Small-world Properties Research Articles

Topological disruption of low- and high-order functional networks in presbycusis.

Prior efforts have manifested that functional connectivity (FC) network disruptions are concerned with cognitive disorder in presbycusis. The present research was designed to investigate the topological reorganization and classification performance of low-order functional connectivity (LOFC) and high-order functional connectivity (HOFC) networks in patients with presbycusis. Resting-state functional magnetic resonance imaging (Rs-fMRI) data were obtained in 60 patients with presbycusis and 50 matched healthy control subjects (HCs). LOFC and HOFC networks were then constructed, and the topological metrics obtained from the constructed networks were compared to evaluate topological differences in global, nodal network metrics, modularity and rich-club organization between patients with presbycusis and HCs. The use of HOFC profiles boosted presbycusis classification accuracy, sensitivity and specificity compared to that using LOFC profiles. The brain networks in both patients with presbycusis and HCs exhibited small-world properties within the given threshold range, and striking differences between groups in topological metrics were discovered in the constructed networks (LOFC and HOFC). NBS analysis identified a subnetwork involving 26 nodes and 23 signally altered internodal connections in patients with presbycusis in comparison to HCs in HOFC networks. This study highlighted the topological differences between LOFC and HOFC networks in patients with presbycusis, suggesting that HOFC profiles may help to further identify brain network abnormalities in presbycusis.

Navigating the Mental Lexicon: Network Structures, Lexical Search and Lexical Retrieval

This paper examines the implications of the association patterns in our understanding of the mental lexicon. By applying the principles of graph theory to word association data, we intend to explore which measures tap better into lexical knowledge. To that end, we had different groups of English as Foreign language learners complete a lexical fluency task. Based on these empirical data, a study was undertaken on the corresponding lexical availability graph (LAG). It is observed that the aggregation (mentioned through human coding) of all lexical tokens on a given topic allows the emergence of some lexical-semantic patterns. The most important one is the existence of some key terms, featuring both high centrality in the sense of network theory and high availability in the LAG, which define a hub of related terms. These communities of words, each one organized around an anchor term, or most central word, are nicely apprehended by a well-known network metric called modularity. Interestingly enough, each module seems to describe a conceptual class, showing that the collective lexicon, at least as approximated by LA Graphs, is organised and traversed by semantic mechanisms or associations via hyponymy or hiperonymy, for instance. Another empirical observation is that these conceptual hubs can be appended, resulting in high diameters compared to same-sized random graphs; even so it seems that the small-world hypothesis holds in LA Graphs, as in other social and natural networks.

Construction and Analysis of a New Resting-State Whole-Brain Network Model.

Mathematical modeling and computer simulation are important methods for understanding complex neural systems. The whole-brain network model can help people understand the neurophysiological mechanisms of brain cognition and functional diseases of the brain. In this study, we constructed a resting-state whole-brain network model (WBNM) by using the Wendling neural mass model as the node and a real structural connectivity matrix as the edge of the network. By analyzing the correlation between the simulated functional connectivity matrix in the resting state and the empirical functional connectivity matrix, an optimal global coupling coefficient was obtained. Then, the waveforms and spectra of simulated EEG signals and four commonly used measures from graph theory and small-world network properties of simulated brain networks under different thresholds were analyzed. The results showed that the correlation coefficient of the functional connectivity matrix of the simulated WBNM and empirical brain networks could reach a maximum value of 0.676 when the global coupling coefficient was set to 20.3. The simulated EEG signals showed rich waveform and frequency-band characteristics. The commonly used graph-theoretical measures and small-world properties of the constructed WBNM were similar to those of empirical brain networks. When the threshold was set to 0.22, the maximum correlation between the simulated WBNM and empirical brain networks was 0.709. The constructed resting-state WBNM is similar to a real brain network to a certain extent and can be used to study the neurophysiological mechanisms of complex brain networks.

