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connectivity-based Cortical Parcellation via Contrastive Learning on Spatial-Graph Convolution

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Biomedical Engineering Frontiers 2022年第1期3卷 105-115页

作者： Peiting You Xiang Li Fan Zhang Quanzheng Li Massachusetts General Hospital and Harvard Medical School BostonMAUSA Beijing International Center for Mathematical Research(BICMR) Peking UniversityBeijingChina Brigham and Women’s Hospital and Harvard Medical School BostonMAUSA

*** of this work is the development and evaluation of a cortical parcellation framework based on tractography-derived brain structural *** *** proposed framework utilizes novel spatial-graph representation learning methods for solving the task of cortical parcellation,an important medical image analysis and neuroscientific *** concept of“connectional fingerprint”has motivated many investigations on the connectivity-based cortical parcellation,especially with the technical advancement of diffusion *** studies on multiple brain regions have been conducted with promising ***,performance and applicability of these models are limited by the relatively simple computational scheme and the lack of effective representation of brain imaging *** propose the Spatial-graph Convolution Parcellation(SGCP)framework,a two-stage deep learning-based modeling for the graph representation brain *** the first stage,SGCP learns an effective embedding of the input data through a self-supervised contrastive learning scheme with the backbone encoder of a spatial-graph convolution *** the second stage,SGCP learns a supervised classifier to perform voxel-wise classification for parcellating the desired brain *** is evaluated on the parcellation task for 5 brain regions in a 15-subject DWI *** comparisons between SGCP,traditional parcellation methods,and other deep learning-based methods show that SGCP can achieve superior performance in all the *** good performance of the proposed SGCP framework indicates its potential to be used as a general solution for investigating the regional/subregional composition of human brain based on one or more connectivity measurements.

关键词： connectivity Parcel Spatial

connectivity of the Mandelbrot set for the family of renormalization transformations

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Science China Mathematics 2010年第3期53卷 849-862页

作者： WANG XiaoGuang 1,QIU WeiYuan 1 , YIN YongCheng 1 , QIAO JianYong 2 & GAO JunYang 2 1 School of Mathematical Sciences, Fudan University, Shanghai 200433, China 2 Center of Mathematics, China University of Mining and Technology, Beijing 100083, China School of Mathematical Sciences Fudan University Shanghai China Center of Mathematics China University of Mining and Technology Beijing China

We show that the Mandelbrot set for the family of renormalization transformations of 2-dimensional diamond-like hierachical Potts models in statistical mechanics is connected. We also give an upper bound for the Hausd... 详细信息

关键词： connectivity Mandelbrot set renormalization transformations

connectivity of sparse vehicular ad hoc networks with channel randomness

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High Technology Letters 2010年第4期16卷 389-394页

作者：米振强 Yang Yang An Jianwei Liu Guangjun Department of Information Engineering University of Science and Technology Beijing Beijing 100083 P.R. China Department of Aerospace Engineering Ryerson University Toronto Canada M5A 2C9

In this paper, we investigate the connectivity of vehicular ad hoc networks in free-flow traffic situation with channel randonmess. In order to illustrate the realistic environment, we consider that vehicles are distributed in free-flow highway according to a Poisson point process, and signal propagation between connected vehicles is subjected to log-normal shadowing effects. We obtain the distribution of the space headway between successive vehicles and the distribution of signal coverage, which allows us to use the equivalent M/G/z~ queue theory to model the connectivity of VANETs in the form of average broadcast percolation distance and average number of connected nodes. Then, extensive simulation studies are conducted to evaluate the obtained results. The analytical model presented here is able to describe the impact of various system parameters, including traffic parameters and signal propagation parameters on the con- nectivity. We use our analytical results, along with the common signal propagation data, to understand impact of channel randomness on the connectivity of VANETs.

关键词： vehicular ad hoc networks (VANETs) queuing theory broadcast percolation distance log-normal shadowing connectivity

connectivity and synchronization of Vicsek model

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Science in China(Series F) 2008年第7期51卷 848-858页

作者： LIU ZhiXin GUO Lei Institute of Systems Science Academy of Mathematics and Systems Science Chinese Academy of SciencesBeijing 100190 China

The collective behavior of multi-agent systems is an important studying point for the investigation of complex systems, and a basic model of multi-agent systems is the so called Vicsek model, which possesses some key features of complex systems, such as dynamic behavior, local interaction, changing neighborhood, etc. This model looks simple, but the nonlinearly coupled relationship makes the theoretical analysis quite complicated. Jadbabaie et al. analyzed the linearized heading equations in this model and showed that all agents will synchronize eventually, provided that the neighbor graphs associated with the agents＇ positions satisfy a certain connectivity condition. Much subsequent research effort has been devoted to the analysis of the Vicsek model since the publication of Jadbabaie＇s work. However, an unresolved key problem is when such a connectivity is satisfied. This paper given a sufficient condition to guarantee the synchronization of the Vicsek model, which is imposed on the model parameters only. Moreover, some counterexamples are given to show that the connectivity of the neighbor graphs is not sufficient for synchronization of the Vicsek model if the initial headings are allowed to be in [0,2π）, which reveals some fundamental differences between the Vicsek model and its linearized version.

