Large-scale Network Dynamics Research Articles

Dynamic thermal simulation of a tree-shaped district heating network based on discrete event simulation

The computational complexity involved in modelling district heating (DH) networks impedes the integration of network operations into comprehensive DH system studies. We developed a flexible, accurate, and fast dynamic thermal simulation model utilising discrete event simulation (DES). This model is versatile, suitable for any tree-shaped DH network with a central heating plant and can estimate node temperatures and calculate pipe heat losses. The speed of the model is improved via using variable time steps and by incorporating two advanced techniques: lazy evaluation and a customised priority queue. To further improve the computational speed, we developed a technique to eliminate redundant sampling points. This model was tested and demonstrated excellent consistency with actual measurements. Remarkably, reducing sampling points can speed up the simulation by a factor of three without compromising the temperature accuracy. A 72-day simulation of a network with 102 pipes was completed within 0.219 s. Our findings highlight the significant potential of the DES model for large-scale dynamic network simulations and offer a promising solution for DH network simulations and system optimisation.

Network dynamics-based subtyping of Alzheimer’s disease with microglial genetic risk factors

BackgroundThe potential of microglia as a target for Alzheimer’s disease (AD) treatment is promising, yet the clinical and pathological diversity within microglia, driven by genetic factors, poses a significant challenge. Subtyping AD is imperative to enable precise and effective treatment strategies. However, existing subtyping methods fail to comprehensively address the intricate complexities of AD pathogenesis, particularly concerning genetic risk factors. To address this gap, we have employed systems biology approaches for AD subtyping and identified potential therapeutic targets.MethodsWe constructed patient-specific microglial molecular regulatory network models by utilizing existing literature and single-cell RNA sequencing data. The combination of large-scale computer simulations and dynamic network analysis enabled us to subtype AD patients according to their distinct molecular regulatory mechanisms. For each identified subtype, we suggested optimal targets for effective AD treatment.ResultsTo investigate heterogeneity in AD and identify potential therapeutic targets, we constructed a microglia molecular regulatory network model. The network model incorporated 20 known risk factors and crucial signaling pathways associated with microglial functionality, such as inflammation, anti-inflammation, phagocytosis, and autophagy. Probabilistic simulations with patient-specific genomic data and subsequent dynamics analysis revealed nine distinct AD subtypes characterized by core feedback mechanisms involving SPI1, CASS4, and MEF2C. Moreover, we identified PICALM, MEF2C, and LAT2 as common therapeutic targets among several subtypes. Furthermore, we clarified the reasons for the previous contradictory experimental results that suggested both the activation and inhibition of AKT or INPP5D could activate AD through dynamic analysis. This highlights the multifaceted nature of microglial network regulation.ConclusionsThese results offer a means to classify AD patients by their genetic risk factors, clarify inconsistent experimental findings, and advance the development of treatments tailored to individual genotypes for AD.

The endoplasmic reticulum as an active liquid network

The peripheral endoplasmic reticulum (ER) forms a dense, interconnected, and constantly evolving network of membrane-bound tubules in eukaryotic cells. While individual structural elements and the morphogens that stabilize them have been described, a quantitative understanding of the dynamic large-scale network topology remains elusive. We develop a physical model of the ER as an active liquid network, governed by a balance of tension-driven shrinking and new tubule growth. This minimalist model gives rise to steady-state network structures with density and rearrangement timescales predicted from the junction mobility and tubule spawning rate. Several parameter-independent geometric features of the liquid network model are shown to be representative of ER architecture in live mammalian cells. The liquid network model connects the timescales of distinct dynamic features such as ring closure and new tubule growth in the ER. Furthermore, it demonstrates how the steady-state network morphology on a cellular scale arises from the balance of microscopic dynamic rearrangements.

