Improvement Of The Hopfield Neural Network And Transfer-matrix Calculation Of Positional Distribution In The 2-dimensional Semiflexible Polymer

This paper is divided into two parts. The First part is improvement of the Hopfield Neural Network by MC-adaptation Rule. The Second part is Transfer-matrix calculation of positional distribution in the 2-dimensional semiflexible polymer.In the first part, we show that MC-adaptation Rule can be applied to improve neural networks. We use Hopfield neural network as a example, we show that the performance of the Hopfield neural networks, especially the quality of the recall and the capacity of the effective storing, can be greatly improved by MC-adaptation Rule without altering the whole structure of the network. All the memory patterns are stored exactly as fixed-point attractors of the improved network, and each memory pattern will be recalled perfectly. This feature avoids applying the overlap criterion to judge whether a memory is recalled correctly as does in the Hopfield neural networks.In the second part, we compute statistical distribution of the vector between two points along a dsDNA by transfer matrix method. We compute the transfer matrix elements analytically for a wide variety of polymer models. We pay particular attention to the semiflexible polymer including localized"flexible hinge"and"kinks"excitations. Our calculations emphasize calculation of the end-to-end distributions for finite-length dsDNAs. We specially compute the"J factor"commonly measured in biochemistry laboratory. Results are in excellent agreement with previous cyclization calculations for the semiflexible polymer. We study the effect of hinge for short dsDNA and find that hinge can enhance the"J factor"for short dsDNA, this provides a way to generate the large J factors observed experimentally. We also consider the effect of the boundary conditions for cyclization on the J factor.