The prediction for Multivariate Time Series(MTS)explores the interrelationships among variables at historical moments,extracts their relevant characteristics,and is widely used in finance,weather,complex industries an...The prediction for Multivariate Time Series(MTS)explores the interrelationships among variables at historical moments,extracts their relevant characteristics,and is widely used in finance,weather,complex industries and other fields.Furthermore,it is important to construct a digital twin system.However,existing methods do not take full advantage of the potential properties of variables,which results in poor predicted accuracy.In this paper,we propose the Adaptive Fused Spatial-Temporal Graph Convolutional Network(AFSTGCN).First,to address the problem of the unknown spatial-temporal structure,we construct the Adaptive Fused Spatial-Temporal Graph(AFSTG)layer.Specifically,we fuse the spatial-temporal graph based on the interrelationship of spatial graphs.Simultaneously,we construct the adaptive adjacency matrix of the spatial-temporal graph using node embedding methods.Subsequently,to overcome the insufficient extraction of disordered correlation features,we construct the Adaptive Fused Spatial-Temporal Graph Convolutional(AFSTGC)module.The module forces the reordering of disordered temporal,spatial and spatial-temporal dependencies into rule-like data.AFSTGCN dynamically and synchronously acquires potential temporal,spatial and spatial-temporal correlations,thereby fully extracting rich hierarchical feature information to enhance the predicted accuracy.Experiments on different types of MTS datasets demonstrate that the model achieves state-of-the-art single-step and multi-step performance compared with eight other deep learning models.展开更多
Let∇be a linear connection on a 2n-dimensional almost anti-Hermitian manifold M equipped with an almost complex structure J,a pseudo-Riemannian metric g and the twin metric G=g◦J.In this paper,we first introduce three...Let∇be a linear connection on a 2n-dimensional almost anti-Hermitian manifold M equipped with an almost complex structure J,a pseudo-Riemannian metric g and the twin metric G=g◦J.In this paper,we first introduce three types of conjugate connections of linear connections relative to g,G and J.We obtain a simple relation among curvature tensors of these conjugate connections.To clarify the relations of these conjugate connections,we prove a result stating that conjugations along with an identity operation together act as a Klein group,which is analogue to the known result for the Hermitian case in[2].Secondly,we give some results exhibiting occurrences of Codazzi pairs which generalize parallelism relative to∇.Under the assumption that(∇,J)being a Codazzi pair,we derive a necessary and sufficient condition the almost anti-Hermitian manifold(M,J,g,G)is an anti-K¨ahler relative to a torsion-free linear connection∇.Finally,we investigate statistical structures on M under∇(∇is a J−parallel torsion-free connection).展开更多
数字工程被认为是系统工程在数字化时代的延伸,具有能有效缩短装备研制周期、提升产品质量、优化工程体系等优点,实现装备采办过程由“以文本为中心”向“以数据为中心”的范式转变。为全面系统地分析数字工程的发展概况和研究动态,通过...数字工程被认为是系统工程在数字化时代的延伸,具有能有效缩短装备研制周期、提升产品质量、优化工程体系等优点,实现装备采办过程由“以文本为中心”向“以数据为中心”的范式转变。为全面系统地分析数字工程的发展概况和研究动态,通过对Web of Science数据库中“Digital Engineering”相关文献进行CiteSpace计量分析,分别从发文量、研究领域与文献分布、所属国家与机构分布、作者与机构合作知识图谱、共被引知识图谱、关键词共现等不同角度审视研究主题结构,结合可视化知识图谱对数字工程研究的现状、趋势和热点进行了分析。分析结果表明,数字工程研究具有多学科、跨领域的交叉特性,已跨入快速上升期;已初步形成多个数字工程研究团队,但核心作者较分散;美国、英国、德国等发达国家投入数字工程研究力度大且取得成果丰硕,而我国在数字工程研究的资助和战略部署方面亟待加强。此外,从研究趋势的演进来看,未来数字工程研究的重点将聚焦于基于模型的系统工程、Digital Twin等技术体系。最后,进行全文结论性总结,指出数字工程面临的挑战以及未来重点发展方向。展开更多
The integration of industrial Internet,cloud computing,and big data technology is changing the business and management mode of the industry chain.However,the industry chain is characterized by a wide range of fields,c...The integration of industrial Internet,cloud computing,and big data technology is changing the business and management mode of the industry chain.However,the industry chain is characterized by a wide range of fields,complex environment,and many factors,which creates a challenge for efficient integration and leveraging of industrial big data.Aiming at the integration of physical space and virtual space of the current industry chain,we propose an industry chain digital twin(DT)system framework for the industrial Internet.In addition,an industry chain information model based on a knowledge graph(KG)is proposed to integrate complex and heterogeneous industry chain data and extract industrial knowledge.First,the ontology of the industry chain is established,and an entity alignment method based on scientific and technological achievements is proposed.Second,the bidirectional encoder representations from Transformers(BERT)based multi-head selection model is proposed for joint entity–relation extraction of industry chain information.Third,a relation completion model based on a relational graph convolutional network(R-GCN)and a graph sample and aggregate network(GraphSAGE)is proposed which considers both semantic information and graph structure information of KG.Experimental results show that the performances of the proposed joint entity–relation extraction model and relation completion model are significantly better than those of the baselines.Finally,an industry chain information model is established based on the data of 18 industry chains in the field of basic machinery,which proves the feasibility of the proposed method.展开更多
