Factors affecting the process of proficient mental addition and subtraction: case studies of flexible and inflexible computers

The relationship between mental computation and number sense is complex: mental computation can facilitate number sense when students are encouraged to be flexible, but flexibility and number sense is neither sufficient nor necessary for accuracy in mental computation. It is possible for familiarity with a strategy to compensate for a lack of number sense and inefficient processes. This study reports on six case studies exploring Year 3 students’ procedures for and understanding of mental addition and subtraction, and understanding of number sense and other cognitive, metacognitive, and affective factors associated with mental computation. The case studies indicate that the mental computation process is composed of four stages in which cognitive, metacognitive and affective factors operate differently for flexible and inflexible computers. The authors propose a model in which the differences between computer types are seen in terms of the application of different knowledges in number facts, numeration, effect of operation on number, and beliefs and metacognition on strategy choice and strategy implementation.     

极端损失条件下分组群体的主观概率累积偏差仿真研究

为了研究个体死亡这种极端损失条件下分组群体的主观概率累积偏差的形成与演化规律,构建不同分组方式下的群体主观概率元胞自动机模型并运用Netlogo仿真平台进行实验。在对仿真结果进行图形分析的基础上,进一步对实验数据进行了回归分析和案例验证分析。结果表明:分组群体的主观概率演化一般会经历从急速变化到趋于稳定的过程;分组作业方式能够提高安全冗余,但不利于个体事故经验积累;个体死亡等极端损失会导致群体的主观概率低估和分化,但分组措施能够降低此作用;客观事故概率的减少会增大群体内部主观概率的差异,但分组措施能够降低此作用;事故率与死亡率之间存在互补效应,分组措施对其存在双向调节作用;群体人数增加有助于减少主观概率偏差和差异。     

LOOK: A Lazy Object-Oriented Kernel design for geometric computation

In this paper we describe and discuss a new kernel design for geometric computation in the plane. It combines different kinds of floating-point filter techniques and a lazy evaluation scheme with the exact number types provided by LEDA allowing for efficient and exact computation with rational and algebraic geometric objects.

It is the first kernel design which uses floating-point filter techniques on the level of geometric constructions.

The experiments we present—partly using the CGAL framework—show a great improvement in speed and—maybe even more important for practical applications—memory consumption when dealing with more complex geometric computations.     

Self-normalization: Taming a wild population in a heavy-tailed world

The past two decades have witnessed the active development of a rich probability theory of Studentized statistics or self-normalized processes, typified by Student's t-statistic as introduced by W. S. Gosset more than a century ago, and their applications to statistical prob-lems in high dimensions, including feature selection and ranking, large-scale multiple testing and sparse, high dimensional signal detection. Many of these applications rely on the robust-ness property of Studentization/self-normalization against heavy-tailed sampling distributions. This paper gives an overview of the salient progress of self-normalized limit theory, from Studen-t's t-statistic to more general Studentized nonlinear statistics. Prototypical examples include Studentized one- and two-sample U-statistics. Furthermore, we go beyond independence and glimpse some very recent advances in self-normalized moderate deviations under dependence.     

符号和数值混合计算

符号计算和数值计算是两种不同的解决科学和技术发展中问题的计算方法.符号计算可以得到问题精确的完备解,但是计算量大且表达形式往往十分庞大;数值计算可以快速地处理很多实际应用中的问题,但是一般只能得到近似的局部解.特别地,数值计算处理病态问题时,收敛往往较慢且容易出错.着重介绍了符号计算和数值计算之间的密切联系,以及如何运用这两大领域的最新研究成果,探索和开发符号和数值混合计算算法和软件,使之兼备符号计算的完备化和数值计算的高效性.     

零误差计算

研究采用有误差的数值计算来获得无误差的准确值具有重要的理论价值和应用价值.这种通过近似的数值方法获得准确结果的计算被称为零误差计算.本文首先指出,只有一致离散集合中的数才能够开展零误差计算,即有非零隔离界的数集,这也是"数"可以进行零误差计算的一个充要条件.以此为基本出发点,本文分析代数数零误差计算的最低理论精度,该精度对应于恢复近似代数数的准确值时必要的误差控制条件,但由于所采用恢复算法的局限性,这一理论精度往往不能保证成功恢复出代数数的准确值.为此,本文给出采用PSLQ (partial-sum-LQ-decomposition)算法进行代数数零误差计算所需的精度控制条件,与基于LLL (Lenstra-Lenstra-Lovász)算法相比,该精度控制条件关于代数数次数的依赖程度由二次降为拟线性,从而可降低相应算法的复杂度.最后探讨零误差计算未来的发展趋势.     

