In this paper,we consider the graph of the product of continuous functions in terms of Hausdorff and packing dimensions.More precisely,we show that,given a real number 1≤β≤2,any real-valued continuous function in C...In this paper,we consider the graph of the product of continuous functions in terms of Hausdorff and packing dimensions.More precisely,we show that,given a real number 1≤β≤2,any real-valued continuous function in C([0,1])can be decomposed into a product of two real-valued continuous functions,each having a graph of Hausdorff dimensionβ.In addition,a product decomposition result for the packing dimension is obtained.This work answers affirmatively two questions raised by Verma and Priyadarshi[14].展开更多
Fractal interpolation function (FIF) is a special type of continuous function which interpolates certain data set and the attractor of the Iterated Function System (IFS) corresponding to a data set is the graph of the...Fractal interpolation function (FIF) is a special type of continuous function which interpolates certain data set and the attractor of the Iterated Function System (IFS) corresponding to a data set is the graph of the FIF. Coalescence Hidden-variable Fractal Interpolation Function (CHFIF) is both self-affine and non self-affine in nature depending on the free variables and constrained free variables for a generalized IFS. In this article, graph directed iterated function system for a finite number of generalized data sets is considered and it is shown that the projection of the attractors on is the graph of the CHFIFs interpolating the corresponding data sets.展开更多
Let Z(λ,G)denote the zeta function of a graph G.In this paper the complement G^Cand the G^(xyz)-transformation G^(xyz)of an r-regular graph G with n vertices and m edges for x,y,z∈{0,1,+,-},are considerd.The relatio...Let Z(λ,G)denote the zeta function of a graph G.In this paper the complement G^Cand the G^(xyz)-transformation G^(xyz)of an r-regular graph G with n vertices and m edges for x,y,z∈{0,1,+,-},are considerd.The relationship between Z(λ,G)and Z(λ,G^C)is obtained.For all x,y,z∈{0,1,+,-},the explicit formulas for the reciprocal of Z(λ,G^(xyz))in terms of r,m,n and the characteristic polynomial of G are obtained.Due to limited space,only the expressions for G^(xyz)with z=0,and xyz∈{0++,+++,1+-}are presented here.展开更多
The concepts of complementary cofactor pairs, normal double-graphs and feasible torn vertex seta are introduced. By using them a decomposition theorem for first-order cofactor C(Y) is derived. Combining it with the mo...The concepts of complementary cofactor pairs, normal double-graphs and feasible torn vertex seta are introduced. By using them a decomposition theorem for first-order cofactor C(Y) is derived. Combining it with the modified double-graph method, a new decomposition analysis-modified double-graph decomposition analysis is presented for finding symbolic network functions. Its advantages are that the resultant symbolic expressions are compact and contain no cancellation terms, and its sign evaluation is very simple.展开更多
Program comprehension is one of the most important applications in decompilation. The more abstract the decompilation result the better it is understood. Intrinsic function is introduced by a compiler to reduce the ov...Program comprehension is one of the most important applications in decompilation. The more abstract the decompilation result the better it is understood. Intrinsic function is introduced by a compiler to reduce the overhead of a function call and is inlined in the code where it is called. When analyzing the decompiled code with lots of inlined intrinsic functions, reverse engineers may be confused by these detailed and repeated operations and lose the goal. In this paper, we propose a method based graph isomorphism to detect intrinsic function on the CFG (Control Flow Graph) of the target function first. Then we identify the boundary of the intrinsic function, determine the parameter and return value and reduce the intrinsic function to a single function call in the disassembled program. Experimental results show that our method is more efficient at reducing intrinsic functions than the state-of-art decompilers such as Hex-Rays, REC and RD (Retargetable Decompiler).展开更多
To meet the requirement of the real-time, accuracy and multi-target diagnosis of the large radar system,a new fuzzy fault diagnosis method based on directed graph model is proposed in this paper. In this method, the l...To meet the requirement of the real-time, accuracy and multi-target diagnosis of the large radar system,a new fuzzy fault diagnosis method based on directed graph model is proposed in this paper. In this method, the large complex system model is defined using the directed graph model firstly, in which the nodes observing the fault by the hierarchical reconstruction of the directed graph are located, then the fault dependency matrix between these nodes and the fault sources are established. And then, we utilize the sensors' alarm probabilities under different situations to build the characteristic fault observation matrix in the fault observation space. Finally,the optimized corresponding diagnosis method using a fuzzy function, which describes the similarity between the actual observation vector and the fault's characteristic vector, is designed. The experimental results demonstrate that the proposed method can achieve high diagnosis efficiency and accuracy. It can be widely used in the real radar system.展开更多
