Health information spreads rapidly,which can effectively control epidemics.However,the swift dissemination of information also has potential negative impacts,which increasingly attracts attention.Message fatigue refer...Health information spreads rapidly,which can effectively control epidemics.However,the swift dissemination of information also has potential negative impacts,which increasingly attracts attention.Message fatigue refers to the psychological response characterized by feelings of boredom and anxiety that occur after receiving an excessive amount of similar information.This phenomenon can alter individual behaviors related to epidemic prevention.Additionally,recent studies indicate that pairwise interactions alone are insufficient to describe complex social transmission processes,and higher-order structures representing group interactions are crucial.To address this,we develop a novel epidemic model that investigates the interactions between information,behavioral responses,and epidemics.Our model incorporates the impact of message fatigue on the entire transmission system.The information layer is modeled using a static simplicial network to capture group interactions,while the disease layer uses a time-varying network based on activity-driven model with attractiveness to represent the self-protection behaviors of susceptible individuals and self-isolation behaviors of infected individuals.We theoretically describe the co-evolution equations using the microscopic Markov chain approach(MMCA)and get the epidemic threshold.Experimental results show that while the negative impact of message fatigue on epidemic transmission is limited,it significantly weakens the group interactions depicted by higher-order structures.Individual behavioral responses strongly inhibit the epidemic.Our simulations using the Monte Carlo(MC)method demonstrate that greater intensity in these responses leads to clustering of susceptible individuals in the disease layer.Finally,we apply the proposed model to real networks to verify its reliability.In summary,our research results enhance the understanding of the information-epidemic coupling dynamics,and we expect to provide valuable guidance for managing future emerging epidemics.展开更多
Let V be a finite set.Let K be a simplicial complex with its vertices in V.In this paper,the author discusses some differential calculus on V.He constructs some constrained homology groups of K by using the differenti...Let V be a finite set.Let K be a simplicial complex with its vertices in V.In this paper,the author discusses some differential calculus on V.He constructs some constrained homology groups of K by using the differential calculus on V.Moreover,he defines an independence hyper graph to be the complement of a simplicial complex in the complete hypergraph on V.Let L be an independence hypergraph with its vertices in V.He constructs some constrained cohomology groups of L by using the differential calculus on V.展开更多
Let△bea simplicial complex on[n].TheNF-complex of△is the simplicial complexδ_(NF)(△)on[n]for which the facet ideal of△is equal to the Stanley-Reisner ideal ofδ_(NF)(△).Furthermore,for each k=2,3,....,we introdu...Let△bea simplicial complex on[n].TheNF-complex of△is the simplicial complexδ_(NF)(△)on[n]for which the facet ideal of△is equal to the Stanley-Reisner ideal ofδ_(NF)(△).Furthermore,for each k=2,3,....,we introduce the kth NF-complexδ_(NF)^(k)(△),which is inductively defined asδ_(NF)(k)(△)=δ_(NF)(δ_(NF)^(k-1)(△))by settingδ_(NF)^(1)(△)=δ_(NF)(△).One canδ_(NF)^(0)(△)=△.The NF-number of△is the smallest integer k>0 for whichδ_(NF)^(k)(△)■△.In the present paper we are especilly interested in the NF-number of a finite graph,which can be regraded as a simplicial complex of dimension one.It is shown that the NF-number of the finite graph K_(n)■K_(m)on[n+m],which is the disjoint union of the complete graphs K_(n)on[n]and K_(m)on[m]for n≥2 and m≥2 with(n,m)≠(2,2),is equal to n+m+2.As a corollary,we find that the NF-number of the complete bipartite graph K_(n,m)on[n+m]is also equal to n+m+2.展开更多
Granular Computing on partitions(RST),coverings(GrCC) and neighborhood systems(LNS) are examined: (1) The order of generality is RST, GrCC, and then LNS. (2) The quotient structure: In RST, it is called quotient set. ...Granular Computing on partitions(RST),coverings(GrCC) and neighborhood systems(LNS) are examined: (1) The order of generality is RST, GrCC, and then LNS. (2) The quotient structure: In RST, it is called quotient set. In GrCC, it is a simplical complex, called the nerve of the covering in combinatorial topology. For LNS, the structure has no known description. (3) The approximation space of RST is a topological space generated by a partition, called a clopen space. For LNS, it is a generalized/pretopological space which is more general than topological space. For GrCC,there are two possibilities. One is a special case of LNS,which is the topological space generated by the covering. There is another topological space, the topology generated by the finite intersections of the members of a covering The first one treats covering as a base, the second one as a subbase. (4) Knowledge representations in RST are symbol-valued systems. In GrCC, they are expression-valued systems. In LNS, they are multivalued system; reported in 1998 . (5) RST and GRCC representation theories are complete in the sense that granular models can be recaptured fully from the knowledge representations.展开更多
