Bayesian inference is the process of narrowing down the hypotheses (causes) to the one that best explains the observational data (effects). To accurately estimate a cause, a considerable amount of data is required to be observed for as long as possible. However, the object of inference is not always constant. In this case, a method such as exponential moving average (EMA) with a discounting rate is used to improve the ability to respond to a sudden change; it is also necessary to increase the discounting rate. That is, a trade-off is established in which the followability is improved by increasing the discounting rate, but the accuracy is reduced. Here, we propose an extended Bayesian inference (EBI), wherein human-like causal inference is incorporated. We show that both the learning and forgetting effects are introduced into Bayesian inference by incorporating the causal inference. We evaluate the estimation performance of the EBI through the learning task of a dynamically changing Gaussian mixture model. In the evaluation, the EBI performance is compared with those of the EMA and a sequential discounting expectation-maximization algorithm. The EBI was shown to modify the trade-off observed in the EMA.

Bayesian inference is the process of narrowing down the hypotheses (causes) to the one that best explains the observational data (effects). To accurately estimate a cause, a considerable amount of data is required to be observed for as long as possible. However, the object of inference is not always constant. In this case, a method such as exponential moving average (EMA) with a discounting rate is used to improve the ability to respond to a sudden change; it is also necessary to increase the discounting rate. That is, a trade-off is established in which the followability is improved by increasing the discounting rate, but the accuracy is reduced. Here, we propose an extended Bayesian inference (EBI), wherein human-like causal inference is incorporated. We show that both the learning and forgetting effects are introduced into Bayesian inference by incorporating the causal inference. We evaluate the estimation performance of the EBI through the learning task of a dynamically changing Gaussian mixture model. In the evaluation, the EBI performance is compared with those of the EMA and a sequential discounting expectation-maximization algorithm. The EBI was shown to modify the trade-off observed in the EMA.

Bayesian inference is the process of narrowing down the hypotheses (causes) to the one that best explains the observational data (effects). To accurately estimate a cause, a considerable amount of data is required to be observed for as long as possible. However, the object of inference is not always constant. In this case, a method such as exponential moving average (EMA) with a discounting rate is used to improve the ability to respond to a sudden change; it is also necessary to increase the discounting rate. That is, a trade-off is established in which the followability is improved by increasing the discounting rate, but the accuracy is reduced. Here, we propose an extended Bayesian inference (EBI), wherein human-like causal inference is incorporated. We show that both the learning and forgetting effects are introduced into Bayesian inference by incorporating the causal inference. We evaluate the estimation performance of the EBI through the learning task of a dynamically changing Gaussian mixture model. In the evaluation, the EBI performance is compared with those of the EMA and a sequential discounting expectation-maximization algorithm. The EBI was shown to modify the trade-off observed in the EMA.

Lévy walks are known to be efficient movements because Lévy walkers search wide areas while restricting returns to previously visited sites. A self-avoiding walk (SAW) is a series of moves on a lattice that visit the same place only once. As such, SAWs can also be effective search algorithms. However, it is not realistic that foragers memorize many visited positions for a long time. In this work, we investigated whether foragers performed optimal searches when having limited memory. The agent in our model followed SAWs to some extent by memorizing and avoiding visited places. However, the agent lost its memory after a while. In that situation, the agent changed its reactions to visited patches by considering global trail patterns based on local memorized information. As a result, we succeeded in making the agent occasionally produce ballistic walks related to power-law tailed movements across some ranges.

Humans sometimes make unreasonable decisions when viewed in objective terms. Even in the real world, we may lose sense of direction by turning around the corner several times or mistaking the estimation of travel distance. We experimented in virtual space how we lose sense of direction under what circumstances. In the experiment, subjects viewed a three-dimensional space displayed on a computer display in the first person's perspective and were instructed to go straight from the start to the goal position. Results showed that unreasonable selections that strayed from the centerline connecting the start and goal positions were frequently made. The change in the direction is more influential than the change in the distance, and the angle of turning also affects. Furthermore, the subject's decision – making process was modeled using Bayesian inference and inverse Bayesian inference. Comparing the two models, when the decision-making pattern suddenly changed, the model by inverse Bayesian inference could follow up faster than the Bayesian inference.

The slime mould Physarum polycephalum has been used in developing unconventional computing devices for in which the slime mould played a role of a sensing, actuating, and computing device. These devices treated the slime mould as an active living substrate, yet it is a self-consistent living creature which evolved over millions of years and occupied most parts of the world, but in any case, that living entity did not own true cognition, just automated biochemical mechanisms. To “rehabilitate” slime mould from the rank of a purely living electronics element to a “creature of thoughts” we are analyzing the cognitive potential of P. polycephalum. We base our theory of minimal cognition of the slime mould on a bottom-up approach, from the biological and biophysical nature of the slime mould and its regulatory systems using frameworks such as Lyon's biogenic cognition, Muller, di Primio-Lengelerś modifiable pathways, Bateson's “patterns that connect” framework, Maturana's autopoietic network, or proto-consciousness and Morgan's Canon.

How can we link challenging issues related to consciousness and/or qualia with natural science? The introduction of endo-perspective, instead of exo-perspective, as proposed by Matsuno, Rössler, and Gunji, is considered one of the most promising candidate approaches. Here, we distinguish the endo-from the exo-perspective in terms of whether the external is or is not directly operated. In the endo-perspective, the external can be neither perceived nor recognized directly
rather, one can only indirectly summon something outside of the perspective, which can be illustrated by a causation–reversal pair. On one hand, causation logically proceeds from the cause to the effect. On the other hand, a reversal from the effect to the cause is non-logical and is equipped with a metaphorical structure. We argue that the differences in exo- and endo-perspectives result not from the difference between Western and Eastern cultures, but from differences between modernism and animism. Here, a causation–reversal pair described using a pair of upward (from premise to consequence) and downward (from consequence to premise) causation and a pair of Bayesian and inverse Bayesian inference (BIB inference). Accordingly, the notion of endo-consciousness is proposed as an agent equipped with BIB inference. We also argue that BIB inference can yield both highly efficient computations through Bayesian interference and robust computations through inverse Bayesian inference. By adapting a logical model of the free will theorem to the BIB inference, we show that endo-consciousness can explain free will as a regression of the controllability of voluntary action.

Foraging fiddler crabs form a strict spatial relationship between their current positions and burrows, allowing them to run directly back to their burrows when startled even without visual contacts. Path integration (PI), the underlying mechanism, is a universal navigation strategy through which animals continuously integrate directions and distances of their movements. However, we report that fiddler crabs also use visual orientation during homing runs using burrow entrances as cues, with the prioritised mechanism (i.e. PI or visual) determined by the distance (which has a threshold value) between the goal, indicated by PI, and the visual cue. When we imposed homing errors using fake entrances (visual cue) and masking their true burrows (goal of PI), we found that frightened fiddler crabs initially ran towards the true burrow following PI, then altered their behaviour depending on the distance between the fake entrance and masked true burrow: if the distance was large, they kept running until they reached the true burrow, ignoring the visual cue; however, if the distance was small, they altered the homing path and ran until they reached the fake entrance. This suggests that PI and visual mechanism in fiddler crabs are mutually mediated to achieve their homing behaviour.

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.

A self-avoiding walk (SAW) is a series of moves on a lattice that visit the same place only once. Several studies reported that repellent reactions of foragers to previously visited sites induced power-law tailed SAWs in animals. In this paper, we show that modelling the agent's multi-avoidance reactions to its trails enables it to show ballistic movements which result in heavy-tailed movements. There is no literature showing emergent ballistic movements in SAWs. While following SAWs, the agent in my model changed its reactions to marked patches (visited sites) by considering global trail patterns based on local trail patterns when the agent was surrounded by previously visited sites. As a result, we succeeded in producing ballistic walks by the agents which exhibited emergent power-law tailed movements.

Although foraging patterns have long been predicted to optimally adapt to environmental conditions, empirical evidence has been found in recent years. This evidence suggests that the search strategy of animals is open to change so that animals can flexibly respond to their environment. In this study, we began with a simple computational model that possesses the principal features of an intermittent strategy, i.e., careful local searches separated by longer steps, as a mechanism for relocation, where an agent in the model follows a rule to switch between two phases, but it could misunderstand this rule, i.e., the agent follows an ambiguous switching rule. Thanks to this ambiguity, the agent's foraging strategy can continuously change. First, we demonstrate that our model can exhibit an optimal change of strategy from Brownian-type to Levy-type depending on the prey density, and we investigate the distribution of time intervals for switching between the phases. Moreover, we show that the model can display higher search efficiency than a correlated random walk.

We argue for the notion of adaptability in collective behavior, treating real fish schools as an example. For evaluation, we use the inconsistent relation local and global perspectives. We show that this inconsistency Would affect whole group behaviors and lead them to use different strategies.

Since Conway proposed the Game of Life, it has attracted researchers’ attention due to complex “life” evolutions despite simple rules. It is known that the Game of Life exhibits self-organized criticality, which might be related to scale-free evolutions. Despite the interesting phenomenon of self-organized criticality, the Game of Life turns to steady states within several generations. Here, we demonstrate a new version of the Game of Life in which cells tried to stay “alive” even though neighboring sites were over- or underpopulated. These rule changings enabled the system to show scale-free evolutions for many generations.

