Impact of time-history terms on reservoir dynamics and prediction accuracy in echo state networks.

The echo state network (ESN) is an excellent machine learning model for processing time-series data. This model, utilising the response of a recurrent neural network, called a reservoir, to input signals, achieves high training efficiency. Introducing time-history terms into the neuron model of the reservoir is known to improve the time-series prediction performance of ESN, yet the reasons for this improvement have not been quantitatively explained in terms of reservoir dynamics characteristics. Therefore, we hypothesised that the performance enhancement brought about by time-history terms could be explained by delay capacity, a recently proposed metric for assessing the memory performance of reservoirs. To test this hypothesis, we conducted comparative experiments using ESN models with time-history terms, namely leaky integrator ESNs (LI-ESN) and chaotic echo state networks (ChESN). The results suggest that compared with ESNs without time-history terms, the reservoir dynamics of LI-ESN and ChESN can maintain diversity and stability while possessing higher delay capacity, leading to their superior performance. Explaining ESN performance through dynamical metrics are crucial for evaluating the numerous ESN architectures recently proposed from a general perspective and for the development of more sophisticated architectures, and this study contributes to such efforts.

The Changes in Relative Blood Volume during Dialysis Are Characterized by Ultrafiltration Rate and Predialysis Blood Test Values.

INTRODUCTION: Continuous monitoring of relative blood volume (percentage BV) in hemodialysis (HD) is critical for determining dry weight and preventing intradialytic hypotension. However, the cause of the BV variation remains unknown. This research aimed to examine factors that influence the percentage BV. METHODS: We devised a formula based on coefficients ("a," "τ," and "b") to predict changes in percentage BV. "a" denotes a significant decrease in percentage BV in the early stages of HD. "τ" represents the transition from early to late phase of HD. "b" denotes the slope of the decrease in percentage BV in the late phase of HD. We measured the percentage BV in 18 patients with end-stage renal disease. The coefficients were estimated by fitting experimental data from patients using a least squares optimization algorithm. A correlation analysis of these parameters and patient predialysis data was performed. RESULTS: Ultrafiltration rate (UFR) was found to be negatively correlated with "b" (r = -0.851, p < 0.01). However, UFR was not significantly related to "a." Predialysis serum total protein level was negatively correlated with "a" (r = -0.531, p = 0.042). Predialysis serum albumin and predialysis sodium were not significantly correlated with "a" and "τ." Plasma osmolarity did not have a significant relationship with "a" and "τ." DISCUSSION/CONCLUSION: UFR influenced the decrease in percentage BV in the late phase but did not influence the decrease of percentage BV in the early phase. "a" was associated with predialysis serum total protein level but not with plasma osmolality or predialysis sodium. This implies that colloid oncotic pressure is important for plasma refilling immediately after dialysis begins. During the change of percentage BV, the decrease in the early phase of dialysis was not related to UFR, but related to other parameters, especially predialysis total protein level. A decrease in the late phase of dialysis is related to UFR.

Analysis of the status and content of consultations with a Cancer Consultation and Support Centre during the COVID-19 pandemic.

PURPOSE: Cancer Consultation and Support Centres (CCSCs) in Japan have been established at designated cancer hospitals nationwide and these centres provide information and consultation support for cancer care. The purpose of this study is to analyse the status and content of consultations during the COVID-19 pandemic using consultation record data from the Cancer Consultation Support Centre (CCSC) database from January 2020 to March 2021. METHODS: First, we examined the number and percentage of cases involving and not involving COVID-19 and compared the items of the entry forms between the groups. The comparison between the two groups suggests that the traditional consultation items used before the COVID-19 pandemic did not adequately cover the consultation content during the COVID-19 pandemic. Therefore, we categorised the content of consultation records related to COVID-19. RESULTS: As a result, the content was consolidated into 16 categories, which were appropriately captured from five different aspects. CONCLUSION: Using the resulting categories, we were able to create a complementary consultation entry form that could be operational during the COVID epidemic and consult consultants for the support they needed. TRIAL REGISTRATION: Not applicable.

Dynamic Characteristics of State Transitions Composed of Neural Activity in the Brain by Circadian Rhythms.

