Ethics and OR: Operationalising discourse ethics

Operational researchers help managers decide what they ought to do and yet this is generally evaluated in terms of efficiency or effectiveness, not ethicality. However, the combination of the tremendous power of global corporations and the financial markets, and the problems the world faces in terms of economic and environmental sustainability, has led to a revival of interest in ethical approaches. This paper explores a relatively recent and innovative process called discourse ethics. This is very different from traditional ethical systems in taking ethical decisions away from individuals or committees and putting them in the hands of the actual people who are involved and affected through processes of debate and deliberation. The paper demonstrates that discourse ethics has strong connections to OR, especially in the areas of soft and critical systems, and that OR can actually contribute to the practical operationalisation of discourse ethics. At the same time, discourse ethics can provide a rigorous discursive framework for “ethics beyond the model”.     

An analysis of context-based similarity tasks in textbooks from Brazil and the United States

Three textbooks from Brazil and three textbooks from the United States were analysed with a focus on similarity and context-based tasks. Students’ opportunities to learn similarity were examined by considering whether students were provided context-based tasks of high cognitive demand and whether those tasks included missing or superfluous information. Although books in the United States included more tasks, the proportion of tasks focused on similarity were about the same. Context-based similarity tasks accounted for 9%–29% of the similarity tasks, and many of these contextual tasks were of low cognitive demand. In addition, the types of contexts that were included in the textbooks were critiqued and examples provided.     

Inspecting the foundations of claims about cognitive demand and student learning: A citation analysis of Stein and Lane (1996)

Educational research communities bear responsibility for establishing a substantial body of evidence to support claims that drive the field. For example, one commonly accepted claim is that there is a relationship between the cognitive demand of mathematical task enactments and students’ learning. One study that is often cited in association with this claim is Stein and Lane (1996), and in 44% of those citations, Stein and Lane (1996) is the sole reference. Citation analysis reveals that many of these claims go beyond the warrants provided by the Stein and Lane study, either by granting more confidence in the relationship than the study design allows or by phrasing the claim as a causal relationship between cognitive demand and student learning. A few other studies are occasionally cited in conjunction with Stein and Lane (1996) and are summarized in this article, but there remains a need for replication studies to provide better empirical support for claims about cognitive demand and student learning and to refine our shared understanding.     

An analysis of neighborhood functions on generic solution spaces

The effectiveness of local search algorithms on discrete optimization problems is influenced by the choice of the neighborhood function. A neighborhood function that results in all local minima being global minima is said to have zero L-locals. A polynomially sized neighborhood function with zero L-locals would ensure that at each iteration, a local search algorithm would be able to find an improving solution or conclude that the current solution is a global minimum. This paper presents a recursive relationship for computing the number of neighborhood functions over a generic solution space that results in zero L-locals. Expressions are also given for the number of tree neighborhood functions with zero L-locals. These results provide a first step towards developing expressions that are applicable to discrete optimization problems, as well as providing results that add to the collection of solved graphical enumeration problems.     

The same tasks,different learning opportunities: An analysis of two exemplary lessons in China and the U.S. from a perspective of variation

This study examined the learning opportunities afforded in two exemplary lessons based on a theory of variation. Implemented in China and the U.S., the two lessons focused on the same topic of patterns in a calendar and were carefully developed through a lesson study approach. Both lessons set similar learning goals but enacted these goals differently. When compared with the U.S. lesson, the Chinese lesson provided more learning opportunities through high cognitively demanding tasks focusing on different identities within patterns. However, the U.S. lesson, which featured fewer tasks and focused on a single pattern identity, may have better supported students in discerning the critical features within the objects of learning. The implications for task design and implementation for effective mathematics teaching are discussed.     

Improved analysis of an algorithm for the coupled task problem with UET jobs

The coupled task problem is to schedule n jobs, each one consisting of two subtasks with exact delay times between them, on a single machine. We derive a new lower bound for the problem variant with unit execution times and correct a previously published analysis.     

An evaluation of continuous assessment in statistics courses for social scientists

This paper reports on the use of continuous assessment in a statistics course for social scientists, in which assignments are open‐ended and use real data. The students' performance in the assignments and a formal examination are compared, and it is found that when students are assessed by a combination of continuous assessment and examination, those students who carry out the majority of the assignments score higher examination marks than do the rest.     

