The segmentation effect of Tsallis entropy method is superior to that of Shannon entropy method, and the computation speed of two-dimensional Shannon cross entropy method can be further improved by optimization. The e...The segmentation effect of Tsallis entropy method is superior to that of Shannon entropy method, and the computation speed of two-dimensional Shannon cross entropy method can be further improved by optimization. The existing two-dimensional Tsallis cross entropy method is not the strict two-dimensional extension. Thus two new methods of image thresholding using two-dimensional Tsallis cross entropy based on either Chaotic Particle Swarm Optimization (CPSO) or decomposition are proposed. The former uses CPSO to find the optimal threshold. The recursive algorithm is adopted to avoid the repetitive computation of fitness function in iterative procedure. The computing speed is improved greatly. The latter converts the two-dimensional computation into two one-dimensional spaces, which makes the computational complexity further reduced from O(L2) to O(L). The experimental results show that, compared with the proposed recently two-dimensional Shannon or Tsallis cross entropy method, the two new methods can achieve superior segmentation results and reduce running time greatly.展开更多
We are concerned with the global existence of entropy solutions of the two-dimensional steady Euler equations for an ideal gas, which undergoes a one-step exothermic chemical reaction under the Arrhenius-type kinetics...We are concerned with the global existence of entropy solutions of the two-dimensional steady Euler equations for an ideal gas, which undergoes a one-step exothermic chemical reaction under the Arrhenius-type kinetics. The reaction rate function φ（T ） is assumed to have a positive lower bound. We first consider the Cauchy problem （the initial value problem）, that is, seek a supersonic downstream reacting flow when the incoming flow is supersonic, and establish the global existence of entropy solutions when the total variation of the initial data is sufficiently small. Then we analyze the problem of steady supersonic, exothermically reacting Euler flow past a Lipschitz wedge, generating an ad-ditional detonation wave attached to the wedge vertex, which can be then formulated as an initial-boundary value problem. We establish the global existence of entropy solutions containing the additional detonation wave （weak or strong, determined by the wedge angle at the wedge vertex） when the total variation of both the slope of the wedge boundary and the incoming flow is suitably small. The downstream asymptotic behavior of the global solutions is also obtained.展开更多
Characterizing the trajectory of the healthy aging brain and exploring age-related structural changes in the brain can help deepen our understanding of the mechanism of brain aging.Currently,most structural magnetic r...Characterizing the trajectory of the healthy aging brain and exploring age-related structural changes in the brain can help deepen our understanding of the mechanism of brain aging.Currently,most structural magnetic resonance imaging literature explores brain aging merely from the perspective of morphological features,which cannot fully utilize the grayscale values containing important intrinsic information about brain structure.In this study,we propose the construction of two-dimensional horizontal visibility graphs based on the pixel intensity values of the gray matter slices directly.Normalized network structure entropy(NNSE)is then introduced to quantify the overall heterogeneities of these graphs.The results demonstrate a decrease in the NNSEs of gray matter with age.Compared with the middle-aged and the elderly,the larger values of the NNSE in the younger group may indicate more homogeneous network structures,smaller differences in importance between nodes and thus a more powerful ability to tolerate intrusion.In addition,the hub nodes of different adult age groups are primarily located in the precuneus,cingulate gyrus,superior temporal gyrus,inferior temporal gyrus,parahippocampal gyrus,insula,precentral gyrus and postcentral gyrus.Our study can provide a new perspective for understanding and exploring the structural mechanism of brain aging.展开更多
基金supported by National Natural Science Foundation of China under Grant No.60872065Open Foundation of State Key Laboratory for Novel Software Technology at Nanjing University under Grant No.KFKT2010B17
文摘The segmentation effect of Tsallis entropy method is superior to that of Shannon entropy method, and the computation speed of two-dimensional Shannon cross entropy method can be further improved by optimization. The existing two-dimensional Tsallis cross entropy method is not the strict two-dimensional extension. Thus two new methods of image thresholding using two-dimensional Tsallis cross entropy based on either Chaotic Particle Swarm Optimization (CPSO) or decomposition are proposed. The former uses CPSO to find the optimal threshold. The recursive algorithm is adopted to avoid the repetitive computation of fitness function in iterative procedure. The computing speed is improved greatly. The latter converts the two-dimensional computation into two one-dimensional spaces, which makes the computational complexity further reduced from O(L2) to O(L). The experimental results show that, compared with the proposed recently two-dimensional Shannon or Tsallis cross entropy method, the two new methods can achieve superior segmentation results and reduce running time greatly.
基金Gui-Qiang CHEN was supported in part by the UK EPSRC Science and Innovation Award to the Oxford Centre for Nonlinear PDE(EP/E035027/1)the NSFC under a joint project Grant 10728101+4 种基金the Royal Society-Wolfson Research Merit Award(UK)Changguo XIAO was supported in part by the NSFC under a joint project Grant 10728101Yongqian ZHANG was supported in part by NSFC Project 11031001NSFC Project 11121101the 111 Project B08018(China)
文摘We are concerned with the global existence of entropy solutions of the two-dimensional steady Euler equations for an ideal gas, which undergoes a one-step exothermic chemical reaction under the Arrhenius-type kinetics. The reaction rate function φ（T ） is assumed to have a positive lower bound. We first consider the Cauchy problem （the initial value problem）, that is, seek a supersonic downstream reacting flow when the incoming flow is supersonic, and establish the global existence of entropy solutions when the total variation of the initial data is sufficiently small. Then we analyze the problem of steady supersonic, exothermically reacting Euler flow past a Lipschitz wedge, generating an ad-ditional detonation wave attached to the wedge vertex, which can be then formulated as an initial-boundary value problem. We establish the global existence of entropy solutions containing the additional detonation wave （weak or strong, determined by the wedge angle at the wedge vertex） when the total variation of both the slope of the wedge boundary and the incoming flow is suitably small. The downstream asymptotic behavior of the global solutions is also obtained.
基金Project supported by the Natural Science Foundation of Jiangsu Province,China(Grant No.BK20190736)the Young Scientists Fund of the National Natural Science Foundation of China(Grant Nos.81701346 and 61603198)Qinglan Team of Universities in Jiangsu Province(Jiangsu Teacher Letter[2020]10 and Jiangsu Teacher Letter[2021]11).
文摘Characterizing the trajectory of the healthy aging brain and exploring age-related structural changes in the brain can help deepen our understanding of the mechanism of brain aging.Currently,most structural magnetic resonance imaging literature explores brain aging merely from the perspective of morphological features,which cannot fully utilize the grayscale values containing important intrinsic information about brain structure.In this study,we propose the construction of two-dimensional horizontal visibility graphs based on the pixel intensity values of the gray matter slices directly.Normalized network structure entropy(NNSE)is then introduced to quantify the overall heterogeneities of these graphs.The results demonstrate a decrease in the NNSEs of gray matter with age.Compared with the middle-aged and the elderly,the larger values of the NNSE in the younger group may indicate more homogeneous network structures,smaller differences in importance between nodes and thus a more powerful ability to tolerate intrusion.In addition,the hub nodes of different adult age groups are primarily located in the precuneus,cingulate gyrus,superior temporal gyrus,inferior temporal gyrus,parahippocampal gyrus,insula,precentral gyrus and postcentral gyrus.Our study can provide a new perspective for understanding and exploring the structural mechanism of brain aging.
