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3s_motifs.py
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3s_motifs.py
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'''
For Studying : http://journals.plos.org/plosbiology/article?id=10.1371/journal.pbio.0020369
And comparing their results against the theory of Integrated Information
TODO: This code is built for deterministic networks, make it work for indeterminate ones as well
Time Warning:
3 nodes = 104 : calculates fast
4 nodes = 3044 :calculates in <1 min
5 nodes = scares me...
'''
import numpy as np
from itertools import combinations, permutations, product
from functools import reduce
from statistics import mean
from normalize_cm import normalize_cm
from normalize_tpm import normalize_tpm
from generate_tpm import generate_tpm, nodes_to_short, AND, OR, XOR, NULL
from generate_tpm import GREATER_THAN as G
from IPython.core.debugger import Tracer
import pyphi
def main():
# Size of Network #######################################################
NUM_NODES = 3
# Useful Constants #######################################################
unique_cms = gen_unique_cms(NUM_NODES)
all_activations = [p for p in product([0,1], repeat=NUM_NODES)] # all possible activation states
past_state = [0 for _ in range(NUM_NODES)]
# Greater-Than mechanisms
G1 = G(1)
G2 = G(2)
G3 = G(3)
# motifs from the paper "Motifs in the Brain", same ordering
motifs_mapping = [
[[0,0,0], [1,0,0], [1,0,0]],
[[0,0,0], [1,0,0], [0,1,0]],
[[0,0,0], [1,0,1], [0,0,0]],
[[0,1,0], [1,0,0], [1,0,0]],
[[0,0,0], [1,0,0], [1,1,0]],
[[0,1,1], [1,0,0], [0,0,0]],
[[0,0,1], [1,0,0], [0,1,0]],
[[0,1,0], [1,0,0], [1,1,0]],
[[0,1,1], [1,0,0], [1,0,0]],
[[0,1,0], [1,0,1], [1,0,0]],
[[0,0,0], [1,0,1], [1,1,0]],
[[0,1,1], [1,0,0], [1,1,0]],
[[0,1,1], [1,0,1], [1,1,0]],
]
# all nodes have self loop
motifs_plus_self_mapping = [
[[1,0,0], [1,1,0], [1,0,1]],
[[1,0,0], [1,1,0], [0,1,1]],
[[1,0,0], [1,1,1], [0,0,1]],
[[1,1,0], [1,1,0], [1,0,1]],
[[1,0,0], [1,1,0], [1,1,1]],
[[1,1,1], [1,1,0], [0,0,1]],
[[1,0,1], [1,1,0], [0,1,1]],
[[1,1,0], [1,1,0], [1,1,1]],
[[1,1,1], [1,1,0], [1,0,1]],
[[1,1,0], [1,1,1], [1,0,1]],
[[1,0,0], [1,1,1], [1,1,1]],
[[1,1,1], [1,1,0], [1,1,1]],
[[1,1,1], [1,1,1], [1,1,1]],
]
# Generate CMs #######################################################
# returns True if there is a self-loop on any nodes
has_self_loops = lambda cm: bool(len([1 for i in range(NUM_NODES) if cm[i][i] == 1]))
# returns True if any node doesn't have a connection with at least one other node
# note, this doesn't guarantee a weakly connected graph (ex A->B C->D, AB isn't connected to CD)
has_unconnected_node = lambda cm: bool(len(
[1 for i in range(NUM_NODES) if
sum(cm[i])==0 and
sum(np.array(cm).T.tolist()[i])==0
]))
# all cms for condition 1
cms1 = [cm for cm in unique_cms
if not has_self_loops(cm)
and not has_unconnected_node(cm)]
# same as cms1, but each node has a self loop
cms2 = [to_2d_list(cm) for cm in cms1]
for i, cm in enumerate(cms2):
for j in range(NUM_NODES):
cm[j][j] = 1
cms2[i] = to_2d_tuple(cm)
# Establish the different conditions #######################################################
condition_names = ['1A', '1B', '2A', '2B']
# sum_to_mech_map = if sum==<index of this array>, mech must be in <value @ index>
conditions = {
'1A':{
'cms': cms1,
'mechanisms': [OR, AND, NULL],
'inputs_sum_to_mech_map': [[NULL],
[OR],
[OR, AND]]
},
'1B':{
'cms': cms1,
'mechanisms': [OR, AND, NULL, XOR],
'inputs_sum_to_mech_map': [[NULL],
[OR],
[OR, AND, XOR]]
},
'2A':{
'cms': cms2,
'mechanisms': [G1, G2, G3, NULL],
'inputs_sum_to_mech_map': [[NULL],
[G1],
[G1, G2],
[G1, G2, G3]]
},
'2B':{
'cms': cms2,
'mechanisms': [G1, G2, G3, NULL, XOR],
'inputs_sum_to_mech_map': [[NULL],
[G1],
[G1, G2, XOR],
[G1, G2, G3, XOR]]
},
}
# Run each condition #######################################################
for condition_name in condition_names:
