Chaotic phenomena are increasingly being observed in all fields of nature,where investigations reveal that a natural phe nomenon exhibits nonlinearities and attempts to reveal their deep underlying mechanisms.Chaos is...Chaotic phenomena are increasingly being observed in all fields of nature,where investigations reveal that a natural phe nomenon exhibits nonlinearities and attempts to reveal their deep underlying mechanisms.Chaos is normally understood as“a state of disorder”,for which there is as yet no universally accepted mathematical definition.A commonly used concept states that,for a dynamical system to be classified as chaotic,it must have the following properties:be sensitive to initial conditions,show topological transitivity,have densely periodical orbits etc.Revealing the rules that govern chaotic motion is thus an important unsolved task for exploring nature.W e present herein a generalised energy conservation law governing chaotic phenomena.Based on two scalar variables,viz.generalised potential and kinetic energies defined in the phase space describing nonlinear dynamical systems,we find that chaotic motion is periodic motion with infinite time period whose time-averaged generalised potential and kinetic energies are conserved over its time period.This implies that,as the averaging time is increased,the time-averaged generalised potential and kinetic energies tend to constants while the time-averaged energy flows,i.e.,their rates of change with time,tend to zero.Numerical simulations on reported chaotic motions,such as the forced van der Pol system,forced Duffing system,forced smooth and discontinuous oscillator,Lorenz’s system,and Rossler's system,show the above conclusions to be correct according to the results presented herein.This discovery may indicate that chaotic phenomena in nature could be controlled because,even though their instantaneous states are disordered,their long-time averages can be predicted.展开更多
We study embeddings between generalised Triebel–Lizorkin–Morrey spacesε_(ϕ,p,q)^(s)(R^(d))and within the scales of further generalised Morrey smoothness spaces like N_(ϕ,p,q)^(s)(R^(d)),B_(p,q)^(s,ϕ)(R^(d))and F_(p...We study embeddings between generalised Triebel–Lizorkin–Morrey spacesε_(ϕ,p,q)^(s)(R^(d))and within the scales of further generalised Morrey smoothness spaces like N_(ϕ,p,q)^(s)(R^(d)),B_(p,q)^(s,ϕ)(R^(d))and F_(p,q)^(s,ϕ)(R^(d)).The latter have been investigated in a recent paper by the first two authors(2023),while the embeddings of the scale N_(ϕ,p,q)^(s)(R^(d))were mainly obtained in a paper of the first and last two authors(2022).Now we concentrate on the characterisation of the spacesε_(ϕ,p,q)^(s)(R^(d)).Our approach requires a wavelet characterisation of those spaces which we establish for the system of Daubechies’wavelets.Then we prove necessary and sufficient conditions for the embeddingε_(ϕ1,p1,q1)^(s1)(R^(d))→ε_(2ϕ2,p2,q2)^(s)(R^(d)).We can also provide some almost final answer to the question whenε_(ϕ,p,q)^(s)(R^(d))is embedded into C(R^(d)),complementing our recent findings in case of N_(ϕ,p,q)^(s)(R^(d)).展开更多
A form invariance and a conserved quantity of the generalised Birkhoffian system are studied. First, a definition and a criterion of the form invariance are given. Secondly, through the form invariance, a new conserve...A form invariance and a conserved quantity of the generalised Birkhoffian system are studied. First, a definition and a criterion of the form invariance are given. Secondly, through the form invariance, a new conserved quantity can be deduced. Finally, an example is given to illustrate the application of the result.展开更多
Four generalised diameter-height equations were developed and compared for pure and even-aged stands of Tecomella undulata in hot arid region of Rajasthan State in India. The data used to fit the equations consisted o...Four generalised diameter-height equations were developed and compared for pure and even-aged stands of Tecomella undulata in hot arid region of Rajasthan State in India. The data used to fit the equations consisted of 1 540 diameter-height observations collected from the plots laid out in uniformly stocked stands of varying age and density. The performance of four equations was tested by non-linear least squares regression and evaluated using different statistical criteria. Finally, these equations, with the same values of coefficients ob- tained during the fitting phase, were validated by an independent data set consisting of 854 diameter-height observations. Overall, equation （4） （Hui and Gadow function） was found to perform best for both the fitting data set as well as validation data set.展开更多
This paper studies the existence of HSlder continuity of bidireetionally coupled generalised synchronisation （GS）. Based on the slaving principle of synergetics and the modified system approach, it classifies the GS...This paper studies the existence of HSlder continuity of bidireetionally coupled generalised synchronisation （GS）. Based on the slaving principle of synergetics and the modified system approach, it classifies the GS into several types. The existences of two main types of HSlder continuous bidirectionally coupled CS inertial manifolds are theoretically analysed and proved by using the Schauder fixed point theorem. Numerical simulations illustrate the theoretical results.展开更多
