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
在低标签率场景下,因监督信息极少,现有的半监督方法在获得令人满意的分类结果方面面临挑战。为此提出1种基于自适应正则化补充交叉熵损失的图卷积网络(graph convolutional network based on adaptive regularization complement with ...在低标签率场景下,因监督信息极少,现有的半监督方法在获得令人满意的分类结果方面面临挑战。为此提出1种基于自适应正则化补充交叉熵损失的图卷积网络(graph convolutional network based on adaptive regularization complement with cross entropy loss,ARCGCN),从损失函数的设计角度出发,通过引入补充熵与图拉普拉斯正则化项,构建适用于标签稀疏数据集并能够抑制标签噪声影响的半监督图卷积网络,从而有效提升模型预测精度与泛化能力。在6个数据集3Sources、Citeseer、GRAZ02、Out-Scene、Noisy-MNIST和NGs上进行实验,通过与9种基线方法对比,证明了ARCGCN性能的有效性和优越性。结果表明:特别在1%的极低标签率下,ARCGCN相较于所有基线方法,其准确率提升尤为显著,充分验证了其处理标签稀疏数据的能力。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。
文摘在低标签率场景下,因监督信息极少,现有的半监督方法在获得令人满意的分类结果方面面临挑战。为此提出1种基于自适应正则化补充交叉熵损失的图卷积网络(graph convolutional network based on adaptive regularization complement with cross entropy loss,ARCGCN),从损失函数的设计角度出发,通过引入补充熵与图拉普拉斯正则化项,构建适用于标签稀疏数据集并能够抑制标签噪声影响的半监督图卷积网络,从而有效提升模型预测精度与泛化能力。在6个数据集3Sources、Citeseer、GRAZ02、Out-Scene、Noisy-MNIST和NGs上进行实验,通过与9种基线方法对比,证明了ARCGCN性能的有效性和优越性。结果表明:特别在1%的极低标签率下,ARCGCN相较于所有基线方法,其准确率提升尤为显著,充分验证了其处理标签稀疏数据的能力。
