Small-world Properties Research Articles

Synergy between Electric Vehicle Manufacturers and Battery Recyclers through Technology and Innovation: A Game Theory Approach

Power battery recycling (PBR) has triggered profound changes in the industrial chain of electric vehicles (EVs). The PBR innovation network provides information channels and resource conditions for enterprises, but the mechanism of its impact on the synergistic innovation benefits and sustainable development ability of EV and PBR enterprises still needs further exploration. In this paper, we collect patent data for PBR from 2012 to 2020, identify the structural characteristics of innovation networks, and construct a synergy game model for PBR technology, aiming to analyze the synergistic effect of network embedding and knowledge spillover in PBR enterprises on technological innovation. First, we find that the PBR innovation network exhibits the small-world effect, which has a double-edged sword effect on technological cooperation innovation. Second, structural holes benefits of the main body of PBR technological innovation have a significant impact on cooperation innovation behavior. Third, the enhancement of the relevance and deep complementarity of knowledge cooperation is sufficient to make up for the input cost of PBR technological cooperation innovation, with additional benefits created by the increase in the output of structural holes. However, companies tend to be more inclined toward non-cooperative innovation as the knowledge spillover effect of the innovation network increases.

Combination of bioaffinity ultrafiltration-UFLC-ESI-Q/TOF-MS/MS, in silico docking and multiple complex networks to explore antitumor mechanism of topoisomerase I inhibitors from Artemisiae Scopariae Herba

BackgroundArtemisiae Scopariae Herba (ASH) has been widely used as plant medicine in East Asia with remarkable antitumor activity. However, the underlying mechanisms have not been fully elucidated.MethodsThis study aimed to construct a multi-disciplinary approach to screen topoisomerase I (topo I) inhibitors from ASH extract, and explore the antitumor mechanisms. Bioaffinity ultrafiltration-UFLC-ESI-Q/TOF-MS/MS was used to identify chemical constitution of ASH extract as well as the topo I inhibitors, and in silico docking coupled with multiple complex networks was applied to interpret the molecular mechanisms.ResultsCrude ASH extract exhibited toxicogenetic and antiproliferative activities on A549 cells. A series of 34 ingredients were identified from the extract, and 6 compounds were screened as potential topo I inhibitors. Docking results showed that the formation of hydrogen bond and π-π stacking contributed most to their binding with topo I. Interrelationships among the 6 compounds, related targets and pathways were analyzed by multiple complex networks model. These networks displayed power-law degree distribution and small-world property. Statistical analysis indicated that isorhamnetin and quercetin were main active ingredients, and that chemical carcinogenesis-reactive oxygen species was the critical pathway. Electrophoretic results showed a therapeutic effect of ASH extract on the conversion of supercoiled DNA to relaxed forms, as well as potential synergistic effect of isorhamnetin and quercetin.ConclusionsThe results improved current understanding of Artemisiae Scopariae Herba on the treatment of tumor. Moreover, the combination of multi-disciplinary methods provided a new strategy for the study of bioactive constituents in medicinal plants.

Smallworldness in hypergraphs

Most real-world networks are endowed with the small-world property, by means of which the maximal distance between any two of their nodes scales logarithmically rather than linearly with their size. The evidence sparkled a wealth of studies trying to reveal possible mechanisms through which the pairwise interactions amongst the units of a network are structured in a way to determine such observed regularity. Here we show that smallworldness occurs also when interactions are of higher order. Namely, by considering Q-uniform hypergraphs and a process through which connections can be randomly rewired with given probability p, we find that such systems may exhibit prominent clustering properties in connection with small average path lengths for a wide range of p values, in analogy to the case of dyadic interactions. The nature of small-world transition remains the same at different orders Q ( and 6) of the interactions, however, the increase in the hyperedge order reduces the range of rewiring probability for which smallworldness emerge.

Ex-utero third trimester developmental changes in functional brain network organization in infants born very and extremely preterm.

