OFFSET
1,3
COMMENTS
These invertible matrices are used in formal neural network theory to generate transient-free state transition graphs with using suitable threshold vectors.
REFERENCES
Labos E.: The most complicated networks of formal neurons. In Proc. of IEEE. first International Conference on Neural Networks. San Diego,USA,1987.[Editors: Caudill,M. and Butler Ch.]; Vol. III, pp. 301-308.
EXAMPLE
n=5: matrix =
+3,-1,-1,-1,-1
+1,+3,-1,-1,-1
+1,+1,+3,-1,-1
+1,+1,+1,+3,-1
+1,+1,+1,+1,+3,
with determinant=528=a(5). a(1)=-1 is the only negative term.
MATHEMATICA
f[x_, y_] := Sign[y-x] g[x_, y_, z_] := (z-2)*(1-Abs[f[x, y]]); a=Table[Table[f[w, s], {w, 1, q}], {s, 1, q}]; b=Table[Table[g[w, s, q], {w, 1, q}], {s, 1, q}]; m=matrix=a+b; Det[m]; Table[Det[Table[Table[f[w, s]+g[w, s, q], {w, 1, q}], {s, 1, q}]], {q, 1, 20}]
CROSSREFS
KEYWORD
sign
AUTHOR
Labos Elemer, Jul 08 2003
STATUS
approved