CAD model retrieval based on functional semantics is more significant than content-based 3D model retrieval during the mechanical conceptual design phase. However, relevant research is still not fully discussed. There...CAD model retrieval based on functional semantics is more significant than content-based 3D model retrieval during the mechanical conceptual design phase. However, relevant research is still not fully discussed. Therefore, a functional semantic-based CAD model annotation and retrieval method is proposed to support mechanical conceptual design and design reuse, inspire designer creativity through existing CAD models, shorten design cycle, and reduce costs. Firstly, the CAD model functional semantic ontology is constructed to formally represent the functional semantics of CAD models and describe the mechanical conceptual design space comprehensively and consistently. Secondly, an approach to represent CAD models as attributed adjacency graphs（AAG） is proposed. In this method, the geometry and topology data are extracted from STEP models. On the basis of AAG, the functional semantics of CAD models are annotated semi-automatically by matching CAD models that contain the partial features of which functional semantics have been annotated manually, thereby constructing CAD Model Repository that supports model retrieval based on functional semantics. Thirdly, a CAD model retrieval algorithm that supports multi-function extended retrieval is proposed to explore more potential creative design knowledge in the semantic level. Finally, a prototype system, called Functional Semantic-based CAD Model Annotation and Retrieval System（FSMARS）, is implemented. A case demonstrates that FSMARS can successfully botain multiple potential CAD models that conform to the desired function. The proposed research addresses actual needs and presents a new way to acquire CAD models in the mechanical conceptual design phase.展开更多
Depression is closely linked to the morphology and functional abnormalities of multiple brain regions; however, its topological structure throughout the whole brain remains unclear. We col- lected resting-state functi...Depression is closely linked to the morphology and functional abnormalities of multiple brain regions; however, its topological structure throughout the whole brain remains unclear. We col- lected resting-state functional MRI data from 36 first-onset unmedicated depression patients and 27 healthy controls. The resting-state functional connectivity was constructed using the Auto- mated Anatomical Labeling template with a partial correlation method. The metrics calculation and statistical analysis were performed using complex network theory. The results showed that both depressive patients and healthy controls presented typical small-world attributes. Compared with healthy controls, characteristic path length was significantly shorter in depressive patients, suggesting development toward randomization. Patients with depression showed apparently abnormal node attributes at key areas in cortical-striatal-pallidal-thalamic circuits. In addition, right hippocampus and right thalamus were closely linked with the severity of depression. We se- lected 270 local attributes as the classification features and their P values were regarded as criteria for statistically significant differences. An artificial neural network algorithm was applied for classification research. The results showed that brain network metrics could be used as an effec- tive feature in machine learning research, which brings about a reasonable application prospect for brain network metrics. The present study also highlighted a significant positive correlation between the importance of the attributes and the intergroup differences; that is, the more sig- nificant the differences in node attributes, the stronger their contribution to the classification. Experimental findings indicate that statistical significance is an effective quantitative indicator of the selection of brain network metrics and can assist the clinical diagnosis of depression.展开更多
The present study was aimed to evaluate restingstate functional connectivity and topological properties of brain networks in narcolepsy patients compared with healthy controls.Resting-state fMRI was performed in 26 ad...The present study was aimed to evaluate restingstate functional connectivity and topological properties of brain networks in narcolepsy patients compared with healthy controls.Resting-state fMRI was performed in 26 adult narcolepsy patients and 30 matched healthy controls.MRI data were first analyzed by group independent component analysis,then a graph theoretical method was applied to evaluate the topological properties in the whole brain.Small-world network parameters and nodal topological properties were measured.Altered topological properties in brain areas between groups were selected as regionof-interest seeds,then the functional connectivity among these seeds was compared between groups.Partial correlation analysis was performed to evaluate the relationship between the severity of sleepiness and functional connectivity or topological properties in the narcolepsy patients.Twenty-one independent components out of 48 were obtained.Compared with healthy controls,the narcolepsy patients exhibited significantly decreased functional connectivity within the executive and salience networks,along with increased functional connectivity in the bilateral frontal lobes