For accurate prediction of normal tissue tolerance, it is important that the volumetric information of dose distribution be considered. However, in dosimetric optimization of intensity modulated beams, the dose-volume factor is usually neglected. In this paper we describe two methods of volume-dependent optimization for intensity modulated beams such as those generated by computer-controlled multileaf collimators. The first method uses a volume sensitive penalty function in which fast simulated annealing is used for cost function minimization (CFM). The second technique is based on the theory of projections onto convex sets (POCS) in which the dose-volume constraint is replaced by a limit on integral dose. The ability of the methods to respect the dose-volume relationship was demonstrated by using a prostate example involving partial volume constraints to the bladder and the rectum. The volume sensitive penalty function used in the CFM method can be easily adopted by existing optimization programs. The convex projection method can find solutions in much shorter time with minimal user interaction.

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In this study, we introduce and investigate a class of neural architectures of Polynomial Neural Networks (PNNs), discuss a comprehensive design methodology and carry out a series of numeric experiments. PNN is a flexible neural architecture whose structure (topology) is developed through learning. In particular, the number of layers of the PNN is not fixed in advance but becomes generated on the fly. In this sense, PNN is a self-organizing network. The essence of the design procedure dwells on the Group Method of Data Handling (GMDH). Each node of the PNN exhibits a high level of flexibility and realizes a polynomial type of mapping (linear, quadratic, and cubic) between input and output variables. The experimental part of the study involves two representative time series such as Box-Jenkins gas furnace data and a pH neutralization process. Ó

An approach is presented for query-based neural network learning. A layered perceptron partially trained for binary classification is considered. The single-output neuron is trained to be either a zero or a one. A test decision is made by thresholding the output at, for example, one-half. The set of inputs that produce an output of one-half forms the classification boundary. The authors adopted an inversion algorithm for the neural network that allows generation of this boundary. For each boundary point, the classification gradient can be generated. The gradient provides a useful measure of the steepness of the multidimensional decision surfaces. Conjugate input pairs are generated using the boundary point and gradient information and presented to an oracle for proper classification. These data are used to refine further the classification boundary, thereby increasing the classification accuracy. The result can be a significant reduction in the training set cardinality in comparison with, for example, randomly generated data points. An application example to power system security assessment is given.