Collaboration and Competition: A Social Network Analysis of Thailand’s Music Industry

This study quantitatively investigates the collaborative framework and competitive landscape of Thailand’s evolving music industry, driven by technological progress and changing consumer preferences. By examining data obtained from Thailand’s Department of Intellectual Property, specifically 138,868 songs, it explores the complex network of relationships among music creators, artists, and various rights-holders, including those associated with recording, music, melodies, and lyrics. Utilizing social network analysis, this research uncovers a power law distribution in these networks, reflecting a scale-free market configuration. This characteristic is marked by a few dominant players exercising considerable market influence, contrasted with numerous less-interconnected participants. This investigation notes regular patterns of collaboration between artists and different rights-holders. Furthermore, the network of music creators displays small-world properties, with short collaborative distances fostering efficient information exchange and creative synergy. Crucially, this study identifies key influential players instrumental in directing the industry’s major trends, highlighting their role in market concentration. These significant findings will provide critical evidence for informing future policy development aimed at improving efficiency and equity in the digital content industries.

Synchronization of scale-free neuronal network with small-world property induced by spike-timing-dependent plasticity under time delay

Spike-timing-dependent plasticity (STDP) is one of the important rules for the change of synaptic weights between neurons in biological nervous systems. In this paper, we study the effect of STDP on the synchronization phenomenon induced by time delay in the neuronal network which is the scale-free network with small-world property, and nodes of the network are constructed by Izhikevich neuron and connected by chemical synapses. For appropriate time delay values, there exists an optimal range of STDP maximum weight value in which the synchronization of the network is better, and in addition the synchronization is decreased with the increasing of STDP maximum weight value. The network with high synchronization has a centralized distribution of synaptic weights within it, while conversely, an unsynchronized network has a more discrete distribution of synaptic weights. When the STDP maximum weight value is too small, the collective firing pattern of network is not affected by synaptic current, and the synchronization of the network is also not affected. Interestingly, comparing with the small-world network and the scale-free network, it is found that a network has a smaller range of optimal STDP maximum weight values when the network is of larger average clustering coefficient, shorter average shortest path length, and higher small-world property. Our results can illuminate the potential significance of STDP for information processing and transmission in the nervous system.

Alterations in the brain functional network of abstinent male individuals with methamphetamine use disorder.

Methamphetamine is a highly addictive psychostimulant drug that is abused globally and is a serious threat to health worldwide. Unfortunately, the specific mechanism underlying addiction remains unclear. Thus, this study aimed to investigate the characteristics of functional connectivity in the brain network and the factors influencing methamphetamine use disorder in patients using magnetic resonance imaging. We included 96 abstinent male participants with methamphetamine use disorder and 46 age- and sex-matched healthy controls for magnetic resonance imaging. Compared with healthy controls, participants with methamphetamine use disorder had greater impulsivity, fewer small-world attributes of the resting-state network, more nodal topological attributes in the cerebellum, greater functional connectivity strength within the cerebellum and between the cerebellum and brain, and decreased frontoparietal functional connectivity strength. In addition, after controlling for covariates, the partial correlation analysis showed that small-world properties were significantly associated with methamphetamine use frequency, psychological craving, and impulsivity. Furthermore, we revealed that the small-word attribute significantly mediated the effect of methamphetamine use frequency on motor impulsivity in the methamphetamine use disorder group. These findings may further improve our understanding of the neural mechanism of impulse control dysfunction underlying methamphetamine addiction and assist in exploring the neuropathological mechanism underlying methamphetamine use disorder-related dysfunction and rehabilitation.

Mapping individual structural covariance network in development brain with dynamic time warping.

A conspicuous property of brain development or maturity is coupled with coordinated or synchronized brain structural co-variation. However, there is still a lack of effective approach to map individual structural covariance network. Here, we developed a novel individual structural covariance network method using dynamic time warping algorithm and applied it to delineate developmental trajectories of topological organizations of structural covariance network from childhood to early adulthood with a large sample of 655 individuals from Human Connectome Project-Development dataset. We found that the individual structural covariance network exhibited small-worldness property and the network global topological characteristics including small-worldness, global efficiency, local efficiency, and modularity linearly increase with age while the shortest path length linearly decreases with age. The nodal topological properties including betweenness and degree increased with age in language and emotion regulation related brain areas, while it decreased with age mainly in visual cortex, sensorimotor area, and hippocampus. Moreover, the topological attributes of structural covariance network as features could predict the age of each individual. Taken together, our results demonstrate that dynamic time warping can effectively map individual structural covariance network to uncover the developmental trajectories of network topology, which may facilitate future investigations to establish the links of structural co-variations with respect to cognition and disease vulnerability.

