The effect of group size and task involvement on temporal binding window in clap perception.

We collect various types of information from our environment and organise it to create a coherent representation. Several researchers have suggested that multiple signals within the temporal binding window (TBW) can be integrated into a single coherent experience, such as flashes, beeps, and the McGurk effect. However, there is no evidence that TBW distortion also occurs in group interactions. This study investigates the influence of group size (i.e. the group size effect) and the degree of task involvement in temporal perception using computer-generated clap sound experiments. Participants listened to the randomly generated clap sounds and evaluated whether they were synchronised. We established three conditions based on different levels of task involvement: low (L), middle (M), and high (H) conditions. The varying task involvements reflect how participants interact with the clap sounds, ranging from passive listening in the L condition to actively generating sounds by pressing a key in the M condition, or attempting to synchronise key pressing sounds with the sounds in the H condition. Our experiments show a robust group size effect on TBW, regardless of the different conditions. In other words, as the group size increases, participants perceive the group clap as a single event. Furthermore, we found that the uncertain cause-effect relationship condition (H condition) shows the highest TBW. Interestingly, the TBW in the rigid cause-effect relationship (M condition) is the same as that in the no involvement condition (L condition). Our results suggest that a widened TBW in collective behaviour may facilitate cohesive action, enabling individuals to adapt to the group in relatively uncertain contexts.

Functional duality in group criticality via ambiguous interactions.

Critical phenomena are wildly observed in living systems. If the system is at criticality, it can quickly transfer information and achieve optimal response to external stimuli. Especially, animal collective behavior has numerous critical properties, which are related to other research regions, such as the brain system. Although the critical phenomena influencing collective behavior have been extensively studied, two important aspects require clarification. First, these critical phenomena never occur on a single scale but are instead nested from the micro- to macro-levels (e.g., from a Lévy walk to scale-free correlation). Second, the functional role of group criticality is unclear. To elucidate these aspects, the ambiguous interaction model is constructed in this study; this model has a common framework and is a natural extension of previous representative models (such as the Boids and Vicsek models). We demonstrate that our model can explain the nested criticality of collective behavior across several scales (considering scale-free correlation, super diffusion, Lévy walks, and 1/f fluctuation for relative velocities). Our model can also explain the relationship between scale-free correlation and group turns. To examine this relation, we propose a new method, applying partial information decomposition (PID) to two scale-free induced subgroups. Using PID, we construct information flows between two scale-free induced subgroups and find that coupling of the group morphology (i.e., the velocity distributions) and its fluctuation power (i.e., the fluctuation distributions) likely enable rapid group turning. Thus, the flock morphology may help its internal fluctuation convert to dynamic behavior. Our result sheds new light on the role of group morphology, which is relatively unheeded, retaining the importance of fluctuation dynamics in group criticality.

The ambiguous feeling between "mine" and "not-mine" measured by integrated information theory during rubber hand illusion.

Human body awareness is adaptive to context changes. The illusory sense of body ownership has been studied since the publication of the rubber hand illusion, where ambiguous body ownership feeling was first defined. Phenomenologically, the ambiguous body ownership is attributed to a conflict between feeling and judgement: it characterises a discrepancy between first- and third-person processes. Although Bayesian inference can explain this malleability of body image, it still fails to relate the subjective feeling to physiological data. This study attempts to explain subjective experience during rubber hand illusions by using integrated information theory (IIT). The integrated information [Formula: see text] in IIT measures the difference between the whole system and its subsystems. By analysing seven different time-series of physiological data representing a small body-brain system, we demonstrate that the integrity of the whole system during the illusion decreases, while the integrity of its subsystems increases. These general tendencies agree with many brain-image analyses and subjective reports; furthermore, we found that subjective ratings as ambiguous body ownership were associated with [Formula: see text]. Our result suggests that IIT can explain the general tendency of the sense of ownership illusions and individual differences in subjective experience during the illusions.

Four-Types of IIT-Induced Group Integrity of Plecoglossus altivelis.

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 Plecoglossus altivelis. 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.

Finding continuity and discontinuity in fish schools via integrated information theory.

