Niizato Takayuki, Sakamoto Kotaro, Mototake Yoh-Ichi, Murakami Hisashi, Tomaru Takenori, Hoshika Tomotaro, Fukushima Toshiki
Faculty of Engineering, Information and Systems University of Tsukuba, Tennodai 1-1-1, Tsukuba, Ibaraki 305-8573, Japan.
Leading Graduate School Doctoral Program in Human Biology, University of Tsukuba, Tennodai 1-1-1, Tsukuba, Ibaraki 305-8573, Japan.
Entropy (Basel). 2020 Jun 30;22(7):726. doi: 10.3390/e22070726.
Integrated information theory (IIT) was initially proposed to describe human consciousness in terms of intrinsic-causal brain network structures. Particularly, IIT 3.0 targets the system's cause-effect structure from spatio-temporal grain and reveals the system's irreducibility. In a previous study, we tried to apply IIT 3.0 to an actual collective behaviour in . We found that IIT 3.0 exhibits qualitative discontinuity between three and four schools of fish in terms of Φ value distributions. Other measures did not show similar characteristics. In this study, we followed up on our previous findings and introduced two new factors. First, we defined the global parameter settings to determine a different kind of group integrity. Second, we set several timescales (from Δ t = 5 / 120 to Δ t = 120 / 120 s). The results showed that we succeeded in classifying fish schools according to their group sizes and the degree of group integrity around the reaction time scale of the fish, despite the small group sizes. Compared with the short time scale, the interaction heterogeneity observed in the long time scale seems to diminish. Finally, we discuss one of the longstanding paradoxes in collective behaviour, known as the heap paradox, for which two tentative answers could be provided through our IIT 3.0 analysis.
整合信息理论（IIT）最初是为了从内在因果脑网络结构的角度描述人类意识而提出的。特别是，IIT 3.0从时空粒度着眼于系统的因果结构，并揭示了系统的不可约性。在之前的一项研究中，我们试图将IIT 3.0应用于实际的集体行为。我们发现，就Φ值分布而言，IIT 3.0在三群和四群鱼之间表现出质的不连续性。其他测量方法没有显示出类似的特征。在本研究中，我们跟进了之前的发现并引入了两个新因素。第一，我们定义了全局参数设置以确定一种不同类型的群体整体性。第二，我们设置了几个时间尺度（从Δt = 5 / 120到Δt = 120 / 120秒）。结果表明，尽管鱼群规模较小，但我们成功地根据鱼群的大小以及鱼在反应时间尺度附近的群体整体性程度对鱼群进行了分类。与短时间尺度相比，在长时间尺度上观察到的相互作用异质性似乎有所减弱。最后，我们讨论了集体行为中一个长期存在的悖论，即堆垛悖论，通过我们的IIT 3.0分析可以为其提供两个初步答案。
