5,443
个编辑
更改
跳到导航
跳到搜索
第293行：
第293行： − − 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): − """ − 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. − """ − # generate the statue list of boolean nodes, based on the number of micro elements − Nmi = 2 ** micro − node_list = list(itertools.product(['0', '1'], repeat=micro)) − S_m = torch.zeros((Nmi, Nmi), dtype=torch.float) − − # calculate the transition probability matrix of micro level − 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 − − # calculate the grouping matrix from micro to macro level, based on the elem_group and mech_group. − 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 − − # calculate the transition probability matrix of macro level − S_M = group.t() @ S_m @ group − S_M = S_M / torch.sum(S_M, axis=1).unsqueeze(1) − − # calculate the EI of micro and macro level − micro_ei = effective_information(S_m) − macro_ei = effective_information(S_M) − − 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>
→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]]
=== 时间因果涌现 ===
=== 时间因果涌现 ===