Collective behaviours are known to be the result of diverse dynamics and are sometimes likened to living systems. Although many studies have revealed the dynamics of various collective behaviours, their main focus has been on the information processing performed by the collective, not on interactions within the collective. For example, the qualitative difference between three and four elements in a system has rarely been investigated. Tononi et al. proposed integrated information theory (IIT) to measure the degree of consciousness Φ. IIT postulates that the amount of information loss caused by the minimum information partition 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 obtained two main results from the application of IIT (in particular, IIT 3.0) to the analysis of real fish schools (Plecoglossus altivelis). First, we observed that the discontinuity on 〈Φ(N)〉 distributions emerges for a school of four or more fish. This transition was not observed by measuring the mutual information or the sum of the transfer entropy. We also analysed the IIT on Boids simulations with respect to different coupling strengths; however, the results of the Boids model were found to be quite different from those of real fish. Second, we found a correlation between this discontinuity and the emergence of leadership. We discriminate leadership in this paper from its traditional meaning (e.g. defined by transfer entropy) because IIT-induced leadership refers not to group behaviour, as in other methods, but the degree of autonomy (i.e. group integrity). These results suggest that integrated information Φ can reveal the emergence of a new type of leadership which cannot be observed using other measures.

Propagating wave based on transition of interaction within animal group.

Propagating waves, information transfers of direction of travel in collective groups, have been observed in animal groups of insects, birds, fish, and mammals. Nevertheless, although many previously proposed models of group behaviors have elucidated various aspects of collective motion, none has directly shown the propagating wave constructively. These models consisted of flocking algorithms in which individuals modify their positions or velocities through average responses to their neighbors. The algorithms involve the function of diluting local fluctuations, individual motions, or social cues that initiate coherent decision-making of where to travel and which spread through a group in the form of a wave. The present study challenged physics-inspired models based solely on average interaction and instead proposed a combination with pair interaction: the 'copy' mechanism. By the mechanism, individuals specially attend and mimic the motion of the largest turning neighbor. The model comprises three modes (base, copy, and align modes) that sequentially switch among themselves, depending on the degree of variance in direction. The model therefore involves propagating waves that produce rapid collective responses and quick turning motions of a group. This proposal is an attempt to uncover the mechanisms of self-organized waves in simulation studies of coordinated groups, without explicit signals such as alarm calls. Understanding such mechanisms is expected to contribute to the 'collective mind' metaphor, answering the question of how animal groups obtain higher-order computational capabilities from local inter-individual interactions.

Biased Lévy-walk pattern in the exploratory behavior of the Physarum plasmodium.

The plasmodium of Physarum polycephalum is a unicellular and multinuclear giant amoeba. The plasmodium has the ability to sense and adapt to many kinds of environmental stimuli, and its optimization behavior in closed spaces has been analyzed extensively. However, few studies have tested the behavior of the plasmodium in an open spaces, despite the biological importance of the adaptability of biological entities in such conditions. Accordingly, we established an experimental setup with a very large and strictly homogeneous substrate and observed the long-term exploratory behavior of the plasmodium. As a result, we found that the movement of the plasmodium was consistent with a Lévy-walk, but with anisotropic bias.

Entangled time in flocking: Multi-time-scale interaction reveals emergence of inherent noise.

Collective behaviors that seem highly ordered and result in collective alignment, such as schooling by fish and flocking by birds, arise from seamless shuffling (such as super-diffusion) and bustling inside groups (such as Lévy walks). However, such noisy behavior inside groups appears to preclude the collective behavior: intuitively, we expect that noisy behavior would lead to the group being destabilized and broken into small sub groups, and high alignment seems to preclude shuffling of neighbors. Although statistical modeling approaches with extrinsic noise, such as the maximum entropy approach, have provided some reasonable descriptions, they ignore the cognitive perspective of the individuals. In this paper, we try to explain how the group tendency, that is, high alignment, and highly noisy individual behavior can coexist in a single framework. The key aspect of our approach is multi-time-scale interaction emerging from the existence of an interaction radius that reflects short-term and long-term predictions. This multi-time-scale interaction is a natural extension of the attraction and alignment concept in many flocking models. When we apply this method in a two-dimensional model, various flocking behaviors, such as swarming, milling, and schooling, emerge. The approach also explains the appearance of super-diffusion, the Lévy walk in groups, and local equilibria. At the end of this paper, we discuss future developments, including extending our model to three dimensions.

