Generic red, green, and blue images can be regarded as data sources of coarse (three bins) local spectra, typical data volumes are 104 to 107 spectra. Image data bases often yield hundreds or thousands of images, yielding data sources of 109 to 1010 spectra. There is usually no calibration, and there often are various nonlinear image transformations involved. However, we argue that sheer number...

We establish a coloring theorem for successors of singular cardinals, and use it prove that for any such cardinal μ, we have μ+ 9 [μ+]2 μ+ if and only if μ+ 9 [μ]θ for arbitrarily large θ < μ.

Several generators of graphs are developed and tested with the purpose of reening our knowledge of what makes a graph diicult to color optimally. We study the eeects of reduced variance on hardness, how much we can vary the parameterizations (i.e. n; p; k) that seem to delimit the diicult regions, and the interactions of several diierent algorithms in these diicult regions.

We exhibit a simplified version of the construction of a field of Morley rank p with a predicate of rank p − 1, extracting the main ideas for the construction from previous papers and refining the arguments. Moreover, an explicit axiomatization is given, and ranks are computed.