Tipping prediction of a class of large-scale radial-ring neural networks

Understanding the emergence and evolution of collective dynamics in large-scale neural networks remains a complex challenge. This paper seeks to address this gap by applying dynamical systems theory, with a particular focus on tipping mechanisms. First, we introduce a novel (n+mn)-scale radial-ring neural network and employ Coates’ flow graph topological approach to derive the characteristic equation of the linearized network. Second, through deriving stability conditions and predicting the tipping point using an algebraic approach based on the integral element concept, we identify critical factors such as the synaptic transmission delay, the self-feedback coefficient, and the network topology. Finally, we validate the methodology’s effectiveness in predicting the tipping point. The findings reveal that increased synaptic transmission delay can induce and amplify periodic oscillations. Additionally, the self-feedback coefficient and the network topology influence the onset of tipping points. Moreover, the selection of activation function impacts both the number of equilibrium solutions and the convergence speed of the neural network. Lastly, we demonstrate that the proposed large-scale radial-ring neural network exhibits stronger robustness compared to lower-scale networks with a single topology. The results provide a comprehensive depiction of the dynamics observed in large-scale neural networks under the influence of various factor combinations.

Dynamic properties in functional connectivity changes and striatal dopamine deficiency in Parkinson's disease.

Recent studies in Parkinson's disease (PD) patients reported disruptions in dynamic functional connectivity (dFC, i.e., a characterization of spontaneous fluctuations in functional connectivity over time). Here, we assessed whether the integrity of striatal dopamine terminals directly modulates dFC metrics in two separate PD cohorts, indexing dopamine-related changes in large-scale brain network dynamics and its implications in clinical features. We pooled data from two disease-control cohorts reflecting early PD. From the Parkinson's Progression Marker Initiative (PPMI) cohort, resting-state functional magnetic resonance imaging (rsfMRI) and dopamine transporter (DaT) single-photon emission computed tomography (SPECT) were available for 63 PD patients and 16 age- and sex-matched healthy controls. From the clinical research group 219 (KFO) cohort, rsfMRI imaging was available for 52 PD patients and 17 age- and sex-matched healthy controls. A subset of 41 PD patients and 13 healthy control subjects additionally underwent 18F-DOPA-positron emission tomography (PET) imaging. The striatal synthesis capacity of 18F-DOPA PET and dopamine terminal quantity of DaT SPECT images were extracted for the putamen and the caudate. After rsfMRI pre-processing, an independent component analysis was performed on both cohorts simultaneously. Based on the derived components, an individual sliding window approach (44 s window) and a subsequent k-means clustering were conducted separately for each cohort to derive dFC states (reemerging intra- and interindividual connectivity patterns). From these states, we derived temporal metrics, such as average dwell time per state, state attendance, and number of transitions and compared them between groups and cohorts. Further, we correlated these with the respective measures for local dopaminergic impairment and clinical severity. The cohorts did not differ regarding age and sex. Between cohorts, PD groups differed regarding disease duration, education, cognitive scores and L-dopa equivalent daily dose. In both cohorts, the dFC analysis resulted in three distinct states, varying in connectivity patterns and strength. In the PPMI cohort, PD patients showed a lower state attendance for the globally integrated (GI) state and a lower number of transitions than controls. Significantly, worse motor scores (Unified Parkinson's Disease Rating Scale Part III) and dopaminergic impairment in the putamen and the caudate were associated with low average dwell time in the GI state and a low total number of transitions. These results were not observed in the KFO cohort: No group differences in dFC measures or associations between dFC variables and dopamine synthesis capacity were observed. Notably, worse motor performance was associated with a low number of bidirectional transitions between the GI and the lesser connected (LC) state across the PD groups of both cohorts. Hence, in early PD, relative preservation of motor performance may be linked to a more dynamic engagement of an interconnected brain state. Specifically, those large-scale network dynamics seem to relate to striatal dopamine availability. Notably, most of these results were obtained only for one cohort, suggesting that dFC is impacted by certain cohort features like educational level, or disease severity. As we could not pinpoint these features with the data at hand, we suspect that other, in our case untracked, demographical features drive connectivity dynamics in PD. PRACTITIONER POINTS: Exploring dopamine's role in brain network dynamics in two Parkinson's disease (PD) cohorts, we unraveled PD-specific changes in dynamic functional connectivity. Results in the Parkinson's Progression Marker Initiative (PPMI) and the KFO cohort suggest motor performance may be linked to a more dynamic engagement and disengagement of an interconnected brain state. Results only in the PPMI cohort suggest striatal dopamine availability influences large-scale network dynamics that are relevant in motor control.

