By William J. O'Neil
Presents confirmed, easy-to-apply strategies for construction a ecocnomic portfolio. Cuts during the static of traditional knowledge with a fresh array of commonsense suggestions that assist you safely gauge the marketplace, purchase and promote on the correct second, and effectively deal with your portfolio.
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Extra info for 24 Essential Lessons for Investment Success: Learn the Most Important Investment Techniques from the Founder of Investor's Business Daily
However, if the memory contains many large patterns, this procedure can take quite a long time. We are therefore led to ask the question whether the patterns can be stored in a neural network of N elements (neurons) in such a way that the network evolves from the initial configuration nj, corresponding to the presented pattern, into the desired configuration under its own dynamics. In order to formulate the problem, it is useful to invoke the analogy between neurons and Ising spins, mentioned in Sect.
We shall denote the states of the input neurons by (J'k, (k = 1, ... , Ni)j those of the output neurons are labeled by Sj, (i = 1, ... , No). 1) The fact that the variables (J'k occur only on the right-hand side of this relation, while the Si occur only on the left-hand side, is expression of the directedness of the network: information is fed from the input layer into the neurons of the output layer, but not vice versa. The function f(x) may be considered a stochastic law, where it determines the probability of the values Sj = ±1, or as a continuous function, if the neurons are assigned analog values.
9) We have thus managed to reduce the evolution law to a single equation. Since the slope of the function tanh(,8x) at the origin (x = 0) equals ,8 and falls towards both sides, we have to distiguish the two cases illustrated in Fig. 3. For ,8 < 1 (T > 1; Fig. e. all spins point up or down with equal probability. ) The average magnetization vanishes, as it must in a ferromagnet at high temperature. The temperature T = 1 corresponds to the Curie point, above which the spin system becomes demagnetized.