The latter half of gestation is a period of rapid brain development, including the formation of fundamental functional brain network architecture. Unlike in-utero fetuses, infants born very and extremely preterm undergo these critical maturational changes in the extrauterine environment, with growing evidence suggesting this may result in altered brain networks. To date, however, the development of functional brain architecture has been unexplored. From a prospective cohort of preterm infants, graph parameters were calculated for fMRI scans acquired prior to reaching term equivalent age. Eight graph properties were calculated, Clustering Coefficient (C), Characteristic Path Length (L), Modularity (Q), Local Efficiency (LE), Global Efficiency (GE), Normalized Clustering (λ), Normalized Path Length (γ), and Small-Worldness (σ). Properties were first compared to values generated from random and lattice networks and cost efficiency was evaluated. Subsequently, linear mixed effect models were used to assess relationship with postmenstrual age and infant sex. A total of 111 fMRI scans were acquired from 85 preterm infants born at a mean GA 28.93 ± 2.8. Infants displayed robust small world properties as well as both locally and globally efficient networks. Regression models found that GE increased while L, Q, λ, γ, and σ decreased with increasing postmenstrual age following multiple comparison correction (r2Adj range 0.143-0.401, p < 0048), with C and LE exhibited trending increases with age. This is the first direct investigation on the extra-uterine formation of functional brain architecture in preterm infants. Importantly, our results suggest that changes in functional architecture with increasing age exhibit a different trajectory relative to in utero fetus. Instead, they exhibit developmental changes more similar to the early postnatal period in term born infants.

Topology switching during window thresholding fMRI-based functional networks of patients with major depressive disorder: Consensus network approach.

We present a novel method for analyzing brain functional networks using functional magnetic resonance imaging data, which involves utilizing consensus networks. In this study, we compare our approach to a standard group-based method for patients diagnosed with major depressive disorder (MDD) and a healthy control group, taking into account different levels of connectivity. Our findings demonstrate that the consensus network approach uncovers distinct characteristics in network measures and degree distributions when considering connection strengths. In the healthy control group, as connection strengths increase, we observe a transition in the network topology from a combination of scale-free and random topologies to a small-world topology. Conversely, the MDD group exhibits uncertainty in weak connections, while strong connections display small-world properties. In contrast, the group-based approach does not exhibit significant differences in behavior between the two groups. However, it does indicate a transition in topology from a scale-free-like structure to a combination of small-world and scale-free topologies. The use of the consensus network approach also holds immense potential for the classification of MDD patients, as it unveils substantial distinctions between the two groups.

The Intrinsic Similarity of Topological Structure in Biological Neural Networks.

Most previous studies mainly have focused on the analysis of structural properties of individual neuronal networks from C. elegans. In recent years, an increasing number of synapse-level neural maps, also known as biological neural networks, have been reconstructed. However, it is not clear whether there are intrinsic similarities of structural properties of biological neural networks from different brain compartments or species. To explore this issue, we collected nine connectomes at synaptic resolution including C. elegans, and analyzed their structural properties. We found that these biological neural networks possess small-world properties and modules. Excluding the Drosophila larval visual system, these networks have rich clubs. The distributions of synaptic connection strength for these networks can be fitted by the truncated pow-law distributions. Additionally, compared with the power-law model, a log-normal distribution is a better model to fit the complementary cumulative distribution function (CCDF) of degree for these neuronal networks. Moreover, we also observed that these neural networks belong to the same superfamily based on the significance profile (SP) of small subgraphs in the network. Taken together, these findings suggest that biological neural networks share intrinsic similarities in their topological structure, revealing some principles underlying the formation of biological neural networks within and across species.

Functional Brain Network Alterations in Patients With Systemic Lupus Erythematosus With Different Cognitive Function States: A Graph Theory Analysis Study.

