Stability of explicit Runge—Kutta methods

The classical theory of stability of explicit Runge—Kutta methods is concerned with Lipschitzian problems. It is not useful for stable problems with “large” Lipschitz constants. The classical theory of absolute stability considers some very special problems of this kind. The problems treated arise when a general problem is linearized. It is hoped that the behavior in the case of the special problem provide guidelines as to the behavior in the case of a general problem. A synthesis is proposed here which responds to this unsatisfactory state of affairs in the classical theory.     

Error analysis of variable stepsize Runge–Kutta methods for a class of multiply-stiff singular perturbation problems

In this paper, we present some results on the error behavior of variable stepsize stiffly-accurate Runge–Kutta methods applied to a class of multiply-stiff initial value problems of ordinary differential equations in singular perturbation form, under some weak assumptions on the coefficients of the considered methods. It is shown that the obtained convergence results hold for stiffly-accurate Runge–Kutta methods which are not algebraically stable or diagonally stable. Some results on the existence and uniqueness of the solution of Runge–Kutta equations are also presented.     

基于四阶循环多谱的频谱感知算法

目前,大部分基于能量检测和信号循环平稳的频谱感知算法能够在平稳噪声环境中取得优异的检测性能,在非平稳噪声环境中的检测性能则急剧下降。为了更好地消除频谱感知过程中非平稳噪声的影响,利用信号四阶循环多谱抑制非平稳噪声的性质,提出了一种基于四阶循环多谱的频谱感知算法。该算法首先计算四阶循环多谱的切片形式;然后通过简化的四阶循环多谱幅度平方和对协同用户截取的信号进行检测;最后计算其峰值系数,实现对主用户信号存在性的判断。仿真结果表明,在非平稳噪声环境中,所提出的算法比传统的频谱感知算法识别概率更高,性能更好。     

Symmetric and symplectic exponentially fitted Runge–Kutta methods of high order

The construction of high order symmetric, symplectic and exponentially fitted Runge–Kutta (RK) methods for the numerical integration of Hamiltonian systems with oscillatory solutions is analyzed. Based on the symplecticness, symmetry, and exponential fitting properties, three new four-stage RK integrators, either with fixed- or variable-nodes, are constructed. The algebraic order of the new integrators is also studied, showing that they possess eighth-order of accuracy as the classical four-stage RK Gauss method. Numerical experiments with some oscillatory test problems are presented to show that the new methods are more efficient than other symplectic four-stage eighth-order RK Gauss codes proposed in the scientific literature.     

A fourth-order algorithm with automatic stepsize control for thetransient analysis of DSPNs

This paper presents an efficient and numerically reliable method for the transient analysis of deterministic and stochastic Petri nets. The transient behavior is described by state equations derived by the method of supplementary variables. Significant features of the proposed solution algorithm of fourth order are an automatic stepsize control and a two-stage relative error control. Furthermore, a formal way of dealing with discontinuities in the transient state equations is developed. This resolves the problems posed by initially enabled deterministic transitions and also improves the accuracy of numerical results. Experiments with a queueing system with failure and repair illustrate the efficiency (with respect to both CPU-time and memory space) and the numerical quality of the new algorithm     

A particle swarm optimization algorithm for part–machine grouping

Although in the last years different metaheuristic methods have been used to solve the cell formation problem in group technology, this paper presents the first particle swarm optimization (PSO) algorithm designed to address this problem. PSO is a population-based evolutionary computation technique based on a social behavior metaphor. The criterion used to group the machines in cells is based on the minimization of inter-cell movements. A maximum cell size is imposed. Some published exact results have been used as benchmarks to assess the proposed algorithm. The computational results show that the PSO algorithm is able to find the optimal solutions on almost all instances.     

A sensitivity formula for risk-sensitive cost and the actor–critic algorithm

We propose for risk sensitive control of finite Markov chains a counterpart of the popular ‘actor–critic’ algorithm for classical Markov decision processes. The algorithm is based on a ‘sensitivity formula’ for the risk sensitive cost and is shown to converge with probability one to the desired solution. The proof technique is an adaptation of the ordinary differential equations approach for the analysis of two time-scale stochastic approximation algorithms.     

