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
In our paper Simplicial K(G, 1)’s we constructed a sub-complex of the nerve of a group G determined by a partial group structure, and we proved, under a generalized associativity condition called regularity, that the...In our paper Simplicial K(G, 1)’s we constructed a sub-complex of the nerve of a group G determined by a partial group structure, and we proved, under a generalized associativity condition called regularity, that the sub-complex realizes as a K(G, 1). This type of sub-complex appears naturally in several topological and algebraic contexts. In this note we prove that regularity of a partial group implies that the Kan extension condition is satisfied on its nerve in dimensions greater than one, and in dimension one a weaker version of the extension condition holds.展开更多
The design of mixed finite element methods in linear elasticity with symmetric stress approximations has been a longstanding open problem until Arnold and Winther designed the first family of mixed finite elements whe...The design of mixed finite element methods in linear elasticity with symmetric stress approximations has been a longstanding open problem until Arnold and Winther designed the first family of mixed finite elements where the discrete stress space is the space of H（div,Ω;S）-Pk＋1 tensors whose divergence is a Pk-1 polynomial on each triangle for k ≥ 2. Such a two dimensional family was extended, by Arnold, Awanou and Winther, to a three dimensional family of mixed elements where the discrete stress space is the space of H（div, Ω; S）-Pk＋2 tensors, whose divergence is a Pk-1 polynomial on each tetrahedron for k ≥ 2. In this paper, we are able to construct, in a unified fashion, mixed finite element methods with symmetric stress approximations on an arbitrary simplex in R^n for any space dimension. On the contrary, the discrete stress space here is the space of H（div,Ω; S）-Pk tensors, and the discrete displacement space here is the space of L^2（Ω; R^n）-Pk＋1 vectors for k ≥ n＋ 1. These finite element spaces are defined with respect to an arbitrary simplicial triangulation of the domain, and can be regarded as extensions to any dimension of those in two and three dimensions by Hu and Zhang.展开更多
Hierarchical bases of arbitrary order for H(div)-conforming triangular and tetrahedral elements are constructedwith the goal of improving the conditioning of the mass and stiffness matrices.For the basis with the tria...Hierarchical bases of arbitrary order for H(div)-conforming triangular and tetrahedral elements are constructedwith the goal of improving the conditioning of the mass and stiffness matrices.For the basis with the triangular element,it is found numerically that the conditioning is acceptable up to the approximation of order four,and is better than a corresponding basis in the dissertation by Sabine Zaglmayr[High Order Finite Element Methods for Electromagnetic Field Computation,Johannes Kepler Universit¨at,Linz,2006].The sparsity of the mass matrices from the newly constructed basis and from the one by Zaglmayr is similar for approximations up to order four.The stiffness matrix with the new basis is much sparser than that with the basis by Zaglmayr for approximations up to order four.For the tetrahedral element,it is identified numerically that the conditioning is acceptable only up to the approximation of order three.Compared with the newly constructed basis for the triangular element,the sparsity of the massmatrices fromthe basis for the tetrahedral element is relatively sparser.展开更多
A mapping f ： Z^n → Rn is said to possess the direction preserving property if fi（x） 〉 0 implies fi（y） ≥ 0 for any integer points x and y with ｜｜x - y｜｜∞≤ 1. In this paper, a simplicial algorithm is deve...A mapping f ： Z^n → Rn is said to possess the direction preserving property if fi（x） 〉 0 implies fi（y） ≥ 0 for any integer points x and y with ｜｜x - y｜｜∞≤ 1. In this paper, a simplicial algorithm is developed for computing an integer zero point of a mapping with the direction preserving property. We assume that there is an integer point x^0 with c ≤ x^0≤d satisfying that maxl≤i≤（xi - xi^0）fi（x） 〉 0 for any integer point x with f（x） ≠ 0 on the boundary of H = {x ∈R^n [c-e ≤ x〈d＋e},wherecanddaretwo finite integer points with c 〈 d and e = （1, 1,... , 1）^T E R^n. This assumption is implied by one of two conditions for the existence of an integer zero point of a mapping with the preserving property in van der Laan et al. （2004）. Under this assumption, starting at x^0, the algorithm follows a finite simplicial path and terminates at an integer zero point of the mapping. This result has applications in general economic equilibrium models with indivisible commodities.展开更多
