49 results
Weed Control in Ecofallow Corn (Zea mays) with Clomazone
- Gail A. Wicks, Gary W. Mahnken, Gordon E. Hanson
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- Journal:
- Weed Technology / Volume 10 / Issue 3 / September 1996
- Published online by Cambridge University Press:
- 12 June 2017, pp. 495-501
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Field studies were conducted from 1986 through 1989 to determine the feasibility of using clomazone in a winter wheat-corn-fallow rotation. Clomazone at 1.1 kg ai/ha did not control emerged downy brome in autumn nor did it control redroot pigweed and tumble pigweed that emerged after a spring application of paraquat at 0.6 kg ai/ha. However, clomazone plus atrazine at 0.6 plus 2.2 kg ai/ha provided weed control in winter wheat stubble from October to corn harvest 12 mo later. Corn yields from this treatment were equal to or greater than the conventional practice of applying atrazine plus glyphosate at 2.2 plus 0.4 kg ae/ha in the fall followed by a spring application of metolachlor plus dicamba at 2.8 ai plus 0.3 kg ae/ha. When kochia densities were high, clomazone plus atrazine controlled triazine-resistant kochia better than metolachlor plus dicamba. Atrazine at 2.2 kg/ha applied in autumn followed by clomazone at 0.8 kg/ha in April generally caused more corn injury than when the same rate of clomazone was applied in autumn with the atrazine. The percent of bleached corn plants varied with planter, year, time of application, and rate of clomazone applied. The optimum time to apply clomazone at 0.6 kg/ha was in autumn with atrazine. This treatment caused some corn bleaching but produced the highest corn yield over 3 yr. In a dry autumn and spring, less clomazone injury occurred with a planter equipped with row cleaners than those without. The injury pattern associated with planters was inconsistent when precipitation was average and no injury occurred in a wet autumn and spring.
A multistudy approach to understanding weed population shifts in medium- to long-term tillage systems
- A. Gordon Thomas, Douglas A. Derksen, Robert E. Blackshaw, Rene C. Van Acker, Anne Légère, Paul R. Watson, Gary C. Turnbull
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- Journal:
- Weed Science / Volume 52 / Issue 5 / October 2004
- Published online by Cambridge University Press:
- 20 January 2017, pp. 874-880
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Production systems based on reduced-tillage practices account for over 60% of the cropped land on the Canadian Prairies. Concerns have been expressed regarding potential shifts in weed communities as a result of changing tillage practices. Study objectives were to (1) determine the feasibility of combining and analyzing weed abundance data from 10 medium- to long-term studies on the Canadian Prairies that compared conventional-, reduced-, and zero-tillage systems, (2) identify species that are associated with specific tillage systems, and (3) place species into plant response groups according to the similarity of their tillage system response. Conventional-tillage systems were defined as including both a fall and spring sweep-plow operation before seeding spring crops, whereas reduced tillage consisted of only one sweep-plow operation shortly before seeding. Crops within zero-tillage systems were planted directly into the previous crop's stubble. The association between weed species and tillage systems was investigated using indicator species analysis. Species were assigned to tillage response groups on the basis of the results of the analysis and the expertise of the project scientists. Perennial species such as Canada thistle and perennial sowthistle were associated with reduced- and zero-tillage systems, but annual species were associated with a range of tillage systems. Field pennycress was placed in the conventional-tillage response group, Russian thistle in the zero-tillage group, and wild buckwheat and common lambsquarters were equally abundant in all tillage systems. The goal of classifying weed species based on common functional traits in relation to responses to tillage systems was not realized, in part, because the required information on species biology and ecology was either unavailable or not applicable to local conditions.
Experience With Rapid Microarray-Based Diagnostic Technology and Antimicrobial Stewardship for Patients With Gram-Positive Bacteremia
- Elizabeth A. Neuner, Andrea M. Pallotta, Simon W. Lam, David Stowe, Steven M. Gordon, Gary W. Procop, Sandra S. Richter
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- Journal:
- Infection Control & Hospital Epidemiology / Volume 37 / Issue 11 / November 2016
- Published online by Cambridge University Press:
- 08 August 2016, pp. 1361-1366
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- November 2016
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OBJECTIVE
To describe the impact of rapid diagnostic microarray technology and antimicrobial stewardship for patients with Gram-positive blood cultures.
DESIGNRetrospective pre-intervention/post-intervention study.
SETTINGA 1,200-bed academic medical center.
