The Development of Comprehension of Chance Language: Evaluation and Interpretation

Comprehension of chance language, such as is found in newspapers, is a fundamental aspect of statistical literacy. In this study, students' understandings of chance language were explored through responses to two items in surveys administered to 2,726 students from grades 5 to 11. One item involved evaluating the chance expressed in phrases from newspaper headlines using a number line, and responses were described in four levels of chance language evaluation. The other item involved interpreting, in context, an expression of percent chance, and responses were described in four levels of chance language interpretation. Students in higher grades were more likely to demonstrate higher levels of both evaluation and interpretation. The association between levels of evaluation and interpretation was further explored generally and in relation to one of the headlines involving percent. Implications for mathematics educators in relation to chance language in the curriculum across the years of schooling are discussed.     

Modeling the cochlear nucleus: a site for monaural echo suppression?

Echo suppression plays an important role in identifying and localizing auditory objects. One can distinguish between binaural and monaural echo suppression, although the former is the one commonly referred to. Based on biological findings we introduce and analyze a mathematical model for a neural implementation of monaural echo suppression in the cochlear nucleus. The model's behavior has been verified by analytical calculations as well as by numerical simulations for several types of input signal. It shows that in the perception of a pair of clicks the leading click suppresses the lagging one and that suppression is maximal for an interclick interval of 2-3 ms. Similarly, ongoing stimuli will be affected by the suppression mechanism primarily a couple of milliseconds after onset, resulting in a reduced perception of a sound shortly after its start. Both effects match experimental data.     

Asymptotic behavior of weakly dependent aggregated processes

Aggregated processes appear in many areas of statistics, natural sciences and economics and studying their behavior has a considerable importance from a purely probabilistic point of view as well. Granger (1980) showed that aggregating processes of simple structure can lead to processes with much more complex dynamics, in particular, aggregating random coefficient AR(1) processes can result in long memory processes. This opens a new way to analyze complex processes by constructing such processes from simple ‘building blocks’ via aggregation.     

Generation of potential energy surfaces in high dimensions and their haptic exploration

A method is proposed for the automated generation of potential energy surfaces in high dimensions. It combines the existing algorithm for the definition of new energy data points, based on the interpolating moving least-squares algorithm with a simulated annealing procedure. This method is then studied in a haptic quantum chemistry environment that requires a fast evaluation of gradients on a potential energy surface with automatic improvement of its accuracy. As an example we investigate the nitrogen binding pathway in the Schrock dinitrogen fixation complex with this set-up.     

A classification tree approach for the modeling of competing risks in discrete time

Advances in Data Analysis and Classification - Cause-specific hazard models are a popular tool for the analysis of competing risks data. The classical modeling approach in discrete time consists of...     

The measurement of frequency separations in high-resolution nuclear magnetic resonance spectra using a double-lock spectrometer

The rotation-ring-puckering problem of four-membered ring cyclobutane-type molecules with D _4h -D _2d conformations is formulated as a dynamical system in the eulerian angles and the polar coordinate ?. Classical and quantum-mechanical hamiltonians and their symmetry group O ⁺⁺(3) × D _∞h are discussed. The kinetic energy matrix coefficients g_mm are found to be irrational functions of the trigonometric polynomial 3 + cos 2? in the internal coordinate ?. It is shown that the energy matrix coefficients may all be expressed as Laurent coefficients by means of the hypergeometric function ₂ F ₁, the convergence being determined by the roots of the kinetic determinant. Selection rules and matrix elements for rotation-ring-puckering Raman transitions are given.