Impact of agent-based intervention strategies on the COVID-19 pandemic in large-scale dynamic contact networks

Many intervention strategies, such as patient isolation and contact tracking, had been implemented in different countries to slow down and control the spread because of the enormous threats and losses caused by COVID-19. Since the contact relationships of millions of people within cities change over time, it is difficult to accurately predict the dynamics of large-scale outbreaks and evaluate the impact of the contact tracking and isolation strategy based on individual contact history on epidemic transmission. Here, we propose a non-markov spreading model based on individual contact dynamic network, to simulate the dynamic contact processes in a city with millions of people. In this model, the historical contact population of each infected person can be backtracked and tracked. Our model can accurately describe the COVID-19 epidemic in Wuhan and Hong Kong. We assess the impact of four agent-based epidemic intervention strategies: travel control, contact tracking and isolation, vaccination, and regular nucleic acid testing to all residents on the epidemic evolution and economic losses. We find that for the original SARS-CoV-2 virus, a strict travel control strategy is effective in both suppressing the spread of COVID-19 and minimizing economic losses. For the Omicron variant (BA.2) with stronger infectious capacity, a relatively loose travel control and an appropriate combination of the other three strategies can effectively control the epidemic outbreak while minimize economic losses. This paper provides an efficient framework for assessing the combination of different agent-based strategies by large-scale simulations in the case of unknown historical contact information of large populations, and the studies on different combinations of control strategies can provide theoretical guidance for future prevention and control.

On propagation in networks, promising models beyond network diffusion to describe degenerative brain diseases and traumatic brain injuries.

Introduction: Connections among neurons form one of the most amazing and effective network in nature. At higher level, also the functional structures of the brain is organized as a network. It is therefore natural to use modern techniques of network analysis to describe the structures of networks in the brain. Many studies have been conducted in this area, showing that the structure of the neuronal network is complex, with a small-world topology, modularity and the presence of hubs. Other studies have been conducted to investigate the dynamical processes occurring in brain networks, analyzing local and large-scale network dynamics. Recently, network diffusion dynamics have been proposed as a model for the progression of brain degenerative diseases and for traumatic brain injuries. Methods: In this paper, the dynamics of network diffusion is re-examined and reaction-diffusion models on networks is introduced in order to better describe the degenerative dynamics in the brain. Results: Numerical simulations of the dynamics of injuries in the brain connectome are presented. Different choices of reaction term and initial condition provide very different phenomenologies, showing how network propagation models are highly flexible. Discussion: The uniqueness of this research lies in the fact that it is the first time that reaction-diffusion dynamics have been applied to the connectome to model the evolution of neurodegenerative diseases or traumatic brain injury. In addition, the generality of these models allows the introduction of non-constant diffusion and different reaction terms with non-constant parameters, allowing a more precise definition of the pathology to be studied.

Aberrant brain dynamics of large-scale functional networks across schizophrenia and mood disorder