Multi-agent models of robust open systems such as natural systems are the important theme in the literature of systems science. Heterarchy, which means dynamical hierarchy, is a structural model, which includes the dynamical interplay between different levels. However, it is not easy to build a formal model of a heterarchical system because the interplay between different levels lead a self-referential paradox. In this paper, we propose an continuous double auction model, which includes a formal model of conitnuous transaction. We encode the model into a restriction rule of the order submittion. The proposed model shows a critical behavior of the actual markets, and it can have the relationship with the behaviors of natural systems.

The plasmodium of true slime mold Physarum polycephalum is a unicellular and multinuclear giant amoeba. Since the cellular organism has some computational abilities, it is attracting much attention in the field of information science. However, previous studies have mainly focused on the optimization behavior of the plasmodium for a single-modality stimulus, and there are few studies on how the organism adapts to multi-modal stimuli. We stimulated the plasmodium with mixture of attractant and repellent stimuli, and we observed bifurcation in the chemotactic behavior of the plasmodium.

Continuous asynchronous trading activity is a key to understanding real-world market behavior. However, it is not easy to implement an agent-based computational market model because of the ambiguity between time and space. In this study, we use a model of asynchrony in a continuous double auction market in the form of noise and order restrictions to link inside- and outside- uncertainties in the economic system. Our model shows intermittent behavior with a small parameter value, which leads to the misapplication of the price-update rule, and consequently drives burst behavior. The statistical property of time development shows a similar tendency to that in previous empirical studies. Thus, it demonstrates the relationship between the asynchronous property and the complexity of economic systems.

To overcome the dualism between mind and matter and to implement consciousness in science, a physical entity has to be embedded with a measurement process. Although quantum mechanics have been regarded as a candidate for implementing consciousness, nature at its macroscopic level is inconsistent with quantum mechanics. We propose a measurement-oriented inference system comprising Bayesian and inverse Bayesian inferences. While Bayesian inference contracts probability space, the newly defined inverse one relaxes the space. These two inferences allow an agent to make a decision corresponding to an immediate change in their environment. They generate a particular pattern of joint probability for data and hypotheses, comprising multiple diagonal and noisy matrices. This is expressed as a nondistributive orthomodular lattice equivalent to quantum logic. We also show that an orthomodular lattice can reveal information generated by inverse syllogism as well as the solutions to the frame and symbol-grounding problems. Our model is the first to connect macroscopic cognitive processes with the mathematical structure of quantum mechanics with no additional assumptions. (C) 2016 Elsevier Ireland Ltd. All rights reserved.

The model of self-organized criticality (SOC) is a useful tool to understand the complexity of natural systems in the form of the artificial life and the artificial market. However, SOC remains the question what guarantees the criticality even though the natural systems seem to keep itself in the critical state. In this paper, we focus on the locality of interaction in zero-intelligence plus (ZIP) model. The extremely localized interaction changes the behavior of the ZIP model from equilibrium to intermittency. Although the original ZIP model falls into unstable with some noise, extremely localized interaction model archives robust intermittency against the noise parameter. Further, the statistical property of intermittent behavior shows the power-law nature.

We developed multi-agent models inspired by ant foraging. Previous research shows that ants obey Weber's law and change their moving angles based on pheromone conditions. We constructed trail-laying models in which agents estimate the global pheromone gradients based on local pheromone gradients, which resulting in emergent Weber's law. Agents were also admitted to use directional cues based on motions of other local agents to produce realistic curved paths. We also showed that re-estimation of pheromone gradients based on directional cues yields a balance between exploitation and exploration. (C) 2016 Elsevier B.V. All rights reserved.

We conducted movement analysis using ant experiments and simulation models. In our experiments, Japanese carpenter ants showed Levy-like movements when they were exposed to a bowl-shaped test container filled with other foragers. We also developed a one-dimensional multi-agent random walk algorithm. In our algorithm, agents interact with each other and change their probabilities of movements by locally anticipating other agents' moving directions. Agents also modulate those probabilities on the basis of local information, thereby producing fluctuations in averaged local directional information. We were able to induce agents in our model to achieve Levy-like movements. We also found that an agent occasionally moved or stayed together with another particular agent for a substantial duration in both experiments and simulations. (C) 2016 Elsevier B.V. All rights reserved.

Space-use problems have been well investigated. Spatial memory capacity is assumed in many home-range algorithms; however, actual living things do not always exploit spatial memory, and living entities can exhibit adaptive and flexible behaviour using simple cognitive capacity. We have developed an agent-based model wherein the agent uses only detected local regions and compares global efficiencies for a habitat search within its local conditions based on memorized information. Here, memorized information was acquired by scanning locally perceived environments rather than remembering resource locations. When memorized information matched to its current environments, the agent changed resource selection rules. As a result, the agent revisited previous resource sites while exploring new sites, which was demonstrating a weak home-range property.

The Kanizsa triangle, wherein three Pac-Man configurations symmetrically face inwards, is a well-known illusion. By exposing foraging ants (Lasius niger) to Kanizsa-shaped honeydew solutions, we studied the origin of this illusion. More specifically, we examined whether foraging ants showed different movement reactions to local honeydew patterns formed by nestmates. This novel phenomenon could serve as an abstract model of the Kanizsa triangle illusion under the assumption that such an illusion could arise through the sum of each agent's limited global cognitions, because each agent could not perceive the entire subjective contours. Even a subjective consciousness consists of some parts which have no identical perception and could be an illusion. We succeeded in inducing foragers to move along the sides of a Kanizsa triangle when Pac-Man-shaped inducers were introduced. Furthermore, foragers appeared to form Y-shaped trajectories when dot-shaped or inverse Kanizsa inducers were used. Based on our findings, we propose an agent-based ant model that compares modelled behaviour with experimental phenomena. Our abstract model could be used to explain such cognitive phenomena for bottom-up processes, because ants cannot perceive the given subjective contours, instead simply move along the edges. (C) 2016 Elsevier Ireland Ltd. All rights reserved.

Over the last years, in a series papers by Arecchi and others, a model for the cognitive processes involved in decision making has been proposed and investigated. The key element of this model is the expression of apprehension and judgment, basic cognitive process of decision making, as an inverse Bayes inference classifying the information content of neuron spike trains. It has been shown that for successive plural stimuli this inference, equipped with basic non-algorithmic jumps, is affected by quantum-like characteristics. We show here that such a decision making process is related consistently with an ambiguous representation by an observer within a universe of discourse. In our work the ambiguous representation of an object or a stimuli is defined as a pair of maps from objects of a set to their representations, where these two maps are interrelated in a particular structure. The a priori and a posteriori hypotheses in Bayes inference are replaced by the upper and lower approximations, correspondingly, for the initial data sets that are derived with respect to each map. Upper and lower approximations herein are defined in the context of "rough set" analysis. The inverse Bayes inference is implemented by the lower approximations with respect to the one map and for the upper approximation with respect to the other map for a given data set. We show further that, due to the particular structural relation between the two maps, the logical structure of such combined approximations can only be expressed as an orthomodular lattice and therefore can be represented by a quantum rather than a Boolean logic. To our knowledge, this is the first investigation aiming to reveal the concrete logic structure of inverse Bayes inference in cognitive processes. (C) 2016 Published by Elsevier Ireland Ltd.

The soldier crab appears in great numbers and feeds while wandering during daytime low tide. When they see an approaching object, they screw themselves into the sand. The mechanism of formation of mass wandering has not been clarified. In this study, to investigate if the soldier crabs use visual images of neighbors as a stimulus for wandering, dummy crabs were presented to crabs. In the experiments, one, two, four, or eight dummies were placed in a circle on a sand arena. Each crab was placed in the center of the arena and observed whether it burrowed into the sand or wandered. The proportions of wandering individuals in each experimental treatment were compared with the expected value. Significantly more crabs were wanderers when only two and four dummies were present. This result suggests that soldier crabs chose burrowing or wandering depending on visual image of the distribution of the neighbors.

Insects use a navigational toolkit consisting of multiple strategies such as path integration, view-dependent recognition methods and olfactory cues. The question arises as to how directional cues afforded by a visual panorama combine with olfactory cues from a pheromone trail to guide ants towards their nest. We positioned a garden ant Lasius niger on a rotating table, whereon a segment of a pheromone trail relative to the stationary panorama was rotated while the ant walked along the trail towards its nest. The rotational speed of the table (3 r.p.m.) was set so that the table would rotate through about 90 degrees by the time that an ant had walked from the start to the centre of the table. The ant completed a U-turn at about this point and so travelled in a nest-ward direction without leaving the trail. These results suggest that the ants persist on the pheromone trail and use visual input to determine their direction of travel along the trail.

We conducted an experiment in which visual discontinuity between one’s own body parts disturbs the unity of the body and elicits subjective and conscious disownership. Previous studies have demonstrated a decrease in feelings of ownership over an external object from a first-person viewpoint. In contrast, the present study suggests that people can feel explicit disownership of their own body from a third-person viewpoint. The current experiment presented participants with live, lateral images of their own body. During the trial, they moved and observed their arms within the following restrictions: In the “hide” condition, an elbow was hidden behind the upper body, obscuring the smooth connection between the arm and upper body. In the “display” condition, the elbow was displayed in front of the upper body to better display the smooth connection. Questionnaire results demonstrated that the participants felt disownership of their arms while retaining agency. Therefore, this experiment sheds new light on bodily awareness.

