Ichiro Tsuda

Chubu University · Chubu University Academy of Emerging Sciences

By extending the extreme learning machine by additional control inputs, we achieved almost complete reproduction of bifurcation structures of dynamical systems. The learning ability of the proposed neural network system is striking in that the entire structure of the bifurcations of a target one-parameter family of dynamical systems can be nearly r...

Understandings of how visual hallucinations appear have been highly influenced by generative approaches, in particular Friston’s Active Inference conceptualization. Their core proposition is that these phenomena occur when hallucinatory expectations outweigh actual sensory data. This imbalance occurs as the brain seeks to minimize informational fre...

Herein, we briefly review the role of nicotinic acetylcholine receptors in regulating important brain activity by controlled release of acetylcholine from subcortical neuron groups, focusing on a microscopic viewpoint and considering the nonlinear dynamics of biological macromolecules associated with neuron activity and how they give rise to advanc...

Despite decades of research, we do not definitively know how people sometimes see things that are not there. Eight models of complex visual hallucinations have been published since 2000, including Deafferentation, Reality Monitoring, Perception and Attention Deficit, Activation, Input, and Modulation, Hodological, Attentional Networks, Active infer...

The ability of the brain to generate complex spatiotemporal patterns with specific timings is essential for motor learning and temporal processing. An approach that can model this function, using the spontaneous activity of a random neural network (RNN), is associated with orbital instability. We propose a simple system that learns an arbitrary tim...

This chapter provides a dynamical systems viewpoint for various dynamics in neuronal systems, based on the assumption that there exist dynamical systems underlying neural dynamic behaviors. We treat the topological dynamical systems, where qualitative analyses such as phase plane analysis and bifurcation analysis are explained. These analyses can “...

The ability of the brain to generate complex spatiotemporal patterns with a specific timing is essential for motor learning and time series prediction. An approach that tries to replicate this ability using the self-sustained neural activity of a randomly connected recurrent neural network (reservoir) meets the difficulty of orbital instability. We...

Mathematical and computational approaches were used to investigate dementia with Lewy bodies (DLB), in which recurrent complex visual hallucinations (RCVH) is a very characteristic symptom. Beginning with interpretative analyses of pathological symptoms of patients with RCVH-DLB in comparison with the veridical perceptions of normal subjects, we co...

Objective To determine clinically ictal direct current (DC) shifts that can be identified by a time constant (TC) of 2 s and to delineate different types of DC shifts by different attenuation patterns between TC of 10 s and 2 s. Methods Twenty-one patients who underwent subdural electrode implantation for epilepsy surgery were investigated. For ha...

The focus of this article is the self-organization of neural systems under constraints. In 2016, we proposed a theory for self-organization with constraints to clarify the neural mechanism of functional differentiation. As a typical application of the theory, we developed evolutionary reservoir computers that exhibit functional differentiation of n...

One of the most striking characteristics of the developing brain is functional differentiation, while emerging interactions develop between networking differentiated areas. To clarify the neural mechanism of functional differentiation, we constructed a mathematical model of self-organization with constraints. By casting different constraints, we in...

Writing a history of a scientific theory is always difficult because it requires to focus on some key contributors and to “reconstruct” some supposed influences. In the 1970s, a new way of performing science under the name “chaos” emerged, combining the mathematics from the nonlinear dynamical systems theory and numerical simulations. To provide a...

We propose an extended reservoir computer that shows the functional differentiation of neurons. The reservoir computer is developed to enable changing of the internal reservoir using evolutionary dynamics, and we call it an evolutionary reservoir computer. To develop neuronal units to show specificity, depending on the input information, the intern...

Focusing on the developmental process of the brain, we propose a neural network model of functional differentiation including functional parcellation. We explain the emerging process of functional elements, of the system through the constraints, which act on the whole network system. We explain several kinds of differentiation, such as the differen...

Cantor coding provides an information coding scheme for temporal sequences of events. In the hippocampal CA3–CA1 network, Cantor coding-like mechanism was observed in pyramidal neurons and the relationship between input pattern and recorded responses could be described as an iterated function system. However, detailed physiological properties of th...

