Analytic Capacity Program

AnalyticCapacity.exe is a program developed by Irvin Chang and myself for the numerical computation of Analytic Capacity and applications to the Subadditivity Problem.

You can download the program by clicking HERE. I recommend saving the program before opening it (otherwise it seems to take longer to start). Note that in order to execute the program, you will first need to install MATLAB runtime.

Once you open the program, you can specify the number of red disks ("red disks"), the number of blue disks ("blue disks") and the common radius for each disk ("disk radii"). Then click on "reset disks". You can now move any disk by clicking on its center and slowly dragging it.

The program computes the following:

  • Red: analytic capacity of the union of the red disks
  • Blue: analytic capacity of the union of the blue disks
  • Sum: the sum of Red and Blue
  • Union: analytic capacity of the union of all the disks
  • Ratio: the ratio union divided by sum
  • Diff: the difference union minus sum

  • The Subadditivity Problem for analytic capacity is equivalent to Ratio being less than one, or Diff being negative. Try to find a counterexample! If you do, you can extract the center of the disks by clicking on "point locations".

    Irvin Chang was supported by a Faculty Mentoring Grant for Summer Undergraduate Research and Creative Works sponsored by the Undergraduate Research Opportunities Program.

    Malik Younsi was supported by NSF Grant DMS-1758295.