Role of Layers and Neurons in Deep Learning With the Rectified Linear Unit.

Deep learning is used to classify data into several groups based on nonlinear curved surfaces. In this paper, we focus on the theoretical analysis of deep learning using the rectified linear unit (ReLU) activation function. Because layers approximate a nonlinear curved surface, increasing the number of layers improves the approximation accuracy of the curved surface. While neurons perform a layer-by-layer approximation of the most appropriate hyperplanes, increasing their number cannot improve the results obtained via canonical correlation analysis (CCA). These results illustrate the functions of layers and neurons in deep learning with ReLU.

Effect of ligand substituents in olefin polymerisation by half-sandwich titanium complexes containing monoanionic iminoimidazolidide ligands-MAO catalyst systems.

Various half-sandwich titanium complexes containing iminoimidazolidide ligands, CpTiCl(2)[1,3-R(2)(CH(2)N)(2)C=N] (1a-d) [R = Ph (a), 2,6-Me(2)C(6)H(3) (b), cyclohexyl (c), (t)Bu (d)], have been employed as the catalyst precursors for ethylene polymerisation, syndiospecific styrene polymerisation, and copolymerisation of ethylene with 1-hexene in the presence of MAO cocatalyst; 1d showed the highest catalytic activity for ethylene polymerisation whereas 1b showed the highest activity for syndiospecific styrene polymerisation.