In recent years, as a treatment for mental disorders in addition to drug treatment, a non-drug treatment called chronotherapy has been attracting attention. However, the achievement of optimized chronotherapy for each subject's condition requires that the disturbance of the patient's circadian rhythm must be captured over a long duration. Therefore, it is necessary to develop biomarkers that are easy to measure, quantitative, and continuously measured. Complexity analysis of electroencephalograms revealed specific patterns related to circadian rhythms. However, such complexity analysis cannot capture variability in spatial patterns, although moment-to-moment temporal dynamic characteristics can be captured. Therefore, it is necessary to evaluate the dynamic characteristics of the interaction of neural activity throughout the brain. To evaluate the dynamic whole-brain interaction, we proposed a new microstate approach based on the instantaneous frequency distribution. In this context, we hypothesized that it would be possible to detect circadian rhythms using the microstate approach. In this study, to clarify the dynamic interactions of the entire neural network of the brain by circadian rhythms, we measured EEG data at day and night, and detected dynamic state transitions based on the instantaneous frequency distribution of the whole brain from EEG. The results showed the probability of transition among region-specific phase-leading states related to circadian rhythms. This finding might be widely utilized to detect circadian rhythms in healthy and pathological conditions.

Development of a Systematic Approach to Consultation Record Data from Cancer Consultation and Support Centers.

The purpose of this study is to extract features and structure them using text mining and to analyze changes over time on consultation records accumulated in a cancer consultation and support center database from 2009 to 2018. The text-mining approach worked effectively under conditions of expanding data, and a co-occurrence network revealed patterns and trends in the content of consultations.

An Approach for Stabilizing Abnormal Neural Activity in ADHD Using Chaotic Resonance.

Reduced integrity of neural pathways from frontal to sensory cortices has been suggested as a potential neurobiological basis of attention-deficit hyperactivity disorder. Neurofeedback has been widely applied to enhance reduced neural pathways in attention-deficit hyperactivity disorder by repeated training on a daily temporal scale. Clinical and model-based studies have demonstrated that fluctuations in neural activity underpin sustained attention deficits in attention-deficit hyperactivity disorder. These aberrant neural fluctuations may be caused by the chaos-chaos intermittency state in frontal-sensory neural systems. Therefore, shifting the neural state from an aberrant chaos-chaos intermittency state to a normal stable state with an optimal external sensory stimulus, termed chaotic resonance, may be applied in neurofeedback for attention-deficit hyperactivity disorder. In this study, we applied a neurofeedback method based on chaotic resonance induced by "reduced region of orbit" feedback signals in the Baghdadi model for attention-deficit hyperactivity disorder. We evaluated the stabilizing effect of reduced region of orbit feedback and its robustness against noise from errors in estimation of neural activity. The effect of chaotic resonance successfully shifted the abnormal chaos-chaos intermittency of neural activity to the intended stable activity. Additionally, evaluation of the influence of noise due to measurement errors revealed that the efficiency of chaotic resonance induced by reduced region of orbit feedback signals was maintained over a range of certain noise strengths. In conclusion, applying chaotic resonance induced by reduced region of orbit feedback signals to neurofeedback methods may provide a promising treatment option for attention-deficit hyperactivity disorder.

Long-Tailed Characteristic of Spiking Pattern Alternation Induced by Log-Normal Excitatory Synaptic Distribution.

Studies of structural connectivity at the synaptic level show that in synaptic connections of the cerebral cortex, the excitatory postsynaptic potential (EPSP) in most synapses exhibits sub-mV values, while a small number of synapses exhibit large EPSPs ( >~1.0 [mV]). This means that the distribution of EPSP fits a log-normal distribution. While not restricting structural connectivity, skewed and long-tailed distributions have been widely observed in neural activities, such as the occurrences of spiking rates and the size of a synchronously spiking population. Many studies have been modeled this long-tailed EPSP neural activity distribution; however, its causal factors remain controversial. This study focused on the long-tailed EPSP distributions and interlateral synaptic connections primarily observed in the cortical network structures, thereby having constructed a spiking neural network consistent with these features. Especially, we constructed two coupled modules of spiking neural networks with excitatory and inhibitory neural populations with a log-normal EPSP distribution. We evaluated the spiking activities for different input frequencies and with/without strong synaptic connections. These coupled modules exhibited intermittent intermodule-alternative behavior, given moderate input frequency and the existence of strong synaptic and intermodule connections. Moreover, the power analysis, multiscale entropy analysis, and surrogate data analysis revealed that the long-tailed EPSP distribution and intermodule connections enhanced the complexity of spiking activity at large temporal scales and induced nonlinear dynamics and neural activity that followed the long-tailed distribution.

