详细介绍了一种新的机器学习的方法——流形学习。流形学习是一种新的非监督学习方法,可以有效地发现高维非线性数据集的内在维数并进行维数约简,近年来越来越受到机器学习和认知科学领域的研究者的重视。目前已经出现了很多有效的流形...详细介绍了一种新的机器学习的方法——流形学习。流形学习是一种新的非监督学习方法,可以有效地发现高维非线性数据集的内在维数并进行维数约简,近年来越来越受到机器学习和认知科学领域的研究者的重视。目前已经出现了很多有效的流形学习算法,如等度规映射(ISOMAP)、局部线性嵌套(Locally Linear Embedding,LLE)等。详细讲述了当前常用的几种流形学习算法以及在流形方面已经取得的研究成果,并对流形学习目前在各方面的应用作了较为细致的阐述。最后展望了流形学习的研究发展趋势,且提出了流形学习中仍需解决的关键问题。展开更多
Starting from an extended mapping approach, a new type of variable separation solution with arbitrary functions of generalized (2+1)-dimensional Broer-Kaup system (GBK) system is derived. Then based on the derived sol...Starting from an extended mapping approach, a new type of variable separation solution with arbitrary functions of generalized (2+1)-dimensional Broer-Kaup system (GBK) system is derived. Then based on the derived solitary wave solution, we obtain some specific chaotic solitons to the (2+1)-dimensional GBK system.展开更多
By means of an improved mapping method and a variable separation method, a series of variable separation solutions including solitary wave solutions, periodic wave solutions and rational function solutions） to the （...By means of an improved mapping method and a variable separation method, a series of variable separation solutions including solitary wave solutions, periodic wave solutions and rational function solutions） to the （2＋1）-dimensional breaking soliton system is derived. Based on the derived solitary wave excitation, we obtain some special annihilation solitons and chaotic solitons in this short note.展开更多
By using a mapping approach and a linear variable separation approach, a new family of solitary wave solutions with arbitrary functions for the （2＋1）-dimensional modified dispersive water-wave system （MDWW） is de...By using a mapping approach and a linear variable separation approach, a new family of solitary wave solutions with arbitrary functions for the （2＋1）-dimensional modified dispersive water-wave system （MDWW） is derived. Based on the derived solutions and using some multi-valued functions, we obtain some novel folded localized excitations of the system.展开更多
While the region of western Guangxi-southeastern Yunan, China, is known and considered prospective for manganese deposits, carrying out prospectivity mapping in this region is challenging due to the diversity of geolo...While the region of western Guangxi-southeastern Yunan, China, is known and considered prospective for manganese deposits, carrying out prospectivity mapping in this region is challenging due to the diversity of geological factors, the complexity of geological process and the asymmetry of geo-information. In this work, the manganese potential mapping for further exploration targeting is implemented via spatial analysis and modal-adaptive prospectivity modeling. On the basis of targeting criteria developed by the mineral system approach, the spatial analysis is leveraged to extract the predictor variables to identify features of the geological process. Specifically, a metallogenic field analysis approach is proposed to extract metallogenic information that quantifies the regional impacts of the synsedimentary faults and sedimentary basins. In the integration of the extracted predictor variables, a modal-adaptive prospectivity model is built, which allows to adapt different data availability and geological process. The resulting prospective areas of high potential not only correspond to the areas of known manganese deposits but also provide a number of favorable targets in the region for future mineral exploration.展开更多
A general mapping deformation method is presented and applied to a (2+1)-dimensional Boussinesq system. Many new types of explicit and exact travelling wave solutions, which contain solitary wave solutions, periodic w...A general mapping deformation method is presented and applied to a (2+1)-dimensional Boussinesq system. Many new types of explicit and exact travelling wave solutions, which contain solitary wave solutions, periodic wave solutions, Jacobian and Weierstrass doubly periodic wave solutions, and other exact excitations like polynomial solutions, exponential solutions, and rational solutions, etc., are obtained by a simple algebraic transformation relation between the (2+1)-dimensional Boussinesq equation and a generalized cubic nonlinear Klein-Gordon equation.展开更多
