Journal articles: 'Sports – Mathematical models'

1

de la Cruz-Campos, Adrián, Juan Carlos de la Cruz-Campos, Juan Carlos de la Cruz-Márquez, and Belén Cueto-Martín. "Prediction of Sports Injuries by Mathematical Models." International Journal of Sport and Society 3, no. 4 (2014): 167–83. http://dx.doi.org/10.18848/2152-7857/cgp/v03i04/53955.

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Belsole, Robert J., Don R. Hilbelink, J. Anthony Llewellyn, Stephen Stenzler, Thomas L. Greene, and Mark Dale. "Mathematical analysis of computed carpal models." Journal of Orthopaedic Research 6, no. 1 (January 1988): 116–22. http://dx.doi.org/10.1002/jor.1100060115.

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Šarčević, Ana, Damir Pintar, Mihaela Vranić, and Ante Gojsalić. "Modeling In-Match Sports Dynamics Using the Evolving Probability Method." Applied Sciences 11, no. 10 (May 13, 2021): 4429. http://dx.doi.org/10.3390/app11104429.

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The prediction of sport event results has always drawn attention from a vast variety of different groups of people, such as club managers, coaches, betting companies, and the general population. The specific nature of each sport has an important role in the adaption of various predictive techniques founded on different mathematical and statistical models. In this paper, a common approach of modeling sports with a strongly defined structure and a rigid scoring system that relies on an assumption of independent and identical point distributions is challenged. It is demonstrated that such models can be improved by introducing dynamics into the match models in the form of sport momentums. Formal mathematical models for implementing these momentums based on conditional probability and empirical Bayes estimation are proposed, which are ultimately combined through a unifying hybrid approach based on the Monte Carlo simulation. Finally, the method is applied to real-life volleyball data demonstrating noticeable improvements over the previous approaches when it comes to predicting match outcomes. The method can be implemented into an expert system to obtain insight into the performance of players at different stages of the match or to study field scenarios that may arise under different circumstances.

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NAEMI, ROOZBEH, and NACHIAPPAN CHOCKALINGAM. "Mathematical Models to Assess Foot–Ground Interaction." Medicine & Science in Sports & Exercise 45, no. 8 (August 2013): 1524–33. http://dx.doi.org/10.1249/mss.0b013e31828be3a7.

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Martins, Fernando, Ricardo Gomes, Vasco Lopes, Frutuoso Silva, and Rui Mendes. "Mathematical Models to Measure the Variability of Nodes and Networks in Team Sports." Entropy 23, no. 8 (August 19, 2021): 1072. http://dx.doi.org/10.3390/e23081072.

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Pattern analysis is a widely researched topic in team sports performance analysis, using information theory as a conceptual framework. Bayesian methods are also used in this research field, but the association between these two is being developed. The aim of this paper is to present new mathematical concepts that are based on information and probability theory and can be applied to network analysis in Team Sports. These results are based on the transition matrices of the Markov chain, associated with the adjacency matrices of a network with n nodes and allowing for a more robust analysis of the variability of interactions in team sports. The proposed models refer to individual and collective rates and indexes of total variability between players and teams as well as the overall passing capacity of a network, all of which are demonstrated in the UEFA 2020/2021 Champions League Final.

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Budak, Gerçek, İmdat Kara, Yusuf Tansel İç, and Refail Kasımbeyli. "New mathematical models for team formation of sports clubs before the match." Central European Journal of Operations Research 27, no. 1 (September 18, 2017): 93–109. http://dx.doi.org/10.1007/s10100-017-0491-x.

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Tokmakidis, S. P., L. A. Léger, and S. O. Rapagna. "SEARCH FOR THE THRESHOLD RESPONSE WITH MATHEMATICAL MODELS." Medicine and Science in Sports and Exercise 21, Supplement (April 1989): S22. http://dx.doi.org/10.1249/00005768-198904001-00127.

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Selezov, I., and V. Bersenev. "Some mathematical models of reflex-metameric therapy." Journal of Biomechanics 39 (January 2006): S631—S632. http://dx.doi.org/10.1016/s0021-9290(06)85630-7.

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Hendrix, C. Russell, Terry J. Housh, Glen O. Johnson, Michelle Mielke, Clayton L. Camic, Jorge M. Zuniga, and Richard J. Schmidt. "Anaerobic Work Capacity From Linear And Nonlinear Mathematical Models." Medicine & Science in Sports & Exercise 41 (May 2009): 204. http://dx.doi.org/10.1249/01.mss.0000355178.68789.67.

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Whiting, Bill. "Theoretical Models of Skeletal Muscle: Biological and Mathematical Considerations." Medicine & Science in Sports & Exercise 31, no. 7 (July 1999): 1084. http://dx.doi.org/10.1097/00005768-199907000-00028.

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Rossi, R., and P. Ragogna. "Mathematical models for studying the stability of equilibrium." Gait & Posture 30 (October 2009): S70—S71. http://dx.doi.org/10.1016/j.gaitpost.2009.07.071.

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Tangkawsakul, Sakon, Nuttapat Mookda, and Weerawat Thaikam. "Learning Mathematics Through Mathematical Modelling Processes Within Sports Day Activity." Southeast Asian Mathematics Education Journal 10, no. 2 (December 31, 2020): 105–14. http://dx.doi.org/10.46517/seamej.v10i2.108.