IntroductionThe dynamics of large-scale networks, which are known as distributed sets of functionally synchronized brain regions and include the visual network (VIN), somatomotor network (SMN), dorsal attention network (DAN), salience network (SAN), limbic network (LIN), frontoparietal network (FPN), and default mode network (DMN), play important roles in emotional and cognitive processes in humans. Although disruptions in these large-scale networks are considered critical for the pathophysiological mechanisms of psychiatric disorders, their role in psychiatric disorders remains unknown. We aimed to elucidate the aberrant dynamics across large-scale networks in patients with schizophrenia (SZ) and mood disorders. MethodsWe performed energy-landscape analysis to investigate the aberrant brain dynamics of seven large-scale networks across 50 healthy controls (HCs), 36 patients with SZ, and 42 patients with major depressive disorder (MDD) recruited at Wakayama Medical University. We identified major patterns of brain activity using energy-landscape analysis and estimated their duration, occurrence, and ease of transition. ResultsWe identified four major brain activity patterns that were characterized by the activation patterns of the DMN and VIN (state 1, DMN (-) VIN (-); state 2, DMN (+) VIN (+); state 3, DMN (-) VIN (+); and state 4, DMN (+) VIN (-)). The duration of state 1 and the occurrence of states 1 and 2 were shorter in the SZ group than in HCs and the MDD group, and the duration of state 3 was longer in the SZ group. The ease of transition between states 3 and 4 was larger in the SZ group than in the HCs and the MDD group. The ease of transition from state 3 to state 4 was negatively associated with verbal fluency in patients with SZ. The current study showed that the brain dynamics was more disrupted in SZ than in MDD. ConclusionsEnergy-landscape analysis revealed aberrant brain dynamics across large-scale networks between SZ and MDD and their associations with cognitive abilities in SZ, which cannot be captured by conventional functional connectivity analyses. These results provide new insights into the pathophysiological mechanisms underlying SZ and mood disorders.

Efficient Vulnerability Assessment of Large-Scale Dynamic Transportation Networks

Efficient Vulnerability Assessment of Large-Scale Dynamic Transportation Networks

Baseline Large-Scale Network Dynamics Associated with Disease Progression in Huntington's Disease.

Huntington's disease (HD) is a genetically determined disease with motor, cognitive, and neuropsychiatric disorders. However, the links between clinical progression and disruptions to dynamics in motor and cognitive large-scale networks are not well established. To investigate changes in dynamic and static large-scale networks using an established tool of disease progression in Huntington's disease, the composite Unified Huntington's Disease Rating Scale (cUHDRS). Sixty-four mutation carriers were included. Static and dynamic baseline functional connectivity as well as topological features were correlated to 2-year follow-up clinical assessments using the cUHDRS. Decline in cUHDRS scores was associated with higher connectivity between frontal default-mode and motor networks, whereas higher connectivity in posterior, mainly visuospatial regions was associated with a smaller decline in cUHDRS scores. Structural disruptions in HD were evident both in posterior parietal/occipital and frontal motor regions, with reciprocal increases in functional connectivity. However, although higher visuospatial network connectivity was tied to a smaller cUHDRS decline, increased motor and frontal default-mode connections were linked to a larger cUHDRS decreases. Therefore, divergent functional compensation mechanisms might be at play in the clinical evolution of HD.

Respiratory rhythm modulates membrane potential and spiking of nonolfactory neurons.

In recent years, several studies have shown a respiratory drive of the local field potential (LFP) in numerous brain areas so that the respiratory rhythm could be considered as a master clock promoting communication between distant brain locations. However, outside of the olfactory system, it remains unknown whether the respiratory rhythm could shape membrane potential (MP) oscillations. To fill this gap, we co-recorded MP and LFP activities in different nonolfactory brain areas, medial prefrontal cortex (mPFC), primary somatosensory cortex (S1), primary visual cortex (V1), and hippocampus (HPC), in urethane-anesthetized rats. Using respiratory cycle-by-cycle analysis, we observed that respiration could modulate both MP and spiking discharges in all recorded areas during episodes that we called respiration-related oscillations (RRo). Further quantifications revealed that RRo episodes were transient in most neurons (5 consecutive respiratory cycles in average). RRo development in MP was largely correlated with the presence of respiratory modulation in the LFP. By showing that the respiratory rhythm influenced brain activities deep to the MP of nonolfactory neurons, our data support the idea that respiratory rhythm could mediate long-range communication between brain areas.NEW & NOTEWORTHY In this study, we evidenced strong respiratory-driven oscillations of neuronal membrane potential and spiking discharge in various nonolfactory areas of the mammal brain. These oscillations were found in the medial prefrontal cortex, primary somatosensory cortex, primary visual cortex, and hippocampus. These findings support the idea that respiratory rhythm could be used as a common clock to set the dynamics of large-scale neuronal networks on the same slow rhythm.

