Abstract: A method and algorithm for measuring the symmetry (SYM=total symmetry) of N points based on counting the number of “elementary symmetric recognition acts”, or having two distances d(A,B) and d(C,D) be equal within a given tolerance t. The same algorithm can be adapted to measure un-normalized positional entropy deficit (UPED) and positional entropy of N points. These parameters (SYM and UPED) come out almost the same for small occupation numbers (1<=k<=4). Here the occupation number k is the number of equal distances in the figure for a given value d. The algorithm can be incorporated into an imaging device, such as computer graphic programs or cameras, to solve problems of defect detection, say in gems, or object detection.

Abstract: A method and algorithm is given to measure the symmetry (SYM=global symmetry) of N points. The algorithm is based on counting the number of “elementary symmetric recognition acts,” or having two distances d(A,B) and d(C,D) be equal within a given tolerance t. The same algorithm can be adapted to measure un-normalized positional entropy deficit” (UPED) and positional entropy of N point. These parameters (SYM and UPED) represent a “MISSING LINK” connecting symmetry with order/disorder with entropy, since for small occupation numbers (1<=k<=4) they come out almost the same. Here the occupation number, k, is the number of equal distances in the figure for a given value d. The algorithm can be added via software to imaging devices, such as computer graphic programs or cameras to solve problems of defect detection, say in gems, or object detection.

Abstract: A data compression algorithm which computes from a given probability density, in continuous or histogram form, a “probability centrifuge” probability density and also the Fisher information of the density. The density preserves Shannon entropy of the original density and the Fisher information represents the minimum Fisher information obtainable by “lateral” adiabatic reduction. The data compression algorithm can alternately be used to perform a “vertically” adiabatic reduction, a “radial” adiabatic reduction, or a “sectoral” adiabatic reduction. Said algorithm may provide alternate information for applications such as image reconstruction and protein folding analysis.

Abstract: A flexible state-of-the-art plastic bottle fitted with a sealed tube becomes a dynamic system for dispensing water or other fluid in nearly-uniform quantum amounts, in such a way that the apparatus may be used as (1) a timer, such as for cooking a three-minute egg; (2) a toy for enjoyment or learning how to count, etc.; or (3) a model for teaching differential equations or physics. The device is very simple, on the order of a paper clip.