With the help of an extended mapping approach, a new type of variable separation excitation with three arbitrary functions of the (2+1)-dimensional dispersive long-water wave system (DLW) is derived. Based on the deri...With the help of an extended mapping approach, a new type of variable separation excitation with three arbitrary functions of the (2+1)-dimensional dispersive long-water wave system (DLW) is derived. Based on the derived variable separation excitation, abundant non-propagating solitons such as dromion, ring, peakon, and compacton etc.are revealed by selecting appropriate functions in this paper.展开更多
Using the mapping approach via a Riccati equation, a series of variable separation excitations with three arbitrary functions for the （2＋1）-dimensional dispersive long wave （DLW） equation are derived. In addition...Using the mapping approach via a Riccati equation, a series of variable separation excitations with three arbitrary functions for the （2＋1）-dimensional dispersive long wave （DLW） equation are derived. In addition to the usual localized coherent soliton excitations like dromions, rings, peakons and compactions, etc, some new types of excitations that possess fractal behaviour are obtained by introducing appropriate lower-dimensional localized patterns and Jacobian elliptic functions.展开更多
In this work, with the help of the symbolic computation system Maple and the Riccati mapping approach and a linear variable separation approach, a new family of traveling wave solutions of the (2 + 1)-dimensional diss...In this work, with the help of the symbolic computation system Maple and the Riccati mapping approach and a linear variable separation approach, a new family of traveling wave solutions of the (2 + 1)-dimensional dissipative Zabolotskaya-Khokhlov equation (DZK) is derived. Based on the derived solitary wave solution, some novel kind wave excitations are investigated.展开更多
Periodic wave solutions and solitary wave solutions to a generalized （3＋1）-dimensional Gross Pitaevskii equation with time-modulated dispersion, nonlinearity, and potential are derived in terms of an improved homog...Periodic wave solutions and solitary wave solutions to a generalized （3＋1）-dimensional Gross Pitaevskii equation with time-modulated dispersion, nonlinearity, and potential are derived in terms of an improved homogeneous balance principle and a mapping approach. These exact solutions exist under certain conditions via imposing suitable constraints on the functions describing dispersion, nonlinearity, and potential. The dynamics of the derived solutions can be manipulated by prescribing specific time-modulated dispersions, nonlinearities, and potentials. The results show that the periodic waves and solitary waves with novel behaviors are similar to the similaritons reported in other nonlinear systems.展开更多
文摘详细介绍了一种新的机器学习的方法——流形学习。流形学习是一种新的非监督学习方法,可以有效地发现高维非线性数据集的内在维数并进行维数约简,近年来越来越受到机器学习和认知科学领域的研究者的重视。目前已经出现了很多有效的流形学习算法,如等度规映射(ISOMAP)、局部线性嵌套(Locally Linear Embedding,LLE)等。详细讲述了当前常用的几种流形学习算法以及在流形方面已经取得的研究成果,并对流形学习目前在各方面的应用作了较为细致的阐述。最后展望了流形学习的研究发展趋势,且提出了流形学习中仍需解决的关键问题。
基金浙江省自然科学基金，Foundation of New Century "151 Talent Engineering" of Zhejiang Province，丽水学院校科研和教改项目，the Scientific Research Foundation of Key Discipline of Zhejiang Province
文摘Starting from an extended mapping approach, a new type of variable separation solution with arbitrary functions of generalized (2+1)-dimensional Broer-Kaup system (GBK) system is derived. Then based on the derived solitary wave solution, we obtain some specific chaotic solitons to the (2+1)-dimensional GBK system.
基金The project supported by the Natural Science Foundation of Zhejiang Province under Grant No. Y604106, the Foundation of New Century 151 Talent Engineering of Zhejiang Province, and the Natural Science Foundation of Zhejiang Lishui University under Grant No. KZ05010 Acknowledgments The authors would like to thank professor Chun-Long Zheng for his fruitful and helpful suggestions.
文摘By means of an improved mapping method and a variable separation method, a series of variable separation solutions including solitary wave solutions, periodic wave solutions and rational function solutions） to the （2＋1）-dimensional breaking soliton system is derived. Based on the derived solitary wave excitation, we obtain some special annihilation solitons and chaotic solitons in this short note.
