By Clark Jeffries (auth.), Clark Jeffries (eds.)
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Additional info for Code Recognition and Set Selection with Neural Networks
Which value occurs is easier to see in the B format (product form). Thus in dxl/dt, o This improvement is especially clear in higher dimensional models. For example, outside the transition zone T[ in lO-dimensional space, the term Hypergraphs and Neural Networks 45 in a model is clearly 0 except in the (-,+,+,+,-,-,+,-,+,+) orthant relative to T£; in that orthant the term is 1. The A form of the same term would not be so transparent. We establish the equivalence of the two forms in a theorem. 5.
2 can be applied. 2) that the terms o(dx 1/dt)/ox3 and o(dxydt)/oxl are not of constant sign for all x, thus violating a pde sign condition on p. 119 of [Hi]. 1) with limit cycles and, of course, no foundation function. 7) in the previous chapter. In summary, for some applications in content addressable memory and robot arm control, neural networks should only have constant trajectories as attractors. 2, one design route to this feature is the organization of neurons in mutually inhibitory or mutually excitatory interaction subsets (hypergraphs with same sign barycenters) together with the balanced cycle condition.
2. The associated hypergraph is 1 + 4 Because the bypergraph has same sign barycenters and balanced cycles, every nonconstant trajectory must asymptotically approach a constant trajectory. Around every constant trajectory outside the transistion zone T E, the system is linear with approximation matrix -I; stability follows. 5, the only solution with gl = 0 . 5, gl = 0 ~ x2 = -1, same solution. 5, gl = 1, the only solution with g3 = o. 5 ,x2 = 1, x3 = 3, the only solution with gl g2 g3 = 1. 3. This model is associated with a set selection problem, namely: consider the array of elements 1 5 234 6 7 9 8 10 and choose exactly one element from each row and each column.