PubMed · 7180810
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B R Siecker. 1982. Improving inventory efficiency.. https://pubmed.ncbi.nlm.nih.gov/7180810/
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Dose perturbations at tissue interfaces have been of significant concern since the beginning of this century. However, comprehensive studies related to the backscatter perturbation in kilovoltage beams are still limited. The dose perturbation depends on various parameters, including beam energy, field size, and the thickness, width, position, and atomic number, Z, of the inhomogeneity creating the interface with soft tissue. Using a thin window parallel plate ion chamber having relatively flat response at low energies, the dose perturbation was measured as backscatter dose perturbation factor, BSDF, at various interfaces in kilovoltage x-ray beams. The BSDF is defined as the ratio of doses with and without an interface for identical setup conditions. Results indicate that the BSDF is strongly dependent on beam energy, like the backscatter factor. Contrary to its behavior in megavoltage beams, BSDF in kilovoltage beams does depend on the field size, suggesting a contribution from scattered photons and fluorescent radiation, originating in the high-Z material. The thickness of the high-Z medium is not critical, since a fraction of a millimeter is sufficient to provide full backscatter. The interface effect with wide inhomogeneity has two distinct regions: the high dose region (BSDF > 1.0), which is very localized and disappears within a fraction of a millimeter, and the low dose region (BSDF < 1.0), which is observed up to 10 cm. The dependence of BSDF is neither a quadratic function of Z nor a cube root of beam energy, indicating that the interface effect is complex and not predominantly due to photoelectron transport.
In a recent paper, Poggio and Girosi (1990) proposed a class of neural networks obtained from the theory of regularization. Regularized networks are capable of approximating arbitrarily well any continuous function on a compactum. In this paper we consider in detail the learning problem for the one-dimensional case. We show that in the case of output data observed with noise, regularized networks are capable of learning and approximating (on compacta) elements of certain classes of Sobolev spaces, known as reproducing kernel Hilbert spaces (RKHS), at a nonparametric rate that optimally exploits the smoothness properties of the unknown mapping. In particular we show that the total squared error, given by the sum of the squared bias and the variance, will approach zero at a rate of n(-2m)/(2m+1), where m denotes the order of differentiability of the true unknown function. On the other hand, if the unknown mapping is a continuous function but does not belong to an RKHS, then there still exists a unique regularized solution, but this is no longer guaranteed to converge in mean square to a well-defined limit. Further, even if such a solution converges, the total squared error is bounded away from zero for all n sufficiently large.
At first sight, the QSAR issue might appear to be a mere pattern recognition problem; however, a purely "surface" approach to QSAR as a pattern recognition problem, not involving the profound plausibility of the solutions, has often been demonstrated to be devoid of scientific value and of predictive strength. The requirement for such a lateral validation should imply the recognition of the basic differences between the two terms of the QSAR issue: biology and chemistry. In particular, the difficulty to derive strong quantitative theories for the biological aspect of QSAR procedures should be taken into serious consideration. Within this conceptual framework, this paper examines the different families of mathematical models (classical regression, multivariate methods, neural networks) used in the QSAR research.