PubMed · 6638740
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F C Genter. 1983. Nomograms for sample size.. https://doi.org/10.7326/0003-4819-99-5-737_2
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We show that neural networks, with a suitable error function for backpropagation, can be successfully used for metric multidimensional scaling (MDS) (i.e., dimensional reduction while trying to preserve the original distances between patterns) and are in fact able to outdo the standard algebraic approach to MDS, known as classical scaling.
Rotation therapy with photons is currently under investigation for the delivery of intensity modulated radiotherapy (IMRT). An analytical approach for inverse treatment planning of this radiotherapy technique is described. The inverse problem for the delivery of arbitrary 2D dose profiles is first formulated and then solved analytically. In contrast to previously applied strategies for solving the inverse problem, it is shown that the most general solution for the fluence profiles consists of two independent solutions of different parity. A first analytical expression for both fluence profiles is derived. The mathematical derivation includes two different strategies, an elementary expansion of fluence and dose into polynomials and a more practical approach in terms of Fourier transforms. The obtained results are discussed in the context of previous work on this problem.
This paper deals with pattern recognition of the shape of the boundary of closed figures on the basis of a circular sequence of measurements taken on the boundary at equal intervals of a suitably chosen argument with an arbitrary starting point. A distance measure between two boundaries is defined in such a way that it has zero value when the associated sequences of measurements coincide by shifting the starting point of one of the sequences. Such a distance measure, which is invariant to the starting point of the sequence of measurements, is used in identification or discrimination by the shape of the boundary of a closed figure. The mean shape of a given set of closed figures is defined, and tests of significance of differences in mean shape between populations are proposed.