The study aimed to investigate the characteristics of brain functional network disruption in patients with systemic lupus erythematosus (SLE) with different cognitive function states by using graph theory analysis and to explore their relationship with clinical data and neuropsychiatric scales. Resting-state functional magnetic resonance imaging data were collected from 38 female SLE patients and 44 healthy controls. Based on Montreal Cognitive Assessment (MoCA) scores, SLE patients were divided into a high MoCA group (MoCA-H; MoCA score, ≥26) and a low MoCA group (MoCA-L; MoCA score, <26). The matrix of resting-state functional brain networks of subjects in the 3 groups was constructed by using the graph theory approach. The topological properties of the functional brain networks, including global and local metrics, in the 3 groups were calculated. The differences in the topological properties of networks between the 3 groups were compared. In addition, Spearman correlation analysis was used to explore the correlation between altered topological properties of brain networks and clinical indicators, as well as neuropsychiatric scales in SLE patients in the MoCA-L group. At the global level, in the sparsity threshold range of 0.10 to 0.34, the values of small-world properties were greater than 1 in all 3 groups, indicating that functional brain networks of both 3 groups had small-world properties. There were statistically significant differences in the characteristic path length, global, and local efficiency between 3 groups ( F = 3.825, P = 0.0260; F = 3.722, P = 0.0285; and F = 3.457, P = 0.0364, respectively). Systemic lupus erythematosus patients in the MoCA-L group showed increased characteristic path length ( t = 2.816, P = 0.00651), decreased global ( t = -2.729, P = 0.00826), and local efficiency ( t = -2.623, P = 0.0109) compared with healthy controls. No statistically significant differences in local metrics were found between the MoCA-H group and the healthy control, MoCA-L groups. At the local level, there was statistically significant difference in the node efficiency among the 3 groups ( P < 0.05 after Bonferroni correction). Compared with healthy controls, SLE patients in the MoCA-L group showed decreased node efficiency in left anterior cingulate paracingulate gyrus, bilateral putamen, bilateral pallidum, and left Heschl gyrus. No statistically significant differences in the local metrics were found between the MoCA-H, MoCA-L, and healthy control groups. Correlation analysis in SLE patients in the MoCA-L group showed that the characteristic path length was positively correlated with C4 levels ( r = 0.587, P = 0.007), the global and local efficiencies were negatively correlated with C4 levels ( r = -0.599, P = 0.005; r = -0.599, P = 0.005, respectively), and the node efficiency in the bilateral putamen was negatively correlated with C4 levels ( r = -0.611, P = 0.004; r = -0.570, P = 0.009). The node efficiency in the left pallidum was negatively correlated with disease duration ( r = -0.480, P = 0.032). The node efficiency in the left Heschl gyrus was negatively correlated with IgM levels ( r = -0.478, P = 0.033). No correlation was noted between other network metrics, clinical indicators, and neuropsychological scales. The topological properties of functional brain networks were disrupted in SLE patients with low MoCA scores, suggesting that altered topological properties of the brain networks were associated with cognitive function in SLE patients. Correlation between altered topological properties of the brain networks and clinical indicators was noted in SLE patients with low MoCA scores, suggesting that altered topological properties of brain networks in SLE patients may have clinical significance as imaging markers for monitoring disease changes in patients with SLE.

Single-subject cortical morphological brain networks across the adult lifespan.

Age-related changes in focal cortical morphology have been well documented in previous literature; however, how interregional coordination patterns of the focal cortical morphology reorganize with advancing age is not well established. In this study, we performed a comprehensive analysis of the topological changes in single-subject morphological brain networks across the adult lifespan. Specifically, we constructed four types of single-subject morphological brain networks for 650 participants (aged from 18 to 88 years old), and characterized their topological organization using graph-based network measures. Age-related changes in the network measures were examined via linear, quadratic, and cubic models. We found profound age-related changes in global small-world attributes and efficiency, local nodal centralities, and interregional similarities of the single-subject morphological brain networks. The age-related changes were mainly embodied in cortical thickness networks, involved in frontal regions and highly connected hubs, concentrated on short-range connections, characterized by linear changes, and susceptible to connections between limbic, frontoparietal, and ventral attention networks. Intriguingly, nonlinear (i.e., quadratic or cubic) age-related changes were frequently found in the insula and limbic regions, and age-related cubic changes preferred long-range morphological connections. Finally, we demonstrated that the morphological similarity in cortical thickness between two frontal regions mediated the relationship between age and cognition measured by Cattell scores. Taken together, these findings deepen our understanding of adaptive changes of the human brain with advancing age, which may account for interindividual variations in behaviors and cognition.