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In this study, we adapted the school sports day to provide opportunities to relate real-life situations with mathematical knowledge and skills. The purpose of this study was to describe the way that the teachers interact with their students and the students’ responses during mathematical modelling processes. The designing of the modelling task was inspired by the Realistic Fermi Problems about the bleacher in the school sports day. The modelling task was designed by a collaboration of mathematics teachers and educators and experimented with 10th-grade students. Each experiment lasted for 45 minutes and was conducted in the one-day camp with 45 students. The results showed that the students who had no previous experience of mathematical modelling engaged in mathematical modelling processes with their friends under the guidance and supporting of the teacher. Most of them were able to think, make assumptions, collect data, observe, make conjectures and create mathematical models to understand and solve the modelling task.

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Busso, Thierry, and Luc Thomas. "Using Mathematical Modeling in Training Planning." International Journal of Sports Physiology and Performance 1, no. 4 (December 2006): 400–405. http://dx.doi.org/10.1123/ijspp.1.4.400.

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This report aims to discuss the strengths and weaknesses of the application of systems modeling to analyze the effects of training on performance. The simplifications inherent to the modeling approach are outlined to question the relevance of the models to predict athletes’ responses to training. These simplifications include the selection of the variables assigned to the system’s input and output, the specification of model structure, the collection of data to estimate the model parameters, and the use of identified models and parameters to predict responses. Despite the gain in insight to understand the effects of an intensification or reduction of training, the existing models would not be accurate enough to make predictions for a particular athlete in order to monitor his or her training.

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TEKİN, Nedim. "Analysis of the Mathematical Thinking Levels of Individual and Team Athletes in Terms of Different Variables." International Journal of Psychology and Educational Studies 8, no. 2 (April 19, 2021): 148–57. http://dx.doi.org/10.52380/ijpes.2021.8.2.403.

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This study was carried out to examine athletes' mathematical thinking levels who do individual and team sports in different variables. The study was conducted with a relational screening model, which is one of the general screening models. The data were collected by a survey method. "Mathematical Thinking Scale" was used to determine the mathematical thinking levels of athletes. The research population was composed of licensed athletes studying in high schools and universities in the 2020-2021 academic year in Turkey, while 459 licensed athletes determined among these students by a simple random method made up the sample group. The Independent-Samples T-Test was applied to determine the differences between the participants' gender, education and branch variables, and their mathematical thinking level. The Pearson Correlation test was applied to determine the relationship between age, sports year, and mathematical thinking levels. As a result of the analysis, a significant difference was observed favouring female participants in the gender variable and mathematical thinking skills sub-dimension. Additionally, it was determined that there was a significant positive relationship between the sports year and the reasoning sub-dimension. As a result, it is thought that the more inclusion of individual or team sports types in education programs will contribute to an individual's mathematics and academic success.

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Pop, S. R., S. L. Waters, G. Richardson, L. Lucas, C. A. Mitchell, and O. E. Jensen. "Mathematical models of capillary sprouts in developing microvascular networks." Journal of Biomechanics 39 (January 2006): S623. http://dx.doi.org/10.1016/s0021-9290(06)85591-0.

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16

Krijger, Johan K. B., Berend Hillen, and Hendrik W. Hoogstraten. "Mathematical models of the flow in the basilar artery." Journal of Biomechanics 22, no. 11-12 (January 1989): 1193–202. http://dx.doi.org/10.1016/0021-9290(89)90221-2.

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17

Smith, J. C., and D. W. Hill. "MATHEMATICAL MODELS OF THE POWER-TIME RELATIONSHIP IN HIGH INTENSITY CYCLING." Medicine & Science in Sports & Exercise 24, Supplement (May 1992): S74. http://dx.doi.org/10.1249/00005768-199205001-00444.

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Martins, Fernando, Ricardo Gomes, Vasco Lopes, Frutuoso Silva, and Rui Mendes. "Node and Network Entropy—A Novel Mathematical Model for Pattern Analysis of Team Sports Behavior." Mathematics 8, no. 9 (September 9, 2020): 1543. http://dx.doi.org/10.3390/math8091543.

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Pattern analysis is a well-established topic in team sports performance analysis, and is usually centered on the analysis of passing sequences. Taking a Bayesian approach to the study of these interactions, this work presents novel entropy mathematical models for Markov chain-based pattern analysis in team sports networks, with Relative Transition Entropy and Network Transition Entropy applied to both passing and reception patterns. To demonstrate their applicability, these mathematical models were used in a case study in football—the 2016/2017 Champions League Final, where both teams were analyzed. The results show that the winning team, Real Madrid, presented greater values for both individual and team transition entropies, which indicate that greater levels of unpredictability may bring teams closer to victory. In conclusion, these metrics may provide information to game analysts, allowing them to provide coaches with accurate and timely information about the key players of the game.

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SCHULTZ, ALBERT B. "The Use of Mathematical Models for Studies of Scoliosis Biomechanics." Spine 16, no. 10 (October 1991): 1211–16. http://dx.doi.org/10.1097/00007632-199110000-00014.

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20

Law, Laura A. Frey, and Richard K. Shields. "Predicting Human Paralyzed Soleus Muscle Force Properties Using Three Mathematical Muscle Models." Medicine & Science in Sports & Exercise 37, Supplement (May 2005): S35. http://dx.doi.org/10.1249/00005768-200505001-00193.

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Law, Laura A. Frey, and Richard K. Shields. "Predicting Human Paralyzed Soleus Muscle Force Properties Using Three Mathematical Muscle Models." Medicine & Science in Sports & Exercise 37, Supplement (May 2005): S35. http://dx.doi.org/10.1097/00005768-200505001-00193.

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22

Frey Law, L. A., and R. K. Shields. "Mathematical models of human paralyzed muscle after long-term training." Journal of Biomechanics 40, no. 12 (January 2007): 2587–95. http://dx.doi.org/10.1016/j.jbiomech.2006.12.015.

