Deduction of the quantum numbers of low-lying states of 6-nucleon systems based on symmetry

The inherent nodal structures of the wavefunctions of 6-nucleon systems have been investigated. The existence of a group of six low-lying states dominated by L=0 has been deduced. The spatial symmetries of these six states are found to be mainly {4,2} and {2,2,2}.Comment: 8 pages, no figure

Spin evolution of spin-1 Bose-Einstein condensates

An analytical formula is obtained to describe the evolution of the average populations of spin components of spin-1 atomic gases. The formula is derived from the exact time-dependent solution of the Hamiltonian $H_{S}=c mathbf{S}^{2}$ without using approximation. Therefore it goes beyond the mean field theory and provides a general, accurate, and complete description for the whole process of non-dissipative evolution starting from various initial states. The numerical results directly given by the formula coincide qualitatively well with existing experimental data, and also with other theoretical results from solving dynamic differential equations. For some special cases of initial state, instead of undergoing strong oscillation as found previously, the evolution is found to go on very steadily in a very long duration.Comment: 7 pages, 3 figures

Reduced pattern training based on task decomposition using pattern distributor

Task Decomposition with Pattern Distributor (PD) is a new task decomposition method for multilayered feedforward neural networks. Pattern distributor network is proposed that implements this new task decomposition method. We propose a theoretical model to analyze the performance of pattern distributor network. A method named Reduced Pattern Training is also introduced, aiming to improve the performance of pattern distribution. Our analysis and the experimental results show that reduced pattern training improves the performance of pattern distributor network significantly. The distributor module’s classification accuracy dominates the whole network’s performance. Two combination methods, namely Cross-talk based combination and Genetic Algorithm based combination, are presented to find suitable grouping for the distributor module. Experimental results show that this new method can reduce training time and improve network generalization accuracy when compared to a conventional method such as constructive backpropagation or a task decomposition method such as Output Parallelism

Hierarchical incremental class learning with reduced pattern training

Hierarchical Incremental Class Learning (HICL) is a new task decomposition method that addresses the pattern classification problem. HICL is proven to be a good classifier but closer examination reveals areas for potential improvement. This paper proposes a theoretical model to evaluate the performance of HICL and presents an approach to improve the classification accuracy of HICL by applying the concept of Reduced Pattern Training (RPT). The theoretical analysis shows that HICL can achieve better classification accuracy than Output Parallelism [1]. The procedure for RPT is described and compared with the original training procedure. RPT reduces systematically the size of the training data set based on the order of sub-networks built. The results from four benchmark classification problems show much promise for the improved model