![]() ![]() Mental fatigue has become one of the most significant causes of traffic accidents. Mental fatigue, referring to a state of reduced mental alertness and impaired performances, is often associated with worsening performance on cognitive tasks, such as increased propensities for errors and slowed reaction times. However, the meaning of maximum eigenvalue in BFN analysis and the relationship between maximum eigenvalue and network characters in different network types with the same mean degree are still not explicitly revealed by the previous studies. It has been also reported that a bigger maximum eigenvalue of AMs means more numbers of functional connectivities (network edges) in the corresponding BFNs, resulting in a larger degree and clustering coefficient and smaller characteristic path length. Existing works indicate that the spectra of large-scale networks turn out to obey characteristic power-law distribution on the basis of the spectral analysis of the networks. The eigenvalues, defined as the spectra of the AM, are supposed to contain a wealth of information in regard to network features. They believe that the topological structure of BFN can be completely depicted by the corresponding AM. In addition, some other researchers concentrate on the adjacency matrix (AM) of BFN. BFN has become a widely-used method to study the brain sciences. These BFN characters have been applied to explore the changes in brain functions, such as the normal subjects that in different states, that with different education levels, that in different age stages, and that at different sleep stages, as well as the subjects that suffering from mental disorders. Commonly explored BFN characters involve the degree, centrality, characteristic path length, clustering coefficient, and efficiency. For the establishment of BFNs, some methods of measuring the functional connectivity between different brain regions have been used, such as cross correlation, partial correlation, Pearson correlation, coherence, mutual information (MI), synchronization likelihood, etc. ![]() The mapping techniques of the BFNs is mainly based on the data of electroencephalogram (EEG), magnetoencephalogram (MEG), positron emission tomography (PET), functional magnetic resonance imaging (fMRI), near infrared reflectance spectroscopy (NIRS), etc. It should ignore some technical details when constructing BFNs, such as the size, location, and shape of the network node, and the physical distance and geometric shapes of the connective edge. What is more, the maximum eigenvalue, which increased with the deepening of mental fatigue, can become a good indicator for mental fatigue estimation.īrain functional network (BFN), as one type of the complex networks, is a demonstration of the temporal and topological correlations among different brain regions in the processes of brain neural activities. Interestingly, the maximum eigenvalue of AM was always a little larger than that of the corresponding random matrix (RM), and had an obvious linearity with the sum of the AM elements, indicating that the maximum eigenvalue can be able to distinguish the network structures which have the same mean degree. The results indicated that large maximum eigenvalue means more edges in the corresponding network, along with a high degree and a short characteristic path length both in weighted and binary BFNs. Both maximum eigenvalue and corresponding network characters in BFNs and RNs were considered to explore the changes during the formation of mental fatigue. To this end, AM was constructed using mutual information (MI) to determine the functional connectivity with electroencephalogram (EEG) data recorded with a mental fatigue model, and then was converted into both binary and weighted brain functional network (BFN) and corresponding random networks (RNs). An experimental study focused on revealing the meaning and application of the maximum eigenvalue is missing. ![]() I'm also trying to use information hiding, so I have my code divided into two different files: a header file containing type definitions and function prototypes and a file containing code.The maximum eigenvalue of the adjacency matrix (AM) has been supposed to contain rich information about the corresponding network. I'm writing my own Matrix type version in C programming language.
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