arXiv subjects
Publications and source records attributed to Xi-Jun Qiu.
A set of fixed points of the Hopfield type neural network was under investigation. Its connection matrix is constructed with regard to the Hebb rule from a highly symmetric set of the memorized patterns. Depending on the external parameter the analytic description of the fixed points set had been obtained. And as a conclusion, some exact results of Hopfield neural networks were gained.
The N=1 self-dual supergravity has SL(2.C) symmetry. This symmetry results in SU(2) charges as the angular-momentum. As in the non-supersymmetric self-dual gravity, the currents are also of their potentials and are therefore identically conserved. The charges are generally invariant and gauge covariant under local SU(2) transforms approaching to be rigid at spatial infinity. The Poisson brackets constitute su(2) algebra and hence can be interpreted as the generally covariant conservative angular-momentum.