Data modeling in elementary and middle school classes : a shared experience

This paper argues for a renewed focus on statistical reasoning in the elementary school years, with opportunities for children to engage in data modeling. Data modeling involves investigations of meaningful phenomena, deciding what is worthy of attention, and then progressing to organizing, structuring, visualizing, and representing data. Reported here are some findings from a two-part activity (Baxter Brown’s Picnic and Planning a Picnic) implemented at the end of the second year of a current three-year longitudinal study (grade levels 1-3). Planning a Picnic was also implemented in a grade 7 class to provide an opportunity for the different age groups to share their products. Addressed here are the grade 2 children’s predictions for missing data in Baxter Brown’s Picnic, the questions posed and representations created by both grade levels in Planning a Picnic, and the metarepresentational competence displayed in the grade levels’ sharing of their products for Planning a Picnic.

Establishing statistical foundations early : data modeling with young learners

This paper addresses research from a three-year longitudinal study that engaged children in data modeling experiences from the beginning school year through to third year (6-8 years). A data modeling approach to statistical development differs in several ways from what is typically done in early classroom experiences with data. In particular, data modeling immerses children in problems that evolve from their own questions and reasoning, with core statistical foundations established early. These foundations include a focus on posing and refining statistical questions within and across contexts, structuring and representing data, making informal inferences, and developing conceptual, representational, and metarepresentational competence. Examples are presented of how young learners developed and sustained informal inferential reasoning and metarepresentational competence across the study to become “sophisticated statisticians”.

Cardiovascular diseases and vulnerable plaques: data, modeling, predictions and clinical applications PREFACE

Introduction Two symposia on “cardiovascular diseases and vulnerable plaques” Cardiovascular disease (CVD) is the leading cause of death worldwide. Huge effort has been made in many disciplines including medical imaging, computational modeling, bio- mechanics, bioengineering, medical devices, animal and clinical studies, population studies as well as genomic, molecular, cellular and organ-level studies seeking improved methods for early detection, diagnosis, prevention and treatment of these diseases [1-14]. However, the mechanisms governing the initiation, progression and the occurrence of final acute clinical CVD events are still poorly understood. A large number of victims of these dis- eases who are apparently healthy die suddenly without prior symptoms. Available screening and diagnostic methods are insufficient to identify the victims before the event occurs [8,9]. Most cardiovascular diseases are associated with vulnerable plaques. A grand challenge here is to develop new imaging techniques, predictive methods and patient screening tools to identify vulnerable plaques and patients who are more vulnerable to plaque rupture and associated clinical events such as stroke and heart attack, and recommend proper treatment plans to prevent those clinical events from happening. Articles in this special issue came from two symposia held recently focusing on “Cardio-vascular Diseases and Vulnerable Plaques: Data, Modeling, Predictions and Clinical Applications.” One was held at Worcester Polytechnic Institute (WPI), Worcester, MA, USA, July 13-14, 2014, right after the 7th World Congress of Biomechanics. This symposium was endorsed by the World Council of Biomechanics, and partially supported by a grant from NIH-National Institute of Biomedical Image and Bioengineering. The other was held at Southeast University (SEU), Nanjing, China, April 18-20, 2014.

A design pattern approach to bitemporal data modeling

The importance of patterns in constructing complex systems has long been recognised in other disciplines. In software engineering, for example, well-crafted object-oriented architectures contain several design patterns. Focusing on mechanisms of constructing software during system development can yield an architecture that is simpler, clearer and more understandable than if design patterns were ignored or not properly applied. In this paper, we propose a model that uses object-oriented design patterns to develop a core bitemporal conceptual model. We define three core design patterns that form a core bitemporal conceptual model of a typical bitemporal object. Our framework is known as the Bitemporal Object, State and Event Modelling Approach (BOSEMA) and the resulting core model is known as a Bitemporal Object, State and Event (BOSE) model. Using this approach, we demonstrate that we can enrich data modelling by using well known design patterns which can help designers to build complex models of bitemporal databases.