within the executive network.There were no differences in small-world network properties between patients and controls.The altered brain areas in nodal topological properties between groups were mainly in the inferior frontal cortex,basal ganglia,anterior cingulate,sensory cortex,supplementary motor cortex,and visual cortex.In the partial correlation analysis,nodal topological properties in the putamen,anterior cingulate,and sensory cortex as well as functional connectivity between these regions were correlated with the severity of sleepiness(sleep latency,REM sleep latency,and Epworth sleepiness score)among narcolepsy patients.Altered connectivity within the executive and salience networks was found in narcolepsy patients.Functional connection changes between the left frontal cortex and left caudate nucleus may be one of the parameters describing the severity of narcolepsy.Changes in the nodal topological properties in the left putamen and left posterior cingulate,changes in functional connectivity between the left supplementary motor area and right occipital as well as in functional connectivity between the left anterior cingulate gyrus and bilateral postcentral gyrus can be considered as a specific indicator for evaluating the severity of narcolepsy.展开更多
This paper continues the research on theoretical foundations for computer simulation.We introduce the concept of word-updating dynamical systems(WDS)on directed graphs,which is a kind of generalization of sequential d...This paper continues the research on theoretical foundations for computer simulation.We introduce the concept of word-updating dynamical systems(WDS)on directed graphs,which is a kind of generalization of sequential dynamical systems(SDS)on graphs.Some properties on WDS,especially some results on NOR-WDS,which are different from that on NOR-SDS,are obtained.展开更多
Background: The mechanisms by which acupuncture affects poststroke cognitive impairment (PSCI) remain unclear. Objective: To investigate brain functional network (BFN) changes in patients with PSCI after acupuncture t...Background: The mechanisms by which acupuncture affects poststroke cognitive impairment (PSCI) remain unclear. Objective: To investigate brain functional network (BFN) changes in patients with PSCI after acupuncture therapy. Methods: Twenty-two PSCI patients who underwent acupuncture therapy in our hospital were enrolled as research subjects. Another 14 people matched for age, sex, and education level were included in the normal control (HC) group. All the subjects underwent resting-state functional magnetic resonance imaging (rs-fMRI) scans;the PSCI patients underwent one scan before acupuncture therapy and another after. The network metric difference between PSCI patients and HCs was analyzed via the independent-sample t test, whereas the paired-sample t test was employed to analyze the network metric changes in PSCI patients before vs. after treatment. Results: Small-world network attributes were observed in both groups for sparsities between 0.1 and 0.28. Compared with the HC group, the PSCI group presented significantly lower values for the global topological properties (γ, Cp, and Eloc) of the brain;significantly greater values for the nodal attributes of betweenness centrality in the CUN. L and the HES. R, degree centrality in the SFGdor. L, PCG. L, IPL. L, and HES. R, and nodal local efficiency in the ORBsup. R, ORBsupmed. R, DCG. L, SMG. R, and TPOsup. L;and decreased degree centrality in the MFG. R, IFGoperc. R, and SOG. R. After treatment, PSCI patients presented increased degree centrality in the LING.L, LING.R, and IOG. L and nodal local efficiency in PHG. L, IOG. R, FFG. L, and the HES. L, and decreased betweenness centrality in the PCG. L and CUN. L, degree centrality in the ORBsupmed. R, and nodal local efficiency in ANG. R. Conclusion: Cognitive decline in PSCI patients may be related to BFN disorders;acupuncture therapy may modulate the topological properties of the BFNs of PSCI patients.展开更多
In this work a method called “signal flow graph (SFG)” is presented. A signal-flow graph describes a system by its signal flow by directed and weighted graph;the signals are applied to nodes and functions on edges. ...In this work a method called “signal flow graph (SFG)” is presented. A signal-flow graph describes a system by its signal flow by directed and weighted graph;the signals are applied to nodes and functions on edges. The edges of the signal flow graph are small processing units, through which the incoming signals are processed in a certain form. In this case, the result is sent to the outgoing node. The SFG allows a good visual inspection into complex feedback problems. Furthermore such a presentation allows for a clear and unambiguous description of a generating system, for example, a netview. A Signal Flow Graph (SFG) allows a fast and practical network analysis based on a clear data presentation in graphic format of the mathematical linear equations of the circuit. During creation of a SFG the Direct Current-Case (DC-Case) was observed since the correct current and voltage directions was drawn from zero frequency. In addition, the mathematical axioms, which are based on field algebra, are declared. In this work we show you in addition: How we check our SFG whether it is a consistent system or not. A signal flow graph can be verified by generating the identity of the signal flow graph itself, illustrated by the inverse signal flow graph (SFG−1). Two signal flow graphs are always generated from one circuit, so that the signal flow diagram already presented in previous sections corresponds to only half of the solution. The other half of the solution is the so-called identity, which represents the (SFG−1). If these two graphs are superposed with one another, so called 1-edges are created at the node points. In Boolean algebra, these 1-edges are given the value 1, whereas this value can be identified with a zero in the field algebra.展开更多