关键词： Vicsek model synchronization stochastic matrix connectivity neighbor graph

connectivity of Minimum Non-5-injectively Colorable Planar Cubic Graphs

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Journal of the Operations Research Society of China 2020年第1期8卷 105-116页

作者： Jing Jin Bao-Gang Xu Institute of Mathematics School of Mathematical SciencesNanjing Normal UniversityNanjing 210023China College of Taizhou Nanjing Normal UniversityTaizhou 225300JiangsuChina

Suppose that G is a planar cubic graph withχi(G)>*** show that ifχi(H)<χi(G)for each planar cubic graph H of order less thanG,thenG is either a 3-connected simple planar cubic graph,or a planar graph obtained from a simple cubic 3-connected planar graph by adding some *** shows that a minimum non-5-injectively colorable simple planar cubic graph must be 3-connected.

关键词： Planar cubic graphs connectivity 3-connected Injective coloring

connectivity OF CARTESIAN PRODUCT DIGRAPHS AND FAULT-TOLERANT ROUTINGS OF GENERALIZED HYPERCUBE

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Applied Mathematics(A Journal of Chinese Universities) 1998年第2期13卷 179-187页

作者： XU JUNMING Department of Mathematics University of Science and Technology of China Hefei

Abstract In this paper, the problem of fault tolerant routings in fault tolerant networks is considered. A routing in a network assigns to each ordered pair of nodes a fixed path. All communication among nodes must go on this routing. When either a node or a link in a fault tolerant network fails, the communication from one node to another using this faulty element must be sent via one or more intermediate nodes along a sequence of paths determined by this routing. An important and practical problem is how to choose a routing in the network such that intermediate nodes to ensure communication are small for any fault set. Let C d be a directed cycle of order d . In this paper. The author first discusses connectivity of Cartesian product digraphs, then proves that the Cartesian product digraph C d 1 ×C d 2 ×...×C d n (d i≥2,1≤i≤n) has a routing such that at most one intermediate node is needed to ensure transmission of messages among all non faulty nodes so long as the number of faults is less than n . This is a generalization of Dolev et al's result for the n dimensional cube.

关键词： Fault-tolerant networks routings digraphs hypercube connectivity diameter

Local Natural connectivity in Complex Networks

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Chinese Physics Letters 2011年第6期28卷 360-363页

作者： SHANG Yi-Lun Institute for Cyber Security University of Texas at San AntonioSan AntonioTX 78249USA

In network theory,a complex network represents a system whose evolving structure and dynamic behavior contribute to its *** natural connectivity is recently proposed as a spectral measure to characterize the robustness of complex *** decompose the natural connectivity of a network as local natural connectivity of its connected components and quantify their contributions to the network *** addition,we compare the natural connectivity of a network with that of an induced subgraph of it based on interlacing *** an application,we derive an inequality for eigenvalues of Erdös-Rényi random graphs.

关键词： connectivity inequality connected

FLOCKING OF MULTI-AGENT DYNAMIC SYSTEMS WITH GUARANTEED GROUP connectivity

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Journal of Systems Science & Complexity 2008年第3期21卷 337-346页

作者： Xiaoli LI Yugeng XI Department of Automation Shanghai Jiao Tong University Shanghai 200240 China

This paper investigates distributed flocking problem where the information exchange among agents is modeled by the communication topology changing with time. Previous research on this problem establishes group stabilization by assuming that the dynamic topology is connected all the time, which however cannot be guaranteed by most proposed distributed control laws. In this paper, a distributed algorithm to distill a necessary subgraph of the initial communication topology is presented. This subgraph covers all the vertices of the communication topology and is proved to be connected as long as the initial communication topology is connected. A distributed control law is then designed to pursue the flocking motion while preserving all the edges in this subgraph. In this way, connectivity can be preserved all the time, and flocking problem is thus solved only provided the initial communication topology of multi-agent system is connected.

关键词： connectivity distributed control flocking multi-agent system

Cross-frequency network analysis of functional brain connectivity in temporal lobe epilepsy

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Chinese Physics B 2019年第4期28卷 392-400页

作者： Hai-TaoYu Li-Hui Cai Xin-Yu Wu Jiang Wang Jing Liu Hong Zhang School of Electrical and Information Engineering Tianjin University Department of Neurology Tangshan Gongren Hospital

In this study, we investigate the cross-frequency coupling and functional brain networks in the subjects with temporal lobe epilepsy(TLE) using interictal EEG signals. The phase to phase synchronization within and across frequency bands is calculated and a significant difference between the epilepsy and control groups is observed. Compared with the controls,the epilepsy patients exhibit a stronger within-frequency coupling(WFC) within theta and beta bands, and shows a stronger cross-frequency coupling(CFC) in the delta–alpha and theta–alpha band pairs, but a weakened CFC in alpha–beta band pairs. The weakened coupling between alpha and high frequency band reflects a suppression of phase modulation between the brain regions related to epilepsy. Moreover, WFC and CFC are positively correlated, which is higher in the patients relative to controls. We further reconstruct functional brain connectivity and find that both WFC and CFC networks show small-world properties. For the epilepsy, the small-world efficiency is enhanced in the CFC networks in delta–alpha and theta–alpha band pairs, whereas weakened between alpha and beta bands, which suggests a shift away from the optimal operating point in the epileptic brain with a new balance between WFC and CFC. Our results may help us to understand the important role of information communication across different frequency bands and shed new light on the study of pathology of epilepsy.

关键词： cross-frequency coupling epilepsy functional connectivity phase synchronization