The complexity of the kinematics and dynamics of a manipulator makes it necessary to simplify the modeling process.However,the traditional representations cannot achieve this because of the absence of coordinate invar...The complexity of the kinematics and dynamics of a manipulator makes it necessary to simplify the modeling process.However,the traditional representations cannot achieve this because of the absence of coordinate invariance.Therefore,the coordinate invariant method is an important research issue.First,the rigid-body acceleration,the time derivative of the twist,is proved to be a screw,and its physical meaning is explained.Based on the twist and the rigid-body acceleration,the acceleration of the end-effector is expressed as a linear-bilinear form,and the kinematics Hessian matrix of the manipulator（represented by Lie bracket）is deduced.Further,Newton-Euler＇s equation is rewritten as a linear-bilinear form,from which the dynamics Hessian matrix of a rigid body is obtained.The formulae and the dynamics Hessian matrix are proved to be coordinate invariant.Referring to the principle of virtual work,the dynamics Hessian matrix of the parallel manipulator is gotten and the detailed dynamic model is derived.An index of dynamical coupling based on dynamics Hessian matrix is presented.In the end,a foldable parallel manipulator is taken as an example to validate the deduced kinematics and dynamics formulae.The screw theory based method can simplify the kinematics and dynamics of a manipulator,also the corresponding dynamics Hessian matrix can be used to evaluate the dynamical coupling of a manipulator.展开更多
A new algorithm for segmentation of suspected lung ROI(regions of interest)by mean-shift clustering and multi-scale HESSIAN matrix dot filtering was proposed.Original image was firstly filtered by multi-scale HESSIAN ...A new algorithm for segmentation of suspected lung ROI(regions of interest)by mean-shift clustering and multi-scale HESSIAN matrix dot filtering was proposed.Original image was firstly filtered by multi-scale HESSIAN matrix dot filters,round suspected nodular lesions in the image were enhanced,and linear shape regions of the trachea and vascular were suppressed.Then,three types of information,such as,shape filtering value of HESSIAN matrix,gray value,and spatial location,were introduced to feature space.The kernel function of mean-shift clustering was divided into product form of three kinds of kernel functions corresponding to the three feature information.Finally,bandwidths were calculated adaptively to determine the bandwidth of each suspected area,and they were used in mean-shift clustering segmentation.Experimental results show that by the introduction of HESSIAN matrix of dot filtering information to mean-shift clustering,nodular regions can be segmented from blood vessels,trachea,or cross regions connected to the nodule,non-nodular areas can be removed from ROIs properly,and ground glass object(GGO)nodular areas can also be segmented.For the experimental data set of 127 different forms of nodules,the average accuracy of the proposed algorithm is more than 90%.展开更多
Hessian matrices are square matrices consisting of all possible combinations of second partial derivatives of a scalar-valued initial function. As such, Hessian matrices may be treated as elementary matrix systems of ...Hessian matrices are square matrices consisting of all possible combinations of second partial derivatives of a scalar-valued initial function. As such, Hessian matrices may be treated as elementary matrix systems of linear second-order partial differential equations. This paper discusses the Hessian and its applications in optimization, and then proceeds to introduce and derive the notion of the Jaffa Transform, a new linear operator that directly maps a Hessian square matrix space to the initial corresponding scalar field in nth dimensional Euclidean space. The Jaffa Transform is examined, including the properties of the operator, the transform of notable matrices, and the existence of an inverse Jaffa Transform, which is, by definition, the Hessian matrix operator. The Laplace equation is then noted and investigated, particularly, the relation of the Laplace equation to Poisson’s equation, and the theoretical applications and correlations of harmonic functions to Hessian matrices. The paper concludes by introducing and explicating the Jaffa Theorem, a principle that declares the existence of harmonic Jaffa Transforms, which are, essentially, Jaffa Transform solutions to the Laplace partial differential equation.展开更多
Hemipteran and dipteran insects have behavioral,cellular and chemical strategies for evading or coping with the host plant defenses making these insects particularly destructive pests worldwide. A critical component o...Hemipteran and dipteran insects have behavioral,cellular and chemical strategies for evading or coping with the host plant defenses making these insects particularly destructive pests worldwide. A critical component of a host plant＇s defense to herbivory is innate immunity. Here we review the status of our understanding of the receptors that contribute to perception of hemipteran and dipteran pests and highlight the gaps in our knowledge in these early events in immune signaling. We also highlight recent advances in identification of the effectors that activate pattern-triggered immunity and those involved in effector-triggered immunity.展开更多
