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In recent years complexity of the brain structure in healthy and disordered subjects has been studied increasingly. But to the best of the authors' knowledge, researchers so far have investigated the structural complexity only in the context of two restricted networks known as Small-World and Scale-free networks; whereas other aspects of the structural complexity of brain activities may be affected by aging and neurodegenerative disorders such as the Alzheimer's disease and autism spectrum disorder. In this study, two general complexity metrics of graphs, Graph Index Complexity and Offdiagonal Complexity are proposed as general measures of complexity, not restricted to SWN only. They are adopted to measure the structural complexity of the weighted graphs instead of the common binary graphs. Fuzzy Synchronization Likelihood is applied to the EEGs and their sub-bands, as a functional connectivity metric of the brain, to construct the functional connectivity graphs. Two applications are used to evaluate the efficacy of the complexity measures: diagnosis of autism and aging, both based on EEG. It was discovered that the Graph Index Complexity of gamma band is discriminative in distinguishing autistic children from non-autistic children. Also, Offdiagonal Complexity of theta band in young subjects was observed to be significantly different than old subjects. This study shows that changes in the structure of functional connectivity of brain in disorders and different healthy states can be revealed by unrestricted metrics of graph complexity. While the applications presented in this paper are based on EEG, the approach is general and can be used with other modalities such as fMRI, MEG, etc. Further, it can be used to study every other neurological and psychiatric disorder.

Objective To explore how the global organization or topology of the functional brain connectivity (FBC) is affected in Down Syndrome (DS). Methods As the brain is a highly complex network including numerous nonlinearly interacted neuronal areas, the FBCs of typically developing (TD) children and DS patients were computed using a nonlinear synchronization method. Then the differences in global organization of the obtained FBCs of the two groups were analyzed, in all electroencephalogram (EEG) frequency bands, in the framework of Small-Worldness Network (a network with optimum balance between segregation and integration of information). Results The topology of the functional connectivity of DS patients is disrupted in the whole brain in alpha and theta bands, and especially in the left intra-hemispheric brain networks in upper alpha band. Conclusions The global organization of the DS brain does not resemble a Small-World network, but it works as a random network. Significance It is the first study on global organization of the FBC in DS.

This study was carried out to determine linear and nonlinear changes of brain dynamics and their relationships with the motor dysfunctions in CP children. For this purpose power of EEG frequency bands (as a linear analysis) and EEG fractality (as a nonlinear analysis) were computed in eyes-closed resting state and statistically compared between 26 CP and 26 normal children. Based on these characteristics accuracy of the classification between the two groups was obtained by enhanced probabilistic neural network (EPNN). Severity of gross motor and manual disabilities was determined by standard systems and the relation between the deficient brain dynamics and severity of the motor dysfunctions was obtained by Pearson's correlation coefficient. A definitely higher delta and lower theta and alpha powers, and higher EEG complexity in CP patients. As such a high accuracy of 94.8% in distinguishing the two groups was obtained. Moreover significant positive correlations were found between beta power and severity of manual disabilities and gross motor dysfunctions in the boys with CP. It is concluded that the obtained brain dynamics' characteristics are useful in diagnosis of CP. Furthermore severity of the motor dysfunctions in boys with CP could be evaluated by the beta activity.

Recently, the visibility graph (VG) algorithm was proposed for mapping a time series to a graph to study complexity and fractality of the time series through investigation of the complexity of its graph. The visibility graph algorithm converts a fractal time series to a scale-free graph. VG has been used for the investigation of fractality in the dynamic behavior of both artificial and natural complex systems. However, robustness and performance of the power of scale-freeness of VG (PSVG) as an effective method for measuring fractality has not been investigated. Since noise is unavoidable in real life time series, the robustness of a fractality measure is of paramount importance. To improve the accuracy and robustness of PSVG to noise for measurement of fractality of time series in biological time-series, an improved PSVG is presented in this paper. The proposed method is evaluated using two examples: a synthetic benchmark time series and a complicated real life Electroencephalograms (EEG)-based diagnostic problem, that is distinguishing autistic children from non-autistic children. It is shown that the proposed improved PSVG is less sensitive to noise and therefore more robust compared with PSVG. Further, it is shown that using improved PSVG in the wavelet-chaos neural network model of Adeli and c-workers in place of the Katz fractality dimension results in a more accurate diagnosis of autism, a complicated neurological and psychiatric disorder.

