By Daniel J. Amit
Exploring the most fascinating and most likely worthwhile parts of medical examine, the examine of the foundations and mechanisms underlying mind functionality, this ebook introduces and explains the innovations introduced from physics to the examine of neural networks and the insights they've got influenced. colossal growth in figuring out reminiscence, the training strategy, and self-organization by way of learning the homes of versions of neural networks have led to discoveries of vital parallels among the houses of statistical, nonlinear cooperative platforms in physics and neural networks. the writer provides a coherent and transparent, nontechnical view of the entire simple principles and effects. extra technical facets are limited to big sections and appendices in each one bankruptcy.
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Example text
4). Their interaction with matter is mainly via two processes: collisions with shell electrons and capture by nuclei followed by spallation. The first reaction is essentially identical to that just described for ions if the differences in charge and mass are introduced into the respective formulae. Towards the end of the meson range, however, the situation is quite different: Because of their negative charge, 1r- mesons are not repelled by the atomic nuclei in the medium, on the contrary, they are captured which leads to highly excited states.
Extensive tabulated data are available in ICRU Report 16 (1970) and 37 (1984). 10. 28) can also be written as: R = ml r T10 Jo d(TI/ml) dTI/dx and with Eq. 23): R = ml Z*2 . 11. Ion ranges in water (after KIEFER and STRAATEN 1987) where Rp is the range of a proton of equal velocity (or equal Tim). 28a) constitutes a practical scaling rule. All charged particles lose energy when travelling through matter. This leads also to changes in stopping power. The dependence of stopping power on penetration depth is called the "BRAGG curve" .
14) in its given form is strictly true only for non-relativistic cases. 16) The quantity ]L = mlma/(ml + rna) is termed "reduced mass". 16) shows that in the cog system, the two particles have the same momentum but with opposing signs. This means that in the collision, only the direction is altered and that the entry angle equals the exit angle (denoted tP in the following). This is not true in the "laboratory system" where, upon collision, the two particles are scattered by angles al and aa from the original direction of VI (the second particle assumed to be initially at rest).