PATIENTSInpatients with blood cultures positive for Staphylococcus aureus, Enterococcus faecalis, E. faecium, Streptococcus pneumoniae, S. pyogenes, S. agalactiae, S. anginosus, Streptococcus spp., and Listeria monocytogenes during the 6 months before and after implementation of Verigene Gram-positive blood culture microarray (BC-GP) with an antimicrobial stewardship intervention.
METHODSBefore the intervention, no rapid diagnostic technology was used or antimicrobial stewardship intervention was undertaken, except for the use of peptide nucleic acid fluorescent in situ hybridization and MRSA agar to identify staphylococcal isolates. After the intervention, all Gram-positive blood cultures underwent BC-GP microarray and the antimicrobial stewardship intervention consisting of real-time notification and pharmacist review.
RESULTSIn total, 513 patients with bacteremia were included in this study: 280 patients with S. aureus, 150 patients with enterococci, 82 patients with stretococci, and 1 patient with L. monocytogenes. The number of antimicrobial switches was similar in the pre–BC-GP (52%; 155 of 300) and post–BC-GP (50%; 107 of 213) periods. The time to antimicrobial switch was significantly shorter in the post–BC-GP group than in the pre–BC-GP group: 48±41 hours versus 75±46 hours, respectively (P<.001). The most common antimicrobial switch was de-escalation and time to de-escalation, was significantly shorter in the post-BC-GP group than in the pre–BC-GP group: 53±41 hours versus 82±48 hours, respectively (P<.001). There was no difference in mortality or hospital length of stay as a result of the intervention.
CONCLUSIONSThe combination of a rapid microarray diagnostic test with an antimicrobial stewardship intervention improved time to antimicrobial switch, especially time to de-escalation to optimal therapy, in patients with Gram-positive blood cultures.
Infect Control Hosp Epidemiol 2016;1–6
Ruptured and Unruptured Intracranial Aneurysms – Surgical Outcome
- Gary A. Dix, William Gordon, Anthony M. Kaufmann, Ian S. Sutherland, Garnette R. Sutherland
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- Canadian Journal of Neurological Sciences / Volume 22 / Issue 3 / August 1995
- Published online by Cambridge University Press:
- 18 September 2015, pp. 187-191
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Background
The treatment of unruptured, intracranial aneurysms has been the topic of debate. Although recent studies have advocated surgical intervention for unruptured aneurysms, the risk of such treatment in comparison to outcome from ruptured aneurysms has not been established.
MethodThis retrospective study examines the outcome of 134 patients with 179 ruptured and unruptured intracranial, saccular aneurysms treated by a single surgeon.
ResultsOf the 98 ruptured aneurysms where early surgical intervention was undertaken (less than 48 hours post hemorrhage), 70 had an excellent outcome, 13 were good, four were moderate, two poor and nine patients died postoperatively. Outcome assessment in these cases was correlated to preoperative neurological status. Patients who presented with unruptured aneurysms fell into two categories: symptomatic and asymptomatic. Seven incidental, asymptomatic aneurysms were clipped concurrently to the surgical isolation of the culprit lesion following subarachnoid hemorrhage without influencing outcome, whilst, for varying reasons, eight unruptured aneurysms were not operated upon. Of the remaining 66 surgically treated, unruptured aneurysms, 64 had an excellent postoperative result, one was good (persisting right incomplete third nerve palsy) and one was moderate (left hemiparesis). Thirteen of these aneurysms were symptomatic, whilst 21 were asymptomatic, multiple aneurysms requiring secondary elective repair and 32 were true incidental aneurysms.
ConclusionUnruptured aneurysms less than 25 mm in size may be safely, surgically treated relative to the expected natural history and, certainly, with less risk than operative intervention upon ruptured cerebral aneurysms.
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
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- 05 August 2015
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- 27 April 2015, pp ix-xxx
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Contributors
- Edited by Olivia Bloechl, University of California, Los Angeles, Melanie Lowe, Vanderbilt University, Tennessee, Jeffrey Kallberg, University of Pennsylvania
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- Rethinking Difference in Music Scholarship
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- 18 December 2014
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- 08 January 2015, pp xi-xv
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Presence of Irritability During Depressive Episodes in Bipolar Disorder
- Thilo Deckersbach, Roy H. Perlis, W. Gordon Frankle, Stephen M. Gray, Louisa Grandin, Darin D. Dougherty, Andrew A. Nierenberg, Gary S. Sachs
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- CNS Spectrums / Volume 9 / Issue 3 / March 2004
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- 07 November 2014, pp. 227-231
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Background:This study examined the prevalence of irritability in patients with bipolar I disorder during an episode of Diagnostic and Statistical Manual of Mental Disorders, Fourth Edition (DSM-IV) major depression who do not meet criteria for a mixed episode.