In this paper, we explore the spanning simplicial complex of wheel graph Wn on vertex set [n]. Combinatorial properties of the spanning simplicial complex of wheel graph are discussed, which are then used to compute t...In this paper, we explore the spanning simplicial complex of wheel graph Wn on vertex set [n]. Combinatorial properties of the spanning simplicial complex of wheel graph are discussed, which are then used to compute the f-vector and Hilbert series of face ring k[Δs(Wn)] for the spanning simplicial complex Δs(Wn). Moreover, the associated primes of the facet ideal IF(Δs(Wn)) are also computed.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
In this article,we give a generalization of δ-twisted homology introduced by Jingyan Li,Vladimir Vershinin and Jie Wu,called Δ-twisted homology,which enriches the theory of δ-(co)homology introduced by Alexander Gr...In this article,we give a generalization of δ-twisted homology introduced by Jingyan Li,Vladimir Vershinin and Jie Wu,called Δ-twisted homology,which enriches the theory of δ-(co)homology introduced by Alexander Grigor’yan,Yuri Muranov and Shing-Tung Yau.We show that the Mayer-Vietoris sequence theorem holds for Δ-twisted homology.Applying the Δ-twisted ideas to Cartesian products,we introduce the notion of Δ-twisted Cartesian product on simplicial sets,which generalizes the classical work of Barratt,Gugenheim and Moore on twisted Cartesian products of simplicial sets.Under certain hypothesis,we show that the coordinate projection of Δ-twisted Cartesian product admits a fibre bundle structure.展开更多
In this paper a triangulation of continuous and arbitrary refinement of grid sizes is proposed for simplicial homotopy algorithms to compute zero points on a polytope P. The proposed algorithm generates a piecewise li...In this paper a triangulation of continuous and arbitrary refinement of grid sizes is proposed for simplicial homotopy algorithms to compute zero points on a polytope P. The proposed algorithm generates a piecewise linear path in P × [1,∞) from any chosen interior point x0 of P on level {1} to a solution of the underlying problem. The path is followed by making linear programming pivot steps in a linear system and replacement steps in the triangnlation.The starting point x0 is left in a direction to one vertex of P. The direction in which x0 leaves depends on the function value at x0 and the polytope P. Moreover, we also give a new equivalent form of the Brouwer fixed point theorem on polytopes. This form has many important applications in mathematical programming and the theory of differential equations.展开更多
The connected sum is a fundamental operation in geometric topology and combinatorics.In this paper,we study the connection between connected sums of simplicial spheres and the algebraic topology of their corresponding...The connected sum is a fundamental operation in geometric topology and combinatorics.In this paper,we study the connection between connected sums of simplicial spheres and the algebraic topology of their corresponding moment-angle manifolds.The cohomology rings of moment-angle manifolds corresponding to connected sums of simplicial spheres are computed,which leads to a conjecture on the topology of such moment-angle manifolds.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
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.
文摘In our paper Simplicial K(G, 1)’s we constructed a sub-complex of the nerve of a group G determined by a partial group structure, and we proved, under a generalized associativity condition called regularity, that the sub-complex realizes as a K(G, 1). This type of sub-complex appears naturally in several topological and algebraic contexts. In this note we prove that regularity of a partial group implies that the Kan extension condition is satisfied on its nerve in dimensions greater than one, and in dimension one a weaker version of the extension condition holds.
文摘The design of mixed finite element methods in linear elasticity with symmetric stress approximations has been a longstanding open problem until Arnold and Winther designed the first family of mixed finite elements where the discrete stress space is the space of H（div,Ω;S）-Pk＋1 tensors whose divergence is a Pk-1 polynomial on each triangle for k ≥ 2. Such a two dimensional family was extended, by Arnold, Awanou and Winther, to a three dimensional family of mixed elements where the discrete stress space is the space of H（div, Ω; S）-Pk＋2 tensors, whose divergence is a Pk-1 polynomial on each tetrahedron for k ≥ 2. In this paper, we are able to construct, in a unified fashion, mixed finite element methods with symmetric stress approximations on an arbitrary simplex in R^n for any space dimension. On the contrary, the discrete stress space here is the space of H（div,Ω; S）-Pk tensors, and the discrete displacement space here is the space of L^2（Ω; R^n）-Pk＋1 vectors for k ≥ n＋ 1. These finite element spaces are defined with respect to an arbitrary simplicial triangulation of the domain, and can be regarded as extensions to any dimension of those in two and three dimensions by Hu and Zhang.
