Generating diverse motor behaviors critical for survival is a challenge that confronts the central nervous system(CNS)of all animals.During movement execution,the CNS performs complex calculations to control a large n...Generating diverse motor behaviors critical for survival is a challenge that confronts the central nervous system(CNS)of all animals.During movement execution,the CNS performs complex calculations to control a large number of neuromusculoskeletal elements.The theory of modular motor control proposes that spinal interneurons are organized in discrete modules that can be linearly combined to generate a variety of behavioral patterns.These modules have been previously represented as stimulus-evoked force fields(FFs)comprising isometric limb-endpoint forces across workspace locations.Here,we ask whether FFs elicited by different stimulations indeed represent the most elementary units of motor control or are themselves the combination of a limited number of even more fundamental motor modules.To probe for potentially more elementary modules,we optogenetically stimulated the lumbosacral spinal cord of intact and spinalized Thy1-ChR2 transgenic mice(n=21),eliciting FFs from as many single stimulation loci as possible(20-70 loci per mouse)at minimally necessary power.We found that the resulting varieties of FFs defied simple categorization with just a few clusters.We used gradient descent to further decompose the FFs into their underlying basic force fields(BFFs),whose linear combination explained FF variability.Across mice,we identified 4-5 BFFs with partially localizable but overlapping representations along the spinal cord.The BFFs were structured and topographically distributed in such a way that a rostral-to-caudal traveling wave of activity across the lumbosacral spinal cord may generate a swing-to-stance gait cycle.These BFFs may represent more rudimentary submodules that can be flexibly merged to produce a library of motor modules for building different motor behaviors.展开更多
This paper studies the problem of coordinated motion generation for a group of rigid bodies. Two classes of coordinated motion primitives, relative equilibria and ma- neuvers, are given as building blocks for generati...This paper studies the problem of coordinated motion generation for a group of rigid bodies. Two classes of coordinated motion primitives, relative equilibria and ma- neuvers, are given as building blocks for generating coordi- nated motions. In a motion-primitive based planning frame- work, a control method is proposed for the robust execution of a coordinated motion plan in the presence of perturba- tions. The control method combines the relative equilibria stabilization with maneuver design, and results in a close- loop motion planning framework. The performance of the control method has been illustrated through a numerical sim- ulation.展开更多
To integrate driver experience and heterogeneous vehicle platform characteristics in a motion-planning algorithm,based on the driver-behavior-based transferable motion primitives(MPs), a general motion-planning framew...To integrate driver experience and heterogeneous vehicle platform characteristics in a motion-planning algorithm,based on the driver-behavior-based transferable motion primitives(MPs), a general motion-planning framework for offline generation and online selection of MPs is proposed. Optimal control theory is applied to solve the boundary value problems in the process of generating MPs, where the driver behaviors and the vehicle motion characteristics are integrated into the optimization in the form of constraints. Moreover, a layered, unequal-weighted MP selection framework is proposed that utilizes a combination of environmental constraints, nonholonomic vehicle constraints,trajectory smoothness, and collision risk as the single-step extension evaluation index. The library of MPs generated offline demonstrates that the proposed generation method realizes the effective expansion of MP types and achieves diverse generation of MPs with various velocity attributes and platform types. We also present how the MP selection algorithm utilizes a unique MP library to achieve online extension of MP sequences. The results show that the proposed motion-planning framework can not only improve the efficiency and rationality of the algorithm based on driving experience but can also transfer between heterogeneous vehicle platforms and highlight the unique motion characteristics of the platform.展开更多
Several new concepts of enhanced pullback attractors for nonautonomous dynamical systems are introduced here by uniformly enhancing the compactness and attraction of the usual pullback attractors over an infinite forw...Several new concepts of enhanced pullback attractors for nonautonomous dynamical systems are introduced here by uniformly enhancing the compactness and attraction of the usual pullback attractors over an infinite forward time-interval under strong and weak topologies.Then we provide some theoretical results for the existence,regularity and asymptotic stability of these enhanced pullback attractors under general theoretical frameworks which can be applied to a large class of PDEs.The existence of these enhanced attractors is harder to obtain than the backward case[33],since it is difficult to uniformly control the long-time pullback behavior of the systems over the forward time-interval.As applications of our theoretical results,we consider the famous 3D primitive equations modelling the large-scale ocean and atmosphere dynamics,and prove the existence,regularity and asymptotic stability of the enhanced pullback attractors in V×V and H^(2)×H^(2) for the time-dependent forces which satisfy some weak conditions.展开更多