We propose an extended reservoir computer that shows the functional differentiation of neurons. The reservoir computer is developed to enable changing of the internal reservoir using evolutionary dynamics, and we call it an evolutionary reservoir computer. To develop neuronal units to show specificity, depending on the input information, the intern...

In this paper, we propose a new method based on the dynamic mode decomposition (DMD) to find a distinctive contrast between the ictal and interictal patterns in epileptic electroencephalography (EEG) data. The features extracted from the method of DMD clearly capture the phase transition of a specific frequency among the channels corresponding to t...

We attempted to create a mathematical model for neuronal differentiation. The present study was performed within the framework of self-organization with constraints by looking for an optimized informational unit. We treated networks of individual dynamical system units with an external input, which was provided by coupled one-dimensional maps with...

Constrained chaos introduced into a three-module neural network having feedforward inter-module structure could have potential abilities to execute multiple tasks simultaneously. Each module consists of a large number of binary state (±1) neurons. The entire activity pattern (neuron state) is updated by recurrent rule under certain external input t...

In the present study, we attempted to characterize two characteristic features within the dynamic behavior of wideband electrocorticography data, which were recorded as the brain waves of epilepsy, comprising high-frequency oscillations (HFOs) and interictal epileptic slow (red slow). The results of power spectrum and nonlinear time series analysis...

Devil’s Advocate This paper addresses a provocative remark advocating the field theory of Kozma and Freeman, by proposing a new mathematical model for functional differentiation in neural systems. The computational result suggests the presence of self-organization of the second kind.

It is not at all uncommon to see people, animals, or objects that other people cannot perceive. Data from studies of pathological hallucinations suggests that distributed functional changes within visual and associated systems increases the risk of visual hallucinations, though how this occurs is not yet clear. Candidate theories developed in the c...

This study proposes mathematical models for functional differentiations that are viewed as self-organization with external constraints. From the viewpoint of system development, the present study investigates how system components emerge under the presence of constraints that act on a whole system. Cell differentiation in embryos and functional dif...

Neural oscillations with various frequency bands have been observed in several brain regions during behavioral and cognitive tasks. Communication via these oscillations among brain regions has similarities with frequency division multiplexing (FDM) in telecommunications, which is used for multiplex transmission. If FDM-like information transmission...

A simple model of learning that describes changes in an animal’s behavior based on its actions and rewards from the environment was analyzed by Karlin in 1953. The model can be formulated as an iterated function system with state-dependent probability. To develop a simple mathematical model of learning in which animals repeatedly alternate strategi...

This study proposes self-organization of a second kind, by contrast with a conventional self-organization producing macroscopic patterns via cooperativity at the microscopic level of molecular dynamics. As a case study, we deal with two models yielding elementary components via global constraints controlling a whole system’s dynamics: one is the ge...

The memory neural network is organized as an attractor space by both bottom-up (sensory) and top-down (contextual) information. This paper presents a possible mechanism of spatiotemporal attractors in one layer neural network based on the experimental data and their theoretical models in learning and memory. The model consists of following importan...

We propose a neural mechanism of the concept of innate time, which may lead to a Kantian a priori time. The proposition is based on the assumption that Cantor coding and decoding associated with specific oscillatory behaviors in the hippocampus determines the ratio of internal compression of time intervals.

Hippocampal-VTA microcircuit is one of the most important components of reward system. As a prominent feature in hippocampus, theta rhythm involves a strong correlation with learning, memory and decision making. However, the relation between theta rhythm and reward representation remains unclear. Based on some recent experimental discovery, a compu...

From the viewpoint of system development, we investigate how components emerge in a network system consisting of interacting units. We propose two mathematical models with ‘variational’ principles: one treats the emergence of neuron-like components from interacting maps, and the other one treats the emergence of hierarchical module-like components...

The aim of this study is, together with a companion paper, to present a hypothetical description of the core mechanisms of recurrent complex visual hallucinations (RCVH) associated with dementia with Lewy bodies (DLB). This paper focusses on giving some illustrative numerical examples on how the brain hallucinates, and to see whether mathematical m...