Method:A chart review of 111 patients with bipolar I disorder treated at the Massachusetts General Hospital Bipolar Clinic between 1998 and 2000 identified 34 patients who met criteria for a DSM-IV major depressive episode in the absence of (1) mood elevation and/or (2) irritability associated with any additional above threshold DSM-IV symptoms of mania. Data gathered from the charts utilized prospective ratings made routinely at each clinic visit using the Clinical Monitoring Form (CMF), a structured assessment instrument which includes modified versions of the mood modules of the Structured Clinical Interview for DSM-IV. Data from these 34 patients were reviewed to determine the presence of irritability.
Results:The frequency of abnormal irritability in these 34 patients followed a bimodal distribution: 26% of the patients showed abnormal irritability ≥75% of the time, compared with 68% of the patients with abnormal irritabihty ≤30% of the time. Of the high-irritability patients, psychomotor agitation was rated as definitely present to a significant degree in 44%. Talkativeness and distractibility were rated present but subthreshold in one patient each. All other symptoms of DSM-IV mania were absent.
Conclusion:Approximately 25% of patients with bipolar I disorder who meet criteria for a DSM-IV major depressive episode also experienced substantial irritability in the absence of associated symptoms of mania. Our results suggest that abnormal irritability is not limited to mania or mixed states.
Good is not Good Enough: The Benchmark Stroke Door-to-Needle Time Should be 30 Minutes
- Noreen Kamal, Oscar Benavente, Karl Boyle, Brian Buck, Ken Butcher, Leanne K. Casaubon, Robert Côté, Andrew M Demchuk, Yan Deschaintre, Dar Dowlatshahi, Gordon J Gubitz, Gary Hunter, Tom Jeerakathil, Albert Jin, Eddy Lang, Sylvain Lanthier, Patrice Lindsay, Nancy Newcommon, Jennifer Mandzia, Colleen M. Norris, Wes Oczkowski, Céline Odier, Stephen Phillips, Alexandre Y Poppe, Gustavo Saposnik, Daniel Selchen, Ashfaq Shuaib, Frank Silver, Eric E Smith, Grant Stotts, Michael Suddes, Richard H. Swartz, Philip Teal, Tim Watson, Michael D. Hill
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- Canadian Journal of Neurological Sciences / Volume 41 / Issue 6 / November 2014
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- 20 October 2014, pp. 694-696
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7 - Understanding subsurface contamination using conceptual and mathematical models
- Edited by John A. Wiens
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- Oil in the Environment
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- 05 July 2013
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- 18 July 2013, pp 144-175
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Summary
Introduction
Petroleum spills and other sources of hydrocarbon contamination represent risks for society. Regardless of whether oil is stranded on a shoreline, spilled from a pipeline, or leaked from underground storage tanks, the same basic physical and chemical principles characterize exposure levels of contaminants. The purpose of this chapter is to explain and illustrate these principles. In particular, we use these principles to explain the apparent paradox of how oil residues persist at some shorelines of Prince William Sound (PWS) as isolated subsurface patches, but yet pose little if any exposure risk to the local ecology. We resolve this apparent paradox using well-established scientific and engineering tools.
One of the biggest challenges of any study of a contaminated site is identifying the most important questions and the most important observations and data needed to answer these questions. This challenge is discussed in this chapter in both a general way and for the PWS study in particular. One of the key lessons learned from this study was the need for experts in multiphase flow in contaminated sediments to be a central part of the team addressing these questions. Our goal is to convey a coherent understanding and perspective that brings all of the observations and measurements by various environmental experts of different scientific disciplines into a consistent explanation.
7 - Other matroids
- Gary Gordon, Lafayette College, Pennsylvania, Jennifer McNulty, University of Montana
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- Matroids: A Geometric Introduction
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- 05 November 2012
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- 02 August 2012, pp 261-295
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Summary
Matroids are an important generalization of graphs and matrices; graphic and representable matroids have been the focus of much of the text. But other important combinatorial structures also have interpretations as matroids. In this chapter, we concentrate on two well-studied applications: transversalmatroids (which arise from bipartite graphs) and hyperplane arrangements in ℝn, which are closely related to representable matroids.
