Effects of parity, frustration, and stochastic fluctuations on integrated conceptual information for networks with two small-sized loops

Abstract

This paper presents an evaluation of the system-level integrated conceptual information of a major complex for a small-scale network containing two loops in accordance with the integrated information theory 3.0 framework. We focus on the following parameters characterizing the system model: (1) number of nodes in the loop, (2) frustration of the loop, and (3) temperature controlling the stochastic fluctuation of the state transition. Effects of these parameters on the integrated conceptual information and conditions for major complexes formed by a single loop, rather than the entire network, are investigated. Our first finding is that parity of the number of nodes forming a loop has a strong effect on the integrated conceptual information. For loops with an even number of nodes, the number of concepts tends to decrease, and the integrated conceptual information becomes smaller. Our second finding is that a major complex is more likely to be formed by a small number of nodes under small stochastic fluctuations. On the other hand, the entire network can easily become a major complex under larger stochastic fluctuations, and this tendency can be reinforced by frustration. It is also shown that, although counterintuitive, the integrated conceptual information can be maximized in the presence of stochastic fluctuations. These results suggest that even when several small subnetworks are connected by only a few connections, such as a bridge, the entire network may become a major complex by introducing some stochastic fluctuations and by frustrating loops with an even number of nodes.