def find_len_2_control_kernals(deterministic_transition_graph, nodes_list, attractor_ID):
"""uses the deterministic_transition_graph and specified attractor to find
all pairs of control nodes if they exist
note: these aren't "strict" control kernels because they specify the states needed to be in the
main attractor. controlling them doesn't necessarily change what attractor you'll be in.
"""
subgraphs = [g for g in nx.weakly_connected_components(deterministic_transition_graph)]
# index_of_largest_subgraph = max(enumerate(all_subgraph_sets), key = lambda tup: len(tup[1]))[0]
all_subgraph_sets = []
all_but_attractor_subgraph = []
for sg in subgraphs:
if attractor_ID not in sg:
all_state_sets = []
for nID in sg:
all_state_sets.append(set(time_evol.decimal_to_binary(nodes_list,nID).items()))
all_subgraph_sets.append(all_state_sets)
all_but_attractor_subgraph.append(all_state_sets)
else:
all_state_sets = []
for nID in sg:
all_state_sets.append(set(time_evol.decimal_to_binary(nodes_list,nID).items()))
all_subgraph_sets.append(all_state_sets)
state_0_list = [0 for i in range(len(nodes_list))]
state_1_list = [1 for i in range(len(nodes_list))]
possible_states = zip(nodes_list,state_0_list) + zip(nodes_list,state_1_list) # list of (node,state)
possible_pairs = [combo for combo in combinations(possible_states, 2)]
possible_pairs_pared = copy.deepcopy(possible_pairs)
# remove pairs where both keys are the same (eg. gF and gF)
for pair in possible_pairs:
if pair[0][0] == pair[1][0] and (pair in possible_pairs_pared):
possible_pairs_pared.remove(pair)
# remove pairs when any of the networks in the non-attractor subgraph contain that pair
# (ie. that pair can not possibly be a control kernel because it is present in the wrong attractor)
for sg in all_but_attractor_subgraph:
for state_set in sg:
for pair in possible_pairs:
if (pair[0] in state_set) and (pair[1] in state_set) and (pair in possible_pairs_pared):
possible_pairs_pared.remove(pair)
return possible_pairs_pared # return a list ((node,state),(node,state)) pairs that are control kernels
def test_create_state_transition_dict(state_trans_dict):
""" a function to test if the create_state_trans_dict function is working as intended"""
# print state_trans_dict
for nID in state_trans_dict:
# print nID
bID = time_evol.decimal_to_binary(nodes_list,nID)
# print "."*40
for possible_nID in state_trans_dict[nID]:
bID_next = time_evol.decimal_to_binary(nodes_list,possible_nID)
if abs(sum(bID.values())-sum(bID_next.values())) != 1:
print " more than one thing changed. wtf."
def find_len_1_control_kernals(deterministic_transition_graph, nodes_list, attractor_ID):
"""uses the deterministic_transition_graph and specified attractor to find
all single control nodes if they exist"""
subgraphs = [g for g in nx.weakly_connected_components(deterministic_transition_graph)]
# index_of_largest_subgraph = max(enumerate(all_subgraph_sets), key = lambda tup: len(tup[1]))[0]
all_subgraph_sets = []
all_but_attractor_subgraph = []
for sg in subgraphs:
if attractor_ID not in sg:
all_state_sets = []
for nID in sg:
all_state_sets.append(set(time_evol.decimal_to_binary(nodes_list,nID).items()))
all_subgraph_sets.append(all_state_sets)
all_but_attractor_subgraph.append(all_state_sets)
else:
all_state_sets = []
for nID in sg:
all_state_sets.append(set(time_evol.decimal_to_binary(nodes_list,nID).items()))
all_subgraph_sets.append(all_state_sets)
state_0_list = [0 for i in range(len(nodes_list))]
state_1_list = [1 for i in range(len(nodes_list))]
possible_states = zip(nodes_list,state_0_list) + zip(nodes_list,state_1_list) # list of (node,state)
possible_states_pared = copy.deepcopy(possible_states)
for sg in all_but_attractor_subgraph:
for state_set in sg:
for state in possible_states:
if (state in state_set) and (state in possible_states_pared):
possible_states_pared.remove(state)
return possible_states_pared
def find_len_2_control_kernals_fo_real(deterministic_transition_graph, nodes_list, attractor_ID):
"""uses the deterministic_transition_graph and specified attractor to find
all pairs of control nodes if they exist
note: THESE ARE STRICT CONTROL KERNALS--but they don't appear to actually exist