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23

Juan Llamas, María del Carmen. "Modelización matemática para la predicción y prevención de lesiones deportivas (Mathematical modeling for prediction and prevention of sports injuries)." Retos, no. 39 (September 21, 2020): 681–85. http://dx.doi.org/10.47197/retos.v0i39.81315.

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La predicción de lesiones deportivas a través de modelos matemáticos proporciona a entrenadores y deportistas información y herramientas para su prevención. Sabiendo dónde y/o cuándo pueden surgir problemas físicos en los atletas, se tratará de evitar que efectivamente aparezcan a través de estrategias como la modificación de los planes de entrenamiento y/o su intensidad, el tratamiento preventivo de posibles lesiones futuras, etc. En este artículo se lleva a cabo una revisión bibliográfica con el fin de determinar si el uso de modelos matemáticos para pronosticar lesiones es un método válido como medida de prevención en la práctica deportiva. Se concluye que las ecuaciones de regresión logística desarrolladas hasta la fecha no tienen en cuenta todos los factores que influyen en la aparición de lesiones, como variables psicológicas y factores externos que afectan a la vulnerabilidad del deportista. Por tanto, se propone la realización de nuevas fórmulas que engloben más factores causales de éstas, además de la creación de aplicaciones informáticas que utilicen dichos modelos para facilitar la labor de los especialistas del deporte. Abstract. The prediction of sports injuries using mathematical models provides coaches and athletes with information and tools for their prevention. By knowing where and/or when physical problems may arise in athletes, we can try to prevent them from appearing through strategies such as the modification of training plans and/or workout intensity, the preventive treatment of possible future injuries, etc. In this paper a systematic literature review was carried out to establish if the use of mathematical models for prediction of injuries is a valid method to be used in sports practice as a preventive measure. It is concluded that the logistic regression equations developed to date do not have in consideration all the variables that influence the appearance of injuries, such as psychological variables and external factors that affect the athlete’s vulnerability. Therefore, it is proposed to make new formulas that include more causal factors of these, in addition to the creation of computer applications that apply these equations in order to facilitate the work of the sports specialist.

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Booth, Kyle E. C., Timothy C. Y. Chan, and Yusuf Shalaby. "A mathematical optimization framework for expansion draft decision making and analysis." Journal of Quantitative Analysis in Sports 15, no. 1 (February 25, 2019): 27–40. http://dx.doi.org/10.1515/jqas-2018-0024.

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Abstract In this paper, we present and analyze a mathematical programming approach to expansion draft optimization in the context of the 2017 NHL expansion draft involving the Vegas Golden Knights, noting that this approach can be generalized to future NHL expansions and to those in other sports leagues. In particular, we present a novel mathematical optimization approach, consisting of two models, to optimize expansion draft protection and selection decisions made by the various teams. We use this approach to investigate a number of expansion draft scenarios, including the impact of “collaboration” between existing teams, the trade-off between team performance and salary cap flexibility, as well as opportunities for Vegas to take advantage of side agreements in a “leverage” experiment. Finally, we compare the output of our approach to what actually happened in the expansion draft, noting both similarities and discrepancies between our solutions and the actual outcomes. Overall, we believe our framework serves as a promising foundation for future expansion draft research and decision-making in hockey and in other sports.

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Damaser, Margot S., and Steven L. Lehman. "Two mathematical models explain the variation in cystometrograms of obstructed urinary bladders." Journal of Biomechanics 29, no. 12 (December 1996): 1615–19. http://dx.doi.org/10.1016/s0021-9290(96)80013-3.

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Sofiia, Kokhanska. "MODERNIZATION OF SPORTS EQUIPMENT AS A FACTOR OF INCREASING OF DIFFICULTY SCORE OF COMPETITIVE ROUTINES IN TRAMPOLINE GYMNASTICS." Sport Science and Human Health 4, no. 2 (2020): 50–63. http://dx.doi.org/10.28925/2664-2069.2020.2.5.

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Introduction.Trampoline gymnastics is a modern sport that has been included in the program of the Olympic Games since 2000. Constant improvement of the sports equipment, changes and innovations to the international rules of competitions ensure the continuous development of the sport and the wide world popularity of trampoline gymnastics. Aim is to acknowledge the relationship between the modernization of sports equipment and increasing of the difficulty score of competitive routines of athletes in trampoline gymnastics. Material and methods: theoretical analysis of scientific and methodical literature, retrospective analysis of protocols of international competitions, video analysis, methods of mathematical statistics. Results. The conducted research allowed to determine the main models of trampolines used at the international competitions in different historical periods; video analysis revealed the basic elements which formed athletes' competitive routines in 1964-1972; retrospective analysis of protocols of international competitions permitted to calculate the average, maximum and minimum difficulty scores of competitive routines of leading athletes in trampoline gymnastics at the World Championships and the World Cups from 1972 to 2020 and identify the interconnection between modernization of the trampolines and increasing of the difficulty scores of competitive routines of trampoline athletes in different historical periods of the sport development. Conclusions. The led studies confirmed the interconnection between increasing of numbers of high difficult elements and difficulty scores of competitive routines of athletes and modernization of sports equipment in trampoline. According to the results of the research, the average difficulty score of competitive routines of qualified athletes raised from 0.2 to 0.5 points and maximum difficulty score from 0.1 to 0.7 points after introduction of each new model of trampoline.

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Заневський, І. П., and Л. Г. Заневська. "model of the reliability of the test, alternative models inside class correlation." Teorìâ ta Metodika Fìzičnogo Vihovannâ, no. 1 (March 31, 2014): 43–52. http://dx.doi.org/10.17309/tmfv.2014.1.1044.