The Achilles heel of interconnected user networks: Network firms and the vulnerability of rapid decline

Digital technologies have amplified firms' ability to gain and sustain competitive advantages by leveraging network effects and large user bases. They allow cheaper and better building, scaling, and operation of user networks, more efficient data collection, lower transaction costs, and ever-stronger scale advantages. Yet, the seemingly stable competitive advantage of large-scale user networks may have an “Achilles heel” that creates a strategic vulnerability. We examine this overlooked effect by studying how structural network characteristics affect the risk of rapid decline after users start to depart. We find that for user networks with small-world and scale-free properties, the departure of a few influential users can prompt strong negative network effects and accelerate the speed of a decline. To arrive at these insights, we use an analytical approach inspired by the computational networks literature to assess the impact of different structural characteristics on the likelihood of rapid collapse. Our research enriches the platform and network literature by providing fresh insights into the vulnerabilities of interconnected user networks, highlighting the risk of rapid decline. We also suggest practical implications for firms that depend on such networks for a competitive edge.

Alteration of White Matter Connectivity for MR-Guided Focused Ultrasound in the Treatment of Essential Tremor.

Magnetic resonance-guided focused ultrasound (MRgFUS) thalamotomy has been implemented as a therapeutic alternative for the treatment of drug-refractory essential tremor (ET). However, its impact on the brain structural network is still unclear. To investigate both global and local alterations of the white matter (WM) connectivity network in ET after MRgFUS thalamotomy. Retrospective. Twenty-seven ET patients (61 ± 11 years, 19 males) with MRgFUS thalamotomy and 28 healthy controls (HC) (61 ± 11 years, 20 males) were recruited for comparison. A 3 T/single shell diffusion tensor imaging by using spin-echo-based echo-planar imaging, three-dimensional T1 weighted imaging by using gradient-echo-based sequence. Patients were undergoing MRgFUS thalamotomy and their clinical data were collected from pre-operation to 6-month post-operation. Network topological metrics, including rich-club organization, small-world, and efficiency properties were calculated. Correlation between the topological metrics and tremor scores in ET groups was also calculated to assess the role of neural remodeling in the brain. Two-sample independent t-tests, chi-squared test, ANOVA, Bonferroni test, and Spearman's correlation. Statistical significance was set at P < 0.05. For ET patients, the strength of rich-club connection and clustering coefficient significantly increased vs. characteristic path length decreased at 6-month post-operation compared with pre-operation. The distribution pattern of rich-club regions was different in ET groups. Specifically, the order of the rich-club regions was changed according to the network degree value after MRgFUS thalamotomy. Moreover, the altered nodal efficiency in the right temporal pole of the superior temporal gyrus (R = 0.434-0.596) and right putamen (R = 0.413-0.436) was positively correlated with different tremor improvement. These findings might improve understanding of treatment-induced modulation from a network perspective and may work as an objective marker in the assessment of ET tremor control with MRgFUS thalamotomy. 3 TECHNICAL EFFICACY: Stage 4.

Modeling spatial networks by contact graphs of disk packings

Spatial networks are ubiquitous in the real world, with examples including Internet, power grids, neural networks, and so on. In this paper, based on a proposed disk packing, we present a contact graph as an exactly solvable model for spatial networks. We then derive analytically some critical structural properties of the model, including degree distribution, clustering coefficient, and diameter, and show that it displays simultaneously the striking scale-free small-world phenomena observed in most real networks. We also determine all the eigenvalues and their multiplicities of the transition probability matrix for the contact graph, and exploit the eigenvalues to derive closed-form expressions for Kemeny constant of random walks and the number of spanning trees on the contact graph. Finally, we derive closed-form expressions for some interesting quantities about resistance distances, including Kirchhoff index, additive degree-Kirchhoff index, multiplicative degree-Kirchhoff index, as well as average resistance distance. As an application of resistance distances, we study the coherence of the first-order consensus dynamics, which tends to a small constant as the graph grows, implying that the graph is resistant to noise.

Brain network characteristics between subacute and chronic stroke survivors in active, imagery, passive movement task: a pilot study.

