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
为确立船舶营运过程中的风险涌现特征,需要考虑复杂系统组成因子的不确定结构问题。以复杂性系统为视角,提出了一种复杂网络不确定结构的风险功能共振分析模型。首先,利用Apriori算法对船舶系统组分进行风险分析,计算组成因子间的非线...为确立船舶营运过程中的风险涌现特征,需要考虑复杂系统组成因子的不确定结构问题。以复杂性系统为视角,提出了一种复杂网络不确定结构的风险功能共振分析模型。首先,利用Apriori算法对船舶系统组分进行风险分析,计算组成因子间的非线性交互效用,生成交互强度矩阵,从而确立船舶营运安全风险的功能共振分析模型(Functional Resonance Analysis Model,FRAM)。随后,采用图卷积网络(Graph Convolutional Network,GCN)构建系统组分网络,识别关键节点,并对因子交互关系网络结构进行重塑。最后,引入深度优先搜索(Depth First Search,DFS)算法,识别关键风险路径,计算出船舶系统组分因子的影响度。结合港口国监督(Port State Control,PSC)缺陷数据,运用前述模型对船舶营运风险进行仿真应用。应用结果表明,船舶的不安全状态受到内外部组成因子的属性影响,并存在关键共振路径关系,其中消防系统、船舶结构状态等是影响船舶不安全状态的核心节点。构建的风险功能共振分析模型能够基于不同的数据输入,自适应生成相应的风险路径依赖。基于复杂网络结构的风险功能共振模型有助于分析不确定结构复杂系统的风险涌现。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
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).
文摘为确立船舶营运过程中的风险涌现特征,需要考虑复杂系统组成因子的不确定结构问题。以复杂性系统为视角,提出了一种复杂网络不确定结构的风险功能共振分析模型。首先,利用Apriori算法对船舶系统组分进行风险分析,计算组成因子间的非线性交互效用,生成交互强度矩阵,从而确立船舶营运安全风险的功能共振分析模型(Functional Resonance Analysis Model,FRAM)。随后,采用图卷积网络(Graph Convolutional Network,GCN)构建系统组分网络,识别关键节点,并对因子交互关系网络结构进行重塑。最后,引入深度优先搜索(Depth First Search,DFS)算法,识别关键风险路径,计算出船舶系统组分因子的影响度。结合港口国监督(Port State Control,PSC)缺陷数据,运用前述模型对船舶营运风险进行仿真应用。应用结果表明,船舶的不安全状态受到内外部组成因子的属性影响,并存在关键共振路径关系,其中消防系统、船舶结构状态等是影响船舶不安全状态的核心节点。构建的风险功能共振分析模型能够基于不同的数据输入,自适应生成相应的风险路径依赖。基于复杂网络结构的风险功能共振模型有助于分析不确定结构复杂系统的风险涌现。
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.