Here, we show that an optimized Levy-like walk (mu approximate to 2.00) and the Weber Fechner law can be achieved in our new multi-agent based model that depends on step lengths. Weber Fechner equation is strongly related to power-law. This equation is sometimes used in order to obtain power-law tailed distributions in observational levels. However, no study has reported how these two popular equations were achieved in micro or mechanistic levels. We propose a new random walk algorithm based on a re-valued algorithm, in which an agent has limited memory capacity, i.e., an agent has a memory of only four recent random numbers (limitation number). Using these random numbers, the agent alters the directional heuristic if the agent experiences moving directional biases. In this paper, the initial limitation number varies depending on the interaction among agents. Thus, agents change their limitation number and produce time delay in respect to rule change events. We show that slope values are variable compared with isolate foraging even though both indicate power-law tailed walks derived from Weber Fechner equation. (C) 2015 Elsevier B.V. All rights reserved.

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 Levy 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, Levy walk in schools can be regarded as a well-balanced movement to facilitate dynamic collective motion and information transfer throughout the group.

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.

Here, we developed 2-dimensional multi agent random walk algorithm. In our algorithm, agents interact with each other and change their directional rules by detecting other agents' moving direction locally. In addition to that, modulation effects in which agents control rule intervals depending on amount of local other agents are equipped to our model. We show that modulation effects which introduce global ambiguity play a crucial role to establish optimal random walk by checking the slope value (mu) depending on dense of agents. We set modulation-added model and non-modulation model. The latter is control model. In case of non-modulation model, the slope values (mu) highly depends on dense of agents. However, in case of modulation-added model, the slope values (mu) are flexible and independent from dense of agents.

Asynchronous cellular automata were studied in a term of information theory in this decade. While there are various methods to implement asynchronous updating, we define that each cell has its own internal clock which is interacted with neighboring clocks and that updating is controlled by the internal clock. The modulation of period of the internal clock results in a global and periodic synchronization which is not found in patterns of cells' state but in the pattern of development of local active information storage.

We demonstrate that plasmodium of Physarum polycephalum perceives an ambiguous stimulus made from oatmeal and KCl as it is either attractant or repellent. While there is no intermediate behavior of being attracted and avoiding a stimulus, each plasmodium makes a decision whether a given stimulus is either attractant or repellent evenly. We propose a model explaining why the plasmodium either covers a stimulus perfectly or avoids a stimulus without entering a stimulus. The model is based on a rough set analysis. We propose that the plasmodium has two perception models with respect to attractant and repellent. These two models conflict with each other. Due to the composition of two models, the effect of one of the models can be evoked and the effect of another model is suppressed.

In this paper, we mainly address three issues: externality of an agent, purpose of an agent, and a kind of "softness" of components in a system. Agents are independent of a system in an ordinary multi-agent model, hence the behavior of a system is not autonomous but influenced by the agents. If a multi-agent model is considered as a completely autonomous one, agents in the model are inevitably deprived of their externality and independence from the model. In order to treat the completely autonomous transition of a system, we introduce an agent which is part of a system, and has a purpose which is independent from the system. The interaction between a system and an agent transforms a random graph corresponding to the system into the graph which represents formal logic adequately. In the emergent graph, there are many complete subgraphs, which can be regarded as conceptualized matters. We modify the definition of a conceptualized matter into a subgraph which is a cycle of arrows, and regard the density of arrows of each conceptualized matter as validness. We define this object with the density as a soft object. A complete graph has a maximum number of arrows, hence is the most reliable soft object. In a similar way, we call an arrow with validness a soft arrow, and treat the relation between soft objects and soft arrows. The argument of this paper is relevant to dynamical formal logic, and at the same time, is intended to serve as a basis for an agent model. (C) 2014 Elsevier Ireland Ltd. All rights reserved.

Punctuated equilibrium, recently regarded as the power law distribution of lifespan, is estimated with respect to self-organized criticality. Previous explanations were based on a global property, such as the selection of species depending on their fitness, however a particular entity defined through such global property cannot be relevant to the notion of "self". Here, we introduce local ambiguity of a niche with respect to function and define a function network by using two types of maps. Due to the local complex structure of the function network, motif and lateral connections, some species are easily replaced by others, and other species have long lives. Punctuated equilibrium can, therefore, be explained by local ambiguous interaction, which suggests the notion of self and supports the idea of self-organized criticality. (C) 2014 Elsevier Ireland Ltd. All rights reserved.

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.

Recently, we proposed a new random walk algorithm, termed the REV algorithm, in which the agent alters the directional rule that governs it using the most recent four random numbers. Here, we examined how a non-bounded number, i.e., "randomness" regarding move direction, was important for optimal searching and power-law distributed step lengths in rule change. We proposed two algorithms: the REV and REV-bounded algorithms. In the REV algorithm, one of the four random numbers used to change the rule is non-bounded. In contrast, all four random numbers in the REV-bounded algorithm are bounded. We showed that the REV algorithm exhibited more consistent power-law ;distributed step lengths and flexible searching behavior. (C) 2014 Elsevier B.V. All rights reserved.

The plasmodium of Physarum polycephalum is often used in the implementation of non-linear computation to solve optimization problems, and this organismal feature was not used in this analysis to compute perception and/or sensation in humans. In this paper, we focused on the Kanizsa illusion, which is a well-known visual illusion resulting from the differentiation-integration of the visual field, and compared the illusion with the adaptive network in the plasmodium of P.polycephalum. We demonstrated that the network pattern mimicking the Kanizsa illusion can be produced by an asynchronous automata-fashioned model of the foraging slime mold and by the real plasmodia of P polycephalum. Because the protoplasm of the plasmodium is transported depending on both local and global computation, it may contain differentiation-integration processes. In this sense, we can extend the idea of perception and computation.

In this paper, we introduced Kanizsa triangle figures equipped with stripe notches on its inducers to experimental participants. It is obtained that illusion contour depends on the location and direction of the stripe notches. If notches were on the edge or at inner part of inducers, participants reported less magnitude of the contour illusion. These results suggest that there were plenty of room to consider the mechanism of Kanizsa triangle illusion by paying attention to the information which local inducer carries referring to global functional property.

Systems at a critical point in phase transitions can be regarded as being relevant to biological complex behaviour. Such a perspective can only result, in a mathematical consistent manner, from a recursive structure. We implement a recursive structure based on updating by asynchronously tuned elementary cellular automata (AT ECA), and show that a large class of elementary cellular automata (ECA) can reveal critical behavior due to the asynchronous updating and tuning. We show that the obtained criticality coincides with the criticality in phase transitions of asynchronous ECA with respect to density decay, and that multiple distributed ECAs, synchronously updated, can emulate critical behavior in AT_ECA. Our approach draws on concepts and tools from category and set theory, in particular on "adjunction dualities" of pairs of adjoint functors.

The Muller-Lyer illusion is a classical geometric illusion in which the apparent (perceived) length of a line depends on whether the line terminates in an arrow tail or arrowhead. This effect may be caused by economic compensation for the gap between the physical stimulus and visual fields. Here, we show that the Muller-Lyer illusion can also be produced by the foraging patterns of garden ants (Lasius niger) and that the pattern obtained can be explained by a simple, asynchronously updated foraging ant model. Our results suggest that the geometric illusion may be a byproduct of the foraging process, in which local interactions underlying efficient exploitation can also give rise to global exploration, and that visual information processing in human could implement similar modulation between local efficient processing and widespread computation.

Libet et al. (1983) revealed that brain activity precedes conscious intention. For convenience in this study, we divide brain activity into two parts: a conscious field (CF) and an unconscious field (U F). Most studies have assumed a comparator mechanism or an illusion of CF and discuss the difference of prediction and postdiction. We propose that problems to be discussed here are a twisted sense of agency between CF and UF, and another definitions of prediction and postdiction in a mediation process for the twist. This study specifically examines the definitions throughout an observational heterarchy model based on internal measurement. The nature of agency must be emergence that involves observational heterarchy. Consequently, awareness involves processes having duality in the sense that it is always open to the world (postdiction) and that it also maintains self robustly (prediction).

In reports addressing animal foraging strategies, it has been stated that Levy-like algorithms represent an optimal search strategy in an unknown environment, because of their super-diffusion properties and power-law-distributed step lengths. Here, starting with a simple random walk algorithm, which offers the agent a randomly determined direction at each time step with a fixed move length, we investigated how flexible exploration is achieved if an agent alters its randomly determined next step forward and the rule that controls its random movement based on its own directional moving experiences. We showed that our algorithm led to an effective food-searching performance compared with a simple random walk algorithm and exhibited super-diffusion properties, despite the uniform step lengths. Moreover, our algorithm exhibited a power-law distribution independent of uniform step lengths.

Slime mould Physarum polycephalum is large single cell with intriguingly smart behaviour. The slime mould shows outstanding abilities to adapt its protoplasmic network to varying environmental conditions. The slime mould can solve tasks of computational geometry, image processing, logics and arithmetics when data are represented by configurations of attractants and repellents. We attempt to map behavioural patterns of slime onto the cognitive control vs. schizotypy spectrum phase space and thus interpret slime mould's activity in terms of creativity.

Although it has been shown that visual cues play an essential role in navigation by the garden ant Lasius niger, no previous studies have addressed the way in which information from local visual cues is acquired and utilized in navigation. We found that in the absence of pheromone trails, ants whose homing motivation was triggered by feeding returned to the nest following local visual cues. In our experiments, the ants travelled through a maze to reach a feeder. They explored the maze and sometimes became trapped in its dead ends. We found that the ants more effectively used visual cues during their homeward journey if they experienced a dead end during their outward journey. This result suggested that the ants used the information acquired from visual cues during the outward journey to avoid a dead end on their return journey.