condition = conditions[condition_name]
MECHANISMS = condition['mechanisms']
INPUTS_SUM_TO_MECH_MAP = condition['inputs_sum_to_mech_map']
CMS = condition['cms']
print('\n\nCondition: ', condition_name)
seen_tpms_by_condition = {}
for cm in CMS:
seen_tpms_by_condition[cm] = {}
seen_tpms_by_condition[cm]['seen'] = set()
seen_tpms_by_condition[cm]['num_concepts'] = []
seen_tpms_by_condition[cm]['phi_concepts'] = []
seen_tpms_by_condition[cm]['phi_network'] = []
seen_tpms_by_condition[cm]['phi_main_complex'] = []
for nodes in product(MECHANISMS, repeat=NUM_NODES):
# ignore systems that don't match the INPUTS_SUM_TO_MECH_MAP
ignore = False
for sm, mechs in enumerate(INPUTS_SUM_TO_MECH_MAP):
if not all_nodes_where_incoming_sum_is_x_are_mech_y(cm, nodes, sm, mechs):
ignore = True
break
if ignore:
continue
tpm = generate_tpm(nodes, cm)
n_tpm = normalize_tpm(tpm)
# continue next loop if this tpm has already been seen on this condition
if to_2d_tuple(n_tpm) in seen_tpms_by_condition[to_2d_tuple(cm)]['seen']:
continue
seen_tpms_by_condition[cm]['seen'].add(to_2d_tuple(n_tpm))
# # DEBUG CODE
# debug_flag = False
# for debug_i, debug_cm in enumerate(motifs_mapping):
# if normalize_cm(debug_cm) == normalize_cm(cm):
# if debug_i == 3:
# debug_flag = True
# print("MOTIF: ", debug_i)
# print(cm)
# print(tpm)
for current_state in all_activations:
network = pyphi.Network(tpm, current_state, past_state, connectivity_matrix=cm)
subsystem = pyphi.Subsystem(range(network.size), network)
constellations = pyphi.compute.constellation(subsystem)
# Record stats of interest
seen_tpms_by_condition[cm]['num_concepts'].append(len(constellations))
if len(constellations) > 0:
seen_tpms_by_condition[cm]['phi_concepts'].append(mean([x.phi for x in constellations]))
else:
seen_tpms_by_condition[cm]['phi_concepts'].append(0)
seen_tpms_by_condition[cm]['phi_network'].append(pyphi.compute.big_phi(subsystem))
main = pyphi.compute.main_complex(network)
seen_tpms_by_condition[cm]['phi_main_complex'].append(main.phi)
# if debug_flag:
# print(tpm, current_state, '--', pyphi.compute.big_phi(subsystem))
print('')
# Prepare and print the results to the screen #######################################################
seen = seen_tpms_by_condition
# i=motif no., m=motif's cm, row=row from `seen`
printer = lambda i, m, row: ['\'%2d'%(i+1),
str(m),
str(len( row['seen'])),
'%.2f' % (mean(row['num_concepts'])) if len(row['num_concepts'])>0 else 'null' ,
'%.2f' % (mean(row['phi_concepts'])) if len(row['phi_concepts'])>0 else 'null' ,
'%.2f' % (mean(row['phi_network'])) if len(row['phi_concepts'])>0 else 'null' ,
'%.2f' % (mean(row['phi_main_complex'])) if len(row['phi_network'])>0 else 'null']
with open('results.txt', 'a') as f:
if condition_name in ['1A', '1B']:
for i, m in enumerate(motifs_mapping):
row = seen[to_2d_tuple(normalize_cm(m))]
f.write('\t'.join(printer(i, m, row)) + '\n')
else:
for i, m in enumerate(motifs_plus_self_mapping):
row = seen[to_2d_tuple(normalize_cm(m))]
f.write('\t'.join(printer(i, m, row)) + '\n')
#########################################################################################
# Utility Functions
#########################################################################################
def to_2d_tuple(arr):
''' takes a (mutable) 2D array and converts it to an (immutable) tuple '''
return tuple(tuple(row) for row in arr)
def to_2d_list(arr):
''' takes a (immutable) 2D tuple and converts it to an (mutable) list '''
return list(list(row) for row in arr)
def count_outgoing(cm):
'''
TODO: correct counts for non-deterministic connections
TODO: IE strengths aren't 0 or 1
return the count of outgoing connections for each node
args:
cm: a connectivity matrix / 2d array
cm[0][x] = outgoing connections
cm[x][0] = incoming connections
returns:
a list of how many outgoing connections each node has, eg:
[2, 2, 0, 1]
where node0 has 2 outgoing connections, node2 has none, etc.
