The relation between parietal GABA concentration and numerical skills

Several scientific, engineering, and medical advancements are based on breakthroughs made by people who excel in mathematics. Our current understanding of the underlying brain networks stems primarily from anatomical and functional investigations, but our knowledge of how neurotransmitters subserve numerical skills, the building block of mathematics, is scarce. Using 1H magnetic resonance spectroscopy (N = 54, 3T, semi-LASER sequence, TE = 32 ms, TR = 3.5 s), the study examined the relation between numerical skills and the brain’s major inhibitory (GABA) and excitatory (glutamate) neurotransmitters. A negative association was found between the performance in a number sequences task and the resting concentration of GABA within the left intraparietal sulcus (IPS), a key region supporting numeracy. The relation between GABA in the IPS and number sequences was specific to (1) parietal but not frontal regions and to (2) GABA but not glutamate. It was additionally found that the resting functional connectivity of the left IPS and the left superior frontal gyrus was positively associated with number sequences performance. However, resting GABA concentration within the IPS explained number sequences performance above and beyond the resting frontoparietal connectivity measure. Our findings further motivate the study of inhibition mechanisms in the human brain and significantly contribute to our current understanding of numerical cognition's biological bases.

Comparison of undirected frequency-domain connectivity measures for cerebro-peripheral analysis

Analyses of cerebro-peripheral connectivity aim to quantify ongoing coupling between brain activity (measured by MEG/EEG) and peripheral signals such as muscle activity, continuous speech, or physiological rhythms (such as pupil dilation or respiration). Due to the distinct rhythmicity of these signals, undirected connectivity is typically assessed in the frequency domain. This leaves the investigator with two critical choices, namely a) the appropriate measure for spectral estimation (i.e., the transformation into the frequency domain) and b) the actual connectivity measure. As there is no consensus regarding best practice, a wide variety of methods has been applied. Here we systematically compare combinations of six standard spectral estimation methods (comprising fast Fourier and continuous wavelet transformation, bandpass filtering, and short-time Fourier transformation) and six connectivity measures (phase-locking value, Gaussian-Copula mutual information, Rayleigh test, weighted pairwise phase consistency, magnitude squared coherence, and entropy). We provide performance measures of each combination for simulated data (with precise control over true connectivity), a single-subject set of real MEG data, and a full group analysis of real MEG data. Our results show that, overall, wppc and gcmi tend to outperform other connectivity measures, while entropy was the only measure sensitive to bimodal deviations from a uniform phase distribution. For group analysis, choosing the appropriate spectral estimation method appeared to be more critical than the connectivity measure. We discuss practical implications (sampling rate, SNR, computation time, and data length) and aim to provide recommendations tailored to particular research questions.

Single-Trial Kernel-Based Functional Connectivity for Enhanced Feature Extraction in Motor-Related Tasks

Motor learning is associated with functional brain plasticity, involving specific functional connectivity changes in the neural networks. However, the degree of learning new motor skills varies among individuals, which is mainly due to the between-subject variability in brain structure and function captured by electroencephalographic (EEG) recordings. Here, we propose a kernel-based functional connectivity measure to deal with inter/intra-subject variability in motor-related tasks. To this end, from spatio-temporal-frequency patterns, we extract the functional connectivity between EEG channels through their Gaussian kernel cross-spectral distribution. Further, we optimize the spectral combination weights within a sparse-based ℓ2-norm feature selection framework matching the motor-related labels that perform the dimensionality reduction of the extracted connectivity features. From the validation results in three databases with motor imagery and motor execution tasks, we conclude that the single-trial Gaussian functional connectivity measure provides very competitive classifier performance values, being less affected by feature extraction parameters, like the sliding time window, and avoiding the use of prior linear spatial filtering. We also provide interpretability for the clustered functional connectivity patterns and hypothesize that the proposed kernel-based metric is promising for evaluating motor skills.

Methods to Measure the Network Path Connectivity

The functionalities, such as connectivity and communication capability of complex networks, are related to the number and length of paths between node pairs in the networks. In this paper, we propose a new path connectivity measure by considering the number and length of paths of the network (PCNL) to evaluate network path connectivity. By comparing the PCNL with the typical natural connectivity, we prove the effectiveness of the PCNL to measure the path connectivity of networks. Because of the importance of the shortest paths, we further propose the shortest paths connectivity measure (SPCNL) based on the number and length of the shortest paths. Then, we use edge-betweenness-based malicious attacks to study the relationship between the SPCNL and network topology in five types of networks. The results show that the SPCNLs of the networks have a significant corresponding relationship and similar changing trend with their network topology heterogeneities with the increase of the number of deleted edges. These findings mean that the SPCNL is positively correlated with the heterogeneity of the network topology, which provides a new perspective for designing complex networks with high path connectivity.