This paper proposes a new method to estimate the distribution of some similar objects that have no specific feature like color and shape. In the field of animal behavior analysis, the estimation of the crowded swarm distribution with automated way of image processing is necessary. However, to trace the individual objects those may overlap each other in video sequence is quite difficult. This paper proposes to introduce a value function effective for the crowded swarm analysis, and shows the affirmative results acquired for the Soldier Crab behavior analysis.

Collision-based computing schemes are implemented using propagating and interacting localisations. When two or more travelling localisations collide, they may reflect or merge into a new localisation. Presence/absence of a localisation in a specified site of a physical space represents True/False values of Boolean variables. Incoming trajectories symbolise inputs and outgoing trajectories are outputs. Logical gates are implemented by collisions between the localisations. We demonstrate how primitives of the collision-based computing can be implemented using swarms of soldier crabs in laboratory experiments. Soldier crabs, Mictyris guinotae, exhibit coherent collective behaviour on an intertidal flat at a daytime low-tide period. The soldier crabs' swarm often moves as a single entity with definite yet dynamically changing boundary. We utilise swarms of soldier crabs to implement a Boolean logic gate. The gate has two inputs and three outputs. Values of the inputs and outputs are represented by crab swarm size or a proportion of crabs in the input and output channels. We demonstrate that the gate performs logical conjunction and negation. © 2013 Taylor and Francis Group, LLC.

This paper proposes a new method to estimate the distribution of some similar objects that have no specific feature like color and shape. In the field of animal behavior analysis, the estimation of the crowded swarm distribution with automated way of image processing is necessary. However, to trace the individual objects those may overlap each other in video sequence is quite difficult. This paper proposes to introduce a value function effective for the crowded swarm analysis, and shows the affirmative results acquired for the Soldier Crab behavior analysis.

Modeling of figure-ground information is a key issue in the field of cognitive vision and visionbased object recognition. We have used rough set derived lattices in order to express such figureground relations. Complement relations in lattices turn out to be suited for modeling such relations. We have applied this method to a virtual world created by a literary text. We have investigated the figure-ground property of characters in the mystery novel The Murders in the Rue Morgue by Edgar Allan Poe. We have found that in this story, the characters have a clear figure-ground relation most of the time. This can be explained by the style of writing where the culprit does not blend in with the rest of the character from the beginning of the story. In other words, most of the characters' attribute information is different. Due to our lattice representation, the evolution of the story can be expressed numerically in terms of figure and ground.

The dynamics of panic attacks in both functional individuals and panic disorder patients are qualitatively evaluated by using coupled nonlinear differential equations. Each panic attack is described by two variables, fear and physical symptoms. Different thresholds for these variables are defined for functional individuals, patients in the acute phase, and patients in the chronic phase. Integral lines, vector fields, and time series of solutions, based on the proposed coupled nonlinear differential equations, are shown. The efficacy of treatment and severity of each panic attack are also evaluated. Under our hypothesized condition, it is shown that particular pharmacological treatment could change the final states of patients in the acute phase, but could not change either the final states of patients in the chronic phase or those of functional individuals. Our model is consistent with the well-known major features of panic attacks, and sheds new light on the dynamics of panic attacks.

Canalization is a typical self-organization process leading to complementarity between parts and the whole. In the field of developmental biology, concerns about morphogenesis canalization are often framed as the French flag problem, questioning how each cell knows its own position in the whole system. Although chemical gradients have been suggested to provide positional information, there is no direct evidence that gradients are used to gain positional information. The chemical gradient hypothesis is based on the assumption that agents (e.g., cells) in a domain that locally interact with each other can generate a chemical gradient thanks to a global reference point. Instead of a chemical gradient, we here propose a model based on agents that are equipped with sociality that is based not on a global reference but rather on the ability to sense other neighboring agents, or potential resonance. The interaction among the agents with sociality, developed from undifferentiated types or tokens, is implemented using asynchronous updating automata equipped with potential resonance. We show that these automata can generate a French flag pattern that is very robust against perturbations without positional information by comparing automata with synchronous updating and asynchronous automata without potential resonance. (C) 2012 Elsevier Ireland Ltd. All rights reserved.

A flexible body image is required by animals if they are to adapt to body changes and move effectively within a structurally complex environment. Here, we show that terrestrial hermit crabs, Coenobita rugosus, which frequently change shells, can modify walking behaviour, dependent on the shape of the shell. Hermit crabs walked along a corridor that had alternating left and right corners; if it was narrow at the corner, crabs rotated their bodies to avoid the wall, indicating an awareness of environmental obstacles. This rotation increased when a plastic plate was attached to the shell. We suggest that the shell, when extended by the plate, becomes assimilated to the hermit crab's own body. While there are cases of a tool being assimilated with the body, our result is the first example of the habitat where an animal lives and/or carries being part of a virtual body.

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 metrictopological 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.

Although landmarks are used as global one in the model of navigation, the insects in temperate zone have to use local landmarks and local visual cues. Because local landmarks could be equipped with fundamental ambiguity, the landmarks are destined to be both Go- and Stop-signs. We propose the agent-fashioned pilot navigation model resulting from the vague local landmarks. The agent of the model can explore by making landmarks step by step, and can go home by tracing stored memories of landmarks.

Animal navigation based on local landmark is here expressed by a topological system consisting of point logic and open logic. Because disjunction of points is inconsistent with conjunction of opens, directed disjunction is introduced to improve the inconsistency. Choosing a directed set implies that a set of particular landmarks are mixed with up and they are regarded as one mass as a territory. It is nothing but an origin of a meta-symbol and/ or familiar territory.

The plasmodium of Physarum polycephalum is a unicellular and multinuclear giant amoeba that has macroscopic size, and by this particular nature the organism is attracting a lot of attention in the research fields such as systems science, nature-inspired bio-computing and swarm behavioural study. In this paper, we investigated how the plasmodium generates new motility and morphology, and found that there are allometric relationships between the cell volume and morphology, and between cell size and cell motility. We further discuss how these relationships are realised, and these relationships are deeply connected to the organism's benefit of being a large-scale unicellular organism.

Many simulations of collective behavior have been presented in recent years. Recently, a pioneering study by Ballerini et al. (2008a,b) suggested that the interactions of birds in a flock should be modeled using the topological distance rather than the metric distance. The concept of topological distance is deemed important for explaining collective behavior. However, few studies have discussed the distinctions between the metric and topological distances. In this paper, we clarify the difference between models based on the topological and metric distances and propose a new hybrid model of these models. The agent of our model switches between these two interactions by tuning the threshold parameters. We show that this hybrid flocking model has the medium property between the metric and the topological distance. In other words, the agents of our hybrid model can dramatically make and divide flock by tuning their neighborhoods. This result suggests that making and dividing flock would be deeply connected with animal's cognition. (C) 2011 Elsevier B.V. All rights reserved.

The plasmodium of Physarum polycephalum is a unicellular and multinuclear giant amoeba that shows adaptive behaviors. To test the presence of memory and learning ability in the plasmodium, we performed an associative learning experiment using the unicellular organism. The plasmodium in this experiment seemed to acquire a reversed thermotactic property, a new preference for the lower temperature. The result implied a possibility of unicellular learning, though in a preliminary way. We also discuss a possible mechanism of learning by the organism. © 2011 Elsevier Ltd.

The main interest of the organizational learning is that the agent balances between exploring and exploiting. When the agent decides the answer in finite time, it gives rise to the problem that is trade-off between exploring and exploiting. This problem never arises in the given enough time. The agent must decide answer from his imperfect information, when the time is given finite for the task. 2-arms bandit problem is often taken into consideration in this problem. In previous article, we proposed the model for weak identity that is dynamically changing the hierarchy of his knowledge. Recently, the method of the heuristic model is attracted to approach this problem. In this article, we proposed different approaches for 2-arms bandit problem, and the model we proposed can adapt to the environment when the condition of the problem is changed and shows another approach to the organizational learning. (C) 2010 Wiley Periodicals, Inc. Complexity 16: 10-21, 2011

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. (c) 2010 Elsevier Ltd. All rights reserved.

Based on the field observation of soldier crabs, we previously proposed a model for a swarm of soldier crabs. Here, we describe the interaction of coherent swarms in the simulation model, which is implemented in a logical gate. Because a swarm is generated by inherent perturbation, a swarm can be generated and maintained under highly perturbed conditions. Thus, the model reveals a robust logical gate rather than stable one. In addition, we show that the logical gate of swarms is also implemented by real soldier crabs (Mictyris guinotae).

We explore lattice theoretic aspects in rough set theory in terms of the duality between algebra and representation. Approximation spaces are dual to complete atomic Boolean algebras in the sense that there is an adjunction between corresponding suitable categories. This is an analogy with the adjunction between the category of topological spaces and the opposite of the category of frames in pointless topology. In this paper we consider a generalization of approximation spaces called double approximation systems. A double approximation system consists of a set and two equivalence relations on it. We construct an adjunction generalizing this concept for approximation spaces. To achieve this goal, we first introduce a natural generalization of complete atomic Boolean algebras called complete prime lattices. Then we select double approximation systems that can be dual to complete prime lattices and prove the adjunction.

The plasmodium of Physarum polycephalum is a large, unicellular and multinuclear organism whose computational ability is attracting a lot of attention in the field of nature-inspired Unconventional computing. To test the computational capability of the organism and its utility for future applications, we have implemented the computation of a Voronoi diagram and a collision-free path in an experimental system using Physarum plasmodium. Attractants and repellents for the plasmodium were arranged in the experimental system to induce the plasmodium to form the graphs. The plasmodium solved the complex problem and successfully formed Voronoi diagrams and collision-free paths, demonstrating its computational ability.

