p.p1 the galaxy is far enough, it

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PAUS is called a photometric survey, which means that the raw images consist of the fluxes in several bands, obtained by collecting photons during the time of exposure. In photometric surveys all the objects present in a given region of observation, are imaged. This is to be contrasted with another kind of surveys called spectroscopic, in which one chooses a priory the objects to be observed (from existing images) and diverts their light to a spectrograph to measure their spectra. A spectrum actually consists of the fluxes in a very large number of wavelength bins (typically xxxx), much larger that the 40 bins measured in PAUS. But for a photometric survey 40 is a large number. In fact it is the highest in any past or present photometric project. For this reason we say that PAUS data are effectively “low resolution spectra”.
Having the spectrum of an object it is relatively simple to tell whether or not it is a galaxy or a star (this is explained in Appendix A). But with the images of a photometric survey it is in general not simple to make such a classification. When observing a star, we expect to see a point source, and for a galaxy, an irregular blob if close. However, if the galaxy is far enough, it would also be seen as a point source. Typically, in photometric surveys one has to combine the spectral information, that is, the fluxes in whatever filters are available, with morphological information, such as the shape of the images of the objects, obtained from the light distribution in the camera pixels. With the arrival of PAUS the question was raised as if it would be possible to make the classification in stars or galaxies with simply the fluxes in 40 bands (the “low-resolution spectra”). 
Another issue is the method to actually make the classification. In template bases techniques on relays in the comparison of whatever information one measures from the object with appropriate existing information templates of many galaxies and stars. In machine learning techniques one develops and algorithm that can learn from the data, namely with a sample of objects whose class is known. This is called the learning sample. What the algorithm does is to adjust a very large number of parameters (weights) in such a way that the classification is correct. Once these parameters are fixed the algorithm evaluates, for the objects that need to be classified, a probability for belonging to a given class, This is explained further in section xx.yy.

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