Transversal matroids
Finding matchings in bipartite graphs is an extremely important and well-studied topic in combinatorics. For instance, the job assignment problem introduced in Example 1.20 in Chapter 1 asks you to determine which applicants to hire for a collection of jobs. This motivates the notion of a transversal matroid, a matroid associated with matchings in a bipartite graph. These matroids were defined in Example 1.20, and Theorem 7.2 asserts the collections of vertices that can be matched to satisfy the independent set axioms. In Chapter 1, we postponed the proof until “later.” Now, it's later.
In an effort to make this chapter self-contained (and to spare you the trouble of leafing back to Chapter 1), we remind you of all the relevant definitions. Let G be a bipartite graph with vertex bipartition V = X ∪ Y. Recall a subset of edges N is called a matching if no two edges ofN share any vertex. We writeN = (I, J) for I ⊆ X and J ⊆ Y for the vertices that the matching N uses in X and Y, respectively.
4 - Graphic matroids
- Gary Gordon, Lafayette College, Pennsylvania, Jennifer McNulty, University of Montana
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- Matroids: A Geometric Introduction
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- 05 November 2012
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- 02 August 2012, pp 152-179
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Preface
- Gary Gordon, Lafayette College, Pennsylvania, Jennifer McNulty, University of Montana
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- Matroids: A Geometric Introduction
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Summary
Matroids – a quick prehistory
Matroid theory is an active area of mathematics that uses ideas from abstract and linear algebra, geometry, combinatorics and graph theory. The study of matroids thus offers students a unique opportunity to synthesize several different areas within mathematics typically studied at the undergraduate level. Furthermore, matroids are an active area of research; Mathematical Reviews lists some 2000 publications with the word “matroid” in the title, with more than a third of these appearing in the last decade.
Why have we written this book? Our motivation is direct: There is no comprehensive text written for undergraduates on this topic. There are several more advanced treatments of the subject, suitable for graduate students or researchers, butmost of these are difficult for undergraduates to read. To paraphrase an old joke, this text seeks to fill this “muchneeded gap.”
This text introduces matroids by emphasizing geometry, focusing especially on geometric (affine) dependence. Interpreting this approach for finite subsets of a vector space, points in Euclidean space or the edges of a graph gives a matroid spin to linear algebra, discrete geometry and graph theory. We believe the geometric approach, which both authors learned from their common Ph.D. advisor, Thomas Brylawski, to be the most natural, useful and powerful in understanding the subject.
The common thread that ties the various classes of matroids together is the abstract notion of independence. This unifying idea is due to Hassler Whitney, who defined matroids in his foundational paper [42] in 1935.
Appendix: Matroid axiom systems
- Gary Gordon, Lafayette College, Pennsylvania, Jennifer McNulty, University of Montana
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- Matroids: A Geometric Introduction
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- 02 August 2012, pp 381-384
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6 - Representable matroids
- Gary Gordon, Lafayette College, Pennsylvania, Jennifer McNulty, University of Montana
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- Matroids: A Geometric Introduction
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- 05 November 2012
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- 02 August 2012, pp 221-260
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Summary
Matrices are matroids
In Whitney's foundational paper [42], matroids were introduced as an abstraction of linear dependence. Throughout the history of the subject, connections between matrices and matroids have motivated an enormous amount of research. The first three questions we consider are fundamental:
Q1. Does every subset of vectors give rise to a matroid, i.e., do the subsets of linearly independent column vectors of a matrix always satisfy the independent set axioms? (Answer: Yes – Theorem 6.1.)
Q2. When do two different matrices give the same matroid? (Answer: Sometimes – Section 6.2.)
Q3. Does every matroid arise from the linear dependences of some collection of vectors? (Answer: No – Example 6.20.)
Concerning Q1, we've seen plenty of examples of matroids that come from specific matrices so far. In Chapter 1, matrices were the first examples we considered, and, in Chapter 3, we interpreted the matroid operations of deletion, contraction and duality for matrices. But, if you've been paying close attention, we never proved the subsets of linearly independent vectors satisfy the axioms (I1), (I2) and (I3). We fix that now by giving a proof that linear independence satisfies the matroid independence axioms.
Column dependences of a matrix
Theorem 6.1. Let E be the columns of a matrix A with entries in a field F, and let I be those subsets of E that are linearly independent. Then I is the family of independent sets of a matroid.
