Quantization dimension for some Moran measures

Quantization dimension via quantization numbers

We give a characterization of the quantization dimension of Borel probability measures on R in terms of ε-quantization numbers. Using this concept, we show that the upper rate distortion dimension is not greater than the upper quantization dimension of order one. We also prove that the upper quantization dimension of a product measure is not greater than the sum of that of its marginals. Finall...

Quantization Dimension for Random Self-conformal Measures with Respect to the Geometric Error

In this paper, we study the quantization dimension for a random self-conformal measure μ supported on the random self-conformal set E. We establish that the quantization dimension of μ coincides with its Hausdorff dimension with probability one under the strong separation condition.

Quantization Dimension for Conformal Iterated Function Systems

Fractal dimension and vector quantization

We show that the performance of a vector quantizer for a self-similar data set is related to the intrinsic (“fractal”) dimension of the data set. We derive a formula for predicting the error-rate, given the fractal dimension and discuss how we can use our result for evaluating the performance of vector quantizers quickly.

Asymptotic Spectral Measures , Quantization

We study the relationship between POV-measures in quantum theory and asymptotic morphisms in the operator algebra E-theory of Connes-Higson. This is done by introducing the theory of “asymptotic” PV-measures and their integral correspondence with positive asymptotic morphisms on locally compact spaces. Examples and applications involving various aspects of quantum physics, including quantum noi...