A rubidium clock for GPS

The design objectives and approach; the more important design features; the signal parameters and error budget; and early test results in the development of a second-source rubidium frequency standard for use in the GPS navigation satellites are discussed. Tests of a breadboard version of the RFS show that the measured time-domain stability is within the goal specification. The results are uncorrected for the conribution of the reference and are probably limited by the reference stability in the medium term region. The Rb reference is bbetter in the medium term region, but the Cs reference is etter at 10,000 seconds and longer, probably because of the barometric sensitivity of the rubidium reference unit

Becoming a Better American through Study Abroad

Postcard from Riley Brown, during the Linfield College Semester Abroad Program at the Institut Américain Universitaire in Aix-en-Provence, Franc

The absence of efficient dual pairs of spanning trees in planar graphs

A spanning tree T in a finite planar connected graph G determines a dual spanning tree T* in the dual graph G such that T and T* do not intersect. We show that it is not always possible to find T in G, such that the diameters of T and T* are both within a uniform multiplicative constant (independent of G) of the diameters of their ambient graphs.Comment: 7 pages, 3 figure

A study of early stopping, ensembling, and patchworking for cascade correlation neural networks

The constructive topology of the cascade correlation algorithm makes it a popular choice for many researchers wishing to utilize neural networks. However, for multimodal problems, the mean squared error of the approximation increases significantly as the number of modes increases. The components of this error will comprise both bias and variance and we provide formulae for estimating these values from mean squared errors alone. We achieve a near threefold reduction in the overall error by using early stopping and ensembling. Also described is a new subdivision technique that we call patchworking. Patchworking, when used in combination with early stopping and ensembling, can achieve an order of magnitude improvement in the error. Also presented is an approach for validating the quality of a neural network’s training, without the explicit use of a testing dataset

The direct numerical simulations of the turbulent wakes of axisymmetric bodies

Results of direct numerical simulations of turbulence are compared with both laboratory data and self-similarity theory for the case of the turbulent wakes of towed, axisymmetric bodies. In general, the agreement of the simulation results with both the laboratory data and the self-similarity theory is good, although the comparisons are hampered by inadequate procedures for initializing the numerical simulations

Improving the performance of cascade correlation neural networks on multimodal functions

Intrinsic qualities of the cascade correlation algorithm make it a popular choice for many researchers wishing to utilize neural networks. Problems arise when the outputs required are highly multimodal over the input domain. The mean squared error of the approximation increases significantly as the number of modes increases. By applying ensembling and early stopping, we show that this error can be reduced by a factor of three. We also present a new technique based on subdivision that we call patchworking. When used in combination with early stopping and ensembling the mean improvement in error is over 10 in some cases

Power law burst and inter-burst interval distributions in the solar wind: turbulence or dissipative SOC ?

We calculate for the first time the probability density functions (PDFs) P of burst energy e, duration T and inter-burst interval tau for a known turbulent system in nature. Bursts in the earth-sun component of the Poynting flux at 1 AU in the solar wind were measured using the MFI and SWE experiments on the NASA WIND spacecraft. We find P(e) and P(T) to be power laws, consistent with self-organised criticality (SOC). We find also a power law form for P(tau) that distinguishes this turbulent cascade from the exponential P(tau) of ideal SOC, but not from some other SOC-like sandpile models. We discuss the implications for the relation between SOC and turbulence.Comment: 3 pages, 1 figure. Submitted to PRL on 25th February 2000. Revised version re-submitted on 9th May 2000. Second revised version submitted Phys. Rev. E on 26th June, 200