A graph whose edges are labeled either as positive or negative is called a signed graph.Hameed et al.introduced signed distance and distance compatibility in 2021,initially to characterize balanced signed graphs which...A graph whose edges are labeled either as positive or negative is called a signed graph.Hameed et al.introduced signed distance and distance compatibility in 2021,initially to characterize balanced signed graphs which have nice spectral properties.This article mainly studies the conjecture proposed by Shijin et al.on the distance compatibility of the direct product of signed graphs,and provides necessary and sufficient conditions for the distance compatibility of the direct product of signed graphs.Some further questions regarding distance compatibility are also posed.展开更多
The unique structure of signed networks,characterized by positive and negative edges,poses significant challenges for analyzing network topology.In recent years,various statistical algorithms have been developed to ad...The unique structure of signed networks,characterized by positive and negative edges,poses significant challenges for analyzing network topology.In recent years,various statistical algorithms have been developed to address this issue.However,there remains a lack of a unified framework to uncover the nontrivial properties inherent in signed network structures.To support developers,researchers,and practitioners in this field,we introduce a Python library named SNSAlib(Signed Network Structure Analysis),specifically designed to meet these analytical requirements.This library encompasses empirical signed network datasets,signed null model algorithms,signed statistics algorithms,and evaluation indicators.The primary objective of SNSAlib is to facilitate the systematic analysis of micro-and meso-structure features within signed networks,including node popularity,clustering,assortativity,embeddedness,and community structure by employing more accurate signed null models.Ultimately,it provides a robust paradigm for structure analysis of signed networks that enhances our understanding and application of signed networks.展开更多
A signed graph S=(S^(u),σ)has an underlying graph Suand a functionσ:E(S^(u))-→{+,-}.Let E^(-)(S)denote the set of negative edges of S.Then S is eulerian signed graph(or subeulerian signed graph,or balanced eulerian...A signed graph S=(S^(u),σ)has an underlying graph Suand a functionσ:E(S^(u))-→{+,-}.Let E^(-)(S)denote the set of negative edges of S.Then S is eulerian signed graph(or subeulerian signed graph,or balanced eulerian signed graph,respectively)if Suis eulerian(or subeulerian,or eulerian and|E-(S)|is even,respectively).We say that S is balanced subeulerian signed graph if there exists a balanced eulerian signed graph S′such that S′is spanned by S.The signed line graph L(S)of a signed graph S is a signed graph with the vertices of L(S)being the edges of S,where an edge eiej is in L(S)if and only if the edges e_(i)and e_(j)of S have a vertex in common in S such that an edge eiej in L(S)is negative if and only if both edges ei and ej are negative in S.In this paper,two families of signed graphs S and S′are identified,which are applied to characterize balanced subeulerian signed graphs and balanced subeulerian signed line graphs.In particular,it is proved that a signed graph S is balanced subeulerian if and only if S∈S,and that a signed line graph of signed graph S is balanced subeulerian if and only if S∈S′.展开更多
While progress has been made in information source localization,it has overlooked the prevalent friend and adversarial relationships in social networks.This paper addresses this gap by focusing on source localization ...While progress has been made in information source localization,it has overlooked the prevalent friend and adversarial relationships in social networks.This paper addresses this gap by focusing on source localization in signed network models.Leveraging the topological characteristics of signed networks and transforming the propagation probability into effective distance,we propose an optimization method for observer selection.Additionally,by using the reverse propagation algorithm we present a method for information source localization in signed networks.Extensive experimental results demonstrate that a higher proportion of positive edges within signed networks contributes to more favorable source localization,and the higher the ratio of propagation rates between positive and negative edges,the more accurate the source localization becomes.Interestingly,this aligns with our observation that,in reality,the number of friends tends to be greater than the number of adversaries,and the likelihood of information propagation among friends is often higher than among adversaries.In addition,the source located at the periphery of the network is not easy to identify.Furthermore,our proposed observer selection method based on effective distance achieves higher operational efficiency and exhibits higher accuracy in information source localization,compared with three strategies for observer selection based on the classical full-order neighbor coverage.展开更多
