2D spatial grid of neurons
We will stack glyphs, representing firings, on top (in Z) of this grid.
A subset (first 500) of neuron firings at start of time series (with z-scaled cubic glyphs).
Packed: remove time delays
For the following visualizations, we simply removed the time-delays between firings, i.e., instead of using the actual time as the z-coord, we simply increment z by 1 for each new time recording. This compresses (in z) the glyphs considerably.
500 firings (and zoom of lower-right region).
5000 firings.
50000 firings.
All (~120000) firings.
Transfer Entropy (TE) Matrix
In MATLAB:
>> load InVitroExperiment_133neurons_ASDF
>> TEmatrix = ASDFTEdelay(asdf,1);
>> size(TEmatrix)
ans =
133 133
>> whos TEmatrix
Name Size Bytes Class Attributes
TEmatrix 133x133 141512 double
>> TEmatrix
TEmatrix =
1.0e-03 *
Columns 1 through 10
0 0.0000 0.0008 0.0046 0.0001 0.0035 0.0532 0.0024 0.0008 0.0053
0.0000 0 0.0015 0.0000 0.0000 0.0019 0.0000 0.0000 0.0027 0.0000
0.0008 0.0015 0 0.0033 0.0001 0.0001 0.0072 0.0000 0.0011 0.0000
0.0027 0.0000 0.0000 0 0.0000 0.0005 0.0234 0.0000 0.0033 0.0000
0.0003 0.0000 0.0001 0.0000 0 0.0000 0.0002 0.0001 0.0005 0.0000
0.0024 0.0007 0.0003 0.0046 0.0000 0 0.0006 0.0001 0.0036 0.0000
0.0458 0.0000 0.0020 0.0132 0.0009 0.0095 0 0.0243 0.0071 0.0123
0.0062 0.0000 0.0012 0.0000 0.0001 0.0001 0.0196 0 0.0012 0.0000
0.0022 0.0000 0.0000 0.0000 0.0001 0.0003 0.0113 0.0012 0 0.0015
0.0053 0.0000 0.0000 0.0071 0.0000 0.0074 0.0125 0.0069 0.0000 0
>> save teMtx TEmatrix
Then, from Python:
import scipy
from scipy import io
te = {}
scipy.io.loadmat("full-path-to/teMtx",te)
In [2]: teMtx = te['TEmatrix']
In [3]: teMtx.size
Out[3]: 17689
In [4]: teMtx.shape
Out[4]: (133, 133)
In [6]: teMtx[0:9,0:9]
Out[6]:
array([[ 0.00000000e+00, 1.68033989e-08, 7.59139762e-07,
4.62332534e-06, 1.39243600e-07, 3.50863669e-06,
5.32143167e-05, 2.44901501e-06, 7.68650565e-07],
[ 1.73985789e-08, 0.00000000e+00, 1.45115517e-06,
4.93031343e-09, 3.11438363e-08, 1.92049751e-06,
2.16824470e-08, 6.40914027e-09, 2.65017478e-06],
[ 7.59736245e-07, 1.45118790e-06, 0.00000000e+00,
3.30347955e-06, 7.32821449e-08, 1.20916632e-07,
7.22468653e-06, 1.50957302e-08, 1.05983595e-06],
[ 2.70174543e-06, 4.93023466e-09, 1.16339858e-08,
0.00000000e+00, 4.09147792e-08, 5.44135943e-07,
2.33556551e-05, 8.26447814e-09, 3.32418446e-06],
[ 2.56281682e-07, 3.11322475e-08, 7.34055651e-08,
4.09002090e-08, 0.00000000e+00, 3.82542228e-09,
2.11237318e-07, 5.35178533e-08, 5.05555796e-07],
[ 2.41442747e-06, 6.50163414e-07, 3.05966530e-07,
4.62225512e-06, 3.72983776e-09, 0.00000000e+00,
5.57714298e-07, 8.77744168e-08, 3.57742867e-06],
[ 4.58499154e-05, 1.91341003e-08, 2.02548314e-06,
1.32224727e-05, 9.27983365e-07, 9.52643411e-06,
0.00000000e+00, 2.43260508e-05, 7.10147031e-06],
[ 6.24163376e-06, 6.42654021e-09, 1.20168903e-06,
8.31400729e-09, 5.35358119e-08, 8.76587892e-08,
1.95692578e-05, 0.00000000e+00, 1.21180911e-06],
[ 2.15953316e-06, 8.75691293e-09, 2.06638852e-08,
1.15044561e-08, 7.26714240e-08, 3.17082577e-07,
1.12806867e-05, 1.20285631e-06, 0.00000000e+00]])
Then visualize (note that each matrix below has its color LUT scaled accordingly):
10x10 submatrix: red square = 0.0532 * 1.0e-03 (in the Matlab above)
Python: maxTE = 5.32143167096e-05 at idx,idy = (6,0)
Full 133x133 TE matrix (no spaces between colored square glyphs) and zoomed lower-right region.
Python: maxTE = 0.000224195159452 at idx,idy = (117,124))
Representing the TE matrix as graphs (edge values * 10000000 --> "%.1f")
(Note: we temporarily disregard the spatial layout of the neurons)
ForceDirected (thresh=1000). Zoomed in on the largest (1 of 3) clusters. (Recall maxTE at 117->124)
Circular (thresh=1000).
Circular (thresh=500).