The role of long-term power-law memory in controlling large-scale dynamical networks

Controlling large-scale dynamical networks is crucial to understand and, ultimately, craft the evolution of complex behavior. While broadly speaking we understand how to control Markov dynamical networks, where the current state is only a function of its previous state, we lack a general understanding of how to control dynamical networks whose current state depends on states in the distant past (i.e. long-term memory). Therefore, we require a different way to analyze and control the more prevalent long-term memory dynamical networks. Herein, we propose a new approach to control dynamical networks exhibiting long-term power-law memory dependencies. Our newly proposed method enables us to find the minimum number of driven nodes (i.e. the state vertices in the network that are connected to one and only one input) and their placement to control a long-term power-law memory dynamical network given a specific time-horizon, which we define as the ‘time-to-control’. Remarkably, we provide evidence that long-term power-law memory dynamical networks require considerably fewer driven nodes to steer the network’s state to a desired goal for any given time-to-control as compared with Markov dynamical networks. Finally, our method can be used as a tool to determine the existence of long-term memory dynamics in networks.

Resting-State EEG Microstates and Power Spectrum in Borderline Personality Disorder: A High-Density EEG Study

Borderline personality disorder (BPD) is a debilitating psychiatric condition characterized by emotional dysregulation, unstable sense of self, and impulsive, potentially self-harming behavior. In order to provide new neurophysiological insights on BPD, we complemented resting-state EEG frequency spectrum analysis with EEG microstates (MS) analysis to capture the spatiotemporal dynamics of large-scale neural networks. High-density EEG was recorded at rest in 16 BPD patients and 16 age-matched neurotypical controls. The relative power spectrum and broadband MS spatiotemporal parameters were compared between groups and their inter-correlations were examined. Compared to controls, BPD patients showed similar global spectral power, but exploratory univariate analyses on single channels indicated reduced relative alpha power and enhanced relative delta power at parietal electrodes. In terms of EEG MS, BPD patients displayed similar MS topographies as controls, indicating comparable neural generators. However, the MS temporal dynamics were significantly altered in BPD patients, who demonstrated opposite prevalence of MS C (lower than controls) and MS E (higher than controls). Interestingly, MS C prevalence correlated positively with global alpha power and negatively with global delta power, while MS E did not correlate with any measures of spectral power. Taken together, these observations suggest that BPD patients exhibit a state of cortical hyperactivation, represented by decreased posterior alpha power, together with an elevated presence of MS E, consistent with symptoms of elevated arousal and/or vigilance. This is the first study to investigate resting-state MS patterns in BPD, with findings of elevated MS E and the suggestion of reduced posterior alpha power indicating a disorder-specific neurophysiological signature previously unreported in a psychiatric population.

MICROSTATELAB: The EEGLAB Toolbox for Resting-State Microstate Analysis

Microstate analysis is a multivariate method that enables investigations of the temporal dynamics of large-scale neural networks in EEG recordings of human brain activity. To meet the enormously increasing interest in this approach, we provide a thoroughly updated version of the first open source EEGLAB toolbox for the standardized identification, visualization, and quantification of microstates in resting-state EEG data. The toolbox allows scientists to (i) identify individual, mean, and grand mean microstate maps using topographical clustering approaches, (ii) check data quality and detect outlier maps, (iii) visualize, sort, and label individual, mean, and grand mean microstate maps according to published maps, (iv) compare topographical similarities of group and grand mean microstate maps and quantify shared variances, (v) obtain the temporal dynamics of the microstate classes in individual EEGs, (vi) export quantifications of these temporal dynamics of the microstates for statistical tests, and finally, (vii) test for topographical differences between groups and conditions using topographic analysis of variance (TANOVA). Here, we introduce the toolbox in a step-by-step tutorial, using a sample dataset of 34 resting-state EEG recordings that are publicly available to follow along with this tutorial. The goals of this manuscript are (a) to provide a standardized, freely available toolbox for resting-state microstate analysis to the scientific community, (b) to allow researchers to use best practices for microstate analysis by following a step-by-step tutorial, and (c) to improve the methodological standards of microstate research by providing previously unavailable functions and recommendations on critical decisions required in microstate analyses.

