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Levy walks, random walks where the frequency of occurrence of a linear step length follows a power-law distribution, are found in the migratory behavior of organisms at various levels, from bacteria and T cells to humans. However, it has been pointed out that in human migratory behavior, the step length series may have temporal correlation (i.e., it is not random walk) and that there is some relationship between this time dependency and the fact that the frequency distribution of step length follows the power-law distribution. Furthermore, some large marine organisms have been found to switch between Levy and Brownian walks, wherein the frequency of occurrence of the step length is characterized by an exponential distribution (EP), depending on the difficulty of prey acquisition. However, as of now it has not been clarified how the aforementioned three phenomena arise: the positive correlation created in the step length series, the relation between the positive correlation of the step length series and the form of an individual’s step length distribution, and the switching between Levy and Brownian behavior depending on the abundance of prey. The purpose of this study is to simulate foraging behavior by three Bayesian decision-making agents: an agent simultaneously performing both knowledge learning and knowledge-based inference, an agent performing only learning, an agent performing only inference, and to analyze how the aforementioned three phenomena arise. The simulation results show that only the agent with both learning and inference has a mechanism that simultaneously causes all the phenomena. This suggests that simultaneous learning on prey distribution and inference based on the knowledge gained in exploratory behavior under incomplete information may be the key to the emergence of Levy walk-like patterns found in humans and marine organisms.

In this study, we start by proposing a causal induction model that incorporates symmetry bias. This model is important in two aspects. First, it can reproduce causal induction of human judgment with higher accuracy than conventional models. Second, it allows us to estimate the level of symmetry bias of subjects from experimental data. We further propose an inference method that incorporates the aforementioned causal induction model into Bayesian inference. In this method, the component of Bayesian inference, which updates the degree of confidence for each hypothesis, and the component of inverse Bayesian inference that modifies the model of the hypothesis coexist. Our study demonstrates that inverse Bayesian inference enables us to deal flexibly with unstable situations where the object of inference changes from time to time.nnAuthor summaryWe acquire knowledge through learning and make various inferences based on such knowledge and observational data (evidence). If the evidence is insufficient, then the certainty of the conclusion will decline. Moreover, even if the evidence is sufficient, the conclusion may be wrong if the knowledge is incomplete in the first place. In order to model such inference based on incomplete knowledge, we proposed an inference system that performs learning and inference simultaneously and seamlessly. Prepare two coins A and B with different probabilities of landing heads, and repeat the coin toss using either of them. However, the coin that is being tossed is also replaced repeatedly. The system observes only the result of coin toss each time, and estimates the probability of landing heads of coin tossed at the moment. In this task, it is necessary not only to estimate the probabilities of the landing heads of coin A and B, but also to estimate which coin is being used at the moment. In this paper, we show that the proposed system handles such tasks very efficiently by simultaneously performing inference and learning.

We show the appearance of emergent hierarchical structure by a generalized system based on hyper-dilation (P.-Y. Gunji, S. Toyoda, Biosystem 38 (1996) 127-133), that is a new approach for complex systems. Hyper-dilation comprises a measurement problem hidden in any formal system. In hyper-dilation, the measurement process is expressed as the interface between an infinite lattice, which is an infinite loop of a rule, and a finite lattice, which is a tree structure of a rule. Hyper-dilation shows two intrinsic properties, one is degeneracy of a Cantor set in return map, and the other is generation of 1/f noise. We present various versions of hyper-dilation and suggest that to generate 1/f noise, it is required that the rules of the system are changed through a coherent process and that the system is closed for information. From these two properties of hyper-dilation, we discuss that the degeneracy is regarded as the model of emergence of a new hierarchy, and in hyper-dilation, actually we show the motion of a system that can be regarded as the appearance of a new hierarchy.

Almost all flock models are constructed using a self-propelled particle system (SPPs). In an SPP method, each individual will interact with neighbors found within a certain radius. Recent investigations are forcing us to reconsider the notion of the neighborhood in flocks. Cavagna et al. found a scale-free correlation in which the sub-flocks use the same information and where their size is proportional to the flock size. This finding indicates that the flock neighborhood dynamically changes the shape and formation of the flock. They defined this state of the flock as the "noise critical phenomenon". However, is it a sufficient interpretation of the scale-free correlation? The agent of the type-token model, which we proposed, changes its neighborhood by adjusting between the type and token cognitions. These differences in the neighborhood of each agent enables their flock to rapidly change direction without external noise and shows a scale-free correlation that is supported with empirical research. The typetoken model suggests that the flock emerges as a scale-free correlation without considering noise critical phenomena.