Upper bound for ruin probabilities under optimal investment and proportional reinsurance

In this paper, we consider the optimal investment and reinsurance from an insurer's point of view to maximize the adjustment coefficient. We obtain the explicit expressions for the optimal results in the diffusion approximation (D‐A) case as well as in the jump‐diffusion (J‐D) case. Furthermore, we derive a sharper bound on the ruin probability, from which we conclude that the case with investment is always better than the case without investment. Some numerical examples are presented to show that the ruin probability in the D‐A case sometimes underestimates the ruin probability in the J‐D case. Copyright © 2007 John Wiley & Sons, Ltd.     

Tuned preconditioners for the eigensolution of large SPD matrices arising in engineering problems

In this paper, we study a class of tuned preconditioners that will be designed to accelerate both the DACG–Newton method and the implicitly restarted Lanczos method for the computation of the leftmost eigenpairs of large and sparse symmetric positive definite matrices arising in large‐scale scientific computations. These tuning strategies are based on low‐rank modifications of a given initial preconditioner. We present some theoretical properties of the preconditioned matrix. We experimentally show how the aforementioned methods benefit from the acceleration provided by these tuned/deflated preconditioners. Comparisons are carried out with the Jacobi–Davidson method onto matrices arising from various large realistic problems arising from finite element discretization of PDEs modeling either groundwater flow in porous media or geomechanical processes in reservoirs. The numerical results show that the Newton‐based methods (which includes also the Jacobi–Davidson method) are to be preferred to the – yet efficiently implemented – implicitly restarted Lanczos method whenever a small to moderate number of eigenpairs is required. Copyright © 2016 John Wiley & Sons, Ltd.     

面向隐私保护的个性化搜索结果排序方法研究

针对个性化搜索中用户隐私保护的需求,提出一种面向隐私保护的个性化搜索结果排序方法.方法基于向量空间模型,引入安全点积计算方法来计算搜索相似度,旨在实现用户隐私保护的同时提高个性化搜索服务质量.首先分析了目前常用的搜索排序相似度计算方法存在的不足,然后分别介绍了向量空间模型和安全点积计算,最后详细介绍了面向隐私保护的个性化搜索结果排序方法,并对其性能进行了分析.     

On a Solvable Diffusion with Time Dependent “Killing”

Abstract

In this paper we consider a diffusion process with arbitrary time dependent diffusion coefficient and no drift, on which a quadratic time dependent killing rate operates. We determine the corresponding Kac's semigroup (KS) and the distribution function of the lifetime of the particle. A criteria is given to characterize the survival probability. The Holder exponent and the tightness properties of the process are determined. Applications include the determination of the law of certain functionals and Ito processes associated with the diffusion and the construction of martingales adapted to Brownian filtrations.     

Analyses of baby name popularity distribution in U.S. for the last 131 years

We examine the complete dataset of baby name popularity collected by U.S. Social Security Administration for the last 131 years (1880–2010). The ranked baby name popularity can be fitted empirically by a piecewise function consisting of Beta function for the high‐ranking names and power‐law function for low‐ranking names, but not power‐law (Zipf's law) or Beta function by itself. © 2012 Wiley Periodicals, Inc. Complexity, 2012     

Space Saving Calculation of Symbolic Resultants

We describe an approach to the computation of symbolic resultants in which factors are removed during the course of the calculation, so reducing the stack size required for intermediate expressions and the storage space needed. We apply the technique to three well-established methods for calculating resultants. We demonstrate the advantages of our approach when the resultants are large and show that some otherwise intractable problems can be resolved. In certain cases a significant reduction in the cpu time required to calculate the resultant is also evident.      

Boundary element approximation for Maxwell's eigenvalue problem

We introduce a new method for computing eigenvalues of the Maxwell operator with boundary finite elements. On bounded domains with piecewise constant material coefficients, the Maxwell solution for fixed wave number can be represented by boundary integrals, which allows to reduce the eigenvalue problem to a nonlinear problem for determining the wave number along with boundary and interface traces. A Galerkin discretization yields a smooth nonlinear matrix eigenvalue problem that is solved by Newton's method or, alternatively, the contour integral method. Several numerical results including an application to the band structure computation of a photonic crystal illustrate the efficiency of this approach. Copyright © 2013 John Wiley & Sons, Ltd.     