Let G = （V, E） be a graph, and let f ： V →{-1, 1} be a two-valued function. If ∑x∈N（v） f（x） ≥ 1 for each v ∈ V, where N（v） is the open neighborhood of v, then f is a signed total dominating function on ...Let G = （V, E） be a graph, and let f ： V →{-1, 1} be a two-valued function. If ∑x∈N（v） f（x） ≥ 1 for each v ∈ V, where N（v） is the open neighborhood of v, then f is a signed total dominating function on G. A set {fl, f2,… fd} of signed d total dominating functions on G with the property that ∑i=1^d fi（x） ≤ 1 for each x ∈ V, is called a signed total dominating family （of functions） on G. The maximum number of functions in a signed total dominating family on G is the signed total domatic number on G, denoted by dt^s（G）. The properties of the signed total domatic number dt^s（G） are studied in this paper. In particular, we give the sharp bounds of the signed total domatic number of regular graphs, complete bipartite graphs and complete graphs.展开更多
A signed(res. signed total) Roman dominating function, SRDF(res.STRDF) for short, of a graph G =(V, E) is a function f : V → {-1, 1, 2} satisfying the conditions that(i)∑v∈N[v]f(v) ≥ 1(res.∑v∈N(v)f(v) ≥ 1) for ...A signed(res. signed total) Roman dominating function, SRDF(res.STRDF) for short, of a graph G =(V, E) is a function f : V → {-1, 1, 2} satisfying the conditions that(i)∑v∈N[v]f(v) ≥ 1(res.∑v∈N(v)f(v) ≥ 1) for any v ∈ V, where N [v] is the closed neighborhood and N(v) is the neighborhood of v, and(ii) every vertex v for which f(v) =-1 is adjacent to a vertex u for which f(u) = 2. The weight of a SRDF(res. STRDF) is the sum of its function values over all vertices.The signed(res. signed total) Roman domination number of G is the minimum weight among all signed(res. signed total) Roman dominating functions of G. In this paper,we compute the exact values of the signed(res. signed total) Roman domination numbers of complete bipartite graphs and wheels.展开更多
Let G=(V,E) be a simple graph. For any real valued function f:V →R, the weight of f is f(V) = ∑f(v) over all vertices v∈V . A signed total dominating function is a function f:V→{-1,1} such ...Let G=(V,E) be a simple graph. For any real valued function f:V →R, the weight of f is f(V) = ∑f(v) over all vertices v∈V . A signed total dominating function is a function f:V→{-1,1} such that f(N(v)) ≥1 for every vertex v∈V . The signed total domination number of a graph G equals the minimum weight of a signed total dominating function on G . In this paper, some properties of the signed total domination number of a graph G are discussed.展开更多
This is subsequent of , by using the theory of additive fuzzy measure and signed additive fuzzy measure , we prove the Radon_Nikodym Theorem and Lebesgue decomposition Theorem of signed additive fuzzy measure.
In this paper, we introduce the concept of signed additive fuzzy measure on a class of fuzzy sets, then, on certain condition, a series of decomposition theorems of signed additive fuzzy measure are proved.
A function f:E(G)→{−1,1}is called a signed edge dominating function(SEDF for short)of G if f[e]=f(N[e])=Σ_( e′∈N[e])f(e′)≥1,for every edge e∈E(G).w(f)=Σ_(e∈E) f(e)is called the weight of f.The signed edge dom...A function f:E(G)→{−1,1}is called a signed edge dominating function(SEDF for short)of G if f[e]=f(N[e])=Σ_( e′∈N[e])f(e′)≥1,for every edge e∈E(G).w(f)=Σ_(e∈E) f(e)is called the weight of f.The signed edge domination numberγs′(G)of G is the minimum weight among all signed edge dominating functions of G.In this paper,we initiate the study of this parameter for G a complete multipartite graph.We provide the lower and upper bounds ofγs′(G)for G a complete r-partite graph with r even and all parts equal.展开更多