Network is considered naturally as a wide range of different contexts, such as biological systems, social relationships as well as various technological scenarios. Investigation of the dynamic phenomena taking place i...Network is considered naturally as a wide range of different contexts, such as biological systems, social relationships as well as various technological scenarios. Investigation of the dynamic phenomena taking place in the network, determination of the structure of the network and community and description of the interactions between various elements of the network are the key issues in network analysis. One of the huge network structure challenges is the identification of the node(s) with an outstanding structural position within the network. The popular method for doing this is to calculate a measure of centrality. We examine node centrality measures such as degree, closeness, eigenvector, Katz and subgraph centrality for undirected networks. We show how the Katz centrality can be turned into degree and eigenvector centrality by considering limiting cases. Some existing centrality measures are linked to matrix functions. We extend this idea and examine the centrality measures based on general matrix functions and in particular, the logarithmic, cosine, sine, and hyperbolic functions. We also explore the concept of generalised Katz centrality. Various experiments are conducted for different networks generated by using random graph models. The results show that the logarithmic function in particular has potential as a centrality measure. Similar results were obtained for real-world networks.展开更多
In this paper, we study the connectedness of the invariant sets of a graph-directed iterated function system（IFS）. For a graph-directed IFS with N states, we construct N graphs. We prove that all the invariant sets ...In this paper, we study the connectedness of the invariant sets of a graph-directed iterated function system（IFS）. For a graph-directed IFS with N states, we construct N graphs. We prove that all the invariant sets are connected, if and only if all the N graphs are connected; in this case, the invariant sets are all locally connected and path connected. Our result extends the results on the connectedness of the self-similar sets.展开更多
Given a graph g=( V,A ) , we define a space of subgraphs M with the binary operation of union and the unique decomposition property into blocks. This space allows us to discuss a notion of minimal subgraphs (minimal c...Given a graph g=( V,A ) , we define a space of subgraphs M with the binary operation of union and the unique decomposition property into blocks. This space allows us to discuss a notion of minimal subgraphs (minimal coalitions) that are of interest for the game. Additionally, a partition of the game is defined in terms of the gain of each block, and subsequently, a solution to the game is defined based on distributing to each player (node and edge) present in each block a payment proportional to their contribution to the coalition.展开更多
基金supported by the NSFC (11701001,11626030)the Support Plan for Outstanding Young Talents in Colleges in Anhui Province (Key project) (gxyqzD2020021)the Scientific Research Project of Colleges and Universities in Anhui Province,2023。
文摘In this paper,we consider the graph of the product of continuous functions in terms of Hausdorff and packing dimensions.More precisely,we show that,given a real number 1≤β≤2,any real-valued continuous function in C([0,1])can be decomposed into a product of two real-valued continuous functions,each having a graph of Hausdorff dimensionβ.In addition,a product decomposition result for the packing dimension is obtained.This work answers affirmatively two questions raised by Verma and Priyadarshi[14].
文摘Fractal interpolation function (FIF) is a special type of continuous function which interpolates certain data set and the attractor of the Iterated Function System (IFS) corresponding to a data set is the graph of the FIF. Coalescence Hidden-variable Fractal Interpolation Function (CHFIF) is both self-affine and non self-affine in nature depending on the free variables and constrained free variables for a generalized IFS. In this article, graph directed iterated function system for a finite number of generalized data sets is considered and it is shown that the projection of the attractors on is the graph of the CHFIFs interpolating the corresponding data sets.
基金National Natural Science Foundation of China(No.11671258)
文摘Let Z(λ,G)denote the zeta function of a graph G.In this paper the complement G^Cand the G^(xyz)-transformation G^(xyz)of an r-regular graph G with n vertices and m edges for x,y,z∈{0,1,+,-},are considerd.The relationship between Z(λ,G)and Z(λ,G^C)is obtained.For all x,y,z∈{0,1,+,-},the explicit formulas for the reciprocal of Z(λ,G^(xyz))in terms of r,m,n and the characteristic polynomial of G are obtained.Due to limited space,only the expressions for G^(xyz)with z=0,and xyz∈{0++,+++,1+-}are presented here.
