This paper addresses the estimation problem of an unknown drift parameter matrix for a fractional Ornstein-Uhlenbeck process in a multi-dimensional setting.To tackle this problem,we propose a novel approach based on r...This paper addresses the estimation problem of an unknown drift parameter matrix for a fractional Ornstein-Uhlenbeck process in a multi-dimensional setting.To tackle this problem,we propose a novel approach based on rough path theory that allows us to construct pathwise rough path estimators from both continuous and discrete observations of a single path.Our approach is particularly suitable for high-frequency data.To formulate the parameter estimators,we introduce a theory of pathwise Itôintegrals with respect to fractional Brownian motion.By establishing the regularity of fractional Ornstein-Uhlenbeck processes and analyzing the long-term behavior of the associated Lévy area processes,we demonstrate that our estimators are strongly consistent and pathwise stable.Our findings offer a new perspective on estimating the drift parameter matrix for fractional Ornstein-Uhlenbeck processes in multi-dimensional settings,and may have practical implications for fields including finance,economics,and engineering.展开更多
The influence maximization problem aims to select a small set of influential nodes, termed a seed set, to maximize their influence coverage in social networks. Although the methods that are based on a greedy strategy ...The influence maximization problem aims to select a small set of influential nodes, termed a seed set, to maximize their influence coverage in social networks. Although the methods that are based on a greedy strategy can obtain good accuracy, they come at the cost of enormous computational time, and are therefore not applicable to practical scenarios in large-scale networks. In addition, the centrality heuristic algorithms that are based on network topology can be completed in relatively less time. However, they tend to fail to achieve satisfactory results because of drawbacks such as overlapped influence spread. In this work, we propose a discrete two-stage metaheuristic optimization combining quantum-behaved particle swarm optimization with Lévy flight to identify a set of the most influential spreaders. According to the framework,first, the particles in the population are tasked to conduct an exploration in the global solution space to eventually converge to an acceptable solution through the crossover and replacement operations. Second, the Lévy flight mechanism is used to perform a wandering walk on the optimal candidate solution in the population to exploit the potentially unidentified influential nodes in the network. Experiments on six real-world social networks show that the proposed algorithm achieves more satisfactory results when compared to other well-known algorithms.展开更多
In the past few years,attention has mainly been focused on the symmetric Brownian motor(BM)with Gaussian noises,whose current and energy conversion efficiency are very low.Here,we investigate the operating performance...In the past few years,attention has mainly been focused on the symmetric Brownian motor(BM)with Gaussian noises,whose current and energy conversion efficiency are very low.Here,we investigate the operating performance of the symmetric BM subjected to Lévy noise.Through numerical simulations,it is found that the operating performance of the motor can be greatly improved in asymmetric Lévy noise.Without any load,the Lévy noises with smaller stable indexes can let the motor give rise to a much greater current.With a load,the energy conversion efficiency of the motor can be enhanced by adjusting the stable indexes of the Lévy noises with symmetry breaking.The results of this research are of great significance for opening up BM’s intrinsic physical mechanism and promoting the development of nanotechnology.展开更多
The formation of spatial patterns is an important issue in reaction–diffusion systems.Previous studies have mainly focused on the spatial patterns in reaction–diffusion models equipped with symmetric diffusion(such ...The formation of spatial patterns is an important issue in reaction–diffusion systems.Previous studies have mainly focused on the spatial patterns in reaction–diffusion models equipped with symmetric diffusion(such as normal or fractional Laplace diffusion),namely,assuming that spatial environments of the systems are homogeneous.However,the complexity and heterogeneity of spatial environments of biochemical reactions in vivo can lead to asymmetric diffusion of reactants.Naturally,there arises an open question of how the asymmetric diffusion affects dynamical behaviors of biochemical reaction systems.To answer this,we build a general asymmetric L´evy diffusion model based on the theory of a continuous time random walk.In addition,we investigate the two-species Brusselator model with asymmetric L´evy diffusion,and obtain a general condition for the formation of Turing and wave patterns.More interestingly,we find that even though the Brusselator model with symmetric diffusion cannot produce steady spatial patterns for some parameters,the asymmetry of L´evy diffusion for this model can produce wave patterns.This is different from the previous result that wave instability requires at least a three-species model.In addition,the asymmetry of L´evy diffusion can significantly affect the amplitude and frequency of the spatial patterns.Our results enrich our knowledge of the mechanisms of pattern formation.展开更多
基金supported by Shanghai Artificial Intelligence Laboratory.