The taxicab locus of Apollonius: promoting exploratory routes to the punchline using rich undergraduate tasks

ABSTRACT

A key motivational tactic in undergraduate mathematics teaching is to launch topics with fundamental questions that originate from surprising or remarkable phenomena. Nonetheless, constructing a sequence of tasks that promotes students' own routes to resolving such questions is challenging. This note aims to address this challenge in two ways. First, to illustrate the motivational tactic, the taxicab manifestation of a locus attributed to Apollonius is introduced and a natural question arising from comparison with the analogous Euclidean locus is considered, namely, does the taxicab locus of Apollonius ever coincide with a taxicab circle? Second, a companion sequence of rich undergraduate tasks is elaborated using theoretical design principles, with the tasks culminating in this fundamental geometric question. This note therefore provides a design approach that can be replicated in undergraduate teaching contexts based around similarly motivating mathematical phenomena.     

Cluster Analysis for Large Datasets: An Effective Algorithm for Maximizing the Mixture Likelihood

Abstract

The primary model for cluster analysis is the latent class model. This model yields the mixture likelihood. Due to numerous local maxima, the success of the EM algorithm in maximizing the mixture likelihood depends on the initial starting point of the algorithm. In this article, good starting points for the EM algorithm are obtained by applying classification methods to randomly selected subsamples of the data. The performance of the resulting two-step algorithm, classification followed by EM, is compared to, and found superior to, the baseline algorithm of EM started from a random partition of the data. Though the algorithm is not complicated, comparing it to the baseline algorithm and assessing its performance with several classification methods is nontrivial. The strategy employed for comparing the algorithms is to identify canonical forms for the easiest and most difficult datasets to cluster within a large collection of cluster datasets and then to compare the performance of the two algorithms on these datasets. This has led to the discovery that, in the case of three homogeneous clusters, the most difficult datasets to cluster are those in which the clusters are arranged on a line and the easiest are those in which the clusters are arranged on an equilateral triangle. The performance of the two-step algorithm is assessed using several classification methods and is shown to be able to cluster large, difficult datasets consisting of three highly overlapping clusters arranged on a line with 10,000 observations and 8 variables.     

Investigating the geometry curriculum in Palestinian textbooks: towards multimodal analysis of Arabic mathematics discourse

ABSTRACT

The analytical scheme used in the project The Evolution of the Discourse of School Mathematics (EDSM) was developed to analyse the change over time in examination texts. An adapted version of the EDSM scheme has been deployed to analyse the nature of mathematics construed in Palestinian schools’ textbooks and the mathematical activity expected of students in the geometry textbooks for students aged 10 to 16 years. The adaptation includes adding further tools for analysing visual components of texts, as well as accounting for some differences between English and Arabic. This article outlines these adaptations and illustrates the use of the adapted scheme with a different genre of texts from those studied in the EDSM project. Some of the challenges in the adaptation process in relation to Arabic mathematics discourse are discussed.     

Knowledge sharing in communities of practice: A game theoretic analysis

This research applies game theory to analyze the incentives of knowledge-sharing activities in various types of communities of practice (COPs), characterized by individual profiles and decision structures. Indeed, individual decision making results in the under-provision of knowledge; however, the benefit of knowledge sharing may be raised by IT investment and suitable incentive mechanisms we study here. In general conditions, improving communication and collaboration technologies should be prior to developing data mining technologies. However, when the number of community members is sufficiently small and the heterogeneity of the expected value of knowledge among community members is sufficiently large, developing data mining technologies should be considered more important than the other if most community members are low-type ones. On the other hand, based on a screening technique, we find that the benefit of knowledge sharing in the incomplete information setting can be the same as that in the complete information setting if the cost of more efficient community member is smaller than that of less efficient one.     

Multifractal analysis of divergence points of deformed measure theoretical Birkhoff averages

We introduce and develope a unifying multifractal framework. The framework developed in this paper is based on the notion of deformations of empirical measures. This approach leads to significant extensions of already know results. However, our approach not only leads to extensions of already know results, but also, by considering non-linear deformations, provides the basis for the study of several new and non-linear local characteristic. We also initiate a detailed study of the fractal structure of so-called divergence points. We define multifractal spectra that provides extremely precise quantitative information about the distribution of individual divergence points of arbitrary (possibly non-linear) deformations, thereby extending and unifying many diverse qualitative results on the behaviour of divergence points. The techniques used in proving the main results are taken from large deviation theory and are completely different from previous techniques in the literature.     

An extension of Ekeland's variational principle to locally complete spaces

We prove an extension of Ekeland's variational principle to locally complete spaces which uses subadditive, strictly increasing continuous functions as perturbations.     

An elementary proof of the principle of local reflexivity

We give an elementary proof of the principle of local reflexivity.

