Computational Power of Asynchronously Tuned Automata Enhancing the Unfolded Edge of Chaos.

Asynchronously tuned elementary cellular automata (AT-ECA) are described with respect to the relationship between active and passive updating, and that spells out the relationship between synchronous and asynchronous updating. Mutual tuning between synchronous and asynchronous updating can be interpreted as the model for dissipative structure, and that can reveal the critical property in the phase transition from order to chaos. Since asynchronous tuning easily makes behavior at the edge of chaos, the property of AT-ECA is called the unfolded edge of chaos. The computational power of AT-ECA is evaluated by the quantitative measure of computational universality and efficiency. It shows that the computational efficiency of AT-ECA is much higher than that of synchronous ECA and asynchronous ECA.

Breaking of the Trade-Off Principle between Computational Universality and Efficiency by Asynchronous Updating.

Although natural and bioinspired computing has developed significantly, the relationship between the computational universality and efficiency beyond the Turing machine has not been studied in detail. Here, we investigate how asynchronous updating can contribute to the universal and efficient computation in cellular automata (CA). First, we define the computational universality and efficiency in CA and show that there is a trade-off relation between the universality and efficiency in CA implemented in synchronous updating. Second, we introduce asynchronous updating in CA and show that asynchronous updating can break the trade-off found in synchronous updating. Our finding spells out the significance of asynchronous updating or the timing of computation in robust and efficient computation.

Inverse Bayesian inference in swarming behaviour of soldier crabs.

Animals making a group sometimes approach and sometimes avoid a dense area of group mates, and that reveals the ambiguity of density preference. Although the ambiguity is not expressed by a simple deterministic local rule, it seems to be implemented by probabilistic inference that is based on Bayesian and inverse Bayesian inference. In particular, the inverse Bayesian process refers to perpetual changing of hypotheses. We here analyse a time series of swarming soldier crabs and show that they are employed to Bayesian and inverse Bayesian inference. Comparing simulation results with data of the real swarm, we show that the interpretation of the movement of soldier crabs which can be based on the inference can lead to the identification of a drastic phase shift-like transition of gathering and dispersing.This article is part of the theme issue 'Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 2)'.

Computation Implemented by the Interaction of Chemical Reaction, Clustering, and De-Clustering of Molecules.

A chemical reaction and its reaction environment are intrinsically linked, especially within the confines of narrow cellular spaces. Traditional models of chemical reactions often use differential equations with concentration as the primary variable, neglecting the density heterogeneity in the solution and the interaction between the reaction and its environment. We model the interaction between a chemical reaction and its environment within a geometrically confined space, such as inside a cell, by representing the environment through the size of molecular clusters. In the absence of fluctuations, the interplay between cluster size changes and the activation and inactivation of molecules induces oscillations. However, in unstable environments, the system reaches a fluctuating steady state. When an enzyme is introduced to this steady state, oscillations akin to action potential spike trains emerge. We examine the behavior of these spike trains and demonstrate that they can be used to implement logic gates. We discuss the oscillations and computations that arise from the interaction between a chemical reaction and its environment, exploring their potential for contributing to chemical intelligence.

Quantum logic automata generate class IV-like patterns and 1/f noise.

Owing to recent advancements in brain science and AI, researchers tend to focus on the concept of self-organized criticality or the edge of chaos. On the other hand, quantum cognition, which is rooted in quantum mechanics, is promising for resolving various cognitive illusions. However, until recently, no connection between criticality and quantum mechanics was proposed. Gunji et al. (2024) recently introduced a linkage termed quantum logic automata, which encompasses not only quantum logic but also criticality characterized by power-law distributions. While quantum logic automata can be derived from various structures, only one of them has been proposed and discussed. Here, we define another type of quantum logic automata involving quantum logic and demonstrate that symmetric quantum logic automata lead to complex Class IV-like patterns and power-law distributions. Our findings support the association between criticality and quantum theory.

Feeling of hand deformation as a monkey's hand: an experiment on a visual body with discomfort and its algebraic analysis.

While there are many studies in which body ownership can be transferred to a virtual body, there are few experimental studies of how subjects feel about their own bodies being deformed since a real body cannot be deformed. Here, we propose such an experimental setup, in which a twisted hand is diagonally viewed from behind, which is called a "monkey's hand." Although the subject cannot see the thumb hidden behind his or her arm, he or she feels that the monkey's hand has an ambiguous thumb that functionally never exists but structurally exists. This ambiguity is consistent with experimental results on proprioceptive drift, by which the deformation of the hand is measured. The ambiguity of the presence and absence of the thumb is finally analyzed with a specific algebraic structure called a lattice. This can help us understand disownership as being different from the absence of ownership.

Mathematical models of panic disorder.

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.

How do soldier crabs behave when seeing vibrating robots?