Particle swarm optimization aided orthogonal forward regression for unified data modeling

We propose a unified data modeling approach that is equally applicable to supervised regression and classification applications, as well as to unsupervised probability density function estimation. A particle swarm optimization (PSO) aided orthogonal forward regression (OFR) algorithm based on leave-one-out (LOO) criteria is developed to construct parsimonious radial basis function (RBF) networks with tunable nodes. Each stage of the construction process determines the center vector and diagonal covariance matrix of one RBF node by minimizing the LOO statistics. For regression applications, the LOO criterion is chosen to be the LOO mean square error, while the LOO misclassification rate is adopted in two-class classification applications. By adopting the Parzen window estimate as the desired response, the unsupervised density estimation problem is transformed into a constrained regression problem. This PSO aided OFR algorithm for tunable-node RBF networks is capable of constructing very parsimonious RBF models that generalize well, and our analysis and experimental results demonstrate that the algorithm is computationally even simpler than the efficient regularization assisted orthogonal least square algorithm based on LOO criteria for selecting fixed-node RBF models. Another significant advantage of the proposed learning procedure is that it does not have learning hyperparameters that have to be tuned using costly cross validation. The effectiveness of the proposed PSO aided OFR construction procedure is illustrated using several examples taken from regression and classification, as well as density estimation applications.

The application of Prony’s method to time-domain waveform data modeling in the presence of noise

In this paper,the Prony's method is applied to the time-domain waveform data modelling in the presence of noise.The following three problems encountered in this work are studied:(1)determination of the order of waveform;(2)de-termination of numbers of multiple roots;(3)determination of the residues.The methods of solving these problems are given and simulated on the computer.Finally,an output pulse of model PG-10N signal generator and the distorted waveform obtained by transmitting the pulse above mentioned through a piece of coaxial cable are modelled,and satisfactory results are obtained.So the effectiveness of Prony's method in waveform data modelling in the presence of noise is confirmed.

Comparing novice designer performance using a rule -based approach versus a pattern -based approach in conceptual data modeling tasks

Conceptual database design is an unusually difficult and error-prone task for novice designers. This study examined how two training approaches---rule-based and pattern-based---might improve performance on database design tasks. A rule-based approach prescribes a sequence of rules for modeling conceptual constructs, and the action to be taken at various stages while developing a conceptual model. A pattern-based approach presents data modeling structures that occur frequently in practice, and prescribes guidelines on how to recognize and use these structures. This study describes the conceptual framework, experimental design, and results of a laboratory experiment that employed novice designers to compare the effectiveness of the two training approaches (between-subjects) at three levels of task complexity (within subjects). Results indicate an interaction effect between treatment and task complexity. The rule-based approach was significantly better in the low-complexity and the high-complexity cases; there was no statistical difference in the medium-complexity case. Designer performance fell significantly as complexity increased. Overall, though the rule-based approach was not significantly superior to the pattern-based approach in all instances, it out-performed the pattern-based approach at two out of three complexity levels. The primary contributions of the study are (1) the operationalization of the complexity construct to a degree not addressed in previous studies; (2) the development of a pattern-based instructional approach to database design; and (3) the finding that the effectiveness of a particular training approach may depend on the complexity of the task.

‘Modeling and Analysis of Competing Risks Data’

there has been much research on analyzing various forms of competing risks data. Nevertheless, there are several occasions in survival studies, where the existing models and methodologies are inadequate for the analysis competing risks data. ldentifiabilty problem and various types of and censoring induce more complications in the analysis of competing risks data than in classical survival analysis. Parametric models are not adequate for the analysis of competing risks data since the assumptions about the underlying lifetime distributions may not hold well. Motivated by this, in the present study. we develop some new inference procedures, which are completely distribution free for the analysis of competing risks data.

Beyond statistical procedures for predictive modelling: Data mining algorithms and support for university research at QUT

In a seminal data mining article, Leo Breiman [1] argued that to develop effective predictive classification and regression models, we need to move away from the sole dependency on statistical algorithms and embrace a wider toolkit of modeling algorithms that include data mining procedures. Nevertheless, many researchers still rely solely on statistical procedures when undertaking data modeling tasks; the sole reliance on these procedures has lead to the development of irrelevant theory and questionable research conclusions ([1], p.199). We will outline initiatives that the HPC & Research Support group is undertaking to engage researchers with data mining tools and techniques; including a new range of seminars, workshops, and one-on-one consultations covering data mining algorithms, the relationship between data mining and the research cycle, and limitations and problems with these new algorithms. Organisational limitations and restrictions to these initiatives are also discussed.

Young children’s metarepresentational competence in data modelling

longitudinal study of data modelling across grades 1-3. The activity engaged children in designing, implementing, and analysing a survey about their new playground. Data modelling involves investigations of meaningful phenomena, deciding what is worthy of attention (identifying complex attributes), and then progressing to organising, structuring, visualising, and representing data. The core components of data modelling addressed here are children’s structuring and representing of data, with a focus on their display of metarepresentational competence (diSessa, 2004). Such competence includes students’ abilities to invent or design a variety of new representations, explain their creations, understand the role they play, and critique and compare the adequacy of representations. Reported here are the ways in which the children structured and represented their data, the metarepresentational competence displayed, and links between their metarepresentational competence and conceptual competence.

