用Mathematica求解Runge—Kutta法的稳定域

提出了一种研究高阶Ｒｎｇｅ－Ｋｕｔｔａ法及其嵌套方法的稳定域。该方法简便,直观,并可方便地应用于其它数值积分法。利用计算机代数系统Ｍａｔｈｅｍａｔｉｃａ,给出了一些常用高阶ＲＫ法,嵌套ＲＫ法的稳定域及其在复平面的图形表示,所得结果为月球探测器轨道设计等实际工程计算中自适应积分器的选择提供了重要的依据。     

一类并行多步Runge－Kutta预校算法

一类并行多步Ｒｕｎｇｅ－Ｋｕｔｔａ预校算法李寿佛，甘四清（湘潭大学数学系）ＡＣＬＡＳＳＯＦＰＡＲＡＬＬＥＬＭＵＬＴＩＳＴＥＰＲＵＮＧＥ－ＫＵＴＴＡＰＲＥＤＩＣＴＯＲ－ＣＯＲＲＥＣＴＯＲＡＬＧＯＲＩＴＨＭＳ￥ＬｉＳｈｏｕ－ｆｏ；ＧａｎＳｉ－ｑｉｎｇ（Ｄ...     

并行显式Runge－Kutta公式的实现

本文讨论并行显式Ｒｕｎｇｅ－Ｋｕｔｔａ公式在多处理机系统上的实现方法，并且给出实现的加速比与常微分方程右端函数复杂性的关系曲线。     

多步Runge-Kutta方法的PDIRK实现

１．引言考虑Ｎ维刚性常微分方程的初值问题其中ｆ是充分光滑的非线性函数,由于问题（１）为刚性问题,所以仅有隐式方法能用于求解该类问题．隐式Ｒｕｎｇｅ－Ｋｕｔｔａ方法和隐式线性多步法是其中广泛用于求解形如（１）的方法,但这两种方法都具有各自的缺点：隐式线性多步法在方法的阶升高的时候不能保持很好的稳定性（Ｗｉｄｌｕｎｄ证明了所有Ａ稳定的这类方法的阶都不超过２）,而ｓ级隐式Ｒｕｎｇｅ－Ｋｕｔｔａ方法虽然能够将较高的方法阶和稳定性结合起来,却需要更多的计算量,在每个积分步中,都需要求解一个ｓＮ维的非线性的…     

计算微分代数系统的实时仿真算法

§１．引言 对于由微分代数方程所表示的动力系统的数值算法,针对微分代数方程的一些特殊形式已经构造了一些有效算法如文献[1]-［４］．这些数值算法大部分都是基于常微分方程的一些隐式公式如隐式Ｒｕｎｇｅ－Ｋｕｔｔａ方法,向后微分公式（ＢＤＦ）等,因此这些算法都是非实时仿真算法．如果我们直接用求解常微分方程的显式公式如显式 Ｒｕｎｇｅ－Ｋｕｔｔａ方法,显式线性多步法等,虽然满足了实时仿真算法的一些特点,但是这些数值公式对微分代数方程的求解不甚理想．由于一个实时仿真算法具有实时性、周期性、可靠性等特性要求,因…     

计算机仿真建模方法（二）

本讲给出两种建模方法的设计思想，作为这些思想应用的例子，介绍了Ａｄａｍｓ方法和ＲｕｎｇｅＫｕｔｔａ方法。     

求解非线性悬梁方程行波解的变分算法Mountain Pass算法

§１．引言 经典的求解微分方程初一边值问题的算法，无不要求我们事先对解的某些性质有所了解．例如利用Ｒｕｎｇｅ－Ｋｕｔｔａ法解四阶常微分方程，我们至少需要知道解及其１—３阶导数的初值；又如广义牛顿法则对于初始点的选取有较高的要求，等等．如果事先对所求之解没有足够的了解，就给求解一般（特别是非线性）问题带来困难． １９７３年由 Ａｍｂｒｏｓｅｔｔｉ和 Ｒａｂｉｎｏｗｉｔｚ提出的 Ｍｏｕｎｔａｉｎ Ｐａｓｓ理论（一译“爬山理论”，又译“山径理论”）现己发展成为讨论非线性泛函临界值问题的一个重要方法之一．其几…     

高倍速光驱全景曝光

第一篇认识高倍速ＣＤ－ＲＯＭＣＤ－ＲＯＭ是ＤＩＹｅｒ目前最主要和最常用的光驱设备,其主要的性能指标之一是数据传输率,也就是每秒钟所能传送的最大字节数自１９８２年第一台ＣＤ－ＲＯＭ驱动器面世以来,ＣＤ－ＲＯＭ的数据传输率已经成为其更新换代的标志。第一代ＣＤ－ＲＯＭ驱动器为了兼容ＣＤ－ＤＡ红皮书每秒传送７．３５Ｋ个音频数据帧的要求,其数据传输率被设计为１５０ＫＢ／Ｓ。这样的数据传输率显然太慢了,很快出现了数据传输率为３００ＫＢ／Ｓ的光驱。对ＣＤ-ＲＯＭ光驱而言,数据传输率是以１５０ＫＢ／Ｓ为基准成倍…     

