I'm fairly certain that the math is just to take up space.  I'm an engineer and it's looking like probabilities (the curve with j-1, j, and j+1) are being calculated.  The equation below the curve appears to be something along the lines of the standard deviation of the mean but the exponential factor is throwing me off; we don't need that to figure out what this is, though.  The graph below that is x(t) vs. t, or distance over time.  You'll notice that at a certain point the graph crosses the axis, indicating an instantaneous change in direction, a telePORTAtion, if you wilL.  It then rises back up.  The graph to the right of this is the plot of the individual points of data, I would guess in an experiment.  The bottom text is  the equation for the distance with time, where xi is the distance at time i and w is the angular velocity (I hope you see where this is all heading).  Finally, the top graph:  Full, 1/2, and 1/4.  Given ANGULAR velocity and FULL, 1/2, and 1/4, what does it look like to you? 
PORTAL MATH <3 PHYSICS