-day periods throughout the experiments were presented. Pigs given 3 lb. of meal/day throughout, or 3 lb. reduced to 2 lb./day, consumed up to approximately 3¼–3½ or 3¾–4 gal. of whey/day respectively.
Contributors
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- By Graham Allan, Donna M. Allen, Irwin Altman, Arthur Aron, Donald H. Baucom, Steven R. H. Beach, Ellen Berscheid, Rosemary Blieszner, Jeffrey Boase, Tyfany M. J. Boettcher, Barbara B. Brown, Abraham P. Buunk, Lorne Campbell, Daniel J. Canary, Rodney Cate, John P. Caughlin, Mahnaz Charania, Jennie Y. Chen, F. Scott Christopher, Jennifer A. Clarke, Marilyn Coleman, W. Andrew Collins, Michael K. Coolsen, Nathan R. Cottle, Carolyn E. Cutrona, Marianne Dainton, Valerian J. Derlega, Lisa M. Diamond, Pieternel Dijkstra, Steve Duck, Pearl A. Dykstra, Norman B. Epstein, Beverley Fehr, Frank D. Fincham, Helen E. Fisher, Julie Fitness, Garth J. O. Fletcher, Myron D. Friesen, Lawrence Ganong, Kelli A. Gardner, Jenny de Jong Gierveld, Robin Goodwin, Christine R. Gray, Kathryn Greene, David W. Harris, Willard W. Hartup, John H. Harvey, Kathi L. Heffner, Ted L. Huston, William J. Ickes, Emily A. Impett, Michael P. Johnson, Deborah J. Jones, Deborah A. Kashy, Janice K. Kiecolt‐Glaser, Jeffrey L. Kirchner, Brighid M. Kleinman, Galena H. Kline, Mark L. Knapp, Ascan Koerner, Jean‐Philippe Laurenceau, Kim Leon, Timothy J. Loving, Stephanie D. Madsen, Howard J. Markman, Alicia Mathews, Mario Mikulincer, Patricia Noller, Nickola C. Overall, Letitia Anne Peplau, Daniel Perlman, Sally Planalp, Urmila Pillay, Nicole D. Pleasant, Caryl E. Rusbult, Barbara R. Sarason, Irwin G. Sarason, Phillip R. Shaver, Alan L. Sillars, Jeffry A. Simpson, Susan Sprecher, Susan Stanton, Greg Strong, Catherine A. Surra, Anita L. Vangelisti, C. Arthur VanLear, Theo van Tilburg, Barry Wellman, Amy Wenzel, Carol M. Werner, Adam R. West, Sarah W. Whitton, Heike A. Winterheld
- Edited by Anita L. Vangelisti, University of Texas, Austin, Daniel Perlman, University of British Columbia, Vancouver
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- The Cambridge Handbook of Personal Relationships
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- 05 June 2012
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- 05 June 2006, pp xvii-xxii
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Looking Backward, Looking Forward: MLA Members Speak
- April Alliston, Elizabeth Ammons, Jean Arnold, Nina Baym, Sandra L. Beckett, Peter G. Beidler, Roger A. Berger, Sandra Bermann, J.J. Wilson, Troy Boone, Alison Booth, Wayne C. Booth, James Phelan, Marie Borroff, Ihab Hassan, Ulrich Weisstein, Zack Bowen, Jill Campbell, Dan Campion, Jay Caplan, Maurice Charney, Beverly Lyon Clark, Robert A. Colby, Thomas C. Coleman III, Nicole Cooley, Richard Dellamora, Morris Dickstein, Terrell Dixon, Emory Elliott, Caryl Emerson, Ann W. Engar, Lars Engle, Kai Hammermeister, N. N. Feltes, Mary Anne Ferguson, Annie Finch, Shelley Fisher Fishkin, Jerry Aline Flieger, Norman Friedman, Rosemarie Garland-Thomson, Sandra M. Gilbert, Laurie Grobman, George Guida, Liselotte Gumpel, R. K. Gupta, Florence Howe, Cathy L. Jrade, Richard A. Kaye, Calhoun Winton, Murray Krieger, Robert Langbaum, Richard A. Lanham, Marilee Lindemann, Paul Michael Lützeler, Thomas J. Lynn, Juliet Flower MacCannell, Michelle A. Massé, Irving Massey, Georges May, Christian W. Hallstein, Gita May, Lucy McDiarmid, Ellen Messer-Davidow, Koritha Mitchell, Robin Smiles, Kenyatta Albeny, George Monteiro, Joel Myerson, Alan Nadel, Ashton Nichols, Jeffrey Nishimura, Neal Oxenhandler, David Palumbo-Liu, Vincent P. Pecora, David Porter, Nancy Potter, Ronald C. Rosbottom, Elias L. Rivers, Gerhard F. Strasser, J. L. Styan, Marianna De Marco Torgovnick, Gary Totten, David van Leer, Asha Varadharajan, Orrin N. C. Wang, Sharon Willis, Louise E. Wright, Donald A. Yates, Takayuki Yokota-Murakami, Richard E. Zeikowitz, Angelika Bammer, Dale Bauer, Karl Beckson, Betsy A. Bowen, Stacey Donohue, Sheila Emerson, Gwendolyn Audrey Foster, Jay L. Halio, Karl Kroeber, Terence Hawkes, William B. Hunter, Mary Jambus, Willard F. King, Nancy K. Miller, Jody Norton, Ann Pellegrini, S. P. Rosenbaum, Lorie Roth, Robert Scholes, Joanne Shattock, Rosemary T. VanArsdel, Alfred Bendixen, Alarma Kathleen Brown, Michael J. Kiskis, Debra A. Castillo, Rey Chow, John F. Crossen, Robert F. Fleissner, Regenia Gagnier, Nicholas Howe, M. Thomas Inge, Frank Mehring, Hyungji Park, Jahan Ramazani, Kenneth M. Roemer, Deborah D. Rogers, A. LaVonne Brown Ruoff, Regina M. Schwartz, John T. Shawcross, Brenda R. Silver, Andrew von Hendy, Virginia Wright Wexman, Britta Zangen, A. Owen Aldridge, Paula R. Backscheider, Roland Bartel, E. M. Forster, Milton Birnbaum, Jonathan Bishop, Crystal Downing, Frank H. Ellis, Roberto Forns-Broggi, James R. Giles, Mary E. Giles, Susan Blair Green, Madelyn Gutwirth, Constance B. Hieatt, Titi Adepitan, Edgar C. Knowlton, Jr., Emanuel Mussman, Sally Todd Nelson, Robert