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2011 13th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing最新文献

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Long Integers and Polynomial Evaluation with Estrin's Scheme 用Estrin格式求长整数和多项式
Marco Bodrato, A. Zanoni
In this paper the problem of univariate polynomial evaluation is considered. When both polynomial coefficients and the evaluation "point" are integers, unbalanced multiplications (one factor having many more digits than the other one) in classical Ruffini-Horner rule do not let computations completely benefit of sub quadratic methods, like Karatsuba, Toom-Cook and Schonhage-Strassen's. We face this problem by applying an approach originally proposed by Estrin to augment parallelism exploitation in computation. We show that it is also effective in the sequential case, whenever data dimensions grow, e.g. in the long integer case. We add some adjustments to Estrin's proposal obtaining a smoother behavior around corner cases, and to avoid performance degradation when most of the coefficients are zero. This way, a new general algorithm is obtained, improving both theoretical complexity and actual performance. The algorithm itself is very simple, and its use can be usefully extended to evaluation of polynomials on rationals or on polynomials (polynomial composition). Some tests, results and comparisons obtained with PARI/GP are also presented, for both dense and "sparse" polynomials.
本文研究了单变量多项式的求值问题。当多项式系数和评估“点”都是整数时,经典Ruffini-Horner规则中的不平衡乘法(一个因子比另一个因子有更多的数字)不能让计算完全受益于次二次方法,如Karatsuba, Toom-Cook和schonhager - strassen的方法。我们通过应用Estrin最初提出的方法来增强计算中的并行性利用来解决这个问题。我们证明了它在序列情况下也是有效的,当数据维度增长时,例如在长整数情况下。我们对Estrin的建议进行了一些调整,以获得在极端情况下更平滑的行为,并避免在大多数系数为零时性能下降。这样得到了一种新的通用算法,提高了理论复杂度和实际性能。该算法本身非常简单,它的使用可以有效地扩展到对有理数或多项式(多项式复合)的多项式求值。本文还介绍了用PARI/GP对密集多项式和“稀疏”多项式进行的一些测试、结果和比较。
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引用次数: 11
Computational Tools for Mathematical Collaboration 数学协作的计算工具
S. Watt
Research collaboration has always been important and has recently become even more so. I wish therefore to address a topic I believe to require attention now, and that is software support for mathematical collaboration.
研究合作一直都很重要,最近更是如此。因此,我想谈谈我认为现在需要注意的一个主题,那就是对数学协作的软件支持。
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引用次数: 0
Integration of Association Rule Detection with Rule-Based Ontological Support for Product Recommendation 关联规则检测与基于规则的本体支持在产品推荐中的集成
Anita Hejja, R. Buchmann, A. Szekely
Recommender systems can increase the sales by suggesting to users additional products, that were selected by their preferences. Availability of efficient mechanisms for generating the adequate products and for capturing the eligible information are the most important challenges of Web users. The Apriori algorithm is the best-known association rules mining algorithm, whose objective is to find all co-occurrence relationships between data items. In order to obtain a well defined information in an open standard format, we propose, an ontology-based recommender system, which describes the item features in terms of semantic concepts. In this paper, a methodology that combines the Apriori algorithm with a domain-specific ontology is proposed. The proposed model transfers the association rules on custom OWLIM rules, and by using OWLIM semantic repositories the detected associations will become public and can be interconnected with other information from the Internet. In this way, new facts can be deduced, therefore new relationships and rules between product items will be generated.