Synchronous visuo-tactile stimulation of the type in the rubber hand illusion (RHI)^1-3^ and in out of body experience (OBE)^4,5^ can induce the brain to incorporate external objects or images into a part or whole of body image. Whether in the context of RHI or OBE, since the participant passively receives visuo-tactile stimulations, body image appears only with the sense of ownership (SoO), not with the sense of agency (the registration that we are the initiators of our actions; SoA)^6,7^. Insofar as self-consciousness as a body image is a unity acting in its environments, body image has to be investigated in the relationship between SoO and SoA^8,9^. It requires an experimental condition in which SoO and SoA can be independently separated in an active condition. However, no experimental condition that is opposite to RHI and OBE in which a subject can feel SoA but not SoO has been proposed to date^10^. Here, we show that a person loses SoO for his own hand that he can freely move by his own will when he sees himself in a lateral view through a head mounted display. It was previously thought that SoO can be represented by synchronous inter-modal stimulations^10^, and that SoO appears to be complemented by SoA11. Our findings show that SoO can be lost under a synchronous visuo-proprioceptive condition while SoA can be maintained. SoO and SoA are two aspects of body representation, and similar dissociations have been proposed in various contexts, such as body image and body schema^12,13^, and 'Acting I' and 'Mine'^14^. Our result suggests that the two-centric-self consisting of SoA and SoO can enhance dynamically robust self-consciousness.

The boundary conditions of biological systems are not controllable, due to the perpetual disequilibration of force. This means that the possibilities for the future are open (i.e. one-to-many mapping). However, the future is uniquely determined a posteriori. We argue that such an idea is a basic concept for biological and evolutionary systems and implies unprogrammable systems. But it cannot be described only in a forward-time description. We propose a model in which the uncontrollable boundaries can be described in introducing a backward-time dynamics (a posteriori description). With respect to the extent of the controllability of boundary conditions, systems are classified into constant, microscopic, macroscopic, and disequilibrium systems. In the last, the local transition rule is perpetually transformed as time progresses, due to the uncontrollable microscopic boundary conditions. Our paradigm deviates from the Newtonian paradigm (i.e. the paradigm of prediction), and its purpose is not to describe the physics of being but to describe that of becoming (evolution).

In the present paper the self-consistency or operational closure of autopoiesis is described by introducing time explicitly. It is an extension of Spencer-Brown's idea of time, however. The definition of time is segregated into two parts, corresponding to the syntax and semantics of language, respectively. In this context, time reversibility is defined by the formalization of the relationship between time and self-consistency. This idea has also been discussed in the context of designation and/or naming. Here we will discuss it in the context of cellular automata and explain the structure of one-to-many type mappings. Our approach is the first attempt to extend autopoietic systems in terms of dynamics. It illustrates how to introduce an autopoietic time which looks irreversible, but without the concept of entropy.

Pigment color patterns of molluscs are studied from the viewpoint of autonomy. Brownian algebra developed by Spencer-Brown (1969) is extensively used for the expression of cellular-automaton rules. When asynchronous updating is introduced for the transition of cellular automata, various kinds of patterns such as traveling waves, kinks, oscillatory local patterns etc. are generated from the same transitional rule. The type of patterns depends more sensitively on the asynchronous updating relationship rather than the transitional rule itself. Therefore, pattern changes in ontogeny can be explained without any changes in transitional rules or reaction processes. It is proposed that asynchronousness is intrinsic to living systems and that recognition of the intrinsic time is essential in understanding living systems.

Gunji, Yukio 1987 07 15: Metamorphosis of the loop in Cenozoic dallinacean brachiopods and its developmental constraint. The well-known metamorphosis of loop development in select species of Dallinacea is investigated by numerical analysis. It is shown how loop transformation depends on the location of the ‘loop center’, that stage forms are determined by the position of the center, and that there may be two ‘shift directions’. The succession found in Campages, Laqueur and Dallina can be explained by a posterior shift, while the succession found in Terebratalia and Coptothyris is explained by an anterior shift. These two directions may be linked, because both are found in a single species Nipponithyris afra. Loop development in species of Dallinacea can therefore be transformed through variation of a specific constraint; this is regarded as an example of developmental constraint. Developmental constraints as common features are useful in studying comparative morphology during ontogeny and phylogeny.

Extending the analysis of the ribbing patterns of Recent branchiopods, pattern transformation with the progression of growth is discussed. In ribbing patterns of brachiopods, each rib grows wider and higher, and sometimes branches off. It is proposed that median patterns appear as predictable outcomes of a simple space-filling process with stochastic properties, as shown by some investigators. From the analysis by the modified Fly method, it is found that branching points are determined by deterministic long range waves (breather-like solitons) which strongly interact with one another. For these patterns, all possible Interactive Lindenmayer systems with two sided inputs of most neighbouring cells were simulated, and all patterns were classified, compared to solutions with non-linear wave equations. It is concluded that ribbing patterns with deterministic signals are realized by coupling automata between I-L system developing kinks, and cell automata developing solitons. The importance of a morphogenetic control theory involving coupling and long range signals is emphasized.

A living system with autonomously emerging boundaries was presented in previous work. This paper gives a precise mathematical construction of this system by a classification of the flow diagrams and rigorous definition of the global inverse rules of cellular automata. Our model is based on the macroscopic and microscopic perpetual disequilibrations which were first introduced and studied by Mastuno. Because of the perpetual disequilibrations, the boundary conditions are determined a posteriori in succession. This means that our biological model contains the uncontrollability of both the macroscopic and the microscopic boundary conditions. Furthermore, in a typical case of this model, the local transition rule is perpetually changed because of the uncontrollable boundary conditions. Thus, an interaction between the dynamics and boundary conditions which plays an important role in living systems appears in this autonomous artificial life.