In 2020,Alexander Grigor'yan,Yong Lin and Shing-Tung Yau[6]introduced the Reidemeister torsion and the analytic torsion for digraphs by means of the path complex and the path homology theory.Based on the analytic ...In 2020,Alexander Grigor'yan,Yong Lin and Shing-Tung Yau[6]introduced the Reidemeister torsion and the analytic torsion for digraphs by means of the path complex and the path homology theory.Based on the analytic torsion for digraphs introduced in[6],we consider the notion of weighted analytic torsion for vertex-weighted digraphs.For any non-vanishing real functions f and g on the vertex set,we consider the vertex-weighted digraphs with the weights(f;g).We calculate the(f;g)-weighted analytic torsion by examples and prove that the(f;g)-weighted analytic torsion only depend on the ratio f=g.In particular,if the weight is of the diagonal form(f;f),then the weighted analytic torsion equals to the usual(un-weighted)torsion.展开更多
We introduce first the spanning simplicial complex(SSC)of a multigraph g,which gives a generalization of the SSC associated with a simple graph G.Combinatorial properties are discussed for the SSC of a family of uni-c...We introduce first the spanning simplicial complex(SSC)of a multigraph g,which gives a generalization of the SSC associated with a simple graph G.Combinatorial properties are discussed for the SSC of a family of uni-cyclic multigraphs U_(n)^(r),m with n edges including r multiple edges within and outside the cycle of length m,which are then used to compute the f-vector and Hilbert series of face ring k[△s(U_(n)^(r),m)]for the SSC △s(U_(n)^(r),m)(un,m).Moreover,we find the associated primes of the facet ideal I_(F)(△s(U_(n)^(r),m).Finally,we device a formula for homology groups of △s(U_(n)^(r),m) prove that the SsC of a family of uni-cyclic multigraphs is Cohen-Macaulay.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.72171136 and 72134004)Humanities and Social Science Research Project,Ministry of Education of China(Grant No.21YJC630157)+1 种基金the Natural Science Foundation of Shandong Province(Grant No.ZR2022MG008)Shandong Provincial Colleges and Universities Youth Innovation Technology of China(Grant No.2022RW066)。
文摘Health information spreads rapidly,which can effectively control epidemics.However,the swift dissemination of information also has potential negative impacts,which increasingly attracts attention.Message fatigue refers to the psychological response characterized by feelings of boredom and anxiety that occur after receiving an excessive amount of similar information.This phenomenon can alter individual behaviors related to epidemic prevention.Additionally,recent studies indicate that pairwise interactions alone are insufficient to describe complex social transmission processes,and higher-order structures representing group interactions are crucial.To address this,we develop a novel epidemic model that investigates the interactions between information,behavioral responses,and epidemics.Our model incorporates the impact of message fatigue on the entire transmission system.The information layer is modeled using a static simplicial network to capture group interactions,while the disease layer uses a time-varying network based on activity-driven model with attractiveness to represent the self-protection behaviors of susceptible individuals and self-isolation behaviors of infected individuals.We theoretically describe the co-evolution equations using the microscopic Markov chain approach(MMCA)and get the epidemic threshold.Experimental results show that while the negative impact of message fatigue on epidemic transmission is limited,it significantly weakens the group interactions depicted by higher-order structures.Individual behavioral responses strongly inhibit the epidemic.Our simulations using the Monte Carlo(MC)method demonstrate that greater intensity in these responses leads to clustering of susceptible individuals in the disease layer.Finally,we apply the proposed model to real networks to verify its reliability.In summary,our research results enhance the understanding of the information-epidemic coupling dynamics,and we expect to provide valuable guidance for managing future emerging epidemics.