High Phase Synchronization in Alpha Band Activity in Older Subjects With High Creativity.

Despite growing evidence that high creativity leads to mental well-being in older individuals, the neurophysiological bases of creativity remain elusive. Creativity reportedly involves multiple brain areas and their functional interconnections. In particular, functional magnetic resonance imaging (fMRI) is used to investigate the role of patterns of functional connectivity between the default network and other networks in creative activity. These interactions among networks play the role of integrating various neural processes to support creative activity and involve attention, cognitive control, and memory. The electroencephalogram (EEG) enables researchers to capture a pattern of band-specific functional connectivity, as well as moment-to-moment dynamics of brain activity; this can be accomplished even in the resting-state by exploiting the excellent temporal resolution of the EEG. Furthermore, the recent advent of functional connectivity analysis in EEG studies has focused on the phase-difference variable because of its fine spatio-temporal resolution. Therefore, we hypothesized that the combining method of EEG signals having high-temporal resolution and the phase synchronization analysis having high-spatio-temporal resolutions brings a new insight of functional connectivity regarding high creative activity of older participants. In this study, we examined the resting-state EEG signal in 20 healthy older participants and estimated functional connectivities using the phase lag index (PLI), which evaluates the phase synchronization of EEG signals. Individual creativity was assessed using the S-A creativity test in a separate session before the EEG recording. In the analysis of associations of EEG measures with the S-A test scores, the covariate effect of the intelligence quotient was evaluated. As a result, higher individual S-A scores were significantly associated with higher node degrees, defined as the average PLI of a node (electrode) across all links with the remaining nodes, across all nodes at the alpha band. A conventional power spectrum analysis revealed no significant association with S-A scores in any frequency band. Older participants with high creativity exhibited high functional connectivity even in the resting-state, irrespective of intelligence quotient, which supports the theory that creativity entails widespread brain connectivity. Thus, PLIs derived from EEG data may provide new insights into the relationship between functional connectivity and creativity in healthy older people.

Deterministic characteristics of spontaneous activity detected by multi-fractal analysis in a spiking neural network with long-tailed distributions of synaptic weights.

Cortical neural networks maintain autonomous electrical activity called spontaneous activity that represents the brain's dynamic internal state even in the absence of sensory stimuli. The spatio-temporal complexity of spontaneous activity is strongly related to perceptual, learning, and cognitive brain functions; multi-fractal analysis can be utilized to evaluate the complexity of spontaneous activity. Recent studies have shown that the deterministic dynamic behavior of spontaneous activity especially reflects the topological neural network characteristics and changes of neural network structures. However, it remains unclear whether multi-fractal analysis, recently widely utilized for neural activity, is effective for detecting the complexity of the deterministic dynamic process. To verify this point, we focused on the log-normal distribution of excitatory postsynaptic potentials (EPSPs) to evaluate the multi-fractality of spontaneous activity in a spiking neural network with a log-normal distribution of EPSPs. We found that the spiking activities exhibited multi-fractal characteristics. Moreover, to investigate the presence of a deterministic process in the spiking activity, we conducted a surrogate data analysis against the time-series of spiking activity. The results showed that the spontaneous spiking activity included the deterministic dynamic behavior. Overall, the combination of multi-fractal analysis and surrogate data analysis can detect deterministic complex neural activity. The multi-fractal analysis of neural activity used in this study could be widely utilized for brain modeling and evaluation methods for signals obtained by neuroimaging modalities.

Transition of Neural Activity From the Chaotic Bipolar-Disorder State to the Periodic Healthy State Using External Feedback Signals.

