Two hybrid algorithms for solving split equilibrium problems

The paper considers split equilibrium problems (EPs) in Hilbert spaces and proposes two hybrid algorithms for finding their solution approximations. Three methods including the diagonal subgradient method, the projection method and the proximal method have been used to design the algorithms. Using the diagonal subgradient method for EPs has allowed us to reduce complex computations on bifunctions and feasible sets. The first algorithm is designed with two projections on feasible set and with the prior knowledge of operator norm while the second algorithm is simpler in computations where only one projection on feasible set needs to be implemented and the information of operator norm is not necessary to construct solution approximations. The strongly convergent theorems are established under suitable assumptions imposed on equilibrium bifunctions. The computational performance of the proposed algorithms over existing methods is also illustrated by several preliminary numerical experiments.     

Vector-channel lattice filters for the delta operator: Complete derivation

The numerical difficulties associated with high sampling rates have been the main motivation for the recent interest in application of delta-operator formulation in adaptive identification and control techniques, as an alternative to the traditional shift operator. In this article, the derivation of the vector-channel lattice algorithm for least-squares parameter estimation of an input/output model based on the delta operator is presented. Since the vector-channel formulation is a generalization of the standard multichannel forms, results presented here apply to the multichannel lattices as a special case. In addition to the basic derivation, algorithms for residual errors and autoregressive coefficients, a simple example, and issues regarding implementation are discussed. Editor: H. Stalford     

Identification of Continuous-Time ARX Models From Irregularly Sampled Data

The problem of estimating the parameters in a continuous-time ARX process from unevenly sampled data is studied. A solution where the differentiation operator is replaced by a difference operator is suggested. In the paper, results are given for how the difference operator should be chosen in order to obtain consistent parameter estimates. The proposed method is considerably faster than conventional methods, such as the maximum likelihood method. The Crameacuter-Rao bound for estimation of the parameters is computed. In the derivation, the Slepian-Bangs formula is used together with a state-space framework, resulting in a closed form expression for the Crameacuter-Rao bound. Numerical studies indicate that the Crameacuter-Rao bound is reached by the proposed method     

The use of matrix visualization in algorithmic design

The use of matrix visualization in the design and development of numerical algorithms for supercomputers is discussed. Using color computer graphics, numerical analysts can gain new insights into algorithm behavior, which can then be used to design more efficient (parallel) numerical algorithms. The application of a matrix visualization tool, MatVu, in the design of algorithms from numerical linear algebra is the primary focus. Specific examples include the derivation of optimal preconditioning matrices for a conjugate gradient method, the design of parallel hybrid algorithms for solving the symmetric eigenvalue problem, the effects of operator splitting in the solution of incompressible Navier-Stokes equations, and the monitoring of Jacobian matrices associated with the application of Newton's method to a corresponding nonlinear system of equations.     

Iterative automatic test generation method for telecommunication protocols

Standardized languages used for protocol specification provide an excellent basis for both automatic and manual test generation. Test generation is composed of two steps, the derivation of test cases from the specification, and the selection of the test cases to be included in the final test suite in order to reduce its execution time. This article proposes a new method that aims to decrease the total number of test cases generated automatically by a test derivation algorithm and at the same time to reduce the computation requirements for the test selection procedure. It creates an iteration cycle on the model of evolutionary algorithms, where the test derivation and selection are done simultaneously. In each cycle first a “small” test suite is derived then optimized, evaluated and finally compared to the best suite so far. It is kept as the best suite, if it is found better according to some well-defined evaluation criteria and test suite metrics. This iteration condition is based on the test selection criteria. The article presents an experiment where iterative algorithms are compared to two simple test derivation methods from different aspects.     

New methods for picture reconstruction: recursive and causal techniques

The methods proposed by Kashyap and Mittal [1], [2] for the reconstruction of pictures from projections are reformulated under a regression model. These reinterpretations are based on least-squares and Bayesian formulations of a statistical linear model and lead to the derivation of recursive and causal algorithms which are more efficient. Experimental results with simulation of the filters are also presented.     

用网格实现交叉操作的遗传算法

遗传算法可以看成是在某个空间求最大值的搜索技术。本文从理论上分析了在搜索技术中,用格点法比胡机法好,并用格点理论（佳点是格点的一种）设计了遗传交叉算子。模拟结果显示,与传统的胡机法实现交叉操作的遗传算法相比,本文算法不仅在效率、精度上有所提高,而且克服了“早熟”现象。     

Numerical techniques for lattice QCD in the ?-regime

In lattice QCD it is possible, in principle, to determine the parameters in the effective chiral Lagrangian (including weak interaction couplings) by performing numerical simulations in the ?-regime, i.e. at quark masses where the physical extent of the lattice is much smaller than the Compton wave length of the pion. The use of a formulation of the lattice theory that preserves chiral symmetry is attractive in this context, but the numerical implementation of any such approach requires special care in this kinematical situation due to the presence of some very low eigenvalues of the Dirac operator. We discuss a set of techniques (low-mode preconditioning and adapted-precision algorithms in particular) that make such computations numerically safe and more efficient by a large factor.     

