This work focuses on radial basis functions containing no parameters with themain objective being to comparatively explore more of their effectiveness.For this,a total of sixteen forms of shapeless radial basis functi...This work focuses on radial basis functions containing no parameters with themain objective being to comparatively explore more of their effectiveness.For this,a total of sixteen forms of shapeless radial basis functions are gathered and investigated under the context of the pattern recognition problem through the structure of radial basis function neural networks,with the use of the Representational Capability(RC)algorithm.Different sizes of datasets are disturbed with noise before being imported into the algorithm as‘training/testing’datasets.Each shapeless radial basis function is monitored carefully with effectiveness criteria including accuracy,condition number(of the interpolation matrix),CPU time,CPU-storage requirement,underfitting and overfitting aspects,and the number of centres being generated.For the sake of comparison,the well-known Multiquadric-radial basis function is included as a representative of shape-contained radial basis functions.The numerical results have revealed that some forms of shapeless radial basis functions show good potential and are even better than Multiquadric itself indicating strongly that the future use of radial basis function may no longer face the pain of choosing a proper shape when shapeless forms may be equally(or even better)effective.展开更多
The idea of space-time as a combination of shapeless fundamental elements is proposed.The history of the development of ideas about the discrete space-time structure is analyzed.Quantum space-time is considered as a s...The idea of space-time as a combination of shapeless fundamental elements is proposed.The history of the development of ideas about the discrete space-time structure is analyzed.Quantum space-time is considered as a set of quantum states defined on a set of discretizations with an arbitrary shape of the boundaries of regions.The fundamental element of such space-time is described by the totality of its probabilistic characteristics.We consider a concept in which space-time is the only quantum object,and all material particles and interaction carriers are described as excited states of the fundamental elements of this quantum object.展开更多
This paper is to examine two significant landscapes and settings in E.M.Forster's novel A Passage to India.Most of the impression and atmosphere of them are chaotic,shapeless and mysterious,which helps to convey F...This paper is to examine two significant landscapes and settings in E.M.Forster's novel A Passage to India.Most of the impression and atmosphere of them are chaotic,shapeless and mysterious,which helps to convey Forster's idea that man's wish for order and harmonious links with other people and the universe is insignificant and ineffective.The Marabar hills and caves fully represent this idea.展开更多
文摘This work focuses on radial basis functions containing no parameters with themain objective being to comparatively explore more of their effectiveness.For this,a total of sixteen forms of shapeless radial basis functions are gathered and investigated under the context of the pattern recognition problem through the structure of radial basis function neural networks,with the use of the Representational Capability(RC)algorithm.Different sizes of datasets are disturbed with noise before being imported into the algorithm as‘training/testing’datasets.Each shapeless radial basis function is monitored carefully with effectiveness criteria including accuracy,condition number(of the interpolation matrix),CPU time,CPU-storage requirement,underfitting and overfitting aspects,and the number of centres being generated.For the sake of comparison,the well-known Multiquadric-radial basis function is included as a representative of shape-contained radial basis functions.The numerical results have revealed that some forms of shapeless radial basis functions show good potential and are even better than Multiquadric itself indicating strongly that the future use of radial basis function may no longer face the pain of choosing a proper shape when shapeless forms may be equally(or even better)effective.
文摘The idea of space-time as a combination of shapeless fundamental elements is proposed.The history of the development of ideas about the discrete space-time structure is analyzed.Quantum space-time is considered as a set of quantum states defined on a set of discretizations with an arbitrary shape of the boundaries of regions.The fundamental element of such space-time is described by the totality of its probabilistic characteristics.We consider a concept in which space-time is the only quantum object,and all material particles and interaction carriers are described as excited states of the fundamental elements of this quantum object.
文摘This paper is to examine two significant landscapes and settings in E.M.Forster's novel A Passage to India.Most of the impression and atmosphere of them are chaotic,shapeless and mysterious,which helps to convey Forster's idea that man's wish for order and harmonious links with other people and the universe is insignificant and ineffective.The Marabar hills and caves fully represent this idea.