Chronotherapy is a treatment for mood disorders, including major depressive disorder, mania, and bipolar disorder (BD). Neurotransmitters associated with the pathology of mood disorders exhibit circadian rhythms. A functional deficit in the neural circuits related to mood disorders disturbs the circadian rhythm; chronotherapy is an intervention that helps resynchronize the patient's biological clock with the periodic daily cycle, leading to amelioration of symptoms. In previous reports, Hadaeghi et al. proposed a non-linear dynamic model composed of the frontal and sensory cortical neural networks and the hypothalamus to explain the relationship between deficits in neural function in the frontal cortex and the disturbed circadian rhythm/mood transitions in BD (hereinafter referred to as the Hadaeghi model). In this model, neural activity in the frontal and sensory lobes exhibits periodic behavior in the healthy state; while in BD, this neural activity is in a state of chaos-chaos intermittency; this temporal departure from the healthy periodic state disturbs the circadian pacemaker in the hypothalamus. In this study, we propose an intervention based on a feedback method called the "reduced region of orbit" (RRO) method to facilitate the transition of the disturbed frontal cortical neural activity underlying BD to healthy periodic activity. Our simulation was based on the Hadaeghi model. We used an RRO feedback signal based on the return-map structure of the simulated frontal and sensory lobes to induce synchronization with a relatively weak periodic signal corresponding to the healthy condition by applying feedback of appropriate strength. The RRO feedback signal induces chaotic resonance, which facilitates the transition to healthy, periodic frontal neural activity, although this synchronization is restricted to a relatively low frequency of the periodic input signal. Additionally, applying an appropriate strength of the RRO feedback signal lowered the amplitude of the periodic input signal required to induce a synchronous state compared with the periodic signal applied alone. In conclusion, through a chaotic-resonance effect induced by the RRO feedback method, the state of the disturbed frontal neural activity characteristic of BD was transformed into a state close to healthy periodic activity by relatively weak periodic perturbations. Thus, RRO feedback-modulated chronotherapy might be an innovative new type of minimally invasive chronotherapy.

Classification Methods Based on Complexity and Synchronization of Electroencephalography Signals in Alzheimer's Disease.

Electroencephalography (EEG) has long been studied as a potential diagnostic method for Alzheimer's disease (AD). The pathological progression of AD leads to cortical disconnection. These disconnections may manifest as functional connectivity alterations, measured by the degree of synchronization between different brain regions, and alterations in complex behaviors produced by the interaction among wide-spread brain regions. Recently, machine learning methods, such as clustering algorithms and classification methods, have been adopted to detect disease-related changes in functional connectivity and classify the features of these changes. Although complexity of EEG signals can also reflect AD-related changes, few machine learning studies have focused on the changes in complexity. Therefore, in this study, we compared the ability of EEG signals to detect characteristics of AD using different machine learning approaches one focused on functional connectivity and the other focused on signal complexity. We examined functional connectivity, estimated by phase lag index (PLI) in EEG signals in healthy older participants [healthy control (HC)] and patients with AD. We estimated signal complexity using multi-scale entropy. Utilizing a support vector machine, we compared the identification accuracy of AD based on functional connectivity at each frequency band and complexity component. Additionally, we evaluated the relationship between synchronization and complexity. The identification accuracy of functional connectivity of the alpha, beta, and gamma bands was significantly high (AUC 1.0), and the identification accuracy of complexity was sufficiently high (AUC 0.81). Moreover, the relationship between functional connectivity and complexity exhibited various temporal-scale-and-regional-specific dependency in both HC participants and patients with AD. In conclusion, the combination of functional connectivity and complexity might reflect complex pathological process of AD. Applying a combination of both machine learning methods to neurophysiological data may provide a novel understanding of the neural network processes in both healthy brains and pathological conditions.

Temporal-specific complexity of spiking patterns in spontaneous activity induced by a dual complex network structure.

Temporal fluctuation of neural activity in the brain has an important function in optimal information processing. Spontaneous activity is a source of such fluctuation. The distribution of excitatory postsynaptic potentials (EPSPs) between cortical pyramidal neurons can follow a log-normal distribution. Recent studies have shown that networks connected by weak synapses exhibit characteristics of a random network, whereas networks connected by strong synapses have small-world characteristics of small path lengths and large cluster coefficients. To investigate the relationship between temporal complexity spontaneous activity and structural network duality in synaptic connections, we executed a simulation study using the leaky integrate-and-fire spiking neural network with log-normal synaptic weight distribution for the EPSPs and duality of synaptic connectivity, depending on synaptic weight. We conducted multiscale entropy analysis of the temporal spiking activity. Our simulation demonstrated that, when strong synaptic connections approach a small-world network, specific spiking patterns arise during irregular spatio-temporal spiking activity, and the complexity at the large temporal scale (i.e., slow frequency) is enhanced. Moreover, we confirmed through a surrogate data analysis that slow temporal dynamics reflect a deterministic process in the spiking neural networks. This modelling approach may improve the understanding of the spatio-temporal complex neural activity in the brain.

