Clustering with constraints is a developing area of machine learning. Various papers have used constraints to enforce particular clusterings, seed clustering algorithms and even learn distance functions which are then used for clustering. We present intractability results for some constraint

Sharp front for the QG equation Two contour dynamics problems in incompressible flows: the Muskat problem and the QG sharp front

Zeckendorf’s Theorem Every positive integer can be written in a unique way as a sum of non-consecutive Fibonacci numbers. 4

We perform new experiments on the Kolmogorov-Sinai entropy, Lyapunov exponents, and the mean free time in billiards. We study their dependence on the geometry of the scatterers made up of two interpenetrating square lattices, each one with circular scatterers with different radius. We find, in particular, that the above quantities are continuous functions of the ratio of the scatterer radius. However, it seems that their derivative is discontinuous around the radius ratio which separates the diffusive and nondiffusive types of geometries.

Policy assurance architecture

elliptic problems with convection term

We prove optimal, up to an arbitrary ffl? 0, inapproximability results for Max-Ek-Sat for k * 3, maximizing the number of satisfied linear equations in an over-determined system of linear equations modulo a prime p and Set Splitting. As a consequence of these results we get improved lower bounds

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particular realization of the N = 2 theories, the resulting string field theory is equivalent to a topological theory in six dimensions, the Kodaira– Spencer theory, which may be viewed as the closed string analog of the Chern–Simon theory. Using the mirror map this leads to computation of the ‘number