Segmenting the touching objects in an image has been remaining as a hot subject due to the problematic complexities, and a vast number of algorithms designed to tackle this issue have come into being since a decade ag...Segmenting the touching objects in an image has been remaining as a hot subject due to the problematic complexities, and a vast number of algorithms designed to tackle this issue have come into being since a decade ago. In this paper, a new granule segmentation algorithm is developed using saddle point as the cutting point. The image is binarized and then sequentially eroded to form a gray-scale topographic counterpart, followed by using Hessian matrix computation to search for the saddle point. The segmentation is performed by cutting through the saddle point and along the maximal gradient path on the topographic surface. The results of the algorithm test on the given real images indicate certain superiorities in both the segmenting robustness and execution time to the referenced methods.展开更多
In this paper,we study fully nonlinear equations of Krylov type in conformal geometry on compact smooth Riemannian manifolds with totally geodesic boundary.We prove the a priori estimates for solutions to these equati...In this paper,we study fully nonlinear equations of Krylov type in conformal geometry on compact smooth Riemannian manifolds with totally geodesic boundary.We prove the a priori estimates for solutions to these equations and establish an existence result.展开更多
Due to the diversity of work requirements and environment,the number of degrees of freedom(DOFs)and the complexity of structure of industrial robots are constantly increasing.It is difficult to establish the accurate ...Due to the diversity of work requirements and environment,the number of degrees of freedom(DOFs)and the complexity of structure of industrial robots are constantly increasing.It is difficult to establish the accurate dynamical model of industrial robots,which greatly hinders the realization of a stable,fast and accurate trajectory tracking control.Therefore,the general expression of the constraint relation in the explicit dynamic equation of the multi-DOF industrial robot is derived on the basis of solving the Jacobian matrix and Hessian matrix by using the kinematic influence coefficients method.Moreover,an explicit dynamic equation with general constraint relation expression is established based on the Udwadia-Kalaba theory.The problem of increasing the time of establishing constraint relationship when the multi-DOF industrial robots complete complex task constraints is solved.With the SCARA robot as the research object,the simulation results show that the proposed method can provide a new idea for industrial robot system modeling with complex constraints.展开更多
In this paper,we consider the exterior Dirichlet problem of Hessian equationsσk(λ(D^(2)u))=g(x)with g being a perturbation of a general positive function at infinity.The existence of the viscosity solutions with gen...In this paper,we consider the exterior Dirichlet problem of Hessian equationsσk(λ(D^(2)u))=g(x)with g being a perturbation of a general positive function at infinity.The existence of the viscosity solutions with generalized asymptotic behavior at infinity is established by the Perron’s method which extends the previous results for Hessian equations.By the solutions of Bernoulli ordinary differential equations,the viscosity subsolutions and supersolutions are constructed.展开更多
基金Supported by National Natural Science Foundation of China(Grant Nos.51375420,51105322)
文摘The complexity of the kinematics and dynamics of a manipulator makes it necessary to simplify the modeling process.However,the traditional representations cannot achieve this because of the absence of coordinate invariance.Therefore,the coordinate invariant method is an important research issue.First,the rigid-body acceleration,the time derivative of the twist,is proved to be a screw,and its physical meaning is explained.Based on the twist and the rigid-body acceleration,the acceleration of the end-effector is expressed as a linear-bilinear form,and the kinematics Hessian matrix of the manipulator（represented by Lie bracket）is deduced.Further,Newton-Euler＇s equation is rewritten as a linear-bilinear form,from which the dynamics Hessian matrix of a rigid body is obtained.The formulae and the dynamics Hessian matrix are proved to be coordinate invariant.Referring to the principle of virtual work,the dynamics Hessian matrix of the parallel manipulator is gotten and the detailed dynamic model is derived.An index of dynamical coupling based on dynamics Hessian matrix is presented.In the end,a foldable parallel manipulator is taken as an example to validate the deduced kinematics and dynamics formulae.The screw theory based method can simplify the kinematics and dynamics of a manipulator,also the corresponding dynamics Hessian matrix can be used to evaluate the dynamical coupling of a manipulator.
基金Projects(61172002,61001047,60671050)supported by the National Natural Science Foundation of ChinaProject(N100404010)supported by Fundamental Research Grant Scheme for the Central Universities,China
文摘A new algorithm for segmentation of suspected lung ROI(regions of interest)by mean-shift clustering and multi-scale HESSIAN matrix dot filtering was proposed.Original image was firstly filtered by multi-scale HESSIAN matrix dot filters,round suspected nodular lesions in the image were enhanced,and linear shape regions of the trachea and vascular were suppressed.Then,three types of information,such as,shape filtering value of HESSIAN matrix,gray value,and spatial location,were introduced to feature space.The kernel function of mean-shift clustering was divided into product form of three kinds of kernel functions corresponding to the three feature information.Finally,bandwidths were calculated adaptively to determine the bandwidth of each suspected area,and they were used in mean-shift clustering segmentation.Experimental results show that by the introduction of HESSIAN matrix of dot filtering information to mean-shift clustering,nodular regions can be segmented from blood vessels,trachea,or cross regions connected to the nodule,non-nodular areas can be removed from ROIs properly,and ground glass object(GGO)nodular areas can also be segmented.For the experimental data set of 127 different forms of nodules,the average accuracy of the proposed algorithm is more than 90%.
