In the past few decades, the study of collective motion phase transition process has made great progress. It is also important for the description of the spatial distribution of particles. In this work, we propose a n...In the past few decades, the study of collective motion phase transition process has made great progress. It is also important for the description of the spatial distribution of particles. In this work, we propose a new order parameter φ to quantify the degree of order in the spatial distribution of particles. The results show that the spatial distribution order parameter can effectively describe the transition from a disorderly moving phase to a phase with a coherent motion of the particle distribution and the same conclusion could be obtained for systems with different sizes. Furthermore, we develop a powerful molecular dynamic graph network(MDGNet) model to realize the long-term prediction of the self-propelled collective system solely from the initial particle positions and movement angles. Employing this model, we successfully predict the order parameters of the specified time step. And the model can also be applied to analyze other types of complex systems with local interactions.展开更多
In this paper, we propose a new perspective to discuss the N-order fixed point theory of set-valued and single-valued mappings. There are two aspects in our work: we first define a product metric space with a graph fo...In this paper, we propose a new perspective to discuss the N-order fixed point theory of set-valued and single-valued mappings. There are two aspects in our work: we first define a product metric space with a graph for the single-valued mapping whose conversion makes the results and proofs concise and straightforward, and then we propose an <em>SG</em>-contraction definition for set-valued mapping which is more general than some recent contraction’s definition. The results obtained in this paper extend and unify some recent results of other authors. Our method to discuss the N-order fixed point unifies <em>N</em>-order fixed point theory of set-valued and single-valued mappings.展开更多
In this paper, we use a combinatorial analysis method. In the complete graph K N with edges colored arbitrarily by red or blue, we consider the proposition of the subgraph of the red graph or blue graph induced by t...In this paper, we use a combinatorial analysis method. In the complete graph K N with edges colored arbitrarily by red or blue, we consider the proposition of the subgraph of the red graph or blue graph induced by the neighborhood of some vertex in V(K N). Inspired by the main results of Jayawardene and Rousseau (Ars Combinatoria, 2000, 163-173), we determine the Ramsey numbers of r(K 1, 4, G), where G is the three-partite graph of order six without isolate vertex.展开更多
The Kirchhoff index Kf(G) of a graph G is defined to be the sum of the resistance distances between all pairs of vertices of G. In this paper, we develop a novel method for ordering the Kirchhoff indices of the comple...The Kirchhoff index Kf(G) of a graph G is defined to be the sum of the resistance distances between all pairs of vertices of G. In this paper, we develop a novel method for ordering the Kirchhoff indices of the complements of trees and unicyclic graphs. With this method, we determine the first five maximum values of Kf■ and the first four maximum values of Kf(ū),where ■ and ū are the complements of a tree T and unicyclic graph U, respectively.展开更多
Discovering publication hierarchically-ordered contexts is the main task in context-based searching paradigm. The proposed techniques to discover publication contexts relies on the availability of domain-specific inpu...Discovering publication hierarchically-ordered contexts is the main task in context-based searching paradigm. The proposed techniques to discover publication contexts relies on the availability of domain-specific inputs, namely a pre-specified ontology terms. A problem with this technique is that the needed domain-specific inputs may not be available in some scientific disciplines. In this paper, we propose utilizing a powerful input that is naturally available in any scientific discipline to discover the hierarchically-ordered contexts of it, namely paper citation and co-authorship graphs. More specifically, we propose a set of domain-specific bibliometry-aware features that are automatically computable instead of domain-specific inputs that need experts’ efforts to prepare. Another benefit behind considering bibliometric-features to adapt to the special characteristics of the literature environment being targeted, which in turn facilitates contexts membership decision making. One key advantage of our proposal is that it considers temporal changes of the targeted publication set.展开更多
多视图聚类已经被广泛研究,它能够采用可用的多源信息来实现更好的聚类性能.然而,大多数之前的工作仍存在两个不足:(1)它们通常关注多视图属性特征的场景,很少留意到多视图属性图数据;(2)它们主要尝试发现一致的结构或多个视图之间的关...多视图聚类已经被广泛研究,它能够采用可用的多源信息来实现更好的聚类性能.然而,大多数之前的工作仍存在两个不足:(1)它们通常关注多视图属性特征的场景,很少留意到多视图属性图数据;(2)它们主要尝试发现一致的结构或多个视图之间的关系,而忽略了多视图观测之间潜在的高阶相关性。为了解决这些问题,我们从广义角度出发,提出了一种新颖的方法,称为混合阶相似性的多视图聚类(Multiview Clustering by Hybridorder Affinity,MCHA).它将结构图和多视图属性特征巧妙融合,同时考虑了低秩概率相似性图和混合阶的相关性.具体而言,我们通过图过滤策略构建了一组保留几何结构的视图特定的平滑表示.同时,我们将从平滑表示中学习得到的多视图概率相似性图堆叠成一个张量,并对该张量给予低秩属性的约束.这可以很好地恢复视图间更高阶的相关性.在八个基准数据集上的实验表明,我们所提出的MCHA方法具有最先进的有效性.展开更多
基金the National Natural Science Foundation of China (Grant No. 11702289)Key core technology and generic technology research and development project of Shanxi Province of China (Grant No. 2020XXX013)the National Key Research and Development Project of China。
文摘In the past few decades, the study of collective motion phase transition process has made great progress. It is also important for the description of the spatial distribution of particles. In this work, we propose a new order parameter φ to quantify the degree of order in the spatial distribution of particles. The results show that the spatial distribution order parameter can effectively describe the transition from a disorderly moving phase to a phase with a coherent motion of the particle distribution and the same conclusion could be obtained for systems with different sizes. Furthermore, we develop a powerful molecular dynamic graph network(MDGNet) model to realize the long-term prediction of the self-propelled collective system solely from the initial particle positions and movement angles. Employing this model, we successfully predict the order parameters of the specified time step. And the model can also be applied to analyze other types of complex systems with local interactions.