Patients with dementia with Lewy bodies (DLB) frequently experience the phenomenon of visual hallucination (VH), which Collerton (2005) aptly described as “people see things that are not there.” The possible involvement of cholinergic deficiency in the VH seen in DLB have long been proposed, but the precise neural mechanism to account for the parti...

By re-examining the neuronal activity energy model, we show the inadequacies in the current understanding of the energy consumption associated with neuron activity. Specifically, we show computationally that a neuron first absorbs and then consumes energy during firing action potential, and this result cannot be produced from any current neuron mod...

The purpose of the research project entitled “The study on the neural dynamics for understanding communication in terms of complex hetero systems” was to establish a new research area named “neural information science for communication” by elucidating its neural mechanism. The research was performed in collaboration with applied mathematicians in c...

Patients with dementia with Lewy bodies (DLB) frequently experience visual hallucination (VH), which has been aptly described as people seeing things that are not there. The distinctive character of VH in DLB necessitates a new theory of visual cognition. We have conducted a series of studies with the aim to understand the mechanism of this dysfunc...

Chaotic itinerancy is an autonomously excited trajectory through high-dimensional state space of cortical neural activity that causes the appearance of a temporal sequence of quasi-attractors. A quasi-attractor is a local region of weakly convergent flows that represent ordered activity, yet connected to divergent flows representing disordered, cha...

Modular architecture has been found in most cortical areas of mammalian brains, but little is known about its evolutionary origin. It has been proposed by several researchers that maximizing information transmission among subsystems can be used as a principle for understanding the development of complex brain networks. In this paper, we study how h...

We analyze a time series of the combustion pressure in the idle state, measured from a spark ignition engine of a motorcycle. It is clarified that the engine system can be described by a lowdimensional deterministic dynamics perturbed by some stochastic process.We also propose a method to stabilize the chaotic behaviour of engine’s data by adopting...

Motivated by studies on the dynamics of heterogeneously interacting systems in neocortical neural networks, we studied heterogeneously-coupled chaotic systems. We used information-theoretic measures to investigate directions of information flow in heterogeneously coupled Rössler systems, which we selected as a typical chaotic system. In bi-directio...

The brain contains multiple yet distinct systems involved in reward prediction. To understand the nature of these processes, we recorded single-unit activity from the lateral prefrontal cortex (LPFC) and the striatum in monkeys performing a reward inference task using an asymmetric reward schedule. We found that neurons both in the LPFC and in the...

We propose a dynamical model that represents a process of deductive inference. We discuss the stability of logic dynamics and a neural basis for the dynamics. We propose a new concept of descriptive stability, thereby enabling a structure of stable descriptions of mathematical models concerning dynamic phenomena to be clarified. The present theory...

A number of memory models have been proposed. These all have the basic structure that excitatory neurons are reciprocally connected by recurrent connections together with the connections with inhibitory neurons, which yields associative memory (i.e., pattern completion) and successive retrieval of memory. In most of the models, a simple mathematica...

The medial frontal cortex has been thought to be crucially involved in temporal structuring of behavior in monkeys and humans. We examined neuronal activity in the supplementary and presupplementary motor areas of monkeys to investigate how the nervous system deals with the coding of 16 motor sequences resulting from multiple actions involving bila...

We treated the interactions between two nonequilibrium neural networks, each of which possesses memories that are different from those of the other. In this respect, we developed a kind of hetero interaction that is a crucial ingredient for assuring communication.We propose a new learning algorithm for assuring different neural activity in both the...

We present a mathematical model to describe interacting processes of model neural networks. A model consists of several subsystems, each of which describes each different function. An overall dynamics of the whole model stems from the interactions between different areas of the brain, influenced by the incoming dynamics of the other brains. In part...

It has been proposed an abstract memory model of cortex that the recurrent network with inhibitory interneurons shows the successive retrieval of memories. It has not, however, been clarified whether such behavior appears in the realistic network model with the Hodgkin-Huxley type of neuron. By using the realistic model that consists of excitatory...

