Recent progress in research on the finite element method (FEM) for optical waveguide design and analysis is reviewed, focusing on the author's works. After briefly reviewing fundamentals of FEM such as a theoretical framework, a conventional nodal element, a newly developed edge element to eliminate nonphysical, spurious solutions, and a perfectly matched layer to avoid undesirable reflections from computational window edges, various FEM techniques for a guided-mode analysis, a beam propagation analysis, and a waveguide discontinuity analysis are described. Some design examples are introduced, including current research activities on multi-core fibers.

A new algorithm is proposed for finding all solutions of piecewise-linear resistive circuits using separable programming. In this algorithm, the problem of finding all solutions is formulated as a separable programming problem, and it is solved by the modified simplex method using the restricted-basis entry rule. Since the modified simplex method finds one solution per application, the proposed algorithm can find all solutions efficiently. Numerical examples are given to confirm the effectiveness of the proposed algorithm.

Recently, cooperative spectrum sensing is being studied to greatly improve the sensing performance of cognitive radio networks. To develop an adaptable cooperative sensing algorithm, an important issue is how to properly induce selfish users to participate in spectrum sensing work. In this paper, a new cognitive radio spectrum sharing scheme is developed by employing the trust-based bargaining model. The proposed scheme dynamically adjusts bargaining powers and adaptively shares the available spectrum in real-time online manner. Under widely different and diversified network situations, this approach is so dynamic and flexible that it can adaptively respond to current network conditions. Simulation results demonstrate that the proposed scheme can obtain better network performance and bandwidth efficiency than existing schemes.

In this study, we extracted articles describing problems, articles describing their solutions, and articles describing their causes from a Japanese Q&A style Web forum using a supervised machine learning with 0.70, 0.86, and 0.56 F values, respectively. We confirmed that these values are significantly better than their baselines. This extraction will be useful to construct an application that can search for problems provided by users and display causes and potential solutions.

This paper presents an approach for improving proximity and diversity in multiobjective evolutionary algorithms (MOEAs). The idea is to discover new nondominated solutions in the promising area of search space. It can be achieved by applying mutation only to the most converged and the least crowded individuals. In other words, the proximity and diversity can be improved because new nondominated solutions are found in the vicinity of the individuals highly converged and less crowded. Empirical results on multiobjective knapsack problems (MKPs) demonstrate that the proposed approach discovers a set of nondominated solutions much closer to the global Pareto front while maintaining a better distribution of the solutions.

This letter proposes closed form solutions to the L2-sensitivity minimization of second-order state-space digital filters with real poles. We consider two cases of second-order digital filters: distinct real poles and multiple real poles. In case of second-order digital filters, we can express the L2-sensitivity of second-order digital filters by a simple linear combination of exponential functions and formulate the L2-sensitivity minimization problem by a simple polynomial equation. As a result, the minimum L2-sensitivity realizations can be synthesized by only solving a fourth-degree polynomial equation, which can be analytically solved.

This paper proposes closed form solutions to the L2-sensitivity minimization subject to L2-scaling constraints for second-order state-space digital filters with real poles. We consider two cases of second-order digital filters: distinct real poles and multiple real poles. The proposed approach reduces the constrained optimization problem to an unconstrained optimization problem by appropriate variable transformation. We can express the L2-sensitivity by a simple linear combination of exponential functions and formulate the L2-sensitivity minimization problem by a simple polynomial equation. As a result, L2-sensitivity is expressed in closed form, and its minimization subject to L2-scaling constraints is achieved without iterative calculations.

This paper presents the analysis and design of a reflection-cancelling transverse slot-pair array antenna with baffles by using the Spectrum of Two-Dimensional Solutions (S2DS) method. For the transverse slot array, the slot spacings with more than one free-space wavelength cause the grating-lobes. The baffles suppress the grating-lobes effectively. A one-dimensional slot array is extracted from the 2D array with in-phase excitation by assuming periodicity in the transversal direction. The uniform excitation over the finite array is synthesized iteratively to demonstrate the fast and accurate results by S2DS. A unit design model with the baffles is introduced to determine the initial parameters of the slot-pairs, which greatly accelerate the iterations process. Experiments at 25.3 GHz demonstrate the suppression of the grating lobes to the level less than -20.0 dB and also the good uniformity of the aperture field distribution.