Network architecture of intrinsic connectivity in a mammalian spinal cord (the central nervous system’s caudal sector)

The vertebrate spinal cord (SP) is the long, thin extension of the brain forming the central nervous system's caudal sector. Functionally, the SP directly mediates motor and somatic sensory interactions with most parts of the body except the face, and it is the preferred model for analyzing relatively simple reflex behaviors. Here, we analyze the organization of axonal connections between the 50 gray matter regions forming the bilaterally symmetric rat SP. The assembled dataset suggests that there are about 385 of a possible 2,450 connections between the 50 regions for a connection density of 15.7%. Multiresolution consensus cluster analysis reveals a hierarchy of structure-function subsystems in this neural network, with 4 subsystems at the top level and 12 at the bottom-level. The top-level subsystems include a) a bilateral subsystem related most clearly to somatic and autonomic motor functions and centered in the ventral horn and intermediate zone; b) a bilateral subsystem associated with general somatosensory functions and centered in the base, neck, and head of the dorsal horn; and c) a pair of unilateral, bilaterally symmetric subsystems associated with nociceptive information processing and occupying the apex of the dorsal horn. The intrinsic SP network displayed no hubs, rich club, or small-world attributes, which are common measures of global functionality. Advantages and limitations of our methodology are discussed in some detail. The present work is part of a comprehensive project to assemble and analyze the neurome of a mammalian nervous system and its interactions with the body.

Exploring alterations of brain networks of AD patients using WTC method

Objective: To explore the influences of different frequency bands on preprocessing of resting-state fMRI datasets used by the Wavelet Transform Coherence (WTC) method, and to study changes in the functional brain networks of AD patients. Method: Resting-state fMRI datasets of 10 AD patients and 11 healthy controls were collected in this study and time series of 90 brain regions defined by AAL (Automated Anatomical Labeling) were exacted after preprocessing. Wavelet transformation was performed for each time series, and a functional brain network were established in different frequencies (0.125Hz, 0.0625Hz) using the WTC (Wavelet Transform Coherence) method. The topology parameters of networks, containing global efficiency, clustering coefficient, average short paths length and small world property were calculated and averaged within each group. Result: The results imply that there are significant differences of topology parameters in networks of different frequencies. Likewise, statistical analysis of topology parameters of AD and HC (Healthy Controls) show that global efficiency, clustering coefficient and small world properties of AD all decreased by varying degrees, while the short path length of AD remained longer. Conclusion: Our research provides a theoretical basis for the choice of filter bands for data preprocessing in functional magnetic resonance imaging. The findings may serve as indicators for early diagnosis of AD patients.

Topological regularization of networks in temporal lobe epilepsy: a structural MRI study.

Patients with temporal lobe epilepsy (TLE) often exhibit neurocognitive disorders; however, we still know very little about the pathogenesis of cognitive impairment in patients with TLE. Therefore, our aim is to detect changes in the structural connectivity networks (SCN) of patients with TLE. Thirty-five patients with TLE were compared with 47 normal controls (NC) matched according to age, gender, handedness, and education level. All subjects underwent thin-slice T1WI scanning of the brain using a 3.0 T MRI. Then, a large-scale structural covariance network was constructed based on the gray matter volume extracted from the structural MRI. Graph theory was then used to determine the topological changes in the structural covariance network of TLE patients. Although small-world networks were retained, the structural covariance network of TLE patients exhibited topological irregularities in regular architecture as evidenced by an increase in the small world properties (p < 0.001), normalized clustering coefficient (p < 0.001), and a decrease in the transfer coefficient (p < 0.001) compared with the NC group. Locally, TLE patients showed a decrease in nodal betweenness and degree in the left lingual gyrus, right middle occipital gyrus and right thalamus compared with the NC group (p < 0.05, uncorrected). The degree of structural networks in both TLE (Temporal Lobe Epilepsy) and control groups was distributed exponentially in truncated power law. In addition, the stability of random faults in the structural covariance network of TLE patients was stronger (p = 0.01), but its fault tolerance was lower (p = 0.03). The objective of this study is to investigate the potential neurobiological mechanisms associated with temporal lobe epilepsy through graph theoretical analysis, and to examine the topological characteristics and robustness of gray matter structural networks at the network level.