文摘Hessian matrices are square matrices consisting of all possible combinations of second partial derivatives of a scalar-valued initial function. As such, Hessian matrices may be treated as elementary matrix systems of linear second-order partial differential equations. This paper discusses the Hessian and its applications in optimization, and then proceeds to introduce and derive the notion of the Jaffa Transform, a new linear operator that directly maps a Hessian square matrix space to the initial corresponding scalar field in nth dimensional Euclidean space. The Jaffa Transform is examined, including the properties of the operator, the transform of notable matrices, and the existence of an inverse Jaffa Transform, which is, by definition, the Hessian matrix operator. The Laplace equation is then noted and investigated, particularly, the relation of the Laplace equation to Poisson’s equation, and the theoretical applications and correlations of harmonic functions to Hessian matrices. The paper concludes by introducing and explicating the Jaffa Theorem, a principle that declares the existence of harmonic Jaffa Transforms, which are, essentially, Jaffa Transform solutions to the Laplace partial differential equation.
基金supported by National Institute of Food and Agriculture(Award No.2010-65106-20675)supported by the National Science Foundation(Award No.IOS-072093 and IOSEAGER-1450331)Bill&Melinda Gates Foundation via a subcontract(B0426×5)from the National Research Institute,University of Greenwich,UK
文摘Hemipteran and dipteran insects have behavioral,cellular and chemical strategies for evading or coping with the host plant defenses making these insects particularly destructive pests worldwide. A critical component of a host plant＇s defense to herbivory is innate immunity. Here we review the status of our understanding of the receptors that contribute to perception of hemipteran and dipteran pests and highlight the gaps in our knowledge in these early events in immune signaling. We also highlight recent advances in identification of the effectors that activate pattern-triggered immunity and those involved in effector-triggered immunity.
基金Ningbo Natural Science Foundation (No.2006A610016)Foundation of the Ministry of Education Ministry for Returned Overseas Students & Scholars (SRF for ROCS, SEM. No.2006699).
文摘Segmenting the touching objects in an image has been remaining as a hot subject due to the problematic complexities, and a vast number of algorithms designed to tackle this issue have come into being since a decade ago. In this paper, a new granule segmentation algorithm is developed using saddle point as the cutting point. The image is binarized and then sequentially eroded to form a gray-scale topographic counterpart, followed by using Hessian matrix computation to search for the saddle point. The segmentation is performed by cutting through the saddle point and along the maximal gradient path on the topographic surface. The results of the algorithm test on the given real images indicate certain superiorities in both the segmenting robustness and execution time to the referenced methods.
文摘In this paper,we study fully nonlinear equations of Krylov type in conformal geometry on compact smooth Riemannian manifolds with totally geodesic boundary.We prove the a priori estimates for solutions to these equations and establish an existence result.
基金the Beijing Municipal Scienceand Technology Project (No.KM202111417006)the Academic Research Projects of Beijing Union University (Nos.ZK10202305 and ZK80202004)the Beijing Municipal Science and Technology Project (No.KM202111417005)。
文摘Due to the diversity of work requirements and environment,the number of degrees of freedom(DOFs)and the complexity of structure of industrial robots are constantly increasing.It is difficult to establish the accurate dynamical model of industrial robots,which greatly hinders the realization of a stable,fast and accurate trajectory tracking control.Therefore,the general expression of the constraint relation in the explicit dynamic equation of the multi-DOF industrial robot is derived on the basis of solving the Jacobian matrix and Hessian matrix by using the kinematic influence coefficients method.Moreover,an explicit dynamic equation with general constraint relation expression is established based on the Udwadia-Kalaba theory.The problem of increasing the time of establishing constraint relationship when the multi-DOF industrial robots complete complex task constraints is solved.With the SCARA robot as the research object,the simulation results show that the proposed method can provide a new idea for industrial robot system modeling with complex constraints.
文摘Hessian LLE算法是一种经典的流形学习算法,但该方法是以批处理的方式进行的,当新的数据点加入时,必须重新运行整个算法,计算所有数据点低维嵌入,原来的运算结果被全部丢弃。鉴于此,提出了一种保持局部邻域关系的增量Hessian LLE(LIHLLE)算法,该方法通过保证流形新增样本点在原空间和嵌入空间局部邻域的线性关系不变,用其已有邻域点的低维坐标线性表示新增样本点,来得到新增点的低维嵌入,实现增量学习。在Swiss roll withhole和frey_rawface数据集上的实验表明,该方法简便、有效可行。
基金supported in part by the Natural Science Foundation of Tianjin City of China(Grant No.19JCQNJC14700).
文摘In this paper,we consider the exterior Dirichlet problem of Hessian equationsσk(λ(D^(2)u))=g(x)with g being a perturbation of a general positive function at infinity.The existence of the viscosity solutions with generalized asymptotic behavior at infinity is established by the Perron’s method which extends the previous results for Hessian equations.By the solutions of Bernoulli ordinary differential equations,the viscosity subsolutions and supersolutions are constructed.
