We study two systems that are based on sums of weakly dependentBernoulli random variables that take values ± 1 with equalprobabilities. We show that already one step of the so-calledsoft decision parallel interference cancellation, used in the thirdgeneration of mobile telecommunication CDMA, is able to considerablyincrease the number of users such a system can host. We alsoconsider a variant of the well-known Hopfield model of neuralnetworks. We show that this variant proposed by Amari and Yanai[CITE] has a larger storage capacity than the original model. Both situations lead to the question of the moderatedeviations behavior of a sum of weakly dependent Bernoulli randomvariables. We prove a moderate deviations principle for such a sumon the appropriate scale.

The troposphere affects electromagnetic signal propagation causing signal path bending and the alteration of the electromagnetic wave velocity. Tropospheric delay can introduce a considerable error in satellite positioning if it is not properly estimated. The GPS signal delay can vary from 2 to 20 m depending on the elevation angles between the receiver and the satellite. Two basic types of delay prediction models exist. The first use surface meteorological parameters to estimate the value of the tropospheric delay, and the other models that do not require real-time meteorological input use average and seasonal variation data related to the receiver's latitude and day-of-year. This paper compares the performance of both types of model over a period of one year, comprising all seasons, to verify their accuracy over a longer period. The Saastamoinen model, known as one of the best performing prediction models, was taken as a reference and the global EGNOS model was used to check how the global estimates of the yearly averages of the meteorological parameters and their related seasonal variations comply with the real-time surface parameters.

We prove a sharp upper bound on the number of patterns that can be stored in the Hopfield model if the stored patterns are required to be fixed points of the gradient dynamics. We also show corresponding bounds on the one-step convergence of the sequential gradient dynamics. The bounds coincide with the known lower bounds and confirm the heuristic expectations. The proof is based on a crucial idea of Loukianova (1997) using the negative association properties of some random variables arising in the analysis.