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The aim was to create a model of the reliability of the test, the application of which would in the practical work with the tests to receive the value of the coefficient of reliability in the theoretical framework from zero to one, as is customary in classical theory of reliability tests. The basic idea of solving this problem was in determining the true variance of the test results, the value of which is equal to the arithmetical average of the results of the repeated measurements. Methodology of the research was based on provisions of the classical theory of sports tests, mathematical theory of reliability of motor tests, on the model of intraclass correlation, ANOVA, using the method of Shapiro-Wilk. Calculations were carried out using Excel and Mathematica computer programs. It was shown that the intraclass correlation model is incomplete with the line of the classical theory of reliability tests. The proposed model of retest reliability does not have this shortage, and the corresponding coefficient is defined in terms of the classical theory of reliability (0 ÷ 1). In the range of almost important quantities of the proposed model and the intraclass model correlations lead to different estimates of the reliability of the test not only quantitatively (≈ 20%), but also qualitatively, i.e., with significant excess width of the ranges of test estimation of reliability coefficient of the corresponding size.

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McGrowder, Donovan, Paul Brown, Ruby Lisa Alexander-Lindo, Shirley Budall, Rachael Irving, and Lorenzo Gordon. "The Use of Soluble Transferrin Receptor in the Detection of rHuEPO abuse in Sports." Biochemistry Insights 3 (January 2010): BCI.S3943. http://dx.doi.org/10.4137/bci.s3943.

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Erythropoietin (EPO) increases the number of circulating erythrocytes and muscle oxygenation. The recombinant forms of EPO have indiscriminately been used by athletes, mainly in endurance sports to increase their erythrocytes concentration, thus generating a better delivery of oxygen to the muscle tissue. The administration of recombinant human erythropoietin (rHuEPO) except for therapeutic use was prohibited by the International Olympic Committee (IOC) and its unauthorized use considered as doping. In the last few years, a number of studies using parameters indicative of accelerated erythropoiesis have investigated a number of indirect methods for the detection of rHuEPO abuse. No single indirect marker has been found that can satisfactorily demonstrated rHuEPO misuse. Soluble transferrin receptor (sTfR) is a new marker of iron status and erythropoietic activity. It has been included in multivariable blood testing models for the detection of performance enhancing EPO abuse in sports. Indirect markers of altered erythropoiesis give reliable evidence of current or discontinued rHuEPO usage. This review describes the physical, biological and pharmacokinetic properties of endogenous EPO and its recombinant form. It also discusses the available strategies for the detection of rHuEPO abuse in sports, involving the use of sTfR concentration directly or in mathematical multivariate models.

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HENDRIX, C. RUSSELL, TERRY J. HOUSH, MICHELLE MIELKE, JORGE M. ZUNIGA, CLAYTON L. CAMIC, GLEN O. JOHNSON, and RICHARD J. SCHMIDT. "Critical Torque, Estimated Time to Exhaustion, and Anaerobic Work Capacity from Linear and Nonlinear Mathematical Models." Medicine & Science in Sports & Exercise 41, no. 12 (December 2009): 2185–90. http://dx.doi.org/10.1249/mss.0b013e3181ab8cc0.

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Olha, Borysova, Shutova Svitlana, Nagorna Viktoriia, Shlonska Olha, Serebriakov Oleh, and Mytko Artur. "CHARACTERISTICS OF COMPETITIVE ACTIVITY OF UKRAINIAN NATIONAL TEAMS IN SPORTS GAMES IN THE INTERNATIONAL AREA." Sport Science and Human Health 4, no. 2 (2020): 27–37. http://dx.doi.org/10.28925/2664-2069.2020.2.3.

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Introduction. At the present development stage of the high achievement sport, global transformations are taking place all over the world, which have influenced the intensification of competitive practices and the introduction of innovative technologies in the process of training elite athletes. Unfortunately, both external factors and internal political and economic problems in Ukraine become a serious obstacle to the effective competitive activity of national teams at major international sports competitions, namely: the socio-economic situation in the country calls into question the ability to prepare quality reserve, children's and youth sports suffer as a result of the financial and economic crisis; Insufficient level of logistics and the possibility of migration of the best players and coaches abroad, negatively affects the level of performance of the national team in the international arena. The planning of preparation of highly qualified athletes for the main international competitions should take into account the peculiarities of tournament loads in team and individual sports. Why is it necessary to determine the main factors influencing the quality and effectiveness of the performances of the best athletes and teams in sports games. Aim of our research is to analyze the effectiveness of competitive activities of highly qualified athletes in sports games. Material and methods: analysis of planning and competition documents and generalization of special literature, method of expert assessments, pedagogical observation, pedagogical experiment, psychophysiological methods, methods of mathematical statistics. Conclusions: the implementation of effective performance of athletes of Ukrainian national teams in sports on the international arena requires optimization of the process of sports training based on individualization with the parallel use of technical-tactical, psychophysiological models of training of leading players in the world combined with modern capabilities.

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Wan, Fang Xing, Dong Hu, and Jing Tian. "Evaluation of College Coach Capacity in USA." Advanced Materials Research 998-999 (July 2014): 1693–96. http://dx.doi.org/10.4028/www.scientific.net/amr.998-999.1693.

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To manage operation mechanism of sports coaching teams, the mathematical models are introduced based on the coach evaluation system in USA. Using datum of college coaches and economy in USA from 1913 to 2013, we select top 3 college coaches in basketball, football and baseball field respectively from nearly 4,000 coaches by the AHP model and the Input-Output model. The conclusion is that economic factors should be considered in evaluating coach capacity.