Let G =（V, E） be a simple graph with vertex set V and edge set E. A signed mixed dominating function of G is a function f： VUE→{-1,1}such that ∑y∈Nm（x）U{x}f（y） ≥1 for every element x ∈ V U E, where Nm （x...Let G =（V, E） be a simple graph with vertex set V and edge set E. A signed mixed dominating function of G is a function f： VUE→{-1,1}such that ∑y∈Nm（x）U{x}f（y） ≥1 for every element x ∈ V U E, where Nm （x） is the set of elements of V U E adjacent or incident to x. The weight of f isw（f）∑x∈VUEf（x）.The signed mixed domination problem is to find a minimum-weight signed mixed dominating function of a graph. In this paper we study the computational complexity of signed mixed domination problem. We prove that the signed mixed domination problem is NP-complete for bipartite graphs, chordal graphs, even for planar bipartite graphs.展开更多
The concept of social stratification and hierarchy among human dates is back to the origin of human race. Presently, the growing reputation of social networks has given us with an opportunity to analyze these well-stu...The concept of social stratification and hierarchy among human dates is back to the origin of human race. Presently, the growing reputation of social networks has given us with an opportunity to analyze these well-studied phenomena over different networks at different scales. Generally, a social network could be defined as a collection of actors and their interactions. In this work, we concern ourselves with a particular type of social networks, known as trust networks. In this type of networks, there is an explicit show of trust (positive interaction) or distrust (negative interaction) among the actors. In a social network, actors tend to connect with each other on the basis of their perceived social hierarchy. The emergence of such a hierarchy within a social community shows the manner in which authority manifests in the community. In the case of signed networks, the concept of social hierarchy can be interpreted as the emergence of a tree-like structure comprising of actors in a top-down fashion in the order of their ranks, describing a specific parent-child relationship, viz. child trusts parent. However, owing to the presence of positive as well as negative interactions in signed networks, deriving such “trust hierarchies” is a non-trivial challenge. We argue that traditional notions (of unsigned networks) are insufficient to derive hierarchies that are latent within signed networks.展开更多
Let G(V, E) be a finite connected simple graph with vertex set V(G). A function is a signed dominating function f : <em style="white-space:normal;">V<span style="white-space:normal;"&...Let G(V, E) be a finite connected simple graph with vertex set V(G). A function is a signed dominating function f : <em style="white-space:normal;">V<span style="white-space:normal;">(<em style="white-space:normal;">G<span style="white-space:normal;">)<span style="white-space:nowrap;">→{<span style="white-space:nowrap;"><span style="white-space:nowrap;">−1,1} if for every vertex v <span style="white-space:nowrap;">∈ V(G), the sum of closed neighborhood weights of v is greater or equal to 1. The signed domination number γ<sub>s</sub>(G) of G is the minimum weight of a signed dominating function on G. In this paper, we calculate the signed domination numbers of the Cartesian product of two paths P<sub>m</sub> and P<sub>n</sub> for m = 6, 7 and arbitrary n.展开更多
Let <img src="Edit_092a0db1-eefa-4bff-81a0-751d038158ad.png" width="58" height="20" alt="" /> be a graph. A function <img src="Edit_b7158ed5-6825-41cd-b7f0-5ab5e16...Let <img src="Edit_092a0db1-eefa-4bff-81a0-751d038158ad.png" width="58" height="20" alt="" /> be a graph. A function <img src="Edit_b7158ed5-6825-41cd-b7f0-5ab5e16fc53d.png" width="79" height="20" alt="" /> is said to be a Signed Dominating Function (SDF) if <img src="Edit_c6e63805-bcaa-46a9-bc77-42750af8efd4.png" width="135" height="25" alt="" /> holds for all <img src="Edit_bba1b366-af70-46cd-aefe-fc68869da670.png" width="42" height="20" alt="" />. The signed domination number <img src="Edit_22e6d87a-e3be-4037-b4b6-c1de6a40abb0.png" width="284" height="25" alt="" />. In this paper, we determine the exact value of the Signed Domination Number of graphs <img src="Edit_36ef2747-da44-4f9b-a10a-340c61a3f28c.png" width="19" height="20" alt="" /> and <img src="Edit_26eb0f74-fcc2-49ad-8567-492cf3115b73.png" width="19" height="20" alt="" /> for <img src="Edit_856dbcc1-d215-4144-b50c-ac8a225d664f.png" width="32" height="20" alt="" />, which is generalized the known results, respectively, where <img src="Edit_4b7e4f8f-5d38-4fd0-ac4e-dd8ef243029f.png" width="19" height="20" alt="" /> and <img src="Edit_6557afba-e697-4397-994e-a9bda83e3219.png" width="19" height="20" alt="" /> are denotes the k-th power graphs of cycle <img src="Edit_27e6e80f-85d5-4208-b367-a757a0e55d0b.png" width="21" height="20" alt="" /> and path <img src="Edit_70ac5266-950b-4bfd-8d04-21711d3ffc33.png" width="18" height="20" alt="" />.展开更多
