A projection neural network with mixed delays for solving linear variational inequality
This paper presents a projection neural network with discrete delays and distributed delays (i.e. mixed delays) for solving linear variational inequality (LVI). By the Lyapunov theory and the linear matrix inequality (LMI) approach, the neural network is proved to be globally exponentially convergent to the solution of LVI. Compared with existing neural networks for solving LVI, the proposed one features the ability of solving a class of non-monotone LVI. One numerical example is provided to illustrate the effectiveness and the satisfactory performance of the neural network.
We describe preliminary results from an effort to quantify the uncertainties in parton distribution functions and the resulting uncertainties in predicted physical quantities. The production cross section of the $W$ boson is given as a first example. Constraints due to the full data sets of the CTEQ global analysis are used in this study. Two complementary approaches, based on the Hessian and the Lagrange multiplier method respectively, are outlined. We discuss issues on obtaining meaningful uncertainty estimates that include the effect of correlated experimental systematic uncertainties and illustrate them with detailed calculations using one set of precision DIS data.