Post BWT stages of the Burrows–Wheeler compression algorithm

The lossless Burrows–Wheeler compression algorithm has received considerable attention over recent years for both its simplicity and effectiveness. It is based on a permutation of the input sequence—the Burrows–Wheeler transformation (BWT)—which groups symbols with a similar context close together. In the original version, this permutation was followed by a Move‐To‐Front transformation and a final entropy coding stage. Later versions used different algorithms, placed after the BWT, since the following stages have a significant influence on the compression rate. This paper describes different algorithms and improvements for these post BWT stages including a new context‐based approach. The results for compression rates are presented together with compression and decompression times on the Calgary corpus, the Canterbury corpus, the large Canterbury corpus and the Lukas 2D 16‐bit medical image corpus. Copyright © 2010 John Wiley & Sons, Ltd.     

Generalized Needleman–Wunsch algorithm for the recognition of T-cell epitopes

In this paper, we propose a new encoding technique that combines the different physicochemical properties of amino acids together with Needleman–Wunsch algorithm. The algorithm was tested in the recognition of T-cell epitopes. A series of SVM classifiers, where each SVM is trained using a different physicochemical property, combined with the “max rule” enables us to obtain an improvement over the state-of-the-art approaches.     

Extended Ho–Kalman algorithm for systems represented in generalized orthonormal bases

This paper considers the construction of minimal state space models of linear time-invariant systems on the basis of system representations in terms of generalized orthogonal basis function expansions. Starting from the classical Ho–Kalman algorithm that solves the problem using Markov parameter expansions, a generalization is obtained by analysing the matrix representations of the Hankel operators in generalized orthonormal bases. Using the so-called Hambo-domain techniques an efficient algorithm is given to implement the proposed method.     

Size optimization of space trusses using Big Bang–Big Crunch algorithm

A Hybrid Big Bang–Big Crunch (HBB–BC) optimization algorithm is employed for optimal design of truss structures. HBB–BC is compared to Big Bang–Big Crunch (BB–BC) method and other optimization methods including Genetic Algorithm, Ant Colony Optimization, Particle Swarm Optimization and Harmony Search. Numerical results demonstrate the efficiency and robustness of the HBB–BC method compared to other heuristic algorithms.     

Extended Games–Chan algorithm for the 2-adic complexity of FCSR-sequences

Binary sequences generated by feedback shift registers with carry operation (FCSR) share many of the important properties enjoyed by sequences generated by linear feedback shift registers. We present an FCSR analog of the (extended) Games–Chan algorithm, which efficiently determines the linear complexity of a periodic binary sequence with period length T = 2ⁿ or pⁿ, where p is an odd prime and 2 is a primitive element modulo p². The algorithm to be presented yields an upper bound for the 2-adic complexity, an FCSR analog of the linear complexity, of a pⁿ-periodic binary sequence.     

A scheduling quasi–min-max model predictive control algorithm for nonlinear systems

In this paper, a model predictive control algorithm is designed for nonlinear systems. Combination of a linear model with a linear parameter varying model approximates the nonlinear behavior. The linear model is used to express the current nonlinear dynamics, and the linear parameter varying model is used to cover the future nonlinear behavior. In the algorithm, a “quasi-worst-case” value of an infinite horizon objective function is minimized. Closed-loop stability is guaranteed when the algorithm is implemented in a receding horizon fashion by including a Lyapunov constraint in the formulation. The proposed approach is applied to control a jacketed styrene polymerization reactor.     

Computational experience with an algorithm for 0–1 integer programming

In a previous paper in this journal, the authors described an implicit enumeration algorithm for the all integer programming problem. In this paper, a specialization of the aforementioned algorithm for 0–1 integer programming problems is developed. The computational efficiency of this specialization is investigated by solving a set of test problems, using a computer code of the algorithm written for this purpose.     

Incremental frequency count—a post BWT‐stage for the Burrows–Wheeler compression algorithm

The stage after the Burrows–Wheeler transform (BWT) has a key function inside the Burrows–Wheeler compression algorithm as it transforms the BWT output from a local context into a global context. This paper presents the Incremental Frequency Count stage, a post‐BWT stage. The new stage is paired with a run length encoding stage between the BWT and the entropy coding stage of the algorithm. It offers high throughput similar to a Move To Front stage, and at the same time good compression rates like the strong but slow Weighted Frequency Count stage. The properties of the Incremental Frequency Count stage are compared to the Move To Front and Weighted Frequency Count stages by their compression rates and speeds on the Calgary and large Canterbury corpora. Copyright © 2006 John Wiley & Sons, Ltd.     