This work presents a different approach to twin primes, an approach from the perspective of the Tesla numbers and gives a refresh and new observation of twin primes that could lead us to an answer to the Twin Prime Co...This work presents a different approach to twin primes, an approach from the perspective of the Tesla numbers and gives a refresh and new observation of twin primes that could lead us to an answer to the Twin Prime Conjecture problem. We expose a peculiar relation between twin primes and the generation of prime numbers with Tesla numbers. Tesla numbers seem to be present in so many domains like time, vibration and frequency [1], and the space between twin primes is not the exception. Let us say that twin primes are more than just prime numbers plus 2 or minus 2, and Tesla numbers are more involved with twin primes than we think, and hopefully, this approach give us a better understanding of the distribution of the twin pairs.展开更多
A new approach to the research into the distribution of prime pairs is developed, attached with corollaries about the distribution of prime triplets and generally about that of prime h-tuplets. It differs from the usu...A new approach to the research into the distribution of prime pairs is developed, attached with corollaries about the distribution of prime triplets and generally about that of prime h-tuplets. It differs from the usual methods(involving the sieve method) for this kind of research, and bases on Chebyshev inequality and on the computation of average concentration of all the related subsets, and leads to the proofs of following lemma and theorem, attached with four corollaries:[Lemma 1] Among all the prime-pair-subsets there exists at least one such subset (namely one of the sets of generalized prime twins) which is an infinite set.[Theorem 1] All the prime-pair-subsets (namely all sets of generalized prime twins) or infinitely many prime-pair-subsets are infinite sets.[Corollary 1] Among all the prime-triplet-subsets there exists at least one such subset which is an infinite set.[Corollary 2] All the prime-triplet-subsets or infinitely many prime-triplet-subsets are infinite sets.[Corollary 3] Among all the prime-h-tuplet-subsets there exists at least one such subset which is an infinite set, where h is an arbitrary finite integer ≥2.[Corollary 4] All the prime-h-tuplet-subsets or infinitely many prime-h-tuplet-subsets are infinite sets, where h is an arbitrary finite integer ≥2.展开更多
基金supported by the China Scholarship Council and the CERNET Innovation Project under grant No.20170111.
文摘The prediction for Multivariate Time Series(MTS)explores the interrelationships among variables at historical moments,extracts their relevant characteristics,and is widely used in finance,weather,complex industries and other fields.Furthermore,it is important to construct a digital twin system.However,existing methods do not take full advantage of the potential properties of variables,which results in poor predicted accuracy.In this paper,we propose the Adaptive Fused Spatial-Temporal Graph Convolutional Network(AFSTGCN).First,to address the problem of the unknown spatial-temporal structure,we construct the Adaptive Fused Spatial-Temporal Graph(AFSTG)layer.Specifically,we fuse the spatial-temporal graph based on the interrelationship of spatial graphs.Simultaneously,we construct the adaptive adjacency matrix of the spatial-temporal graph using node embedding methods.Subsequently,to overcome the insufficient extraction of disordered correlation features,we construct the Adaptive Fused Spatial-Temporal Graph Convolutional(AFSTGC)module.The module forces the reordering of disordered temporal,spatial and spatial-temporal dependencies into rule-like data.AFSTGCN dynamically and synchronously acquires potential temporal,spatial and spatial-temporal correlations,thereby fully extracting rich hierarchical feature information to enhance the predicted accuracy.Experiments on different types of MTS datasets demonstrate that the model achieves state-of-the-art single-step and multi-step performance compared with eight other deep learning models.