Emergence of a coherent and cohesive swarm based on mutual anticipation.

Collective behavior emerging out of self-organization is one of the most striking properties of an animal group. Typically, it is hypothesized that each individual in an animal group tends to align its direction of motion with those of its neighbors. Most previous models for collective behavior assume an explicit alignment rule, by which an agent matches its velocity with that of neighbors in a certain neighborhood, to reproduce a collective order pattern by simple interactions. Recent empirical studies, however, suggest that there is no evidence for explicit matching of velocity, and that collective polarization arises from interactions other than those that follow the explicit alignment rule. We here propose a new lattice-based computational model that does not incorporate the explicit alignment rule but is based instead on mutual anticipation and asynchronous updating. Moreover, we show that this model can realize densely collective motion with high polarity. Furthermore, we focus on the behavior of a pair of individuals, and find that the turning response is drastically changed depending on the distance between two individuals rather than the relative heading, and is consistent with the empirical observations. Therefore, the present results suggest that our approach provides an alternative model for collective behavior.

Inherent noise appears as a Lévy walk in fish schools.

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.

Ongoing Processes in a Fitness Network Model under Restricted Resources.

In real networks, the resources that make up the nodes and edges are finite. This constraint poses a serious problem for network modeling, namely, the compatibility between robustness and efficiency. However, these concepts are generally in conflict with each other. In this study, we propose a new fitness-driven network model for finite resources. In our model, each individual has its own fitness, which it tries to increase. The main assumption in fitness-driven networks is that incomplete estimation of fitness results in a dynamical growing network. By taking into account these internal dynamics, nodes and edges emerge as a result of exchanges between finite resources. We show that our network model exhibits exponential distributions in the in- and out-degree distributions and a power law distribution of edge weights. Furthermore, our network model resolves the trade-off relationship between robustness and efficiency. Our result suggests that growing and anti-growing networks are the result of resolving the trade-off problem itself.

Emergent runaway into an avoidance area in a swarm of soldier crabs.

Emergent behavior that arises from a mass effect is one of the most striking aspects of collective animal groups. Investigating such behavior would be important in order to understand how individuals interact with their neighbors. Although there are many experiments that have used collective animals to investigate social learning or conflict between individuals and society such as that between a fish and a school, reports on mass effects are rare. In this study, we show that a swarm of soldier crabs could spontaneously enter a water pool, which are usually avoided, by forming densely populated part of a swarm at the edge of the water pool. Moreover, we show that the observed behavior can be explained by the model of collective behavior based on inherent noise that is individuals' different velocities in a directed group. Our results suggest that inherent noise, which is widely seen in collective animals, can contribute to formation and/or maintenance of a swarm and that the dense swarm can enter the pool by means of enhanced inherent noise.

Emergence of the scale-invariant proportion in a flock from the metric-topological interaction.

Recently, it has become possible to more precisely analyze flocking behavior. Such research has prompted a reconsideration of the notion of neighborhoods in the theoretical model. Flocking based on topological distance is one such result. In a topological flocking model, a bird does not interact with its neighbors on the basis of a fixed-size neighborhood (i.e., on the basis of metric distance), but instead interacts with its nearest seven neighbors. Cavagna et al., moreover, found a new phenomenon in flocks that can be explained by neither metric distance nor topological distance: they found that correlated domains in a flock were larger than the metric and topological distance and that these domains were proportional to the total flock size. However, the role of scale-free correlation is still unclear. In a previous study, we constructed a metric-topological interaction model on three-dimensional spaces and showed that this model exhibited scale-free correlation. In this study, we found that scale-free correlation in a two-dimensional flock was more robust than in a three-dimensional flock for the threshold parameter. Furthermore, we also found a qualitative difference in behavior from using the fluctuation coherence, which we observed on three-dimensional flocking behavior. Our study suggests that two-dimensional flocks try to maintain a balance between the flock size and flock mobility by breaking into several smaller flocks.