推荐系统可以通过向用户推荐根据他们的喜好选择的额外产品来增加销售额。是否有有效的机制来生成适当的产品和获取合格的信息是Web用户面临的最重要的挑战。Apriori算法是最著名的关联规则挖掘算法,其目标是发现数据项之间的所有共现关系。为了以开放的标准格式获得定义良好的信息,我们提出了一个基于本体的推荐系统,该系统根据语义概念描述项目特征。本文提出了一种将Apriori算法与特定领域本体相结合的方法。所提出的模型在自定义OWLIM规则上传输关联规则,并且通过使用OWLIM语义存储库,检测到的关联将成为公开的,并且可以与来自Internet的其他信息相互连接。通过这种方式,可以推断出新的事实,从而生成产品项之间的新关系和规则。
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引用次数: 2
Proof Techniques for Synthesis of Sorting Algorithms 排序算法综合的证明技术
I. Dramnesc, T. Jebelean
In the context of constructive synthesis of sorting algorithms, starting from the specification of the problem (input and output conditions), the proof of existence of a sorted tuple is performed inductively and we design, implement, and experiment with different proof techniques: First we use a back-chaining mechanism similar to a Prolog engine for first order logic, in which meta-variables are used for finding the existential witnesses. In order to overcome the search space explosion, we introduce various specific prove-solve methods for the theory of tuples. For instance, the equivalence relation on tuples "have same elements'' can be treated using a normal form based on multisets -- this leads to a very efficient inference rule for rewriting. When reasoning about sorting, we also have an ordering relation between elements. We extend this to an ordering between an element and a tuple, and even between tuples. Ordering relations create specific problems in Prolog style reasoning, because of transitivity and reflexivity. We demonstrate that ordering can be treated very efficiently by decomposing atomic statements into simpler ones (containing only symbols instead of terms), both for goals (backward reasoning) as well as for assumptions (forward reasoning). This leads to an interesting combination of backward and forward inferences which goes beyond and complements Prolog style reasoning. Finally, we develop a solving mechanism for finding sorted tuples, which performs the proof more efficiently, by combining relatively simple inference rules and small searches with goal directed solving rules. The techniques are implemented in the Theorem a system and are able to produce automatically proofs and algorithms for various problems: Insertion Sort, Insertion, Merge Sort, and Merge. Besides the special proof techniques, this work also gives useful hints about finding appropriate induction principles for tuples, as well as for the construction of appropriate collections of properties of tuples which are necessary for reasoning about sorting.
在排序算法的建设性综合背景下,从问题的规范(输入和输出条件)开始,对排序元组的存在性进行归纳性证明,我们设计、实现和实验了不同的证明技术:首先,我们使用类似于一阶逻辑Prolog引擎的后链机制,其中使用元变量来寻找存在性见证。为了克服搜索空间爆炸的问题,我们介绍了元组理论的各种具体的证明求解方法。例如,元组上“具有相同元素”的等价关系可以使用基于多集的标准形式来处理——这导致了非常有效的重写推理规则。在对排序进行推理时,元素之间也有排序关系。我们将其扩展到元素和元组之间的排序,甚至元组之间的排序。由于及物性和反身性,排序关系在Prolog风格的推理中产生了特定的问题。我们证明,通过将原子语句分解为更简单的语句(只包含符号而不是术语),对于目标(向后推理)和假设(向前推理),可以非常有效地处理排序。这导致了向后和向前推理的有趣组合,超越并补充了Prolog风格的推理。最后,我们开发了一种查找排序元组的求解机制,通过将相对简单的推理规则和小搜索与目标导向求解规则相结合,可以更有效地执行证明。这些技术在定理a系统中实现,能够自动生成各种问题的证明和算法:插入排序、插入排序、合并排序和合并。除了特殊的证明技术之外,这项工作还提供了关于为元组找到适当的归纳原则的有用提示,以及对于排序推理所必需的元组属性的适当集合的构造。
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引用次数: 14
An Upper Bound on Checking Test Complexity for Almost All Cographs 几乎所有图检验测试复杂度的上界
O. V. Zubkov, D. Chistikov, A. A. Voronenko
The concept of a checking test is of prime interest to the study of a variant of exact identification problem, in which the learner is given a hint about the unknown object. A graph F is said to be a checking test for a co graph G iff for any other co graph H there exists an edge in F distinguishing G and H, that is, contained in exactly one of the graphs G and H. It is known that for any co graph G there exists a unique irredundant checking test, the number of edges in which is called the checking test complexity of G. We show that almost all co graphs on n vertices have relatively small checking test complexity of O(n log n). Using this result, we obtain an upper bound on the checking test complexity of almost all read-once Boolean functions over the basis of disjunction and parity functions.