In the past 30 years,signed directed graph(SDG) ,one of the qualitative simulation technologies,has been widely applied for chemical fault diagnosis.However,SDG based fault diagnosis,as any other qualitative method,ha...In the past 30 years,signed directed graph(SDG) ,one of the qualitative simulation technologies,has been widely applied for chemical fault diagnosis.However,SDG based fault diagnosis,as any other qualitative method,has poor diagnostic resolution.In this paper,a new method that combines SDG with qualitative trend analysis(QTA) is presented to improve the resolution.In the method,a bidirectional inference algorithm based on assumption and verification is used to find all the possible fault causes and their corresponding consistent paths in the SDG model.Then an improved QTA algorithm is used to extract and analyze the trends of nodes on the consis-tent paths found in the previous step.New consistency rules based on qualitative trends are used to find the real causes from the candidate causes.The resolution can be improved.This method combines the completeness feature of SDG with the good diagnostic resolution feature of QTA.The implementation of SDG-QTA based fault diagno-sis is done using the integrated SDG modeling,inference and post-processing software platform.Its application is illustrated on an atmospheric distillation tower unit of a simulation platform.The result shows its good applicability and efficiency.展开更多
Fault diagnosis of various systems on rolling stock has drawn the attention of many researchers. However, obtaining an optimized sensor set of these systems, which is a prerequisite for fault diagnosis, remains a majo...Fault diagnosis of various systems on rolling stock has drawn the attention of many researchers. However, obtaining an optimized sensor set of these systems, which is a prerequisite for fault diagnosis, remains a major challenge. Available literature suggests that the configuration of sensors in these systems is presently dependent on the knowledge and engineering experiences of designers, which may lead to insufficient or redundant development of various sensors. In this paper, the optimization of sensor sets is addressed by using the signed digraph （SDG） method. The method is modified for use in braking systems by the introduction of an effect-function method to replace the traditional quantitative methods. Two criteria are adopted to evaluate the capability of the sensor sets, namely, observability and resolution. The sensors configuration method of braking system is proposed. It consists of generating bipartite graphs from SDG models and then solving the set cover problem using a greedy algorithm. To demonstrate the improvement, the sensor configuration of the HP2008 braking system is investigated and fault diagnosis on a test bench is performed. The test results show that SDG algorithm can improve single-fault resolution from 6 faults to 10 faults, and with additional four brake cylinder pressure （BCP） sensors it can cover up to 67 double faults which were not considered by traditional fault diagnosis system. SDG methods are suitable for reducing redundant sensors and that the sensor sets thereby obtained are capable of detecting typical faults, such as the failure of a release valve. This study investigates the formal extension of the SDG method to the sensor configuration of braking system, as well as the adaptation supported by the effect-function method.展开更多
This paper gives the Radon-Nikodym theorem in signed Loeb space under 1-saturated nonstandard model. First,the nonstandard characterization of absolute continuity is discussed,on which Radon-Nikodym theorem in signed ...This paper gives the Radon-Nikodym theorem in signed Loeb space under 1-saturated nonstandard model. First,the nonstandard characterization of absolute continuity is discussed,on which Radon-Nikodym theorem in signed Loeb space is obtained. Then,some facts about a finite signed Loeb measure and its variation are shown.展开更多
Digraph-based causal models have been widely used to model the cause and effect behavior of process systems. Signed digraphs （SDG） capture the direction of the effect. It should be mentioned that there are loops in ...Digraph-based causal models have been widely used to model the cause and effect behavior of process systems. Signed digraphs （SDG） capture the direction of the effect. It should be mentioned that there are loops in SDG generated from chemical process. From the point of the inherent operability, the worst unsafe factor is the SDG having positive loops that means any disturbance occurring within the loop will propagate through the nodes one by one and are amplified gradually, so the system may lose control, which may lead to an accident. So finding the positive loops in a SDG and treating these unsafe factors in a proper manner can improve the inherent safety of a chemical process. This article proposed a method that can detect the above-mentioned unsafe factors in the proc- ess conceptual design stage automatically through the analysis of the SDG generated from the chemical process. A case study is illustrated to show the working of the algorithm, and then a complicated case from industry is studied to depict the effectiveness of the proposed algorithm.展开更多