基金supported in part by a DOE grant DEFG0205ER25678 and NSF grant DMS-1005441。
文摘Hierarchical bases of arbitrary order for H(div)-conforming triangular and tetrahedral elements are constructedwith the goal of improving the conditioning of the mass and stiffness matrices.For the basis with the triangular element,it is found numerically that the conditioning is acceptable up to the approximation of order four,and is better than a corresponding basis in the dissertation by Sabine Zaglmayr[High Order Finite Element Methods for Electromagnetic Field Computation,Johannes Kepler Universit¨at,Linz,2006].The sparsity of the mass matrices from the newly constructed basis and from the one by Zaglmayr is similar for approximations up to order four.The stiffness matrix with the new basis is much sparser than that with the basis by Zaglmayr for approximations up to order four.For the tetrahedral element,it is identified numerically that the conditioning is acceptable only up to the approximation of order three.Compared with the newly constructed basis for the triangular element,the sparsity of the massmatrices fromthe basis for the tetrahedral element is relatively sparser.
文摘A mapping f ： Z^n → Rn is said to possess the direction preserving property if fi（x） 〉 0 implies fi（y） ≥ 0 for any integer points x and y with ｜｜x - y｜｜∞≤ 1. In this paper, a simplicial algorithm is developed for computing an integer zero point of a mapping with the direction preserving property. We assume that there is an integer point x^0 with c ≤ x^0≤d satisfying that maxl≤i≤（xi - xi^0）fi（x） 〉 0 for any integer point x with f（x） ≠ 0 on the boundary of H = {x ∈R^n [c-e ≤ x〈d＋e},wherecanddaretwo finite integer points with c 〈 d and e = （1, 1,... , 1）^T E R^n. This assumption is implied by one of two conditions for the existence of an integer zero point of a mapping with the preserving property in van der Laan et al. （2004）. Under this assumption, starting at x^0, the algorithm follows a finite simplicial path and terminates at an integer zero point of the mapping. This result has applications in general economic equilibrium models with indivisible commodities.
文摘In this paper, we explore the spanning simplicial complex of wheel graph Wn on vertex set [n]. Combinatorial properties of the spanning simplicial complex of wheel graph are discussed, which are then used to compute the f-vector and Hilbert series of face ring k[Δs(Wn)] for the spanning simplicial complex Δs(Wn). Moreover, the associated primes of the facet ideal IF(Δs(Wn)) are also computed.
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 NSFC(Grant No.11971144)High-level Scientific Research Foundation of Hebei Province+1 种基金the start-up research fund from BIMSAsupported by Postgraduate Innovation Funding Project of Hebei Province(Grant No.CXZZBS2022073)。
文摘In this article,we give a generalization of δ-twisted homology introduced by Jingyan Li,Vladimir Vershinin and Jie Wu,called Δ-twisted homology,which enriches the theory of δ-(co)homology introduced by Alexander Grigor’yan,Yuri Muranov and Shing-Tung Yau.We show that the Mayer-Vietoris sequence theorem holds for Δ-twisted homology.Applying the Δ-twisted ideas to Cartesian products,we introduce the notion of Δ-twisted Cartesian product on simplicial sets,which generalizes the classical work of Barratt,Gugenheim and Moore on twisted Cartesian products of simplicial sets.Under certain hypothesis,we show that the coordinate projection of Δ-twisted Cartesian product admits a fibre bundle structure.
文摘In this paper a triangulation of continuous and arbitrary refinement of grid sizes is proposed for simplicial homotopy algorithms to compute zero points on a polytope P. The proposed algorithm generates a piecewise linear path in P × [1,∞) from any chosen interior point x0 of P on level {1} to a solution of the underlying problem. The path is followed by making linear programming pivot steps in a linear system and replacement steps in the triangnlation.The starting point x0 is left in a direction to one vertex of P. The direction in which x0 leaves depends on the function value at x0 and the polytope P. Moreover, we also give a new equivalent form of the Brouwer fixed point theorem on polytopes. This form has many important applications in mathematical programming and the theory of differential equations.
基金supported by National Natural Science Foundation of China(Grant Nos.11801580 and 11871284)supported by National Natural Science Foundation of China(Grant Nos.11871284 and 11761072).
文摘The connected sum is a fundamental operation in geometric topology and combinatorics.In this paper,we study the connection between connected sums of simplicial spheres and the algebraic topology of their corresponding moment-angle manifolds.The cohomology rings of moment-angle manifolds corresponding to connected sums of simplicial spheres are computed,which leads to a conjecture on the topology of such moment-angle manifolds.
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.
