We introduce a novel neural network called the T-Model and investigates the learning ability of the T-Model neural network. A learning algorithm based on the least mean square (LMS) algorithm is used to train the T-Model and produces a very good result for the T-Model network. We present simulation results on several practical problems to illustrate the efficiency of the learning techniques. As a result, the T-Model network learns successfully, but the Hopfield model fails to and the T-Model learns much more effectively and more quickly than a multi-layer network.

Topographic maps begin to be recognized as one of the major computational structures underlying neural computation in the brain. They provide dimension-reducing projections between feature spaces that seem to be established and maintained under the participation of selforganizing, adaptive processes. In this contribution, we investigate how well the structure of such maps can be replicated by simple adaptive processes of the kind proposed by Kohonen. We will particularly address the important issue, how the dimensionality of the input space affects the spatial organization of the resulting map.

The purpose of the present paper is to review a state of the art of nonlinear analysis with the self-validating numerical method. The self-validating numerics based method provides a tool for performing computer assisted proofs of nonlinear problems by taking the effect of rounding errors in numerical computations rigorously into account. First, Kantorovich's approach of a posteriori error estimation method is surveyed, which is based on his convergence theorem of Newton's method. Then, Urabe's approach for computer assisted existence proofs is likewise discussed. Based on his convergence theorem of the simplified Newton method, he treated practical nonlinear differential equations such as the Van der Pol equation ahd the Duffing equation, and proved the existence of their periodic and quasi-periodic solutions by the self-validating numerics. An approach of the author for generalization and abstraction of Urabe's method are also discribed to more general funcional equations. Furthermore, methods for rigorous estimation of rounding errors are surveyed. Interval analytic methods are discussed. Then an approach of the author which uses rational arithmetic is reviewed. Finally, approaches for computer assisted proofs of nonlinear problems are surveyed, which are based on the self-validating numerics.

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.

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(1))n both for the second (n2) and third-order (n3) 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.

This paper proposes a new construction of the minimum knowledge undeniable signature scheme which solves a problem inherent in Chaum's scheme. We formulate a new proof system, the minimum knowledge interactive bi-proof system, and a pair of languages, the common witness problem, based on the random self-reducible problem. We show that any common witness problem has the minimum knowledge interactive bi-proof system. A practical construction for undeniable signature schemes is proposed based on such a proof system. These schemes provide signature confirmation and disavowal with the same protocol (or at the same time).