This article discusses the perturbation of a non-symmetric Dirichlet form, （ε, D（ε））, by a signed smooth measure u, where u=u1 -u2 with u1 and u2 being smooth measures. It gives a sufficient condition for the pe...This article discusses the perturbation of a non-symmetric Dirichlet form, （ε, D（ε））, by a signed smooth measure u, where u=u1 -u2 with u1 and u2 being smooth measures. It gives a sufficient condition for the perturbed form （ε^u ,D（ε^u）） （for some a0 ≥ 0） to be a coercive closed form.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.12071260)。
文摘A graph whose edges are labeled either as positive or negative is called a signed graph.Hameed et al.introduced signed distance and distance compatibility in 2021,initially to characterize balanced signed graphs which have nice spectral properties.This article mainly studies the conjecture proposed by Shijin et al.on the distance compatibility of the direct product of signed graphs,and provides necessary and sufficient conditions for the distance compatibility of the direct product of signed graphs.Some further questions regarding distance compatibility are also posed.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.72371031,62173065,62476045)Fundamental Research Funds for the Central Universities(Grant No.124330008)。
文摘The unique structure of signed networks,characterized by positive and negative edges,poses significant challenges for analyzing network topology.In recent years,various statistical algorithms have been developed to address this issue.However,there remains a lack of a unified framework to uncover the nontrivial properties inherent in signed network structures.To support developers,researchers,and practitioners in this field,we introduce a Python library named SNSAlib(Signed Network Structure Analysis),specifically designed to meet these analytical requirements.This library encompasses empirical signed network datasets,signed null model algorithms,signed statistics algorithms,and evaluation indicators.The primary objective of SNSAlib is to facilitate the systematic analysis of micro-and meso-structure features within signed networks,including node popularity,clustering,assortativity,embeddedness,and community structure by employing more accurate signed null models.Ultimately,it provides a robust paradigm for structure analysis of signed networks that enhances our understanding and application of signed networks.
基金Supported by the National Natural Science Foundation of China(Grant No.12261016)。
文摘A signed graph S=(S^(u),σ)has an underlying graph Suand a functionσ:E(S^(u))-→{+,-}.Let E^(-)(S)denote the set of negative edges of S.Then S is eulerian signed graph(or subeulerian signed graph,or balanced eulerian signed graph,respectively)if Suis eulerian(or subeulerian,or eulerian and|E-(S)|is even,respectively).We say that S is balanced subeulerian signed graph if there exists a balanced eulerian signed graph S′such that S′is spanned by S.The signed line graph L(S)of a signed graph S is a signed graph with the vertices of L(S)being the edges of S,where an edge eiej is in L(S)if and only if the edges e_(i)and e_(j)of S have a vertex in common in S such that an edge eiej in L(S)is negative if and only if both edges ei and ej are negative in S.In this paper,two families of signed graphs S and S′are identified,which are applied to characterize balanced subeulerian signed graphs and balanced subeulerian signed line graphs.In particular,it is proved that a signed graph S is balanced subeulerian if and only if S∈S,and that a signed line graph of signed graph S is balanced subeulerian if and only if S∈S′.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.62103375 and 62006106)the Zhejiang Provincial Philosophy and Social Science Planning Project(Grant No.22NDJC009Z)+1 种基金the Education Ministry Humanities and Social Science Foundation of China(Grant Nos.19YJCZH056 and 21YJC630120)the Natural Science Foundation of Zhejiang Province of China(Grant Nos.LY23F030003 and LQ21F020005).