Improved coupling of time integration and hydrodynamic interaction in particle suspensions using the lattice Boltzmann and discrete element methods

This paper introduces improvements to the simulation of particle suspensions using the lattice Boltzmann method (LBM) and the discrete element method (DEM). First, the benefit of using a two-relaxation-time (TRT) collision operator, instead of the popular Bhatnagar–Gross–Krook (BGK) collision operator, is demonstrated. Second, a modified solid weighting function for the partially saturated method (PSM) for fluid–solid interaction is defined and tested. Results are presented for a range of flow configurations, including sphere packs, duct flows, and settling spheres, with good accuracy and convergence observed. Past research has shown that the drag, and consequently permeability, predictions of the LBM exhibit viscosity-dependence when used with certain boundary conditions such as bounce-back or interpolated bounce-back, and this is most pronounced when the BGK collision operator is employed. The improvements presented here result in a range of computational viscosities, and therefore relaxation parameters, within which drag and permeability predictions remain invariant. This allows for greater flexibility in using the relaxation parameter to adjust the LBM timestep, which can subsequently improve synchronisation with the time integration of the DEM. This has significant implications for the simulation of large-scale suspension phenomena, where the limits of computational hardware persistently constrain the resolution of the LBM lattice.     

A Network Flow Algorithm for Reconstructing Binary Images from Continuous X-rays

Tomography is a powerful technique to obtain accurate images of the interior of an object in a nondestructive way. Conventional reconstruction algorithms, such as filtered backprojection, require many projections to obtain high quality reconstructions. If the object of interest is known in advance to consist of only a few different materials, corresponding to known image intensities, the use of this prior knowledge in the reconstruction procedure can dramatically reduce the number of required projections. In previous work we proposed a network flow algorithm for reconstructing a binary image defined on a lattice from its projections. In this paper we propose a new algorithm for the reconstruction of binary images that do not have an intrinsic lattice structure and are defined on a continuous domain, from a small number of their projections. Our algorithm relies on the fact that the problem of reconstructing an image from only two projections can be formulated as a network flow problem in a graph. We derive this formulation for parallel beam and fan beam tomography and show how it can be used to compute binary reconstructions from more than two projections. Our algorithm is capable of computing high quality reconstructions from very few projections. We evaluate its performance on both simulated and real experimental projection data and compare it to other reconstruction algorithms.

On reduction of computational cost of imitation Monte Carlo algorithms for modeling rarefied gas flows

This article describes Monte Carlo methods and algorithms for the Boltzmann equation for rarefied gases problems in the case of large-scale flow areas. We consider imitation or continuous-time Monte Carlo methods where frequencies of interactions of pairs of particles depend on the difference of the coordinates of particles. The question about reduction of computational costs of algorithms is examined using the specificity of the problem. First, algorithms of an approximated method are constructed, analyzed, and implemented. This method is obtained by using splitting (over groups of particles) of the operator in master equations system. Second, we investigate the fictitious collisions technique, where the upper bound for the number of interacting pairs is specified. The plane Poiseuille flow (in the field of external forces) problem, the heat transfer problem, and the temperature discontinuity propagation problem are numerically solved using the developed algorithms. Asymptotical estimates of the computational costs are confirmed with the data of the computational processes and the comparative properties of the later are fixed. The suggested algorithms of the method with splitting allow parallelization of a certain type.     

Visual routines for eye location using learning and evolution

Eye location is used as a test bed for developing navigation routines implemented as visual routines within the framework of adaptive behavior-based AI. The adaptive eye location approach seeks first where salient objects are, and then what their identity is. Specifically, eye location involves: 1) the derivation of the saliency attention map, and 2) the possible classification of salient locations as eve regions. The saliency (“where”) map is derived using a consensus between navigation routines encoded as finite-state automata exploring the facial landscape and evolved using genetic algorithms (GAs). The classification (“what”) stage is concerned with the optimal selection of features, and the derivation of decision trees, using GAs, to possibly classify salient locations as eyes. The experimental results, using facial image data, show the feasibility of our method, and suggest a novel approach for the adaptive development of task-driven active perception and navigational mechanisms     

Recursive least squares lattice algorithms--A geometrical approach

Several time-recursive least squares algorithms have been developed in recent years. In this paper a geometrical formalism is defined which utilizes a nested family of metric spaces indexed by the data time interval. This approach leads to a simplified derivation of the so-called recursive least squares lattice algorithms (recursive in time and order). In particular, it is found that the resulting structure provides a single framework which encompasses an entire family of fairly complex algorithms, as well as providing geometrical insight into their behavior.     

A D-step predictor in lattice and ladder form

We use the orthogonalizing property of the two-multiplier linear prediction lattice filter to construct ad-step ahead predictor in lattice form. The predictor generatesd-step forward and backward residuals in a recursive way and possesses most of the interesting properties of the basic one-step prediction lattice filter. An exact solution is presented first assuming a stationary observation process, using orthogonal projections in Hilbert space. Two adaptive implementations are also proposed for the case where the statistics of the signal process are unknown or time varying: a gradient method and a recursive least-squares scheme. Finally, we show how to construct an adaptived-step ahead predictor by adding a ladder part to thed-step lattice structure.     