In this paper, we rigorously derive the governing equations describing the motion of a stable stratified fluid, from the mathematical point of view. In particular, we prove that the scaled Boussinesq equations strongl...In this paper, we rigorously derive the governing equations describing the motion of a stable stratified fluid, from the mathematical point of view. In particular, we prove that the scaled Boussinesq equations strongly converge to the viscous primitive equations with density stratification as the aspect ratio goes to zero, and the rate of convergence is of the same order as the aspect ratio. Moreover, in order to obtain this convergence result, we also establish the global well-posedness of strong solutions to the viscous primitive equations with density stratification.展开更多
Let { W(t);t≥0 } be a standard Brownian motion.For a positive integer m ,define a Gaussian processX m(t)=1m!∫ t 0(t-s) m d W(s).In this paper the liminf behavior of the increments of this process is discu...Let { W(t);t≥0 } be a standard Brownian motion.For a positive integer m ,define a Gaussian processX m(t)=1m!∫ t 0(t-s) m d W(s).In this paper the liminf behavior of the increments of this process is discussed by establishing some probability inequalities.Some previous results are extended and improved.展开更多
The accelerating urbanization process leads to aggravated environmental problems, thus garden design which is a creative activity connecting human and nature has attracted much attention, and also garden designers hav...The accelerating urbanization process leads to aggravated environmental problems, thus garden design which is a creative activity connecting human and nature has attracted much attention, and also garden designers have had to rethink about environmental ethics and morals. This study, from the perspective of environmental ethics, duly proposed the brand-new concept of 'appropriate garden of primitive ecology', proceeded from the orientation, form, value, theoretical basis, realistic significance, culture and consumption psychology of 'garden of primitive ecology', fully developed outstanding ecological wisdoms and morals in traditional Chinese garden culture, boosted garden designs to the environmental ethics level of eco-justice, to seek for the approach to 'garden of primitive ecology' with indigenous Chinese environmental ethic characteristics.展开更多
基金supported by the CUHK Faculty of Medicine Faculty Innovation Award FIA2016/A/04(to V.C.K.C.)Group Research Scheme NL/JW/rc/grs1819/0426/19hc(to V.C.K.C.)The Hong Kong Research Grants Council 24115318,CUHK-R4022-18,14114721,and 14119022(to V.C.K.C)。
文摘Generating diverse motor behaviors critical for survival is a challenge that confronts the central nervous system(CNS)of all animals.During movement execution,the CNS performs complex calculations to control a large number of neuromusculoskeletal elements.The theory of modular motor control proposes that spinal interneurons are organized in discrete modules that can be linearly combined to generate a variety of behavioral patterns.These modules have been previously represented as stimulus-evoked force fields(FFs)comprising isometric limb-endpoint forces across workspace locations.Here,we ask whether FFs elicited by different stimulations indeed represent the most elementary units of motor control or are themselves the combination of a limited number of even more fundamental motor modules.To probe for potentially more elementary modules,we optogenetically stimulated the lumbosacral spinal cord of intact and spinalized Thy1-ChR2 transgenic mice(n=21),eliciting FFs from as many single stimulation loci as possible(20-70 loci per mouse)at minimally necessary power.We found that the resulting varieties of FFs defied simple categorization with just a few clusters.We used gradient descent to further decompose the FFs into their underlying basic force fields(BFFs),whose linear combination explained FF variability.Across mice,we identified 4-5 BFFs with partially localizable but overlapping representations along the spinal cord.The BFFs were structured and topographically distributed in such a way that a rostral-to-caudal traveling wave of activity across the lumbosacral spinal cord may generate a swing-to-stance gait cycle.These BFFs may represent more rudimentary submodules that can be flexibly merged to produce a library of motor modules for building different motor behaviors.
基金supported by the National Natural Science Foundation of China (11072002,10832006)
文摘This paper studies the problem of coordinated motion generation for a group of rigid bodies. Two classes of coordinated motion primitives, relative equilibria and ma- neuvers, are given as building blocks for generating coordi- nated motions. In a motion-primitive based planning frame- work, a control method is proposed for the robust execution of a coordinated motion plan in the presence of perturba- tions. The control method combines the relative equilibria stabilization with maneuver design, and results in a close- loop motion planning framework. The performance of the control method has been illustrated through a numerical sim- ulation.