Metaheuristic algorithms are a method of searching for a suboptimal solution and are implemented by a large number of agents, such as a swarm of animals. In this method, it is very important to adjust the relationships and/or interplay between individual freedoms and constraints as a group. The phenomena related to this interplay are strongly relevant for self-organized criticality showing a power law distribution. Since individuals' independent behavior and translation as a group coexist in a swarm of soldier crabs, we conducted an experiment involving soldier crabs to estimate whether a power law distribution results from that interplay. The engine of translation was implemented by the directed movement of robot crabs. Soldier crabs confronting moving robot crabs were observed in the experiment. Here, we show that the interaction between robots and soldier crabs entails a Lévy walk characterized by a power law distribution of step length as well as the real swarm. This result suggests that soldier crabs could be attracted by the directed motion of robots and that combining a random walk with ballistic movement can realize a Lévy walk.

Psychological origin of quantum logic: An orthomodular lattice derived from natural-born intelligence without Hilbert space.

While the role of quantum theory becomes increasingly important through molecular computing and quantum cognition, it is still unclear how quantum mechanics can be involved in macroscopic phenomena. We previously argued the origin of quantum logic in terms of lattice theory; however, we do not refer to Hilbert space very much. Here, we show the psychological origin of quantum logic (i.e., orthomodular lattice) by not using Hilbert space. After showing how Hilbert space plays a role in constructing an orthomodular lattice, we show the idea of natural-born intelligence, in which a binary opposition pair can constitute not only positive but negative antinomy. In taking an object outside and an image inside a brain as that binary opposition pair, the structure entailing positive and negative antinomy is expressed as a specific binary relation consisting of multiple diagonal relations, which is called traumatic relation. Finally, we show that the traumatic relation leads to an orthomodular lattice without Hilbert space.

Connecting the free energy principle with quantum cognition.

It appears that the free energy minimization principle conflicts with quantum cognition since the former adheres to a restricted view based on experience while the latter allows deviations from such a restricted view. While free energy minimization, which incorporates Bayesian inference, leads to a Boolean lattice of propositions (classical logic), quantum cognition, which seems to be very dissimilar to Bayesian inference, leads to an orthomodular lattice of propositions (quantum logic). Thus, we address this challenging issue to bridge and connect the free energy minimization principle with the theory of quantum cognition. In this work, we introduce "excess Bayesian inference" and show that this excess Bayesian inference entails an underlying orthomodular lattice, while classic Bayesian inference entails a Boolean lattice. Excess Bayesian inference is implemented by extending the key idea of Bayesian inference beyond classic Bayesian inference and its variations. It is constructed by enhancing the idea of active inference and/or embodied intelligence. The appropriate lattice structure of its logic is obtained from a binary relation transformed from a distribution of the joint probabilities of data and hypotheses by employing a rough-set lattice technique in accordance with quantum cognition logic.

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

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

Effect of Hidden Vector on the Speech of PRVA.

This study aimed to propose a novel method for designing a product recommendation virtual agent (PRVA) that can keep users motivated to interact with the agent. In prior papers, many methods of keeping users motivated postulated real-time and multi-modal interactions. The proposed novel method can be used in one-direction interaction. We defined the notion of the "hidden vector," that is, information that is not mentioned by a PRVA and that the user can suppose spontaneously. We conducted an experiment to verify the hypothesis that PRVAs having a hidden vector are more effective than other PRVAs. As a result, it was shown that PRVAs having a hidden vector were perceived as being more persuasive than other PRVAs and strongly motivated the users to use the PRVAs. From these results, the proposed method was shown to be effective.

Lévy Walk in Swarm Models Based on Bayesian and Inverse Bayesian Inference.

While swarming behavior is regarded as a critical phenomenon in phase transition and frequently shows the properties of a critical state such as Lévy walk, a general mechanism to explain the critical property in swarming behavior has not yet been found. Here, we address this problem with a simple swarm model, the Self-Propelled Particle (SPP) model, and propose a way to explain this critical behavior by introducing agents making decisions via the data-hypothesis interaction in Bayesian inference, namely, Bayesian and inverse Bayesian inference (BIB). We compare three SPP models, namely, the simple SPP, the SPP with Bayesian-only inference (BO) and the SPP with BIB models. We show that only the BIB model entails coexisting tornado, splash and translation behaviors, and the Lévy walk pattern.

Analysis and synthesis of a growing network model generating dense scale-free networks via category theory.

We propose a growing network model that can generate dense scale-free networks with an almost neutral degree-degree correlation and a negative scaling of local clustering coefficient. The model is obtained by modifying an existing model in the literature that can also generate dense scale-free networks but with a different higher-order network structure. The modification is mediated by category theory. Category theory can identify a duality structure hidden in the previous model. The proposed model is built so that the identified duality is preserved. This work is a novel application of category theory for designing a network model focusing on a universal algebraic structure.

Three types of logical structure resulting from the trilemma of free will, determinism and locality.

