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This paper addresses the integration of fuzziness with On-Line Analytical Processing (OLAP) based association rules mining. It contributes to the ongoing research on multidimensional online association rules mining by proposing a general architecture that utilizes a fuzzy data cube for knowledge discovery. A data cube is mainly constructed to provide users with the flexibility to view data from different perspectives as some dimensions of the cube contain multiple levels of abstraction. The first step of the process described in this paper involves introducing fuzzy data cube as a remedy to the problem of handling quantitative values of dimensional attributes in a cube. This facilitates the online mining of fuzzy association rules at different levels within the constructed fuzzy data cube. Then, we investigate combining the concepts of weight and multiple-level to mine fuzzy weighted multi-cross-level association rules from the constructed fuzzy data cube. For this purpose, three different methods are introduced for single dimension, multidimensional and hybrid (integrates the other two methods) fuzzy weighted association rules mining. Each of the three methods utilizes a fuzzy data cube constructed to Suite the particular method. To the best of our knowledge, this is the first effort in this direction. We compared, the proposed approach to an existing approach that does not utilize fuzziness. Experimental results obtained for each of the three methods on a synthetic dataset and on the adult data of the United States census in year 2000 demonstrate the effectiveness and applicability of the proposed fuzzy OLAP based mining approach. [ABSTRACT FROM AUTHOR]

Problem Statement: The acquisition of certain mathematical skills is part of many curricula around the world. These skills involve problem-solving, effective use of mathematics in daily life, thinking logically and systematically, taking risks and making decisions. The US National Council of Teachers of Mathematics ([NCTM], 1991) relates these skills to mathematical power. Knowledge construction and abstraction might have an impact on mathematical power. In this paper, the primary concern is with the construction of new knowledge structures rather than with consolidation or abstraction for that matter. Recognizing, Building-with, and Constructing (RBC hereafter) theory of abstraction provides a particularly useful framework in achieving a detailed examination of the new mathematical constructions through epistemic actions. Therefore, this paper, with reference to the RBC epistemic actions, examines the knowledge construction process of students with different mathematical power. Purpose of Study: The purpose of the study is to explain the similarities and differences between the knowledge construction processes of 6th grade students with different mathematical power. Methods: A case study was used as the main research approach. The mathematical power scale was applied to 282 students. The case study was conducted with four students who were chosen purposefully among them. The RBC theory of abstraction was used as an analytical tool. The patterns noticed in the case study were determined and interpreted. Findings and Results: According to findings, it was seen that the students with low mathematical power, whose knowledge constructing processes were examined, could recognize structures while they could not building with and constructing. When observing that the students with low mathematical power have low communication, connection and reasoning skills, in general, it can be said that for building-with and constructing, it is important to have these three skills. The students who reflected themselves and used the feedback to continue had high mathematical power. They also were able to construct mathematical knowledge more quickly. Conclusions and Recommendations: The RBC theory of abstraction can be useful in explaining the relationship between the components of mathematical power and other mental activities. For this purpose, the usage of the RBC theory of abstraction in the mathematical knowledge construction process in the classroom can be proposed as a new study. [ABSTRACT FROM AUTHOR]

Social network analysis is an active area of study beyond sociology. It uncovers the invisible relationships between actors in a network and provides understanding of social processes and behaviors. It has become an important technique in a variety of application areas such as the Web, organizational studies, and homeland security. This paper presents a visual analytics tool, OntoVis, for understanding large, heterogeneous social networks, in which nodes and links could represent different concepts and relations, respectively. These concepts and relations are related through an ontology (also known as a schema). OntoVis is named such because it uses information in the ontology associated with a social network to semantically prune a large, heterogeneous network. In addition to semantic abstraction, OntoVis also allows users to do structural abstraction and importance filtering to make large networks manageable and to facilitate analytic reasoning. All these unique capabilities of OntoVis are illustrated with several case studies. [ABSTRACT FROM AUTHOR]

The structured inequalities of capital investment and disinvestment are prominent themes in critical urban and regional research, but many accounts portray ‘capital’ as a global, faceless and placeless abstraction operating according to a hidden, unitary logic. Sweeping political-economic shifts in the last generation demonstrate that capital may shape urban and regional processes in many different ways, and each of these manifestations creates distinct constraints and opportunities. In this paper, we analyze a new institutional configuration in the USA that is reshaping access to wealth among the poor – a policy ‘consensus’ to expand home-ownership among long-excluded populations. This shift has opened access to some low- and moderate-income households, and racial and ethnic minorities, but the necessary corollary is a greater polarization between those who are able to own and those who are not. We provide a critical analysis of these changes, drawing on national housing finance statistics as well as a multivariate analysis of differences between owners and renters in the 1990s in New York City. As home-ownership strengthens its role as a privatized form of stealth urban and housing policy in the USA, its continued expansion drives a corresponding reconstruction of its value for different groups, and inscribes a sharper axis of property-rights inequalities among owners and renters in the working classes. [ABSTRACT FROM AUTHOR]

This paper describes methods for automatically analyzing formal, state-based requirements specifications for some aspects of completeness and consistency. The approach uses a low-level functional formalism, simplifying the analysis process. State-space explosion problems are eliminated by applying the analysis at a high level of abstraction; i.e., instead of generating a reachability graph for analysis, the analysis is performed directly on the model. The method scales up to large systems by decomposing the specification into smaller, analyzable parts and then using functional composition rules to ensure that verified properties hold for the entire specification. The analysis algorithms and tools have been validated on TCAS II, a complex, airborne, collision-avoidance system required on all commercial aircraft with more than 30 passengers that fly in U.S. airspace. [ABSTRACT FROM AUTHOR]

