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ASYMPTOTIC LINEAR PROGRAMMING LOWER BOUNDS FOR THE ENERGY OF MINIMIZING RIESZ AND GAUSS CONFIGURATIONS
- Part of
- D. P. Hardin, T. J. Michaels, E. B. Saff
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- Journal:
- Mathematika / Volume 65 / Issue 1 / 2019
- Published online by Cambridge University Press:
- 27 September 2018, pp. 157-180
- Print publication:
- 2019
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Utilizing frameworks developed by Delsarte, Yudin and Levenshtein, we deduce linear programming lower bounds (as $N\rightarrow \infty$) for the Riesz energy of $N$-point configurations on the $d$-dimensional unit sphere in the so-called hypersingular case; i.e., for non-integrable Riesz kernels of the form $|x-y|^{-s}$ with $s>d$. As a consequence, we immediately get (thanks to the poppy-seed bagel theorem) lower estimates for the large $N$ limits of minimal hypersingular Riesz energy on compact $d$-rectifiable sets. Furthermore, for the Gaussian potential $\exp (-\unicode[STIX]{x1D6FC}|x-y|^{2})$ on $\mathbb{R}^{p}$, we obtain lower bounds for the energy of infinite configurations having a prescribed density.
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. 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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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- Book:
- The Cambridge Dictionary of Philosophy
- Published online:
- 05 August 2015
- Print publication:
- 27 April 2015, pp ix-xxx
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Contributors
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- By Syed S. Ali, Nathan Allen, John E. Arbo, Elizabeth Arrington, Ani Aydin, Kenneth R. L. Bernard, Amy Caggiula, Nolan Caldwell, Jennifer L. Carey, Jennifer Carnell, Jayaram Chelluri, Michael N. Cocchi, Cristal Cristia, Vishal Demla, Bram Dolcourt, Andrew Eyre, Shawn Fagan, Brandy Ferguson, Sarah Fisher, Jonathan Friedstat, Brian C. Geyer, Brandon Godbout, Jeremy Gonda, Jeremy Goverman, Ashley L. Greiner, Casey Grover, Carla Haack, Abigail Hankin, John W. Hardin, Katrina L. Harper, Gregory Hayward, Stephen Hendriksen, Daniel Herbert-Cohen, Nadine Himelfarb, Calvin E. Hwang, Jacob D. Isserman, Joshua Jauregui, Joshua W. Joseph, Elena Kapilevich, Feras H. Khan, Sarvotham Kini, Karen A. Kinnaman, Ruth Lamm, Calvin Lee, Jarone Lee, Charles Lei, John Lemos, Daniel J. Lepp, Elisabeth Lessenich, Brandon Maughan, Julie Mayglothling, Kevin McConnell, Laura Medford-Davis, Kamal Medlej, Heather Meissen, Payal Modi, Joel Moll, Jolene H. Nakao, Matthew Nicholls, Lindsay Oelze, Carolyn Maher Overman, Viral Patel, Timothy C. Peck, Jeffrey Pepin, Candace Pettigrew, Byron Pitts, Zubaid Rafique, Chanu Rhee, Jonathan C. Roberts, Daniel Rolston, Steven C. Rougas, Benjamin Schnapp, Kathryn A. Seal, Raghu Seethala, Todd A. Seigel, Navdeep Sekhon, Kaushal Shah, Robert L. Sherwin, Kirill Shishlov, Ashley Shreves, Sebastian Siadecki, Jeffrey N. Siegelman, Liza Gonen Smith, Ted Stettner, Marie Carmelle Tabuteau, Joseph E. Tonna, N. Seth Trueger, Chad Van Ginkel, Bina Vasantharam, Graham Walker, Susan Wilcox, Sandra J. Williams, Matthew L. Wong, Nelson Wong, Samantha Wood, John Woodruff, Benjamin Zabar
- Edited by Kaushal Shah, Jarone Lee, Kamal Medlej, American University of Beirut, Scott D. Weingart
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- Practical Emergency Resuscitation and Critical Care
- Published online:
- 05 November 2013
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- 24 October 2013, pp xi-xx
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4 - Goal-directed behavior: evolution and ontogeny
- from Section 1 - Normal developmental processes
- Edited by Judith M. Rumsey, National Institute of Mental Health, Bethesda, Maryland, Monique Ernst, National Institute of Mental Health, Bethesda, Maryland
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- Neuroimaging in Developmental Clinical Neuroscience
- Published online:
- 04 August 2010
- Print publication:
- 19 February 2009, pp 53-72
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Contributors
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- By James M. Bjork, Hilary P. Blumberg, Nathalie Boddaert, Susan Bookheimer, Silvia A. Bunge, Beata Buzas, B. J. Casey, Nadia Chabane, Eveline A. Crone, Mirella Dapretto, John A. Detre, Vaibhav A. Diwadkar, Jeffery N. Epstein, Monique Ernst, Guido K. W. Frank, David C. Glahn, David Goldman, Daniel A. Gorman, Ian H. Gotlib, Michael G. Hardin, Clinton D. Hermes, Rebecca M. Jones, Jutta Joormann, Jessica H. Kalmar, Walter H. Kaye, Matcheri S. Keshavan, Dae-Shik Kim, Liat Levita, Lisa H. Lu, Rachel Marsh, Kristin McNealy, Kevin A. Pelphrey, Susan B. Perlman, Bradley S. Peterson, Daniel S. Pine, Steven R. Pliszka, Konasale Prasad, Hengyi Rao, Allan L. Reiss, Perry Renshaw, Susan M. Rivera, Jason Royal, Judith M. Rumsey, Maulik P. Shah, Marisa M. Silveri, Elizabeth R. Sowell, Jeffrey A. Stanley, Henning U. Voss, Jiong-Jiong Wang, Ke Xu, Deborah Yurgelun-Todd, Monica Zilbovicius
- Edited by Judith M. Rumsey, National Institute of Mental Health, Bethesda, Maryland, Monique Ernst, National Institute of Mental Health, Bethesda, Maryland
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- Book:
- Neuroimaging in Developmental Clinical Neuroscience
- Published online:
- 04 August 2010
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- 19 February 2009, pp vii-xii
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Triadic model of the neurobiology of motivated behavior in adolescence
- MONIQUE ERNST, DANIEL S. PINE, MICHAEL HARDIN
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- Journal:
- Psychological Medicine / Volume 36 / Issue 3 / March 2006
- Published online by Cambridge University Press:
- 13 September 2005, pp. 299-312
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Background. Risk-taking behavior is a major cause of morbidity and mortality in adolescence. In the context of decision theory and motivated (goal-directed) behavior, risk-taking reflects a pattern of decision-making that favors the selection of courses of action with uncertain and possibly harmful consequences. We present a triadic, neuroscience systems-based model of adolescent decision-making.
