Index of critical points in rational l-approximation

This article is concerned with the l²-approximation of a given transfer function f by a rational one whose order is prescribed. We show that the sum of the indices of the critical points of the criterion is generically equal to 1, and in particular does not depend on f.     

最大重迭对称性分子轨道和分子几何参数计算

建立了AMl级别的最大重迭对称性分子轨道计算方案(MOSMO)。采用通常的半经验分子轨道方法AMl级别中完全相同的参数，计算了各种分子的几何参数等。所得计算结果与实验值及HF／6-31G*从头算方法计算结果相符，说明提出的计算方案是可行的。同时，由于提出的计算方案过程简单，更易推广使用到从头算方法难以解决的大分子体系和超分子体系的结构和性质研究。     

Step response classification for model-based autotuning via polygonal curve approximation

A model-based autotuning method consists of an identification and a regulator tuning phase. To achieve satisfactory performance and robustness, it is advisable that both phases be tailored a priori to the characteristics of the observed process dynamics. Such characteristics include, but are not limited to, the model structure. For example, overdamped and underdamped models with the same pole-zero structure are parametrised and controlled in different ways. Step response data, that are typically used for the identification phase in the autotuning context, can also be pre-processed to reveal those characteristics. This paper presents a step response classification method suitable for the above purpose. The method is based on a polygonal curve approximation technique for data pre-processing, followed by a neural network classifier. Only normalised I/O data are employed, so that the neural network can be trained off-line with simulated data. Simulation results are reported to show the effectiveness of the proposed classification method in terms of the achievable tuning results.     

Modelling diffusion-controlled kinetics in equilibrium and driven alloys

Summary We introduce a very simple model for thermally activated atomic migration on a lattice, and several techniques to handle it. For thermodynamical systems, the model can be used for simulating decomposition paths taking into account relevant metallurgical features. Close to equilibrium, the simplest mean-field approximation of the model can be linearized with respect to the departure from equilibrium; one then gets a microscopic interpretation of classical phenomenological coefficients, such as mobility, interfacial transfer coefficient, rate constants for the coupled relaxation of concentration and order fields. Further away from the equilibrium, the nonlinearities can be taken into account in a consistent way. For driven alloys, i.e. alloys submitted to external forcing, forced atomic migration is added to the model and new features emerge: the model is supported by several experimental results some of which confirmed its predictions a posteriori.     

强激光大气传输热晕方程的积分表示

基于菲涅耳 基尔霍夫近似，运用格林函数方法导出了热晕方程的积分表达式，并以连续波(CW)稳态热晕为例进行了数值计算和讨论，结果表明我们所采用的方法是可行的。众所周知的菲涅耳 基尔霍夫衍射积分则是我们所得积分表达的一个特例。     

Development and implementation of a NURBS curve motion interpolator

This paper deals with the issues of development and implementation of a real-time NURBS interpolator for a six-axis robot. Using an open-architecture controller system as a testbed, a real-time NURBS curve interpolator was developed, implemented and tested. Sample runs were conducted with the resulting trajectories measured in real-time during robot motion. The resulting trajectories are analyzed, discussed and compared with those from a commonly used point-to-point approximation technique. The real-time NURBS curve interpolator's feasibility, advantages and related issues are also discussed.     

An actor-critic algorithm for constrained Markov decision processes

An actor-critic type reinforcement learning algorithm is proposed and analyzed for constrained controlled Markov decision processes. The analysis uses multiscale stochastic approximation theory and the envelope theorem' of mathematical economics.     

Best analytic approximation of rational functions of degree 2: Symmetrization of formulae of N. J. Young

Formulae, explicitly symmetric in the roots of the denominator, are derived for the best approximation to a rational function of degree 2 by an analytic function and by a function with at most one pole.     

Deterministic learning of completely resonant nonlinear wave systems with Dirichlet boundary conditions

In this paper, we investigate the approximation of completely resonant nonlinear wave systems via deterministic learning. The plants are distributed parameter systems (DPS) describing homogeneous and isotropic elastic vibrating strings with fixed endpoints. The purpose of the paper is to approximate the infinite-dimensional dynamics, rather than the parameters of the wave systems. To solve the problem, the wave systems are first transformed into finite-dimensional dynamical systems described by ordinary differential equation (ODE). The properties of the finite-dimensional systems, including the convergence of the solution, as well as the dominance of partial system dynamics according to point-wise measurements, are analyzed. Based on the properties, second, by using the deterministic learning algorithm, an approximately accurate neural network (NN) approximation of the the finite-dimensional system dynamics is achieved in a local region along the recurrent trajectories. Simulation studies are included to demonstrate the effectiveness of the proposed approach.     

Thermodynamics-inspired inverse halftoning viamultiple halftone images

Based on an analogy between thermodynamics and Bayesian inference,inverse halftoning was formulated using multiple halftone images based on Bayesian inference using the maximizer of the posterior marginal(MPM) estimate.Applying Monte Carlo simulation to a set of snapshots of the Q-Ising model,it was demonstrated that optimal performance is achieved around the Bayes-optimal condition within statistical uncertainty and that the performance of the Bayes-optimal solution is superior to that of the maximum-a-posteriori(MAP) estimation which is a deterministic limit of the MPM estimate.These properties were qualitatively confirmed by the mean-field theory using an infinite-range model established in statistical mechanics.Additionally,a practical and useful method was constructed using the statistical mechanical iterative method via the Bethe approximation.Numerical simulations for a 256-grayscale standard image show that Bethe approximation works as good as the MPM estimation if the parameters are set appropriately.