基金Supported by National Natural Science Foundation of China (Grant Nos. 91420203 and 61703041)。
文摘To integrate driver experience and heterogeneous vehicle platform characteristics in a motion-planning algorithm,based on the driver-behavior-based transferable motion primitives(MPs), a general motion-planning framework for offline generation and online selection of MPs is proposed. Optimal control theory is applied to solve the boundary value problems in the process of generating MPs, where the driver behaviors and the vehicle motion characteristics are integrated into the optimization in the form of constraints. Moreover, a layered, unequal-weighted MP selection framework is proposed that utilizes a combination of environmental constraints, nonholonomic vehicle constraints,trajectory smoothness, and collision risk as the single-step extension evaluation index. The library of MPs generated offline demonstrates that the proposed generation method realizes the effective expansion of MP types and achieves diverse generation of MPs with various velocity attributes and platform types. We also present how the MP selection algorithm utilizes a unique MP library to achieve online extension of MP sequences. The results show that the proposed motion-planning framework can not only improve the efficiency and rationality of the algorithm based on driving experience but can also transfer between heterogeneous vehicle platforms and highlight the unique motion characteristics of the platform.
基金supported by China Postdoctoral Science Foundation (2020TQ0053 and 2020M680456)the research funds of Qianshixinmiao[2022]B16,Qianjiaoji[2022]124 and Qiankehepingtairencai-YSZ[2022]022+1 种基金supported by the NSFC (11731014 and 11571254)supported by the NSFC (11971067,11631008,11771183)。
文摘Several new concepts of enhanced pullback attractors for nonautonomous dynamical systems are introduced here by uniformly enhancing the compactness and attraction of the usual pullback attractors over an infinite forward time-interval under strong and weak topologies.Then we provide some theoretical results for the existence,regularity and asymptotic stability of these enhanced pullback attractors under general theoretical frameworks which can be applied to a large class of PDEs.The existence of these enhanced attractors is harder to obtain than the backward case[33],since it is difficult to uniformly control the long-time pullback behavior of the systems over the forward time-interval.As applications of our theoretical results,we consider the famous 3D primitive equations modelling the large-scale ocean and atmosphere dynamics,and prove the existence,regularity and asymptotic stability of the enhanced pullback attractors in V×V and H^(2)×H^(2) for the time-dependent forces which satisfy some weak conditions.
基金Pu was supported in part by the NNSF of China(11871172)the Science and Technology Projects in Guangzhou (202201020132)Zhou was supported by the Innovation Research for the Postgraduates of Guangzhou University (2021GDJC-D09)。
文摘In this paper, we rigorously derive the governing equations describing the motion of a stable stratified fluid, from the mathematical point of view. In particular, we prove that the scaled Boussinesq equations strongly converge to the viscous primitive equations with density stratification as the aspect ratio goes to zero, and the rate of convergence is of the same order as the aspect ratio. Moreover, in order to obtain this convergence result, we also establish the global well-posedness of strong solutions to the viscous primitive equations with density stratification.
基金Project Supported by National Science Fundation of China(1 9571 0 2 1 ) and Zhejiang Province
文摘Let { W(t);t≥0 } be a standard Brownian motion.For a positive integer m ,define a Gaussian processX m(t)=1m!∫ t 0(t-s) m d W(s).In this paper the liminf behavior of the increments of this process is discussed by establishing some probability inequalities.Some previous results are extended and improved.
文摘The accelerating urbanization process leads to aggravated environmental problems, thus garden design which is a creative activity connecting human and nature has attracted much attention, and also garden designers have had to rethink about environmental ethics and morals. This study, from the perspective of environmental ethics, duly proposed the brand-new concept of 'appropriate garden of primitive ecology', proceeded from the orientation, form, value, theoretical basis, realistic significance, culture and consumption psychology of 'garden of primitive ecology', fully developed outstanding ecological wisdoms and morals in traditional Chinese garden culture, boosted garden designs to the environmental ethics level of eco-justice, to seek for the approach to 'garden of primitive ecology' with indigenous Chinese environmental ethic characteristics.