文摘In this paper, we propose a new perspective to discuss the N-order fixed point theory of set-valued and single-valued mappings. There are two aspects in our work: we first define a product metric space with a graph for the single-valued mapping whose conversion makes the results and proofs concise and straightforward, and then we propose an <em>SG</em>-contraction definition for set-valued mapping which is more general than some recent contraction’s definition. The results obtained in this paper extend and unify some recent results of other authors. Our method to discuss the N-order fixed point unifies <em>N</em>-order fixed point theory of set-valued and single-valued mappings.
文摘In this paper, we use a combinatorial analysis method. In the complete graph K N with edges colored arbitrarily by red or blue, we consider the proposition of the subgraph of the red graph or blue graph induced by the neighborhood of some vertex in V(K N). Inspired by the main results of Jayawardene and Rousseau (Ars Combinatoria, 2000, 163-173), we determine the Ramsey numbers of r(K 1, 4, G), where G is the three-partite graph of order six without isolate vertex.
基金Supported by the National Natural Science Foundation of China(11861011,11501133,11661010)。
文摘The Kirchhoff index Kf(G) of a graph G is defined to be the sum of the resistance distances between all pairs of vertices of G. In this paper, we develop a novel method for ordering the Kirchhoff indices of the complements of trees and unicyclic graphs. With this method, we determine the first five maximum values of Kf■ and the first four maximum values of Kf(ū),where ■ and ū are the complements of a tree T and unicyclic graph U, respectively.
文摘Discovering publication hierarchically-ordered contexts is the main task in context-based searching paradigm. The proposed techniques to discover publication contexts relies on the availability of domain-specific inputs, namely a pre-specified ontology terms. A problem with this technique is that the needed domain-specific inputs may not be available in some scientific disciplines. In this paper, we propose utilizing a powerful input that is naturally available in any scientific discipline to discover the hierarchically-ordered contexts of it, namely paper citation and co-authorship graphs. More specifically, we propose a set of domain-specific bibliometry-aware features that are automatically computable instead of domain-specific inputs that need experts’ efforts to prepare. Another benefit behind considering bibliometric-features to adapt to the special characteristics of the literature environment being targeted, which in turn facilitates contexts membership decision making. One key advantage of our proposal is that it considers temporal changes of the targeted publication set.
文摘多视图聚类已经被广泛研究,它能够采用可用的多源信息来实现更好的聚类性能.然而,大多数之前的工作仍存在两个不足:(1)它们通常关注多视图属性特征的场景,很少留意到多视图属性图数据;(2)它们主要尝试发现一致的结构或多个视图之间的关系,而忽略了多视图观测之间潜在的高阶相关性。为了解决这些问题,我们从广义角度出发,提出了一种新颖的方法,称为混合阶相似性的多视图聚类(Multiview Clustering by Hybridorder Affinity,MCHA).它将结构图和多视图属性特征巧妙融合,同时考虑了低秩概率相似性图和混合阶的相关性.具体而言,我们通过图过滤策略构建了一组保留几何结构的视图特定的平滑表示.同时,我们将从平滑表示中学习得到的多视图概率相似性图堆叠成一个张量,并对该张量给予低秩属性的约束.这可以很好地恢复视图间更高阶的相关性.在八个基准数据集上的实验表明,我们所提出的MCHA方法具有最先进的有效性.
