Patients with mild traumatic brain injury have a diverse clinical presentation,and the underlying pathophysiology remains poorly understood.Magnetic resonance imaging is a non-invasive technique that has been widely u...Patients with mild traumatic brain injury have a diverse clinical presentation,and the underlying pathophysiology remains poorly understood.Magnetic resonance imaging is a non-invasive technique that has been widely utilized to investigate neuro biological markers after mild traumatic brain injury.This approach has emerged as a promising tool for investigating the pathogenesis of mild traumatic brain injury.G raph theory is a quantitative method of analyzing complex networks that has been widely used to study changes in brain structure and function.However,most previous mild traumatic brain injury studies using graph theory have focused on specific populations,with limited exploration of simultaneous abnormalities in structural and functional connectivity.Given that mild traumatic brain injury is the most common type of traumatic brain injury encounte red in clinical practice,further investigation of the patient characteristics and evolution of structural and functional connectivity is critical.In the present study,we explored whether abnormal structural and functional connectivity in the acute phase could serve as indicators of longitudinal changes in imaging data and cognitive function in patients with mild traumatic brain injury.In this longitudinal study,we enrolled 46 patients with mild traumatic brain injury who were assessed within 2 wee ks of injury,as well as 36 healthy controls.Resting-state functional magnetic resonance imaging and diffusion-weighted imaging data were acquired for graph theoretical network analysis.In the acute phase,patients with mild traumatic brain injury demonstrated reduced structural connectivity in the dorsal attention network.More than 3 months of followup data revealed signs of recovery in structural and functional connectivity,as well as cognitive function,in 22 out of the 46 patients.Furthermore,better cognitive function was associated with more efficient networks.Finally,our data indicated that small-worldness in the acute stage could serve as a predictor of longitudinal changes in connectivity in patients with mild traumatic brain injury.These findings highlight the importance of integrating structural and functional connectivity in unde rstanding the occurrence and evolution of mild traumatic brain injury.Additionally,exploratory analysis based on subnetworks could serve a predictive function in the prognosis of patients with mild traumatic brain injury.展开更多
The problem for the solvability of pseudo-tearing subnetwork is one of the essentialinvestigations of network theory.The results presented would be not only mathematical conditionsbut also topological conditions for s...The problem for the solvability of pseudo-tearing subnetwork is one of the essentialinvestigations of network theory.The results presented would be not only mathematical conditionsbut also topological conditions for subnetwork solvability.These conditions are necessary andalmost sufficient.It should guide one intuitively to the design of accessible nodes.展开更多
Time delay and coupling strength are important factors that affect the synchronization of neural networks.In this study,a modular neural network containing subnetworks of different scales was constructed using the Hod...Time delay and coupling strength are important factors that affect the synchronization of neural networks.In this study,a modular neural network containing subnetworks of different scales was constructed using the Hodgkin–Huxley(HH)neural model;i.e.,a small-scale random network was unidirectionally connected to a large-scale small-world network through chemical synapses.Time delays were found to induce multiple synchronization transitions in the network.An increase in coupling strength also promoted synchronization of the network when the time delay was an integer multiple of the firing period of a single neuron.Considering that time delays at different locations in a modular network may have different effects,we explored the influence of time delays within each subnetwork and between two subnetworks on the synchronization of modular networks.We found that when the subnetworks were well synchronized internally,an increase in the time delay within both subnetworks induced multiple synchronization transitions of their own.In addition,the synchronization state of the small-scale network affected the synchronization of the large-scale network.It was surprising to find that an increase in the time delay between the two subnetworks caused the synchronization factor of the modular network to vary periodically,but it had essentially no effect on the synchronization within the receiving subnetwork.By analyzing the phase difference between the two subnetworks,we found that the mechanism of the periodic variation of the synchronization factor of the modular network was the periodic variation of the phase difference.Finally,the generality of the results was demonstrated by investigating modular networks at different scales.展开更多
The active-subnetwork-extraction theorem and the passive-subnetwork-extraction theorem are derived from one of the author’s previous work. Using them to find the fully symbolic network functions, the multilevel-teari...The active-subnetwork-extraction theorem and the passive-subnetwork-extraction theorem are derived from one of the author’s previous work. Using them to find the fully symbolic network functions, the multilevel-tearing topological analysis for active networks can be substantially simplified so that it can be conducted conveniently on a computer. Using them to find partially symbolic network functions, one finds it possible to extend not only the electrical network that can be analysed on a computer to the order that can be processed by an ordinary numerical analysis program, but also the symbolic subnetwork to the order that can be processed by an ordinary topological analysis program. So far the latter cannot be achieved with the current conventional methods, i. e. the parameter-extraction method and interpolative approach.展开更多
The fault analysis of analog circuits at subnetwork-level is confronted with two essentialcore problems: (ⅰ) Is it necessary that all the torn nodes are accessible? (ⅱ) Are there any topological conditions of subnet...The fault analysis of analog circuits at subnetwork-level is confronted with two essentialcore problems: (ⅰ) Is it necessary that all the torn nodes are accessible? (ⅱ) Are there any topological conditions of subnetwork which guarantee the fault at subnetwork-level to bediagnosed correctly? This paper answers the two problems in two theorems. The conditions are necessary and almost sufficient, and if all the torn nodes are accessible, the required topological conditions can be almost satisfied automatically. This is a special situation of our research on the distribution of the accessible nodes.展开更多