文摘The concepts of complementary cofactor pairs, normal double-graphs and feasible torn vertex seta are introduced. By using them a decomposition theorem for first-order cofactor C(Y) is derived. Combining it with the modified double-graph method, a new decomposition analysis-modified double-graph decomposition analysis is presented for finding symbolic network functions. Its advantages are that the resultant symbolic expressions are compact and contain no cancellation terms, and its sign evaluation is very simple.
文摘Program comprehension is one of the most important applications in decompilation. The more abstract the decompilation result the better it is understood. Intrinsic function is introduced by a compiler to reduce the overhead of a function call and is inlined in the code where it is called. When analyzing the decompiled code with lots of inlined intrinsic functions, reverse engineers may be confused by these detailed and repeated operations and lose the goal. In this paper, we propose a method based graph isomorphism to detect intrinsic function on the CFG (Control Flow Graph) of the target function first. Then we identify the boundary of the intrinsic function, determine the parameter and return value and reduce the intrinsic function to a single function call in the disassembled program. Experimental results show that our method is more efficient at reducing intrinsic functions than the state-of-art decompilers such as Hex-Rays, REC and RD (Retargetable Decompiler).
基金the National Natural Science Foundation of China(No.61371024)the Aviation Science Fund of China(No.2013ZD53051)+1 种基金the IndustryAcademy-Research Project of Aviation Industry Corporation of China(No.cxy2013XGD14)the Space Support Technology Fund of China
文摘To meet the requirement of the real-time, accuracy and multi-target diagnosis of the large radar system,a new fuzzy fault diagnosis method based on directed graph model is proposed in this paper. In this method, the large complex system model is defined using the directed graph model firstly, in which the nodes observing the fault by the hierarchical reconstruction of the directed graph are located, then the fault dependency matrix between these nodes and the fault sources are established. And then, we utilize the sensors' alarm probabilities under different situations to build the characteristic fault observation matrix in the fault observation space. Finally,the optimized corresponding diagnosis method using a fuzzy function, which describes the similarity between the actual observation vector and the fault's characteristic vector, is designed. The experimental results demonstrate that the proposed method can achieve high diagnosis efficiency and accuracy. It can be widely used in the real radar system.
基金Supported by National Natural Science Foundation of China (Grant No.51175287)National Science and Technology Major Project of China (Grant No.2011ZX02403)
文摘CAD model retrieval based on functional semantics is more significant than content-based 3D model retrieval during the mechanical conceptual design phase. However, relevant research is still not fully discussed. Therefore, a functional semantic-based CAD model annotation and retrieval method is proposed to support mechanical conceptual design and design reuse, inspire designer creativity through existing CAD models, shorten design cycle, and reduce costs. Firstly, the CAD model functional semantic ontology is constructed to formally represent the functional semantics of CAD models and describe the mechanical conceptual design space comprehensively and consistently. Secondly, an approach to represent CAD models as attributed adjacency graphs（AAG） is proposed. In this method, the geometry and topology data are extracted from STEP models. On the basis of AAG, the functional semantics of CAD models are annotated semi-automatically by matching CAD models that contain the partial features of which functional semantics have been annotated manually, thereby constructing CAD Model Repository that supports model retrieval based on functional semantics. Thirdly, a CAD model retrieval algorithm that supports multi-function extended retrieval is proposed to explore more potential creative design knowledge in the semantic level. Finally, a prototype system, called Functional Semantic-based CAD Model Annotation and Retrieval System（FSMARS）, is implemented. A case demonstrates that FSMARS can successfully botain multiple potential CAD models that conform to the desired function. The proposed research addresses actual needs and presents a new way to acquire CAD models in the mechanical conceptual design phase.