检查测试的概念对研究一种精确识别问题的变体具有重要意义,在这种问题中,学习者被给予关于未知物体的提示。图F是一个检查测试有限公司图G敌我识别其他公司图H存在F区分G和H的边缘,也就是说,包含在一个图G和H .众所周知,对于任何公司图G存在一个唯一irredundant检查测试,边的数量,被称为G .检查测试的复杂性,我们表明,几乎所有对n公司图顶点相对较小的检查测试的复杂性O (n log n)。使用这个结果,在析取函数和奇偶函数的基础上,我们得到了几乎所有读一次布尔函数的检验复杂度的上界。
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引用次数: 1
Communication Schemes of a Parallel Fluid Solver for Multi-scale Environmental Simulations 多尺度环境模拟中并行流体求解器的通信方案
J. Frisch, R. Mundani, E. Rank
A lot of different environmental simulations use computational fluid dynamics for detailed airflow computation and pollution transportation. Unfortunately, a multi-scale computational fluid dynamics simulation is very time consuming and computational intensive, as a high geometric discretisation has to be chosen in order to capture all required physical phenomena, so that without any parallelisation strategies, these computations tend to be impossible to perform. In this paper, we will discuss communication schemes using the message passing paradigm implemented in a previously validated fluid simulation code. Advantages and disadvantages of the current implementation will be discussed and improvements will be proposed.
许多不同的环境模拟使用计算流体力学进行详细的气流计算和污染输送。不幸的是,多尺度计算流体动力学模拟非常耗时和计算密集,因为必须选择高几何离散化以捕获所有所需的物理现象,因此如果没有任何并行化策略,这些计算往往无法执行。在本文中,我们将讨论使用在先前验证的流体模拟代码中实现的消息传递范式的通信方案。将讨论当前实施的优点和缺点,并提出改进意见。
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引用次数: 10
Tracking Method for Reparametrized Geometrical Constraint Systems 重参数化几何约束系统的跟踪方法
Rémi Imbach, P. Mathis, P. Schreck
In CAD, constraint solvers allow a user to describe a figure or an object with a set of constraints like distances, angles, tangencies, incidences and so on. Geometric solvers proceed in two stages. First, a symbolic construction plan is provided from the set of constraints. Then, the dimensions of constraints are used in a numerical stage to evaluate the construction plan. However, construction plans can not be easily provided for many problems in 3D. A classic idea consists in removing and adding some constraints in order to make the problem solvable by a geometric method. This leads to a numerical problem in which numerical values for the added constraints have to be computed in order to find the values of the added dimensions that validate the removed dimensions. Finding these values is usually done by sampling which is very time-consuming when there are more than 2 variables to sample. In this paper we address the numerical stage by adapting a path-tracking method. This allows to find several solutions and this method is efficient when the number of values is greater than 2.