There is evidence of presynaptic modulation of inhibitions on pyramidal neurons in cortical layers 2/3, mediated by muscarinic M2-receptors activated by transient releases of the corticopetal acetylcholine associated with top-down attention. Little is known, however, regarding its system-level consequences and possible implications for cognitive fu...

In this paper, a communicative model with two nonequilibrium neural networks is proposed to emulate the dynamical process of how we can understand each other. A novelty-induced learning process is introduced to realize memory transmission between heterogeneous neural network models. The simulation results suggest that the communicative model could...

In this paper, we mathematically study a particular process for assimilation in the brain. The research aims to establish a theoretical model at computational level of the mechanism in a cognitive process operated by the mirror-neuron system, to generate a multi-dimensional system from this model, and to analyze the fundamentals of the related cogn...

Because episodic memory includes a time series of events, an underlying dynamics for the formation of episodic memory is considered to employ a mechanism of encoding sequences of events. The “Cantor coding” hypothesis in hippocampal CA1 has been proposed, which provides a scheme for encoding temporal sequences of events. Here, in order for investig...

The hippocampus has been considered responsible for the formation of episodic memory. It has also been pointed out that the hippocampus plays an important role in imagination, which is related to future events. The fact that atrophy of the hippocampus could lead to Alzheimer’s disease implies that the network structure of the hippocampus may provid...

We studied heterogeneously‐coupled Rössler oscillators in order to understand dynamics of hetero‐interactions. By using an information‐theoretic measure called transfer entropy, the directions of information flows in hetero‐interacting systems were investigated. We found the asymmetry of information flow emerged in the mutually‐coupled systems. Fur...

Although the role of corticopetal acetylcholine (ACh) in higher cognitive functions is increasingly recognized, the questions as (1) how ACh works in attention(s), memory dynamics and cortical state transitions, and also (2) why and how loss of ACh is involved in dysfunctions such as visual hallucinations in dementia with Lewy bodies and deficit of...

In this paper, four spatiotemporal coding mechanisms in the CA3-CA1were examined.

For the last few decades, extensive research has been continuing in neuroscience supported by great development of experimental techniques (fMRI, PET, EEG, ECoG, EMG, Optical Recording, etc.) and/or computer experiment technologies. In a large number of works, many applied mathematical or physical approaches have been proposed, in particular, dynam...

We study collective behaviors of diffusively coupled oscillators which exhibit out-of-phase synchrony for the case of weakly interacting two oscillators. In large populations of such oscillators interacting via one-dimensionally nearest neighbor couplings, there appear various collective behaviors depending on the coupling strength, regardless of t...

Recent studies suggest that the hippocampus is crucial for memory of sequentially organized information. Cantor coding in hippocampal CA1 is theoretically hypothesized to provide a scheme for encoding temporal sequences of events. Here, in order to investigate this Cantor coding in detail, we construct a CA1 network model consisting of conductance-...

Cortical layer 1 is the main entrance of top-down signals from other higher cortices and subcortical nuclei. Recent findings challenge the view that top-down signals play just a modulatory role. However, how top-down signals are implemented to help reconstruct the internal representations of images, or an episode of events is poorly understood. Rec...

Cantor coding provides an information coding scheme for temporal sequences of events. In this paper, we analyzed a inhibitory network dependency in Cantor coding from hippocampal CA1 neurons of rat acute slice preparation by using GABAA receptor blocker (gabazine). After gabazine application, clustering index was lower under subthreshold condition...

In this paper, we study a dynamic structure of discretized vector fields obtained from the Brusselator, which is described by two-dimensional ordinary differential equations (ODEs). We found that a bifurcation structure of the logistic map is embedded in the discretized vector field. The embedded bifurcation structure was unraveled by the dynamical...

How does the information of spatiotemporal sequence stemming from the hippocampal CA3 area affect the postsynaptic membrane potentials of the hippocampal CA1 neurons? In a recent study, we observed hierarchical clusters of the distribution of membrane potentials of CA1 neurons, arranged according to the history of input sequences (Fukushima et al C...

