not depending on the absolute values of the data.

Before identification with SINDy begins, the possible state indicators (relay hysterons, Section \[modelingDiscreteStates\]) have to be computed from the data. This is done in three steps: Building indicator functions, pairwise matching of indicator functions and evaluating the relay hysterons.

We assume a change of the system behavior as soon as a value $x$ rises above $\beta \in \mathbb{R} $ or falls below $\alpha \in \mathbb{R} $. We also assume $\alpha$ and $\beta$ are included in our data. The first step is to build differences between all time series in our data. If the units of the time series are known, it is helpful only to build differences between commensurable data, e.g. time series which share the same unit, as exemplarily done in Eq. . $$\begin{aligned}
        \label{eq:differences}
        \tilde{x}_1 &= x-\alpha \\
        \tilde{x}_2 &= x-\beta \\
        \tilde{x}_3 &= \alpha - \beta
    \end{aligned}$$

We then create indicator functions masking these differences depending on the sign of the value. $I(\tilde{x}_2)$ masks ranges, where $x \geq \beta$. $\bar{I}(\tilde{x}_1)$ on the other hand masks ranges, where $x < \alpha$. $$\begin{aligned}
\begin{split}
I(x) &= \begin{cases}
1,  & \text{if $x \geq 0 $} \\
0,  & \text{if $x < 