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第370行： − python代码实现：+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + 第391行：
第428行： − − 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) − 第431行：
第458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]]
布尔网络EI计算python代码：<syntaxhighlight lang="python3">
import torch
import itertools
def Entropia(a):
b = torch.nonzero(a > 0).squeeze(1)
return -torch.sum(a[b]*torch.log2(a[b]))
def effective_information(G1):
"""
Calculate EI value of transition probability matrix
:param G1: TPM matrix
:return: EI value
"""
N = G1.shape[0]
G = torch.zeros_like(G1)
nozero_number = 0
for i in range(N):
if torch.sum(G1[i]) != 0:
G[i] = G1[i] / torch.sum(G1[i])
nozero_number += 1
Wout = torch.zeros(N)
Win = torch.zeros(N)
for i in range(N):
if torch.sum(G[i]) != 0:
Wout[i] = torch.tensor(Entropia(G[i]))
for i in range(N):
for j in range(N):
if G[i][j] != 0:
Win[j] += G[i][j] / nozero_number
Wout_average = torch.sum(Wout) / nozero_number
Win_entropy = Entropia(Win)
return Win_entropy - Wout_average
def calc_bn_ei(micro_mech, micro, edges, elem_group, mech_group):
def calc_bn_ei(micro_mech, micro, edges, elem_group, mech_group):
"""
"""
-------
-------
the EI value of micro and macro level.
the EI value of micro and macro level.
"""
"""
Nmi = 2 ** micro
Nmi = 2 ** micro
return micro_ei, macro_ei
return micro_ei, macro_ei
# Example：提高确定性实例
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)
</syntaxhighlight>
=== 时间因果涌现 ===
=== 时间因果涌现 ===