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In many fields of science and technology we are confronted with complex networks. Making sense of these networks often require the ability to visualize and explore their intermingled structure consisting of nodes and links. To facilitate the identification of significant connectivity patterns, many methods have been developed based on the rearrangement of the nodes so as to avoid link criss-cross. However, real networks are often embedded in a geometrical space and the nodes code for an intrinsic physical feature of the system that one might want to preserve. For these spatial networks, it is therefore crucial to find alternative strategies operating on the links and not on the nodes. Here, we introduce Vizaj a javascript web application to render spatial networks based on optimized geometrical criteria that reshape the link profiles. While optimized for 3D networks, Vizaj can also be used for 2D networks and offers the possibility to interactively customize the visualization via several controlling parameters, including network filtering and the effect of internode distance on the link trajectories. Vizaj is further equipped with additional options allowing to improve the final aesthetics, such as the color/size of both nodes and links, zooming/rotating/translating, and superimposing external objects. Vizaj is an open-source software which can be freely downloaded and updated via a github repository. Here, we provide a detailed description of its main features and algorithms together with a guide on how to use it. Finally, we validate its potential on several synthetic and real spatial networks from infrastructural to biological systems. We hope that Vizaj will help scientists and practitioners to make sense of complex networks and provide aesthetic while informative visualizations., Competing Interests: The authors have declared that no competing interests exist., (Copyright: © 2023 Rolland, De Vico Fallani. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.)

Parametric resampling schemes have been recently introduced in complex network analysis with the aim of assessing the statistical significance of graph clustering and the robustness of community partitions. We propose here a method to replicate structural features of complex networks based on the non-parametric resampling of the transition matrix associated with an unbiased random walk on the graph. We test this bootstrapping technique on synthetic and real-world modular networks and we show that the ensemble of replicates obtained through resampling can be used to improve the performance of standard spectral algorithms for community detection.

The main purpose of electroencephalography (EEG)-based brain-computer interface (BCI) technology is to provide an alternative channel to support communication and control when motor pathways are interrupted. Despite the considerable amount of research focused on the improvement of EEG signal detection and translation into output commands, little is known about how learning to operate a BCI device may affect brain plasticity. This study investigated if and how sensorimotor rhythm-based BCI training would induce persistent functional changes in motor cortex, as assessed with transcranial magnetic stimulation (TMS) and high-density EEG. Motor imagery (MI)-based BCI training in naïve participants led to a significant increase in motor cortical excitability, as revealed by post-training TMS mapping of the hand muscle's cortical representation; peak amplitude and volume of the motor evoked potentials recorded from the opponens pollicis muscle were significantly higher only in those subjects who develop a MI strategy based on imagination of hand grasping to successfully control a computer cursor. Furthermore, analysis of the functional brain networks constructed using a connectivity matrix between scalp electrodes revealed a significant decrease in the global efficiency index for the higher-beta frequency range (22-29 Hz), indicating that the brain network changes its topology with practice of hand grasping MI. Our findings build the neurophysiological basis for the use of non-invasive BCI technology for monitoring and guidance of motor imagery-dependent brain plasticity and thus may render BCI a viable tool for post-stroke rehabilitation.

In the present work, we used the brain electroencephalografic activity as an alternative means to identify individuals. 50 healthy subjects participated to the study and 56 EEG signals were recorded through a high-density cap during one minute of resting state either with eyes open and eyes closed. By computing the power spectrum density (PSD) on segments of 10 seconds, we obtained a feature vector of 40 points, notably the PSD values in the standard frequency range (1-40 Hz), for each EEG channel. By using a naive Bayes classifier and K-fold cross-validations, we observed high correct recognition rates (CRR) at the parieto-occipital electrodes (~78% during eyes open, ~89% during eyes closed). Notably, the eyes closed resting state elicited the highest CRRs at the occipital electrodes (92% O2, 91% O1), suggesting these biometric characteristics as the most suitable, among those investigated here, for identifying individuals.

Partial Directed Coherence (PDC) is a powerful tool to estimate a frequency domain description of Granger causality between multivariate time series. One of the main limitation of this estimator, however, has been so far the criteria used to assess the statistical significance, which have been obtained through surrogate data approach or arbitrarily imposed thresholds. The aim of this work is to test the performances of a validation approach based on the rigorous asymptotic distributions of PDC, recently proposed in literature. The performances of this method, defined in terms of percentages of false positives and false negatives, were evaluated by means of a simulation study taking into account factors like the Signal to Noise Ratio (SNR) and the amount of data available for the estimation and the use of different methods for the statistical corrections for multiple comparisons. Results of the Analysis Of Variance (ANOVA) performed on false positives and false negatives revealed a strong dependency of the performances from all the factors investigated. In particular, results indicate an amount of Type I errors below 7% for all conditions, while Type II errors are below 10% when the SNR is at least 1, the data length of at least 50 seconds and the appropriate correction for multiple comparisons is applied.

In this paper, different linear and nonlinear methodologies for the estimation of cortical connectivity from neuroelectric and hemodynamic measurements are reviewed and applied on common data set in order to highlight similarities and differences in the results. Different effective and functional connectivity methods were applied to motor and cognitive data sets, including structural equation modeling (SEM), directed transfer function (DTF), partial directed coherence (PDC), and direct directed transfer function (dDTF). Comparisons were made between the results in order to understand if, for a same dataset, effective and functional connectivity estimators can return the same cortical connectivity patterns. An application of a nonlinear method [phase synchronization index (PSI)] to similar executed and imagined movements was also reviewed. Connectivity patterns estimated with the use of the neuroelectric information and of the information from the multimodal integration of neuroelectric and hemodynamic data were also compared. Results suggests that the estimation of the cortical connectivity patterns performed with the linear methods (SEM, DTF, PDC, dDTF) or with the nonlinear method (PSI) on movement related potentials returned similar cortical networks. Differences in cortical connectivity were noted between the patterns estimated with the use of multimodal integration and those estimated by using only the neuroelectric data.