The activation patterns and functional network characteristics between stroke survivors and healthy individuals based on resting-or task-state neuroimaging and neurophysiological techniques have been extensively explored. However, the discrepancy between stroke patients at different recovery stages remains unclear. To investigate the changes in brain connectivity and network topology between subacute and chronic patients, and hope to provide a basis for rehabilitation strategies at different stages after stroke. Fifteen stroke survivors were assigned to the subacute group (SG, N = 9) and chronic group (CG, N = 6). They were asked to perform hand grasping under active, passive, and MI conditions when recording EEG. The Fugl-Meyer Assessment Upper Extremity subscale (FMA_UE), modified Ashworth Scale (MAS), Manual Muscle Test (MMT), grip and pinch strength, modified Barthel Index (MBI), and Berg Balance Scale (BBS) were measured. Functional connectivity analyses showed significant interactions on frontal, parietal and occipital lobes connections in each frequency band, particularly in the delta band. The coupling strength of premotor cortex, M1, S1 and several connections linked to frontal, parietal, and occipital lobes in subacute subjects were lower than in chronic subjects in low alpha, high alpha, low beta, and high beta bands. Nodal clustering coefficient (CC) analyses revealed that the CC in chronic subjects was higher than in subacute subjects in the ipsilesional S1 and occipital area, contralesional dorsolateral prefrontal cortex and parietal area. Characteristic path length (CPL) analyses showed that CPL in subacute subjects was lower than in chronic subjects in low beta, high beta, and gamma bands. There were no significant differences between subacute and chronic subjects for small-world property. Subacute stroke survivors were characterized by higher transfer efficiency of the entire brain network and weak local nodal effects. Transfer efficiency was reduced, the local nodal role was strengthened, and more neural resources needed to be mobilized to perform motor tasks for chronic survivors. Overall, these results may help to understand the remodeling pattern of the brain network for different post-stroke stages on task conditions and the mechanism of spontaneous recovery.

Global ginseng trade networks: structural characteristics and influencing factors.

Background: Ginseng is a rare and highly valued Chinese materia medica with a rich trading history and has a wide range of application, including medicine, food, healthcare, and daily chemical production. However, the global trade of ginseng exhibits diverse features and uneven development across different countries and regions. Surprisingly, the intricate network relationship and the underlying characteristics and influencing factors of ginseng trade networks remain unexplored. Methods: This study analyzed ginseng trade data obtained from the UN-Comtrade database and used social network analysis to construct global ginseng trade networks. To elucidate the structural characteristics, we analyzed the indicators of the overall network structure and node attributes. Core-periphery analysis is used to examine the evolutionary patterns within the global ginseng trade networks. Furthermore, we apply the quadratic assignment procedure to investigate the impact and relevance of spatial proximity, cultural differences, economic indicators, population size, technological similarity, and institutional distance. Results: The findings reveal that the global ginseng trade networks exhibit typical small-world and scale-free properties, as well as a core-periphery structure. Several core countries, including China, South Korea, Germany, and the United States, exert significant control over both trade volume and trade partners. South Korea and China initially occupied central positions in the export market due to their resource endowments, their prominence has gradually diminished with the ascendancy of Germany and the United States. According to the core-periphery analysis, the ginseng trade has shown a gradual concentration within specific trade groups comprising core and semi-periphery countries, most of which are along the "Belt and Road" religion. We also found that geographic distance and GDP per capita exert negative effects on ginseng trade, while factors such as land adjacency, technology and economic gap, population size, and institution similarity play significant positive roles. Conclusion: The global ginseng trade has experienced increasing concentration and close linkage among a limited numbers of participants. It is crucial to pay close attention to the relationship between ginseng industry development and resource conservation. Strategies such as expanding trade channels, implementing trade substitution measures, and optimizing the quality and standards of ginseng products can effectively enhance trade security.