文摘While progress has been made in information source localization,it has overlooked the prevalent friend and adversarial relationships in social networks.This paper addresses this gap by focusing on source localization in signed network models.Leveraging the topological characteristics of signed networks and transforming the propagation probability into effective distance,we propose an optimization method for observer selection.Additionally,by using the reverse propagation algorithm we present a method for information source localization in signed networks.Extensive experimental results demonstrate that a higher proportion of positive edges within signed networks contributes to more favorable source localization,and the higher the ratio of propagation rates between positive and negative edges,the more accurate the source localization becomes.Interestingly,this aligns with our observation that,in reality,the number of friends tends to be greater than the number of adversaries,and the likelihood of information propagation among friends is often higher than among adversaries.In addition,the source located at the periphery of the network is not easy to identify.Furthermore,our proposed observer selection method based on effective distance achieves higher operational efficiency and exhibits higher accuracy in information source localization,compared with three strategies for observer selection based on the classical full-order neighbor coverage.
基金Project supported by the National Natural Science Foundation of China （Grant No.1057117）, and the Science Foundation of Shanghai Municipal Commission of Education （Grant No.05AZ04）.
文摘Let G = （V, E） be a graph, and let f ： V →{-1, 1} be a two-valued function. If ∑x∈N（v） f（x） ≥ 1 for each v ∈ V, where N（v） is the open neighborhood of v, then f is a signed total dominating function on G. A set {fl, f2,… fd} of signed d total dominating functions on G with the property that ∑i=1^d fi（x） ≤ 1 for each x ∈ V, is called a signed total dominating family （of functions） on G. The maximum number of functions in a signed total dominating family on G is the signed total domatic number on G, denoted by dt^s（G）. The properties of the signed total domatic number dt^s（G） are studied in this paper. In particular, we give the sharp bounds of the signed total domatic number of regular graphs, complete bipartite graphs and complete graphs.
基金The NSF(11271365)of Chinathe NSF(BK20151117)of Jiangsu Province
文摘A signed(res. signed total) Roman dominating function, SRDF(res.STRDF) for short, of a graph G =(V, E) is a function f : V → {-1, 1, 2} satisfying the conditions that(i)∑v∈N[v]f(v) ≥ 1(res.∑v∈N(v)f(v) ≥ 1) for any v ∈ V, where N [v] is the closed neighborhood and N(v) is the neighborhood of v, and(ii) every vertex v for which f(v) =-1 is adjacent to a vertex u for which f(u) = 2. The weight of a SRDF(res. STRDF) is the sum of its function values over all vertices.The signed(res. signed total) Roman domination number of G is the minimum weight among all signed(res. signed total) Roman dominating functions of G. In this paper,we compute the exact values of the signed(res. signed total) Roman domination numbers of complete bipartite graphs and wheels.
文摘Let G=(V,E) be a simple graph. For any real valued function f:V →R, the weight of f is f(V) = ∑f(v) over all vertices v∈V . A signed total dominating function is a function f:V→{-1,1} such that f(N(v)) ≥1 for every vertex v∈V . The signed total domination number of a graph G equals the minimum weight of a signed total dominating function on G . In this paper, some properties of the signed total domination number of a graph G are discussed.
文摘This is subsequent of , by using the theory of additive fuzzy measure and signed additive fuzzy measure , we prove the Radon_Nikodym Theorem and Lebesgue decomposition Theorem of signed additive fuzzy measure.
文摘In this paper, we introduce the concept of signed additive fuzzy measure on a class of fuzzy sets, then, on certain condition, a series of decomposition theorems of signed additive fuzzy measure are proved.
基金Supported by the National Natural Science Foundation of China (Grant No. 71774078)。
文摘A function f:E(G)→{−1,1}is called a signed edge dominating function(SEDF for short)of G if f[e]=f(N[e])=Σ_( e′∈N[e])f(e′)≥1,for every edge e∈E(G).w(f)=Σ_(e∈E) f(e)is called the weight of f.The signed edge domination numberγs′(G)of G is the minimum weight among all signed edge dominating functions of G.In this paper,we initiate the study of this parameter for G a complete multipartite graph.We provide the lower and upper bounds ofγs′(G)for G a complete r-partite graph with r even and all parts equal.
