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
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
The aim of the present study is to investigate the brain functional network changes of patients with frontal lobe epilepsy(FLE)by resting-state functional magnetic resonance imaging(rsfMRI)and graph theoretical analys...The aim of the present study is to investigate the brain functional network changes of patients with frontal lobe epilepsy(FLE)by resting-state functional magnetic resonance imaging(rsfMRI)and graph theoretical analysis.rsfMRI is performed in 46 adult patients with FLE and 46 age matched healthy controls(HCs).A functional network is built from these subjects,and the topological properties of such network are analyzed quantitatively using graph theoretical methods.According to the results,both FLE patients and HCs exhibit prominent small world features.Compared with HCs,FLE shows a decrease in local efficiency(Eloc),clustering coefficient,nodal efficiency as well as nodal degree.Furthermore,FLE(seven)has fewer hubs than HCs(ten).The functional abnormalities in the network organization suggest functional disturbances in patients with FLE.This study helps to gain new insights into the functional disorder in patients with FLE.The networks built here can also be a set of potential biomarkers for the diagnosis,monitoring and the treatment of FLE.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
目的研究视觉对人体姿势控制影响及其脑功能网络连接机制。方法以15名健康青年为研究对象,要求受试者分别进行30 s睁眼、闭眼的双腿站立平衡,采集平衡过程中身体压力中心(center of pressure,COP)和脑电。对COP进行样本熵(SampleEn)计算...目的研究视觉对人体姿势控制影响及其脑功能网络连接机制。方法以15名健康青年为研究对象,要求受试者分别进行30 s睁眼、闭眼的双腿站立平衡,采集平衡过程中身体压力中心(center of pressure,COP)和脑电。对COP进行样本熵(SampleEn)计算;对脑电θ、α和β频段,计算相位滞后指数(phase lag index,PLI)构建大脑功能网络,并基于图论计算集聚系数(C)、特征路径长度(L)及小世界网络属性(σ)。结果人体在双腿站立平衡过程中,闭眼COPY样本熵显著高于睁眼(P<0.05)。闭眼α频段PLI平均值显著高于睁眼(P<0.05);闭眼α频段C、σ显著高于睁眼,L显著低于睁眼(P<0.05)。闭眼时α频段额区-中央区-顶区之间的网络连接以及中央区和顶区内连接强度显著高于睁眼(P<0.05)。闭眼时α频段PLI平均值以及C值与COPY样本熵中度呈中度负相关(P<0.05)。睁眼时左前额区、左顶区、左枕区α频段PLI平均值与COPY样本熵呈中度负相关;闭眼时左中央区、右枕区α频段PLI平均值则与COPY样本熵呈中度负相关。结论人体在站立平衡时,当没有视觉信息输入时,身体平衡稳定性下降,同时伴随着脑电α频段的脑网络连接增强以及大脑处理信息的效率需提升。人体在不同的视觉条件下进行姿势控制时,大脑会采用不同的神经策略。展开更多
癫痫是一种慢性神经系统疾病,其分类广泛、机制复杂,具有反复发作和不可预测的特点,对患者的生活造成了一定的影响。深度了解其病理生理机制对疾病的治疗和提高患者生活质量十分重要,静息态功能磁共振成像(resting-state functional mag...癫痫是一种慢性神经系统疾病,其分类广泛、机制复杂,具有反复发作和不可预测的特点,对患者的生活造成了一定的影响。深度了解其病理生理机制对疾病的治疗和提高患者生活质量十分重要,静息态功能磁共振成像(resting-state functional magnetic resonance imaging,rs-fMRI)现已成为探究癫痫脑功能改变的有效方法。目前基于rs-fMRI研究癫痫的数据分析方法主要有低频振幅(amplitude of low frequency fluctuation,ALFF)、局部一致性(regional homogeneity,ReHo)、功能连接(function connection,FC)和图论分析。本文将对rs-fMRI的各种分析方法在癫痫中的应用作一综述,为癫痫的病理生理机制及术前定位、治疗提供重要参考。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.
基金supported by the Natural Science Foundation of China (Nos. 81422022, 81271553, 81201155, 81171328, 61131003, 81401402, and 81201161)the Grant for a Young Scholar of Jinling Hospital (No. 2015055)12.5 Key Grants (Nos. BWS11J063 and 10z026)
文摘The aim of the present study is to investigate the brain functional network changes of patients with frontal lobe epilepsy(FLE)by resting-state functional magnetic resonance imaging(rsfMRI)and graph theoretical analysis.rsfMRI is performed in 46 adult patients with FLE and 46 age matched healthy controls(HCs).A functional network is built from these subjects,and the topological properties of such network are analyzed quantitatively using graph theoretical methods.According to the results,both FLE patients and HCs exhibit prominent small world features.Compared with HCs,FLE shows a decrease in local efficiency(Eloc),clustering coefficient,nodal efficiency as well as nodal degree.Furthermore,FLE(seven)has fewer hubs than HCs(ten).The functional abnormalities in the network organization suggest functional disturbances in patients with FLE.This study helps to gain new insights into the functional disorder in patients with FLE.The networks built here can also be a set of potential biomarkers for the diagnosis,monitoring and the treatment of FLE.
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).
文摘目的研究视觉对人体姿势控制影响及其脑功能网络连接机制。方法以15名健康青年为研究对象,要求受试者分别进行30 s睁眼、闭眼的双腿站立平衡,采集平衡过程中身体压力中心(center of pressure,COP)和脑电。对COP进行样本熵(SampleEn)计算;对脑电θ、α和β频段,计算相位滞后指数(phase lag index,PLI)构建大脑功能网络,并基于图论计算集聚系数(C)、特征路径长度(L)及小世界网络属性(σ)。结果人体在双腿站立平衡过程中,闭眼COPY样本熵显著高于睁眼(P<0.05)。闭眼α频段PLI平均值显著高于睁眼(P<0.05);闭眼α频段C、σ显著高于睁眼,L显著低于睁眼(P<0.05)。闭眼时α频段额区-中央区-顶区之间的网络连接以及中央区和顶区内连接强度显著高于睁眼(P<0.05)。闭眼时α频段PLI平均值以及C值与COPY样本熵中度呈中度负相关(P<0.05)。睁眼时左前额区、左顶区、左枕区α频段PLI平均值与COPY样本熵呈中度负相关;闭眼时左中央区、右枕区α频段PLI平均值则与COPY样本熵呈中度负相关。结论人体在站立平衡时,当没有视觉信息输入时,身体平衡稳定性下降,同时伴随着脑电α频段的脑网络连接增强以及大脑处理信息的效率需提升。人体在不同的视觉条件下进行姿势控制时,大脑会采用不同的神经策略。
文摘癫痫是一种慢性神经系统疾病,其分类广泛、机制复杂,具有反复发作和不可预测的特点,对患者的生活造成了一定的影响。深度了解其病理生理机制对疾病的治疗和提高患者生活质量十分重要,静息态功能磁共振成像(resting-state functional magnetic resonance imaging,rs-fMRI)现已成为探究癫痫脑功能改变的有效方法。目前基于rs-fMRI研究癫痫的数据分析方法主要有低频振幅(amplitude of low frequency fluctuation,ALFF)、局部一致性(regional homogeneity,ReHo)、功能连接(function connection,FC)和图论分析。本文将对rs-fMRI的各种分析方法在癫痫中的应用作一综述,为癫痫的病理生理机制及术前定位、治疗提供重要参考。
