Jun-ichi Inoue

Stabilization of organic field-effect transistors in hexamethylenetetrathiafulvalene derivatives substituted by bulky alkyl groups

Hexamethylenetetrathiafulvalene (HMTTF) derivatives substituted by tert-butyl, n-pentyl, and 1,1-dimethylpropyl groups are prepared, and the transistor properties are investigated. The compounds substituted by bulky tertiary groups exhibit high mobilities up to 0.98 cm2/Vs in the thin-film transistors and 2.3 cm2/Vs in the single-crystal transistors. At the same time these compounds realize low threshold voltages close to zero and large on–off ratios. The high mobility and the low threshold voltage are maintained more than one month in air. The single-crystal X-ray structure analyses reveal uniform stacking structures. These observations demonstrate that the low threshold voltage and the stable device performance are not solely determined by the energy levels, but are remarkably improved by the closely packed structures derived from the bulky alkyl groups.

Image restoration using the chiral Potts spin glass.

We report on the image reconstruction (IR) problem by making use of the random chiral q-state Potts model, whose Hamiltonian possesses the same gauge invariance as the usual Ising spin glass model. We show that the pixel representation by means of the Potts variables is suitable for the gray-scale level image which cannot be represented by the Ising model. We find that the IR quality is highly improved by the presence of a glassy term, besides the usual ferromagnetic term under random external fields, as very recently pointed out by Nishimori and Wong. We give the exact solution of the infinite range model with q=3, the three-gray-scale-level case. In order to check our analytical result and the efficiency of our model, two-dimensional Monte Carlo simulations have been carried out on real-world pictures with three and eight gray-scale levels.

Convergence of simulated annealing using the generalized transition probability

We prove weak ergodicity of the inhomogeneous Markov process generated by the generalized transition probability of Tsallis and Stariolo under power-law decay of the temperature. We thus have a mathematical foundation to conjecture convergence of simulated annealing processes with the generalized transition probability to the minimum of the cost function. An explicitly solvable example in one dimension is analyzed in which the generalized transition probability leads to a fast convergence of the cost function to the optimal value. We also investigate how far our arguments depend upon the specific form of the generalized transition probability proposed by Tsallis and Stariolo. It is shown that a few requirements on analyticity of the transition probability are sufficient to assure fast convergence in the case of the solvable model in one dimension.

Retrieval phase diagrams of non-monotonic Hopfield networks

We investigate the retrieval phase diagrams of an asynchronous fully connected attractor network with non-monotonic transfer function by means of a mean-field approximation. We find for the noiseless zero-temperature case that this non-monotonic Hopfield network can store more patterns than a network with monotonic transfer function investigated by Amit et al. Properties of retrieval phase diagrams of non-monotonic networks agree with the results obtained by Nishimori and Opris who treated synchronous networks. We also investigate the optimal storage capacity of the non-monotonic Hopfield model with state-dependent synaptic couplings introduced by Zertuche et al. We show that the non-monotonic Hopfield model with state-dependent synapses stores more patterns than the conventional Hopfield model. Our formulation can be easily extended to a general transfer function.

On-line AdaTron learning of unlearnable rules

We study the on-line AdaTron learning of linearly nonseparable rules by a simple perceptron. Training examples are provided by a perceptron with a nonmonotonic transfer function that reduces to the usual monotonic relation in a certain limit. We find that, although the on-line AdaTron learning is a powerful algorithm for the learnable rule, it does not give the best possible generalization error for unlearnable problems. Optimization of the learning rate is shown to greatly improve the performance of the AdaTron algorithm, leading to the best possible generalization error for a wide range of the parameter that controls the shape of the transfer function. @S1063-651X~97!10204-5#

On-line learning of non-monotonic rules by simple perceptron

We study the generalization ability of a simple perceptron which learns unlearnable rules. The rules are presented by a teacher perceptron with a non-monotonic transfer function. The student is trained in the on-line mode. The asymptotic behaviour of the generalization error is estimated under various conditions. Several learning strategies are proposed and improved to obtain the theoretical lower bound of the generalization error.

Statistical mechanics of the multi-constraint continuous knapsack problem

We apply the replica analysis established by Gardner to the multi-constraint continuous knapsack problem, which is one of the linear programming problems and a most fundamental problem in the field of operations research (OR). For a large problem size, we analyse the space of solution and its volume, and estimate the optimal number of items to go into the knapsack as a function of the number of constraints. We study the stability of the replica symmetric (RS) solution and find that the RS calculation cannot estimate the optimal number of items in the knapsack correctly if many constraints are required. In order to obtain a consistent solution in the RS region, we try the zero-entropy approximation for this continuous solution space and get a stable solution within the RS ansatz. On the other hand, in the replica symmetry breaking (RSB) region, the one-step RSB solution is found by Parisis scheme. It turns out that this problem is closely related to the problem of optimal storage capacity and of generalization by maximum-stability rule of a spherical perceptron.

Learning of non-monotonic rules by simple perceptrons

In this paper, we study the generalization ability of a simple perceptron which learns an unrealizable Boolean function represented by a perceptron with a non-monotonic transfer function of reversed-wedge type. This type of non-monotonic perceptron is considered as a variant of multilayer perceptron and is parametrized by a single `wedge parameter a. Reflecting the non-monotonic nature of the target function, a discontinuous transition from the poor generalization phase to the good generalization phase is observed in the learning curve for intermediate values of a. We also find that asymptotic learning curves are classified into the following two categories depending on a. For large a, the learning curve obeys a power law with exponent 1. On the other hand, a power law with exponent is obtained for small a. Although these two exponents are obtained from unstable replica symmetric solutions by using the replica method, they are consistent with the results obtainable without using the replica method in a low-dimensional version of this learning problem. This suggests that our results are good approximations even if they are not exact.

Image restoration using quantum fluctuation

Quantum fluctuation is introduced into the Markov random field (MRF) model for image restoration in the context of a Bayesian approach. We investigate the dependence of the quantum fluctuation on the quality of BW image restoration by making use of statistical mechanics. We find that the maximum posterior marginal (MPM) estimate based on the quantum fluctuation gives a fine restoration in comparison with the maximum a posterior (MAP) estimate or the thermal fluctuation-based MPM estimate.

Generalization ability of a perceptron with nonmonotonic transfer function

We investigate the generalization ability of a perceptron with nonmonotonic transfer function of a reversed-wedge type in on-line mode. This network is identical to a parity machine, a multilayer network. We consider several learning algorithms. By the perceptron algorithm the generalization error is shown to decrease by the