Turning a Differential Delay Equation into a High-Dimensional Map

2020 ◽  
pp. 99-114
Author(s):  
Jérôme Losson ◽  
Michael C. Mackey ◽  
Richard Taylor ◽  
Marta Tyran-Kamińska
Keyword(s):  
Delay Equation ◽  
High Dimensional ◽  
Differential Delay Equation ◽  
Differential Delay

scholarly journals Response of an oscillatory differential delay equation to a single stimulus

2016 ◽  
Vol 74 (5) ◽  
pp. 1139-1196 ◽  
Author(s):  
Michael C. Mackey ◽  
Marta Tyran-Kamińska ◽  
Hans-Otto Walther
Keyword(s):  
Single Stimulus ◽  
Delay Equation ◽  
Differential Delay Equation ◽  
Differential Delay

A Tree-Structured Algorithm for Reducing Computation in Networks with Separable Basis Functions

1991 ◽  
Vol 3 (1) ◽  
pp. 67-78 ◽  
Author(s):  
Terence D. Sanger
Keyword(s):  
Input Data ◽  
Continuous Functions ◽  
Basis Functions ◽  
Tree Structure ◽  
High Dimensional ◽  
Efficient Computation ◽  
Variable Size ◽  
Differential Delay Equation ◽  
Differential Delay ◽  
The Individual

I describe a new algorithm for approximating continuous functions in high-dimensional input spaces. The algorithm builds a tree-structured network of variable size, which is determined both by the distribution of the input data and by the function to be approximated. Unlike other tree-structured algorithms, learning occurs through completely local mechanisms and the weights and structure are modified incrementally as data arrives. Efficient computation in the tree structure takes advantage of the potential for low-order dependencies between the output and the individual dimensions of the input. This algorithm is related to the ideas behind k-d trees (Bentley 1975), CART (Breiman et al. 1984), and MARS (Friedman 1988). I present an example that predicts future values of the Mackey-Glass differential delay equation.

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