A cell is a minimal self-sustaining system that can move and compute. Previous work has shown that a unicellular slime mold, Physarum, can be utilized as a biological computer based on cytoplasmic flow encapsulated by a membrane. Although the interplay between the modification of the boundary of a cell and the cytoplasmic flow surrounded by the boundary plays a key role in Physarum computing, no model of a cell has been developed to describe this interplay. Here we propose a toy model of a cell that shows amoebic motion and can solve a maze, Steiner minimum tree problem and a spanning tree problem. Only by assuming that cytoplasm is hardened after passing external matter (or softened part) through a cell, the shape of the cell and the cytoplasmic flow can be changed. Without cytoplasm hardening, a cell is easily destroyed. This suggests that cytoplasmic hardening and/or sol-gel transformation caused by external perturbation can keep a cell in a critical state leading to a wide variety of shapes and motion.
Collective behaviour is known to be the result of diverse dynamics and is sometimes likened to a living system. Although many studies have revealed the dynamics of various collective behaviours, their main focus was on the information process inside the collective, not on the whole system itself. For example, the qualitative difference between two elements and three elements as a system has rarely been investigated. Tononi et al. have proposed Integrated Information Theory (IIT) to measure the degree of consciousness Φ. IIT postulates that the amount of information loss caused by certain partitions is equivalent to the degree of information integration in the system. This measure is not only useful for estimating the degree of consciousness but can also be applied to more general network systems. Here we applied IIT (in particular, IIT 3.0 using PyPhi) to analyse real fish schools (Plecoglossus altivelis). Our hypothesis in this study is a very simple one: a living system evolves to raise its Φ value. If we accept this hypothesis, IIT reveals the existence of continuous and discontinuous properties as group size varies. For example, leadership in the fish school emerged for a school size of four or above; but not below three. Furthermore, this transition was not observed by measuring mutual information or in a simple Boids model. This result suggests that integrated information Φ can reveal some inherent properties which cannot be observed using other measures. We also discuss how the fish recognition of the figure-ground relation, that is, what determines the relevant ON and OFF states, may reveal various optimal paths for obtaining the functional evolution of collective behaviour.
Recent experimental and observational data have revealed that the internal structures of collective animal groups are not fixed in time. Rather, individuals can produce noise continuously within their group. These individuals’ movements on the inside of the group, which appear to collapse the global order and information transfer, can enable interactions with various neighbors. In this study, we show that noise generated inherently in a school of ayus (Plecoglossus altivelis) is characterized by various power-law behaviors. First, we show that individual fish move faster than Brownian walkers with respect to the center of the mass of the school as a super-diffusive behavior, as seen in starling flocks. Second, we assess neighbor shuffling by measuring the duration of pair-wise contact and find that this distribution obeys the power law. Finally, we show that an individual’s movement in the center of a mass reference frame displays a Lévy walk pattern. Our findings suggest that inherent noise (i.e., movements and changes in the relations between neighbors in a directed group) is dynamically self-organized in both time and space. In particular, Lévy walk in schools can be regarded as a well-balanced movement to facilitate dynamic collective motion and information transfer throughout the group.
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