This paper presents a study of visco-elastic flow of an incompressible generalized Oldroyd-B fluid between two infinite parallel plates in which the constitutive equation involves fractional order time derivative. The...This paper presents a study of visco-elastic flow of an incompressible generalized Oldroyd-B fluid between two infinite parallel plates in which the constitutive equation involves fractional order time derivative. The solutions of field equations are being obtained for the motion of the said fluid between two parallel plates where the lower plate starts to move with steady velocity and the upper plate remains fixed in the first problem and the upper plate oscillates with constant frequency and the other being at rest in the second problem. The exact solutions for the velocity field are obtained by using the Laplace transform and finite Fourier Sine transform technique in terms of Mittag Leffler and generalised functions. The analytical expression for the velocity fields are derived and the effect of fractional parameters upon the velocity field is depicted graphically.展开更多
The unsteady incompressible viscous flow of a Generalised Maxwell fluid between two coaxial rotating infinite parallel circular disks is studied by using the method of integral transforms. The motion of the fluid is c...The unsteady incompressible viscous flow of a Generalised Maxwell fluid between two coaxial rotating infinite parallel circular disks is studied by using the method of integral transforms. The motion of the fluid is created by the rotation of the upper and lower circular disks with different angular velocities. A fractional calculus approach is utilized to determine the velocity profile in series form in terms of Mittag-Leffler function. The influence of the fractional as well as the material parameters on the velocity field is illustrated graphically.展开更多
This study presented a multi-objective linear fractional inventory (LFI) problem with generalised intuitionistic fuzzy numbers. In modelling, the authors have assumed the ambiances where generalised trapezoidal intuit...This study presented a multi-objective linear fractional inventory (LFI) problem with generalised intuitionistic fuzzy numbers. In modelling, the authors have assumed the ambiances where generalised trapezoidal intuitionistic fuzzy numbers (GTIFNs) used to handle the uncertain information in the data. Then, the given multi-objective generalised intuitionistic fuzzy LFI model was transformed into its equivalent deterministic linear fractional programming problem by employing the possibility and necessity measures. Finally, the applicability of the model is demonstrated with a numerical example and the sensitivity analysis under several parameters is investigated to explore the study.展开更多
Motivated by the effort to understand the mathematical structure underlying the Teukolsky equations in a Kerr metric background, a homogeneous integral equation related to the prolate spheroidal function is studied. F...Motivated by the effort to understand the mathematical structure underlying the Teukolsky equations in a Kerr metric background, a homogeneous integral equation related to the prolate spheroidal function is studied. From the consideration of the Fredholm determinant of the integral equation, a family of generalized error function is defined, with which the Fredholm determinant of the sinc kernel is also evaluated. An analytic solution of a special ease of the fifth Painlev~ transcendent is then worked out explicitly.展开更多
The generalised BCS dislocation group model and the generalised DB atomic cohesive force zone model have obtained the sarne results on nonlinear fracture study of some one-, two- and three-dimensional quasicrystals. T...The generalised BCS dislocation group model and the generalised DB atomic cohesive force zone model have obtained the sarne results on nonlinear fracture study of some one-, two- and three-dimensional quasicrystals. This work reveals some inherent connection between the two models, and finds that their common basis is the generalised Eshelby integral based on the generalised Eshelby energy momentum tensor for quasicrystals. Further applications of the theory in solving nonlinear fracture problems of the materials are also discussed.展开更多
This paper constructs an almost-Poisson structure for the non-self-adjoint dynamical systems, which can be decomposed into a sum of a Poisson bracket and the other almost-Poisson bracket. The necessary and sufficient ...This paper constructs an almost-Poisson structure for the non-self-adjoint dynamical systems, which can be decomposed into a sum of a Poisson bracket and the other almost-Poisson bracket. The necessary and sufficient condition for the decomposition of the almost-Poisson bracket to be two Poisson ones is obtained. As an application, the almost- Poisson structure for generalised Chaplygin＇s systems is discussed in the framework of the decomposition theory. It proves that the almost-Poisson bracket for the systems can be decomposed into the sum of a canonical Poisson bracket and another two noneanonical Poisson brackets in some special cases, which is useful for integrating the equations of motion.展开更多