PLC在自动磨口机上的应用

介绍韩国金星ＭＡＳＴＥＲ－Ｋ系列可编程控制器在自动磨口机上的应用及其系统组成与程序设计。该机稳定可靠，功能强，实现了化纤高速纺筒管端面磨口的自动加工。     

一种评价2—DMesh网络性能的方法

本文提出了一种评价２－ＤＭｅｓｈ性能的方法－消息流量法，并且利用这种方法对切换机制为Ｓｔｏｒ－ａｎｄ－Ｆｏｒｗａｒｄ，路由算法分别为ＡＲ和ＤＯＲ时间的２－ＤＭｅｓｈ性能进行了分析，最后给出了分析和模拟的比较结果。     

A convex programming with nested constraints on the amount of resources

This paper investigates the resource allocation problem of maximizing a strictly concave objective function under nested constraints on a weighted amount of resources. The resources are distributed in a multi-dimensional space and the distribution gives a planner some reward. The constraints on the resources are set in such a way that a weighted amount of resources is limited in each level of subspace as well as in the whole space. We call such constraints nested. The purpose of this paper is to devise efficient methods for an optimal distribution of resources under the constraints. For the concave maximization problem, first we derive necessary and sufficient conditions for an optimal solution and, secondly, propose two methods to solve the problem. Both methods manipulate the so-called Lagrangian multipliers and make a sequence of feasible solutions so as to satisfy all the necessary and sufficient conditions. Numerical examination confirms that the proposed methods perform better than some well-known methods of nonlinear programming in terms of computational time.     

复杂非紧密嵌套循环变换在并行编译中的应用

在并行编译中,循环变换是开发程序并行度的主要方法,但存在复杂控制流的非紧密嵌套循环往往无法得到有效的并行化。文章结合分析Benchmark和实现自动并行化系统AFT中复杂非紧密嵌套循环变换的经验,给出复杂非紧密嵌套循环变换的特点及其在并行编译中的应用。     

Termination of Nested and Mutually Recursive Algorithms

This paper deals with automated termination analysis for functional programs. Previously developed methods for automated termination proofs of functional programs often fail for algorithms with nested recursion and they cannot handle algorithms with mutual recursion.We show that termination proofs for nested and mutually recursive algorithms can be performed without having to prove the correctness of the algorithms simultaneously. Using this result, nested and mutually recursive algorithms do no longer constitute a special problem and the existing methods for automated termination analysis can be extended to nested and mutual recursion in a straightforward way. We give some examples of algorithms whose termination can now be proved automatically (including well-known challenge problems such as McCarthys f_91 function).     

Surrogate modeling of impedance matching transformers by means of variable‐fidelity electromagnetic simulations and nested cokriging

Accurate performance evaluation of microwave components can be carried out using full‐wave electromagnetic (EM) simulation tools, routinely employed for circuit verification but also in the design process itself. Unfortunately, the computational cost of EM‐driven design may be high. This is especially pertinent to tasks entailing considerable number of simulations (eg, parametric optimization, statistical analysis). A possible way of alleviating these difficulties is utilization of fast replacement models, also referred to as surrogates. Notwithstanding, conventional modeling methods exhibit serious limitations when it comes to handling microwave components. The principal challenges include large number of geometry and material parameters, highly nonlinear characteristics, as well as the necessity of covering wide ranges of operating conditions. The latter is mandatory from the point of view of the surrogate model utility. This article presents a novel modeling approach that incorporates variable‐fidelity EM simulations into the recently reported nested kriging framework. A combination of domain confinement due to nested kriging, and low‐/high‐fidelity EM data blending through cokriging, enables the construction of reliable surrogates at a fraction of cost required by single‐fidelity nested kriging. Our technique is validated using a three‐section miniaturized impedance matching transformer with its surrogate model rendered over wide range of operating frequencies. Comprehensive benchmarking demonstrates superiority of the proposed method over both conventional models and nested kriging.     

Macroergonomics and patient safety: The impact of levels on theory, measurement, analysis and intervention in patient safety research

The study and practice of patient safety has seen a surge over the last 10 years. New resident training and staffing policies, health information technologies, error reporting systems, team models of care, training methods, patient involvement, information handoff strategies, just cultures, and many other interventions have been mandated or attempted to improve the safety of patient care. While some of these interventions focus on individual providers and others focus on organization-level changes, little, if any, patient safety research has purposefully sought to understand how variables at different levels, such as the provider level or organization level, interact to impact patient safety outcomes such as errors, adverse drug events, or patient harm. Looking at relationships across levels is important because adverse events might be related to variables at different levels; consider that adverse events may be nested within patients, patients nested within nurses and physicians, nurses and physicians nested within shifts, shifts nested within hospital units, and so forth. Because these nested levels exist, they may exert as yet untested influence on the levels below. In this paper the impact of levels on theory, measurement, analysis and intervention in patient safety research is discussed.     

