5,443
个编辑
更改
跳到导航
跳到搜索
第369行：
第369行： + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
→空间因果涌现
[[文件:图4空间因果涌现(抵消退化).png|无框|居左|400x400像素]]
[[文件:图4空间因果涌现(抵消退化).png|无框|居左|400x400像素]]
python代码实现：
def calc_bn_ei(micro_mech, micro, edges, elem_group, mech_group):
"""
Calculate the effective information of boolean network in micro and macro level, given the micro mechanism and
coarse-graining methods.
Parameters
----------
micro_mech: boolean function, e.g., {'00': [0.7, 0.3], '01': [0.7, 0.3], '10': [0.7, 0.3], '11': [0, 1]} the
value means the probability of transferring to '0' and '1', correspondingly.
micro: the number of micro elements
edges: a list of tuple. the list means the input micro elements. e.g., edges[1] = (2, 3) means
the input of elements[1] is [2] and [3]
elem_group: the coarse-graining methods of micro elements, e.g., [(0, 1), (2, 3)] means coarse-graining
elements[0],[1] to be a macro element, and the [2] and [3] to be another.
mech_group: the coarse-graining method of micro_mech, e.g., mech_group = {'00': '0', '01': '0', '10': '0',
'11': '1'}
Returns
-------
the EI value of micro and macro level.
Example
-------
micro_mech = {'00': [0.7, 0.3], '01': [0.7, 0.3], '10': [0.7, 0.3], '11': [0, 1]}
micro = 4
edges = [(2, 3), (2, 3), (0, 1), (0, 1)]
elem_group = [(0, 1), (2, 3)]
mech_group = {'00': '0', '01': '0', '10': '0', '11': '1'}
micro_ei, macro_ei = calc_bn_ei(micro_mech, micro, edges, elem_group, mech_group)
"""
Nmi = 2 ** micro
node_list = list(itertools.product(['0', '1'], repeat=micro))
S_m = torch.zeros((Nmi, Nmi), dtype=torch.float)
for i, pre in enumerate(node_list):
for j, tmp in enumerate(node_list):
tr_pr = 1
for z in range(micro):
srce1 = pre[edges[z][0]]
srce2 = pre[edges[z][1]]
tr_pr *= micro_mech[srce1 + srce2][int(tmp[z])]
S_m[i][j] = tr_pr
unique = set(mech_group.values())
Nma = len(unique) ** len(elem_group)
group = torch.zeros((Nmi, Nma), dtype=torch.float)
for i, item in enumerate(node_list):
Sma = ''
for elem in elem_group:
Smi = ''.join(item[idx] for idx in elem)
Sma += mech_group[Smi]
group[i, int(Sma, base=len(unique))] = 1
S_M = group.t() @ S_m @ group
S_M = S_M / torch.sum(S_M, axis=1).unsqueeze(1)
micro_ei = effective_information(S_m)
macro_ei = effective_information(S_M)
return micro_ei, macro_ei
=== 时间因果涌现 ===
=== 时间因果涌现 ===