Coupled map lattices are taken as examples to study the synchronisation of spatiotemporal chaotic systems. First, a generalised synchronisation of two coupled map lattices is realised through selecting an appropriate ...Coupled map lattices are taken as examples to study the synchronisation of spatiotemporal chaotic systems. First, a generalised synchronisation of two coupled map lattices is realised through selecting an appropriate feedback function and appropriate range of feedback parameter. Based on this method we use the phase compression method to extend the range of the parameter. So, we integrate the feedback control method with the phase compression method to implement the generalised synchronisation and obtain an exact range of feedback parameter. This technique is simple to implement in practice. Numerical simulations show the effectiveness and the feasibility of the proposed program.展开更多
In this paper, the problem of generalised synchronisation of two different chaotic systems is investigated. Some less conservative conditions are derived using linear matrix inequality other than existing results. Fur...In this paper, the problem of generalised synchronisation of two different chaotic systems is investigated. Some less conservative conditions are derived using linear matrix inequality other than existing results. Furthermore, a simple adaptive control scheme is proposed to achieve the generalised synchronisation of chaotic systems. The proposed method is simple and easy to implement in practice and can be applied to secure communications. Numerical simulations are also given to demonstrate the effectiveness and feasibility of the theoretical analysis.展开更多
By virtue of the generalised Hermann-Feynmam theorem we re-derive the energy average formula of photon gas. This is another useful application of the theorem.
Reinforcement Learning(RL)techniques are being studied to solve the Demand and Capacity Balancing(DCB)problems to fully exploit their computational performance.A locally gen-eralised Multi-Agent Reinforcement Learning...Reinforcement Learning(RL)techniques are being studied to solve the Demand and Capacity Balancing(DCB)problems to fully exploit their computational performance.A locally gen-eralised Multi-Agent Reinforcement Learning(MARL)for real-world DCB problems is proposed.The proposed method can deploy trained agents directly to unseen scenarios in a specific Air Traffic Flow Management(ATFM)region to quickly obtain a satisfactory solution.In this method,agents of all flights in a scenario form a multi-agent decision-making system based on partial observation.The trained agent with the customised neural network can be deployed directly on the corresponding flight,allowing it to solve the DCB problem jointly.A cooperation coefficient is introduced in the reward function,which is used to adjust the agent’s cooperation preference in a multi-agent system,thereby controlling the distribution of flight delay time allocation.A multi-iteration mechanism is designed for the DCB decision-making framework to deal with problems arising from non-stationarity in MARL and to ensure that all hotspots are eliminated.Experiments based on large-scale high-complexity real-world scenarios are conducted to verify the effectiveness and efficiency of the method.From a statis-tical point of view,it is proven that the proposed method is generalised within the scope of the flights and sectors of interest,and its optimisation performance outperforms the standard computer-assisted slot allocation and state-of-the-art RL-based DCB methods.The sensitivity analysis preliminarily reveals the effect of the cooperation coefficient on delay time allocation.展开更多
For two graphs G and H,the Ramsey number R(G,H)is the smallest integer n such that for any n-vertex graph,either it contains G or its complement contains H.Let S_(n)be a star of order n and W_(s,m)be a generalised whe...For two graphs G and H,the Ramsey number R(G,H)is the smallest integer n such that for any n-vertex graph,either it contains G or its complement contains H.Let S_(n)be a star of order n and W_(s,m)be a generalised wheel K_(s)V C_(m).Previous studies by Wang and Chen(Graphs Comb 35(1):189-193,2019)and Chng et al.(Discret Math 344(8):112440,2021)imply that a tree is W_(s,4)-good,W_(s,5)-good,W_(s,6)-good,and W_(s,7)-good for s≥2.In this paper,we study the Ramsey numbers R(S_(n),W_(s,8)),and our results indicate that trees are not always W_(s,8)-good.展开更多
In this research, we propose longitudinal generalised variance functions (LGVFs) to produceconvenient estimates of variances by incorporating time effect into modelling. Asymptoticproperties of some certain type of es...In this research, we propose longitudinal generalised variance functions (LGVFs) to produceconvenient estimates of variances by incorporating time effect into modelling. Asymptoticproperties of some certain type of estimators are investigated. Simulation studies and implementation of the proposed methods to Current Population Survey (CPS) data show that LGVFswork well in producing standard error estimates.展开更多
