diff --git a/main.tex b/main.tex index 6ece362..8d37d3d 100644 --- a/main.tex +++ b/main.tex @@ -700,8 +700,8 @@ \subsection{Utility of the Logistic Model and Extrapolation to Natural Falls} applied angular impulse $L$, and dividing this by $\sigma_{L}$. The same applies for the perturbation order $j$, initial roll angle $\phi_0$, and initial steer angle $\delta_0$. If we take the coefficients estimated for -cycling at 6~\si{\kph}, the log-odds of falling can be calculated as follows: -\todo{Check this equation, where is \(\bar{L}\) 100N in the equation?} +cycling at 6~\si{\kph} and example means, the log-odds of falling can be +calculated as follows: % \begin{equation} \begin{split} @@ -711,11 +711,11 @@ \subsection{Utility of the Logistic Model and Extrapolation to Natural Falls} = & -0.29 + 1.69\cdot\frac{110~\si{\newton} - 100\si{\newton}}{15\si{\newton}} -0.77\cdot\frac{10-20}{11.54} \\ & -0.25\cdot\frac{-6\si{\degree}-2\si{\degree}}{10\si{\degree}} - -0.14\cdot\frac{1\si{\degree}+3\si{\degree}}{5\si{\degree}} -0.64\cdot s \\ + -0.14\cdot\frac{1\si{\degree}+3\si{\degree}}{5\si{\degree}} -0.64 s \\ = & - 1.59 -0.64 \cdot s - \end{split} + 1.59 -0.64 s \textrm{.} + \end{split} \end{equation} % The state of the balance assist \(s\) is a binary variable. If the @@ -723,10 +723,10 @@ \subsection{Utility of the Logistic Model and Extrapolation to Natural Falls} 0.64. The odds and probability can be calculated: % \begin{align} - \frac{p_{ij}}{1-p_{ij}} & = e^{1.59-0.64c} = - e^{1.59}\cdot e^{-0.64s} = 4.90 \cdot 0.53c \\ - p_{ij}|_{c=0} & = \frac{4.90}{1 + 4.90} = 0.83 \\ - p_{ij}|_{c=1} & = \frac{4.90\cdot0.53}{1 + 4.90\cdot{0.53}} = 0.72 + \frac{p_{ij}}{1-p_{ij}} & = e^{1.59-0.64s} = + e^{1.59}\cdot e^{-0.64s} = 4.90 \cdot e^{-0.64s} \\ + p_{ij}|_{s=0} & = \frac{4.90}{1 + 4.90} = 0.83 \\ + p_{ij}|_{s=1} & = \frac{4.90\cdot0.53}{1 + 4.90\cdot{0.53}} = 0.72 \end{align} % Turning on the balance assist system reduces the probability that the @@ -858,9 +858,10 @@ \section*{Acknowledgements} \section*{Funding} % This study is funded by Dutch Research Council, Nederlandse Organisatie voor -Wetenschappelijk Onderzoek (NWO), under the Citius Altius Sanius program and in -collaboration with Bosch eBike Systems and Royal Dutch Gazelle. The funders had -no role in the data collection and analysis or preparation of the manuscript. +Wetenschappelijk Onderzoek (NWO), under the Citius Altius Sanius Perspectief +program and in collaboration with Bosch eBike Systems and Royal Dutch Gazelle. +The funders had no role in the data collection and analysis or preparation of +the manuscript. \section*{Code and Data Availability} %