We propose a dynamical model of formal logic which realizes a representation of logical inferences, deduction and induction. In addition, it also represents abduction which is classified by Peirce as the third inference following deduction and induction. The three types of inference are represented as transformations of a directed graph. The state of a relation between objects of the model fluctuates between the collective and the distinctive. In addition, the location of the relation in the sequence of the relation influences its state.

The central notion of a rough set is the indiscernibility that is based on an equivalence relation. Because an equivalence relation shows strong bondage in an equivalence class, it forms a Galois connection and the difference between the upper and lower approximations is lost. Here, we introduce two different equivalence relations, one for the upper approximation and one for the lower approximation, and construct a composite approximation operator consisting of different equivalence relations. We show that a collection of fixed points with respect to the operator is a lattice and there exists a representation theorem for that construction. © 2010 Springer-Verlag.

The internal description of spacetime can reveal ambiguity regarding an observer's perception of the present, where an observer can refer to the present as if he were outside spacetime while actually existing in the present. This ambiguity can be expressed as the compatibility between an element and a set, and is here called a/{a}-compatibility. We describe a causal set as a lattice and a causal history as a quotient lattice, and implement the a/{a}-compatibility in the framework of a causal histories approach. This leads to a perpetual change or a pair of causal set and causal history, and can be used to describe subjective spacetime including the deja vu experience and/or schizophrenic time. (C) 2009 Elsevier B.V. All rights reserved.

We experimentally demonstrate that both Voronoi diagram and its dual graph Delaunay triangulation are simultaneously constructed - for specific - conditions - in cultures of plasmodium, a vegetative state of Physarum polycephalum. Every point of a given planar data set is represented by a tiny mass of plasmodium. The plasmodia spread from their initial locations but, in certain conditions, stop spreading when they encounter plasmodia originated from different locations. Thus space loci not occupied by the plasmodia represent edges of Voronoi diagram of the given planar set. At the same time, the plasmodia originating at neighboring locations form merging protoplasmic tubes, where the strongest tubes approximate Delaunay triangulation of the given planar set. The problems are solved by plasmodium only for limited data sets, however the results presented lay a sound ground for further investigations.

In this paper we address balancing process of ecological flow networks. In existing approaches, macroscopic objectives to which systems organize are assumed. Flow balance provides only constraints for the optimization. Since flow balance and objectives are separated from each other, it is impossible to address how the appearance of objectives is related to flow balance. Therefore, we take an alternative approach, in which we directly describe a dynamics of balancing process. We propose a simple mathematical formula for local balancing dynamics and show that it can generate a self-organizing property, which could be seen as a primitive objective. (C) 2008 Elsevier B.V. All rights reserved.

A representation theorem for complete lattices by double approximation systems proved in [Gunji, Y-P., Haruna, T., submitted] is analyzed in terms of category theory. A double approximation system consists of two equivalence relations on a, set. One equivalence relation defines the lower approximation and the other defines the upper approximation. It is proved that the representation theorem can be extended to an equivalence of categories.

We here concentrate on equivalence relation, and show that the composition of upper approximation of one equivalence relation and the lower one of the other equivalence relation can form a lattice. We also show that this method can be used to define computational complementarity in automata.

In this paper we address network motifs found in information processing biological networks. Network motifs are local structures hi a whole network on one hand, they are materializations of a kind of wholeness to have biological functions oil the other hand. We formalize the wholeness by the notion of sheaf. We also formalize a, feature of information processing by considering an internal structure of nodes ill terms of their information processing ability. We show that two network motifs called bi-fan (BF) and feed-forward loop (FFL) can be obtained by purely algebraic considerations.

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. (C) 2008 Elsevier Ltd. All rights reserved.

Heterarchical structure is important for understanding robustness and evolvability in a wide variety of levels of biological systems. Although many studies emphasize the heterarchical nature of biological systems, only a few computational representations of heterarchy have been created thus far. We propose here the time-state-scale re-entrant form to address the self-referential property derived from setting heterarchical structure. In this paper, we apply the time-state-scale re-entrant form to abstract self-referential modeling for a functional manifestation of biological network presented by [Tsuda, I., Tadaki, K., 1997. A logic-based dynamical theory for a genesis of biological threshold. BioSystems 42, 45-64]. The numerical results of this system show different intermittent phase transitions and power-law distribution of time spent in activating functional manifestation. The Hierarchically separated time-scales obtained from spectrum analysis imply that the reactions at different levels simultaneously appear in a dynamical system. The results verify the mutual inter-relationship between heterarchical structure in biological systems and the self-referential property of computational heterarchical systems. (c) 2008 Elsevier Ireland Ltd. All rights reserved.

We propose a model based on Elementary Cellular Automata (ECA) where each cell has its own semantics defined by a lattice. Semantics play the following two roles: (1) a state space for computation and (2) a mediator generating and negotiating the discrepancy between the rule and the state. We call semantics playing such roles 'local semantics'. A lattice is a mathematical structure with certain limits. Weakening the limits reveals local semantics. Firstly, we implement local semantics for ECA and call the result 'Lattice-Driven Cellular Automata' (LDCA). In ECA rules are common and invariant for all cells, and uniquely determine the state changes, whereas in LDCA rules and states interplay with each other dynamically and directly in each cell. Secondly, we compare the space-time patterns of LDCA with those of ECA with respect to the relationship between the mean value and variance of the 'input-entropy'. The comparison reveals that LDCA generate complex patterns more universally than ECA. Lastly, we discuss the observation that the direct interplay between levels yields wholeness dynamically. (c) 2007 Elsevier B.V. All rights reserved.

Although life is destined to be approximately described as a self-referential form, the self-reference is invalidated and life avoids a contradiction. Since life does not include any contradiction, it reveals a unity as a, whole. Since life is not a self-circulation, it implements diversity and evolvability. Here we show life as invalidated self-reference by constructing a model cell driven by damaged damage. Since life is always close to destruction. it exhibits both of the amoebic motion and the intelligent Physarum-like behavior.

A heterarchy is a dynamical hierarchical system inheriting logical inconsistencies between levels. Because of these inconsistencies, it is very difficult to formalize a heterarchy as a dynamical system. Here, the essence of a heterarchy is proposed as a pair of the property of self-reference and the property of a frame problem interacting with each other. The coupling of them embodies a one-ity inheriting logical inconsistency. The property of self-reference and a frame problem are defined in terms of logical operations, and are replaced by two kinds of dynamical system, temporal dynamics and state-scale dynamics derived from the same "liar statement". A modified tent map serving as the temporal dynamics is twisted and coupled with a tent map serving as the state-scale dynamics, and this results in a discontinuous self-similar map as a dynamical system. This reveals that the state-scale and temporal dynamics attribute to the system, and shows both robust and emergent behaviors. (C) 2007 Elsevier Ireland Ltd. All rights reserved.

We propose a mathematical model of economic agents to study origin of money. This multi-agent model is based on commodity theory of money, which says that a commodity used as money emerges from barter transaction. Each agent has a different value system which is given by a Heyting algebra, and exchanges one's commodities based on the value system. In each value system, necessity and unnecessity of commodities are expressed by some elements and their compliments on a Heyting Algebra. Moreover, the concept of the compliment is extended. Consequently, the duality of the necessity-unnecessity is weakened, and the exchanges of the commodities are promoted. The commodities which keeps being exchanged for a long time can correspond to money.

We pursue anticipation in second person or normative anticipation. As the first step, we make the three concepts second person, internal measurement and asynchroneity clearer by introducing the velocity of logic vi and the velocity of communication v, in the context of social communication. After proving anticipatory nature of rule-following or language use in general via Kripke's "rule-following paradox", we present a mathematical model expressing the internality essential to second person, taking advantage of equivalences and differences in the formal language theory. As a consequence, we show some advantages of negatively considered concepts and arguments by concretizing them into an elementary and explicit formal model. The time development of the model shows a self-organizing property which never results if we adopt a third person stance.

Identity expressed in terms of second person descriptions is addressed in relation to robustness, and a simple computational model is proposed for preserving identity. Robustness is enhanced in the model by means of computational rules for chaotic cellular automata. The robustness enhancement mechanism is explained qualitatively. (C) 2007 Elsevier B.V. All rights reserved.

Two ideas in theoretical biology, 'decomposition into functions' and 'gluing functions', are formalized as endofunctors on the category of directed graphs. We prove that they constitute an adjunction. The invariant structures of the adjunction are obtained. They imply two biologically significant conditions: the existence of cycles in finite graphs and anticipatory diagrams. (c) 2007 Elsevier Ireland Ltd. All rights reserved.

We propose a dialogue-based society model which explains how the transitive law of the causality is originated. Causality is, in general, formalized by using axiomatic approaches. Instead of using axiomatic methods, we, however, compose a model consisting of agents who have knowledge about causal relations among objects. The model society can reveal the transitive law through interactional dialogues among themselves. The agents are reciprocally influenced, if they have either completely same opinions, or a particular pattern of opinions, that are regarded as the extension of such exact accordance. In addition, we add some vagueness to the dialogue, which is closer to a real communication than the former model. A set of knowledge of each agent is expressed as a directed graph, hence the every model can be construed as mere transformations of directed graphs through the interactions among directed graphs themselves. Following this perspective, the models are the systems that connect local logic with global one, while the union of the directed graphs is regarded as the global. (c) 2007 Elsevier Ireland Ltd. All rights reserved.

