Quantized Gromov–Hausdorff distance

Quantized Gromov-hausdorff Distance

A quantized metric space is a matrix order unit space equipped with an operator space version of Rieffel’s Lip-norm. We develop for quantized metric spaces an operator space version of quantum Gromov-Hausdorff distance. We show that two quantized metric spaces are completely isometric if and only if their quantized Gromov-Hausdorff distance is zero. We establish a completeness theorem. As appli...

Landmark vector model with quantized distance for homing navigation

Inspired by astonishing navigation ability of insects and other animals, many studies observed their behaviors, and considered biomimetic application to robotic systems by investigating mechanisms based on various senses. In this paper, we suggest a new landmark vector model for homing navigation with quantized distance information. The method is highly successful for homing navigation in both ...

Quantized Poker

Poker has become a popular pastime all over the world. At any given moment one can find tens, if not hundreds, of thousands of players playing poker via their computers on the major on-line gaming sites. Indeed, according to the Vancouver, B.C. based pokerpulse.com estimates, more than 190 million US dollars daily is bet in on-line poker rooms. But communication and computation are changing as ...

Dynamically Quantized Pyramids

Introduction Dynamically Quantized (DO) spaces have been developed [O'Rourke] in response to the need for high-precision, high-dimensional Hough-like transforms. [Ballard; Sloan and Ballard) Their purpose is to cover a parameter space with a limited number of accumulators in such a way that fine precision is maintained where it is needed. O'Rourke's solution to this problem is to maintain a bin...

The Quantized Hall Effect