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Localized electrical stimulation within this map triggers flexion and extension movements of the arm joints, varying systematically with the location of the stimulus. It is highly probable that a large portion of the organization of such maps is genetically determined. However, considering the estimated 1013 synapses of a brain, it would be impossible to specify this organization on the basis of a detailed connectivity scheme. A way out of this dilemma is the genetic coding of mechanisms of structure formation, as a result of whose operation the desired connectivity would then be created.

The factor in front of the expression determines the “learning step size” and must be positive. Eq. 4) then acts as an error correction rule: In case of a correct answer from the element r, dr = 0, and all of the weights wri remain unchanged. In case of an incorrect output value, dr = ±1 and Eq. 4) implies a change in the sum i wri xi by ± i xi 2. If the output value was too small, this causes an increase in the sum (dr = 1) if the input pattern x is repeated, and a reduction (dr = −1) if the output was too large.

An appropriate condition is the minimization of the squared sum ri wri 2 of all weights wri . This requirement can be incorporated easily into the original ansatz by minimizing the new functional E[W] + α ri wri 2 instead of E[W]. This, besides measuring error, also measures the magnitude of an average weight. Here, α is a positive constant, and we take the limit of α approaching zero at the end in order to recover the original minimization problem. 3. Neural Network Models 36 This leads to the new minimization condition W(XXT + α1) = YXT .

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A spoken Mongol-English dictionary: With pronunciations in roman scripts by Chimpa


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