Understanding dockless bike-sharing spatiotemporal travel patterns: Evidence from ten cities in China

Dockless bike-sharing (DBS) has gained popularity in many cities in recent years. However, little attention has been given to the commonalities and differences in DBS travel patterns from multiple cities. This study aims to fill this gap by comparing DBS travel patterns in ten Chinese cities of varying scales. It collected data from these cities and analysed them from two perspectives: service usage characteristics and complex network properties. The results reveal a coexistence of similarities and differences in DBS travel patterns across different cities. The ten major cities show significant similarities in temporal distribution, with a similarity coefficient exceeding 0.7. Southern cities have a higher percentage of night riding compared to their northern counterparts. Moreover, over 85% of the travel distances are within 2 km. Concerning spatial distribution, all ten cities demonstrate an imbalanced demand distribution during peak hours, particularly in downtown areas, exhibiting evident tidal patterns. Network analysis outcomes demonstrate that the DBS networks in all ten cities possess small-world and scale-free properties. Furthermore, nodes with high degree centrality and closeness centrality are predominantly concentrated in downtown areas, displaying a diminishing trend from the city centre to the outskirts and showcasing strong global spatial autocorrelation. The betweenness centrality exhibits a property of random distribution. Nodes with high PageRank values are mainly concentrated in the city centre and around metro stations. The findings offer valuable insights for transportation planners and managers seeking to enhance their understanding of DBS systems.

Network Structure of Atmospheric Perturbations

Abstract Accurate atmospheric-state analysis is essential for understanding and prediction of the atmosphere and is a difficult scientific problem due to the chaotic nature of the atmosphere; namely, small atmospheric perturbations (APs) grow rapidly in nonlinear processes. The key to atmospheric-state analysis is knowing the structure of the APs. We analyzed the AP structure in terms of network theory using a 192-member AP ensemble. The AP ensemble was generated by an ensemble of variational data assimilation (DA) with the perturbed observation method using the operational numerical weather prediction system at the Japan Meteorological Agency. The generated APs captured flow-dependent AP structures corresponding to atmospheric normal modes, and their use in DA improved accuracy of atmospheric-state predictions. These show the usefulness of the APs. The network property of the APs are as follows. The atmosphere has a small average network distance compared with the square root of the number of nodes, and a large clustering coefficient (about 0.6). These show that the APs have small-world network properties. The degree distribution of APs shows the heavy-tailed structure. These three properties of APs are common to various complex networks in other systems. Hubs in the AP network correspond to atmospheric disturbances. The network community detection using network modularity shows about 18 communities with 0.8 modularity. These basic network properties of APs represent efficient information exchange in the atmosphere, which provides a complementary atmospheric picture to its traditional physical picture based on fluid dynamics and thermodynamics, and would be basic information for atmospheric sciences and extension of application target of the network theory. Significance Statement The purpose of this paper is to analyze properties of atmospheric perturbations using the network theory and an accurate ensemble of the atmospheric perturbations. This is important for atmospheric-state estimation and forecasting because the atmosphere is chaotic and small perturbations grow rapidly. Our results show that the atmosphere has a small average network distance and a large clustering coefficient, which are the properties of a small-world network, and a heavy-tailed degree distribution. These three properties of atmospheric perturbations are common to various complex networks in other systems.

Efficiently Approximating Vertex Cover on Scale-Free Networks with Underlying Hyperbolic Geometry

Finding a minimum vertex cover in a network is a fundamental NP-complete graph problem. One way to deal with its computational hardness, is to trade the qualitative performance of an algorithm (allowing non-optimal outputs) for an improved running time. For the vertex cover problem, there is a gap between theory and practice when it comes to understanding this trade-off. On the one hand, it is known that it is NP-hard to approximate a minimum vertex cover within a factor of sqrt{2}. On the other hand, a simple greedy algorithm yields close to optimal approximations in practice. A promising approach towards understanding this discrepancy is to recognize the differences between theoretical worst-case instances and real-world networks. Following this direction, we narrow the gap between theory and practice by providing an algorithm that efficiently computes nearly optimal vertex cover approximations on hyperbolic random graphs; a network model that closely resembles real-world networks in terms of degree distribution, clustering, and the small-world property. More precisely, our algorithm computes a (1 + o(1))-approximation, asymptotically almost surely, and has a running time of {mathcal {O}}(m log (n)). The proposed algorithm is an adaptation of the successful greedy approach, enhanced with a procedure that improves on parts of the graph where greedy is not optimal. This makes it possible to introduce a parameter that can be used to tune the trade-off between approximation performance and running time. Our empirical evaluation on real-world networks shows that this allows for improving over the near-optimal results of the greedy approach.