基金supported by the National Natural Science Foundation of China,Nos.81671671(to JL),61971451(to JL),U22A2034(to XK),62177047(to XK)the National Defense Science and Technology Collaborative Innovation Major Project of Central South University,No.2021gfcx05(to JL)+6 种基金Clinical Research Cen terfor Medical Imaging of Hunan Province,No.2020SK4001(to JL)Key Emergency Project of Pneumonia Epidemic of Novel Coronavirus Infection of Hu nan Province,No.2020SK3006(to JL)Innovative Special Construction Foundation of Hunan Province,No.2019SK2131(to JL)the Science and Technology lnnovation Program of Hunan Province,Nos.2021RC4016(to JL),2021SK53503(to ML)Scientific Research Program of Hunan Commission of Health,No.202209044797(to JL)Central South University Research Program of Advanced Interdisciplinary Studies,No.2023Q YJC020(to XK)the Natural Science Foundation of Hunan Province,No.2022JJ30814(to ML)。
文摘Patients with mild traumatic brain injury have a diverse clinical presentation,and the underlying pathophysiology remains poorly understood.Magnetic resonance imaging is a non-invasive technique that has been widely utilized to investigate neuro biological markers after mild traumatic brain injury.This approach has emerged as a promising tool for investigating the pathogenesis of mild traumatic brain injury.G raph theory is a quantitative method of analyzing complex networks that has been widely used to study changes in brain structure and function.However,most previous mild traumatic brain injury studies using graph theory have focused on specific populations,with limited exploration of simultaneous abnormalities in structural and functional connectivity.Given that mild traumatic brain injury is the most common type of traumatic brain injury encounte red in clinical practice,further investigation of the patient characteristics and evolution of structural and functional connectivity is critical.In the present study,we explored whether abnormal structural and functional connectivity in the acute phase could serve as indicators of longitudinal changes in imaging data and cognitive function in patients with mild traumatic brain injury.In this longitudinal study,we enrolled 46 patients with mild traumatic brain injury who were assessed within 2 wee ks of injury,as well as 36 healthy controls.Resting-state functional magnetic resonance imaging and diffusion-weighted imaging data were acquired for graph theoretical network analysis.In the acute phase,patients with mild traumatic brain injury demonstrated reduced structural connectivity in the dorsal attention network.More than 3 months of followup data revealed signs of recovery in structural and functional connectivity,as well as cognitive function,in 22 out of the 46 patients.Furthermore,better cognitive function was associated with more efficient networks.Finally,our data indicated that small-worldness in the acute stage could serve as a predictor of longitudinal changes in connectivity in patients with mild traumatic brain injury.These findings highlight the importance of integrating structural and functional connectivity in unde rstanding the occurrence and evolution of mild traumatic brain injury.Additionally,exploratory analysis based on subnetworks could serve a predictive function in the prognosis of patients with mild traumatic brain injury.
基金This project supported by National Natural Science Foundation of China
文摘The problem for the solvability of pseudo-tearing subnetwork is one of the essentialinvestigations of network theory.The results presented would be not only mathematical conditionsbut also topological conditions for subnetwork solvability.These conditions are necessary andalmost sufficient.It should guide one intuitively to the design of accessible nodes.
基金supported by the National Natural Science Foundation of China(No.12175080)the Fundamental Research Funds for the Central Universities,China(No.CCNU22JC009)。
文摘Time delay and coupling strength are important factors that affect the synchronization of neural networks.In this study,a modular neural network containing subnetworks of different scales was constructed using the Hodgkin–Huxley(HH)neural model;i.e.,a small-scale random network was unidirectionally connected to a large-scale small-world network through chemical synapses.Time delays were found to induce multiple synchronization transitions in the network.An increase in coupling strength also promoted synchronization of the network when the time delay was an integer multiple of the firing period of a single neuron.Considering that time delays at different locations in a modular network may have different effects,we explored the influence of time delays within each subnetwork and between two subnetworks on the synchronization of modular networks.We found that when the subnetworks were well synchronized internally,an increase in the time delay within both subnetworks induced multiple synchronization transitions of their own.In addition,the synchronization state of the small-scale network affected the synchronization of the large-scale network.It was surprising to find that an increase in the time delay between the two subnetworks caused the synchronization factor of the modular network to vary periodically,but it had essentially no effect on the synchronization within the receiving subnetwork.By analyzing the phase difference between the two subnetworks,we found that the mechanism of the periodic variation of the synchronization factor of the modular network was the periodic variation of the phase difference.Finally,the generality of the results was demonstrated by investigating modular networks at different scales.
文摘The active-subnetwork-extraction theorem and the passive-subnetwork-extraction theorem are derived from one of the author’s previous work. Using them to find the fully symbolic network functions, the multilevel-tearing topological analysis for active networks can be substantially simplified so that it can be conducted conveniently on a computer. Using them to find partially symbolic network functions, one finds it possible to extend not only the electrical network that can be analysed on a computer to the order that can be processed by an ordinary numerical analysis program, but also the symbolic subnetwork to the order that can be processed by an ordinary topological analysis program. So far the latter cannot be achieved with the current conventional methods, i. e. the parameter-extraction method and interpolative approach.
基金Project supported by the National Natural Science Foundation of China
文摘The fault analysis of analog circuits at subnetwork-level is confronted with two essentialcore problems: (ⅰ) Is it necessary that all the torn nodes are accessible? (ⅱ) Are there any topological conditions of subnetwork which guarantee the fault at subnetwork-level to bediagnosed correctly? This paper answers the two problems in two theorems. The conditions are necessary and almost sufficient, and if all the torn nodes are accessible, the required topological conditions can be almost satisfied automatically. This is a special situation of our research on the distribution of the accessible nodes.
