1) In the case of Mu, how exactly does the ball move?
As you suggest, movement upward means a more-than-average amplitude of the mu rhythm at the selected electrode and frequency.
If one wants to increase Theta power, could we just have a program where the ball just moves upwards to a target from the bottom of the screen, assuming downwards movement means a decrease in theta power?
If you want to increase theta power, you cannot use the mu rhythm feedback setup because it will suggest increase as much as decrease, swinging around a mean value in order to transfer information, which is the purpose of a BCI.
However, you can configure the CursorTask to display only a single target at the top by setting the NumberTargets parameter to 1.
In summary, I am unclear on how the power extracted from a frequency band actually gets translated to movement.
After normalization, the power is taken to be the vertical speed of the cursor. The Normalizer removes the mean, so above-average power will move the cursor upward, below-average power will move it downward, provided the sign of the normalizer gain is positive. If it is negative, direction will be reversed.
I understand from the documentation that when the bar is down, that means the subject must perform motor imagery and if the bar is up the subject must rest. How does that relate to our case of trying to increase theta? Does this mean we must have a task that increases theta (Compared to rest) to use BCI2000?
If you want to use BCI2000's mu rhythm task as a BCI, you will need a modulation of the brain signal that can be achieved voluntarily by the subject. If you want to control BCI2000 by theta, you need to provide the subject with two different instructions, one to increase theta, one to decrease theta. The increase needs only to be relative, so one of the instructions may be "rest".
If you don't want to use BCI2000's mu rhythm task as a BCI but only to provide feedback about the subject's current theta activity, then set the NumberTargets parameter to 1 and switch off adaptation as described above.
2) Is there a way to prevent noisy electrode(s) from being used in CAR? For example, if O2, F1, Pz are noisy, is there a way to not let them be included in CAR?
Specify the electrodes you want to keep in the TransmitChList parameter.
Finally, the task that is present in the documentation is different than the one titled "Mu Rhythm Feedback.prm" provided in the .prm in BCI2000. I am not sure if you are aware of this.
This is an obsolete parameter file, I don't think it was mentioned in the documentation. Thanks anyway.