Evaluation of three interventions teaching area measurement as spatial structuring to young children

We evaluated the effects of three instructional interventions designed to support young children’s understanding of area measurement as a structuring process. Replicating microgenetic procedures we used in previous research with older children to ascertain whether we can build these competencies earlier, we also extended the previous focus on correctness to include analyses of children’s use of procedural and conceptual knowledge and examined individual differences in strategy shifts before and after transitions, enabling a more detailed examination of the hypothesized necessity of development through each level of a learning trajectory. The two experimental interventions focused on a dynamic conception of area measurement while also emphasizing unit concepts, such as unit identification, iteration, and composition. The findings confirm and extend earlier results that seeing a complete record of the structure of the 2D array—in the form of a drawing of organized rows and columns—supported children’s spatial structuring and performance.     

Constraint-Based Representations of Statistical Graphs

Abstract

Pictor is an environment for statistical graphics that promotes simple commands for common uses and offers the ability to experiment with whole new paradigms. Pictor describes graphs as graphical objects whose component pieces are related by several sorts of constraints. This article describes in detail the constraint system that Pictor uses.     

Extremal A-statistical limit points via ideals

In this paper, following the line of recent work of Savaş et al. [20] we apply the notion of ideals to A-statistical limit superior and inferior for a sequence of real numbers.     

A statistical model for global optimization by means of select and clone

A statistical model tor giobai optimization is constructed generalizing some properties ofthe Wiener process to the multidimensional case. A new approach, which is similar to the Branch and Bound approach, is proposed to the construction of algorithms based on statistical models. A two dimensional version of the algorithm is implemented, and test results are presented     

线型和非线型分子转动光谱强度的统计模型

In this study, we found regular behavior, from a statistical point of view, in the intensities of rotational spectra for several organic and inorganic molecules at room temperature. Non-linear molecules, for which a common intensity behavior was derived, were especially interesting. We provided theoretical support for the obtained results based on the Boltzmann distribution. Boltzmann power laws were used to reproduce the statistical behavior of the intensities from the spectra of linear and non-linear molecules. We only used statistical arguments and no specific details of any molecule were used. Therefore, these results are applicable to a large class of atoms and molecules and the model is valid when considering similar conditions to those used in this study.     

A decision theory for partially consonant belief functions

Partially consonant belief functions (pcb), studied by Walley, are the only class of Dempster-Shafer belief functions that are consistent with the likelihood principle of statistics. Structurally, the set of foci of a pcb is partitioned into non-overlapping groups and within each group, foci are nested. The pcb class includes both probability function and Zadeh’s possibility function as special cases. This paper studies decision making under uncertainty described by pcb. We prove a representation theorem for preference relation over pcb lotteries to satisfy an axiomatic system that is similar in spirit to von Neumann and Morgenstern’s axioms of the linear utility theory. The closed-form expression of utility of a pcb lottery is a combination of linear utility for probabilistic lottery and two-component (binary) utility for possibilistic lottery. In our model, the uncertainty information, risk attitude and ambiguity attitude are separately represented. A tractable technique to extract ambiguity attitude from a decision maker behavior is also discussed.     

Large deviation theory for a homogenized and “corrected” elliptic ODE

We study a one-dimensional elliptic problem with highly oscillatory random diffusion coefficient. We derive a homogenized solution and a so-called Gaussian corrector. We also prove a “pointwise” large deviation principle (LDP) for the full solution and approximate this LDP with a more tractable form. Applications to uncertainty quantification are considered.     

Prediction of work-related accidents according to working conditions using support vector machines

Support vector machines (SVMs), which are a kind of statistical learning methods, were applied in this research work to predict occupational accidents with success. In the first place, semi-parametric principal component analysis (SPPCA) was used in order to perform a dimensional reduction, but no satisfactory results were obtained. Next, a dimensional reduction was carried out using an innovative and intelligent computing regression algorithm known as multivariate adaptive regression splines (MARS) model with good results. The variables selected as important by the previous MARS model were taken as input variables for a SVM model. This SVM technique was able to classify, according to their working conditions, those workers that have suffered a work-related accident in the last 12 months and those that have not. SVM technique does not over-fit the experimental data and gives place to a better performance than back-propagation neural network models. Finally, the results and conclusions of this study are presented.     

A sequential perspective on searching for static targets

We present a sequential approach to detect static targets with imperfect sensors, which range from tower-mounted cameras to satellites. The scenario is operationally relevant to many military, homeland security, search and rescue, environmental engineering, counter-narcotics, and law enforcement applications. The idea is to stop the search as soon as there is enough probabilistic evidence about the targets’ locations, given an operator-prescribed error tolerance, knowledge of the sensors’ parameters, and a sequence of detection signals from the sensors. By stopping the search as soon as possible, we promote efficiency by freeing up sensors and operators to perform other tasks. The model we develop has the added benefits of decreasing operator workload and providing negative information as a search progresses.