Resonance phenomena controlled by external feedback signals and additive noise in neural systems.

Chaotic resonance is a phenomenon that can replace the fluctuation source in stochastic resonance from additive noise to chaos. We previously developed a method to control the chaotic state for suitably generating chaotic resonance by external feedback even when the external adjustment of chaos is difficult, establishing a method named reduced region of orbit (RRO) feedback. However, a feedback signal was utilized only for dividing the merged attractor. In addition, the signal sensitivity in chaotic resonance induced by feedback signals and that of stochastic resonance by additive noise have not been compared. To merge the separated attractor, we propose a negative strength of the RRO feedback signal in a discrete neural system which is composed of excitatory and inhibitory neurons. We evaluate the features of chaotic resonance and compare it to stochastic resonance. The RRO feedback signal with negative strength can merge the separated attractor and induce chaotic resonance. We also confirm that additive noise induces stochastic resonance through attractor merging. The comparison of these resonance modalities verifies that chaotic resonance provides more applicability than stochastic resonance given its capability to handle attractor separation and merging.

Atypical temporal-scale-specific fractal changes in Alzheimer's disease EEG and their relevance to cognitive decline.

Recent advances in nonlinear analytic methods for electroencephalography have clarified the reduced complexity of spatiotemporal dynamics in brain activity observed in Alzheimer's disease (AD). However, there are far fewer studies exploring temporal scale dependent fractal properties in AD, despite the importance of studying the dynamics of brain activity within physiologically relevant frequency ranges. Higuchi's fractal dimension is a widely used index for evaluating fractality in brain activity, but temporal-scale-specific characteristics are lost due to its requirement of averaging over the entire range of temporal scales. In this study, we adapted Higuchi's fractal algorithm into a method for investigating temporal-scale-specific fractal properties. We then compared the values of the temporal-scale-specific fractal dimension between healthy control (HC) and AD patient groups. Our data indicate that relative to the HC group, the AD group demonstrated reduced fractality at both slow and fast temporal scales. Moreover, we confirmed that the fractality at fast temporal scales correlates with cognitive decline. These properties might serve as a basis for a useful approach to characterizing temporal neural dynamics in AD or other neurodegenerative disorders.

Routes to Chaos Induced by a Discontinuous Resetting Process in a Hybrid Spiking Neuron Model.

Several hybrid spiking neuron models combining continuous spike generation mechanisms and discontinuous resetting processes following spiking have been proposed. The Izhikevich neuron model, for example, can reproduce many spiking patterns. This model clearly possesses various types of bifurcations and routes to chaos under the effect of a state-dependent jump in the resetting process. In this study, we focus further on the relation between chaotic behaviour and the state-dependent jump, approaching the subject by comparing spiking neuron model versions with and without the resetting process. We first adopt a continuous two-dimensional spiking neuron model in which the orbit in the spiking state does not exhibit divergent behaviour. We then insert the resetting process into the model. An evaluation using the Lyapunov exponent with a saltation matrix and a characteristic multiplier of the Poincar'e map reveals that two types of chaotic behaviour (i.e. bursting chaotic spikes and near-period-two chaotic spikes) are induced by the resetting process. In addition, we confirm that this chaotic bursting state is generated from the periodic spiking state because of the slow- and fast-scale dynamics that arise when jumping to the hyperpolarization and depolarization regions, respectively.

Chaotic Resonance in Typical Routes to Chaos in the Izhikevich Neuron Model.

Chaotic resonance (CR), in which a system responds to a weak signal through the effects of chaotic activities, is a known function of chaos in neural systems. The current belief suggests that chaotic states are induced by different routes to chaos in spiking neural systems. However, few studies have compared the efficiency of signal responses in CR across the different chaotic states in spiking neural systems. We focused herein on the Izhikevich neuron model, comparing the characteristics of CR in the chaotic states arising through the period-doubling or tangent bifurcation routes. We found that the signal response in CR had a unimodal maximum with respect to the stability of chaotic orbits in the tested chaotic states. Furthermore, the efficiency of signal responses at the edge of chaos became especially high as a result of synchronization between the input signal and the periodic component in chaotic spiking activity.