This paper presents the formulation for the evaluation of external coupling in the alternating-phase feed single-layer slotted waveguide array antenna with baffles by using the Spectrum of Two-Dimensional Solutions (S2DS) method. A one-dimensional slot array is extracted from the array by assuming the periodicity in transversal direction and introducing the perfect electric conductors in the external region. The uniform excitation over the finite array is synthesized iteratively to demonstrate the fast and accurate results by S2DS. A unit design model with the baffles is introduced to determine the initial parameters of the slot pair which accelerate the iteration. Experiment at 25.3 GHz demonstrates good uniformity of the aperture field distribution as well as the effects of the baffles. The directivity is 32.7 dB which corresponds to the aperture efficiency 90.5% and the reflection is below -15.0 dB over 1.3 GHz.

This paper presents a new method for reconstruction of trigonometric polynomials, a specific class of bandlimited signals, from a number of integrated values of input signals. It is applied in signal reconstruction, spectral estimation, system identification, as well as in other important signal processing problems. The proposed method of processing can be used for precise rms measurements of periodic signal (or power and energy) based on the presented signal reconstruction. Based on the value of the integral of the original input (analogue) signal, with a known frequency spectrum but unknown amplitudes and phases, a reconstruction of its basic parameters is done by the means of derived analytical and summarized expressions. Subsequent calculation of all relevant indicators related to the monitoring and processing of ac voltage and current signals is provided in this manner. Computer simulation demonstrating the precision of these algorithms. We investigate the errors related to the signal reconstruction, and provide an error bound around the reconstructed time domain waveform.

A branch-and-bound algorithm (BB for short) is the most general technique to deal with various combinatorial optimization problems. Even if it is used, computation time is likely to increase exponentially. So we consider its parallelization to reduce it. It has been reported that the computation time of a parallel BB heavily depends upon node-variable selection strategies. And, in case of a parallel BB, it is also necessary to prevent increase in communication time. So, it is important to pay attention to how many and what kind of nodes are to be transferred (called sending-node selection strategy). In this paper, for the graph coloring problem, we propose some sending-node selection strategies for a parallel BB algorithm by adopting MPI for parallelization and experimentally evaluate how these strategies affect computation time of a parallel BB on a PC cluster network.

The subject of this paper is maximum weight matchings of graphs. An edge set M of a given graph G is called a matching if and only if any pair of edges in M share no endvertices. A maximum weight matching is a matching whose total weight (total sum of edge-weights) is maximum among those of G. The maximum weight matching problem (MWM for short) is to find a maximum weight matching of a given graph. Polynomial algorithms for finding an optimum solution to MWM have already been proposed: for example, an O(|V|4) time algorithm proposed by J. Edmonds, and an O(|E||V|log |V|) time algorithm proposed by H.N. Gabow. Some applications require obtaining a matching of large total weight (not necessarily a maximum one) in realistic computing time. These existing algorithms, however, spend extremely long computing time as the size of a given graph becomes large, and several fast approximation algorithms for MWM have been proposed. In this paper, we propose six approximation algorithms GRS+, GRS_F+, GRS_R+, GRS_S+, LAM_a+ and LAM_as+. They are enhanced from known approximation ones by adding some postprocessings that consist of improved search of weight augmenting paths. Their performance is evaluated through results of computing experiment.

Frequency-domain and time-domain novel uniform asymptotic solutions for the scattered fields by an impedance cylinder and a dielectric cylinder, with a radius of curvature sufficiently larger than the wavelength, are presented in this paper. The frequency-domain novel extended UTD and the modified UTD solutions, derived by retaining the higher-order terms in the integrals for the scattered fields, may be applied in the deep shadow region in which the conventional UTD solutions produce the substantial errors. The novel time-domain uniform asymptotic solutions are derived by applying the saddle point technique in evaluating the inverse Fourier transform. We have confirmed the accuracy and validity of the uniform asymptotic solutions both in the frequency-domain and in the time-domain by comparing those solutions with the reference solutions calculated from the eigenfunction expansion (frequency-domain) and from the hybrid eigenfunction expansion and fast Fourier transform (FFT) method (time-domain).

