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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.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.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.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.Ictal DC shifts can be distinguished by their attenuation patterns.

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.

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 GABA(A) 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.

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 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.

International audience; 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.

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 investigated the mathematical structures of functional differentiation and obtained the following specific behaviors. (1) We observed the genesis of a neuron-like unit in the developmental process of networking dynamical systems. (2) We observed the genesis of neuron-like units that respond specifically to visual and auditory stimuli, respectively. (3) We observed the genesis of functional modules from randomly uniform networks of oscillations, where the modular organization can be interpreted as the differentiation of a higher cognitive area and a lower motor area interacting with the body. In all cases, the appearance of chaos and chaotic itinerancy in the whole network system brings about the generation of functional elements via an acceleration of symmetry breaking.

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.

In cephalopods, all species are considered to be polyandrous because of their common life history and reproductive traits reflecting a polyandrous mating system. Contrary to this belief, here we show several lines of evidence for monogamy in the firefly squid, Watasenia scintillans. In this species, females are capable of long-term storage of spermatangia, and of egg spawning even after the complete disappearance of males following the breeding season. The stored spermatangia are distributed equally between bilateral pouches under the female’s neck collar. Such a nonrandom pattern of sperm storage prompted us to hypothesize that females might engage in lifetime monandry. Hence, we genotyped female-stored spermatangia and offspring, and found that in 95% of females (18/19), all the spermatangia had been delivered from a single male and all the embryos in a clutch had been sired by spermatozoa from stored spermatangia. In males, throughout the reproductive season, relative testis mass was much smaller in W. scintillans than in all other cephalopods examined previously. The mean number of male-stored spermatophores was ~ 30, equivalent to only 2.5 matings. Our genetic, demographic and morphometrical data agree with a mathematical model predicting that monogyny is favored when potential mates are scarce. Together, these results suggest mutual monogamy in W. scintillans.

Although polygamy has versatile benefits for both sexes, many species favor monogamy for reasons with the clarity or unclarity. In cephalopods, all species are regarded to be polygamous, which could be attributed to their common life-history traits. Contrary to this prediction, we show empirical evidence for monogamy in the firefly squid, Watasenia scintillans. The peak spawning season comes after male disappearance owning to long-reserved spermatangia deposited by male at exact locations (bilateral pouches under neck collar) on female with a symmetric distribution. Such a non-random placement of spermatangia prompted us to hypothesize that females engage in lifetime monoandry. Hence we assigned genotypes of female-stored spermatangia and offspring. We found that in 94.7 % females, the spermatangia were delivered from a single male and all embryos in the same egg string sired by sperm from stored spermatangia. Throughout the season, relative testes mass was much smaller in W. scintillans than all other cephalopods previously examined. The mean number of male-stored spermatophores was approximately 30, the equivalent to 2.5 mates. Our demographic and morphometrical data agree with the prediction that monogyny is favored when potential mates are scarce such as absence of female remating. Together, these results suggest the likelihood of mutual monogamy.

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.

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.

This paper reports a three-modules scenario in a computational interpretation of Recurrent Complex Visual Hallucination in Dementia with Lewy Bodies (RCVH-DLB). An algorithmic representation of the interpretation is proposed and preliminary results of computer experiments based on a recurrent neural network model consisting of three modules are shown. The three modules are considered to be visual module, memory module, and perceiving module, respectively. Intra-module and inter-module interactions via asymmetric synaptic connection strength are introduced, where each module consists of a rather large number of binary state neurons. Corresponding to certain inputs to visual module, veridical perception is conceptualized as dynamic convergence to particular states (perceiving attractors) of neuron activity patterns in high dimensional state space. The key idea is that, as a possible origin of hallucination, systematic reducing of neurons and pruning of synaptic connections following the observed data in physical measurements of grey matter loss and white matter atrophy in DLB patients obtained by using DTI-MR, MRI or SPECT are introduced. Preliminary experimental results suggest that these defects can cause desta-bilizing of perceiving attractors and mutual penetration of them which results in hallucination-like outputs in perceiving module can occur.

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, 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., Comment: Revised manuscript. 15 figures. This article has been submitted to Chaos. After it is published, it will be found at https://aip.scitation.org/journal/cha

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, chaotic activity between the regions. In a cognitive neurodynamic aspect, quasi-attractors represent perceptions, thoughts and memories, chaotic trajectories between them with intelligent searches, such as history-dependent trial-and-error via exploration, and itinerancy with history-dependent sequences in thinking, speaking and writing.