基金supported by the National Natural Science Foundation of China,No.61070077,61170136,61373101,81171290the Natural Science Foundation of Shanxi Province in China,No.2010011020-2,2011011015-4+3 种基金Programs for Science and Technology Social Development of Shanxi Province,No.20130313012-2Science and Technology Projects by Shanxi Provincial Ed-ucation Ministry,No.20121003Youth Fund by Taiyuan University of Technology,No.2012L014Youth Team Fund by Taiyuan University of Technology,No.2013T047
文摘Depression is closely linked to the morphology and functional abnormalities of multiple brain regions; however, its topological structure throughout the whole brain remains unclear. We col- lected resting-state functional MRI data from 36 first-onset unmedicated depression patients and 27 healthy controls. The resting-state functional connectivity was constructed using the Auto- mated Anatomical Labeling template with a partial correlation method. The metrics calculation and statistical analysis were performed using complex network theory. The results showed that both depressive patients and healthy controls presented typical small-world attributes. Compared with healthy controls, characteristic path length was significantly shorter in depressive patients, suggesting development toward randomization. Patients with depression showed apparently abnormal node attributes at key areas in cortical-striatal-pallidal-thalamic circuits. In addition, right hippocampus and right thalamus were closely linked with the severity of depression. We se- lected 270 local attributes as the classification features and their P values were regarded as criteria for statistically significant differences. An artificial neural network algorithm was applied for classification research. The results showed that brain network metrics could be used as an effec- tive feature in machine learning research, which brings about a reasonable application prospect for brain network metrics. The present study also highlighted a significant positive correlation between the importance of the attributes and the intergroup differences; that is, the more sig- nificant the differences in node attributes, the stronger their contribution to the classification. Experimental findings indicate that statistical significance is an effective quantitative indicator of the selection of brain network metrics and can assist the clinical diagnosis of depression.
基金supported by the National Natural Science Foundation of China (81700088 and 81671765)the Key International (Regional) Cooperation Program of the National Natural Science Foundation of China (81420108002)+1 种基金the National Basic Research Development Program (973 Program) of China (2015CB856405)the Beijing Municipal Natural Science Foundation (7172121)
文摘The present study was aimed to evaluate restingstate functional connectivity and topological properties of brain networks in narcolepsy patients compared with healthy controls.Resting-state fMRI was performed in 26 adult narcolepsy patients and 30 matched healthy controls.MRI data were first analyzed by group independent component analysis,then a graph theoretical method was applied to evaluate the topological properties in the whole brain.Small-world network parameters and nodal topological properties were measured.Altered topological properties in brain areas between groups were selected as regionof-interest seeds,then the functional connectivity among these seeds was compared between groups.Partial correlation analysis was performed to evaluate the relationship between the severity of sleepiness and functional connectivity or topological properties in the narcolepsy patients.Twenty-one independent components out of 48 were obtained.Compared with healthy controls,the narcolepsy patients exhibited significantly decreased functional connectivity within the executive and salience networks,along with increased functional connectivity in the bilateral frontal lobes within the executive network.There were no differences in small-world network properties between patients and controls.The altered brain areas in nodal topological properties between groups were mainly in the inferior frontal cortex,basal ganglia,anterior cingulate,sensory cortex,supplementary motor cortex,and visual cortex.In the partial correlation analysis,nodal topological properties in the putamen,anterior cingulate,and sensory cortex as well as functional connectivity between these regions were correlated with the severity of sleepiness(sleep latency,REM sleep latency,and Epworth sleepiness score)among narcolepsy patients.Altered connectivity within the executive and salience networks was found in narcolepsy patients.Functional connection changes between the left frontal cortex and left caudate nucleus may be one of the parameters describing the severity of narcolepsy.Changes in the nodal topological properties in the left putamen and left posterior cingulate,changes in functional connectivity between the left supplementary motor area and right occipital as well as in functional connectivity between the left anterior cingulate gyrus and bilateral postcentral gyrus can be considered as a specific indicator for evaluating the severity of narcolepsy.
文摘This paper continues the research on theoretical foundations for computer simulation.We introduce the concept of word-updating dynamical systems(WDS)on directed graphs,which is a kind of generalization of sequential dynamical systems(SDS)on graphs.Some properties on WDS,especially some results on NOR-WDS,which are different from that on NOR-SDS,are obtained.
