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Mathematics Colloquium by Zach Dekko '23, Wednesday, December 7

Wed, December 7th, 2022
1:00 pm
- 1:45 pm

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Mathematical Modeling of Athletic Performance: Laplace Transforms, Convolutions, and Influence Curves for Optimizing Performance by Zach Dekko ’23, Mathematics Colloquium, Wednesday, December 7, 1 – 1:45 pm, North Science Building 113, Wachenheim.

Abstract:  There exists two methods for modeling athletic training and performance: the Critical Power (CP) and Impulse Response (IR) models.  This presentation will focus on the derivation of Eric Banister’s Impulse Response model using Laplace Transforms and convolutions to account for the daily impulses in a standard athletic training program.  I will present on the interaction between positive training effects and negative training effects that are dependent on exercise impulses, fixed decay constants for both fitness and fatigue, and training multipliers to determine an individual’s performance at a given time, t.  Using influence curves to determine the optimal training and rest times for maximizing performance, I will utilize running data to demonstrate the effectiveness and accuracy of the model in a comparison of the projected outcomes against real data.

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