Episodic Visual Hallucinations, Inference and Free Energy.

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 free energy, a measure of the distance between predicted and actual sensory data in a stationary open system. We review this approach in the light of old and new information on the role of environmental factors in episodic hallucinations. In particular, we highlight the possible relationship of specific visual triggers to the onset and offset of some episodes. We use an analogy from phase transitions in physics to explore factors which might account for intermittent shifts between veridical and hallucinatory vision. In these triggered forms of hallucinations, we suggest that there is a transient disturbance in the normal one-to-one correspondence between a real object and the counterpart perception such that this correspondence becomes between the real object and a hallucination. Generative models propose that a lack of information transfer from the environment to the brain is one of the key features of hallucinations. In contrast, we submit that specific information transfer is required at onset and offset in these cases. We propose that this transient one-to-one correspondence between environment and hallucination is mediated more by aberrant discriminative than by generative inference. Discriminative inference can be conceptualized as a process for maximizing shared information between the environment and perception within a self-organizing nonstationary system. We suggest that generative inference plays the greater role in established hallucinations and in the persistence of individual hallucinatory episodes. We further explore whether thermodynamic free energy may be an additional factor in why hallucinations are temporary. Future empirical research could productively concentrate on three areas. Firstly, subjective perceptual changes and parallel variations in brain function during specific transitions between veridical and hallucinatory vision to inform models of how episodes occur. Secondly, systematic investigation of the links between environment and hallucination episodes to probe the role of information transfer in triggering transitions between veridical and hallucinatory vision. Finally, changes in hallucinatory episodes over time to elucidate the role of learning on phenomenology. These empirical data will allow the potential roles of different forms of inference in the stages of hallucinatory episodes to be elucidated.

On the Nature of Functional Differentiation: The Role of Self-Organization with Constraints.

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 neurons. Regarding the self-organized structure of neural systems, Warren McCulloch described the neural networks of the brain as being "heterarchical", rather than hierarchical, in structure. Unlike the fixed boundary conditions in conventional self-organization theory, where stationary phenomena are the target for study, the neural networks of the brain change their functional structure via synaptic learning and neural differentiation to exhibit specific functions, thereby adapting to nonstationary environmental changes. Thus, the neural network structure is altered dynamically among possible network structures. We refer to such changes as a dynamic heterarchy. Through the dynamic changes of the network structure under constraints, such as physical, chemical, and informational factors, which act on the whole system, neural systems realize functional differentiation or functional parcellation. Based on the computation results of our model for functional differentiation, we propose hypotheses on the neuronal mechanism of functional differentiation. Finally, using the Kolmogorov-Arnold-Sprecher superposition theorem, which can be realized by a layered deep neural network, we propose a possible scenario of functional (including cell) differentiation.

Functional differentiations in evolutionary reservoir computing networks.

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 internal dynamics should be controlled to produce contracting dynamics after expanding dynamics. Expanding dynamics magnifies the difference of input information, while contracting dynamics contributes to forming clusters of input information, thereby producing multiple attractors. The simultaneous appearance of both dynamics indicates the existence of chaos. In contrast, the sequential appearance of these dynamics during finite time intervals may induce functional differentiations. In this paper, we show how specific neuronal units are yielded in the evolutionary reservoir computer.

Some elements for a history of the dynamical systems theory.

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 direct testimony of how contributors can be influenced by other scientists or works, we here collected some writings about the early times of a few contributors to chaos theory. The purpose is to exhibit the diversity in the paths and to bring some elements-which were never published-illustrating the atmosphere of this period. Some peculiarities of chaos theory are also discussed.

Reward inference by primate prefrontal and striatal neurons.

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 striatum predicted reward values for stimuli that had been previously well experienced with set reward quantities in the asymmetric reward task. Importantly, these LPFC neurons could predict the reward value of a stimulus using transitive inference even when the monkeys had not yet learned the stimulus-reward association directly; whereas these striatal neurons did not show such an ability. Nevertheless, because there were two set amounts of reward (large and small), the selected striatal neurons were able to exclusively infer the reward value (e.g., large) of one novel stimulus from a pair after directly experiencing the alternative stimulus with the other reward value (e.g., small). Our results suggest that although neurons that predict reward value for old stimuli in the LPFC could also do so for new stimuli via transitive inference, those in the striatum could only predict reward for new stimuli via exclusive inference. Moreover, the striatum showed more complex functions than was surmised previously for model-free learning.

Two-dimensional representation of action and arm-use sequences in the presupplementary and supplementary motor areas.