Lexical Characterization of Ancient and Modern Chinese Combined with Semantic Association Network Modeling

Abstract This paper explores the linguistic features of ancient and modern Chinese, focuses on capturing the knowledge of the relevant domains of ancient and contemporary Chinese using semantic models, and carries out the corresponding semantic resource extraction and semantic representation through the resource expression mechanism in the framework of the Semantic Association Network Model (SANM), and then analyzes the historical evolution of the lexicalization patterns of the Chinese language and the linguistic features of the Chinese language in different periods. In the historical evolution of Chinese lexicalization patterns, it is found that the distribution of lexicalization patterns of ancient Chinese table-cutting action lexical items is [action+object] &gt; [action+method] &gt; [action result] &gt; [action+tool], and the distribution of lexicalization patterns of modern Chinese table-cutting action lexical items is [action+method] &gt; [action+tool] &gt; [action+result] &gt; [action+object]. The linguistic features of different periods show that all networks have small-world properties and scale-free properties, and the statistical parameters of the networks in each period are relatively close to each other, with the modern network having the most significant C (8.59) and the smallest L (0.92) and γ (0.40). Ancient and modern Chinese words and phrases with relational word collocations in the interval [0,23] have the most extensive and densest distribution of relational words. These data present the similarities and differences between linguistic features between ancient and modern Chinese, which is significant for studying ancient and modern Chinese.

Delineating abnormal individual structural covariance brain network organization in pediatric epilepsy with unilateral resection of visual cortex

Although several previous studies have used resting-state functional magnetic resonance imaging and diffusion tensor imaging to report topological changes in the brain in epilepsy, it remains unclear whether the individual structural covariance network (SCN) changes in epilepsy, especially in pediatric epilepsy with visual cortex resection but with normal functions. Herein, individual SCNs were mapped and analyzed for seven pediatric patients with epilepsy after surgery and 15 age-matched healthy controls. A whole-brain individual SCN was constructed based on an automated anatomical labeling template, and global and nodal network metrics were calculated for statistical analyses. Small-world properties were exhibited by pediatric patients after brain surgery and by healthy controls. After brain surgery, pediatric patients with epilepsy exhibited a higher shortest path length, lower global efficiency, and higher nodal efficiency in the cuneus than those in healthy controls. These results revealed that pediatric epilepsy after brain surgery, even with normal functions, showed altered topological organization of the individual SCNs, which revealed residual network topological abnormalities and may provide initial evidence for the underlying functional impairments in the brain of pediatric patients with epilepsy after surgery that can occur in the future.

Corticomuscular Coupling Analysis in Stroke Rehabilitation Based on Variational Mode Decomposition-Transfer Entropy.

This study aims to explore alterations in corticomuscular and cortical coupling during the rehabilitation of stroke patients. We initiated the analysis by employing variational modal decomposition (VMD) on electromyography (EMG) data, followed by the application of VDM-transfer entropy (VMD-TE) to quantify the coupling strength between electroencephalogram (EEG) and EMG signals. Subsequently, we constructed the VMD-TE connection matrix and analyzed the clustering coefficient and small-world attributes within the cortico-muscular functional network (CMFN). Finally, a random forest algorithm was employed to extract features from the VMD-TE connection matrix across different rehabilitation periods. Beta waves in EEG were emerged as the key information carrier between the cortex and muscle, and the CMFN of patients with the beta frequency band has small-world characteristics. During rehabilitation, we observed a decrease in coupling between the initially affected motor cortex and muscle, accompanied by an increase in coupling between the frontal region and muscle. Our findings suggest potential neuro-remodeling in stroke patients after rehabilitation, with CFMN serving as a valuable metric for assessing cortico-muscular coupling.

THREE PROPERTIES OF FRACTAL NETWORKS BASED ON BEDFORD–MCMULLEN CARPET

In this paper, we consider the networks modeled by several self-affine sets based on the Bedford–Mcmullen carpet. We calculate three properties of the networks, including the cumulative degree distribution, the average clustering coefficient and the average path length. We show that such networks have scale-free and small-world effects.

COMPLEX NETWORKS GENERATED BY A SELF-SIMILAR PLANAR FRACTAL

Many complex networks have scale-free and small-world effects. In this paper, a family of evolving networks is constructed modeled by a non-symmetric self-similar planar fractal, using the encoding method in fractal geometry. Based on the self-similar structure, we study the degree distribution, clustering coefficient and average path length of our evolving network to verify their scale-free and small-world characteristics.

