Finding a nonnegative integer solution x for Ax = b (A Zmn, b Zm1) in Petri nets is NP-complete. Being NP-complete, even algorithms with theoretically bad worst case and with average complexity can be useful for a special class of problems, hence deserve investigation. Then a Grobner basis approach to integer programming problems was proposed in 1991 and some symbolic computation systems became to have useful tools for ideals, varieties, and algorithms for algebraic geometry. In this letter, Grobner basis approach is applied to three typical problems with respect to state equation in P/T Petri nets. In other words, after Grobner bases are derived by the tool Maple 7, we consider how to derive the T-invariants and particular solutions of the Petri nets by using them in this letter.

Several reliability based code search algorithms for maximum likelihood decoding have been proposed. These algorithms search the most likely codeword, using the most reliable information set where the leftmost k (the dimension of code) columns of generator matrix are the most reliable and linearly independent. Especially, D. Gazelle and J. Snyders have proposed an efficient decoding algorithm and this algorithm requires small number of candidate codewords to find out the most likely codeword. In this paper, we propose new efficient methods for both generating candidate codewords and computing metrics of candidate codewords to obtain the most likely codeword at the decoder. The candidate codewords constructed by the proposed method are identical those in the decoding algorithm of Gazelle et al. Consequently, the proposed decoding algorithm reduces the time complexity in total, compared to the decoding algorithm of Gazelle et al. without the degradation in error performance.

A rectangular-to-radial waveguide transformer through a crossed slot is proposed as a feeder of a radial line slot antenna (RLSA) for use in a system of solar power satellite (SPS). The transformer is analyzed and designed by using the MoM with numerical eigenmode basis functions. The measured ripple of the amplitude is 3.0 dB in the φ-direction and a 7.0% frequency bandwidth for rotating mode with the ripple below 6 dB is obtained. This bandwidth is wider than that of conventional ring slot or cavity resonator with a coaxial feeder. The antenna measurements at 5.8 GHz show reasonable rotational symmetry both in the near-field distribution and the far field radiation patterns. The reflection is -27.7 dB at the design frequency and below -15 dB in the 7.0% bandwidth. The gain of the antenna with the diameter of 300 mm is 22.7 dBi and the efficiency is 56%.

In many cryptographic applications, a large-order finite field is used as a definition field, and accordingly, many researches on a fast implementation of such a large-order extension field are reported. This paper proposes a definition field Fpm with its characteristic p a pseudo Mersenne number, the modular polynomial f(x) an irreducible all-one polynomial (AOP), and using a suitable basis. In this paper, we refer to this extension field as an all-one polynomial field (AOPF) and to its basis as pseudo polynomial basis (PPB). Among basic arithmetic operations in AOPF, a multiplication between non-zero elements and an inversion of a non-zero element are especially time-consuming. As a fast realization of the former, we propose cyclic vector multiplication algorithm (CVMA), which can be used for possible extension degree m and exploit a symmetric structure of multiplicands in order to reduce the number of operations. Accordingly, CVMA attains a 50% reduction of the number of scalar multiplications as compared to the usually adopted vector multiplication procedure. For fast realization of inversion, we use the Itoh-Tsujii algorithm (ITA) accompanied with Frobenius mapping (FM). Since this paper adopts the PPB, FM can be performed without any calculations. In addition to this feature, ITA over AOPF can be composed with self reciprocal vectors, and by using CVMA this fact can also save computation cost for inversion.

Partial face images, e.g., eyes, nose, and ear images are significant for face recognition. In this paper, we present a method for partial face extraction and recognition based on Radial Basis Function (RBF) networks. Focus has been centered on using ear images because they are not influenced by facial expression, and the influences of aging are negligible. Original human side face image with 320240 pixels is input, and then the RBF network locates the ear and extracts it with a 200120 pixel image. Next, another RBF network is constructed for the purpose of recognition. An algorithm that determines the radius of an RBF function is proposed. Dynamic radius, so called as compared to static one, is found through the algorithm that makes RBF functions adaptable to the training samples. We built a database that contains 600 side face images, from 100 people, to test the method and the results of both extraction and recognition are satisfied.