Early abstract reasoning has typically been characterized by a "relational shift," in which children initially focus on object features but increasingly come to interpret similarity in terms of structured relations. An alternative possibility is that this shift reflects a learned bias, rather than a typical waypoint along a universal developmental trajectory. If so, consistent differences in the focus on objects or relations in a child's learning environment could create distinct patterns of relational reasoning, influencing the type of hypotheses that are privileged and applied. Specifically, children in the United States may be subject to culture-specific influences that bias their reasoning toward objects, to the detriment of relations. In experiment 1, we examine relational reasoning in a population with less object-centric experience-3-y-olds in China-and find no evidence of the failures observed in the United States at the same age. A second experiment with younger and older toddlers in China (18 to 30 mo and 30 to 36 mo) establishes distinct developmental trajectories of relational reasoning across the two cultures, showing a linear trajectory in China, in contrast to the U-shaped trajectory that has been previously reported in the United States. In a third experiment, Chinese 3-y-olds exhibit a bias toward relational solutions in an ambiguous context, while those in the United States prefer objectbased solutions. Together, these findings establish populationlevel differences in relational bias that predict the developmental trajectory of relational reasoning, challenging the generality of an initial object focus and suggesting a critical role for experience. [ABSTRACT FROM AUTHOR]

Throughout the nineteenth century, the sciences in the United States went through many professional and disciplinary shifts. While the impact of these changes on university education has been well established, their consequences at the level of high school education have been often overlooked. In mathematics, debates at the level of university officials found clear outlets in the reform movement concerning secondary school offerings and college entrance requirements. This article therefore focuses on these debates and also the attempts to achieve compromises through standardized curricula in the recommendations of the Committee of Ten. In discussing the interplay between university and secondary education, it exposes a feature of the history of science education that has been neglected. [ABSTRACT FROM AUTHOR]

The poet John Ashbery lived in Paris from roughly 1955 to 1965. It was during this period that Ashbery began writing art reviews, often examining the work of various Americans also living in Paris at this time. Among the many painters Ashbery was to review and publish about, one was the Chicago-born, Paris-based abstract expressionist Joan Mitchell and an exhibition of hers at a Paris gallery in 1964. In this essay I examine the early, more ''abstract'' poetry that Ashbery was developing during this period, thinking about it alongside the paintings of Mitchell (and, in particular, his writings about them). My contention is that Ashbery was in many ways emboldened by Mitchell's complex engagements with representation and abstraction, especially as they relate to the landscape. Ashbery was, through his close examination of such work, moved towards ever greater poetic and linguistic experimentations of his own. [ABSTRACT FROM AUTHOR]

As part of an exploratory study at three universities (two in the UK and one in the USA) of how first-year students in three disciplines (biology, electrical engineering and history) learn to argue, we conducted interviews (individual and group) with university faculty and students about the place of argument in their teaching and learning. Here we reflect on the complexity of researching a term that refers both to an abstract concept and process and to diverse actual practices that often appear to be in excess of, or only partially covered by, such abstraction. We found stable, definitive data about argument hard to abstract convincingly from the interviews. The analysis instead drew our attention to how faculty and students inflected the term 'argument' in diverse, nuanced ways; constructed their accounts of 'argument' and of themselves as students or teachers interactively in the interview; and introduced various related terms (e.g. 'analysis', 'interpretation', 'critique'). Reflecting on ways in which the interview can foreclose as well as open up opportunities for sense making around 'argument', we concluded that an approach that anchors talk in detailed accounts of practice is most fruitful in developing our understanding. In this way, interviewing can be a valuable research tool in developing understanding of how 'argument' is used in discourse and manifested in actual practices. [ABSTRACT FROM AUTHOR]

Details the abstraction and figuration at the Ground Zero World Trade Center site in New York City. Issuance of an open Request for Qualifications by the Lower Manhattan Development Corp. for architects; Details of the submitted proposals.

Explores the difficulties encountered by novice mathematicians on mathematical abstraction at Oxford College in Atlanta, Georgia. Genesis of group-theoretical concepts; Concepts of coset, order of an elements, and isomorphism; Completion of the learning cycle.

This article examines the technical issues which deals with the role of the U.S. Census Bureau. The idea to get straight about the federal census is that the counting of population is both an abstraction and an empirical reality. That these alternative notions about the census population count do not nicely correspond to the same standard may be no surprise to the demographer but it is not part of the everyday understanding of the general public. Moreover, legal meanings bearing on population arising in the large body of law on the subject, across the several levels of government, among legislative, judicial and executive pronouncements, introduce additional and further removes from a unified idea of a population count. It is from such different perspectives that charges of reckless failure to fully and accurately enumerate the population arise against the Census Bureau.

The article specifies the need for an activity-centered science program for elementary science education in the United States. Apparently, existing general science programs have become a superficial smattering of unarticulated topics, that is, it has become too general. One of the basic advantages of the doing approach or activity-centered program is its variety for individual differences of ability. More significantly, the guided activities permit tangible evidence of difficult abstractions, leading to increased comprehension and physical evidence.

The article cites a study that aims to present and to illustrate a general approach to the study and the improvement of a group of children's scientific concept development in the U.S. The study also intends to describe and analyze what was learned about the scientific concept development of a group of 29 children through a study of their percepts, interpretations, and problem solving. And the children studied were 10 to 12 years of age, and of superior intelligence. Concept development is essential to effective thinking and learning. Because concept development is so intricately related to children's total development, teachers and parents need to know and understand more about it.