Iconicity and contraction: a semiotic investigation of forms of algebraic generalizations of patterns in different contexts

The aim of this paper is to investigate the progressive manner in which students gain fluency with cultural algebraic modes of reflection and action in pattern generalizing tasks. The first section contains a short discussion of some epistemological aspects of generalization. Drawing on this section, a definition of algebraic generalization of patterns is suggested. This definition is used in the subsequent sections to distinguish between algebraic and arithmetic generalizations and some elementary naïve forms of induction to which students often resort to solve pattern problems. The rest of the paper discusses the implementation of a teaching sequence in a Grade 7 class and focuses on the social, sign-mediated processes of objectification through which the students reached stable forms of algebraic reflection. The semiotic analysis puts into evidence two central processes of objectification—iconicity and contraction.     

Preference aggregation and DEA: An analysis of the methods proposed to discriminate efficient candidates

There are different ways to allow the voters to express their preferences on a set of candidates. In ranked voting systems, each voter selects a subset of the candidates and ranks them in order of preference. A well-known class of these voting systems are scoring rules, where fixed scores are assigned to the different ranks and the candidates with the highest score are the winners. One of the most important issues in this context is the choice of the scoring vector, since the winning candidate can vary according to the scores used. To avoid this problem, Cook and Kress [W.D. Cook, M. Kress, A data envelopment model for aggregating preference rankings, Management Science 36 (11) (1990) 1302–1310], using a DEA/AR model, proposed to assess each candidate with the most favorable scoring vector for him/her. However, the use of this procedure often causes several candidates to be efficient, i.e., they achieve the maximum score. For this reason, several methods to discriminate among efficient candidates have been proposed. The aim of this paper is to analyze and show some drawbacks of these methods.     

Statistics of extremes for IID data and breakthroughs in the estimation of the extreme value index: Laurens de Haan leading contributions

In the last decades there has been a shift from the parametric statistics of extremes for IID random variables, based on the probabilistic asymptotic results in extreme value theory, towards a semi-parametric approach, where the estimation of the right tail-weight, under a quite general framework, is of major importance. After a brief presentation of classical Gumbel’s block methodology and of later improvements in the parametric framework (multivariate and multi-dimensional extreme value models for largest observations and peaks over threshold approaches), we present a coordinated overview, over the last three decades, of the developments on the estimation of the extreme value index under a semiparametric framework. Laurens de Haan has been one of the leading scientists in the field, (co-)author of many seminal ideas, that he generously shared with dozens (literally) of colleagues and students, thus achieving one of the main goals in a scientist’s life: he gathered around him a bunch of colleagues united in the endeavour of building knowledge. The last section is a personal tribute to Laurens, who fully lives his ideal that co-operation is the heart of Science. To Laurens de Haan, a token of friendship.     

An investigation on the sensitivity and stability radius of returns to scale and efficiency in data envelopment analysis

An issue which has received widespread attention in rapidly growing field of DEA is the sensitivity of the results of analysis to perturbations in the data.     

The impact of mismeasurement in performance benchmarking: A Monte Carlo comparison of SFA and DEA with different multi-period budgeting strategies

Performance-based budgeting has received increasing attention from public and for-profit organizations in an effort to achieve a fair and balanced allocation of funds among their individual producers or operating units for overall system optimization. Although existing frontier estimation models can be used to measure and rank the performance of each producer, few studies have addressed how the mismeasurement by frontier estimation models affects the budget allocation and system performance. There is therefore a need for analysis of the accuracy of performance assessments in performance-based budgeting. This paper reports the results of a Monte Carlo analysis in which measurement errors are introduced and the system throughput in various experimental scenarios is compared. Each scenario assumes a different multi-period budgeting strategy and production frontier estimation model; the frontier estimation models considered are stochastic frontier analysis (SFA) and data envelopment analysis (DEA). The main results are as follows: (1) the selection of a proper budgeting strategy and benchmark model can lead to substantial improvement in the system throughput; (2) a “peanut butter” strategy outperforms a discriminative strategy in the presence of relatively high measurement errors, but a discriminative strategy is preferred for small measurement errors; (3) frontier estimation models outperform models with randomly-generated ranks even in cases with relatively high measurement errors; (4) SFA outperforms DEA for small measurement errors, but DEA becomes increasingly favorable relative to SFA as the measurement errors increase.     

Validating DEA as a ranking tool: An application of DEA to assess performance in higher education

There is a general interest in ranking schemes applied to complex entities described by multiple attributes. Published rankings for universities are in great demand but are also highly controversial. We compare two classification and ranking schemes involving universities; one from a published report, ‘Top American Research Universities’ by the University of Florida's TheCenter and the other using DEA. Both approaches use the same data and model. We compare the two methods and discover important equivalences. We conclude that the critical aspect in classification and ranking is the model. This suggests that DEA is a suitable tool for these types of studies.     

