Search

This paper presents a theoretical boundedness and convergence analysis of online gradient method for the training of two-layer feedforward neural networks. The well-known linear difference equation is extended to apply to the general case of linear or nonlinear activation functions. Based on this extended difference equation, we investigate the boundedness and convergence of the parameter sequence of concern, which is trained by finite training samples with a constant learning rate. We show that the uniform upper bound of the parameter sequence, which is very important in the training procedure, is the solution of an inequality regarding the bound. It is further verified that, for the case of linear activation function, a solution always exists and, moreover, the parameter sequence can be uniformly upper bounded, while for the case of nonlinear activation function, some simple adjustment methods on the training set or the activation function can be derived to improve the boundedness property. Then, for the convergence analysis, it is shown that the parameter sequence can converge into a zone around an optimal solution at which the error function attains its global minimum, where the size of the zone is associated with the learning rate. Particularly, for the case of perfect modeling, a strong global convergence result, where the parameter sequence can always converge to an optimal solution, is proved. [ABSTRACT FROM AUTHOR]

The relation between topography, and the 3D structure of patchy eddy-induced mixing in the Southern Ocean is analyzed descriptively by applying diagnostic methods to output from the Southern Ocean State Estimate. A localized cumulative probability density function method is developed to verify the use of Nakamura's (2001) mixing efficiency in the ocean. Both methods reveal enhanced eddy mixing at mid-depths. The spatial pattern of the mid-depth enhancement of eddy mixing is primarily linked to the merging of multiple jets embedded in the Antarctic Circumpolar Current over topography. We suggest that enhanced eddy mixing over topography is due to locally enhanced baroclinicity and instability within the wake itself, partly due to the convergence of eddies in merging branches of the ACC. Interaction of barotropic and baroclinic eddies may be important to setting the strength and vertical structure of eddy mixing associated with topography. [ABSTRACT FROM AUTHOR]

Due to the limited transmission resources for data relay in the tracking and data relay satellite system (TDRSS), there are many job requirements in busy days which will be discarded in the conventional job scheduling model. Therefore, the improvement of scheduling efficiency in the TDRSS can not only help to increase the resource utilities, but also to reduce the scheduling failure ratio. A model of nonhomogeneous parallel machines scheduling problems with time window (NPM-TW) is firstly built up for the TDRSS, considering the distinct features of the variable preparation time and the nonhomogeneous transmission rates for different types of antennas on each tracking and data relay satellite (TDRS). Then, an adaptive subsequence adjustment (ASA) framework with evolutionary asymmetric path-relinking (EvAPR) is proposed to solve this problem, in which an asymmetric progressive crossover operation is involved to overcome the local optima by the conventional job inserting methods. The numerical results show that, compared with the classical greedy randomized adaptive search procedure (GRASP) algorithm, the scheduling failure ratio of jobs can be reduced over 11% on average by the proposed ASA with EvAPR. [ABSTRACT FROM AUTHOR]