Interactions between species and environments from incomplete information.

There are two contradictory aspects of the adaptive process in evolution. The first is that species must optimally increase their own fitness in a given environment. The second is that species must maintain their variation to be ready to respond to changing environments. In a strict sense, these two aspects might consider to be mutually exclusive. If species are optimally adapted, then the variation in the species that is suboptimal decreases and vice versa. To resolve this dilemma, species must find a balance between optimal adaptation and robust adaptation. Finding the balance between these processes requires both the local and global complete, static information. However, the balance between the processes must be dynamic. In this study, we propose a model that illustrates dynamic negotiation between the global and local information using lattice theory. The dynamic negotiation between these two levels results in an overestimate of fitness for each species. The overestimation of fitness in our model represents the multiplicity of fitness which is sometimes discussed as the exaptation. We show that species in our model demonstrate the power law of the lifespan distribution and 1/f fluctuation for the adaptive process. Our model allows for a balance between optimal adaptation and robust adaptation without any arbitrary parameters.

Fluctuation-driven flocking movement in three dimensions and scale-free correlation.

Recent advances in the study of flocking behavior have permitted more sophisticated analyses than previously possible. The concepts of "topological distances" and "scale-free correlations" are important developments that have contributed to this improvement. These concepts require us to reconsider the notion of a neighborhood when applied to theoretical models. Previous work has assumed that individuals interact with neighbors within a certain radius (called the "metric distance"). However, other work has shown that, assuming topological interactions, starlings interact on average with the six or seven nearest neighbors within a flock. Accounting for this observation, we previously proposed a metric-topological interaction model in two dimensions. The goal of our model was to unite these two interaction components, the metric distance and the topological distance, into one rule. In our previous study, we demonstrated that the metric-topological interaction model could explain a real bird flocking phenomenon called scale-free correlation, which was first reported by Cavagna et al. In this study, we extended our model to three dimensions while also accounting for variations in speed. This three-dimensional metric-topological interaction model displayed scale-free correlation for velocity and orientation. Finally, we introduced an additional new feature of the model, namely, that a flock can store and release its fluctuations.

An adaptive and robust biological network based on the vacant-particle transportation model.

A living system reveals local computing by referring to a whole system beyond the exploration-exploitation dilemma. The slime mold, Physarum polycephalum, uses protoplasmic flow to change its own outer shape, which yields the boundary condition and forms an adaptive and robust network. This observation suggests that the whole Physarum can be represented as a local protoplasmic flow system. Here, we show that a system composed of particles, which move and are modified based upon the particle transformation that contains the relationship between the parts and the whole, can emulate the network formed by Physarum. This system balances the exploration-exploitation trade-off and shows a scale-free sub-domain. By decreasing the number of particles, our model, VP-S, can emulate the Physarum adaptive network as it is attracted to a food stimulus. By increasing the number of particles, our model, VP-D, can emulate the pattern of a growing Physarum. The patterns produced by our model were compared with those of the Physarum pattern quantitatively, which showed that both patterns balance exploration with exploitation. This model should have a wide applicability to study biological collective phenomena in general.

A model of network formation by Physarum plasmodium: interplay between cell mobility and morphogenesis.

The plasmodium of Physarum polycephalum has attracted much attention due its intelligent adaptive behavior. In this study, we constructed a model of the organism and attempted to simulate its locomotion and morphogenetic behavior. By modifying our previous model, we were able to get closer to the actual behavior. We also compared the behavior of the model with that of the real organism, demonstrating remarkable similarity between the two.

Imperfect identity of autonomous living system.

We usually think that there is a clear cut between known facts and unknown facts. In category theory, this can correspond to equivalence of categories for partial map and pointed set. If this relation is satisfied, we implicitly ignore the difference of "before encoding" and "after encoding". In this paper, we admit this discrepancy in the context of organizational endo-perspective, and make weak condition of equivalence of categories for partial map and pointed set to connect learning systems.

Minimal model of a cell connecting amoebic motion and adaptive transport networks.

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.