Analysis of the difference between Alzheimer's disease, mild cognitive impairment and normal people by using fractal dimensions and small-world network.

This research examined the distinctions in brain network characteristics among individuals with Alzheimer's disease (AD), mild cognitive impairment (MCI), and a control group. Magnetic resonance imaging (MRI) and mini-mental state examination (MMSE) data were retrieved from the Alzheimer's Disease Neuroimaging Initiative (ANDI) database, comprising 40 subjects in each group. Correlation maps for evaluating brain network connectivity were generated using fractal dimension (FD) analysis, a method capable of quantifying morphological changes in cortical and cerebral regions. Employing graph theory, each parcellated brain region was represented as a node, and edges between nodes were utilized to compute small-world network properties for each group. In the comparison between control and AD demonstrated the significantly lower FD values (P<0.05) in temporal lobe, motor cortex, part of occipital and parietal, hippocampus, amygdala, and entorhinal cortex, which present the atrophy. Similarly, comparing control group to MCIs, regions closely associated with memory, such as the hippocampus, showed significantly lower FD values. Furthermore, both AD and MCI groups displayed diminished connectivity and decreased network efficiency. In conclusion, fractal dimension (FD) analysis illustrate the progression of structural declination from mild cognitive impairment (MCI) to Alzheimer's disease (AD). Additionally, structural small-world network analysis presents itself as a potential method for assessing network efficiency and the progression of AD. Moving forward, further clinical assessments are warranted to validate the findings observed in this study.

Empirical Network Structure of Malicious Programs

A modern binary executable is a composition of various types of networks. Control flow graphs are a commonly used representation of an executable program used for classification tasks. Control flow and term frequency representations are widely adopted, but provide only a partial view of program semantics and present challenges to increases in resolution. By performing a quantitative analysis of program networks, we enable the identification of patterns within these features that are correlated to structure. This allows for increases in feature resolution and pattern recognition in classification tasks. These are necessary steps in order to obtain greater explainability in classification results. We demonstrate the presence of Scale-Free properties of network structure for program data dependency and control flow graphs, and show that data dependency graphs also have Small-World structural properties. We show that program data dependency graphs have a degree correlation that is structurally disassortative, and that control flow graphs have a neutral degree assortativity, indicating the use of random graphs to model the structural properties of program control flow graphs would show increased accuracy. An increase in feature resolution allows for the structural

Sex differences in human brain networks in normal and psychiatric populations from the perspective of small-world properties.

Females and males are known to be different in the prevalences of multiple psychiatric disorders, while the underlying neural mechanisms are unclear. Based on non-invasive neuroimaging techniques and graph theory, many researchers have tried to use a small-world network model to elucidate sex differences in the brain. This manuscript aims to compile the related research findings from the past few years and summarize the sex differences in human brain networks in both normal and psychiatric populations from the perspective of small-world properties. We reviewed published reports examining altered small-world properties in both the functional and structural brain networks between males and females. Based on four patterns of altered small-world properties proposed: randomization, regularization, stronger small-worldization, and weaker small-worldization, we found that current results point to a significant trend toward more regularization in normal females and more randomization in normal males in functional brain networks. On the other hand, there seems to be no consensus to date on the sex differences in small-world properties of the structural brain networks in normal populations. Nevertheless, we noticed that the sample sizes in many published studies are small, and future studies with larger samples are warranted to obtain more reliable results. Moreover, the number of related studies conducted in psychiatric populations is still limited and more investigations might be needed. We anticipate that these conclusions will contribute to a deeper understanding of the sex differences in the brain, which may be also valuable for developing new methods in the treatment of psychiatric disorders.

A longitudinal study of the brain structure network changes in HIV patients with ANI: combined VBM with SCN.

