The Mathematics of the Brain

Abstract

The project develops a formalism for bridging the gap between symbolic and dynamic levels of the mathematical theory of the brain. The formalism is based on the hypotheses that the neocortex processes symbolic information in a nonclassical way. Instead of manipulating data in a read/write memory, as the classical symbolic systems do, the neocortex changes the states of dynamic memory representing different temporary attributes of data stored in a long-term memory. This nonclassical symbolic/dynamic computational paradigm is called the concept of E-machine. Intuitively, an E-machine manipulates characteristic functions over the sets of memory addresses of data rather than addresses and data themselves. The main results include: (1) demonstrating the Turing universality of the E-machine paradigm, (2) showing how an E-machine can learn to simulate a read/write working memory without actually re-writing data, (3) demonstrating how the E-machine paradigm can be efficiently implemented in biologically-realistic neural networks with temporal modulation. Several computer simulations supporting the theoretical results were performed.

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Document Details

Document Type
Technical Report
Publication Date
May 27, 2009
Accession Number
ADA586715

Entities

People

  • Victor Eliashberg
  • Yakov Eliashberg

Tags

Communities of Interest

  • Autonomy
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algorithms
  • Artificial Intelligence
  • Automata
  • Automated Speech Recognition
  • Brain
  • Coding
  • Complex Systems
  • Computational Science
  • Computer Simulations
  • Computers
  • Decoding
  • Grammars
  • Language
  • Linear Accelerators
  • Mathematical Models
  • Neural Networks
  • Physical Theories

Readers

  • Computer Programming and Software Development.
  • Neuroscience
  • Systems Analysis and Design

Technology Areas

  • AI & ML