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1981 1
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Global exponential stability of octonion-valued neural networks with leakage delay and mixed delays.
Popa CA. Popa CA. Neural Netw. 2018 Sep;105:277-293. doi: 10.1016/j.neunet.2018.05.006. Epub 2018 Jun 14. Neural Netw. 2018. PMID: 29890384
This paper discusses octonion-valued neural networks (OVNNs) with leakage delay, time-varying delays, and distributed delays, for which the states, weights, and activation functions belong to the normed division algebra of octonions. The octonion algebra is a non …
This paper discusses octonion-valued neural networks (OVNNs) with leakage delay, time-varying delays, and distributed delays, for which the …
Neurons the decision makers, Part I: The firing function of a single neuron.
Saaty T. Saaty T. Neural Netw. 2017 Feb;86:102-114. doi: 10.1016/j.neunet.2016.04.003. Epub 2016 May 6. Neural Netw. 2017. PMID: 27292267
Because making comparisons requires the reciprocal property, we need mathematics that can cope with division. There are four division algebras that would allow us to use our reciprocals arising from comparisons: The real numbers, the complex numbers, the non-commutative qu …
Because making comparisons requires the reciprocal property, we need mathematics that can cope with division. There are four division alg …
A construction of F(1) as automorphisms of a 196,883-dimensional algebra.
Griess RL. Griess RL. Proc Natl Acad Sci U S A. 1981 Feb;78(2):689-91. doi: 10.1073/pnas.78.2.689. Proc Natl Acad Sci U S A. 1981. PMID: 16592973 Free PMC article.
In this note, I announce the construction of the finite simple group F(1), whose existence was predicted independently in 1973 by Bernd Fischer and by me. The group has order 2(46)3(20)5(9)7(6)11(2)13(3)17.19.23.29.31.41. 47.59.71 = 808,017,424,794,512,875,886,459,904,961, …
In this note, I announce the construction of the finite simple group F(1), whose existence was predicted independently in 1973 by Ber …