From the perspective of a heterarchy, endo-physics, or internal measurement, a time-state-scale re-entrant system has been proposed [Y.-P. Gunji, K. Sasai. S. Wakisaka, BioSystems (submitted for publication)]. However, the dynamical structure of this system has yet to be estimated. Because the return map of the time-space re-entrant system results from the twisted coupling between the temporal and state-scale states. it is analytically determined. The attractors of entrainment in the interactive re-entrant system are also determined by a particular recursive rule, and it is also shown that a resulting return map can control the attractors of the interactive systems. (c) 2007 Published by Elsevier B.V.

Emergence in a system appears through the interaction of its components, giving rise to higher order or complexity in the system. We tested for the presence of emergent properties in a biological system using the simplest biological entity of a unicellular organism; the plasmodium of Physarum polycephalum, a giant unicellular amoeboid organism that forms a network-like tubular structure connecting its food sources. We let two plasmodium networks within a single cell interact with each other, and observed how the intracellular interaction affected the morphologenesis of the plasmodium networks. We found that the two networks developed homologous morphology. We further discuss the presence of autonomous and emergent properties in homologous network formation. (c) 2007 Elsevier B.V. All rights reserved.

At present there exists a large gap in size, performance, adaptability and robustness between natural and artificial information processors for performing coherent perception-action tasks under real-time constraints. Even the simplest organisms have an enviable capability of coping with an unknown dynamic environment. Robots, in contrast, are still clumsy if confronted with such complexity. This paper presents a bio-hybrid architecture developed for exploring an alternate approach to the control of autonomous robots. Circuits prepared from amoeboid plasmodia of the slime mold Physarunt polycephalum are interfaced with an ormaidirectional hexapod robot. Sensory signals from the macro-physical environment of the robot are transduced to cellular scale and processed using the unique micro-physical features of intracellular information processing. Conversely, the response form the cellular computation is amplified to yield a macroscopic output action in the environment mediated through the robot's actuators. (c) 2006 Elsevier Ireland Ltd. All rights reserved.

We propose a recurrent neural network architecture that is capable of incremental learning and test the performance of the network. In incremental learning, the consistency between the existing internal representation and a new sequence is unknown, so it is not appropriate to overwrite the existing internal representation on each new sequence. In the proposed model, the parallel pathways from input to output are preserved as possible, and the pathway which has emitted the wrong output is inhibited by the previously fired pathway. Accordingly, the network begins to try other pathways ad hoc. This modeling approach is based on the concept of the parallel pathways from input to output, instead of the view of the brain as the integration of the state spaces. We discuss the extension of this approach to building a model of the higher functions such as decision making. (c) 2006 Elsevier Ltd. All rights reserved.

On-off intermittency is an aperiodic switching between synchronized dynamics and non-synchronized, chaotic, dynamics. Intermittency is observed near the onset of chaos on a bifurcation diagram produced by varying the parameters of its coupling strength. Therefore, its occurrence depends upon tuning the parameters of the system in a very sensitive way. In the present paper, a concept of observational heterarchy is reviewed with a simple model, and characters of on-off intermittency derived from active coupling systems (ACS) are investigated. Generally, on-off intermittency results from fluctuation of the local transverse Lyapunov exponent through points of marginal stability. ACS can retain such a character of the Lyapunov exponent by the time evolution of the maps, so on-off intermittency occurs on wider parameter regions. This paper presents a certain approach to the notion of robustness that is regarded as a persistent feature, conceptually different from the strict notion of stability on dynamical systems. (c) 2006 Elsevier B.V. All rights reserved.

We used the plasmodium of Physarum polycephalum to investigate a communicative property of a cell. We allowed the plasmodium to form a tubular network that connected three food sources, which were arranged to be located at the vertices of an equilateral triangle. The global condition of the plasmodium is changed by the connection of two networks in such a way that the local solution of each network was not affected. We used several criteria to evaluate the character of the network. The change in the global condition appeared to cause significant difference in the network properties, and two connected networks showed homologous network formation. These data imply the presence of intracellular communication and anticipatory aspect in their communication.

Life-like adaptive behaviour is so far an illusive goal in robot control. A capability to act successfully in a complex, ambiguous, and harsh environment would vastly increase the application domain of robotic devices. Established methods for robot control run up against a complexity barrier, yet living organisms amply demonstrate that this barrier is not a fundamental limitation. To gain an understanding of how the nimble behaviour of organisms can be duplicated in made-for-purpose devices we are exploring the use of biological cells in robot control. This paper describes an experimental setup that interfaces an amoeboid plasmodium of Physarum polycephalum with an omnidirectional hexapod robot to realise an interaction loop between environment and plasticity in control, Through this bio-electronic hybrid architecture the continuous negotiation process between local intracellular reconfiguration on the micro-physical scale and global behaviour of the cell in a macroscale environment can be studied in a device setting.

Marx's argument on 'the form of value' is based on state-oriented physics (SOP) and has 'the problem of transitivity.' This problem is inevitably led by an assumption of SOP that observer is able to identify a rule of exchange, so we cannot solve this problem directly. If we hold a standpoint of measurement-oriented physics (MOP), this problem is not a pardox but can be treated as the possibility to get a new outlook for understanding an aspect of exchange as a movement. The problem of transitivity arises because an observer who can describe individual exchanges only as specific parts of the whole exchange tries to describe a general rule. If we take it as a measurement problem, we can positively use the problem of transitivity and construct an internal measurement model in which exchange has the duality, operator and operand. We construct an internal measurement model of exchange as an interaction between cone-relation and equivalent-relation. Then we get patterns named 'particle' that can be interpreted as a rule that can be regarded adaptable for the whole process of exchange, and the particle also has the duality of stability and instability. (C) 2002 Elsevier Science Inc. All rights reserved.

This report discusses how one can argue the origin of a symbol in animal behaviors, with respect to experiments and models. The results suggest that the frame-problem resulting in the power-law positively plays a role in the origin of a symbol.

If the syntax-semantics interaction is driven by the interface, it also interrupts the interaction on its own right. Because the syntax is verified to be isomorphic to the semantics, the interaction is open to the diagonal argument leading to a contradiction. That is why it is necessary to introduce a particular interface to drive the interface to make the interaction possible despite the contradiction. In this context we propose the system implemented with the syntax-semantics loop by using a concept lattice and a particular weak quantifier, This system is expressed as the self-navigating system which wanders in a two-dimensional space, encounters some landmarks, constructs the relationship among landmarks to which decision making with respect to the move is referred. The syntax of this system is defined as two-dimensional move and the semantics is defined as a concept lattice [B. Ganter, R. Wille, Formal Concept Analysis, Springer, Berlin, 1999] constructed by the binary relation between landmarks and some properties of landmarks, and by Galois connection. To implement the interface driving and interrupting the interaction between syntax and semantics, we divided semantics into local and global concept lattices, and introduce a weak quantifier to connect a local with a global lattice. Because the contradiction results from diagonal argument or using a normal quantifier V, the use of a quantifier is restricted dependent on the situation to avoid a contradiction. It is shown that due to the role of a weak quantifier our self-navigating system is both robust and open to the emergent property through simulating studies. (C) 2001 Elsevier Science Ltd. All rights reserved.

We propose a model of evolutionary systems characterized by internal measurement, or endo-physics, that is based on a particular graph morphism. If we take an internal stance, we have to focus on the influence of the outside of the domain of choice. The outside of the domain is not explicitly expressed as a particular ensemble in advance, although a formal expression generally requires an explicit form of the outside as the possible forms. In our model, a system is expressed by a directed graph, and the time transition is expressed as a particular graph morphism referring to the outside of the domain of the morphism. Referring to the outside of the domain is expressed by dynamical decomposition and synthesis of the relationship between a graph and its possible forms expressed as an underlying free category. Because the transformations from a graph to a category and vice versa are expressed as two adjunctive functors, a graph morphism is defined by a sequence of the operation of a free functor and a special operator standing for invalidation of the operation of the free functor. Time development of this system can generate a particular universal structure like a limit and co-limit as a part of a directed graph, which stands for generation of a higher order. We also argue that the process toward the generation of a universal structure can reveal intermittency, and that an emergent boundary in pattern formation can be demonstrated by the generation of this universal structure. In addition, we discuss emergent computation such as the origin of primitive recursive functions through the origination of a universal structure. (C) 2001 Published by Elsevier Science B.V.

At the beginning, we point out a serious problem which arises when we describe the process of the living system as the computational process of a formal system. The problem is the indefiniteness in terms of correspondences of input and output states. Such indefiniteness can be grasped as the contradiction in a formal system. That is why we can say that the process of the living system is executed properly in spite of the existence of such a serious problem. The process proceeding in spite of a contradiction is represented by a perpetual change of partial function as a transition rule depending on the state. To achieve this purpose, we introduce the Bezier curve as a partial function. Given some control points in a plane, the Bezier curve that roughly connects all control points is calculated, and then all control points are moved horizontally and vertically at the same time as far as such moves can cross the Bezier curve. The new configuration of control points yields for the new Bezier curve. This sequential process is iterated, and that a transition rule of the Bezier curve is recursively re-defined. As a result, we have found that the system can generate particular output states even though the system is constructed without any explicit mechanism ensuring such events. Finally, we show that our system does work as a conceptual tool to embody ourselves who observe the process of the living system. A framework of the argument presented here is so-called internal measurement [1,2].

In this paper we discuss that monetary exchange emerges in a reciprocal system which consists of donations and returns. Agents reciprocate goods alternately without bilateral agreement in the system, that is constructed not from the viewpoint of the recipient, but from the one of the reciprocator. Moreover, reciprocity is regarded as interaction with incomplete identification consisting of the alternate procedure of constructing a map from coarse-grained data by a contraction mapping and of applying the map to fine-grained data. We show that reciprocity gives rise to the monetary exchange which implies globality without the concept of metric space or global semantics. It seems that interaction with incomplete identification does not carry the notion of globality. On the contrary, in our model globality paradoxically occurs from the accumulation of indefinite incomplete identification. (C) 2001 Elsevier Science Inc. All rights reserved.