Comparison of two multicriteria decision aid methods: Net Flow and Rough Set Methods in a high yield pulping process

This investigation presents a synthesis of two multicriteria analysis methods, Rough Set Method (RSM) and Net Flow Method (NFM), applied to the multicriteria optimisation for the manufacture of paper using jack pine as the source of fibres. This work is the result of a collaboration between different Canadian and French laboratories.     

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.     

Richard von Mises and the “problem of two races”: A statistical satire in 1934

The article “Problem of two races,” which appeared in 1934 in French and Russian in the Matematichesky Sbornik (Moscow), authored by the noted applied mathematician and statistician Richard von Mises (1883–1953), is interpreted as having a twofold agenda. On its surface it is merely a detailed mathematical analysis of the statistical problem of comparing the distributions of a quantitative characteristic in two different classes. But on closer examination it serves two auxiliary purposes. On the one hand, von Mises, who as a Jew fled Nazi Germany in 1933, satirically attacked Nazi racial doctrines by resorting to statistical parody. On the other hand, von Mises employed his theoretical results to further his own distinctive program of objective Bayesian statistics.     

Building a set of additive value functions representing a reference preorder and intensities of preference: GRIP method

We present a method called Generalized Regression with Intensities of Preference (GRIP) for ranking a finite set of actions evaluated on multiple criteria. GRIP builds a set of additive value functions compatible with preference information composed of a partial preorder and required intensities of preference on a subset of actions, called reference actions. It constructs not only the preference relation in the considered set of actions, but it also gives information about intensities of preference for pairs of actions from this set for a given decision maker (DM). Distinguishing necessary and possible consequences of preference information on the considered set of actions, GRIP answers questions of robustness analysis. The proposed methodology can be seen as an extension of the UTA method based on ordinal regression. GRIP can also be compared to the AHP method, which requires pairwise comparison of all actions and criteria, and yields a priority ranking of actions. As for the preference information being used, GRIP can be compared, moreover, to the MACBETH method which also takes into account a preference order of actions and intensity of preference for pairs of actions. The preference information used in GRIP does not need, however, to be complete: the DM is asked to provide comparisons of only those pairs of reference actions on particular criteria for which his/her judgment is sufficiently certain. This is an important advantage comparing to methods which, instead, require comparison of all possible pairs of actions on all the considered criteria. Moreover, GRIP works with a set of general additive value functions compatible with the preference information, while other methods use a single and less general value function, such as the weighted-sum.     

Financial sustainability and poverty outreach within a network of village banks in Cameroon: A multi-DEA approach

Microfinance institutions face a double bottom-line. They perform financial tasks by giving microcredits to their customers and support projects aiming at reducing poverty. In doing so, they have to be financially self-sufficient and to target poor people excluded from the traditional financial systems. However, a trade-off may exist between financial sustainability and poverty outreach for these institutions. By using a multi-DEA approach, this paper shows that even if a trade-off exists for 15% of the MC² (Mutuelles Communautaires de Croissance) in Cameroon, there is no trade-off for 46% of them. In order to increase, without trade-off, financial and social performance of inefficient MC², a benchmarking approach combing DEA and performance indicators has been developed. DEA is used for identifying best-practices and setting benchmarking goals. Performance indicators are used for characterizing areas needing improvements and following the evolution of MC² toward their goals, i.e., for implementing benchmarking. Complementarity of both approaches provides a tool box for improving financial and social efficiency and reducing the trade-off between financial sustainability and poverty outreach of microfinance institutions.     

Robust parameter design in resource-constrained environments: An investigation of trade-offs between costs and precision within variable processes

Engineers and scientists often identify robust parameter design as one of the most important process and quality improvement methods. Focused on statistical modeling and numerical optimization strategies, most researchers typically assume a process with reasonably small variability. Realistically, however, industrial processes often exhibit larger variability, particularly in mass production lines. In such cases, many of the modeling assumptions behind the robust parameter design models available in the literature do not hold. Accordingly, the results and recommendations provided to decision makers could generate suboptimal modifications to processes and products. As manufacturers seek improved methods for ensuring quality in resource-constrained environments, experimenters should examine trade-offs to achieve the levels of precision that best support their decision making. In contrast to previous research, this paper proposes a trade-off analysis between the cost of replication and the desired precision of generated solutions. We consider several techniques in the early stages of experimental design, using Monte Carlo simulation as a tool, for revealing potential options to the decision maker. This is perhaps the first study to show the avenue which may lead to more effective robust parameter design models with the optimal combination of cost constraints and desired precision of solutions.     

A boundary value problem for a PDE model in mass transfer theory: Representation of solutions and applications

The system of partial differential equations

An upper bound for the restrained domination number of a graph with minimum degree at least two in terms of order and minimum degree

Let G=(V,E) be a graph. A set S⊆V is a restrained dominating set if every vertex in V−S is adjacent to a vertex in S and to a vertex in V−S. The restrained domination number of G, denoted γ_r(G), is the smallest cardinality of a restrained dominating set of G. We will show that if G is a connected graph of order n and minimum degree δ and not isomorphic to one of nine exceptional graphs, then .