文摘Let∇be a linear connection on a 2n-dimensional almost anti-Hermitian manifold M equipped with an almost complex structure J,a pseudo-Riemannian metric g and the twin metric G=g◦J.In this paper,we first introduce three types of conjugate connections of linear connections relative to g,G and J.We obtain a simple relation among curvature tensors of these conjugate connections.To clarify the relations of these conjugate connections,we prove a result stating that conjugations along with an identity operation together act as a Klein group,which is analogue to the known result for the Hermitian case in[2].Secondly,we give some results exhibiting occurrences of Codazzi pairs which generalize parallelism relative to∇.Under the assumption that(∇,J)being a Codazzi pair,we derive a necessary and sufficient condition the almost anti-Hermitian manifold(M,J,g,G)is an anti-K¨ahler relative to a torsion-free linear connection∇.Finally,we investigate statistical structures on M under∇(∇is a J−parallel torsion-free connection).
文摘数字工程被认为是系统工程在数字化时代的延伸,具有能有效缩短装备研制周期、提升产品质量、优化工程体系等优点,实现装备采办过程由“以文本为中心”向“以数据为中心”的范式转变。为全面系统地分析数字工程的发展概况和研究动态,通过对Web of Science数据库中“Digital Engineering”相关文献进行CiteSpace计量分析,分别从发文量、研究领域与文献分布、所属国家与机构分布、作者与机构合作知识图谱、共被引知识图谱、关键词共现等不同角度审视研究主题结构,结合可视化知识图谱对数字工程研究的现状、趋势和热点进行了分析。分析结果表明,数字工程研究具有多学科、跨领域的交叉特性,已跨入快速上升期;已初步形成多个数字工程研究团队,但核心作者较分散;美国、英国、德国等发达国家投入数字工程研究力度大且取得成果丰硕,而我国在数字工程研究的资助和战略部署方面亟待加强。此外,从研究趋势的演进来看,未来数字工程研究的重点将聚焦于基于模型的系统工程、Digital Twin等技术体系。最后,进行全文结论性总结,指出数字工程面临的挑战以及未来重点发展方向。
基金the Ministry of Industry and Information Technology of China(Nos.TC200802C and TC190A445)。
文摘The integration of industrial Internet,cloud computing,and big data technology is changing the business and management mode of the industry chain.However,the industry chain is characterized by a wide range of fields,complex environment,and many factors,which creates a challenge for efficient integration and leveraging of industrial big data.Aiming at the integration of physical space and virtual space of the current industry chain,we propose an industry chain digital twin(DT)system framework for the industrial Internet.In addition,an industry chain information model based on a knowledge graph(KG)is proposed to integrate complex and heterogeneous industry chain data and extract industrial knowledge.First,the ontology of the industry chain is established,and an entity alignment method based on scientific and technological achievements is proposed.Second,the bidirectional encoder representations from Transformers(BERT)based multi-head selection model is proposed for joint entity–relation extraction of industry chain information.Third,a relation completion model based on a relational graph convolutional network(R-GCN)and a graph sample and aggregate network(GraphSAGE)is proposed which considers both semantic information and graph structure information of KG.Experimental results show that the performances of the proposed joint entity–relation extraction model and relation completion model are significantly better than those of the baselines.Finally,an industry chain information model is established based on the data of 18 industry chains in the field of basic machinery,which proves the feasibility of the proposed method.
文摘This work presents a different approach to twin primes, an approach from the perspective of the Tesla numbers and gives a refresh and new observation of twin primes that could lead us to an answer to the Twin Prime Conjecture problem. We expose a peculiar relation between twin primes and the generation of prime numbers with Tesla numbers. Tesla numbers seem to be present in so many domains like time, vibration and frequency [1], and the space between twin primes is not the exception. Let us say that twin primes are more than just prime numbers plus 2 or minus 2, and Tesla numbers are more involved with twin primes than we think, and hopefully, this approach give us a better understanding of the distribution of the twin pairs.
文摘A new approach to the research into the distribution of prime pairs is developed, attached with corollaries about the distribution of prime triplets and generally about that of prime h-tuplets. It differs from the usual methods(involving the sieve method) for this kind of research, and bases on Chebyshev inequality and on the computation of average concentration of all the related subsets, and leads to the proofs of following lemma and theorem, attached with four corollaries:[Lemma 1] Among all the prime-pair-subsets there exists at least one such subset (namely one of the sets of generalized prime twins) which is an infinite set.[Theorem 1] All the prime-pair-subsets (namely all sets of generalized prime twins) or infinitely many prime-pair-subsets are infinite sets.[Corollary 1] Among all the prime-triplet-subsets there exists at least one such subset which is an infinite set.[Corollary 2] All the prime-triplet-subsets or infinitely many prime-triplet-subsets are infinite sets.[Corollary 3] Among all the prime-h-tuplet-subsets there exists at least one such subset which is an infinite set, where h is an arbitrary finite integer ≥2.[Corollary 4] All the prime-h-tuplet-subsets or infinitely many prime-h-tuplet-subsets are infinite sets, where h is an arbitrary finite integer ≥2.