When considering a behavioral pattern as a specific type of mechanism, an inherent problem is that it is difficult to determine to what extent the mechanism is programmed to behave selectively in individual situations. To probe this question further, we investigated the orientation of the body axis of the young Japanese flounder Paralichthys olivaceus. The pattern of the substrate and the orientation of neighboring fish were recognized as the determining factors for orientation in P. olivaceus. It was expected, therefore, that a group of individuals would exhibit a definite orientation pattern with respect to the striped pattern. However, the global orientation patterns on the striped substrate based on ten individuals could be classified into two categories: perpendicular and cross to the stripe pattern. This suggests that the substrate pattern and the surrounding individuals operated as distinct temporal criteria as stimuli for orientation. Analysis based on the local and global viewpoints reveals the temporality quantitatively. (C) 2000 Elsevier Science B.V. All rights reserved.

We studied animal's learning of spatial discrimination in an experimental environment. Turtles, Chinemys reevesii, were employed for the study. We focused on two independent aspects: (1) turtle's success rate in the task, which is the most common criterion to estimate the ability of the animals. and (2) the statistical properties of the time interval of the task, which is independent on the spatial criterion. For a statistical analysis. we employed the scheme of power law distributions which was recently used to estimate animal behaviors in relation to the idea of the fractal. We addressed the basic problem of whether these two criteria, or any other criteria for this matter, could or could not exclude an observer who studies the animal behavior. To demonstrate inseparability of an observer and the object, we conducted three different learning experiments: (1) complete spatial discrimination, (2) incomplete spatial discrimination, (3) another, different, complete discrimination, in this order. The incomplete one was taken to mean incomplete only for all observer. Our experiments reveal that the same result (success rate) was perceived differently by the animal if the attitude of the observer to the experiments differed. This observation comes to suggest that the notion of autonomous choice on the part of an animal is contingent upon the inseparability between an observer and the object. (C) 2000 Elsevier Science Ireland Ltd. All rights reserved.

On-going process is generally understood in the opposition between on-going and completion, such as duration and state. These two notions, however, are connective by a kind of glue, that is indefiniteness. After manifesting the relationship between on-going process and completion with respect to development and emergence, we propose the formal model of on-going process via completion by dynamical destruction of the duality called adjunction between a program and possible computational sequences. This model can yield the generation of limit in a developmental program, representation, and emergent boundary as the limit.

The issue we address is whether an animal knows or understands the significance of learning. We constructed an animal's own conceptualization via resolving a paradox underlying the process of learning. We found a kind of self-similar pattern in the behavior of goldfish resolving a paradoxical experimental problem. The pattern can be considered as a solution to the paradox in the experiment. An animal's own learning should be revised through solving paradoxes. The dualism of mechanistic thinking and vitalism can thus be avoided. (C) 1999 Elsevier Science Ireland Ltd. All rights reserved.

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 Canter 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. (C) 1999 Elsevier Science Inc. All rights reserved.

We propose a weak definition for the usage of a tool for an ethological study of ants. In particular, we illustrate the usage of a cart in experiments on the transportation of foods by ants as employing a logical structure including a contradiction. The contradiction originates in ruling out the very term 'tool' from the description of the behavior of the animals. Focusing on a self-similar structure underlying the description of a contradiction, we observe a particular time-series sequence of ants' behaviors following a 1/f or Zipf's law. The behaviors following the 1/f or Zipf's law manifest an appropriateness of the notion of a cart as a logical jump. (C) 1999 Elsevier Science Ireland Ltd. All rights reserved.

Fish schools are frequently observed without a leader and an explicit condition forming school. Several models of schooling have been proposed focusing on the influence of neighbors, and introducing probability distributions, while these models are based on the separation of schooling and territorial behavior. We frequently consider the duality of aggregation of animals, in which behavioral patterns involve both attraction and repulsion, antagonistic with each other. The idea of probability does not explain this duality that can provide both schooling and territorial behavior. From these biological facts, we have constructed a behavior model in which the influence of neighbors is formulated by the interface between the states of neighbors and a map of changes in these states. This interface uses a self-similar nowhere differentiable transition map which is temporally constructed, encompassing a crucial duality of repulsive and attractive forces hidden in the interaction among fishes. We tested it with computer simulations against the biological reality of schooling and territorial behavior. Due to the influence neighbors can have on duality, the same model can show both schooling behavior with a high degree of polarization and territorial behavior. (C) 1999 Elsevier Science Ireland Ltd. All rights reserved.

One of us previously proposed a model of internal measurement that is not only an interaction between internal elements but also involves the notion of an indefinite observer measuring the interaction, In this model, all interactions encompass the notion of detection. The latter can be expressed as a process generating a contradiction. Hereby a fixed point becomes invalid after inducing the contradiction. Instead of embedding this process as an instance along the time axis, we here represent the logical jump via a contradiction (fixed point). Specifically a new operation is defined which replaces the operation by which a fixed point is induced, and we show that both a set as a fixed point and this particular operation on a set can give rise to an orthomodular lattice that is a model of quantum logic. The new procedure is a mixture of inducing a fixed point and addressing a fixed point. It can be compared to mixing up indicating an element with indicating a set consisting of elements, that is, to Russel's paradox. Finally, we point out that orthomodularity can ubiquitously be found in the evolutionary complex systems because it is generally relevant to resolving a paradox or a logical jump. (C) 1999 Elsevier Science B.V. All rights reserved.

Endophysics ultimately deduces an indefinite interface between an object and an observer. Objects, given such an interface, cannot be distinguished from the measurement process used to identify them. Evolutionary processes comprising of emergent properties and adaptability are seen in a new light. The concept of indefiniteness and/or paradox appears on the surface to be based on the epistemological framework of the Cartesian cut. However, perpetual processes consisting of generation and resolution of paradoxes are beyond the epistemological framework of measurement. They lead to the notion of progression, which one can refer to as ontological (or inherent) measurement. (C) 1998 Elsevier Science Ireland Ltd. All rights reserved.

We sketch a paradox generally resulting from recursivity, and propose a novel model to express evolutionary processes that requires identification of an interaction with internal measurement. In this model, a paradox is not resolved and the notion of relativity of any resolution is implicit. In a dynamical system a certain transition rule is used recursively along time. If one takes the foundation (or context) of recursivity into consideration, one obtains a fixed point or one confronts a paradox. In order to resolve this paradox, we adopt Scott's technical way to identify the form of a fixed point with a domain equation and to obtain a reflective domain, however we simultaneously show that any resolution is destined to be relative. In utilizing this notion, we construct a model of dynamical process by embedding a measurement process in one time step. Any time transition involves the process of doubting the foundation of a transition rule leading to a fixed point. Solving it and obtaining a reflexive domain is used as a new transition rule. Also, this process perpetually proceeds along time, and then the system perpetually proceeds while any solution is destined to be relative. We illustrate this type of model by using a dynamically changing contraction mapping as the interface of state and transition rule. Finally, we show that one can formalize emergent properties by using this model and discuss the relationship between endo-physics and internal measurement.

We propose a model of interaction based upon incomplete identification consisting of alternate procedure of constructing a map from coarse-grained data by a contraction mapping and of applying the map to fine-grained data. In considering schooling of fish which is a typical emergent global behavior derived from local interactions, we argue that schooling paradoxically results from incomplete or indefinite identification of others. It suggests a system without boundary because any interaction is destined to be incomplete in this framework. (C) 1997 Elsevier Science Ltd.

Social insects ants secrete something like pheromone or wax by which an individual can identify their trail The ants Lasius niger L. show this behavior but sometimes change trails in branched maze experiments. An individual ant can estimate the reliance of its recruitment trail. The estimation is measured by post-information, i.e. by the frequency of turning back on a recruitment trail. The relationship between the post-information rate and the probability of choosing between alternative routes is analyzed. It turns out that (1) a momentary burst of post-information can trigger the retreat of an existing recruitment trail; (2) post-information rate is correlated with pheromone concentration. Post-information sometimes implies the occurrence of an internal decision making, but at other times is a response to pheromone. Due to this cause-effect loop, a straight relation between post-information and pheromone concentration is not observable. Alternate shifting between positive and negative correlation can however be detected. From the precise analysis, it is shown that this cause-effect loop can be used as a model of ant's own decision making. It turns out to be a model of system generating hierarchical structure.

A bootstrapping system is proposed in order to describe nonlogical properties of living systems, in which the velocity of observation propagation is finite. A cellular automaton (CA) model of the system combines two logics which are the a priori non-Boolean logic and the a posteriori Boolean logic. Because of inconsistency between the two logics, the system evolves perpetually generating disequilibrium and perpetually equilibrating the generated disequilibrium. The system tends to self-organize to the border between order and disorder, and shows critical behaviours as class IV CA. Although the critical behaviors of the two systems are similar, the bootstrapping system has twice stronger undecidability than class IV CA or edge of chaos dynamics. It is stressed that real living systems are not computable and should be described by strongly undecidable systems.