Despite the widespread adoption of combination antiretroviral therapy (cART) in managing HIV, the virus's impact on the brain structure of patients remains significant. This study aims to longitudinally explore the persistent effects of HIV on brain structure, focusing on changes in gray matter volume (GMV) and structural covariance network (SCN) among patients at the Asymptomatic Neurocognitive Impairment (ANI) stage. This research involved 45 HIV patients diagnosed with ANI and 45 demographically matched healthy controls (HCs). The participants were observed over a 1.5-year period. Differences in GMV between groups were analyzed using voxel-based morphometry (VBM), while the graph theory model facilitated the establishment of topological metrics for assessing network indices. These differences were evaluated using two-sample t-tests and paired-sample t-tests, applying the network-based statistics method. Additionally, the study examined correlations between GMV and cognitive performance, as well as clinical variables. Compared with HCs, HIV patients demonstrated reduced GMV in the right middle temporal gyrus and left middle frontal gyrus (FWE, p < 0.05), along with decreased betweenness centrality (BC) in the left anterior cingulate and paracingulate cortex. Conversely, an increase in the clustering coefficient (Cp) was observed (FDR, p < 0.05). During the follow-up period, a decline in GMV in the right fusiform gyrus (FWE, p < 0.05) and a reduction in node efficiency (Ne) in the triangular part of the inferior frontal gyrus were noted compared with baseline measurements (FDR, p < 0.05). The SCN of HIV patients exhibited small-world properties across most sparsity levels (Sigma >1), and area under the curve (AUC) analysis revealed no significant statistical differences between groups. The findings suggest that despite the administration of combination antiretroviral therapy (cART), HIV continues to exert slow and sustained damage on brain structures. However, when compared to HCs, the small-world properties of the patients' SCNs did not significantly differ, and the clustering coefficient, indicative of the overall information-processing capacity of the brain network, was slightly elevated in HIV patients. This elevation may relate to compensatory effects of brain area functions, the impact of cART, functional reorganization, or inflammatory responses.

Sex differences in functional and structural alterations of hippocampus region in chronic pain: a DTI and resting-state fMRI study.

It is well known that there are significant differences in the prevalence of chronic pain between males and females. Human and animal imaging studies have shown that chronic pain profoundly alters the structure and function of brain regions. However, there is limited research on the sex-specific mechanisms underlying the brain plasticity and adaptive changes associated with chronic pain. In this article, we conducted a multimodal study to evaluate how nerve injury-induced chronic pain affects the brain. Male and female Sprague-Dawley (SD) rats with spared nerve injury (SNI) model underwent resting-state functional magnetic resonance imaging (rs-fMRI) (male sham group: n = 18; male SNI group: n = 18; female sham group: n = 20; female SNI group: n = 18) and magnetic resonance diffusion tensor imaging (DTI) (male sham group: n = 23; male SNI group: n = 21; female sham group: n = 20; female SNI group: n = 21) scanning. ICA method, Fractional amplitude of low-frequency fluctuations (fALFF), immunofluorescence staining, and graph theory analysis was utilized to extract the rs-fMRI changes of brain regions of each group. Using SNI model, which promotes long-lasting mechanical allodynia, we found that neuropathic pain deeply modified the intrinsic organization of the brain functional network in male and female rats (main effect of operation: F = 298.449, P < 0.001). 64 independent components (ICs) in the brain were divided and assigned to 16 systems. In male rats, we observed significant alterations in the microstructure of the hippocampal cornu ammonis 1 and cornu ammonis 2 (CA1/CA2) region, as indicated by increased mean diffusivity (MD) (CA1_L: P = 0.02; CA1_R: P = 0.031; CA2_L: P = 0.035; CA2_R: P = 0.015) and radial diffusivity (RD) (CA1_L: P = 0.028; CA1_R: P = 0.033; CA2_L: P = 0.037; CA2_R: P = 0.038) values, along with enhanced activating transcription factor 3 (ATF3) expression. Conversely, in female rats, we found significant increases in the fractional amplitude of low frequency fluctuations (fALFF) value within the hippocampal dentate gyrus (DG) (F = 5.419, P = 0.023), accompanied by elevated c-Fos signal (F = 6.269, P = 0.031). Furthermore, graph theory analysis revealed notable differences in the small-world network of the hippocampal system in female rats, characterized by reduced small-world attributes and increased inter-nodal transmission efficiency. Our study indicates sex differences in structural and functional alterations in the hippocampal system in rats under chronic pain conditions. The results suggest that the hippocampus system plays an important role in the different mechanisms of chronic pain in different sexes. These findings provide reliable insights to explore the complex mechanisms underlying sex differences in chronic pain.