Limitations of lower bound methods for deterministic nested word automata

Finite automata operating on nested words were introduced by Alur and Madhusudan in 2006. While nested word automata retain many of the desirable properties of ordinary finite automata, there is no known efficient minimization algorithm for deterministic nested word automata and, interestingly, state complexity bounds for nested word automata turn out to differ significantly from the corresponding bounds for ordinary finite automata. Consequently lower bounds for the state complexity of nested word languages need to rely on fooling set type techniques. We discuss limitations of the techniques and show that, even in the deterministic case, the bounds given by the lower bound methods may be arbitrarily far away from the actual state complexity of the nested word language.     

Sampling Archimedean copulas

The challenge of efficiently sampling exchangeable and nested Archimedean copulas is addressed. Specific focus is put on large dimensions, where methods involving generator derivatives are not applicable. Additionally, new conditions under which Archimedean copulas can be mixed to construct nested Archimedean copulas are presented. Moreover, for some Archimedean families, direct sampling algorithms are given. For other families, sampling algorithms based on numerical inversion of Laplace transforms are suggested. For this purpose, the Fixed Talbot, Gaver Stehfest, Gaver Wynn rho, and Laguerre series algorithm are compared in terms of precision and runtime. Examples are given, including both exchangeable and nested Archimedean copulas.     

COMPILE TIME PARTITIONING OF NESTED LOOP ITERATION SPACES WITH NON-UNIFORM DEPENDENCES*

In this paper we address the problem of partitioning nested loops with non-uniform (irregular) dependence vectors. Parallelizing and partitioning of nested loops requires efficient inter-iteration dependence analysis. Although many methods exist for nested loop partitioning, most of these perform poorly when parallelizing nested loops with irregular dependences. Unlike the case of nested loops with uniform dependences these will have a complicated dependence pattern which forms a non-uniform dependence vector set. We apply the results of classical convex theory and principles of linear programming to iteration spaces and show the correspondence between minimum dependence distance computation and iteration space tiling. Cross-iteration dependences are analyzed by forming an Integer Dependence Convex Hull (IDCH). Every integer point in this IDCH corresponds to a dependence vector in the iteration space of the nested loops. A simple way to compute minimum dependence distances from the dependence distance vectors of the extreme points of the IDCH is presented. Using these minimum dependence distances the iteration space can be tiled. Iterations within a tile can be executed in parallel and the different tiles can then be executed with proper synchronization. We demonstrate that our technique gives much better speedup and extracts more parallelism than the existing techniques.     

中文医疗文本中的嵌套实体识别方法

实体识别是信息抽取的关键技术. 相较于普通文本, 中文医疗文本的实体识别任务往往面对大量的嵌套实体. 以往识别实体的方法往往忽视了医疗文本本身所特有的实体嵌套规则而直接采用序列标注方法, 为此, 提出一种融合实体嵌套规则的中文实体识别方法. 所提方法在训练过程中将实体的识别任务转化为实体的边界识别与边界首尾关系识别的联合训练任务, 在解码过程中结合从实际医疗文本中所总结出来的实体嵌套规则对解码结果进行过滤, 从而使得识别结果能够符合实际文本中内外层实体嵌套组合的组成规律. 在公开的医疗文本实体识别的实验上取得良好的效果. 数据集上的实验表明, 所提方法在嵌套类型实体识别性能上显著优于已有的方法, 在整体准确率方面比最先进的方法提高0.5%.     

Automatic construction of systems of distributed components from nested Petri nets models

Multi-level multi-agent systems (MASs) with dynamic structure are widely used in solving important applied problems in telecommunication, transportation, social, and other systems. Therefore, ensuring correct behavior of such systems is an actual and important task. One of the most error-prone stages of system development in the framework of model-oriented approach is the implementation stage, in the course of which a program code is constructed based on the model developed. This paper presents an algorithm for automated translation of MAS models represented as nested Petri nets into systems of distributed components. Nested Petri nets are the extension of Petri nets in the framework of the nets-within-nets approach, which assumes that tokens in a Petri net may themselves be Petri nets, possess autonomous behavior, and interact with other tokens of the net. This makes it possible to model MASs with dynamic structure in a natural way. The translation presented in this paper preserves distribution level and important behavioral properties (safety, liveness, and conditional liveness) of the original model and ensures fairness of the target system execution. The use of such translation makes it possible to automate construction of distributed MASs by models of nested Petri nets. As a test example, translation of nested Petri nets into systems of distributed components was implemented on the basis of the EJB component technology.