基金supported by China Postdoctoral Science Foundation(No.2022M721023)。
文摘Let V be a finite set.Let K be a simplicial complex with its vertices in V.In this paper,the author discusses some differential calculus on V.He constructs some constrained homology groups of K by using the differential calculus on V.Moreover,he defines an independence hyper graph to be the complement of a simplicial complex in the complete hypergraph on V.Let L be an independence hypergraph with its vertices in V.He constructs some constrained cohomology groups of L by using the differential calculus on V.
基金supported by the Higher Education Commission of Pakistan(No.7515/Punjab/NRPU/R&D/HEC/2017).
文摘Let△bea simplicial complex on[n].TheNF-complex of△is the simplicial complexδ_(NF)(△)on[n]for which the facet ideal of△is equal to the Stanley-Reisner ideal ofδ_(NF)(△).Furthermore,for each k=2,3,....,we introduce the kth NF-complexδ_(NF)^(k)(△),which is inductively defined asδ_(NF)(k)(△)=δ_(NF)(δ_(NF)^(k-1)(△))by settingδ_(NF)^(1)(△)=δ_(NF)(△).One canδ_(NF)^(0)(△)=△.The NF-number of△is the smallest integer k>0 for whichδ_(NF)^(k)(△)■△.In the present paper we are especilly interested in the NF-number of a finite graph,which can be regraded as a simplicial complex of dimension one.It is shown that the NF-number of the finite graph K_(n)■K_(m)on[n+m],which is the disjoint union of the complete graphs K_(n)on[n]and K_(m)on[m]for n≥2 and m≥2 with(n,m)≠(2,2),is equal to n+m+2.As a corollary,we find that the NF-number of the complete bipartite graph K_(n,m)on[n+m]is also equal to n+m+2.
文摘Granular Computing on partitions(RST),coverings(GrCC) and neighborhood systems(LNS) are examined: (1) The order of generality is RST, GrCC, and then LNS. (2) The quotient structure: In RST, it is called quotient set. In GrCC, it is a simplical complex, called the nerve of the covering in combinatorial topology. For LNS, the structure has no known description. (3) The approximation space of RST is a topological space generated by a partition, called a clopen space. For LNS, it is a generalized/pretopological space which is more general than topological space. For GrCC,there are two possibilities. One is a special case of LNS,which is the topological space generated by the covering. There is another topological space, the topology generated by the finite intersections of the members of a covering The first one treats covering as a base, the second one as a subbase. (4) Knowledge representations in RST are symbol-valued systems. In GrCC, they are expression-valued systems. In LNS, they are multivalued system; reported in 1998 . (5) RST and GRCC representation theories are complete in the sense that granular models can be recaptured fully from the knowledge representations.
基金REN Shi-quan is supported by China Postdoctoral Science Foundation(Grant No.2022M721023)WANG Chong is supported by Science and Technology Project of Hebei Education Department(Grant No.ZD2022168)Project of Cangzhou Normal University(Grant No.XNJJLYB2021006).
文摘In 2020,Alexander Grigor'yan,Yong Lin and Shing-Tung Yau[6]introduced the Reidemeister torsion and the analytic torsion for digraphs by means of the path complex and the path homology theory.Based on the analytic torsion for digraphs introduced in[6],we consider the notion of weighted analytic torsion for vertex-weighted digraphs.For any non-vanishing real functions f and g on the vertex set,we consider the vertex-weighted digraphs with the weights(f;g).We calculate the(f;g)-weighted analytic torsion by examples and prove that the(f;g)-weighted analytic torsion only depend on the ratio f=g.In particular,if the weight is of the diagonal form(f;f),then the weighted analytic torsion equals to the usual(un-weighted)torsion.
文摘We introduce first the spanning simplicial complex(SSC)of a multigraph g,which gives a generalization of the SSC associated with a simple graph G.Combinatorial properties are discussed for the SSC of a family of uni-cyclic multigraphs U_(n)^(r),m with n edges including r multiple edges within and outside the cycle of length m,which are then used to compute the f-vector and Hilbert series of face ring k[△s(U_(n)^(r),m)]for the SSC △s(U_(n)^(r),m)(un,m).Moreover,we find the associated primes of the facet ideal I_(F)(△s(U_(n)^(r),m).Finally,we device a formula for homology groups of △s(U_(n)^(r),m) prove that the SsC of a family of uni-cyclic multigraphs is Cohen-Macaulay.