Method. We review the functional role and neurodevelopmental findings of three key structures in the control of motivated behavior, i.e. amygdala, nucleus accumbens, and medial/ventral prefrontal cortex. We adopt a cognitive neuroscience approach to motivated behavior that uses a temporal fragmentation of a generic motivated action. Predictions about the relative contributions of the triadic nodes to the three stages of a motivated action during adolescence are proposed.
Results. The propensity during adolescence for reward/novelty seeking in the face of uncertainty or potential harm might be explained by a strong reward system (nucleus accumbens), a weak harm-avoidant system (amygdala), and/or an inefficient supervisory system (medial/ventral prefrontal cortex). Perturbations in these systems may contribute to the expression of psychopathology, illustrated here with depression and anxiety.
Conclusions. A triadic model, integrated in a temporally organized map of motivated behavior, can provide a helpful framework that suggests specific hypotheses of neural bases of typical and atypical adolescent behavior.
Agitation in Nursing Home Residents: The Role of Gender and Social Context
- Louis D. Burgio, Frieda R. Butler, David L. Roth, J. Michael Hardin, Chuan-Chieh Hsu, Kim Ung
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- Journal:
- International Psychogeriatrics / Volume 12 / Issue 4 / December 2000
- Published online by Cambridge University Press:
- 10 January 2005, pp. 495-511
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We investigated the relationship among gender of resident, staff social interaction, and agitation in 46 (31 male and 15 female) nursing home residents with clinically significant agitation. Direct observations were conducted of resident behaviors and environmental contextual events using a computer-assisted, real-time observational system. The system recored frequency, duration, and temporal sequencing of events. Results show that female residents displayed almost three times the amount of agitation as male residents (35% vs. 13% of total observation time, respectively), although men in the study were more likely to receive psychoactive drugs for their agitation. Staff spent similar amounts of time verbally interacting and touching male and female residents. Sequential analyses were conducted to examine the likelihood of staff verbal and touch interactions both preceding and following resident agitation using Bakeman and Quera's (1995) SDIS-GSEQ program. Results suggest that staff touch and verbal interaction elicit agitation in a significant proportion of residents. Once agitation occurs, staff were likely to respond by interacting verbally, but not physically, with the resident.
Excess Disability During Morning Care in Nursing Home Residents With Dementia
- Joan C. Rogers, Margo B. Holm, Louis D. Burgio, Chuanchieh Hsu, J. Michael Hardin, B. Joan Mcdowell
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- Journal:
- International Psychogeriatrics / Volume 12 / Issue 2 / June 2000
- Published online by Cambridge University Press:
- 10 January 2005, pp. 267-282
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Excess disability was examined in 17 nursing home residents with dementia by comparing their performance of morning care tasks under two activities of daily living (ADL) caregiving approaches—a dependence-supportive one under usual care and an independence-supportive one under functional rehabilitation. The results suggest that excess disability in severely cognitively impaired and functionally disabled residents can be reduced by increasing opportunities for independent activity, and substituting nondirective and directive verbal assists for physical assists. Further, the findings indicate that increased independence in ADL can be achieved without increasing disruptive behaviors and can foster appropriate requests for task-related help during caregiving. Functional rehabilitation, however, requires more time than usual care.
Reflections on the Spirituality of Soren Kierkegaard
- Michael Hardin
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- Journal:
- Scottish Journal of Theology / Volume 45 / Issue 3 / August 1992
- Published online by Cambridge University Press:
- 30 January 2009, pp. 325-340
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- August 1992
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Kierkegaard scholarship has, in the past twenty years, gone a long way toward clearing up issues both historical and interpretive that earlier interpreters had somehow overlooked. This essay is neither an attempt at historical reconstruction or a direct engagement with the Kierkegaard guild. This essay is a reflection on the spirituality of Soren Kierkegaard, a theme he would probably find somewhat inappropriate. He would rather want to challenge us, his readers, to consider the primary subject of theology itself, namely God. But if a consideration of his spirituality should lead the reader in such a pursuit, then it seems one is indirectly led to the ultimate goal ol the Kierkegaardiana.