Mathematical Perspectives on Neural Networks

By Paul Smolensky; Michael C. Mozer et al. | Go to book overview

7 The Mathematical Theory of the Analog Computer
Marian Boykan Pour-El University of Minnesota
1. INTRODUCTION
The word computer conjures up an image of a particular type of device, the digital computer, a deterministic machine that processes discrete bits of information sequentially. Yet, long before the advent of the current computer explosion, there was another kind of device, the analog computer. The analog computer is a parrallel processing machine in which the variables change continuously. Thus, it should be of direct relevance to the theory of neural networks.The purpose of this paper is twofold:
1. to define and describe analog generality and
2. to study the relation between analog generability and computability by a digital computer.

From the theoretical point of view all digital computers are Turing machines and vice versa. Thus, we study the relation between analog generability and Turing computability.

The plan of the paper is as follows. Section 2 is introductory; it provides a brief historical account of analog generability. Section 3 is concerned with the mathematical definitions; it begins with a preliminary account that has a decidedly graph-theoretic flavor. This leads naturally to the final definition that is expressed in terms of differential equations. The relation between analog generability and differential equations is explored still further in Sec. 4. Here one finds a useful mathematical characterization of analog generability in terms of solutions of algebraic differential polynomials. (See Sec. 4 for the definitions.)

-225-

Notes for this page

Add a new note
If you are trying to select text to create highlights or citations, remember that you must now click or tap on the first word, and then click or tap on the last word.
One moment ...
Default project is now your active project.
Project items
Notes
Cite this page

Cited page

Style
Citations are available only to our active members.
Buy instant access to cite pages or passages in MLA 8, MLA 7, APA and Chicago citation styles.

(Einhorn, 1992, p. 25)

(Einhorn 25)

(Einhorn 25)

1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

Note: primary sources have slightly different requirements for citation. Please see these guidelines for more information.

Cited page

Bookmark this page
Mathematical Perspectives on Neural Networks
Table of contents

Table of contents

Settings

Settings

Typeface
Text size Smaller Larger Reset View mode
Search within

Search within this book

Look up

Look up a word

  • Dictionary
  • Thesaurus
Please submit a word or phrase above.
Print this page

Print this page

Why can't I print more than one page at a time?

Help
Full screen
Items saved from this book
  • Bookmarks
  • Highlights & Notes
  • Citations
/ 864

matching results for page

    Questia reader help

    How to highlight and cite specific passages

    1. Click or tap the first word you want to select.
    2. Click or tap the last word you want to select, and you’ll see everything in between get selected.
    3. You’ll then get a menu of options like creating a highlight or a citation from that passage of text.

    OK, got it!

    Cited passage

    Style
    Citations are available only to our active members.
    Buy instant access to cite pages or passages in MLA 8, MLA 7, APA and Chicago citation styles.

    "Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn, 1992, p. 25).

    "Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn 25)

    "Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn 25)

    "Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences."1

    1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

    Cited passage

    Thanks for trying Questia!

    Please continue trying out our research tools, but please note, full functionality is available only to our active members.

    Your work will be lost once you leave this Web page.

    Buy instant access to save your work.

    Already a member? Log in now.

    Search by... Author
    Show... All Results Primary Sources Peer-reviewed

    Oops!

    An unknown error has occurred. Please click the button below to reload the page. If the problem persists, please try again in a little while.