New algorithms for the soft-decision and the hard-decision maximum likelihood decoding (MLD) for binary linear block codes are proposed. It has been widely known that both MLD can be regarded as an integer programming with binary arithmetic conditions. Recently, Conti and Traverso have proposed an efficient algorithm which uses Grobner bases to solve integer programming with ordinary integer arithmetic conditions. In this paper, the Conti-Traverso algorithm is extended to solve integer programming with modulo arithmetic conditions. We also show how to transform the soft-decision and the hard-decision MLD to integer programming for which the extended Conti-Traverso algorithm is applicable.

To design a high-speed m-bit parallel inversion circuit over GF(2m), we study two variations for the repetition-operation of the numerical formula, AB2, in employing square-first and multiply-first type operations. From the proposed two variations, we propose four inversion architectures, adopting the multiplier and square in [10], as follows: simple duplication semi-systolic architecture for multiply-first inversion circuit (MFIC), m-bit parallel semi-systolic architecture for MFIC, simple duplication semi-systolic architecture for square-first inversion circuit (SFIC), and simplified m-bit parallel semi-systolic architecture for SFIC. Among them, performance of the simplified m-bit parallel semi-systolic architecture for SFIC is recommended for a high-speed applications to get a maximum throughput in the sense of small hardware-complexity, and low latency. When we implement the simplified 8-bit parallel semi-systolic architecture for SFIC over GF(28) by using 0.25 µm CMOS library, necessary are 2495 logic-gates and 1848 latches, and the latency is 56 and the estimated clock-rate is 580 MHz at 100% throughput.

Face detection from cluttered images is very challenging due to the wide variety of faces and the complexity of image backgrounds. In this paper, we propose a neural network based approach for locating frontal views of human faces in cluttered images. We use a radial basis function network (RBFN) for separation of face and non-face patterns, and the complexity of RBFN is reduced by principal component analysis (PCA). The influence of the number of hidden units and the configuration of basis functions on the detection performance was investigated. To further improve the performance, we integrate the distance from feature subspace into the RBFN. The proposed method has achieved high detection rate and low false positive rate on testing a large number of images.

In many practical situations in NN learning, training examples tend to be supplied one by one. In such situations, incremental learning seems more natural than batch learning in view of the learning methods of human beings. In this paper, we propose an incremental learning method in neural networks under the projection learning criterion. Although projection learning is a linear learning method, achieving the above goal is not straightforward since it involves redundant expressions of functions with over-complete bases, which is essentially related to pseudo biorthogonal bases (or frames). The proposed method provides exactly the same learning result as that obtained by batch learning. It is theoretically shown that the proposed method is more efficient in computation than batch learning.

In this paper, we present the division algorithm (DA) for the computation of b=c/a over GF(2m) in two aspects. First, we derive a new formulation for the discrete-time Wiener-Hopf equation (DTWHE) Ab = c in GF(2) over any basis. Symmetry of the matrix A is observed on some special bases and a three-step procedure is developed to solve the symmetric DTWHE. Secondly, we extend a variant of Stein's binary algorithm and propose a novel iterative division algorithm EB*. Owing to its structural simplicity, this algorithm can be mapped onto a systolic array with high speed and low area complexity.

In content-based image retrieval (CBIR), the content of an image can be expressed in terms of different features such as color, texture, shape, or text annotations. Retrieval methods based on these features can be varied depending on how the feature values are combined. Many of the existing approaches assume linear relationships between different features, and also require users to assign weights to features for themselves. Other nonlinear approaches have mostly concentrated on indexing technique. While the linearly combining approach establishes the basis of CBIR, the usefulness of such systems is limited due to the lack of the capability to represent high-level concepts using low-level features and human perception subjectivity. In this paper, we introduce a Neural Network-based Image Retrieval (NNIR) system, a human-computer interaction approach to CBIR using the Radial Basis Function (RBF) network. The proposed approach allows the user to select an initial query image and incrementally search target images via relevance feedback. The experimental results show that the proposed approach has the superior retrieval performance over the existing linearly combining approach, the rank-based method, and the BackPropagation-based method.

In this paper, multiuser detector (MUD) based on radial basis function (RBF) is proposed and simulated for a multicode DS/CDMA system in an AWGN and a multipath fading channels. The performance of RBF-based MUD is compared with that of many suboptimal multiuser detectors in terms of bit error probability. To obtain simulation results, importance sampling technique is employed. From the simulation results, it is confirmed that the RBF-based MUD outperforms decorrelating detector, and achieves near-optimum performance under various environments. The results in this paper can be applied to design of MUD for a multicode DS/CDMA system.

