Extremely small aperture radial line slot antennas (RLSAs) are analyzed by method of moments. At first, the analysis model of cylindrical waveguide in terms of rectangular cavity modes is confirmed for a RLSA with a spiral slot arrangement. The overall VSWR as well as rotational symmetry of the actual structure of RLSAs is predicted for the first time and is confirmed experimentally. Secondly, the minimum diameter of the concentric array RLSA is estimated for which the conventional analysis model of a rectangular waveguide is valid for the design of matching slot pairs at the shorted periphery of the radial waveguide. It is found that the curvature and cylindrical short wall at aperture periphery must be considered in the design and analysis of small RLSAs with the gain lower than about 25 dBi.

A generalized radial basis function network consisting of (1 + cosh x)-1 as the basis function of the same class as Gaussian functions is investigated in terms of the feasibility of analog-hardware implementation. A simple way of hardware-implementing (1 + cosh x)-1 is proposed to generate the exact input-output response curve on an analog circuit constructed with bipolar transistors. To demonstrate that networks consisting of the basis function proposed actually work, the networks are applied to numerical experiments of forecasting chaotic time series contaminated with observational random noise. Stochastic gradient descent is used as learning rule. The networks are capable of learning and making short-term forecasts about the dynamic behavior of the time series with comparable performance to Gaussian radial basis function networks.

This paper proposes a new approach to recover the sign of local surface curvature of object from three shading images using neural network. The RBF (Radial Basis Function) neural network is used to learn the mapping of three image irradiances to the position on a sphere. Then, the learned neural network maps the image irradiances at the neighbor pixels of the test object taken from three illuminating directions of light sources onto the sphere images taken under the same illuminating condition. Using the property that basic six kinds of surface curvature has the different relative locations of the local five points mapped on the sphere, not only the Gaussian curvature but also the kind of curvature is directly recovered locally from the relation of the locations on the mapped points on the sphere without knowing the values of surface gradient for each point. Further, two step neural networks which combines the forward mapping and its inverse mapping one can be used to get the local confidence estimate for the obtained results. The entire approach is non-parametric, empirical in that no explicit assumptions are made about light source directions or surface reflectance. Results are demonstrated by the experiments for real images.

In fully connected Multilayer perceptron (MLP), all the hidden units are activated by samples from the whole input space. For complex problems, due to interference and cross coupling of hidden units' activations, the network needs many hidden units to represent the problem and the error surface becomes highly non-linear. Searching for the minimum is then complex and computationally expensive, and simple gradient descent algorithms usually fail. We propose a network, where the input space is partitioned into local sub-regions. Subsequently, a number of smaller networks are simultaneously trained by overlapping subsets of the input samples. Remarkable improvement of training efficiency as well as generalization performance of this combined network are observed through various simulations.

Deterministic nonlinear prediction is applied to both artificial and real time series data in order to investigate orbital-instabilities, short-term predictabilities and long-term unpredictabilities, which are important characteristics of deterministic chaos. As an example of artificial data, bimodal maps of chaotic neuron models are approximated by radial basis function networks, and the approximation abilities are evaluated by applying deterministic nonlinear prediction, estimating Lyapunov exponents and reconstructing bifurcation diagrams of chaotic neuron models. The functional approximation is also applied to squid giant axon response as an example of real data. Two metnods, the standard and smoothing interpolation, are adopted to construct radial basis function networks; while the former is the conventional method that reproduces data points strictly, the latter considers both faithfulness and smoothness of interpolation which is suitable under existence of noise. In order to take a balance between faithfulness and smoothness of interpolation, cross validation is applied to obtain an optimal one. As a result, it is confirmed that by the smoothing interpolation prediction performances are very high and estimated Lyapunov exponents are very similar to actual ones, even though in the case of periodic responses. Moreover, it is confirmed that reconstructed bifurcation diagrams are very similar to the original ones.

A radial line slot antenna (RLSA) is a slotted waveguide planar array for the direct broadcast from satellite (DBS) subscriber antennas. A single-layered RLSA (SL-RLSA) is excited by a radially outward traveling wave. The antenna efficiency of more than 85% has already been realized. These antennas are designed on the assumption of perfectly rotationally symmetrical traveling wave excitation; the slot design is based upon the analysis of a slot pair on the rectangular waveguide model with periodic boundary walls. However, the slots perturb the inner field and the actual antenna operation is not perfectly symmetrical. This causes the efficiency reduction especially for very small size antenna. This paper presents a fundamental analysis of the inner field of the radial waveguide. It is impossible to analyze all the slot pairs in the aperture as it is and only the slots in the inner few turns are considered since these provide dominant perturbation. The calculated results are verified by the experiments and reasonable agreement is demonstrated. Some design policies are suggested for enhancing the rotational symmetry.

In this paper we introduce the Piecewise Linear Radial Basis Function Model (PWL-RBFM), a new nonlinear model that uses the well known RBF framework to build a PWL functional approximation by combining an l1 norm with a linear RBF function. A smooth generalization of the PWL-RBF is proposed: it is obtained by substituting the modulus function with the logistic function. These models are applied to several time series prediction tasks.

A radial line slot antenna (RLSA) is a high gain and high efficiency planar array. A single-layered RLSA is much simple in structure but the slot length must be varied to synthesize uniform aperture illumination. These are now commercialized for 12GHz band DBS reception. In RLSAs, considerable power is dissipated in the termination as is common to other traveling wave antennas; the uniform aperture illumination is not the optimum condition for high gain in RLSAs. Authors proposed a theoretical method reducing the termination loss for further efficiency enhancement. This paper presents the measured performances of the SL-RLSAs of this design with non-uniform aperture illumination. The efficiency enhancement of about 10% is observed; the measured gain of 36.7dBi (87%) and 32.9dBi (81%) for a 0.6mφ and 0.4mφ antennas respectively verify this technique.