基金Supported by the Natural Science Foundation of Jiangsu Province(Grant No.BK20151117)the Key Scientific Research Foundation of Higher Education Institutions of Henan Province(Grant No.15B110009)
文摘Let G =（V, E） be a simple graph with vertex set V and edge set E. A signed mixed dominating function of G is a function f： VUE→{-1,1}such that ∑y∈Nm（x）U{x}f（y） ≥1 for every element x ∈ V U E, where Nm （x） is the set of elements of V U E adjacent or incident to x. The weight of f isw（f）∑x∈VUEf（x）.The signed mixed domination problem is to find a minimum-weight signed mixed dominating function of a graph. In this paper we study the computational complexity of signed mixed domination problem. We prove that the signed mixed domination problem is NP-complete for bipartite graphs, chordal graphs, even for planar bipartite graphs.
文摘The concept of social stratification and hierarchy among human dates is back to the origin of human race. Presently, the growing reputation of social networks has given us with an opportunity to analyze these well-studied phenomena over different networks at different scales. Generally, a social network could be defined as a collection of actors and their interactions. In this work, we concern ourselves with a particular type of social networks, known as trust networks. In this type of networks, there is an explicit show of trust (positive interaction) or distrust (negative interaction) among the actors. In a social network, actors tend to connect with each other on the basis of their perceived social hierarchy. The emergence of such a hierarchy within a social community shows the manner in which authority manifests in the community. In the case of signed networks, the concept of social hierarchy can be interpreted as the emergence of a tree-like structure comprising of actors in a top-down fashion in the order of their ranks, describing a specific parent-child relationship, viz. child trusts parent. However, owing to the presence of positive as well as negative interactions in signed networks, deriving such “trust hierarchies” is a non-trivial challenge. We argue that traditional notions (of unsigned networks) are insufficient to derive hierarchies that are latent within signed networks.
文摘Let G(V, E) be a finite connected simple graph with vertex set V(G). A function is a signed dominating function f : <em style="white-space:normal;">V<span style="white-space:normal;">(<em style="white-space:normal;">G<span style="white-space:normal;">)<span style="white-space:nowrap;">→{<span style="white-space:nowrap;"><span style="white-space:nowrap;">−1,1} if for every vertex v <span style="white-space:nowrap;">∈ V(G), the sum of closed neighborhood weights of v is greater or equal to 1. The signed domination number γ<sub>s</sub>(G) of G is the minimum weight of a signed dominating function on G. In this paper, we calculate the signed domination numbers of the Cartesian product of two paths P<sub>m</sub> and P<sub>n</sub> for m = 6, 7 and arbitrary n.
文摘Let <img src="Edit_092a0db1-eefa-4bff-81a0-751d038158ad.png" width="58" height="20" alt="" /> be a graph. A function <img src="Edit_b7158ed5-6825-41cd-b7f0-5ab5e16fc53d.png" width="79" height="20" alt="" /> is said to be a Signed Dominating Function (SDF) if <img src="Edit_c6e63805-bcaa-46a9-bc77-42750af8efd4.png" width="135" height="25" alt="" /> holds for all <img src="Edit_bba1b366-af70-46cd-aefe-fc68869da670.png" width="42" height="20" alt="" />. The signed domination number <img src="Edit_22e6d87a-e3be-4037-b4b6-c1de6a40abb0.png" width="284" height="25" alt="" />. In this paper, we determine the exact value of the Signed Domination Number of graphs <img src="Edit_36ef2747-da44-4f9b-a10a-340c61a3f28c.png" width="19" height="20" alt="" /> and <img src="Edit_26eb0f74-fcc2-49ad-8567-492cf3115b73.png" width="19" height="20" alt="" /> for <img src="Edit_856dbcc1-d215-4144-b50c-ac8a225d664f.png" width="32" height="20" alt="" />, which is generalized the known results, respectively, where <img src="Edit_4b7e4f8f-5d38-4fd0-ac4e-dd8ef243029f.png" width="19" height="20" alt="" /> and <img src="Edit_6557afba-e697-4397-994e-a9bda83e3219.png" width="19" height="20" alt="" /> are denotes the k-th power graphs of cycle <img src="Edit_27e6e80f-85d5-4208-b367-a757a0e55d0b.png" width="21" height="20" alt="" /> and path <img src="Edit_70ac5266-950b-4bfd-8d04-21711d3ffc33.png" width="18" height="20" alt="" />.
