In this paper, some classes of arithmetic circuits are introduced that capture the computational complexity of computing the determinant of matrices with entries either indeterminates or constants from a field. An arithmetic circuit is just like a Boolean circuit, except that all AND and OR gates (with fan-in two) are replaced by gates realizing a multiplication and an addition, respectively, of two polynomials over some indeterminates with coefficients from the field, and the circuit computes a (formal multivariate) polynomial in the obvious sense. An arithmetic circuit is said to be skew if at least one of the inputs of each multiplication gate is either an indeterminate or a constant. Then it is shown that for all square matrices M of dimension q, the determinant of M can be computed by a skew arithmetic circuit of (q20) gates, and is shown that for all skew arithmetic circuits C of size q, the polynomial computed by C can be defined as the determinant of a square matrix M of dimension (q). Thus the size of skew arithmetic circuit is polynomially related to the dimension of square matrices when it is considered to represent multivariate polynomials in both arithmetic circuits and the determinant. The results are extended to some other classes of arithmetic circuits less restricted than skew ones, and by using such an extended result, a difference and a similarity are demonstrated between polynomials represented as the determinant of matrix of relatively small dimension and those polynomials computed by arithmetic formulas and arithmetic circuits of relatively small size and degree.

We review the role of optics in interconnects, analog processing, neural networks, and digital computing. The properties of low interference, massively parallel interconnections, and very high data rates promise extremely high performance for optical information processing systems.

This paper presents an approximation method for deriving the availability of a parallel redundant system with preventive maintenance (PM) and common-cause failures. The system discussed is composed of two identical units. A single service facility is available for PM and repair. The repair times, the PM times and the failure times except for common-cause failures are all assumed to be arbitrarily distributed. The presented method formulates the problem of the availability analysis of a parallel redundant system as a Markov renewal process which represents the state transitions of one specified unit in the system. This method derives the availability easily and accurately. Further, the availability obtained by this method is exact in a special case.

The VSTEP concept and its practical application in the form of an LED-type pnpn-VSTEP demonstrating low power consumption through electro-photonic operational modes are both shown. Further, with focus primarily on the new laser-mode VSTEP with high-intensity light output and narrow optical beam divergence, the design features such as threshold gain and optical absorptivity, device fabrication, and characteristics are explained. The possibility of ultimate performance based mainly on electrical to optical power conversion efficiency, important from the application viewpoint of optical interconnection, are also discussed. Also, as two examples of functional optical interconnection achieved by VSTEP, serial-to-parallel data conversion and optical self-routing switches are shown. Finally, future opto-electronic technologies to be developed for two-dimensionally integrable surface-type optical semiconductor devices, including the VSTEP, are discussed.

The nonlinear optical properties of organics with unsaturated bonds were compared with those of inorganics including semiconductors and dielectrics. Because of the mesomeric effect, namely quantum mechanical resonance effect among configurations, aromatic molecules and polymers have larger optical nonlinear parameters defined as δ(n)=X(n)/(X(l))n both for the second (n=2) and third-order (n=3) nonlinearities. Experimental results of ultrafast nonlinear response of conjugated polymers, especially polydiacetylenes, were described and a model is proposed to explain the relaxation processes of photoexcitations in the conjugated polymers. Applying the model constructed on the basis of the extensive experimental study, we propose model polymers to obtain ultrafast resonant optical nonlinearity.

A rigorous theoretical method for predicting "ratio of desired signal power to interference power [c/i]" and "ratio of signal power to noise plus interference power [c/(n+i)]" where both desired and interference signals vary with time under the Nakagami-Rice fading conditions is presented. An alternative simple prediction method which is more desirable from the viewpoint of engineering application is then proposed. Prediction errors given by the simple method are evaluated by comparing to the errors given by the rigorous method, and it is confirmed that the simple method gives reasonable accuracy. This method is expected to serve in the development of frequency re-use technologies and the coordination of various systems for mobile satellite communications in the near future.