文摘Background: The mechanisms by which acupuncture affects poststroke cognitive impairment (PSCI) remain unclear. Objective: To investigate brain functional network (BFN) changes in patients with PSCI after acupuncture therapy. Methods: Twenty-two PSCI patients who underwent acupuncture therapy in our hospital were enrolled as research subjects. Another 14 people matched for age, sex, and education level were included in the normal control (HC) group. All the subjects underwent resting-state functional magnetic resonance imaging (rs-fMRI) scans;the PSCI patients underwent one scan before acupuncture therapy and another after. The network metric difference between PSCI patients and HCs was analyzed via the independent-sample t test, whereas the paired-sample t test was employed to analyze the network metric changes in PSCI patients before vs. after treatment. Results: Small-world network attributes were observed in both groups for sparsities between 0.1 and 0.28. Compared with the HC group, the PSCI group presented significantly lower values for the global topological properties (γ, Cp, and Eloc) of the brain;significantly greater values for the nodal attributes of betweenness centrality in the CUN. L and the HES. R, degree centrality in the SFGdor. L, PCG. L, IPL. L, and HES. R, and nodal local efficiency in the ORBsup. R, ORBsupmed. R, DCG. L, SMG. R, and TPOsup. L;and decreased degree centrality in the MFG. R, IFGoperc. R, and SOG. R. After treatment, PSCI patients presented increased degree centrality in the LING.L, LING.R, and IOG. L and nodal local efficiency in PHG. L, IOG. R, FFG. L, and the HES. L, and decreased betweenness centrality in the PCG. L and CUN. L, degree centrality in the ORBsupmed. R, and nodal local efficiency in ANG. R. Conclusion: Cognitive decline in PSCI patients may be related to BFN disorders;acupuncture therapy may modulate the topological properties of the BFNs of PSCI patients.
文摘In this work a method called “signal flow graph (SFG)” is presented. A signal-flow graph describes a system by its signal flow by directed and weighted graph;the signals are applied to nodes and functions on edges. The edges of the signal flow graph are small processing units, through which the incoming signals are processed in a certain form. In this case, the result is sent to the outgoing node. The SFG allows a good visual inspection into complex feedback problems. Furthermore such a presentation allows for a clear and unambiguous description of a generating system, for example, a netview. A Signal Flow Graph (SFG) allows a fast and practical network analysis based on a clear data presentation in graphic format of the mathematical linear equations of the circuit. During creation of a SFG the Direct Current-Case (DC-Case) was observed since the correct current and voltage directions was drawn from zero frequency. In addition, the mathematical axioms, which are based on field algebra, are declared. In this work we show you in addition: How we check our SFG whether it is a consistent system or not. A signal flow graph can be verified by generating the identity of the signal flow graph itself, illustrated by the inverse signal flow graph (SFG−1). Two signal flow graphs are always generated from one circuit, so that the signal flow diagram already presented in previous sections corresponds to only half of the solution. The other half of the solution is the so-called identity, which represents the (SFG−1). If these two graphs are superposed with one another, so called 1-edges are created at the node points. In Boolean algebra, these 1-edges are given the value 1, whereas this value can be identified with a zero in the field algebra.
文摘Network is considered naturally as a wide range of different contexts, such as biological systems, social relationships as well as various technological scenarios. Investigation of the dynamic phenomena taking place in the network, determination of the structure of the network and community and description of the interactions between various elements of the network are the key issues in network analysis. One of the huge network structure challenges is the identification of the node(s) with an outstanding structural position within the network. The popular method for doing this is to calculate a measure of centrality. We examine node centrality measures such as degree, closeness, eigenvector, Katz and subgraph centrality for undirected networks. We show how the Katz centrality can be turned into degree and eigenvector centrality by considering limiting cases. Some existing centrality measures are linked to matrix functions. We extend this idea and examine the centrality measures based on general matrix functions and in particular, the logarithmic, cosine, sine, and hyperbolic functions. We also explore the concept of generalised Katz centrality. Various experiments are conducted for different networks generated by using random graph models. The results show that the logarithmic function in particular has potential as a centrality measure. Similar results were obtained for real-world networks.
基金Supported by the Teaching Research Project of Hubei Province(2013469)the 12th Five-Year Project of Education Plan of Hubei Province(2014B379)
文摘In this paper, we study the connectedness of the invariant sets of a graph-directed iterated function system（IFS）. For a graph-directed IFS with N states, we construct N graphs. We prove that all the invariant sets are connected, if and only if all the N graphs are connected; in this case, the invariant sets are all locally connected and path connected. Our result extends the results on the connectedness of the self-similar sets.
文摘Given a graph g=( V,A ) , we define a space of subgraphs M with the binary operation of union and the unique decomposition property into blocks. This space allows us to discuss a notion of minimal subgraphs (minimal coalitions) that are of interest for the game. Additionally, a partition of the game is defined in terms of the gain of each block, and subsequently, a solution to the game is defined based on distributing to each player (node and edge) present in each block a payment proportional to their contribution to the coalition.
