A coordinate-free definition of complex-structure multidimensional item response theory (MIRT) for dichotomously scored items is presented. The point of view taken emphasizes the possibilities and subtleties of understanding MIRT as a multidimensional extension of the classical unidimensional item response theory models. The main theorem of the…

Background: Since the 1990s, people with intellectual disability (ID) in the Netherlands have been moving from institutions to supported accommodation in the community. The Government is in need of recent data on the numbers of these people, to ensure adequate care provision and funding. This paper reports on the prevalence of people with ID in…

There has been a growing interest in understanding the computations involved in the processes underlying visual segmentation and interpolation in conditions of occlusion. P. J. Kellman, P. Garrigan, T. F. Shipley, and B. P. Keane and M. K. Albert defended the view that identical contour interpolation mechanisms underlie modal and amodal…

Special ability in computing the day of the week from given dates was observed in a 18 years old male, L.E., suffering from autism. Neuropsychological testing revealed severe deficits in all cognitive domains and poor explicit knowledge of calendar structure. The subject scored well above the chance level on dates of the past and future decades.…

This article presents some identities on the sum of the entries in the first half of a row in Pascal's triangle. The results were discovered while the author was working on a problem involving Laplace transforms, which are used in proving of the identities.

This article considers an old version of the classical pursuit problem as posed by Francis Godwin in 1599, who imagines a wedge of swans flying from the earth to the moon in twelve days, always flying at constant speed toward the moon. The return trip, during which the swans always fly toward the earth at the same speed, takes eight days. A little…

A ball placed on the edge of a horizontal table is hit with a pendulum and thrown over the floor. The fall time is measured by recording the sounds produced by the collisions with the pendulum and the floor. If the height of the ball with respect to the floor is known, one can determine the acceleration of gravity.

We observed, using polarized light microscopy, the supercooling of the blue phase (BPI) of cholesteryl proprionate and measured the corresponding liquid crystalline phase transition temperatures. From these temperatures and additional published data we have provided, for the benefit of undergraduate physics students, a nontraditional example…

Bayesian methods for analyzing longitudinal data in social and behavioral research are recommended for their ability to incorporate prior information in estimating simple and complex models. We first summarize the basics of Bayesian methods before presenting an empirical example in which we fit a latent basis growth curve model to achievement data…

Almost all introductory and intermediate level statistics textbooks include the topic of confidence interval for the population mean. Almost all these texts introduce the median as a robust measure of central tendency. Only a few of these books, however, cover inference on the population median and in particular confidence interval for the median.…

This note considers a family of piece-wise linear functions that can be used in the classroom to illustrate various concepts involved in iteration theory such as periodicity. These functions require minimal background on the part of the student. (Contains 2 figures.)

Describing the world in terms of energy is necessarily quantitative: one must be able to do the sums for the description to gain a purchase. Whilst teaching younger children (say 11-14 years old) the full quantitative description is not available and this has made the introductory teaching of energy a contentious area. By focusing on…

The analysis explains the basis set superposition error (BSSE) and fragment relaxation involved in calculating the interaction energies using various first principle theories. Interacting the correlated fragment and increasing the size of the basis set can help in decreasing the BSSE to a great extent.

Vieta's famous product using factors that are nested radicals is the oldest infinite product as well as the first non-iterative method for finding [pi]. In this paper a simple geometric construction intimately related to this product is described. The construction provides the same approximations to [pi] as are given by partial products from…

After prolonged viewing of a slowly drifting or rotating pattern under strict fixation, the pattern appears to slow down and then momentarily stop. The authors show that grouping can slow down the process of "motion fading," suggesting that cortical configural form analysis interacts with the computation of motion signals during motion fading. The…