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Sarafyniuk, L. A., A. V. Syvak, V. V. Piliponova, S. V. Dus, and O. V. Lezhnova. "The variation pulsometry correct indicators` modeling in volleyball players with mesomorphic somatotype depending on the anthropometric features of the organism." Reports of Vinnytsia National Medical University 23, no. 4 (December 30, 2019): 567–72. http://dx.doi.org/10.31393/reports-vnmedical-2019-23(4)-02.

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Annotation. Appropriate cardiointervalographic parameters establishment, for highly skilled athletes of a particular sport, is relevant and can be used for diagnostic purposes and because of connection with the widespread prevalence of cardiovascular pathology. The purpose of the work was to construct regression models of the variations of the pulsometry in volleyball players of the mesomorphic somatotype, depending on the features of anthropometric indicators. The study involved 24 volleyball players with a high level of sportsmanship (from the first adult category to candidates for the master of sports), aged 17–21 years. We carried out anthropometric research by Bunak's method (1941), somatotypological - by the calculated modification of the Heath-Carter method (1990), determination of the component composition of the body weight by the method of Matejko (1992) and cardiointervalographic examination using a computer diagnostic complex “OPTW” following the recommendations of the European and North American Cardiac Association [1996]. The following indicators of variation heart rate were determined: moda, moda amplitude, average minimum and maximum R-R intervals, and variation range. The mathematical models were constructed in the “STATISTICA 5.5” package for Windows using direct stepwise regression analysis. The article presents the results of regression analysis for determining the dependence of variation heart rate indicators in volleyball players of mesomorphic somatotype on the total complex of constitutional characteristics. Mathematical models for determination of individual proper cardiointervalographic parameters based on features of the external structure of the body of youth volleyball players of high level of sportsmanship. The analysis of constitutional predictors that determine the variability of indicators of variation heart rate in a group of volleyball players of mesomorphic somatotype has been performed.

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Roehrnbauer, B., T. Schratzenstaller, E. Wintermantel, and R. Mongrain. "Mathematical and experimental development of two types of stent models for fluid dynamical investigations." Journal of Biomechanics 39 (January 2006): S617. http://dx.doi.org/10.1016/s0021-9290(06)85565-x.

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Chekanushkina, Elena, Elena Ryabinova, and Diera Pirova. "The Application of Mathematical Modeling in Building of Social and Environmental Competence of Future Technical Specialists in the Health Care Area." BIO Web of Conferences 26 (2020): 00036. http://dx.doi.org/10.1051/bioconf/20202600036.

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The paper considers building of social and environmental competence of future technical specialists. It shows that health care competence building is becoming more pressing issue each year. Behavioral patterns are formed in the process of training, upbringing and observing people around. They allow forming the ability or readiness to use the acquired interdisciplinary knowledge in professional activities related to health, safety of human life, as well as in the process of studying such disciplines as the “Elective Courses on Physical Education and Sports” and “Physical Education and Sports”. The patterns offer the possibility to develop a behavioral socio-ecological algorithm efficiently. In pedagogy and didactic processes, mathematical modeling is aimed at clarifying phenomena that are not amenable to experiment or unobservable as well as patterns of education for the development of efficient teaching technologies. The paper considers mathematical descriptions of the models for formation, interaction and efficiency of various target groups exemplified by Nordic walking, indoor soccer and interdisciplinary teams. It shows the dependence of student group population on an activity and quantitative composition of potential participants of sports group. This mathematical model is also applicable for building socioecological competence of future technical specialists in the framework of participation in interdisciplinary projects, research activities, Olympiads, social and environmental events that contribute to the assimilation of socio-ecological patterns of behavior, the condition for the development of which is the unity of cognitive and practical activities in the process of studying at the university. The paper includes the interim experiment results.

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Hvattum, Lars Magnus. "A comprehensive review of plus-minus ratings for evaluating individual players in team sports." International Journal of Computer Science in Sport 18, no. 1 (July 1, 2019): 1–23. http://dx.doi.org/10.2478/ijcss-2019-0001.

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AbstractThe increasing availability of data from sports events has led to many new directions of research, and sports analytics can play a role in making better decisions both within a club and at the level of an individual player. The ability to objectively evaluate individual players in team sports is one aspect that may enable better decision making, but such evaluations are not straightforward to obtain. One class of ratings for individual players in team sports, known as plus-minus ratings, attempt to distribute credit for the performance of a team onto the players of that team. Such ratings have a long history, going back at least to the 1950s, but in recent years research on advanced versions of plus-minus ratings has increased noticeably. This paper presents a comprehensive review of contributions to plus-minus ratings in later years, pointing out some key developments and showing the richness of the mathematical models developed. One conclusion is that the literature on plus-minus ratings is quite fragmented, but that awareness of past contributions to the field should allow researchers to focus on some of the many open research questions related to the evaluation of individual players in team sports.

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Fujii, Keisuke. "Data-Driven Analysis for Understanding Team Sports Behaviors." Journal of Robotics and Mechatronics 33, no. 3 (June 20, 2021): 505–14. http://dx.doi.org/10.20965/jrm.2021.p0505.

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Understanding the principles of real-world biological multi-agent behaviors is a current challenge in various scientific and engineering fields. The rules regarding the real-world biological multi-agent behaviors such as those in team sports are often largely unknown due to their inherently higher-order interactions, cognition, and body dynamics. Estimation of the rules from data, i.e., via data-driven approaches such as machine learning, provides an effective way to analyze such behaviors. Although most data-driven models have non-linear structures and high predictive performances, it is sometimes hard to interpret them. This survey focuses on data-driven analysis for quantitative understanding of behaviors in invasion team sports such as basketball and football, and introduces two main approaches for understanding such multi-agent behaviors: (1) extracting easily interpretable features or rules from data and (2) generating and controlling behaviors in visually-understandable ways. The first approach involves the visualization of learned representations and the extraction of mathematical structures behind the behaviors. The second approach can be used to test hypotheses by simulating and controlling future and counterfactual behaviors. Lastly, the potential practical applications of extracted rules, features, and generated behaviors are discussed. These approaches can contribute to a better understanding of multi-agent behaviors in the real world.