Complex systems in which internal agents (observers) interact with each other with finite velocity of information propagation cannot be described with a single consistent logic. We have proposed the bootstrapping system of cellular automata for describing such complex systems using two types of complementary logic: Boolean and non-Boolean. We extend this in this paper to a system of time-discrete continuous maps using fuzzy logic in place of non-Boolean logic. Fuzziness implies the intrinsic ambiguity of internal measurement. The bootstrapping system evolves, changing the dynamics perpetually, so that the discrepancy between the two types of complementary logic may be minimized. The equilibration force defined from the strength of discrepancy forms a landscape for self-organization which is similar to the fitness landscape for evolution. Though they appear similar, the former is derived from the internal dynamics. The goal of evolution, when applied to the map of the Belousov-Zabochinsky reaction, is demonstrated to be near the border between periodicity and chaos. The behavior depends on the degree of fuzziness and the extent of noise. When fuzziness increases too much, the system becomes unstable. Near the boundary, it exhibits intermittent chaos with a background of 1/f noise. (C) 1997 Elsevier Science Ireland Ltd.

Animal behavior should be invariant as long as the innate mechanisms do nor change. Some behavior regulations are thought to be programmed by means of mixed strategy or learning by instinct. Such ideas assume however the occurrence of a unique identification of the surroundings by the animal, thus, external perturbation may contradict expectation. The modification of the symbiotic behavior of the goby Amblyelotris steinitzi, associated with several species of alpheid shrimps, is reported in an experimental environment.

Terrestrial hermit crabs may leave gasteropod shells in accordance with the behavior of other members of the population without consequential corresponding to cannibalism. Such a potentiality usually manifests in the form of behavior plasticity.

A learning experiment was designed using ''Renju (Go-bang)''. The matches could proceed with prior indefiniteness, distinct from probability, as under the finite VOP (velocity of observation propagation). The information of each situation in the first game S-SG and one in the replay S-RE were investigated with the basic strategy derived from the ''Renju'' rules. The behavior of the difference (S-RE (i)-S-SG (i)) suggested that prior indefiniteness turned into definiteness, suggesting that perpetual decision change occurred and that it perpetually allowed observers to construct higher levels of hierarchical learning logic.

Systems involving both intracellular and intercellular computation are destined to be described as non-computable. We propose a model for such systems by introducing the inconsistent relation of Boolean and non-Boolean logic. Cellular automata fashioned model exhibits an evolution like class 4 located at the edge of chaos, while there is no local rule for universality existing over the whole space in our model. A system featuring the inconsistent vertical scheme is approximately articulated into a hierarchical system, whose wholeness cannot be deduced by any approximated local ruler In other words, undecidability between a part and whole comprises a hierarchical structure.

Describing a system in which internal detection or observation proceeds at a finite velocity is always destined to end up with a form of self-contradiction. For any formal language, for such a description, we must assume that the velocity of observation propagation or VOP be infinity. In the present paper, we propose a self-referential scheme intended for formally describing a system exhibiting the process of disequilibration propagating at a finite VOP, and find that a global logic can emerge from local disequilibration. Conservative cellular automata of Margolus type, for instance, enable disequilibration to be replaced by such a process that the number of particles is not conserved globally while appearing to be conserved by local observers. One cannot determine local rules universally. Nevertheless, global logic emerges as a result of the dynamics of a one-to-many type mapping. This is a fundamental aspect of natural languages or communication relevant to natural life and intelligence.

If finite velocity of observation propagation is taken into consideration, one is faced with a paradox or infinite regression in his own logic. It is the same as Goedel's theorem of incompleteness or Wittgenstein's paradox, and in general it can be formally replaced by Lawvere's theorem of a fixed point. To describe time evolution under finite velocity of observation propagation is not to construct a new logic in which the paradox can be removed or improved, but to accept the paradox itself Given a system in which a paradox is deduced by taking the finite velocity of observation propagation, we can regard the whole formal description, which consists of the system and a proof sequence, toward the paradox, as an evolutionary system. A formal evolutionary system defined here is one demonstration of autonomic life.

A principle of self-organization toward a critical state is proposed as a metadynamics of evolutionary processes. When the propagation velocity of information is slow as in living systems, discrepancy occurs between the virtual process and the actual one. The degree of discrepancy is defined for discrete dynamical systems on the scheme of perpetual disequilibration (PD), proposed by Gunji and others. It is supposed that adaptable systems tend to evolve so that the discrepancy may be minimized. A principle of the minimum degree of PD is applied to cellular automata and Boolean networks. These complex systems have the minimum degree of PD at the border between order and chaos, and thus are expected to evolve to the critical state at the edge of chaos. This self-organized criticality is a generalized form of Bak's self-organized criticality.

The question ''What is life,'' has long been discussed, and many concepts representing what are regarded as essential properties of life have been proposed, namely information generating processes, complex systems, indefinite boundaries, and self-reference. Self-referential forms in particular play a central role in autonomous life, because both in ontogenetic and phylogenetic processes we find self-referential forms and self-reference introduces other important features of life. However, because self-reference is strongly connected with self-contradiction and/or unprogrammability, it cannot be described in the paradigm of prediction or dynamics. It is inevitable to estimate the problem of instability of the description itself. We here discuss self-reference and unprogrammability with respect to the mixture between inter- and intracellular computations in biological systems, and we replace the difference between computation velocities at different levels by the difference between the velocity of observation propagation and that of a particle. We also define the formal system of communication and transplant the problem of unprogrammability resulting from the finite velocity of observation propagation in that system. Here it is illustrated that unprogrammability is isomorphic to the incompleteness of a formal system. Further, we formally estimate the relationship of unprogrammability and one-to-many type mapping and propose the formalization using a universal arrow, based on Wittgenstein's idea, language games, and performativeness. Because unprogrammability does not exist as a real entity, but is constituted, we can formalize one-to-many type mapping and even unstable formal description. The concept of autonomy is not beyond formal description; however it is beyond the paradigm of prediction.

The learning process consists of observation and inference. On the one hand, it is understood that the inference process involves internal choice. On the other hand, the internal process is not essentially expressed; however, the internal choice is explicitly written down by sorting of variants in many brain models. Finding out what the learning process is is nothing but to answer whether the origin of variants in variation and selection is a well-defined question or not. It is not whether we can find a sorting process in the brain or not, but whether the internal choice can be replaced by sorting of variants in programmable systems. We estimate here this type of question, and formalize internal choice in another way. In our model, the learning process is communication among elements of a system, in which an element learns the behavior of other elements through observation. However, observation is incomplete resulting from finite velocity of observation propagation. Incomplete identification (observation) is here formalized not by ''variation and selection'' but by decision change a posteriori, introducing backward-time. In our model, we can demonstrate that misreading a posteriori generates information that possibly generates novelty.

However we deny naive realism, it is difficult to describe the form of life in a Newtonian paradigm. Because any formal descriptions of biological systems inevitably include the concept of "function," they entail the problem of self-reference. The description of function can be compared to that of meaning of a word, and in philosophy we no longer understand that there exists meaning inherent in a word of a language. As well as the problem of meaning, we cannot describe the aspect resulting from the function, because we cannot identify the specific function of a shape or morphology with the relationship between the shape itself and its environment. Therefore, even if we construct a new formal language in which the self-contradiction resulting from the self-reference is alleviated, that language is just one of various possible ones. In this sense, the form of life in formal description is possible but not necessary. The phrase "not necessary" just refers to the outside of the formal description. In this paper reference to the outside of a formal system is discussed in the context of time-space complementarity, and it is strongly related to the origin of irreversible time. We have to introduce both forward and backward time, as proposed previously by the author and coworkers, even in this context.

Life seems to be at the border between order and chaos. The Game of Life, which is a cellular automaton to mimic life, also lies at the transition between ordered and chaotic structures. Kauffman recently suggested that the organizations at the edge of chaos may be the characteristic target of selection for systems able to coordinate complex tasks and adapt. In this paper, we present the idea of perpetual disequilibration proposed by Gunji and others as a general principle governing self-organization of complex systems towards the critical state lying at the border of order and chaos. The rule for the Game of Life has the minimum degree of perpetual disequilibrium among 2(18) rules of the class to which it belongs.

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 definitions 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 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.

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).

We propose a perspective for living systems, emphasizing that living systems are organized through the recognition of themselves and their surroundings. Oscillator functions in Brownian Algebra are introduced, supposing that the oscillation can be regarded as metabolism of the living state. We illustrate the idea of the self-repairing model in non-articulated coralline algae. Since various cells of this plant are assumed to be identified with the periodic sequence of oscillations, the individual periodic sequence characterizing a cell is supposed to be determined by a local-interaction rule which can be regarded as the process of self-organization through the recognition of local shape. Owing to accidental injury the rule characterizing a cell's own state can be transformed, and it entails another periodic sequence. We express the oscillator as state flow diagrams, and analyze the relationship between the transformation of the period and the injury which is represented by the removal of transient in flow diagrams.

We propose a perspective for living systems, emphasizing that living systems are organized through the recognition of themselves and their surroundings. Oscillator functions in Brownian Algebra are introduced, supposing that the oscillation can be regarded as metabolism of the living state. We illustrate the idea of the self-repairing model in non-articulated coralline algae. Since various cells of this plant are assumed to be identified with the periodic sequence of oscillations, the individual periodic sequence characterizing a cell is supposed to be determined by a local-interaction rule which can be regarded as the process of self-organization through the recognition of local shape. Owing to accidental injury the rule characterizing a cell's own state can be transformed, and it entails another periodic sequence. We express the oscillator as state flow diagrams, and analyze the relationship between the transformation of the period and the injury which is represented by the removal of transient in flow diagrams. © 1991.

In the present paper the self-consistency or operational closure of autopoiesis is described by introducing time explicity. 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.