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

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.

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

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

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

Valiant’s learnability model is extended to learning classes of concepts defined by regions in Euclidean space E”. The methods in this paper lead to a unified treatment of some of Valiant’s results, along with previous results on distribution-free convergence of certain pattern recognition

previous results for OMP, which require O(m 2) measurements. The new results for OMP are comparable with recent results for another algorithm called Basis Pursuit (BP). The OMP algorithm is faster and easier to implement, which makes it an attractive alternative to BP for signal recovery problems.

optimization algorithms were critical in achieving these results. We present extensive comparisons between models and training methods that confirm and strengthen previous results on shallow parsing and training methods for maximum-entropy models.