After the set-up of a spatial data infrastructure(SDI)and a national information infrastructure(NII)in many countries,the provision of geo-services became one of the most important and attractive tasks.With the integr...After the set-up of a spatial data infrastructure(SDI)and a national information infrastructure(NII)in many countries,the provision of geo-services became one of the most important and attractive tasks.With the integration of global positioning system(GPS),geographic information system(GIS)and remote sensing(RS),we can,in principle,answer any geo-spatial related question:when and where what object has which changes?An intelligent geo-service agent could provide end-users with the most necessary information in the shortest time and at the lowest cost.Unfortunately there is still a long way to go to achieve such goals.The central component in such geo-services is the integration of the spatial information system with a computing grid via wire-and wireless communication networks.This paper will mainly discuss the grid technology and its integration with spatial information technology,expounding potential problems and possible resolutions.A novel categorising of information grids in the context of geospatial information is proposed:generalised and specialised spatial information grids.展开更多
Wepropose a constrained generalised method of moments(CGMM)for enhancing the efficiency of estimators in meta-analysis in which some studies do not measure all covariates associated with the response or outcome.Under ...Wepropose a constrained generalised method of moments(CGMM)for enhancing the efficiency of estimators in meta-analysis in which some studies do not measure all covariates associated with the response or outcome.Under some assumptions,weshow that the proposedCGMMestimators have good asymptotic properties.Wealso demonstrate the effectiveness of the proposed method through simulation studies with fixed sample sizes.展开更多
Geo-information on settlements from Earth Observation offers a base for objective and scalable monitoring of the evolution of cities and settlements,including their location,extent and other attributes.In this work,we...Geo-information on settlements from Earth Observation offers a base for objective and scalable monitoring of the evolution of cities and settlements,including their location,extent and other attributes.In this work,we deploy the best available global knowledge on the presence of human settlements and built-up structures derived from Earth Observation to advance the understanding of the human presence on Earth.We start from a concept of Generalised Settlement Area to identify the Earth surface within which any built-up structure is present.We further characterise the resulted map by using an agreement map among the state of the art of remote sensing products mapping built-up areas or other strictly related semantic abstractions as urban areas or artificial surfaces.The agreement map is formed by a grid of 1 km2,where each cell is classified according to the number of EO-derived products reporting any positive occurrence of the abstractions related to the presence of built-up structures.The paper describes the characteristics of the Generalised Settlement Area,the differences in the agreement map across geographic regions of the world,and outlines the implications for potential users of the EO-derived products used in this study.展开更多
文摘Chaotic phenomena are increasingly being observed in all fields of nature,where investigations reveal that a natural phe nomenon exhibits nonlinearities and attempts to reveal their deep underlying mechanisms.Chaos is normally understood as“a state of disorder”,for which there is as yet no universally accepted mathematical definition.A commonly used concept states that,for a dynamical system to be classified as chaotic,it must have the following properties:be sensitive to initial conditions,show topological transitivity,have densely periodical orbits etc.Revealing the rules that govern chaotic motion is thus an important unsolved task for exploring nature.W e present herein a generalised energy conservation law governing chaotic phenomena.Based on two scalar variables,viz.generalised potential and kinetic energies defined in the phase space describing nonlinear dynamical systems,we find that chaotic motion is periodic motion with infinite time period whose time-averaged generalised potential and kinetic energies are conserved over its time period.This implies that,as the averaging time is increased,the time-averaged generalised potential and kinetic energies tend to constants while the time-averaged energy flows,i.e.,their rates of change with time,tend to zero.Numerical simulations on reported chaotic motions,such as the forced van der Pol system,forced Duffing system,forced smooth and discontinuous oscillator,Lorenz’s system,and Rossler's system,show the above conclusions to be correct according to the results presented herein.This discovery may indicate that chaotic phenomena in nature could be controlled because,even though their instantaneous states are disordered,their long-time averages can be predicted.
