Topics in Stochastics, Symbolic Dynamics and Neural Networks

1996 ◽  
Author(s):  
Robert M. Burton ◽  
Jr
Keyword(s):  
Neural Networks ◽  
Symbolic Dynamics

Application of symbolic dynamics to characterize coordinated activity in the context of biological neural networks

2013 ◽  
Vol 350 (10) ◽  
pp. 2967-2981 ◽  
Author(s):  
David Arroyo ◽  
Roberto Latorre ◽  
Pablo Varona ◽  
Francisco B. Rodríguez
Keyword(s):  
Neural Networks ◽  
Symbolic Dynamics ◽  
Biological Neural Networks

Nonlinear Dynamics and Symbolic Dynamics of Neural Networks

1992 ◽  
Vol 4 (5) ◽  
pp. 621-642 ◽  
Author(s):  
John E. Lewis ◽  
Leon Glass
Keyword(s):  
Nonlinear Dynamics ◽  
Neural Networks ◽  
Efficient Method ◽  
Limit Cycles ◽  
Symbolic Dynamics ◽  
Chaotic Dynamics ◽  
Piecewise Linear ◽  
Stable Limit ◽  
Model Networks ◽  
Stable Limit Cycles

A piecewise linear equation is proposed as a method of analysis of mathematical models of neural networks. A symbolic representation of the dynamics in this equation is given as a directed graph on an N-dimensional hypercube. This provides a formal link with discrete neural networks such as the original Hopfield models. Analytic criteria are given to establish steady states and limit cycle oscillations independent of network dimension. Model networks that display multiple stable limit cycles and chaotic dynamics are discussed. The results show that such equations are a useful and efficient method of investigating the behavior of neural networks.

Determination of S-N curves with the application of artificial neural networks

1999 ◽  
Vol 22 (8) ◽  
pp. 723-728 ◽  
Author(s):  
Artymiak ◽  
Bukowski ◽  
Feliks ◽  
Narberhaus ◽  
Zenner
Keyword(s):  
Neural Networks ◽  
Artificial Neural Networks ◽  
Artificial Neural

D-test: A New Test for Analyzing Scale Invariance Using Symbolic Dynamics and Symbolic Entropy

Methodology ◽  
2011 ◽  
Vol 7 (3) ◽  
pp. 88-95 ◽  
Author(s):  
Jose A. Martínez ◽  
Manuel Ruiz Marín
Keyword(s):  
Symbolic Dynamics ◽  
Scale Invariance ◽  
Rating Scales ◽  
Rating Scale ◽  
Marketing Research ◽  
Response Patterns ◽  
Measurement Scales ◽  
Improve Measurement ◽  
Entropy Measures ◽  
The Difference

The aim of this study is to improve measurement in marketing research by constructing a new, simple, nonparametric, consistent, and powerful test to study scale invariance. The test is called D-test. D-test is constructed using symbolic dynamics and symbolic entropy as a measure of the difference between the response patterns which comes from two measurement scales. We also give a standard asymptotic distribution of our statistic. Given that the test is based on entropy measures, it avoids smoothed nonparametric estimation. We applied D-test to a real marketing research to study if scale invariance holds when measuring service quality in a sports service. We considered a free-scale as a reference scale and then we compared it with three widely used rating scales: Likert-type scale from 1 to 5 and from 1 to 7, and semantic-differential scale from −3 to +3. Scale invariance holds for the two latter scales. This test overcomes the shortcomings of other procedures for analyzing scale invariance; and it provides researchers a tool to decide the appropriate rating scale to study specific marketing problems, and how the results of prior studies can be questioned.

Review of Pattern Recognition by Self-Organizing Neural Networks.

1995 ◽  
Vol 40 (11) ◽  
pp. 1110-1110
Author(s):  
Stephen James Thomas
Keyword(s):  
Neural Networks ◽  
Pattern Recognition ◽  
Self Organizing
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