Recently, Vatan, Roychowdhury and Anantram have presented two types of revised versions of the Calderbank-Shor-Steane code construction, and have also provided an exhaustive procedure for determining bases of quantum error-correcting codes. In this paper, we investigate the revised versions given by Vatan et al., and point out that there is no essential difference between them. In addition, we propose an efficient algorithm for searching for bases of quantum error-correcting codes. The proposed algorithm is based on some fundamental properties of classical linear codes, and has much lower complexity than Vatan et al.'s procedure.

This study presents two new bit-parallel cellular multipliers based on an irreducible all one polynomial (AOP) over the finite field GF(2m). Using the property of the AOP, this work also presents an efficient algorithm of inner-product multiplication for computing AB2 multiplications is proposed, with a structure that can simplify the time and space complexity for hardware implementations. The first structure employs the new inner-product multiplication algorithm to construct the bit-parallel cellular architecture. The designed multiplier only requires the computational delays of (m+1)(TAND+TXOR). The second proposed structure is a modification of the first structure, and it requires (m+2) TXOR delays. Moreover, the proposed multipliers can perform A2iB2j computations by shuffling the coefficients to make i and j integers. For the computing multiplication in GF(2m), the novel multipliers turn out to be efficient as they simplify architecture and accelerate computation. The two novel architectures are highly regular, simpler, and have shorter computation delays than the conventional cellular multipliers.

This paper investigates the modeling of non-linearity on the generation of the single trial evoked potential signal (s-EP) by means of using a mixed radial basis function neural network (M-RBFN). The more emphasis is put on the contribution of spontaneous EEG term to s-EP signal. The method is based on a nonlinear M-RBFN neural network model that is trained simultaneously with the different segments of EEG/EP data. Then, the output of the trained model (estimator) is a both fitted and reduced (optimized) nonlinear model and then provide a global representation of the passage dynamics between spontaneous brain activity and poststimulus periods. The performance of the proposed neural network method is evaluated using a realistic simulation and applied to a real EEG/EP measurement.

This paper proposes a moment based encoding algorithm for iterated function system (IFS) coding of non-homogeneous fractal images with unequal probabilities. Moment based encoding algorithms for IFS coding of non-homogeneous fractal images require a solution of simultaneous algebraic equations that are difficult to handle with numerical root-finding methods. The proposed algorithm employs a variable elimination method using Grobner bases with floating-point coefficients in order to derive a numerically solvable equation with a single unknown. The algorithm also employs a varying associated-probabilities method for the purpose of decreasing the computational complexity of calculating Grobner bases. Experimental results show that the average computation time for encoding a non-homogeneous fractal image of 256256 pixels and 256 gray levels is about 200 seconds on a PC with a 400 MHz AMD K6-III processor.

The purpose of this paper is to deal with the problem of recovering a signal from its noisy version. One example is to restore old images degraded by noise. The recovery solution is given within the framework of series expansion and we shall show that for the general case the recovery functions have to be elements of an extended pseudo biorthogonal basis (EPBOB) in order to suppress efficiently the corruption noise. After we discuss the different situations of noise, we provide some methods to construct the optimal EPBOB in order to deal with these situations.

When we have a singular Cab curve with many rational points, we had better to construct linear codes on its normalization rather than the original curve. The only obstacle to construct linear codes on the normalization is finding a basis of L( Q) having pairwise distinct pole orders at Q, where Q is the unique place of the Cab curve at infinity. We present an algorithm finding such a basis from defining equations of the normalization of the original Cab curve.

In this paper, near real time digital radiography system was implemented for the automatic verification of local errors between simulation plan and radiation therapy. Portal image could be acquired through video camera, image board and PC after therapy radiation was converted into light by a metal/fluorescent screen. Considering the divergence according to the distance between the source and the plate, we made a 340 340 12 cm3 basis point plate on which five rods of 4 cm height and 8 mm diameter lead (Pb) were built to display reference points on the simulator and the portal image. We converted the portal image into the binary image using the optimal threshold value which was gotten through the histogram analysis of the acquired portal image using the basis point plate. we got the location information of the iso-center and basis points from the binary image, and removed the systematic errors which were from the differences between the simulation plan and the portal image. Field size which was measured automatically by optimal threshold portal image, was verified with simulation plan. Anatomic errors were automatically detected and verified with the normalized simulation and the portal image by pattern matching method after irradiating a part of the radiation. Therapy efficiency was improved and radiation side effects were reduced by these techniques, so exact radiation treatment are expected.

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.