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Patent

System and method for N-dimensional parametric analysis

Peter Johnson
TLDR
In this article, the problem of finding conditional overlap probabilities for M objects of N dimensions each by decomposing N-dimensional feature spaces into 3D feature spaces is solved by identifying density intersection cubes in the 3D space.
Abstract
The system and method for n-dimensional parametric analysis solves the problem of finding conditional overlap probabilities for M objects of N dimensions each by decomposing N-dimensional feature spaces into 3-dimensional feature spaces. Intersectors for objects in N-dimensional feature space are used to identify density intersection cubes in the three dimensional feature spaces. Density intersection cubes are split into single density cubic sub-regions that can be associated with other cubic sub-regions of a same density. In association with other single density cubic sub-regions of a same density, the single density cubic sub-regions are recomposed back into an N-dimensional space, becoming single density hyper cubic sub-regions. Ambiguities, among the original M objects of N dimensions may be quantified in terms of the hyper volumes of the single density hyper cubic sub-regions. A method for n-dimensional parametric analysis is implemented in a computer system by a computer program or computer program product.

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References
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Patent

A system and method of optimizing database queries in two or more dimensions

TL;DR: In this paper, a method and system for storing and retrieving spatial data objects from a spatial database is discussed, which stores multi-dimensional objects within the database by determining their position in a multi-tiered coordinate system.
Patent

Method and system for tracking multiple regional objects by multi-dimensional relaxation

TL;DR: In this paper, a region is repeatedly scanned providing a plurality of images or data sets having points corresponding to ojbects in the region to be tracked, and an M-dimensional combinatorial optimization assignment problem is formulated using the points from M-1 of the images or datasets, wherein each point is preferably used in extending at most one track.
Patent

Method of storing and retrieving multi-dimensional data using the hilbert curve

TL;DR: In this article, a method of partitioning and indexing multi-dimensional data that maps data to one-dimensional values according to the sequence in which an approximation of a Hilbert space-filling curve passes through all of the points corresponding to potential multidimensional data in a data space is presented.
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N-dimensional data compression using set partitioning in hierarchical trees

TL;DR: In this article, a data structure in a computer memory for use in encoding and decoding an N-dimensional subband decomposition of data points includes, after initialization, three lists: a list of insignificant sets of points (LIS), a list-of-significant-points (LSP), and a list -of-entities (LIP).