The main contribution of this work is to present several hardware implementations of an "n choose k" counter (C(n,k) counter for short), which lists all n-bit numbers with (n-k) 0's and k 1's, and to show their applications. We first present concepts of C(n,k) counters and their efficient implementations on an FPGA. We then go on to evaluate their performance in terms of the number of used slices and the clock frequency for the Xilinx VirtexII family FPGA XC2V3000-4. As one of the real life applications, we use a C(n,k) counter to accelerate a digital halftoning method that generates a binary image reproducing an original gray-scale image. This method repeatedly replaces an image pattern in small square regions of a binary image by the best one. By the partial exhaustive search using a C(n,k) counter we succeeded in accelerating the task of finding the best image pattern and achieved a speedup factor of more than 2.5 over the simple exhaustive search.

Recently, efficient algorithms have been proposed for finding all characteristic curves of one-port piecewise-linear resistive circuits. Using these algorithms, a middle scale one-port circuit can be represented by a piecewise-linear resistor that is neither voltage nor current controlled. In this letter, an efficient algorithm is proposed for finding all dc operating points of piecewise-linear circuits containing such neither voltage nor current controlled resistors.

For fixed initial and destination states (i.e., markings), M0 and Md, there exist generally infinite firing count vectors in a Petri net. In this letter, it is shown that all fundamental particular solutions as well as all minimal T-invariants w.r.t. firing count vectors are needed to express an arbitrary firing count vector for the fixed M0 and Md. An algorithm for finding a special firing count vector which is expressed by using the only one specified fundamental particular solution is also given.

Conventional vector quantization (VQ) encoding method by full search (FS) is very heavy computationally but it can reach the best PSNR. In order to speed up the encoding process, many fast search methods have been developed. Base on the concept of multi-resolutions, the FS equivalent fast search methods using mean-type pyramid data structure have been proposed already in. In this Letter, an enhanced sum pyramid data structure is suggested to improve search efficiency further, which benefits from (1) exact computing in integer form, (2) one more 2-dimensional new resolution and (3) an optimal pair selecting way for constructing the new resolution. Experimental results show that a lot of codewords can be rejected efficiently by using this added new resolution that features lower dimensions and earlier difference check order.

In a previous study about a combinatorial optimization problem solver using neural networks, since the Hopfield method, convergence to the optimum solution sooner and with more certainty is regarded as important. Namely, only static states are considered as the information. However, from a biological point of view, dynamical systems have attracted attention recently. Therefore, we propose a "dynamical" combinatorial optimization problem solver using hysteresis neural networks. In this paper, the proposed system is evaluated by the N-Queen problem.

An efficient algorithm is proposed for finding all solutions of piecewise-linear resistive circuits containing bipolar transistors. This algorithm is based on a powerful test (termed the LP test) for nonexistence of a solution in a given region using linear programming (LP). In the LP test, an LP problem is formulated by surrounding the exponential functions in the Ebers-Moll model by right-angled triangles, and it is solved by LP, for example, by the simplex method. In this paper, it is shown that the LP test can be performed by the dual simplex method, which makes the number of pivotings much smaller. Effectiveness of the proposed technique is confirmed by numerical examples.

An efficient algorithm is proposed for finding all dc solutions of piecewise-linear (PWL) circuits. This algorithm is based on a powerful test (termed the LP test) for nonexistence of a solution to a system of PWL equations in a given region using the dual simplex method. The proposed algorithm also uses a special technique that decreases the number of regions on which the LP test is performed. By numerical examples, it is shown that the proposed algorithm could find all solutions of large scale problems, including those where the number of variables is 500 and the number of linear regions is 10500, in practical computation time.