# What is sigma function in the YOLO object detector?

I have gone through the YOLO9000 paper, in that they have mentioned that network predicts 5 coordinates of the bounding box, and from that we find the exact centre coordinates and the width and height. I'm confused with those equations.
\begin{align} b_x &= \sigma(t_x) + c_x \\[3pt] b_y &= \sigma(t_y) + c_y \\[3pt] b_w &= p_we^{t_w} \\[3pt] b_h &= p_he^{t_h} \\[3pt] Pr({\rm object})\times IOU(b, {\rm object}) &= \sigma(t_o) \end{align}

In these equations, what does $$\sigma$$ stand for? Why they are using exponential for width and height?

It is the logistic sigmoid function: $$\sigma(x) = \frac 1 {1+e^{-x}}$$ It is bounded between 0 and 1, which is a desired property in their case (image from Wikipedia): In addition to the notation using the symbol $$\sigma$$, the caption to one image names this function the "sigmoid" function. From the paper,
The "sigmoid" function is one of many names for a certain function. This name is especially common in the neural networks literature; for some elaboration, see Does the function $e^x/(1+e^x)$ have a standard name?