基金partially supported by the German Research Foundation(DFG)(Grant No.Ha 2794/8-1)supported by the China Scholarship Council(CSC)(Grant No.202006350058)partially supported by the Center for Mathematics of the University of Coimbra(funded by the Portuguese Government through FCT/MCTES,DOI 10.54499/UIDB/00324/2020)。
文摘We study embeddings between generalised Triebel–Lizorkin–Morrey spacesε_(ϕ,p,q)^(s)(R^(d))and within the scales of further generalised Morrey smoothness spaces like N_(ϕ,p,q)^(s)(R^(d)),B_(p,q)^(s,ϕ)(R^(d))and F_(p,q)^(s,ϕ)(R^(d)).The latter have been investigated in a recent paper by the first two authors(2023),while the embeddings of the scale N_(ϕ,p,q)^(s)(R^(d))were mainly obtained in a paper of the first and last two authors(2022).Now we concentrate on the characterisation of the spacesε_(ϕ,p,q)^(s)(R^(d)).Our approach requires a wavelet characterisation of those spaces which we establish for the system of Daubechies’wavelets.Then we prove necessary and sufficient conditions for the embeddingε_(ϕ1,p1,q1)^(s1)(R^(d))→ε_(2ϕ2,p2,q2)^(s)(R^(d)).We can also provide some almost final answer to the question whenε_(ϕ,p,q)^(s)(R^(d))is embedded into C(R^(d)),complementing our recent findings in case of N_(ϕ,p,q)^(s)(R^(d)).
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 10772025,10932002)the Beijing Municipal Key Disciplines Fund for General Mechanics and Foundation of Mechanics
文摘A form invariance and a conserved quantity of the generalised Birkhoffian system are studied. First, a definition and a criterion of the form invariance are given. Secondly, through the form invariance, a new conserved quantity can be deduced. Finally, an example is given to illustrate the application of the result.
文摘Four generalised diameter-height equations were developed and compared for pure and even-aged stands of Tecomella undulata in hot arid region of Rajasthan State in India. The data used to fit the equations consisted of 1 540 diameter-height observations collected from the plots laid out in uniformly stocked stands of varying age and density. The performance of four equations was tested by non-linear least squares regression and evaluated using different statistical criteria. Finally, these equations, with the same values of coefficients ob- tained during the fitting phase, were validated by an independent data set consisting of 854 diameter-height observations. Overall, equation （4） （Hui and Gadow function） was found to perform best for both the fitting data set as well as validation data set.
基金Project supported by the National Natural Science Foundation of China(Grants Nos.11002061 and 10901073)the Fundamental Research Funds for the Central Universities,China(Grant No.JUSRP10912)
文摘This paper studies the existence of HSlder continuity of bidireetionally coupled generalised synchronisation （GS）. Based on the slaving principle of synergetics and the modified system approach, it classifies the GS into several types. The existences of two main types of HSlder continuous bidirectionally coupled CS inertial manifolds are theoretically analysed and proved by using the Schauder fixed point theorem. Numerical simulations illustrate the theoretical results.
文摘This paper presents a study of visco-elastic flow of an incompressible generalized Oldroyd-B fluid between two infinite parallel plates in which the constitutive equation involves fractional order time derivative. The solutions of field equations are being obtained for the motion of the said fluid between two parallel plates where the lower plate starts to move with steady velocity and the upper plate remains fixed in the first problem and the upper plate oscillates with constant frequency and the other being at rest in the second problem. The exact solutions for the velocity field are obtained by using the Laplace transform and finite Fourier Sine transform technique in terms of Mittag Leffler and generalised functions. The analytical expression for the velocity fields are derived and the effect of fractional parameters upon the velocity field is depicted graphically.
文摘The unsteady incompressible viscous flow of a Generalised Maxwell fluid between two coaxial rotating infinite parallel circular disks is studied by using the method of integral transforms. The motion of the fluid is created by the rotation of the upper and lower circular disks with different angular velocities. A fractional calculus approach is utilized to determine the velocity profile in series form in terms of Mittag-Leffler function. The influence of the fractional as well as the material parameters on the velocity field is illustrated graphically.