Chaotic Resonance in Coupled Inferior Olive Neurons with the Llinás Approach Neuron Model.

It is well known that cerebellar motor control is fine-tuned by the learning process adjusted according to rich error signals from inferior olive (IO) neurons. Schweighofer and colleagues proposed that these signals can be produced by chaotic irregular firing in the IO neuron assembly; such chaotic resonance (CR) was replicated in their computer demonstration of a Hodgkin-Huxley (HH)-type compartment model. In this study, we examined the response of CR to a periodic signal in the IO neuron assembly comprising the Llinás approach IO neuron model. This system involves empirically observed dynamics of the IO membrane potential and is simpler than the HH-type compartment model. We then clarified its dependence on electrical coupling strength, input signal strength, and frequency. Furthermore, we compared the physiological validity for IO neurons such as low firing rate and sustaining subthreshold oscillation between CR and conventional stochastic resonance (SR) and examined the consistency with asynchronous firings indicated by the previous model-based studies in the cerebellar learning process. In addition, the signal response of CR and SR was investigated in a large neuron assembly. As the result, we confirmed that CR was consistent with the above IO neuron's characteristics, but it was not as easy for SR.

Enhancement of Spike-Timing-Dependent Plasticity in Spiking Neural Systems with Noise.

Synaptic plasticity is widely recognized to support adaptable information processing in the brain. Spike-timing-dependent plasticity, one subtype of plasticity, can lead to synchronous spike propagation with temporal spiking coding information. Recently, it was reported that in a noisy environment, like the actual brain, the spike-timing-dependent plasticity may be made efficient by the effect of stochastic resonance. In the stochastic resonance, the presence of noise helps a nonlinear system in amplifying a weak (under barrier) signal. However, previous studies have ignored the full variety of spiking patterns and many relevant factors in neural dynamics. Thus, in order to prove the physiological possibility for the enhancement of spike-timing-dependent plasticity by stochastic resonance, it is necessary to demonstrate that this stochastic resonance arises in realistic cortical neural systems. In this study, we evaluate this stochastic resonance phenomenon in the realistic cortical neural system described by the Izhikevich neuron model and compare the characteristics of typical spiking patterns of regular spiking, intrinsically bursting and chattering experimentally observed in the cortex.

Analysis of Chaotic Resonance in Izhikevich Neuron Model.

In stochastic resonance (SR), the presence of noise helps a nonlinear system amplify a weak (sub-threshold) signal. Chaotic resonance (CR) is a phenomenon similar to SR but without stochastic noise, which has been observed in neural systems. However, no study to date has investigated and compared the characteristics and performance of the signal responses of a spiking neural system in some chaotic states in CR. In this paper, we focus on the Izhikevich neuron model, which can reproduce major spike patterns that have been experimentally observed. We examine and classify the chaotic characteristics of this model by using Lyapunov exponents with a saltation matrix and Poincaré section methods in order to address the measurement challenge posed by the state-dependent jump in the resetting process. We found the existence of two distinctive states, a chaotic state involving primarily turbulent movement and an intermittent chaotic state. In order to assess the signal responses of CR in these classified states, we introduced an extended Izhikevich neuron model by considering weak periodic signals, and defined the cycle histogram of neuron spikes as well as the corresponding mutual correlation and information. Through computer simulations, we confirmed that both chaotic states in CR can sensitively respond to weak signals. Moreover, we found that the intermittent chaotic state exhibited a prompter response than the chaotic state with primarily turbulent movement.

Modeling fluctuations in default-mode brain network using a spiking neural network.

Recently, numerous attempts have been made to understand the dynamic behavior of complex brain systems using neural network models. The fluctuations in blood-oxygen-level-dependent (BOLD) brain signals at less than 0.1 Hz have been observed by functional magnetic resonance imaging (fMRI) for subjects in a resting state. This phenomenon is referred to as a "default-mode brain network." In this study, we model the default-mode brain network by functionally connecting neural communities composed of spiking neurons in a complex network. Through computational simulations of the model, including transmission delays and complex connectivity, the network dynamics of the neural system and its behavior are discussed. The results show that the power spectrum of the modeled fluctuations in the neuron firing patterns is consistent with the default-mode brain network's BOLD signals when transmission delays, a characteristic property of the brain, have finite values in a given range.