基金Supported by the Science and Technological Tackling Project of Heilongjiang Province(GB06A106)
文摘In the past 30 years,signed directed graph(SDG) ,one of the qualitative simulation technologies,has been widely applied for chemical fault diagnosis.However,SDG based fault diagnosis,as any other qualitative method,has poor diagnostic resolution.In this paper,a new method that combines SDG with qualitative trend analysis(QTA) is presented to improve the resolution.In the method,a bidirectional inference algorithm based on assumption and verification is used to find all the possible fault causes and their corresponding consistent paths in the SDG model.Then an improved QTA algorithm is used to extract and analyze the trends of nodes on the consis-tent paths found in the previous step.New consistency rules based on qualitative trends are used to find the real causes from the candidate causes.The resolution can be improved.This method combines the completeness feature of SDG with the good diagnostic resolution feature of QTA.The implementation of SDG-QTA based fault diagno-sis is done using the integrated SDG modeling,inference and post-processing software platform.Its application is illustrated on an atmospheric distillation tower unit of a simulation platform.The result shows its good applicability and efficiency.
基金Supported by National Hi-tech Research and Development Program of China(863 Program,Grant No.2011AA110503-3)Fundamental Research Funds for the Central Universities of China(Grant No.2860219030)Foundation of Traction Power State Key Laboratory of Southwest Jiaotong University,China(Grant No.TPL1308)
文摘Fault diagnosis of various systems on rolling stock has drawn the attention of many researchers. However, obtaining an optimized sensor set of these systems, which is a prerequisite for fault diagnosis, remains a major challenge. Available literature suggests that the configuration of sensors in these systems is presently dependent on the knowledge and engineering experiences of designers, which may lead to insufficient or redundant development of various sensors. In this paper, the optimization of sensor sets is addressed by using the signed digraph （SDG） method. The method is modified for use in braking systems by the introduction of an effect-function method to replace the traditional quantitative methods. Two criteria are adopted to evaluate the capability of the sensor sets, namely, observability and resolution. The sensors configuration method of braking system is proposed. It consists of generating bipartite graphs from SDG models and then solving the set cover problem using a greedy algorithm. To demonstrate the improvement, the sensor configuration of the HP2008 braking system is investigated and fault diagnosis on a test bench is performed. The test results show that SDG algorithm can improve single-fault resolution from 6 faults to 10 faults, and with additional four brake cylinder pressure （BCP） sensors it can cover up to 67 double faults which were not considered by traditional fault diagnosis system. SDG methods are suitable for reducing redundant sensors and that the sensor sets thereby obtained are capable of detecting typical faults, such as the failure of a release valve. This study investigates the formal extension of the SDG method to the sensor configuration of braking system, as well as the adaptation supported by the effect-function method.
基金Supported by the Natural Science Foundation of Shaanxi Province(2007A12)
文摘This paper gives the Radon-Nikodym theorem in signed Loeb space under 1-saturated nonstandard model. First,the nonstandard characterization of absolute continuity is discussed,on which Radon-Nikodym theorem in signed Loeb space is obtained. Then,some facts about a finite signed Loeb measure and its variation are shown.
文摘Digraph-based causal models have been widely used to model the cause and effect behavior of process systems. Signed digraphs （SDG） capture the direction of the effect. It should be mentioned that there are loops in SDG generated from chemical process. From the point of the inherent operability, the worst unsafe factor is the SDG having positive loops that means any disturbance occurring within the loop will propagate through the nodes one by one and are amplified gradually, so the system may lose control, which may lead to an accident. So finding the positive loops in a SDG and treating these unsafe factors in a proper manner can improve the inherent safety of a chemical process. This article proposed a method that can detect the above-mentioned unsafe factors in the proc- ess conceptual design stage automatically through the analysis of the SDG generated from the chemical process. A case study is illustrated to show the working of the algorithm, and then a complicated case from industry is studied to depict the effectiveness of the proposed algorithm.
基金This research is supported by the NSFC andNSF of Hainan Province (Nos. 80529 and 10001)
文摘This article discusses the perturbation of a non-symmetric Dirichlet form, （ε, D（ε））, by a signed smooth measure u, where u=u1 -u2 with u1 and u2 being smooth measures. It gives a sufficient condition for the perturbed form （ε^u ,D（ε^u）） （for some a0 ≥ 0） to be a coercive closed form.