Index
- Gary Gordon, Lafayette College, Pennsylvania, Jennifer McNulty, University of Montana
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- Matroids: A Geometric Introduction
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- 05 November 2012
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- 02 August 2012, pp 390-393
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8 - Matroid minors
- Gary Gordon, Lafayette College, Pennsylvania, Jennifer McNulty, University of Montana
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- Matroids: A Geometric Introduction
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- 05 November 2012
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- 02 August 2012, pp 296-322
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5 - Finite geometry
- Gary Gordon, Lafayette College, Pennsylvania, Jennifer McNulty, University of Montana
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- Book:
- Matroids: A Geometric Introduction
- Published online:
- 05 November 2012
- Print publication:
- 02 August 2012, pp 180-220
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Summary
Matroids can be thought of in many different ways; we tried to make that point in Chapter 2. But the common thread running through all of our different approaches to the subject is the underlying connection to geometry. When we “draw a picture of amatroid,” we are thinking of the elements of the matroid as points and the dependences as lines, planes, and so on.
Geometry in the plane motivates our treatment of affine geometry. Although the word “affine” may be unfamiliar, affine geometry based on coordinates covers very familiar material; points in the plane correspond to ordered pairs (x, y), points in three-dimensions correspond to ordered triples (x, y, z), and so on. Lines in the plane are given by linear equations of the form ax + by = c for constants a, b and c, planes in 3-space are described by equations of the form ax + by + cz = d, and this also generalizes to higher dimensions.
From the geometric point of view, here's what you learned long ago about points and lines in the plane:
A: Every pair of points determines a unique line, and
B: Given a point P and a line l not containing P, there is a unique line through P parallel to l.
Our matroid interpretation for property A is direct;
• If a and b are non-parallel points in a matroid, then they determine a unique rank 2 flat of the matroid – see Figure 5.1.
Matroids: A Geometric Introduction
- Gary Gordon, Jennifer McNulty
-
- Published online:
- 05 November 2012
- Print publication:
- 02 August 2012
-
Matroid theory is a vibrant area of research that provides a unified way to understand graph theory, linear algebra and combinatorics via finite geometry. This book provides the first comprehensive introduction to the field which will appeal to undergraduate students and to any mathematician interested in the geometric approach to matroids. Written in a friendly, fun-to-read style and developed from the authors' own undergraduate courses, the book is ideal for students. Beginning with a basic introduction to matroids, the book quickly familiarizes the reader with the breadth of the subject, and specific examples are used to illustrate the theory and to help students see matroids as more than just generalizations of graphs. Over 300 exercises are included, with many hints and solutions so students can test their understanding of the materials covered. The authors have also included several projects and open-ended research problems for independent study.
9 - The Tutte polynomial
- Gary Gordon, Lafayette College, Pennsylvania, Jennifer McNulty, University of Montana
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- Book:
- Matroids: A Geometric Introduction
- Published online:
- 05 November 2012
- Print publication:
- 02 August 2012, pp 323-380
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Summary
Motivation and history
It's not unusual for an open problem in mathematics to motivate signifi- cant research. One of the touchstone problems of modern combinatorics and graph theory was the Four Color Problem, now the Four Color Theorem after its resolution by Appel and Haken in 1976 [1]. This problem, which dates to a letter Francis Guthrie wrote to his brother Frederick in 1852, asks if it is always possible to color the regions of a map with four (or fewer) colors so that no two adjacent regions receive the same color. This is obviously important when you are looking at a map – you don't want regions (countries or states) that share a border to receive the same color.
Appel and Haken's proof was noteworthy for two reasons:
It resolved (in the affirmative) a 125 year-old conjecture.
It was the first significant mathematical proof that made essential use of a computer.
In fact, Appel and Haken needed more than 1000 hours of computer time to complete the case checking involved in their proof. A more recent proof [28], modeled on the same approach, but streamlined, dramatically reduces the number of cases to check. But even this new proof uses a computer in an essential way to check cases.
Although the original problem is phrased in terms of coloring regions in a map, you can turn the entire enterprise into coloring vertices of a graph.
1 - A tour of matroids
- Gary Gordon, Lafayette College, Pennsylvania, Jennifer McNulty, University of Montana
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- Book:
- Matroids: A Geometric Introduction
- Published online:
- 05 November 2012
- Print publication:
- 02 August 2012, pp 1-38
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