文摘This study presented a multi-objective linear fractional inventory (LFI) problem with generalised intuitionistic fuzzy numbers. In modelling, the authors have assumed the ambiances where generalised trapezoidal intuitionistic fuzzy numbers (GTIFNs) used to handle the uncertain information in the data. Then, the given multi-objective generalised intuitionistic fuzzy LFI model was transformed into its equivalent deterministic linear fractional programming problem by employing the possibility and necessity measures. Finally, the applicability of the model is demonstrated with a numerical example and the sensitivity analysis under several parameters is investigated to explore the study.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11171329,11203003 and 11373013
文摘Motivated by the effort to understand the mathematical structure underlying the Teukolsky equations in a Kerr metric background, a homogeneous integral equation related to the prolate spheroidal function is studied. From the consideration of the Fredholm determinant of the integral equation, a family of generalized error function is defined, with which the Fredholm determinant of the sinc kernel is also evaluated. An analytic solution of a special ease of the fifth Painlev~ transcendent is then worked out explicitly.
基金supported by the National Natural Science Foundation of China(Grant Nos. 10372016 and 10672022)
文摘The generalised BCS dislocation group model and the generalised DB atomic cohesive force zone model have obtained the sarne results on nonlinear fracture study of some one-, two- and three-dimensional quasicrystals. This work reveals some inherent connection between the two models, and finds that their common basis is the generalised Eshelby integral based on the generalised Eshelby energy momentum tensor for quasicrystals. Further applications of the theory in solving nonlinear fracture problems of the materials are also discussed.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 10872084 and 10472040)the Outstanding Young Talents Training Fund of Liaoning Province,China (Grant No. 3040005)the Research Program of Higher Education of Liaoning Province,China (Grant No. 2008S098)
文摘This paper constructs an almost-Poisson structure for the non-self-adjoint dynamical systems, which can be decomposed into a sum of a Poisson bracket and the other almost-Poisson bracket. The necessary and sufficient condition for the decomposition of the almost-Poisson bracket to be two Poisson ones is obtained. As an application, the almost- Poisson structure for generalised Chaplygin＇s systems is discussed in the framework of the decomposition theory. It proves that the almost-Poisson bracket for the systems can be decomposed into the sum of a canonical Poisson bracket and another two noneanonical Poisson brackets in some special cases, which is useful for integrating the equations of motion.
基金supported by the National Natural Science Foundation of China (Grant Nos.60573172 and 60973152)the Doctoral Program Foundation of Institution of Higher Education of China (Grant No.20070141014)the Natural Science Foundation of Liaoning Province,China (Grant No.20082165)
文摘Coupled map lattices are taken as examples to study the synchronisation of spatiotemporal chaotic systems. First, a generalised synchronisation of two coupled map lattices is realised through selecting an appropriate feedback function and appropriate range of feedback parameter. Based on this method we use the phase compression method to extend the range of the parameter. So, we integrate the feedback control method with the phase compression method to implement the generalised synchronisation and obtain an exact range of feedback parameter. This technique is simple to implement in practice. Numerical simulations show the effectiveness and the feasibility of the proposed program.
基金Project supported by the Natural Science Foundation of Jiangsu Province,China (Grant No. BK2007016)
文摘In this paper, the problem of generalised synchronisation of two different chaotic systems is investigated. Some less conservative conditions are derived using linear matrix inequality other than existing results. Furthermore, a simple adaptive control scheme is proposed to achieve the generalised synchronisation of chaotic systems. The proposed method is simple and easy to implement in practice and can be applied to secure communications. Numerical simulations are also given to demonstrate the effectiveness and feasibility of the theoretical analysis.
基金supported by the Special Funds of the National Natural Science Foundation of China (Grant No.10947017/A05)
文摘By virtue of the generalised Hermann-Feynmam theorem we re-derive the energy average formula of photon gas. This is another useful application of the theorem.
基金co-funded by the National Natural Science Foundation of China(No.61903187)the National Key R&D Program of China(No.2021YFB1600500)+2 种基金the China Scholarship Council(No.202006830095)the Natural Science Foundation of Jiangsu Province(No.BK20190414)the Jiangsu Province Postgraduate Innovation Fund(No.KYCX20_0213).