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 bilateral use of the arms. We first found in both areas that this behavioral demand resulted in attribute-based representation of individual motor acts, reflecting functional (action) or anatomical (right/left arm) attributes. Actions were frequently represented according to a body-axis-centered reference frame (supination or pronation) regardless of the arm to be used. Moreover, behavioral sequences were primarily represented with respect to the action- or arm-use sequence rather than the sequence of individual movements. We propose that the two-dimensional attribute-based sequence representation provides a robust and efficient means of processing multiple behavioral sequences.

Review: Nicotinic acetylcholine receptors to regulate important brain activity-what occurs at the molecular level?

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 advanced brain functions of brain.

Learning long-term motor timing/patterns on an orthogonal basis in random neural networks.

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 time series as the linear sum of stable trajectories produced by several small network modules. New finding in computer experiments is that the trajectories of the module outputs are orthogonal to each other. They created a dynamic orthogonal basis acquiring a high representational capacity, which enabled the system to learn the timing of extremely long intervals, such as tens of seconds for a millisecond computation unit, and also the complex time series of Lorenz attractors. This self-sustained system satisfies the stability and orthogonality requirements and thus provides a new neurocomputing framework and perspective for the neural mechanisms of motor learning.

Understanding visual hallucinations: A new synthesis.

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 Inference, and Thalamocortical Dysrhythmia Default Mode Network Decoupling. Each was derived from different understandings of brain organisation. To reduce this variability, representatives from each research group agreed an integrated Visual Hallucination Framework that is consistent with current theories of veridical and hallucinatory vision. The Framework delineates cognitive systems relevant to hallucinations. It allows a systematic, consistent, investigation of relationships between the phenomenology of visual hallucinations and changes in underpinning cognitive structures. The episodic nature of hallucinations highlights separate factors associated with the onset, persistence, and end of specific hallucinations suggesting a complex relationship between state and trait markers of hallucination risk. In addition to a harmonised interpretation of existing evidence, the Framework highlights new avenues of research, and potentially, new approaches to treating distressing hallucinations.

Dynamical analysis on duplicating-and-assimilating process: toward the understanding of mirror-neuron systems.

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 cognitive process in terms of dynamical systems. Finally, to understand the interactions between two individual mirror-neuron systems, we formulate and examine coupled systems that are composed of two distinct systems. We also carry out various numerical simulations to illustrate the assimilation process.

Reward prediction based on stimulus categorization in primate lateral prefrontal cortex.

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 of reward-related neurons were observed in the lateral prefrontal cortex: one type predicted reward independent of physical properties of visual stimuli and the other encoded the reward value specific to a category of stimuli defined by the task requirements. Neurons of the latter type were able to predict reward on the basis of stimuli that had not yet been associated with reward, provided that another stimulus from the same category was paired with reward. The results suggest that prefrontal neurons can represent reward information on the basis of category and propagate this information to category members that have not been linked directly with any experience of reward.

Visual hallucinations in dementia with Lewy bodies originate from necrosis of characteristic neurons and connections in three-module perception model.

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 constructed a three-module scenario concerning function giving rise to perception. The three modules were the visual input module, the memory module, and the perceiving module. Each module interacts with the others, and veridical perceptions were regarded as a certain convergence to one of the perceiving attractors sustained by self-consistent collective fields among the modules. Once a rather large but inhomogeneously distributed area of necrotic neurons and dysfunctional synaptic connections developed due to network disease, causing irreversible damage, then bottom-up information from the input module to both the memory and perceiving modules were severely impaired. These changes made the collective fields unstable and caused transient emergence of mismatched perceiving attractors. This may account for the reason why DLB patients see things that are not there. With the use of our computational model and experiments, the scenario was recreated with complex bifurcation phenomena associated with the destabilization of collective field dynamics in very high-dimensional state space.

Two types of clinical ictal direct current shifts in invasive EEG of intractable focal epilepsy identified by waveform cluster analysis.

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 habitual seizures, we compared (1) the peak amplitude and (2) peak latency of the earliest ictal DC shifts between TC of 10 s and 2 s. Cluster and logistic regression analyses were performed based on the attenuation rate of amplitude and peak latency with TC 10 s. RESULTS: Ictal DC shifts in 120 seizures were analyzed; 89.1% of which were appropriately depicted even by a TC of 2 s. Cluster and logistic regression analyses revealed two types of ictal DC shift. Namely, a rapid development pattern was defined as the ictal DC shifts with a shorter peak latency and they also showed smaller attenuation rate of amplitude (73/120 seizures). Slow development pattern was defined as the ictal DC shifts with crosscurrent of a rapid development pattern, i.e., a longer peak latency and larger attenuation rate of amplitude (47/120 seizures). Focal cortical dysplasia (FCD) 1A tended to show a rapid development pattern (22/29 seizures) and FCD2A tended to show a slow development pattern (13 /18 seizures), indicating there might be some correlations between two types of ictal DC shift and certain pathologies. CONCLUSIONS: Ictal DC shifts, especially rapid development pattern, can be recorded and identified by the AC amplifiers of TC of 2 s which is widely used in many institutes compared to that of TC of 10 s. Two types of ictal DC shifts were identified with possibility of corresponding pathology. SIGNIFICANCE: Ictal DC shifts can be distinguished by their attenuation patterns.