在CAD中,约束求解器允许用户用一组约束(如距离、角度、切线、夹角等)来描述图形或对象。几何求解分两个阶段进行。首先,从约束条件出发,给出了象征性的建筑方案。然后,在数值阶段使用约束的尺寸来评估施工方案。然而,在三维环境中,由于存在许多问题,施工方案不容易提供。一个经典的想法是去除或增加一些约束,以便用几何方法解决问题。这导致了一个数值问题,在这个问题中,必须计算添加约束的数值,以便找到验证已删除维度的添加维度的值。找到这些值通常是通过抽样来完成的,当有两个以上的变量要抽样时,这是非常耗时的。在本文中,我们通过采用路径跟踪方法来解决数值阶段。这允许找到多个解,当值的数量大于2时,这种方法是有效的。
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引用次数: 10
A Supervised Learning Process to Elicit Fraud Cases in Online Auction Sites 在线拍卖网站欺诈案例的监督学习过程
Vinicius Almendra, D. Enachescu
Fraud is a recurring phenomenon at online actions sites like eBay. The enormous amount of transaction data public ally available offers a good opportunity for fraud prevention based on learning methods. However, online auction sites usually neither confirm nor deny fraudulent behavior: they simply suspend seller accounts and publicize feedback information supplied by buyers. While some cases receive media attention, most of them are hidden in the site's database. This limits the possibility of developing and testing new learning methods for fraud prevention, due to the scarcity of fraud samples. In order to overcome this limitation, we designed a system based on supervised learning to recognize in the textual comments left by buyers some common statements regarding seller behavior. Combining the type and frequency of those statements with other public ally available data, we can build a set of sellers who can arguably be considered fraudsters. We implemented a prototype of the system and evaluated it using data extracted from a major online auction site.
在eBay这样的在线交易网站上,欺诈是一个反复出现的现象。海量的公开交易数据为基于学习方法的欺诈预防提供了良好的契机。然而,在线拍卖网站通常既不确认也不否认欺诈行为:他们只是暂停卖家账户,并公布买家提供的反馈信息。虽然有些案件受到媒体的关注,但大多数案件都隐藏在网站的数据库中。由于欺诈样本的稀缺性,这限制了开发和测试防止欺诈的新学习方法的可能性。为了克服这一限制,我们设计了一个基于监督学习的系统来识别买家留下的文本评论中关于卖家行为的一些常见陈述。将这些声明的类型和频率与其他公开可用的数据结合起来,我们可以建立一组可以被认为是欺诈者的卖家。我们实现了系统的原型,并使用从一个主要的在线拍卖网站提取的数据对其进行了评估。
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引用次数: 12
Symbol Elimination in Program Analysis 程序分析中的符号消除
Laura Kov´cs
Automatic understanding of the intended meaning of computer programs is a very hard problem, requiring intelligence and reasoning. In this abstract we discuss a new method for program analysis, called symbol elimination. Symbol elimination uses first-order theorem proving techniques to automatically discover non-trivial program properties, such as loop invariants and loop bounds. Moreover, symbol elimination can be used as an alternative to interpolation for software verification.
自动理解计算机程序的意图是一个非常困难的问题,需要智能和推理。本文讨论了一种新的程序分析方法——符号消去法。符号消除使用一阶定理证明技术来自动发现非平凡的程序属性,如循环不变量和循环边界。此外,符号消除可以作为替代插值软件验证。
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引用次数: 0
Enhancing Objects' Autonomy through the Classification of Objects' Interactions 通过对象交互的分类增强对象的自主性
C. Sandru
The starting point of this research was the observation that object oriented classification mostly reflects one particular perspective which is ascribed to all the objects in the system. It was considered that this is an important limitation when trying to add autonomy to the objects in order to progress towards an agent oriented paradigm. In particular, we consider that agents may have the ability of classifying the external world instead of only relying on the classification being imposed. Therefore this paper proposes a way to add a new type of classification elements into an OO language such as the objects reason about other objects when providing/executing services based on what we call subjective classification.
本研究的出发点是观察到面向对象的分类主要反映了一个特定的视角,该视角被归因于系统中的所有对象。这被认为是一个重要的限制,当试图为对象添加自主性,以便向面向智能体的范式发展时。特别是,我们认为智能体可能具有对外部世界进行分类的能力,而不仅仅依赖于被强加的分类。因此,本文提出了一种方法,将一种新的分类元素添加到OO语言中,例如在提供/执行基于主观分类的服务时,对象对其他对象的判断。
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引用次数: 0
期刊
2011 13th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing
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