Motor network reorganization in stroke patients with dyskinesias during a shoulder-touching task: A fNIRS study

Hemiplegia after stroke has become a major cause of the world’s high disabilities, and it is vital to enhance our understanding of post-stroke neuroplasticity to develop efficient rehabilitation programs. This study aimed to explore the brain activation and network reorganization of the motor cortex (MC) with functional near-infrared spectroscopy (fNIRS). The MC hemodynamic signals were gained from 22 stroke patients and 14 healthy subjects during a shoulder-touching task with the right hand. The MC activation pattern and network attributes analyzed with the graph theory were compared between the two groups. The results revealed that healthy controls presented dominant activation in the left MC while stroke patients exhibited dominant activation in the bilateral hemispheres MC. The MC networks for the two groups had small-world properties. Compared with healthy controls, patients had higher transitivity and lower global efficiency (GE), mean connectivity, and long connections (LCs) in the left MC. In addition, both MC activation and network attributes were correlated with patient’s upper limb motor function. The results showed the stronger compensation of the unaffected motor area, the better recovery of the upper limb motor function for patients. Moreover, the MC network possessed high clustering and relatively sparse inter-regional connections during recovery for patients. Our results promote the understanding of MC reorganization during recovery and indicate that MC activation and network could provide clinical assessment significance in stroke patients. Given the advantages of fNIRS, it shows great application potential in the assessment and rehabilitation of motor function after stroke.

Hierarchical Wilson-Cowan Models and Connection Matrices.

This work aims to study the interplay between the Wilson-Cowan model and connection matrices. These matrices describe cortical neural wiring, while Wilson-Cowan equations provide a dynamical description of neural interaction. We formulate Wilson-Cowan equations on locally compact Abelian groups. We show that the Cauchy problem is well posed. We then select a type of group that allows us to incorporate the experimental information provided by the connection matrices. We argue that the classical Wilson-Cowan model is incompatible with the small-world property. A necessary condition to have this property is that the Wilson-Cowan equations be formulated on a compact group. We propose a p-adic version of the Wilson-Cowan model, a hierarchical version in which the neurons are organized into an infinite rooted tree. We present several numerical simulations showing that the p-adic version matches the predictions of the classical version in relevant experiments. The p-adic version allows the incorporation of the connection matrices into the Wilson-Cowan model. We present several numerical simulations using a neural network model that incorporates a p-adic approximation of the connection matrix of the cat cortex.

Network resilience: impact on small-world network

Lots of complex systems in the real world have network structures, and a number of these structures have small-world property. This kind of structures are called small-world networks. Examples include the world's air transportation system, electric power systems, and human functional brain network, and small-world property is one of the key reasons why these systems function efficiently. However, for complex systems, in addition to their efficiency, resilience or robustness is also one of the concerns, as these systems need to ensure that they do not completely collapse on their own in case of failure of a small number of their components. The purpose of this paper is to try to find and explain the factors that affect the robustness of small-world network by comparing different classes of small-world networks and analysing differences between them and possible causes of these differences, in order to get an idea to optimize the robustness of small-world networks while preserving their small-world property.

Average path length and Fermat distance in fractal networks composed of high-dimensional Sierpiński pyramids

Complex networks created by fractals have been associated with various applications such as social networks, modern communication, and fractal antennas. In this paper, we consider a series of scale-free networks based on the construction of high dimensional Sierpiński pyramids. Using self-similarity and elementary renewal theorem, we derive the asymptotic formulas of the average path length (APL) and the average Fermat distance (AFD) on our network sequence in turn. Our approaches are suitable for various networks modeled on self-similar fractals.It is known that the ratio of AFD to APL is between 3/2 and 2, which implies that AFD is also a key property to characterize small-world effect. Through an elaborate investigation of our networks, the limit of this ratio for our evolving networks is 3/2 and we analyze the result in the light of our interpretation. In fact, in some scale-free networks, the nodes with high degrees have more influence on the choice of Fermat points and thus Fermat distance. Our conclusions may lead to some interesting relations concerning the hyperbolicity, Laplacian spectrum and some multiparameter indices of networks.