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Nordez, Antoine, Christophe Cornu, and Peter McNair. "Acute effects of static stretching on passive stiffness of the hamstring muscles calculated using different mathematical models." Clinical Biomechanics 21, no. 7 (August 2006): 755–60. http://dx.doi.org/10.1016/j.clinbiomech.2006.03.005.

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Nagy, G. T., and C. R. Gentle. "SIGNIFICANCE OF THE ANNULUS PROPERTIES TO FINITE ELEMENT MODELING OF INTERVERTEBRAL DISCS." Journal of Musculoskeletal Research 05, no. 03 (September 2001): 159–71. http://dx.doi.org/10.1142/s0218957701000532.

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Current mathematical material laws work quite accurately with conventional engineering materials because they are linear and isotropic. These laws are much less effective, however, at representing living tissues. Biomechanical engineers therefore often face the problems of modelling material non-linearities, particularly with the soft tissues, muscles and tendons of the human body. The non-linear and often anisotropic structure of these materials makes any mathematical representation very difficult. In particular, the lack of a good general mathematical model of the intervertebral disc has hampered the study of spinal mechanics, as the disc annulus is a nonlinear fibrous tissue with highly directional properties. Previous studies have concentrated on the overall behavior of discs and this has been largely explained but knowledge is still very limited on the effect of the individual disc components. This means that current mathematical models are poor when it comes to describing a prolapsed disc, where there has been failure of at least one of the components. This finite element study described here focuses on the disc annulus properties and their effect on disc behavior. The novelty of this study lies in the material formulation of the annulus fibrosus, which changes its Young's modulus according to a non-linear curve.

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Zagrevskiy, V., and O. Zagrevskiy. "SYNTHESIS OF PROGRAM AND FINITE LAWS OF MOTION IN ANALYTICAL MODELS OF CONTROL OF THE FINAL STATE OF BIOMECHANICAL SYSTEMS." Human Sport Medicine 19, no. 1 (May 27, 2019): 93–99. http://dx.doi.org/10.14529/hsm190113.

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Aim. The article deals with developing a computer program to simulate the movement of the object with a given initial and final speed and fixed travel time. Materials and methods. The analysis, as a method of biomechanics, allows us to assess the biomechanical state of the athlete in real sports exercises. The function of motion synthesis is the ability to predict the trajectory and behavior of the biomechanical system at specified reference points of the phase structure of the simulated motion. The article deals with one of the methods of biomechanical synthesis of movements: synthesis of control of the final state of biomechanical systems, based on the reduction of finite control to a given program control after attenuation of the transient component of acceleration. The mathematical description of the object motion is based on the known law of finite control with feedback. Integration of the mathematical model constructed in the form of the differential equation of the second order was carried out by one of the numerical methods of integration: Runge–Kutta method of the fourth order of accuracy. Consideration of the method is based on a mathematical apparatus describing the motion of a material point, which can be represented by a common center of mass of a biomechanical system, a joint, a center of mass of a segment, etc. Results. The mathematical model of the motion of a material point with the given kinematic parameters of motion at the initial and final moments is implemented in a computer program in the Visual Basic 2010 language environment based on the integrated development environment Visual Studio Express 2013. The output provides numerical and visual support for simulation results. Conclusion. It is shown that the developed computer model of the method always implements the goal of motion: to transfer an object from a given initial state by speed to a given final state for a fixed time of movement.

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Dash, Ranjan K., Ben Korman, and James B. Bassingthwaighte. "Simple accurate mathematical models of blood HbO2 and HbCO2 dissociation curves at varied physiological conditions: evaluation and comparison with other models." European Journal of Applied Physiology 116, no. 1 (August 23, 2015): 97–113. http://dx.doi.org/10.1007/s00421-015-3228-3.

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Sagherian, Knar, Shijun Zhu, Carla Storr, Pamela S. Hinds, Debra Derickson, and Jeanne Geiger-Brown. "Bio-mathematical fatigue models predict sickness absence in hospital nurses: An 18 months retrospective cohort study." Applied Ergonomics 73 (November 2018): 42–47. http://dx.doi.org/10.1016/j.apergo.2018.05.012.

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Selbie, W. S., and C. L. Ludlow. "Developing a mathematical model of the human larynx: Testing two proposed models of the cricoarytenoid joint using videolaryngoscopy." Journal of Biomechanics 27, no. 6 (January 1994): 816. http://dx.doi.org/10.1016/0021-9290(94)91376-5.

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Gobatto, C. A., P. P. M. Scariot, L. F. P. Ribeiro, and F. B. Manchado-Gobatto. "Critical load estimation in young swimming rats using hyperbolic and linear models." Comparative Exercise Physiology 9, no. 2 (January 1, 2013): 85–91. http://dx.doi.org/10.3920/cep13010.