O. Preyer, David Diego Rodriguez, Guy Stern, James Thorpe, Robert J. Wilson, Rebecca S. Beal, Joyce Simutis, Betsy Bowden, Sara Cooper, Wheeler Winston Dixon, Tarek el Ariss, Richard Jewell, John W. Kronik, Wendy Martin, Stuart Y. McDougal, Hugo Méndez-Ramírez, Ivy Schweitzer, Armand E. Singer, G. Thomas Tanselle, Tom Bishop, Mary Ann Caws, Marcel Gutwirth, Christophe Ippolito, Lawrence D. Kritzman, James Longenbach, Tim McCracken, Wolfe S. Molitor, Diane Quantic, Gregory Rabassa, Ellen M. Tsagaris, Anthony C. Yu, Betty Jean Craige, Wendell V. Harris, J. Hillis Miller, Jesse G. Swan, Helene Zimmer-Loew, Peter Berek, James Chandler, Hanna K. Charney, Philip Cohen, Judith Fetterley, Herbert Lindenberger, Julia Reinhard Lupton, Maximillian E. Novak, Richard Ohmann, Marjorie Perloff, Mark Reynolds, James Sledd, Harriet Turner, Marie Umeh, Flavia Aloya, Regina Barreca, Konrad Bieber, Ellis Hanson, William J. Hyde, Holly A. Laird, David Leverenz, Allen Michie, J. Wesley Miller, Marvin Rosenberg, Daniel R. Schwarz, Elizabeth Welt Trahan, Jean Fagan Yellin
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- Journal:
- PMLA / Publications of the Modern Language Association of America / Volume 115 / Issue 7 / December 2000
- Published online by Cambridge University Press:
- 23 October 2020, pp. 1986-2078
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- December 2000
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Sufficiency and the Jacobi Condition in the Calculus of Variations
- Frank H. Clarke, Vera Zeidan
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- Canadian Journal of Mathematics / Volume 38 / Issue 5 / 01 October 1986
- Published online by Cambridge University Press:
- 20 November 2018, pp. 1199-1209
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- 01 October 1986
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Besides stating the problem and the results, we shall give in this section a brief overview of the classical necessary and sufficient conditions in the calculus of variations, in order to clearly situate the contribution of this article.
1.1 The problem. We are given an interval [a, b], two points xa, xb in Rn, and a function L (the Lagrangian) mapping [a, b] × Rn × Rn to R. The basic problem in the calculus of variations, labeled (P), is that of minimizing the functional
over some class X of functions x and subject to the constraints x(a) = xa, x(b) = xb. Let us take for now the class X of functions to be the continuously differentiable mappings from [a, b] to Rn; we call such functions smooth arcs.
The Erdmann Condition and Hamiltonian Inclusions in Optimal Control and the Calculus of Variations
- Frank H. Clarke
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- Journal:
- Canadian Journal of Mathematics / Volume 32 / Issue 2 / February 1980
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- 20 November 2018, pp. 494-509
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- February 1980
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Consider the basic problem in the calculus of variations, that of minimizing
1.1
over a class of functions x satisfying certain boundary conditions at 0 and 1. One of the classical first order necessary conditions for optimality is the second Erdmann condition, which asserts, in the case in which L is independent mof t, that
1.2
along any local solution x. This formula is the customary basis for solving many of the classical problems, such as the brachistochrone. When it is possible to define via the Legendre transform a Hamiltonian H(t, x, p) corresponding to L, the second Erdmann condition, again in the autonomous case, is the assertion that
1.3
a relation which always evokes classical Hamiltonian mechanics and conservation laws.
Pointwise Contraction Criteria for the Existence of Fixed Points
- Frank H. Clarke
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- Journal:
- Canadian Mathematical Bulletin / Volume 21 / Issue 1 / 01 March 1978
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- 20 November 2018, pp. 7-11
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- 01 March 1978
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We show that, in a complete metric space, every selfmap that is a “weak directional contraction” admits a fixed point.
Inequality Constraints in the Calculus of Variations
- Frank H. Clarke
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- Journal:
- Canadian Journal of Mathematics / Volume 29 / Issue 3 / 01 June 1977
- Published online by Cambridge University Press:
- 20 November 2018, pp. 528-540
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- 01 June 1977
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The classical multiplier rule. The purpose of this section is to review the multiplier rule in order to place the results of this report in perspective. Let us begin by considering the following problem of Mayer in the calculus of variations: we seek to minimize