We determine the asymptotically optimal compressor function for a multidimen-sional compander when the source is memoryless. Under certain technical assumptions on the compressor function, it is shown that the best k-dimensional compressor function consists of the best scalar compressor functions for each component of the source vector. The mean-squared error of optimal multidimensional compand...

We develop a framework and numerical method for controlling the full space-time tube of geometrically driven flow. consider an optimal control problem mean curvature flow curve or surface with volume constraint, where parameter acts as forcing term in motion law. The trajectory is achieved by minimizing appropriate tracking-type cost functional. gradient functional obtained via formal sensitivi...