In this paper we illustrate the capability of tracking brain activity during the observation of commercial TV spots by using advanced high resolution EEG statistical techniques in time and frequency domains. In particular, we analyzed the statistically significant cortical spectral power activity in different frequency bands during the observation of a commercial video clip related to the use of a beer in a group of 13 normal subjects. In addition, a TV speech of the prime minister of Italy was analyzed in two groups of swing and "supporter" voters. Results suggested that the cortical activity during the observation of commercial spots could vary consistently across the spot. This fact suggest the possibility to remove the part of the spot that are not particularly attractive by using those cerebral indexes. The cortical activity during the observation of the political speech indicated a major cortical activity in the supporters group when compared to the swing voters. In this case, it is possible to conclude that the communication proposed has failed to raise attention or interest on swing voters. In conclusions, high resolution EEG have been proved able to generate useful insights about the particular fruition of TV messages, related to both commercial as well as political fields.

The extraction of the salient characteristics from brain connectivity patterns is an open challenging topic since often the estimated cerebral networks have a relative large size and complex structure. Since a graph is a mathematical representation of a network, which is essentially reduced to nodes and connections between them, the use of a theoretical graph approach would extract significant information from the functional brain networks estimated through different neuroimaging techniques. The present work intends to support the development of the "brain network analysis:" a mathematical tool consisting in a body of indexes based on the graph theory able to improve the comprehension of the complex interactions within the brain. In the present work, we applied for demonstrative purpose some graph indexes to the time-varying networks estimated from a set of high-resolution EEG data in a group of healthy subjects during the performance of a motor task. The comparison with a random benchmark allowed extracting the significant properties of the estimated networks in the representative Alpha (7-12 Hz) band. Altogether, our findings aim at proving how the brain network analysis could reveal important information about the time-frequency dynamics of the functional cortical networks.

The present work intends to evaluate the dynamics of the cerebral networks during the preparation and the execution of the foot movement. In order to achieve this objective, we have used mathematical tools capable of estimating the cortical activity via high-resolution EEG techniques. Afterwards we estimated, the instantaneous relationships occurring among the time-series of sixteen regions of interest (ROIs) in the Alpha (7-12 Hz) and Beta (13-29 Hz) band through the adaptive multivariate autoregressive models. Eventually, we evaluated the weighted-topology of the cerebral networks by calculating some theoretical graph indexes. The results show that the main structural changes are encoded in the highest spectral contents (Beta band). In particular, during the execution of the foot movement the cingulate motor areas (CM) work as network "hubs" presenting a large amount of outgoing links to the other ROIs. Moreover, the connectivity pattern changes its structure according to the different temporal stages of the task. In particular, the communication between the ROIs reaches its highest level of efficiency during the preparation of the foot movement, as revealed by the "small-world" property of the network, which is characterized by the presence of abundant clustering connections combined with short average distances between the cortical areas.

Eye movements and blinks may produce unusual voltage changes that propagates from the eyeball through the head as volume conductor up to the scalp electrodes, generating severe electroencephalographic artifacts. Several methods are now available to correct the distortion induced by these events on the EEG, having different advantages and drawbacks. The main focus of this work is to quantify the performance of the removal of EOG artifact due to the application of the independent component analysis (ICA) methodology. The precise quantification of the effects of artifact removal by ICA is possible by using a simulation setup, with a realistic head model, that it is able to mimic the occurrence of an eye blink. The electrical activity generated by the simulated eyeblink were propagated through the realistic head model and superimposed to a clean segment of EEG. Then, artifact removal was performed by using the ICA approach. Ocular artifact removal was evaluated in different operative conditions, characterized by different signal to noise ratio and number of electrodes. The error measures used were the relative error and the correlation coefficient between the clear, original EEG segment and those obtained after the application of the ICA procedure.

The Directed Transfer Function (DTF) and the Partial Directed Coherence (PDC) are frequency-domain estimators, based on the multivariate autoregressive modelling (MVAR) of time series, that are able to describe interactions between cortical areas in terms of the concept of Granger causality. However, the classical estimation of these methods requires the stationary of the signals. In this way, transient pathways of information transfer remains hidden. The objective of this study is to test a time-varying multivariate method for the estimation of rapidly changing connectivity relationships between cortical areas of the human brain, based on DTF/PDC and on the use of adaptive MVAR modelling (AMVAR). This approach will allow the observation of transient influences between the cortical areas during the execution of a task. Time-varying DTF and PDC were obtained by the adaptive recursive fit of an MVAR model with time-dependent parameters, by means of a generalized recursive least-square (RLS) algorithm, taking into consideration a set of EEG epochs. Simulations were performed under different levels of Signal to Noise Ratio (SNR), number of trials (TRIALS) and frequency bands (BAND), and of different values of the RLS adaptation factor adopted (factor C). The results indicated that time-varying DTF and PDC are able to estimate correctly the imposed connectivity patterns under reasonable operative conditions of SNR ad number of trials. Moreover, the capability of follow the rapid changes in connectivity is highly increased by the number of trials at disposal, and by the right choice of the value adopted for the adaptation factor C. The results of the simulation study indicate that DTF and PDC computed on adaptive MVAR can be effectively used to estimate time-varying patterns of functional connectivity between cortical activations, under general conditions met in practical EEG recordings.