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We provide scientific foundations for athletic performance prediction on an individual level, exposing the phenomenology of individual athletic running performance in the form of a low-rank model dominated by an individual power law.
An approximate law of fatigue in the speeds of racing animals
Arthur Edwin Kennelly · 1906
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Muscular exercise, lactic acid, and the supply and utilisation of oxygen
Archibald V Hill, CNH Long, and H Lupton · 1924
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An analytical study of world and olympic racing records
Milton H. Lietzke · 1954
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Prediction of world records in running sixty yards to twenty-six miles
Franklin M. Henry · 1955
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Singular value decomposition and least squares solutions
Gene H. Golub and Christian Reinsch · 1970
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A theory of competitive running
Joseph B Keller · 1973
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Anaerobic threshold and respiratory gas exchange during exercise
Karlman Wasserman, Brian J. Whipp, SN Koyl, and WL Beaver · 1973
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Computer generated track and field scoring tables: I. historical development
J Gerry Purdy · 1974
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Computer generated track and field scoring tables: II. theoretical foundation and development of a model
J Gerry Purdy · 1974
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Computer generated track and field scoring tables: III. model evaluation and analysis
J Gerry Purdy · 1976
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Maximum likelihood from incomplete data via the em algorithm
Arthur P Dempster, Nan M Laird, and Donald B Rubin · 1977
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Time predicting
Peter S. Riegel · 1977
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Fibre types and metabolic potentials of skeletal muscles in sedentary man and endurance runners
B. Saltin, J. Henricksson, E. Hygaard, and P. Andersen · 1977
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Athletic records and human endurance
Peter S. Riegel · 1980
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Estimating the error rate of a prediction rule: improvement on cross-validation
Bradley Efron · 1983
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Endurance training in humans: aerobic capacity and structure of skeletal muscle
Hans Hoppeler, Hans Howald, Kevin Conley, Stan L. Lindstedt, Helgard Claassen, Peter Vock, and Ewald R. Weibel · 1985
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Mathematical analysis of running performance and world running records
François Péronnet and Guy Thibault · 1989
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Peak treadmill running velocity during the VO2max test predicts running performance
Timothy D. Noakes, Kathryn H. Myburgh, and Robert Schall · 1990
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Balance of carbohydrate and lipid utilization during exercise: the "crossover" concept
George A. Brooks and Jacques Mercier · 1994
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Fractal (power law) analysis of athletic performance
Leon Katz and J Sylvan Katz · 1994
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VO2 slow component: physiological and functional significance
Methods to determine aerobic endurance
Laurent Bosquet, Luc Léger, and Patrick Legros · 2002
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High-speed running performance: a new approach to assessment and prediction
Matthew W. Bundle, Reed W. Hoyt, and Peter G. Weyand · 2003
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Factors limiting maximal performance in humans
Pietro Enrico Di Prampero · 2003
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Middle and long distance athletics races viewed from the perspective of complexity
Juan M. García-Manso, Juan M. Martín-González, Nancy Dávila, and Enrique Arriaza · 2005
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Determinants of fat oxidation during exercise in healthy men and women: a cross-sectional study
Michelle C. Venables, Juul Achten, and Asker E. Jeukendrup · 2005
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Pattern recognition and machine learning
Christopher M Bishop et al · 2006
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David C. Poole, Thomas J. Barstow, Glenn A. Gaesser, Wayne T. Willis, and Brian J Whipp · 1994
Cited alongside, same era.
Optimisation of sprinting performance in running, cycling and speed skating
Gerrit Jan Ingen van Schenau, Jos J de Koning, and Gert de Groot · 1994
Cited alongside, same era.
A study of cross-validation and bootstrap for accuracy estimation and model selection
Ron Kohavi et al · 1995
Cited alongside, same era.
Use of blood lactate measurements for prediction of exercise performance and for control of training
L Véronique Billat · 1996
Cited alongside, same era.
Significance of the velocity at VO2max and time to exhaustion at this velocity
L Véronique Billat and J Pierre Koralsztein · 1996
Cited alongside, same era.
Improvements on cross-validation: the 632+ bootstrap method
Bradley Efron and Robert Tibshirani · 1997
Cited alongside, same era.
Cross-validation methods
Michael W. Browne · 2000
Cited alongside, same era.
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Exact matrix completion via convex optimization
Emmanuel J. Candès and Benjamin Recht · 2009
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Lactate threshold concepts
Oliver Faude, Wilfried Kindermann, and Tim Meyer · 2009
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Sprint and endurance power and ageing: an analysis of master athletic world records
Jörn Rittweger, Pietro Enrico di Prampero, Nicola Maffulli, and Marco V. Narici · 2009
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The power of convex relaxation: Near-optimal matrix completion
Emmanuel J. Candès and Terence Tao · 2010
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On the extension of trace norm to tensors
Ryota Tomioka, Kohei Hayashi, and Hisashi Kashima · 2010
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Obtaining error-minimizing estimates and universal entry-wise error bounds for low-rank matrix completion
Franz J. Király and Louis Theran · 2013
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Duncan AJ Blythe, Louis Theran, and Franz Kiraly · 2014
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The algebraic combinatorial approach for low-rank matrix completion
Franz J. Király, Louis Theran, and Ryota Tomioka · 2015
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