A probabilistic framework for the design of instance-based supervised ranking algorithms in an ordinal setting

In this article, we present a probabilistic framework which serves as the base from which instance-based algorithms for solving the supervised ranking problem may be derived. This framework constitutes a simple and novel approach to the supervised ranking problem, and we give a number of typical examples of how this derivation can be achieved. In this general framework, we pursue a cumulative and stochastic approach, relying heavily upon the concept of stochastic dominance. We show how the median can be used to extract, in a consistent way, a single (classification) label from a returned cumulative probability distribution function. We emphasize that all operations used are mathematically sound, i.e. they only make use of ordinal properties. Mostly, when confronted with the problem of learning a ranking, the training data is not monotone in itself, and some cleansing operation is performed on it to remove these ‘inconsistent’ examples. Our framework, however, deals with these occurrences of ‘reversed preference’ in a non-invasive way. On the contrary, it even allows to incorporate information gained from the occurrence of these reversed preferences. This is exactly what happens in the second realization of the main theorem.     

Passenger grouping with risk levels in an airport security system

This is a follow-up to the recent paper by Lazar Babu et al. [V.L. Lazar Babu, R. Batta, L. Lin, Passenger grouping under constant threat probability in an airport security system, European Journal of Operational Research 168 (2006) 633–644] which investigated the benefit of classifying passengers into different groups, with the idea that the number of checks and the degree of inspection may vary for different groups. A basic assumption in that paper was that the threat probability is constant across all passengers. In this paper, we relax this assumption and consider the case where passenger risk levels are incorporated. We assume that passengers are classified into several risk classes via some passenger prescreening system, for example, Computer-Assisted Passenger Prescreening System II (CAPPS II). We consider the separate grouping of every class of passengers such that the overall false alarm probability is minimized while maintaining the overall false clear probability within specifications set by a security authority. Meanwhile, we consider the staffing needs at each check station. The problem is formulated as a mixed integer linear program. An illustrative example of the model is presented with comparisons to the model in Lazar Babu et al. (2006) using two performance measures: probability of false alarm and total number of screeners needed. Our conclusion is that incorporation of risk levels through passenger grouping strategies leads to a more efficient security check system.     

Polynomial differential equations compute all real computable functions on computable compact intervals

In the last decade, there have been several attempts to understand the relations between the many models of analog computation. Unfortunately, most models are not equivalent. Euler's Gamma function, which is computable according to computable analysis, but that cannot be generated by Shannon's General Purpose Analog Computer (GPAC), has often been used to argue that the GPAC is less powerful than digital computation. However, when computability with GPACs is not restricted to real-time generation of functions, it has been shown recently that Gamma becomes computable by a GPAC. Here we extend this result by showing that, in an appropriate framework, the GPAC and computable analysis are actually equivalent from the computability point of view, at least in compact intervals. Since GPACs are equivalent to systems of polynomial differential equations then we show that all real computable functions over compact intervals can be defined by such models.     

计算毁伤概率的二项展开优化法

对着发射击高射武器系统毁伤概率的计算公式提出了一种新算法 ,称为二项展开优化法 .它是在原有的常用算法二项展开法基础上改进得到的 .新算法保留了二项展开法实施容易、计算快的特点 ,又在一定程度上克服了原算法由于计算组合数 Ck N而带来的计算机计算过程中的舍入误差 .最后 ,文章又用实例比较了几种算法在计算毁伤概率值的精度与差异 .     

求解混沌映射不变分布的符号计算法

根据Frobenius-Perron方程,可以对混沌映射的不变分布从理论上加以分析,从而对混沌映射不变分布作出大致的估计.由此可以利用符号计算的方法求解得到迭代函数系统不变分布的密度近似函数,从而逼近理论解.用几个计算实例和常见数值解法作了比较,试验结果表明符号计算方法具有一定的优势.     

Dempster's rule of combination

The theory of belief functions is a generalization of probability theory; a belief function is a set function more general than a probability measure but whose values can still be interpreted as degrees of belief. Dempster's rule of combination is a rule for combining two or more belief functions; when the belief functions combined are based on distinct or “independent” sources of evidence, the rule corresponds intuitively to the pooling of evidence. As a special case, the rule yields a rule of conditioning which generalizes the usual rule for conditioning probability measures. The rule of combination was studied extensively, but only in the case of finite sets of possibilities, in the author's monograph A Mathematical Theory of Evidence. The present paper describes the rule for general, possibly infinite, sets of possibilities. We show that the rule preserves the regularity conditions of continuity and condensability, and we investigate the two distinct generalizations of probabilistic independence which the rule suggests.