In contrast to the conventional static view of the brain, recent experimental data show that an alternative view is necessary for an appropriate interpretation of its function. Some selected problems concerning the cortical transitory dynamics are discussed. For the first time, we propose five scenarios for the appearance of chaotic itinerancy, whi...

The following coding mechanisms in the CA3-CA1 hippocampal networks were examined. Firstly, the way in which the information of the spatio-temporal sequence of the hippocampal CA1 pyramidal cells was clarified by using the patch-clamp recording method. The input-output relations were analyzed by applying “spatial clustering index” and its “self-sim...

In rat CA1 pyramidal neurons under sub- and supra-threshold conditions, our previous study showed the potentials of Cantor coding, which is theoretically proposed by Tsuda and Kuroda. However, the coding could be explained by mean rate coding simply depended on input pattern history of the peak amplitude of each input. In order to confirm that Cant...

2008-32-0010 (SAE) / 20084710 (JSAE) We focus on the control issue for engine systems from the perspective of chaos theory, which is based on the fact that engine systems have a low-dimensional chaotic dynamics. Two approaches are discussed: controlling chaos and harnessing chaos, respectively. We apply Pyragas' chaos control method to an actual en...

The hippocampus, which is a part of the old brain, has been considered responsible for the formation of episodic memory. Atrophy of the hippocampus can lead to Alzheimer disease. Alzheimer disease is a problem of the society. It is also expected to pose a serious problem in future societies composed of large numbers of elderly people. Therefore, it...

To adapt to changeable or unfamiliar environments, it is important that animals develop strategies for goal-directed behaviors that meet the new challenges. We used a sequential paired-association task with asymmetric reward schedule to investigate how prefrontal neurons integrate multiple already-acquired associations to predict reward. Two types...

I would like to deal with a process that numbers are generated by the interaction between consciousness and memory, associated with time with a finite width. It is pointed out that this process can be related with the emergence of preafference. It is concluded that only humans can create numbers, whereas animals simply produce 'random' sequences of...

How does the brain encode episode? Based on the fact that the hippocampus is responsible for the formation of episodic memory, we have proposed a mathematical model for the hippocampus. Because episodic memory includes a time series of events, an underlying dynamics for the formation of episodic memory is considered to employ an association of memo...

The Role(s) of corticopetal acetylcholine (ACh) in perception and conscious flow is largely unknown. The attention hypothesis may well be established experimentally. The aim of this talk is to give a small review, and then try to extend further the arguments, on the role of corticopetal ACh in perception from a dynamical systems standpoint, to sear...

To clarify how the information of spatiotemporal sequence of the hippocampal CA3 affects the postsynaptic membrane potentials of single pyramidal cells in the hippocampal CA1, the spatio-temporal stimuli was delivered to Schaffer collaterals of the CA3 through a pair of electrodes and the post-synaptic membrane potentials were recorded using the pa...

In rat CA1 pyramidal neurons, our previous study showed Cantor coding like property, which is theoretically proposed by Tsuda and Kuroda. In this study, we analyzed the clustering properties by one and two steps before the sequences of electrical stimulation in CA1 pyramidal neurons after many action potentials. The membrane responses after action...

A new hypothesis on a possible role for the corticopetal acetylcholine (ACh) is provided from a dynamical systems standpoint. The corticopetal ACh helps to transiently organize a global (inter- and intra-cortical) quasi-attractors via gamma range synchrony when it is behaviorally needed as top-down attentions and expectation.

We review basic concepts of dynamical systems in the first half of this article. In the second half, we focus on cortical transitory dynamic behaviors observed during task-related actions of animals, and provide a dynamical interpretation of such transitory behaviors in terms of chaotic itinerancy.

We propose a framework of neurocognitive experiments that clarifies structures of descriptions for the observed data. This framework can be used to determine the limitation of their possible interpretations and to reveal tacit assumptions of the experiments. We apply the framework to some actual neurocognitive experiment whose aim was to clarify in...

How does the brain encode episode? Episodic memory has become interested in scientific society since finding of malfunction of formation of episodic memory caused by a damage of the hippocampus, especially, the part named CA1, which was clinically observed. On the other hand, simple memory has been explored in various contexts, especially, since Ma...