基金Project supported by the Natural Science Foundation of Zhejiang Province, China (Grant Nos. Y6100257 and Y6110140)
文摘By using a mapping approach and a linear variable separation approach, a new family of solitary wave solutions with arbitrary functions for the （2＋1）-dimensional modified dispersive water-wave system （MDWW） is derived. Based on the derived solutions and using some multi-valued functions, we obtain some novel folded localized excitations of the system.
基金Project(2017YFC0601503)supported by the National Key R&D Program of ChinaProjects(41772349,41972309,41472301,41772348)supported by the National Natural Science Foundation of China。
文摘While the region of western Guangxi-southeastern Yunan, China, is known and considered prospective for manganese deposits, carrying out prospectivity mapping in this region is challenging due to the diversity of geological factors, the complexity of geological process and the asymmetry of geo-information. In this work, the manganese potential mapping for further exploration targeting is implemented via spatial analysis and modal-adaptive prospectivity modeling. On the basis of targeting criteria developed by the mineral system approach, the spatial analysis is leveraged to extract the predictor variables to identify features of the geological process. Specifically, a metallogenic field analysis approach is proposed to extract metallogenic information that quantifies the regional impacts of the synsedimentary faults and sedimentary basins. In the integration of the extracted predictor variables, a modal-adaptive prospectivity model is built, which allows to adapt different data availability and geological process. The resulting prospective areas of high potential not only correspond to the areas of known manganese deposits but also provide a number of favorable targets in the region for future mineral exploration.
文摘A general mapping deformation method is presented and applied to a (2+1)-dimensional Boussinesq system. Many new types of explicit and exact travelling wave solutions, which contain solitary wave solutions, periodic wave solutions, Jacobian and Weierstrass doubly periodic wave solutions, and other exact excitations like polynomial solutions, exponential solutions, and rational solutions, etc., are obtained by a simple algebraic transformation relation between the (2+1)-dimensional Boussinesq equation and a generalized cubic nonlinear Klein-Gordon equation.
文摘With the help of an extended mapping approach, a new type of variable separation excitation with three arbitrary functions of the (2+1)-dimensional dispersive long-water wave system (DLW) is derived. Based on the derived variable separation excitation, abundant non-propagating solitons such as dromion, ring, peakon, and compacton etc.are revealed by selecting appropriate functions in this paper.
基金Project supported by the National Natural Science Foundation of China （Grant No 10272071）, the Natural Science Foundation of Zhejiang Province, China （Grant No Y604106） and the Key Academic Discipline of Zhejiang Province, China （Grant No 200412）.The authors would like to thank Professor Zhang J F for his fruitful discussion and helpful suggestion.
文摘Using the mapping approach via a Riccati equation, a series of variable separation excitations with three arbitrary functions for the （2＋1）-dimensional dispersive long wave （DLW） equation are derived. In addition to the usual localized coherent soliton excitations like dromions, rings, peakons and compactions, etc, some new types of excitations that possess fractal behaviour are obtained by introducing appropriate lower-dimensional localized patterns and Jacobian elliptic functions.
文摘In this work, with the help of the symbolic computation system Maple and the Riccati mapping approach and a linear variable separation approach, a new family of traveling wave solutions of the (2 + 1)-dimensional dissipative Zabolotskaya-Khokhlov equation (DZK) is derived. Based on the derived solitary wave solution, some novel kind wave excitations are investigated.
基金Project supported by the National Natural Science Foundation of China (Grant No. 11172181)the Natural Science Foundation of Guangdong Province, China (Grant No. 10151200501000008)+1 种基金the Special Foundation of Talent Engineering of Guangdong Province, China (Grant No.2009109)the Scientific Research Foundation of Key Discipline of Shaoguan University, China(Grant No. ZD2009001)
文摘Periodic wave solutions and solitary wave solutions to a generalized （3＋1）-dimensional Gross Pitaevskii equation with time-modulated dispersion, nonlinearity, and potential are derived in terms of an improved homogeneous balance principle and a mapping approach. These exact solutions exist under certain conditions via imposing suitable constraints on the functions describing dispersion, nonlinearity, and potential. The dynamics of the derived solutions can be manipulated by prescribing specific time-modulated dispersions, nonlinearities, and potentials. The results show that the periodic waves and solitary waves with novel behaviors are similar to the similaritons reported in other nonlinear systems.