Large-scale network dynamics underlying the first few hundred milliseconds after stimulus presentation: An investigation of visual recognition memory using iEEG.

Recognition memory is the ability to recognize previously encountered objects. Even this relatively simple, yet extremely fast, ability requires the coordinated activity of large-scale brain networks. However, little is known about the sub-second dynamics of these networks. The majority of current studies into large-scale network dynamics is primarily based on imaging techniques suffering from either poor temporal or spatial resolution. We investigated the dynamics of large-scale functional brain networks underlying recognition memory at the millisecond scale. Specifically, we analyzed dynamic effective connectivity from intracranial electroencephalography while epileptic subjects (n = 18) performed a fast visual recognition memory task. Our data-driven investigation using Granger causality and the analysis of communities with the Louvain algorithm spotlighted a dynamic interplay of two large-scale networks associated with successful recognition. The first network involved the right visual ventral stream and bilateral frontal regions. It was characterized by early, predominantly bottom-up information flow peaking at 115 ms. It was followed by the involvement of another network with predominantly top-down connectivity peaking at 220 ms, mainly in the left anterior hemisphere. The transition between these two networks was associated with changes in network topology, evolving from a more segregated to a more integrated state. These results highlight that distinct large-scale brain networks involved in visual recognition memory unfold early and quickly, within the first 300 ms after stimulus onset. Our study extends the current understanding of the rapid network changes during rapid cognitive processes.

GRL-PS: Graph Embedding-Based DRL Approach for Adaptive Path Selection

Forwarding path selection for data traffic is one of the most fundamental operations in computer networks, whose performance drastically impacts both transmission efficiency and reliability in network domains. Although deep reinforcement learning (DRL) has attracted considerable attention for path selection instead of hand-tuned heuristics, few works have considered how to exploit graph-structured information in networks to improve routing and forwarding efficiency. In fact, generating routes is essentially a process for finding a subgraph in a graph-structured network. To this end, this paper proposes an effective and novel graph embedding-based DRL framework for adaptive path selection (termed GRL-PS), aiming at reducing end-to-end (E2E) latency and promoting network throughput while maintaining stability in dynamically changing environments. Specifically, graph representation learning (GRL) is deployed as an effective enabler for the DRL agent to learn the relational knowledge of interacting entities for route decisions in networks. However, training such an agent in a dynamically changing environment encounters a knowledge acquisition bottleneck, since the DRL agent is always forced to learn every task from scratch. To improve the adaptation of behaviors and acquire skills beyond what the source policy can teach, we introduce potential-based reward shaping as a means of knowledge transfer to guide the agent in unfamiliar conditions with sparse rewards. Experimental results show that compared with baseline methods, our solution can achieve nearly-optimal performance with both latency and throughput, especially in large-scale dynamic networks.

EEG Microstates in Mood and Anxiety Disorders: A Meta-analysis

To reduce the psycho-social burden increasing attention has focused on brain abnormalities in the most prevalent and highly co-occurring neuropsychiatric disorders, such as mood and anxiety. However, high inter-study variability in these patients results in inconsistent and contradictory alterations in the fast temporal dynamics of large-scale networks as measured by EEG microstates. Thus, in this meta-analysis, we aim to investigate the consistency of these changes to better understand possible common neuro-dynamical mechanisms of these disorders.In the systematic search, twelve studies investigating EEG microstate changes in participants with mood and anxiety disorders and individuals with subclinical depression were included in this meta-analysis, adding up to 787 participants.The results suggest that EEG microstates consistently discriminate mood and anxiety impairments from the general population in patients and subclinical states. Specifically, we found a small significant effect size for B microstates in patients compared to healthy controls, with larger effect sizes for increased B presence in unmedicated patients with comorbidity. In a subgroup meta-analysis of ten mood disorder studies, microstate D showed a significant effect size for decreased presence. When investigating only the two anxiety disorder studies, we found a significantly small effect size for the increased microstate A and a medium effect size for decreased microstate E (one study). However, more studies are needed to elucidate whether these findings are diagnostic-specific markers.Results are discussed in relation to the functional meaning of microstates and possible contribution to an explanatory mechanism of overlapping symptomatology of mood and anxiety disorders.