"""
subgraphs = [g for g in nx.weakly_connected_components(deterministic_transition_graph)]
# index_of_largest_subgraph = max(enumerate(all_subgraph_sets), key = lambda tup: len(tup[1]))[0]
# combos_of_all_subgraph_sets = []
all_subgraph_sets = []
all_but_attractor_subgraph = []
for sg in subgraphs:
if attractor_ID not in sg:
all_state_sets = []
for nID in sg:
all_state_sets.append(set(time_evol.decimal_to_binary(nodes_list,nID).items()))
all_subgraph_sets.append(all_state_sets)
all_but_attractor_subgraph.append(all_state_sets)
else:
all_state_sets = []
for nID in sg:
all_state_sets.append(set(time_evol.decimal_to_binary(nodes_list,nID).items()))
all_subgraph_sets.append(all_state_sets)
# print [len(i) for i in all_subgraph_sets]
# print len(all_subgraph_sets[0])
state_0_list = [0 for i in range(len(nodes_list))]
state_1_list = [1 for i in range(len(nodes_list))]
possible_states = zip(nodes_list,state_0_list) + zip(nodes_list,state_1_list) # list of (node,state)
possible_pairs = [combo for combo in combinations(possible_states, 2)]
possible_pairs_pared = copy.deepcopy(possible_pairs)
# remove pairs where both keys are the same (eg. gF and gF)
for pair in possible_pairs:
if pair[0][0] == pair[1][0] and (pair in possible_pairs_pared):
possible_pairs_pared.remove(pair)
list_of_all_but_1s = [i for i in combinations(all_subgraph_sets, 2)]
list_of_control_pairs = []
# remove pairs when any of the networks in the non-attractor subgraph contain that pair
# (ie. that pair can not possibly be a control kernel because it is present in the wrong attractor)
for all_but_1_graph in list_of_all_but_1s:
temp_possible_pairs_pared = copy.deepcopy(possible_pairs_pared)
for sg in all_but_1_graph:
for state_set in sg:
for pair in possible_pairs:
if (pair[0] in state_set) and (pair[1] in state_set) and (pair in temp_possible_pairs_pared):
temp_possible_pairs_pared.remove(pair)
list_of_control_pairs.append(temp_possible_pairs_pared)
return list_of_control_pairs # return a list ((node,state),(node,state)) pairs that are control kernels
def create_state_transitions_dict(G):
"""
output a dictionary of key=network_ID, value=list of possible next network_IDs
each of the next possible network_IDs is exactly 1 value different than the previous network ID
this is working correctly- trust past harrison 4/13/16
"""
state_trans_dict = {} # key=network_ID, value=list of next network IDs
n_nodes = len(G.nodes())
n_init_networks = time_evol.n_states**n_nodes
for prev_network_ID in range(0, n_init_networks):
nodes_list = G.nodes()
prev_network_bID = time_evol.decimal_to_binary(nodes_list, prev_network_ID) #same as 'prev_state' within boolean_updating
curr_network_bID = boolean_updating(G, prev_state=prev_network_bID)
# get list of nodes that change when applying update rule
altered_nodes = []
for node in curr_network_bID:
if prev_network_bID[node] != curr_network_bID[node]:
altered_nodes.append(node)
# print prev_network_ID, altered_nodes
# look through altered nodes, and make list of all networks with nodes being altered 1 at a time
state_trans_dict[prev_network_ID] = []
for node in altered_nodes:
possible_bID = copy.deepcopy(prev_network_bID)
# print possible_bID #why is this not changing???
not_flipped = True
# print possible_bID[node]
# if node was updated, flip it
if prev_network_bID[node] == 0:
possible_bID[node] = 1
not_flipped = False
# print "0, flipping"
# print possible_bID[node]
# if node was updated, flip it
elif (prev_network_bID[node] == 1) and (not_flipped == True):
possible_bID[node] = 0
# print "1, flipping"
# print possible_bID[node]
else:
raise ValueError("Node %s of prev_state must be 0 or 1. Something bad happened."%node)
# print possible_bID
# nodes_list = [k for k in possible_bID]
network_ID = time_evol.binary_to_decimal(nodes_list,possible_bID) #get network_ID of this possible next state
state_trans_dict[prev_network_ID].append(network_ID)
# if no nodes are altered, you're in a fixed stable state-- make state_trans_dict[stable_ID]=stable_ID
if len(altered_nodes) == 0:
state_trans_dict[prev_network_ID].append(prev_network_ID)
# print 'prev network ID:',prev_network_ID
return state_trans_dict
