The necessary packages to reconstruct the proof are listed and described below:
| File | Description |
|---|---|
| TwoDimBumpWave.wl | Library defining functions needed for computational proof. |
| ServerScript.wl | Script computes and saves function tables using Interval Arithmetic, capable of running on a compute cluster. |
| run-math.sbatch | Script to run ServerScript.wl using Slurm scheduler. |
| segmentdistances.m | MATLAB script to compute distances between hexagon cells and segment of length Delta, where Delta is the minimum separation between spikes. |
| MakeRecoveryTables.wl | Script computing monotonized and supremum function envelopes (tables). Pre-computed tables can be loaded. Also computes tables for matrix norms, bump wave coefficients, and recovery results. |
To create the function envelopes, the Mathematica script ServerScript.wl must be run.
This script computes supremums for bump and wave functions for a selection of grid spacing intervals, defined therein, using Interval Arithmetic.
We include a script run-math.sbatch which calls ServerScript.wl and provides options for a cluster managed by Slurm job scheduler.
The MATLAB script segmentdistances.m computes distances between a set of hexagonal cells surrounding the origin and N intervals of equal lengths that partition the segment on the horizontal axis from the origin to (1,0).
Its output is a file with name formatted as partition_dists_YYYYMMDD_npartitions_N.mat with date and N substituted.
By default we set N=100.
After running segmentdistances.m, recovery results can be obtained by running MakeRecoveryTables.wl.
First this script computes envelopes, both monotonized and non-monotonic as needed, for the bump and wave functions using the output of ServerScript.wl.
Since this computation is time-consuming these envelopes are saved and can be imported subsequently in future uses by uncommenting the relevant lines.
With these envelopes, recovery results are produced for a list of minimum separation sizes.