New biophysical rate-based modeling of long-term plasticity in mean-field neuronal population models

The formation of customized neural networks as the basis of brain functions such as receptive field selectivity, learning or memory depends heavily on the long-term plasticity of synaptic connections. However, the current mean-field population models commonly used to simulate large-scale neural network dynamics lack explicit links to the underlying cellular mechanisms of long-term plasticity. In this study, we developed a new mean-field population model, the plastic density-based neural mass model (pdNMM), by incorporating a newly developed rate-based plasticity model based on the calcium control hypothesis into an existing density-based neural mass model. Derivation of the plasticity model was carried out using population density methods. Our results showed that the synaptic plasticity represented by the resulting rate-based plasticity model exhibited Bienenstock-Cooper-Munro-like learning rules. Furthermore, we demonstrated that the pdNMM accurately reproduced previous experimental observations of long-term plasticity, including characteristics of Hebbian plasticity such as longevity, associativity and input specificity, on hippocampal slices, and the formation of receptive field selectivity in the visual cortex. In conclusion, the pdNMM is a novel approach that can confer long-term plasticity to conventional mean-field neuronal population models.

Target layer state estimation in multilayer complex dynamical networks using functional observability

In large-scale complex dynamical networks, it is significant to estimate the states of target nodes with only a part of measured nodes. Meanwhile, multilayer complex dynamical networks exist widely in society and engineering. Therefore, it has important theoretic meaning and practical value to study the state estimation of target nodes in multilayer complex dynamical networks with limited node measurements. In this paper, with the measurable state information of a portion of nodes in one layer in the multilayer complex dynamical network, the state estimation of target nodes in other layers is studied. First, we build the model of the multilayer complex dynamical network which includes some target nodes and sensor nodes. Second, auxiliary nodes are selected by using the maximum matching principle in graph theory to construct the augmented node set. Third, we discuss the relationship between the minimum number of auxiliary nodes and interlayer connection probability in the multilayer complex dynamical network. Forth, an appropriate functional state observer is designed with limited number of measured nodes according to a typical model-based algorithm. Finally, numerical simulations are given to demonstrate the accuracy of the proposed method. The proposed method can achieve the accurate estimation with less placement of observers and fewer computational costs in the multilayer complex dynamical network.

Identification and analysis of autism spectrum disorder via large-scale dynamic functional network connectivity.

Autism spectrum disorder (ASD) is a prevalent neurodevelopmental disorder with severe cognitive impairment. Several studies have reported that brain functional network connectivity (FNC) has great potential for identifying ASD from healthy control (HC) and revealing the relationships between the brain and behaviors of ASD. However, few studies have explored dynamic large-scale FNC as a feature to identify individuals with ASD. This study used a time-sliding window method to study the dynamic FNC (dFNC) on the resting-state fMRI. To avoid arbitrarily determining the window length, we set a window length range of 10-75 TRs (TR = 2 s). We constructed linear support vector machine classifiers for all window length conditions. Using a nested 10-fold cross-validation framework, we obtained a grand average accuracy of 94.88% across window length conditions, which is higher than those reported in previous studies. In addition, we determined the optimal window length using the highest classification accuracy of 97.77%. Based on the optimal window length, we found that the dFNCs were located mainly in dorsal and ventral attention networks (DAN and VAN) and exhibited the highest weight in classification. Specifically, we found that the dFNC between DAN and temporal orbitofrontal network (TOFN) was significantly negatively correlated with social scores of ASD. Finally, using the dFNCs with high classification weights as features, we construct a model to predict the clinical score of ASD. Overall, our findings demonstrated that the dFNC could be a potential biomarker to identify ASD and provide new perspectives to detect cognitive changes in ASD.