     

Recognizing and visualizing copulas: An approach using local Gaussian approximation

In this paper we examine the relationship between a newly developed local dependence measure, the local Gaussian correlation, and standard copula theory. We are able to describe characteristics of the dependence structure in different copula models in terms of the local Gaussian correlation. Further, we construct a goodness-of-fit test for bivariate copula models. An essential ingredient of this test is the use of a canonical local Gaussian correlation and Gaussian pseudo-observations which make the test independent of the margins, so that it is a genuine test of the copula structure. A Monte Carlo study reveals that the test performs very well compared to a commonly used alternative test. We also propose two types of diagnostic plots which can be used to investigate the cause of a rejected null. Finally, our methods are applied to a “classical” insurance data set.     

Sensitivity analysis of the combined travel demand model with applications

The conventional sequential four-step procedure of travel demand forecasting has been widely adopted by practitioners. However, it suffers from inconsistent consideration of travel times and congestion effects in various steps of the procedure. A combined travel demand model overcomes the problems associated with the sequential four-step procedure by integrating travel-destination-mode-route choice together. In this paper, a standard sensitivity analysis for non-linear programming is employed for conducting the sensitivity analysis of the combined travel demand model. Explicit expressions of the derivatives of model variables with respect to perturbations of input variables and parameters of the combined travel demand model are developed. These derivatives could be used to assess changes in solution variables and various system performance measures when the network characteristics are changed slightly. To gain insight into the usefulness of the sensitivity expressions, five applications, such as identification of critical parameters, paradox analysis, access control, destination choice, and error and uncertainty analysis, are presented with numerical results.     

品牌的非对称需求价格弹性模型:以中国手机行业为例

本文提出了计算品牌的需求价格弹性的非对称市场反应函数模型,从而使对向上的价格弹性和向下的价格弹性的分别考量成为可能。根据此模型,本文对中国手机行业进行了实证研究,共计算了GSM市场的13个品牌和CDMA市场的9个品牌的向上和向下的价格弹性,并且通过方差分析对国内外手机品牌的价格弹性进行了比较。结果发现,在GSM和CDMA市场上国内外手机品牌的价格弹性都存在显著差异,反映了国内外手机品牌的市场力量的差异。最后根据研究结果为我国国内手机品牌提出对策建议。     

Integrated data envelopment analysis: Global vs. local optimum

Chiou et al. (2010) (A joint measurement of efficiency and effectiveness for non-storable commodities: integrated data envelopment analysis approaches. European Journal of Operational Research 201, 477–489) propose an integrated data envelopment analysis model in measuring decision making units (DMUs) that have a two-stage internal network structure with multiple inputs, outputs, and consumptions. They claim that any optimal solutions determined by their DEA model are a global optimum, not a local optimum. We show that such a conclusion is a false statement due to their misuse of Hessian matrix in examining the concavity of the objective function, and their DEA model is actually a non-convex optimization problem. As a result, their DEA model is unusable in practice due to a lack of efficient algorithm for this particular non-convex DEA model. We further show that Chiou et al.’s (2010) model is a special case of a well-known two-stage network DEA model, and it can be transformed into a parametric linear program for which an approximate global optimal solution can be obtained by solving a sequence of linear programs in combination with a simple search algorithm.     

Explanation,motivation and question posing routines in university mathematics teachers' pedagogical discourse: a commognitive analysis

This paper investigates the teaching practices used by university mathematics teachers when lecturing, a topic within university mathematics education research which is gaining an increasing interest. In the study, a view of mathematics teaching as a discursive practice is taken, and Sfard's commognitive framework is used to investigate the teaching practices of seven Swedish university mathematics teachers on the topic of functions. The present paper looks at the discourse of mathematics teaching, presenting a categorization of the didactical routines into three categories – explanation, motivation and question posing routines. All of these are present in the discourses of all seven teachers, but within these general categories, a number of different sub-categories of routines are found, used in different ways and to different extent by the various teachers. The explanation routines include known mathematical facts, summary and repetition, different representations, everyday language, and concretization and metaphor; the motivation routines include reference to utility, the nature of mathematics, humour and result focus; and the question posing routines include control questions, asking for facts, enquiries and rhetorical questions. This categorization of question posing routines, for instance, complements those already found in the literature. In addition to providing a valuable insight into the teaching of functions at the university level, the categorizations presented in the study can also be useful for investigating the teaching of other mathematical topics.     

Local analysis of the feasible primal-dual interior-point method

In this paper we analyze the rate of local convergence of the Newton primal-dual interior-point method when the iterates are kept strictly feasible with respect to the inequality constraints. It is shown under the classical conditions that the rate is q-quadratic when the functions associated to the binding inequality constraints are concave. In general, the q-quadratic rate is achieved provided the step in the primal variables does not become asymptotically orthogonal to any of the gradients of the binding inequality constraints.