Neural networks are now one of the most successful learning formalisms. Neurons transform inputs x1, ..., xn into an output f(w1x1 + ... + wnxn), where f is a non-linear function and wi are adjustable weights. What f to choose? Usually the logistic function is chosen, but sometimes the use of different functions improves the practical efficiency of the network. We formulate the problem of choos...

Observations of standard stars with NICMOS grism (G096), when compared with the same standards taken by STIS (G750L), show a disagreement over the wavelength range 0.8 to 1 micron. Further comparison with ACS F850LP data confirms thisnon-linearity to be due to NICMOS in the sense that fainter stars in NICMOS appear too faint relative to a brighter normalisation. We investigate this over a wide ...

We have examined the convergence behavior of the LSCMA in some simple environments. Algorithms such as Multi¬ Target CMA, Multistage CMA, and Iterative Least Squares with Projection can be used for this purpose. The results presented here can form a basis for analysis of these multi-signal extraction techniques. Clearly, the variance and distribution of output SINR obtained with the LSCMA is al...

Non-linear effects occurring in photothermal microscopes based on principle of photothermal radiometry are studied as a hnction of the laser power and of the modulation frequency. For stainless steel, a second harmonic component of up to 11 % of the hndamental amplitude is found. Phase shifts of up to 20 degrees are observed as a hnction of the modulation frequency. The nonlinearity is mainly d...

In this paper we evaluate the relative performance of linear, non-linear and time-varying models for about 500 macroeconomic variables for the countries in the Euro area, using a real-time forecasting methodology. It turns out that linear models work well for about 35% of the series under analysis, time-varying models for another 35% and non-linear models for the remaining 30% of the series. Th...

We consider the usefulness of the two-regime SETAR model for out-of-sample forecasting, and compare it with a linear AR model. A range of newly-developed forecast evaluation techniques are employed. Our simulation results show that time-series data need to exhibit a substantial degree of non-linearity before the SETAR model is favoured on some of these criteria. We find only weak evidence that ...

This document describes the work undertaken for characterizing the flux non-linearity of the MIPS 70μm array. The effect, due to the change of rate of incident radiation on the detector, has been described in Gordon et al. (2007) and is typical of Ge:Ga photoconductors. The analysis has made use of MIPS calibration data aquired in Wide Field (WF), Narrow Field (NF) and Spectral Energy Distribut...

We establish an arithmeticity vs. non-linearity alternative for irreducible lattices in suitable product groups, for instance products of topologically simple groups. This applies notably to a (large class of) Kac-Moody groups. The alternative relies heavily on the superrigidity theorem we propose in [Md], since we follow Margulis’ reduction of arithmeticity to superrigidity.