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