Multi-objective optimization with fuzzy measures and its application to flow-shop scheduling

Most of the research in multi-objective scheduling optimization uses the classical weighted arithmetic mean operator to aggregate the various optimization criteria. However, there are scheduling problems where criteria are considered interact and thus a different operator should be adopted. This paper is devoted to the search of Pareto-optimal solutions in a tri-criterion flow-shop scheduling problem (FSSP) considering the interactions among the objectives. A new hybrid meta-heuristic is proposed to solve the problem which combines a genetic algorithm (GA) for solutions evolution and a reduced variable neighborhood search (RVNS) technique for fast solution improvement. To deal with the interactions among the three criteria the discrete Choquet integral method is adopted as a means to aggregate the criteria in the fitness function of each individual solution. Experimental comparisons (over public available FSSP test instances) with five existing multi-objective evolutionary algorithms (including the well known SPEA2 and NSGAII algorithms as well as the recently published L-NSGA algorithm) showed a superior performance for the developed approach in terms of diversity and domination of solutions.     

毕达哥拉斯模糊交叉影响集成算子及其决策应用

定义毕达哥拉斯模糊数的交叉影响加法、数乘、乘法及幂运算,提出毕达哥拉斯模糊交叉影响加权平均算子(PFIWA)、毕达哥拉斯模糊交叉影响有序加权平均算子(PFIOWA)、毕达哥拉斯模糊交叉影响加权几何算子(PFIWG)及毕达哥拉斯模糊交叉影响有序加权几何算子(PFIOWG),推导出它们的数学表达式,并研究其性质.提出基于毕达哥拉斯模糊交叉影响集成算子的决策方法,并通过决策实例验证所提出方法的稳定性和有效性.     

A unified operator splitting approach for multi-scale fluid–particle coupling in the lattice Boltzmann method

A unified framework to derive discrete time-marching schemes for the coupling of immersed solid and elastic objects to the lattice Boltzmann method is presented. Based on operator splitting for the discrete Boltzmann equation, second-order time-accurate schemes for the immersed boundary method, viscous force coupling and external boundary force are derived. Furthermore, a modified formulation of the external boundary force is introduced that leads to a more accurate no-slip boundary condition. The derivation also reveals that the coupling methods can be cast into a unified form, and that the immersed boundary method can be interpreted as the limit of force coupling for vanishing particle mass. In practice, the ratio between fluid and particle mass determines the strength of the force transfer in the coupling. The integration schemes formally improve the accuracy of first-order algorithms that are commonly employed when coupling immersed objects to a lattice Boltzmann fluid. It is anticipated that they will also lead to superior long-time stability in simulations of complex fluids with multiple scales.     

Computing generating sets of lattice ideals and Markov bases of lattices

In this article, we present an algorithm for computing generating sets of lattice ideals or equivalently for computing Markov bases of lattices. Generating sets of lattice ideals and Markov bases of lattices are essentially equivalent concepts. In contrast to other existing methods, the algorithm in this article computes with projections of lattices. This algorithm clearly outperforms other algorithms in our computational experience. Two areas of application for generating sets of lattice ideals and Markov bases lattices are algebraic statistics and integer programming.     

A characterization of attribute evaluation in passes

Summary This paper describes the evaluation of semantic attributes in a bounded number of passes from left-to-right and/or from right-to-left over the derivation tree of a program. Evaluation strategies where different instances of the same attribute in any derivation tree are restricted to be evaluated in one pass, with for every derivation tree the same pass number, are referred to as simple multi-pass whereas the unrestricted pass-oriented strategies are referred to as pure multi-pass.A graph theoretic characterization is given, showing in which cases an attribute grammar meets the simple multi-pass requirements and what are the minimal pass numbers of its attributes for a given sequence of pass directions. For the special cases where only left-to-right passes are made or where left-to-right and right-to-left passes strictly alternate, new algorithms are developed that associate minimal pass numbers with attributes and indicate in case of failure the attributes that cause the rejection of the grammar. Mixing of a simple multi-pass strategy with other evaluation strategies, in case the grammar is not simple multi-pass, is discussed.     

Memetic algorithms for reconstruction of binary images on triangular grids with 3 and 6 projections

When an image is given with only some measurable data, e.g., projections, the most important task is to reconstruct it, i.e., to find an image that provides the measured data. These tomographic problems are frequently used in the theory and applications of image processing. In this paper, memetic algorithms are investigated on triangular grids for the reconstruction of binary images using their three and six direction projections. The algorithm generates an initial population using the network flow algorithm for two of the input projections. The reconstructed images evolve towards an optimal solution or close to the optimal solution, by using crossover operators and guided mutation operators. The quality of the images is improved by using switching components and compactness operator.