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We analysed the viability of critical load (CL) and anaerobic swimming capacity (ASC) estimation by different mathematical models and the effects of varying the number/intensity of predictive trials on these parameters in young swimming rats. After familiarised to swimming, 9 male animals had time to exhaustion (TEX) accessed in efforts against 9, 11, 13 and 15% of their body mass (bm). CL and ASC were calculated by the hyperbolic load vs. TEX (Hyp) as well as linear load vs. 1/TEX (Lin1) and load·TEX vs. TEX (Lin2) models. Moreover, parameters derived from the 11 possible combinations of 2, 3 or 4 efforts using the Lin1 regression were compared. The Lin1 model resulted in a lower R2 compared to Lin2 and Hyp methods (0.968±0.010 vs. 0.995±0.004 and 0.988±0.013; P<0.05), but no significant differences were found between models regarding CL (7.8±1.2, 7.9±1.1 and 7.8±1.0% bm) or ASC (526±129, 521±104 and 534±117% bm?s). Except for the atypical CL (1.4 ± 4.2% bm) and ASC (1079 ± 383% bm⋅s) from trials against 13 and 15% bm, varying the number/intensity of predictive bouts had no significant effects on parameter estimates. The observed viability and robustness of CL and ASC estimation by different mathematical models in young swimming Wistar rats suggest the load-time relationship as an interesting tool to investigate the physiological mechanisms underlying exercise tolerance in laboratory rodents.

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Bergstrom, Haley C., Terry J. Housh, Jorge M. Zuniga, Daniel A. Traylor, Robert W. Lewis, Clayton L. Camic, Richard J. Schmidt, and Glen O. Johnson. "Differences Among Estimates of Critical Power and Anaerobic Work Capacity Derived From Five Mathematical Models and the Three-Minute All-Out Test." Journal of Strength and Conditioning Research 28, no. 3 (March 2014): 592–600. http://dx.doi.org/10.1519/jsc.0b013e31829b576d.

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Nikolaienko, Valerii, Borys Maksymchuk, Ihor Donets, Pavlo Oksom, Nazarii Verbyn, Vadym Shemchuk, and Iryna Maksymchuk. "Cycles of Training Sessions and Competitions of Youth Football Players." Revista Romaneasca pentru Educatie Multidimensionala 13, no. 2 (July 2, 2021): 423–41. http://dx.doi.org/10.18662/rrem/13.2/429.

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At the present level of football development, the requirements for athletic skills are increasing. Given a fierce competition in the international and national sports arena as never before, it is important to mobilize functional reserves and maximize individual inclinations of players to demonstrate the highest capability for sport in the period optimal for it. It is precisely a long-term training programme focused on the demonstration of natural inclinations that is a strategic area in the training of qualified athletes under the current conditions. Adhering to qualitative characteristics of the training process should become the basis for evaluating the rational structure of a long-term training process. The paper aims to theoretically and methodically justify the periods of training sessions and competitions of youth football players. Research methods are the following: general theoretical methods (analysis, synthesis, abstraction, comparison, generalization and descriptive mathematical statistics), systemic theoretical methods (structural analysis, functional analysis, structural-and-functional analysis, historical method, system modelling), a study of the printed and electronic sources of information, description, interviewing, expert survey. An analysis of scientific and methodological literature, legal documents and training programmes adopted in the countries with a high level of football development has made it possible to construct models of annual programs based on the years of study with further regulation of cycles of training sessions and competitions. Rational construction of the system of footballers’ long-term training is based on the introduction of changes in the organization and holding of children’s and youth competitions, pedagogical principles of managing sports activities and technologies for training youth football players, as well as methods of evaluating children’s coaches’ professional performance.

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Kennedy, Michael D. J., and Gordon J. Bell. "A Comparison of Critical Velocity Estimates to Actual Velocities in Predicting Simulated Rowing Performance." Canadian Journal of Applied Physiology 25, no. 4 (August 1, 2000): 223–35. http://dx.doi.org/10.1139/h00-017.

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The most accurate critical velocity (CV) estimate for the prediction of velocity during a simulated 2,000-m rowing race and the relationship to aerobic power were studied. Sixteen male rowers completed randomized maximal exertion trials (200, 400, 600, 800, 1,000, and 1,200 m), a maximal oxygen consumption [Formula: see text] on a Concept II rowing machine, and an actual 2,000-m simulated rowing race. Three mathematical models were applied to 4 rowing distance combinations producing 12 CV estimates. Seven of the 12 possible CV estimates were not significantly different from actual 2,000-m velocity. Comparison of the 3 CV models using all 6 trial distances revealed that the nonlinear model produced a CV estimate lower than the 2 linear CV models. CV was significantly correlated to [Formula: see text] (r = 0.91) and the mean velocity achieved during the 2,000-m simulated rowing race (r = 0.97). [Formula: see text] was significantly correlated to 2,000-m simulated rowing race velocity (r = 0.93). Key words: maximal oxygen consumption, critical power, critical speed

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Kilani, Hashem. "CAN WE DETERMINE FATIGUE IN GAIT BY ANALYZING THE DYNAMICS OF A MATHEMATICAL MODEL?" DRASSA Journal of Development and Research for Sport Science Activities 2, no. 1 (July 8, 2019): 1–11. http://dx.doi.org/10.31377/jdrssa.v2i1.506.

