In this paper, a sufficient condition for the existence of bifurcation points for discrete dynamical systems is presented. The relation between two families of systems is further discussed, and a sufficient condition ...In this paper, a sufficient condition for the existence of bifurcation points for discrete dynamical systems is presented. The relation between two families of systems is further discussed, and a sufficient condition for determining whether they may have the similar bifurcation points is given.展开更多
Community detection is a vital task in many fields,such as social networks and financial analysis,to name a few.The Louvain method,the main workhorse of community detection,is a popular heuristic method.To apply it to...Community detection is a vital task in many fields,such as social networks and financial analysis,to name a few.The Louvain method,the main workhorse of community detection,is a popular heuristic method.To apply it to large-scale graph networks,researchers have proposed several parallel Louvain methods(PLMs),which suffer from two challenges:the latency in the information synchronization,and the community swap.To tackle these two challenges,we propose an isolate sets based parallel Louvain method(IPLM)and a fusion IPLM with the hashtables based Louvain method(FIPLM),which are based on a novel graph partition algorithm.Our graph partition algorithm divides the graph network into subgraphs called isolate sets,in which the vertices are relatively decoupled from others.We first describe the concepts and properties of the isolate set.Second we propose an algorithm to divide the graph network into isolate sets,which enjoys the same computation complexity as the breadth-first search.Third,we propose IPLM,which can efficiently calculate and update vertices information in parallel without latency or community swap.Finally,we achieve further acceleration by FIPLM,which maintains a high quality of community detection with a faster speedup than IPLM.Our two methods are for shared-memory architecture,and we implement our methods on an 8-core PC;the experiments show that IPLM achieves a maximum speedup of 4.62x and outputs higher modularity(maximum 4.76%)than the serial Louvain method on 14 of 18 datasets.Moreover,FIPLM achieves a maximum speedup of 7.26x.展开更多
Using the concept of an isolated invariant set, some existence criteria of orbits connecting two critical points bifurcating from a single critical point for ordinary differential equations depending on a parameter ar...Using the concept of an isolated invariant set, some existence criteria of orbits connecting two critical points bifurcating from a single critical point for ordinary differential equations depending on a parameter are given.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant No.10672146)the Shanghai Leading Academic Discipline Project (Grant No.S30104)
文摘In this paper, a sufficient condition for the existence of bifurcation points for discrete dynamical systems is presented. The relation between two families of systems is further discussed, and a sufficient condition for determining whether they may have the similar bifurcation points is given.
基金supported by the Key Program of National Natural Science Foundation of China under Grant No.61732018the National Natural Science Foundation of China under Grant No.61902415the Open Foundation of Science and Technology on Parallel and Distributed Laboratory(School of Computer,National University of Defense Technology)under Grant No.6142110190201.
文摘Community detection is a vital task in many fields,such as social networks and financial analysis,to name a few.The Louvain method,the main workhorse of community detection,is a popular heuristic method.To apply it to large-scale graph networks,researchers have proposed several parallel Louvain methods(PLMs),which suffer from two challenges:the latency in the information synchronization,and the community swap.To tackle these two challenges,we propose an isolate sets based parallel Louvain method(IPLM)and a fusion IPLM with the hashtables based Louvain method(FIPLM),which are based on a novel graph partition algorithm.Our graph partition algorithm divides the graph network into subgraphs called isolate sets,in which the vertices are relatively decoupled from others.We first describe the concepts and properties of the isolate set.Second we propose an algorithm to divide the graph network into isolate sets,which enjoys the same computation complexity as the breadth-first search.Third,we propose IPLM,which can efficiently calculate and update vertices information in parallel without latency or community swap.Finally,we achieve further acceleration by FIPLM,which maintains a high quality of community detection with a faster speedup than IPLM.Our two methods are for shared-memory architecture,and we implement our methods on an 8-core PC;the experiments show that IPLM achieves a maximum speedup of 4.62x and outputs higher modularity(maximum 4.76%)than the serial Louvain method on 14 of 18 datasets.Moreover,FIPLM achieves a maximum speedup of 7.26x.
基金Research supported by the National Science Foundation of China(No.10271115).
文摘Using the concept of an isolated invariant set, some existence criteria of orbits connecting two critical points bifurcating from a single critical point for ordinary differential equations depending on a parameter are given.