文摘Reinforcement Learning(RL)techniques are being studied to solve the Demand and Capacity Balancing(DCB)problems to fully exploit their computational performance.A locally gen-eralised Multi-Agent Reinforcement Learning(MARL)for real-world DCB problems is proposed.The proposed method can deploy trained agents directly to unseen scenarios in a specific Air Traffic Flow Management(ATFM)region to quickly obtain a satisfactory solution.In this method,agents of all flights in a scenario form a multi-agent decision-making system based on partial observation.The trained agent with the customised neural network can be deployed directly on the corresponding flight,allowing it to solve the DCB problem jointly.A cooperation coefficient is introduced in the reward function,which is used to adjust the agent’s cooperation preference in a multi-agent system,thereby controlling the distribution of flight delay time allocation.A multi-iteration mechanism is designed for the DCB decision-making framework to deal with problems arising from non-stationarity in MARL and to ensure that all hotspots are eliminated.Experiments based on large-scale high-complexity real-world scenarios are conducted to verify the effectiveness and efficiency of the method.From a statis-tical point of view,it is proven that the proposed method is generalised within the scope of the flights and sectors of interest,and its optimisation performance outperforms the standard computer-assisted slot allocation and state-of-the-art RL-based DCB methods.The sensitivity analysis preliminarily reveals the effect of the cooperation coefficient on delay time allocation.
基金supported in part by the National Natural Science Foundation of China(no.11931002).
文摘For two graphs G and H,the Ramsey number R(G,H)is the smallest integer n such that for any n-vertex graph,either it contains G or its complement contains H.Let S_(n)be a star of order n and W_(s,m)be a generalised wheel K_(s)V C_(m).Previous studies by Wang and Chen(Graphs Comb 35(1):189-193,2019)and Chng et al.(Discret Math 344(8):112440,2021)imply that a tree is W_(s,4)-good,W_(s,5)-good,W_(s,6)-good,and W_(s,7)-good for s≥2.In this paper,we study the Ramsey numbers R(S_(n),W_(s,8)),and our results indicate that trees are not always W_(s,8)-good.
文摘In this research, we propose longitudinal generalised variance functions (LGVFs) to produceconvenient estimates of variances by incorporating time effect into modelling. Asymptoticproperties of some certain type of estimators are investigated. Simulation studies and implementation of the proposed methods to Current Population Survey (CPS) data show that LGVFswork well in producing standard error estimates.
文摘After the set-up of a spatial data infrastructure(SDI)and a national information infrastructure(NII)in many countries,the provision of geo-services became one of the most important and attractive tasks.With the integration of global positioning system(GPS),geographic information system(GIS)and remote sensing(RS),we can,in principle,answer any geo-spatial related question:when and where what object has which changes?An intelligent geo-service agent could provide end-users with the most necessary information in the shortest time and at the lowest cost.Unfortunately there is still a long way to go to achieve such goals.The central component in such geo-services is the integration of the spatial information system with a computing grid via wire-and wireless communication networks.This paper will mainly discuss the grid technology and its integration with spatial information technology,expounding potential problems and possible resolutions.A novel categorising of information grids in the context of geospatial information is proposed:generalised and specialised spatial information grids.
基金Research supported by the National Natural Science Foundation of China[grant 11831008]theU.S.National Science Foundation-Division ofMathematical Sciences(US)[grant DMS-1612873].
文摘Wepropose a constrained generalised method of moments(CGMM)for enhancing the efficiency of estimators in meta-analysis in which some studies do not measure all covariates associated with the response or outcome.Under some assumptions,weshow that the proposedCGMMestimators have good asymptotic properties.Wealso demonstrate the effectiveness of the proposed method through simulation studies with fixed sample sizes.
文摘Geo-information on settlements from Earth Observation offers a base for objective and scalable monitoring of the evolution of cities and settlements,including their location,extent and other attributes.In this work,we deploy the best available global knowledge on the presence of human settlements and built-up structures derived from Earth Observation to advance the understanding of the human presence on Earth.We start from a concept of Generalised Settlement Area to identify the Earth surface within which any built-up structure is present.We further characterise the resulted map by using an agreement map among the state of the art of remote sensing products mapping built-up areas or other strictly related semantic abstractions as urban areas or artificial surfaces.The agreement map is formed by a grid of 1 km2,where each cell is classified according to the number of EO-derived products reporting any positive occurrence of the abstractions related to the presence of built-up structures.The paper describes the characteristics of the Generalised Settlement Area,the differences in the agreement map across geographic regions of the world,and outlines the implications for potential users of the EO-derived products used in this study.