Forward–backward analysis of RFID-enabled supply chain using fuzzy cognitive map and genetic algorithm

Supply chain is a non-deterministic system in which uncontrollable external states with probabilistic behaviors (e.g., machine failure rate) influence on internal states (e.g., inventory level) significantly through complex causal relationships. Thanks to Radio frequency identification (RFID) technology, real time monitoring of the states is now possible. The current research on processing RFID data is, however, limited to statistical information. The goal of this research is to mine bidirectional cause-effect knowledge from the state data. In detail, fuzzy cognitive map (FCM) model of supply chain is developed. By using genetic algorithm, the weight matrix of the FCM model is discovered with the past state data, and forward (what-if) analysis is performed. Also, when sudden change in a certain state is detected, its cause is sought from the past state data throughout backward analysis. Simulation based experiments are provided to show the performance of the proposed forward–backward analysis methodology.     

A genetic algorithm and a particle swarm optimizer hybridized with Nelder–Mead simplex search

This paper integrates Nelder–Mead simplex search method (NM) with genetic algorithm (GA) and particle swarm optimization (PSO), respectively, in an attempt to locate the global optimal solutions for the nonlinear continuous variable functions mainly focusing on response surface methodology (RSM). Both the hybrid NM–GA and NM–PSO algorithms incorporate concepts from the NM, GA or PSO, which are readily to implement in practice and the computation of functional derivatives is not necessary. The hybrid methods were first illustrated through four test functions from the RSM literature and were compared with original NM, GA and PSO algorithms. In each test scheme, the effectiveness, efficiency and robustness of these methods were evaluated via associated performance statistics, and the proposed hybrid approaches prove to be very suitable for solving the optimization problems of RSM-type. The hybrid methods were then tested by ten difficult nonlinear continuous functions and were compared with the best known heuristics in the literature. The results show that both hybrid algorithms were able to reach the global optimum in all runs within a comparably computational expense.     

The experimental study of the Bi–Sn, Bi–Zn and Bi–Sn–Zn systems

The binary Bi–Sn was studied by means of SEM (Scanning Electron Microscopy)/EDS (Energy-Dispersive solid state Spectrometry), DTA (Differential Thermal Analysis)/DSC (Differential Scanning Calorimetry) and RT-XRD (Room Temperature X-Ray Diffraction) in order to clarify discrepancies concerning the Bi reported solubility in (Sn). It was found that (Sn) dissolves approximately 10 wt% of Bi at the eutectic temperature.

The experimental effort for the Bi–Zn system was limited to the investigation of the discrepancies concerning the solubility limit of Zn in (Bi) and the solubility of Bi in (Zn). Results indicate that the solubility of both elements in the respective solid solution is approximately 0.3 wt% at 200 C.

Three different features were studied within the Bi–Sn–Zn system. Although there are enough data to establish the liquid miscibility gap occurring in the phase diagram of binary Bi–Zn, no data could be found for the ternary. Samples belonging to the isopleths with w(Bi) 10% and w(Sn) 5%, 13% and 19% were measured by DTA/DSC. The aim was to characterize the miscibility gap in the liquid phase. Samples belonging to the isopleths with w(Sn) 40%, 58%, 77/81% and w(Zn) 12% were also measured by DTA/DSC to complement the study of Bi–Sn–Zn. Solubilities in the solid terminal solutions were determined by SEM/EDS. Samples were also analyzed by RT-XRD and HT-XRD (High Temperature X-Ray Diffraction) confirming the DTA/DSC results for solid state phase equilibria.     

Thermodynamic assessments of the Ni–Pt and Al–Ni–Pt systems

The Ni–Pt system is assessed using the CALPHAD method. The four fcc-based phases, i.e. disordered solid solution phase, Ni₃Pt–L1₂, NiPt–L1₀ and NiPt₃–L1₂, are described by a four-sublattice model. The calculated thermodynamic properties and order/disorder phase transformations are in good agreement with the experimental data. In order to facilitate the assessment, first-principles pseudopotential calculations are also performed to calculate the enthalpy of formation at 0 K, and comparison with the assessed values is discussed. By combining the assessments of Al–Ni and Al–Pt, the Al–Ni–Pt ternary system is assessed within a narrow temperature range, focusing on the fcc-based phases and their phase equilibria with B2 phase.     

State space approach to behavioral systems theory: the Dirac–Bergmann algorithm

This paper develops an approach to behavioral systems theory in which a state space representation of behaviors is utilised. This representation is a first order hybrid representation of behaviors called pencil representation. An algorithm well known after Dirac and Bergmann (DB) is shown to be central in obtaining a constraint free and observable (CFO) state space representation of a behavior. Results and criteria for asymptotic stability, controllability, inclusions and Markovianity of behaviors are derived in terms of the matrices of this representation which involve linear algebraic processes in their computation.