Mean-field modeling of brain-scale dynamics for the evaluation of EEG source-space networks

Understanding the dynamics of brain-scale functional networks at rest and during cognitive tasks is the subject of intense research efforts to unveil fundamental principles of brain functions. To estimate these large-scale brain networks, the emergent method called “electroencephalography (EEG) source connectivity” has generated increasing interest in the network neuroscience community, due to its ability to identify cortical brain networks with good spatio-temporal resolution, while reducing mixing and volume conduction effects. However, the method is still immature and several methodological issues should be carefully accounted for to avoid pitfalls. Therefore, optimizing the EEG source connectivity pipelines is required, which involves the evaluation of several parameters. One key issue to address those evaluation aspects is the availability of a ‘ground truth’. In this paper, we show how a recently developed large-scale model of brain-scale activity, named COALIA, can provide to some extent such ground truth by providing realistic simulations (epileptiform activity) of source-level and scalp-level activity. Using a bottom-up approach, the model bridges cortical micro-circuitry and large-scale network dynamics. Here, we provide an example of the potential use of COALIA to analyze the effect of three key factors involved in the “EEG source connectivity” pipeline: (i) EEG sensors density, (ii) algorithm used to solve the inverse problem, and (iii) functional connectivity measure. Results show that a high electrode density (at least 64 channels) is needed to accurately estimate cortical networks. Regarding the inverse solution/connectivity measure combination, the best performance at high electrode density was obtained using the weighted minimum norm estimate (wMNE) combined with the weighted phase lag index (wPLI). The COALIA model and the simulations used in this paper are freely available and made accessible for the community. We believe that this model-based approach will help researchers to address some current and future cognitive and clinical neuroscience questions, and ultimately transform EEG brain network imaging into a mature technology.

{1,2,3}-Restricted Connectivity of $(n,k)$-Enhanced Hypercubes

The connectivity of a graph is a classic measure for fault tolerance of the network. Restricted connectivity measure is a crucial subject for a multiprocessor system’s ability to tolerate fault processors, and improves the connectivity measurement accuracy. Furthermore, if a network possesses a restricted connectivity property, it is more reliable with a lower vertex failure rate compared with other networks. The $\left (n,k\right )$-dimensional enhanced hypercube, denoted by $Q_{n,k}$, a variant of hypercube, which is a well-known interconnection network. In this paper, we analyze the fault tolerant properties for $\left (n,k\right )$-enhanced hypercube, and establish the $1$-restricted connectivity of $Q_{n,k} (n\ge k+1)$ and $\{2,3\}$-restricted connectivity of $(n,k)$-enhanced hypercube $Q_{n,k} (n=k+1)$. Furthermore, we propose the tight upper bound of $\{2,3\}$-restricted connectivity of $Q_{n,k} (n> k+1)$. Moreover, we show many figures to better illustrate the process of the proofs.

Identifying multiple vulnerable areas of infrastructure network under global connectivity measure

Infrastructure networks provide significant services for our society. Nevertheless, high dependence on physical infrastructures makes infrastructure networks vulnerable to disasters or intentional attacks which being considered as geographically related failures that happened in specific geographical locations and result in failures of neighboring network components. To provide comprehensive network protection against failures, vulnerability of infrastructure network needs to be assessed with various network performance measures. However, when considering about multiple vulnerable areas, available researches just employ measure of total number of affected edges while neglecting edges’ different topologies. In this paper, we focus on identifying multiple vulnerable areas under global connectivity measure: Size Ratio of the Giant Component (SRGC). Firstly, Deterministic Damage Circle Model and Multiple Barycenters Method are presented to determine damage impact and location of damage region. For solving the HP-hard problem of identifying multiple optimal attacks, we transform the problem into combinational optimization problem and propose a mixed heuristic strategy consisted of both Greedy Algorithm and Genetic Algorithm to attain the optimal solution. We obtain numerical results for real-world infrastructure network, thereby demonstrating the effectiveness and applicability of the presented strategy and algorithms. The distinctive results of SRGC indicate the necessity and significance of considering global connectivity measure in assessing vulnerability of infrastructure networks.