Computations of entropy bounds: Multidimensional geometric methods

PDF Version Also Available for Download.

Description

The entropy bounds for constructive upper bound on the needed number-of-bits for solving a dichotomy is represented by the quotient of two multidimensional solid volumes. For minimization of this upper bound exact calculation of the volume of this quotient is needed. Three methods for exact computing of the volume of a given nD volume are presented: (1) general method for calculation any nD volume by slicing it into volumes of decreasing dimension is presented; (2) a method applying appropriate curvilinear coordinate system is described for volume bounded by symmetrical curvilinear hypersurfaces (spheres, cones, hyperboloids, ellipsoids, cylinders, etc.); and (3) an ... continued below

Physical Description

10 p.

Creation Information

Makaruk, H. E. February 1998.

Context

This article is part of the collection entitled: Office of Scientific & Technical Information Technical Reports and was provided by UNT Libraries Government Documents Department to Digital Library, a digital repository hosted by the UNT Libraries. More information about this article can be viewed below.

Who

People and organizations associated with either the creation of this article or its content.

Sponsors

Publisher

Provided By

UNT Libraries Government Documents Department

Serving as both a federal and a state depository library, the UNT Libraries Government Documents Department maintains millions of items in a variety of formats. The department is a member of the FDLP Content Partnerships Program and an Affiliated Archive of the National Archives.

Contact Us

What

Descriptive information to help identify this article. Follow the links below to find similar items on the Digital Library.

Description

The entropy bounds for constructive upper bound on the needed number-of-bits for solving a dichotomy is represented by the quotient of two multidimensional solid volumes. For minimization of this upper bound exact calculation of the volume of this quotient is needed. Three methods for exact computing of the volume of a given nD volume are presented: (1) general method for calculation any nD volume by slicing it into volumes of decreasing dimension is presented; (2) a method applying appropriate curvilinear coordinate system is described for volume bounded by symmetrical curvilinear hypersurfaces (spheres, cones, hyperboloids, ellipsoids, cylinders, etc.); and (3) an algorithm for dividing any nD complex into simplices and computing of the volume of the simplices is presented, supplemented by a general formula for calculation of volume of an nD simplex. These mathematical methods enable exact calculation of volume of any complicated multidimensional solids. The methods allow for the calculation of the minimal volume and lead to tighter bounds on the needed number-of-bits.

Physical Description

10 p.

Notes

OSTI as DE98002919

Source

  • EIS `97: international symposium on engineering of intelligent systems, Tenerife (Spain), 11-13 Feb 1998

Language

Item Type

Identifier

Unique identifying numbers for this article in the Digital Library or other systems.

  • Other: DE98002919
  • Report No.: LA-UR--97-4413
  • Report No.: CONF-980216--
  • Grant Number: W-7405-ENG-36
  • Office of Scientific & Technical Information Report Number: 645550
  • Archival Resource Key: ark:/67531/metadc694034

Collections

This article is part of the following collection of related materials.

Office of Scientific & Technical Information Technical Reports

Reports, articles and other documents harvested from the Office of Scientific and Technical Information.

Office of Scientific and Technical Information (OSTI) is the Department of Energy (DOE) office that collects, preserves, and disseminates DOE-sponsored research and development (R&D) results that are the outcomes of R&D projects or other funded activities at DOE labs and facilities nationwide and grantees at universities and other institutions.

What responsibilities do I have when using this article?

When

Dates and time periods associated with this article.

Creation Date

  • February 1998

Added to The UNT Digital Library

  • Aug. 14, 2015, 8:43 a.m.

Description Last Updated

  • May 5, 2016, 7:21 p.m.

Usage Statistics

When was this article last used?

Yesterday: 0
Past 30 days: 0
Total Uses: 2

Interact With This Article

Here are some suggestions for what to do next.

Start Reading

PDF Version Also Available for Download.

International Image Interoperability Framework

IIF Logo

We support the IIIF Presentation API

Makaruk, H. E. Computations of entropy bounds: Multidimensional geometric methods, article, February 1998; New Mexico. (digital.library.unt.edu/ark:/67531/metadc694034/: accessed June 21, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.