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update to make github render the notes
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kociumba committed Sep 2, 2024
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7 changes: 3 additions & 4 deletions notes.md
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Expand Up @@ -26,10 +26,9 @@ $$f(x) = 100 \tanh(kx)$$
$$f(x) = \frac{100x}{\sqrt{1 + kx^2}}$$

**Piecewise Smoothing:**
$$f(x) = \begin{cases}
\frac{x}{(1 + (\frac{x}{100})^n)^{\frac{1}{n}}} & \text{if } x > 0 \
-\frac{-x}{(1 + (\frac{-x}{100})^n)^{\frac{1}{n}}} & \text{if } x \leq 0
\end{cases}$$
$$f(x) = \frac{x}{(1 + (\frac{x}{100})^n)^{\frac{1}{n}}} \text{ if } x > 0$$

$$f(x) = -\frac{-x}{(1 + (\frac{-x}{100})^n)^{\frac{1}{n}}} \text{ if } x \leq 0$$

Where $k$ and $n$ are adjustable parameters controlling the steepness of the function.

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