'''
counts = [sum(row) for row in cm]
return counts
def count_incoming(cm):
'''
TODO: correct counts for non-deterministic connections
TODO: IE strengths aren't 0 or 1
return the count of incoming connections for each node
args:
cm: a connectivity matrix / 2d array
cm[0][x] = outgoing connections
cm[x][0] = incoming connections
returns:
a list of how many incoming connections each node has, eg:
[2, 2, 0, 1]
where node0 has 2 incoming connections, node2 has none, etc.
'''
counts = reduce(lambda xs, ys: [x+y for x, y in zip(xs, ys)], cm)
return counts
def all_nodes_where_incoming_sum_is_x_are_mech_y(cm, nodes, sm, mechs):
# return true if all nodes of incoming sum==x also have a mech in mechs
in_count = count_incoming(cm)
for count, node in zip(in_count, nodes):
if (count == sm):
if (node in mechs):
continue
return False
return True
def gen_unique_cms(num_nodes):
cms = product(*[[0,1]]*(num_nodes**2)) # Warning: mind-numbingly inefficient (brute force), don't use a lot of nodes (like, more than 4 sounds scary but I haven't tried it)
unique_cms = set() #there will be 104 unique cms at 3 nodes with recurrent loops
# look at all cms, add uniques to unique_cms
for cm in cms:
np_cm = np.array(cm)
np_cm.shape = (num_nodes, num_nodes)
unique_cms.add(tuple([tuple(x) for x in normalize_cm(np_cm)]))
return unique_cms
if __name__ == "__main__":
main()
fours_motifs = [
[[0,0,0,1],[0,0,0,1],[0,0,0,1],[0,0,0,0]],
[[0,0,0,1],[0,0,1,0],[0,0,0,1],[0,0,0,0]],
[[0,0,0,1],[0,0,1,1],[0,0,0,0],[0,0,0,0]],
[[0,0,0,1],[0,0,1,1],[0,0,0,1],[0,0,0,0]],
[[0,0,1,0],[0,0,0,1],[0,0,0,0],[0,1,1,0]],
[[0,0,1,0],[0,0,1,1],[0,0,0,0],[0,1,1,0]],
[[0,0,0,1],[0,0,0,1],[0,0,0,0],[0,0,1,0]],
[[0,0,0,1],[0,0,0,1],[0,0,0,1],[0,0,1,0]],
[[0,0,0,1],[0,0,1,0],[0,0,0,1],[0,0,1,0]],
[[0,0,0,1],[0,0,1,1],[0,0,0,0],[0,0,1,0]],
[[0,0,0,1],[0,0,1,1],[0,0,0,1],[0,0,1,0]],
[[0,0,0,1],[0,0,1,0],[0,0,0,0],[0,1,0,0]],
[[0,0,0,1],[0,0,1,1],[0,0,0,0],[0,1,0,0]],
[[0,0,1,0],[0,0,0,1],[0,0,0,1],[0,1,0,0]],
[[0,0,0,1],[0,0,1,0],[0,0,0,1],[0,1,0,0]],
[[0,0,0,1],[0,0,1,1],[0,0,0,1],[0,1,0,0]],
[[0,0,1,0],[0,0,0,1],[0,0,0,1],[0,1,1,0]],
[[0,0,1,0],[0,0,1,1],[0,0,0,1],[0,1,0,0]],
[[0,0,1,0],[0,0,1,1],[0,0,0,1],[0,1,1,0]],
[[0,0,0,1],[0,0,0,0],[0,0,0,0],[0,1,1,0]],
[[0,0,0,1],[0,0,0,0],[0,0,0,1],[0,1,1,0]],
[[0,0,0,1],[0,0,1,0],[0,0,0,0],[0,1,1,0]],
[[0,0,0,1],[0,0,1,0],[0,0,0,1],[0,1,1,0]],
[[0,0,0,1],[0,0,0,1],[0,0,0,1],[0,1,1,0]],