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Motion analysis implies that sufficiently complex models of the human neuromusculoskeletal system can be used for the simulation and analysis of sports motions and, at least in principle, for the biomechanical optimization of the performance in the various sport disciplines. A new methodological assessment using the Fast Fourier Transform was created to compare the frequency patterns of the gait in terms of Phase space model as a mathematical space that represents all states of a system. In this respect, the n marker coordinates connected to a human body and the respective velocities establish a 2n-dimensional phase space and hence fully describe the movement. For example, the scalar product of the distance between shoulder and ankle was investigated using a Fast Fourier Transform (Muller, Vieten & Kilani, 2012.) Using similar approach, can we provide enough information to identify a certain degree of fatigue in running based just on one parameter, say the distance between the left hip joint and the tip of the left foot as a function of time? Our subjects walked/run at their individual speed on a treadmill by holding at both sidebars to get comparable movement patterns. A motion analysis was investigated with three infrared cameras at a frequency of 100Hz by Lukotronic System (LUKOtronic Lutz-Kovacs-Electronics OEG, Innsbruck, Austria). Eleven reflected markers were placed at the backside of the subjects. The scalar product of the distance between shoulder and ankle was investigated using a Fast Fourier Transform. To amplify the higher harmonical frequencies, the distance data was differentiated with respect to time. To be independent of individual walking speed, the frequency data was normalized afterwards. The area under the first peak (fundamental frequency) and the nine following peaks (higher harmonical frequencies) were measured. Next step in the methodology is filtering; followed by calculating the first derivative and thereafter the plot of the phase space (Vieten, 2007). This paper demonstrates that beside the traditional descriptive" studies (standard equipment and a moderate amount of work expenditure) and the simulations approach (usually with lots of effort, lots of equipment) a third avenue the “dynamical system approach" (DSA) exists. DSA promises new and exciting views of new and old problems while the expenditure in equipment and time is also affordable for smaller research groups.

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de Jesus, Karla, Helon V. H. Ayala, Kelly de Jesus, Leandro dos S. Coelho, Alexandre I. A. Medeiros, José A. Abraldes, Mário A. P. Vaz, Ricardo J. Fernandes, and João Paulo Vilas-Boas. "Modelling and Predicting Backstroke Start Performance Using Non-Linear And Linear Models." Journal of Human Kinetics 61, no. 1 (March 23, 2018): 29–38. http://dx.doi.org/10.1515/hukin-2017-0133.

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AbstractOur aim was to compare non-linear and linear mathematical model responses for backstroke start performance prediction. Ten swimmers randomly completed eight 15 m backstroke starts with feet over the wedge, four with hands on the highest horizontal and four on the vertical handgrip. Swimmers were videotaped using a dual media camera set-up, with the starts being performed over an instrumented block with four force plates. Artificial neural networks were applied to predict 5 m start time using kinematic and kinetic variables and to determine the accuracy of the mean absolute percentage error. Artificial neural networks predicted start time more robustly than the linear model with respect to changing training to the validation dataset for the vertical handgrip (3.95 ± 1.67 vs. 5.92 ± 3.27%). Artificial neural networks obtained a smaller mean absolute percentage error than the linear model in the horizontal (0.43 ± 0.19 vs. 0.98 ± 0.19%) and vertical handgrip (0.45 ± 0.19 vs. 1.38 ± 0.30%) using all input data. The best artificial neural network validation revealed a smaller mean absolute error than the linear model for the horizontal (0.007 vs. 0.04 s) and vertical handgrip (0.01 vs. 0.03 s). Artificial neural networks should be used for backstroke 5 m start time prediction due to the quite small differences among the elite level performances.

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Arango, Ivan, Carlos Lopez, and Alejandro Ceren. "Improving the Autonomy of a Mid-Drive Motor Electric Bicycle Based on System Efficiency Maps and Its Performance." World Electric Vehicle Journal 12, no. 2 (April 8, 2021): 59. http://dx.doi.org/10.3390/wevj12020059.

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Around the world, the e-bike has evolved from a recreational and sports object to an increasingly used means of transportation. Due to this, improving aspects such as range and energy efficiency has become very relevant. This article presents experimental models for the components’ efficiency of a mid-drive motor e-bike (charger; battery; and controller, motor, and reduction gears subsystem), and integrates them with previously elaborated models for the chain transmission system, thus generating an overall efficiency map of the e-bike. The range of the electric bicycle is analyzed by integrating the efficiency map of the system and its performance mathematical model, aiming to determine the per unit of distance battery energy consumption. The above-mentioned calculations are applied to develop a management strategy that can determine the optimal assistance level and chain transmission ratio, maximizing range and leaving speed unaffected. The driving strategy was compared against other driving techniques using computational analysis, this allowed for the observation of the proposed strategy improving the system’s range by reducing the battery energy consumption.

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Chanev, Sasho. "NORMATIVE FRAMEWORK FOR CONTROL AND OPTIMIZATION OF THE PHYSICAL DEVELOPMENT AND SPECIFIC WORKING CAPACITY OF 17-19-YEAR-OLD HANDBALL PLAYERS." Journal of Applied Sports Sciences 1, no. 2021 (July 20, 2021): 22–41. http://dx.doi.org/10.37393/jass.2021.01.3.

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The purpose of this study is to reveal the average level and variability of the signs of physical development and specific working capacity of 17-19-year-old Bulgarian handball players and, on this basis, to develop an up-to-date norm framework for control and optimization of sports training in the studied age group. The object of the study is the characteristics of physical development, specific physical fitness, technical and tactical skills, and some mental characteristics. The research was done among 115 handball players between the age of 17 and 19 from the top 10 teams, participating in the national championship for juniors under 19 years old. Anthropometric measurements and sports-pedagogical testing were conducted for the needs of the study with a total of 34 indicators for establishing the level of physical development, specific physical and technical-tactical preparation and some mental characteristics and qualities of the handball players of the studied age group. The following research methods were applied to solve the purpose and tasks of the research: review study and theoretical analysis of the specialized literature, anthropometry, manual dynamometry, sports-pedagogical testing and ascertaining psychological experiment. Frequency analysis and descriptive statistics, sigma estimation method, and index method were used for mathematical-statistical data analysis. The applied approach allowed developing normative tables for evaluation of the results of each competitor or team, based on which, person or team optimization models could be developed, revealing both strengths and weaknesses in their preparation.

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Journal articles on the topic 'Sports – Mathematical models'

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