This paper uses both network analysis and experiments to confirm that the neural network learning algorithm that minimizes output variation (BPV) provides much more robustness than back-propagation (BP) or BP with noise-modified training samples (BPN). Network analysis clarifies the relationship between sample displacement and what and how the network learns. Sample displacement generates variation in the output of the output units in the output layer. The output variation model introduces two types of deformation error, both of which modify the mean square error. We propose a new error which combines the two types of deformation error. The network analysis using this new error considers that BPV learns two types of training samples where the modification is either towards or away from the category mean, which is defined as the center of sample distribution. The magnitude of modification depends on the position of the training sample in the sample distribution and the degree of leaning completion. The conclusions is that BPV learns samples modified towards to the category mean more stronger than those modified away from the category mean, namely it achieves nonuniform learning. Another conclusion is that BPN learns from uniformly modified samples. The conjecture that BPV is much more robust than the other two algorithms is made. Experiments that evaluate robustness are performed from two kinds of viewpoints: overall robustness and specific robustness. Benchmark studies using distorted handprinted Kanji character patterns examine overall robustness and two specifically modified samples (noise-modified samples and directionally-modified samples) examine specific robustness. Both sets of studies confirm the superiority of BPV and the accuracy of the conjecture.

The modular and growable photonic ATM switch architecture described in this paper uses both time-division and wavelength-division multiplexing technologies, so the switch capacity can be expanded in both the time and frequency domains. It uses a new implementation of output buffering scheme that overcomes the bottleneck in receiving and storing concurrent ultra fast optical cells. The capacity in one stage of a switch with this architecture can be increased from 32 gigabits per second to several terabits per second in a modular fashion. The proposed switch structure with output channel grouping can greatly reduce the amount of hardware and still guarantee the cell sequence.

For systems in which the probability that an incorrect output is observed differs with input values, we adopt the redundant usage of n copies of identical systems which we call the n-redundant system. This paper presents a method to find the optimal redundancy of systems for minimizing the probability of dangerous errors. First, it is proved that a k-out-of-n redundancy or a mixture of two kinds of k-out-of-n redundancies minimizes the probability of D-errors under the condition that the probability of output errors including both dangerous errors and safe errors is below a specified value. Next, an algorithm is given to find the optimal series-parallel redundancy of systems by using the properties of the distance between two structure functions.

We derive the eigenvalue constraint for a neural network with three degrees of freedom. The result implies that the neural network needs a neuron with variable output function to generate chaos. It is also shown that the neuron with the special characteristics can be constructed by ordinary neurons.

An idea of optimal output permutation of multiple-valued sum-of-products expressions is presented. The sum-of-products involve the TSUM operator on the MIN of window literal functions. Some bounds on the maximum number of implicants needed to cover an output permuted function are clarified. One-variable output permuted functions require at most p1 implicants in their minimal sum-of-products expressions, where p is the radix. Two-variable functions with radix between three and six are analyzed. Some speculations of maximum number of the implicants could be established for functions with higher radix and more than 2-variables. The result of computer simulation shows that we can have a saving of approximately 15% on the average using permuting output values. Moreover, we demonstrate the output permutation based on the output density as a simpler method. For the permutation, some speculation is shown and the computer simulation shows a saving of approximately 10% on the average.

A discrete-time neuron model having a refractory period and containing a binary hysteresis output function is introduced. A detailed mathematical analysis of the output response is carried out and the necessary and sufficient condition which a sequence must satisfy in order to be designated as a periodic response of the neuron model under a constant or periodic stimulation is given.

The purpose of our research is to get further improvement in the performance of order statistic filters. The basic idea found in our research is the use of a robust median estimator to obtain median differential order information which the classes of order statistic filter required in order to sort the input signal in the filter window. In order to give the motivation for using a median estimator in the classes of order statistic filters, we derive theorems characterizing the median filters and prove them theoretically using the characteristic that the order statistic filter has the performance for a monotonic signal equivalent with the FIR linear filter. As an application of median operation, we propose and investigate the Median Differential Order Statistic Filter to reduce impulsive noise as well as Gaussian noise and regard it as a subclass of the Order Statistic Filter. Moreover, we introduce the piecewise linear function in the Median Differential Order Statistic Filter to improve performance in terms of edge preservation. We call it the Piecewise Linear Median Differential Order Statistic Filter. The effectiveness of proposed filters is verified theoretically by computing the output Mean Square Error of the filters in parts of edge signals, impulsive noise, small amplitude noise and their combination. Computer simulations also show that the proposed filter can improve the performance in both noise (small-amplitude Gaussian noise and impulsive noise) reduction and edge preservation for one-dimensional signals.