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Linear Approximation in Time Domain01:21

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Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
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The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
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Transfer Function to State Space01:23

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State-space representation is a powerful tool for simulating physical systems on digital computers, necessitating the conversion of the transfer function into state-space form. Consider an nth-order linear differential equation with constant coefficients, like those encountered in an RLC circuit. The state variables are selected as the output and its n−1 derivatives. Differentiating these variables and substituting them back into the original equation produces the state equations.
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Mechanistic models are utilized in individual analysis using single-source data, but imperfections arise due to data collection errors, preventing perfect prediction of observed data. The mathematical equation involves known values (Xi), observed concentrations (Ci), measurement errors (εi), model parameters (ϕj), and the related function (ƒi) for i number of values. Different least-squares metrics quantify differences between predicted and observed values. The ordinary least...
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Model Approaches for Pharmacokinetic Data: Physiological Models

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Physiological models in pharmacokinetics are instrumental in understanding the distribution and elimination of drugs within the body. These models describe the drug concentration within target organs, influenced by factors such as drug uptake, tissue volume, and blood flow. Drug uptake is governed by the partition coefficient, which signifies the drug concentration ratio in tissue to that in the blood. The blood flow rate to a specific tissue is expressed as Qt, and the rate of change in tissue...
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The conversion of state-space representation to a transfer function is a fundamental process in system analysis. It provides a method for transitioning from a time-domain description to a frequency-domain representation, which is crucial for simplifying the analysis and design of control systems.
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Modelling menstrual cycle length in athletes using state-space models.

Thiago de Paula Oliveira1,2,3, Georgie Bruinvels2,4, Charles R Pedlar2,4

  • 1School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland.

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Summary

Predicting menstrual cycle length aids female athletes in optimizing training and nutrition. A new hybrid model accurately forecasts cycle duration, supporting athlete wellness and performance.

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Area of Science:

  • Sports Science
  • Biostatistics
  • Women's Health

Background:

  • Accurate prediction of menstrual cycle length is crucial for female athletes to tailor training and nutrition.
  • Significant inter-individual variation in cycle length necessitates personalized predictive approaches.
  • Existing methods may not fully capture the complexities of menstrual cycle variability.

Purpose of the Study:

  • To develop and validate a hybrid predictive model for forecasting individual menstrual cycle length.
  • To enhance personalized sports management strategies for female athletes through precise cycle prediction.
  • To improve understanding of factors influencing menstrual cycle duration.

Main Methods:

  • A hybrid mixed-effect state-space model was developed using data from 2125 women (16,524 cycles).
  • The model incorporated a Bayesian approach for forecasting, including time trend, autocorrelation, and covariate components.
  • Model performance was assessed using root mean square error (RMSE), concordance correlation coefficient, and Pearson correlation coefficient.

Main Results:

  • The hybrid model demonstrated high accuracy with an RMSE of 1.6412 days.
  • Precision and overall accuracy were reported at 0.7361 and 0.9871, respectively.
  • The model effectively captured within-subject temporal correlations and accounted for overdispersion.

Conclusions:

  • The developed hybrid model provides a reliable method for predicting menstrual cycle length.
  • This predictive capability can significantly support the wellness and performance optimization of female athletes.
  • The model's accuracy supports its application in personalized sports science and healthcare.