EEGs of the frontal brain of patients diagnosed with major depressive disorder (MDD) have been investigated in recent years using linear methods but not based on nonlinear methods. This paper presents an investigation of the frontal brain of MDD patients using the wavelet-chaos methodology and Katz's and Higuchi's fractal dimensions (KFD and HFD) as measures of nonlinearity and complexity. EEGs of the frontal brain of healthy adults and MDD patients are decomposed into 5 EEG sub-bands employing a wavelet filter bank, and the FDs of the band-limited as well as those of their 5 sub-bands are computed. Then, using the ANOVA statistical test, HFDs and KFDs of the left and right frontal lobes in EEG full-band and sub-bands of MDD and healthy groups are compared in order to discover the FDs showing the most meaningful differences between the two groups. Finally, the discovered FDs are used as input to a classifier, enhanced probabilistic neural network (EPNN), to discriminate the MDD from healthy EEGs. The results of HFD show higher complexity of left, right and overall frontal lobes of the brain of MDD compared with non-MDD in beta and gamma sub-bands. Moreover, it is observed that HFD of the beta band is more discriminative than HFD of the gamma band for discriminating MDD and non-MDD participants, while the KFD did not show any meaningful difference. A high accuracy of 91.3% is achieved for classification of MDD and non-MDD EEGs based on HFDs of left, right, and overall frontal brain beta sub-band. The findings of this research, however, should be considered tentative because of limited data available to the authors.

Neurofeedback training is increasingly used for ADHD treatment. However some ADHD patients are not treated through the long-time neurofeedback trainings with common protocols. In this paper a new graph theoretical approach is presented for EEG-based prediction of ADHD patients’ responses to a common neurofeedback training: rewarding SMR activity (12–15 Hz) with inhibiting theta activity (4–8 Hz) and beta2 activity (18–25 Hz). Eyes closed EEGs of two groups before and after neurofeedback training were studied: ADHD patients with (15 children) and without (15 children) positive response to neurofeedback training. Employing a recent method to measure synchronization, fuzzy synchronization likelihood, functional connectivity graphs of the patients’ brains were constructed in the full-band EEGs and 6 common EEG sub-bands produced by wavelet decomposition. Then, efficiencies of the brain networks in synchronizability and high speed information transmission were computed based on mean path length of the graphs, before and after neurofeedback training. The results were analyzed by ANOVA and showed synchronizability of the neocortex activity network at beta band in ADHDs with positive response is obviously less than that of ADHDs resistant to neurofeedback therapy, before treatment. The accuracy of linear discriminant analysis (LDA) in distinguishing these patients based on this feature is so high (84.2%) that this feature can be considered as reliable characteristics for prediction of responses of ADHDs to the neurofeedback trainings. Also difference between flexibility of the neocortex in beta band before and after treatment is obviously larger in the ADHDs with positive response in comparison to those with negative response which may be a neurophysiologic reason for dissatisfaction of the last group to the neurofeedback therapy.

Synchronization is defined as interdependencies among coupled dynamic systems. In most coupled systems the intrinsic and internal variants, and the interdependencies among their subsystems are not accessible. Therefore, in order to quantify the interdependencies among the coupled systems, attempts have been made through measuring the synchronization between their outputs represented mostly as time series. In this paper a new method, called Visibility Graph Similarity (VGS), is presented as a method of measuring Generalized Synchronization. First, each time series is reconstructed as a trajectory in a state space. Next, a Distance Time Series (DTS) is created from a sequence of relative distances of the states to a reference state. Subsequently, a visibility graph (VG) is constructed using DTS. Then, a sequence of degrees of the VG, called Degree Sequence (DS), is obtained. Correlation of the DSs of two coupled systems is called VGS and is presented as a measurement of similarity of dynamics of the coupled systems. The synchronization measurement performance of the VGS is compared with synchronization likelihood (SL) and the classical cross correlation method using two identical and non-identical models of two coupled Henon map over the entire time domain. Also, it is compared with SL for tracing temporal synchronization using both models. It is shown that VGS provides a more accurate measure of the overall synchronization compared with SL. It is more reliable for measuring weak couplings compared with the cross correlation method. Moreover, VGS uses fewer parameters and detects the temporal synchronization sooner than the SL.

Transcranial electrical stimulation is a popular method to modulate brain activity by applying a low electric field to the skull. Despite this, its long-term effects are still ill understood. In this study, we applied anodal transcranial direct current stimulation to the visual cortex of mice while presenting visual stimuli. We used the genetically encoded calcium indicator GCaMP6 to measure the effect of current stimulation on the response in the visual cortex. We found a strong direct increase in the visual response when concurrently applying tDCS. We did not find a lasting effect of the stimulation during an imaging session. However, when we repeated tDCS for four sessions at two days intervals, we found an increase in the visual response in the visual cortex. This increased responses was not specific to the grating stimulus which was coupled to the anodal stimulation, but was also seen for an orthogonal grating presented without electrical stimulation. A similar increase was not found in mice repeatedly imaged without tDCS. We conclude that anodal tDCS of the visual cortex can cause LTP-like plasticity of visual responses.