Surviving an avalanche of data

Open the sports or business section of your daily newspaper, and you are immediately bombarded with an array of graphs, tables, diagrams, and statistical reports that require interpretation. Across all walks of life, the need to understand statistics is fundamental. Given that our youngsters’ future world will be increasingly data laden, scaffolding their statistical understanding and reasoning is imperative, from the early grades on. The National Council of Teachers of Mathematics (NCTM) continues to emphasize the importance of early statistical learning; data analysis and probability was the Council’s professional development “Focus of the Year” for 2007–2008. We need such a focus, especially given the results of the statistics items from the 2003 NAEP. As Shaughnessy (2007) noted, students’ performance was weak on more complex items involving interpretation or application of items of information in graphs and tables. Furthermore, little or no gains were made between the 2000 NAEP and the 2003 NAEP studies. One approach I have taken to promote young children’s statistical reasoning is through data modeling. Having implemented in grades 3 –9 a number of model-eliciting activities involving working with data (e.g., English 2010), I observed how competently children could create their own mathematical ideas and representations—before being instructed how to do so. I thus wished to introduce data-modeling activities to younger children, confi dent that they would likewise generate their own mathematics. I recently implemented data-modeling activities in a cohort of three first-grade classrooms of six year- olds. I report on some of the children’s responses and discuss the components of data modeling the children engaged in.

Conceptual modeling - an epistemological foundation

The success of contemporary organizations depends on their ability to make appropriate decisions. Making appropriate decisions is inevitably bound to the availability and provision of relevant information. Information systems should be able to provide information in an efficient way. Thus, within information systems development a detailed analysis of information supply and information demands has to prevail. Based on Syperski’s information set and subset-model we will give an epistemological foundation of information modeling in general and show, why conceptual modeling in particular is capable of specifying effective and efficient information systems. Furthermore, we derive conceptual modeling requirements based on our findings. A short example illustrates the usefulness of a conceptual data modeling technique for the specification of information systems.

Representation, comparison, and interpretation of metabolome fingerprint data for total composition analysis and quality trait investigation in potato cultivars

Manfred Beckmann, David P. Enot, David P. Overy, and John Draper (2007). Representation, comparison, and interpretation of metabolome fingerprint data for total composition analysis and quality trait investigation in potato cultivars. Journal of Agricultural and Food Chemistry, 55 (9) pp.3444-3451 RAE2008

Uncertainty visualization in 3D scalar data

One problem in most three-dimensional (3D) scalar data visualization techniques is that they often overlook to depict uncertainty that comes with the 3D scalar data and thus fail to faithfully present the 3D scalar data and have risks which may mislead users’ interpretations, conclusions or even decisions. Therefore this thesis focuses on the study of uncertainty visualization in 3D scalar data and we seek to create better uncertainty visualization techniques, as well as to find out the advantages/disadvantages of those state-of-the-art uncertainty visualization techniques. To do this, we address three specific hypotheses: (1) the proposed Texture uncertainty visualization technique enables users to better identify scalar/error data, and provides reduced visual overload and more appropriate brightness than four state-of-the-art uncertainty visualization techniques, as demonstrated using a perceptual effectiveness user study. (2) The proposed Linked Views and Interactive Specification (LVIS) uncertainty visualization technique enables users to better search max/min scalar and error data than four state-of-the-art uncertainty visualization techniques, as demonstrated using a perceptual effectiveness user study. (3) The proposed Probabilistic Query uncertainty visualization technique, in comparison to traditional Direct Volume Rendering (DVR) methods, enables radiologists/physicians to better identify possible alternative renderings relevant to a diagnosis and the classification probabilities associated to the materials appeared on these renderings; this leads to improved decision support for diagnosis, as demonstrated in the domain of medical imaging. For each hypothesis, we test it by following/implementing a unified framework that consists of three main steps: the first main step is uncertainty data modeling, which clearly defines and generates certainty types of uncertainty associated to given 3D scalar data. The second main step is uncertainty visualization, which transforms the 3D scalar data and their associated uncertainty generated from the first main step into two-dimensional (2D) images for insight, interpretation or communication. The third main step is evaluation, which transforms the 2D images generated from the second main step into quantitative scores according to specific user tasks, and statistically analyzes the scores. As a result, the quality of each uncertainty visualization technique is determined.