[[0,0,0,1],[0,0,1,0],[0,1,0,0],[0,1,1,0]],
[[0,0,0,1],[0,0,1,1],[0,0,0,0],[0,1,1,0]],
[[0,0,0,1],[0,0,1,1],[0,0,0,1],[0,1,1,0]],
[[0,0,0,1],[0,0,1,0],[0,1,0,1],[0,1,1,0]],
[[0,0,0,1],[0,0,1,1],[0,1,0,1],[0,1,1,0]],
[[0,0,1,1],[0,0,1,1],[0,0,0,0],[0,0,0,0]],
[[0,0,1,1],[0,0,1,1],[0,0,0,1],[0,0,0,0]],
[[0,0,1,1],[0,0,0,0],[0,0,0,0],[0,1,0,0]],
[[0,0,1,1],[0,0,0,1],[0,0,0,0],[0,1,0,0]],
[[0,0,1,1],[0,0,0,0],[0,1,0,0],[0,1,0,0]],
[[0,0,1,1],[0,0,1,0],[0,0,0,0],[0,1,0,0]],
[[0,0,1,1],[0,0,0,1],[0,1,0,0],[0,1,0,0]],
[[0,0,1,1],[0,0,1,1],[0,0,0,0],[0,1,0,0]],
[[0,0,1,1],[0,0,1,1],[0,1,0,0],[0,1,0,0]],
[[0,0,1,1],[0,0,1,1],[0,0,0,1],[0,0,1,0]],
[[0,0,1,1],[0,0,0,0],[0,0,0,0],[0,1,1,0]],
[[0,0,1,1],[0,0,0,0],[0,0,0,1],[0,1,0,0]],
[[0,0,1,1],[0,0,0,1],[0,0,0,1],[0,1,0,0]],
[[0,0,1,1],[0,0,1,0],[0,0,0,0],[0,1,1,0]],
[[0,0,1,1],[0,0,1,0],[0,0,0,1],[0,1,0,0]],
[[0,0,1,1],[0,0,0,1],[0,0,0,0],[0,1,1,0]],
[[0,0,1,1],[0,0,0,0],[0,1,0,1],[0,1,0,0]],
[[0,0,1,1],[0,0,0,1],[0,1,0,1],[0,1,0,0]],
[[0,0,1,1],[0,0,1,1],[0,0,0,0],[0,1,1,0]],
[[0,0,1,1],[0,0,1,1],[0,0,0,1],[0,1,0,0]],
[[0,0,1,1],[0,0,0,1],[0,1,0,0],[0,1,1,0]],
[[0,0,1,1],[0,0,1,1],[0,1,0,1],[0,1,0,0]],
[[0,0,1,1],[0,0,0,0],[0,0,0,1],[0,1,1,0]],
[[0,0,1,1],[0,0,1,0],[0,0,0,1],[0,1,1,0]],
[[0,0,1,1],[0,0,0,1],[0,0,0,1],[0,1,1,0]],
[[0,0,1,1],[0,0,1,1],[0,0,0,1],[0,1,1,0]],
[[0,0,1,1],[0,0,0,0],[0,1,0,1],[0,1,1,0]],
[[0,0,1,1],[0,0,0,1],[0,1,0,1],[0,1,1,0]],
[[0,0,1,1],[0,0,1,1],[0,1,0,1],[0,1,1,0]],
[[0,1,1,1],[0,0,0,0],[0,0,0,0],[0,0,0,0]],
[[0,1,1,1],[0,0,0,0],[0,0,0,1],[0,0,0,0]],
[[0,1,1,1],[0,0,0,1],[0,0,0,1],[0,0,0,0]],
[[0,1,1,1],[0,0,0,0],[0,0,0,1],[0,0,1,0]],
[[0,1,1,1],[0,0,0,1],[0,0,0,0],[0,0,1,0]],
[[0,1,1,1],[0,0,0,1],[0,0,0,1],[0,0,1,0]],
[[0,1,1,1],[0,0,1,1],[0,0,0,0],[0,0,0,0]],
[[0,1,1,1],[0,0,1,1],[0,0,0,1],[0,0,0,0]],
[[0,1,1,1],[0,0,1,1],[0,0,0,1],[0,0,1,0]],
[[0,1,1,1],[0,0,0,0],[0,0,0,1],[0,1,1,0]],
[[0,1,1,1],[0,0,1,0],[0,0,0,1],[0,1,0,0]],
[[0,1,1,1],[0,0,1,1],[0,0,0,1],[0,1,0,0]],
[[0,1,1,1],[0,0,0,1],[0,0,0,1],[0,1,1,0]],
[[0,1,1,1],[0,0,1,1],[0,0,0,0],[0,1,1,0]],
[[0,1,1,1],[0,0,1,1],[0,0,0,1],[0,1,1,0]],
[[0,1,1,1],[0,0,1,1],[0,1,0,1],[0,1,1,0]],
[[0,0,0,0],[0,0,0,0],[0,0,0,1],[1,1,1,0]],
[[0,0,0,0],[0,0,1,1],[0,0,0,0],[1,1,0,0]],
[[0,0,0,1],[0,0,1,0],[0,0,0,0],[1,1,0,0]],
[[0,0,0,0],[0,0,1,0],[0,0,0,1],[1,1,0,0]],
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