Physiological properties of Cantor coding-like iterated function system in the hippocampal CA1 network.

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 the system in CA1 remain unclear. Here, we performed a detailed analysis of the properties of the system related to the physiological basis of learning and memory. First, we investigated whether the system could be simply based on a series of on-off responses of excitatory postsynaptic potential (EPSP) amplitudes. We applied a series of three spatially distinct input patterns with similar EPSP peak amplitudes. The membrane responses showed significant differences in spatial clustering properties related to the iterated function system. These results suggest that existence of some factors, which do not simply depend on a series of on-off responses but on spatial patterns in the system. Second, to confirm whether the system is dependent on the interval of sequential input, we applied spatiotemporal sequential inputs at several intervals. The optimal interval was 30 ms, similar to the physiological input from CA3 to CA1. Third, we analyzed the inhibitory network dependency of the system. After GABAA receptor blocker (gabazine) application, quality of code discrimination in the system was lower under subthreshold conditions and higher under suprathreshold conditions. These results suggest that the inhibitory network increase the difference between the responses under sub- and suprathreshold conditions. In summary, Cantor coding-like iterated function system appears to be suitable for information expression in relation to learning and memory in CA1 network.

[The Elucidation of Informational Basis of Functional Differentiations in Terms of a Theory of Constrained Self-Organization].

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 differentiation of neuronal cells, functional modules, and the sensory neurons, thereby proposing three hypotheses.

A mathematical model for neuronal differentiation in terms of an evolved dynamical system.

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 possible forms of unidirectionally feed-forward network, random network, small-world network, and fully-connected network. We used a genetic algorithm to maximize the information transmission for each type of network. Optimized maps were obtained depending on the coupling strength and network structure. These maps can be classified into three types: passive, excitable, and oscillatory. In particular, the excitable and oscillatory types of dynamical systems possess characteristics that are quite similar to those of neurons, whereas the passive and oscillatory types of dynamical system may represent glial cells.

Constrained chaos in three-module neural network enables to execute multiple tasks simultaneously.

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 to the first module and input to post-module from pre-module. As a practical example, with use of computer experiments, the proposed idea is applied to a robot actuator in which control system using chaos is installed. The three modules are assigned to the sensory neuron module, the inter neuron module, and the driving (motor) neuron module, respectively. Initially, the actuator system of robot is designed so as to generate the four different kinds of specific driving signals in the motor module via the interneuron module corresponding to the four specific inputs to the entire sensory neurons. Next, chaos is introduced by reducing connectivity in intra-modules and/or inter-modules as well. It results in generating of chaotic motion signals from the motor module. Third, when two fragment inputs which belong to any two of the four specific inputs are applied simultaneously, then the motor module gives corresponding two driving signals simultaneously. Nevertheless, chaotic activities are kept even if strong two fragment inputs to the sensory module are applied. The results are one of the typical examples to show that constrained chaos in neural systems having big redundancy is able to execute multiple tasks simultaneously as brain does.

Mathematical structures for epilepsy: High-frequency oscillation and interictal epileptic slow (red slow).

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 indicate that, on one hand, HFOs at epileptic focus are characterized by one-dimensional dynamical systems in ictal onset time segments at an epileptic focus for two patients' datasets; on the other hand, an interictal epileptic slow is characterized by the residue of power spectrum. The results suggest that the degree of freedom of the brain dynamics during epileptic seizure with HFO degenerates to low-dimensional dynamics; hence, the interictal epileptic slow as the precursors of the seizure onset can be detected simply from interictal brain wave data for the dataset of one patient. Therefore, our results are essential to understand the brain dynamics in epilepsy.

Hypotheses on the functional roles of chaotic transitory dynamics.

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, which provides typical transitory dynamics. Second, we describe the transitory behaviors that have been observed in human and animal brains. Finally, we propose nine hypotheses on the functional roles of such dynamics, focusing on the dynamics embedded in data and the dynamical interpretation of brain activity within the framework of cerebral hermeneutics.

On embedded bifurcation structure in some discretized vector fields.

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 orbits that eventually converge to a fixed point. We provide a detailed mathematical analysis to explain this phenomenon and relate it to the solution of the original ODEs.