文摘This paper addresses the estimation problem of an unknown drift parameter matrix for a fractional Ornstein-Uhlenbeck process in a multi-dimensional setting.To tackle this problem,we propose a novel approach based on rough path theory that allows us to construct pathwise rough path estimators from both continuous and discrete observations of a single path.Our approach is particularly suitable for high-frequency data.To formulate the parameter estimators,we introduce a theory of pathwise Itôintegrals with respect to fractional Brownian motion.By establishing the regularity of fractional Ornstein-Uhlenbeck processes and analyzing the long-term behavior of the associated Lévy area processes,we demonstrate that our estimators are strongly consistent and pathwise stable.Our findings offer a new perspective on estimating the drift parameter matrix for fractional Ornstein-Uhlenbeck processes in multi-dimensional settings,and may have practical implications for fields including finance,economics,and engineering.
基金Project supported by the Zhejiang Provincial Natural Science Foundation (Grant No.LQ20F020011)the Gansu Provincial Foundation for Distinguished Young Scholars (Grant No.23JRRA766)+1 种基金the National Natural Science Foundation of China (Grant No.62162040)the National Key Research and Development Program of China (Grant No.2020YFB1713600)。
文摘The influence maximization problem aims to select a small set of influential nodes, termed a seed set, to maximize their influence coverage in social networks. Although the methods that are based on a greedy strategy can obtain good accuracy, they come at the cost of enormous computational time, and are therefore not applicable to practical scenarios in large-scale networks. In addition, the centrality heuristic algorithms that are based on network topology can be completed in relatively less time. However, they tend to fail to achieve satisfactory results because of drawbacks such as overlapped influence spread. In this work, we propose a discrete two-stage metaheuristic optimization combining quantum-behaved particle swarm optimization with Lévy flight to identify a set of the most influential spreaders. According to the framework,first, the particles in the population are tasked to conduct an exploration in the global solution space to eventually converge to an acceptable solution through the crossover and replacement operations. Second, the Lévy flight mechanism is used to perform a wandering walk on the optimal candidate solution in the population to exploit the potentially unidentified influential nodes in the network. Experiments on six real-world social networks show that the proposed algorithm achieves more satisfactory results when compared to other well-known algorithms.
基金Project supported by the Research Group of Nonequilibrium Statistics(Grant No.14078206)Kunming University of Science and Technology,China.
文摘In the past few years,attention has mainly been focused on the symmetric Brownian motor(BM)with Gaussian noises,whose current and energy conversion efficiency are very low.Here,we investigate the operating performance of the symmetric BM subjected to Lévy noise.Through numerical simulations,it is found that the operating performance of the motor can be greatly improved in asymmetric Lévy noise.Without any load,the Lévy noises with smaller stable indexes can let the motor give rise to a much greater current.With a load,the energy conversion efficiency of the motor can be enhanced by adjusting the stable indexes of the Lévy noises with symmetry breaking.The results of this research are of great significance for opening up BM’s intrinsic physical mechanism and promoting the development of nanotechnology.
基金supported by the National Natural Science Foundation of China(Grant Nos.62066026,62363027,and 12071408)PhD program of Entrepreneurship and Innovation of Jiangsu Province,Jiangsu University’Blue Project’,the Natural Science Foundation of Jiangxi Province(Grant No.20224BAB202026)the Science and Technology Research Project of Jiangxi Provincial Department of Education(Grant No.GJJ2203316).
文摘The formation of spatial patterns is an important issue in reaction–diffusion systems.Previous studies have mainly focused on the spatial patterns in reaction–diffusion models equipped with symmetric diffusion(such as normal or fractional Laplace diffusion),namely,assuming that spatial environments of the systems are homogeneous.However,the complexity and heterogeneity of spatial environments of biochemical reactions in vivo can lead to asymmetric diffusion of reactants.Naturally,there arises an open question of how the asymmetric diffusion affects dynamical behaviors of biochemical reaction systems.To answer this,we build a general asymmetric L´evy diffusion model based on the theory of a continuous time random walk.In addition,we investigate the two-species Brusselator model with asymmetric L´evy diffusion,and obtain a general condition for the formation of Turing and wave patterns.More interestingly,we find that even though the Brusselator model with symmetric diffusion cannot produce steady spatial patterns for some parameters,the asymmetry of L´evy diffusion for this model can produce wave patterns.This is different from the previous result that wave instability requires at least a three-species model.In addition,the asymmetry of L´evy diffusion can significantly affect the amplitude and frequency of the spatial patterns.Our results enrich our knowledge of the mechanisms of pattern formation.