How can one defend free will against determinism? Since quantum mechanics entails non-locality, it enables the co-existence of free will and determinism. Is non-locality in cognition possible, or must quantum mechanics be rejected? Here, we define free will, determinism and locality in terms of a binary relation between objects and representations, and we verify that the three concepts constitute a trilemma. We also show that non-locality in cognition is naturally found in decision making without any assumption of quantum mechanics. Three kinds of relations result from the trilemma. By using a rough set lattice technique, the three kinds of relations can be transformed into three kinds of logical structures. Type I is a naive set theoretical logic or Boolean algebra (i.e., all possible combinations of binary yes-no responses). Type II comprises all possible combinations of various multiple values, such as for the symptoms of schizophrenia. Type III is a non-local disjoint union of multiple contexts. The type III structure can show how non-locality in cognition can lead to the co-existence of free will and determinism. Loss of non-locality could play an essential role in the malfunction of the separation and integration of the self and others.

Virtual Hand with Ambiguous Movement between the Self and Other Origin: Sense of Ownership and 'Other-Produced' Agency.

The feeling that a body part is one's own body (sense of ownership; SoO) and the feeling based on the causal relationship between one's will and action (sense of agency; SoA) have been recognized as the basis of our bodily self-consciousness. Previously, the illusory SoO over a fake body part (e.g., rubber hand) was introduced as the rubber hand illusion (RHI). Furthermore, it was determined that one could also evoke a SoA over an object with movements linked to the one's prior intention. On the other hand, the postdictivity of our spontaneity implies that it is essentially inseparable whether actions originate from self or others. In other words, our SoA or daily experiences are obtained in such as inseparable scenario. Previous research, however, has maintained the premise that self- and other-origin movements are perceptually distinguishable. Here, we implement a protocol to make these aspects ambiguous for the participants and to estimate whether they can feel SoO and/or SoA and how. To this end, we employ an experiment using virtual reality, under which participants observe virtual fingers moving very slowly (or quickly or not moving) while their own fingers do not move. For evaluation of the illusory SoO, measurements of skin conductance responses against a knife threat are adopted. Additionally, we introduce face-to-face interviews to determine whether the feelings regarding the slow movement match the conventional SoA definition. Our representative results suggest that the SoO is evoked over the hand, and various attitudes to accept its movement as the participant's own with awareness that they did not originate it are reported by the majority. As the results show, the novelty of this protocol is discovering that in such a situation, the SoO cooperates with an externally produced SoA to establish one's own bodily experience rather than the independence of the SoO and SoA.

A new method of Bayesian causal inference in non-stationary environments.

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.

Ordinal Preferential Attachment: A Self-Organizing Principle Generating Dense Scale-Free Networks.

Networks are useful representations for analyzing and modeling real-world complex systems. They are often both scale-free and dense: their degree distribution follows a power-law and their average degree grows over time. So far, it has been argued that producing such networks is difficult without externally imposing a suitable cutoff for the scale-free regime. Here, we propose a new growing network model that produces dense scale-free networks with dynamically generated cutoffs. The link formation rule is based on a weak form of preferential attachment depending only on order relations between the degrees of nodes. By this mechanism, our model yields scale-free networks whose scaling exponents can take arbitrary values greater than 1. In particular, the resulting networks are dense when scaling exponents are 2 or less. We analytically study network properties such as the degree distribution, the degree correlation function, and the local clustering coefficient. All analytical calculations are in good agreement with numerical simulations. These results show that both sparse and dense scale-free networks can emerge through the same self-organizing process.

Observing the Transformation of Bodily Self-consciousness in the Squeeze-machine Experiment.

How is our bodily self-consciousness acquired, and how does it affect cognition? To investigate this, we conducted an experiment using the squeeze machine, a device that provides pressure along the length of the user's whole body. The squeeze machine is used to help autistic people relax. The inventor of the machine, Dr. Temple Grandin says that the squeeze machine, beyond bringing her relaxation, enables her to feel empathy for others. This claim is of considerable interest and raises the following two points; first, the problem of empathy in autism is an important issue and Squeeze Machine could be effective. Second, it suggests that the physical action of Squeeze Machine could provide an insight of mind-body problem to us. Here, we hypothesize that the squeeze machine focuses conscious to direct the bodily self, transforming bodily self-consciousness itself. Such intentionality could bring empathy to others. In this study, we tested whether bodily self-consciousness would be transformed through the squeeze-machine experience. In the first part of the protocol, we simplified the original design of Grandin's squeeze machine but ensured that it retained its relaxing effect. In the second part of the protocol, we adopted a preestablished method of peri-personal space (PPS) measurement to estimate changes in extended bodily space. The results showed that the boundaries of PPS that appeared in the control experiment disappeared during the use of the squeeze machine. Indeed, collected subjective reports suggest that bodily self-consciousness continually drifted between the point of action of the external force (squeeze-machine pressure) and of an internal force (balance among body parts that are usually not consciously controlled), leading to the abandonment of the immobilization of individual PPS.

Propagating wave based on transition of interaction within animal group.

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