\(r\left(x,t\middle|\mathcal{H}_{t}\right)=\ \prod_{j:t_{i}}{1+\left[\theta\left(t\right)-1\right]f(||\ x-\ x_{j}\ ||)\},}\) Equation 4
\(f\left(||x-x_{j}\right)=\left\{\begin{matrix}\exp{\{-||\ \ x-\ x_{j}||/\phi}\ \ \ \ \ if\ ||x-x_{j}||\ \ \&<u(x)\\ if\ ||x-x_{\text{j\ }}||,\ \ \&\geq u(x)\\ \end{matrix}\right.\ \)
Equation 5