In 2008, the greatest experiment in history began. When in full operation, the Large Hadron Collider (LHC) at CERN will generate the greatest amount of information that has ever been produced in an experiment before. It will also reveal some of the most fundamental secrets of nature. Despite the enormous amount of information available on this…

Two models for the analysis of longitudinal binary data are discussed: the marginal model and the random intercepts model. In contrast to the linear mixed model (LMM), the two models for binary data are not subsumed under a single hierarchical model. The marginal model provides group-level information whereas the random intercepts model provides…

The Pareto 80/20 Rule, also known as the Pareto principle or law, states that a small number of causes (20%) is responsible for a large percentage (80%) of the effect. Although widely recognized as a heuristic rule, this proportion has not been theoretically based. The article considers derivation of this 80/20 rule and some other standard…

Cognitive or skills diagnosis models are discrete latent variable models developed specifically for the purpose of identifying the presence or absence of multiple fine-grained skills. However, applications of these models typically involve dichotomous or dichotomized data, including data from multiple-choice (MC) assessments that are scored as…

In demand paging virtual memory systems, the page fault rate of a process varies with the number of memory frames allocated to the process. When an increase in the number of allocated frames leads to an increase in the number of page faults, Belady's anomaly is said to occur. In this paper, we present a probability model for Belady's anomaly. We…

The topic "Recurrence relations" and its place in teaching students of Informatics is discussed in this paper. We represent many arguments about the importance, the necessity and the benefit of studying this subject by Informatics students. They are based on investigation of some fundamental books and textbooks on Discrete Mathematics,…

Early lexical acquisition is affected by biases and constraints within learners, but also by patterns and statistical regularities within a learner's environment. Much of the previous work examining the effect of statistical regularities on word learning has been directed at phonological regularities. Particularly, research has focused on the…

This study reports how the difficulty of simple worded percentage problems is affected by the problem structure and the complexity of the numbers involved. We also investigate which methods students know. Results from 677 Year 8 and 9 students are reported. Overall the results indicate that more attention needs to be given to this important topic.…

Randomized trials of educational interventions often face logistical hurdles (Cook, 2002). For example, sometimes they are prevented from reaching their full-term. This would happen if, as a condition of participation, subjects insist on receiving the treatment program within a certain timeframe. This timeframe may be shorter than the full-term…

The Center on Education Policy, an independent nonprofit organization, collected and analyzed data from state Web sites and other sources to determine how many schools in the nation and in each state did not make adequate yearly progress (AYP) under the No Child Left Behind Act (NCLB). Findings of the study include: (1) About one-third of U.S.…

Phase thermodynamics is often perceived as a difficult subject with which many students never become fully comfortable. The Gibbsian geometrical framework can help students to gain a better understanding of phase equilibria. An exercise to interpret the vapor-liquid equilibrium of a binary azeotropic mixture, using the equilibrium condition based…

An overview of a course on modeling and simulation offered at the Nanotechnology Engineering undergraduate program at the University of Waterloo. The motivation for having this course in the undergraduate nanotechnology curriculum, the course structure, and its learning objectives are discussed. Further, one of the computational laboratories…

We propose a simple, direct estimate of the Sun's diameter based on penumbra observation and measurement in a two-level approach, the first for middle-school pupils and making use of simple geometrical arguments, the second more appropriate to high-school students and based on a slightly more sophisticated approach. (Contains 5 figures.)

Interruptions are common in joint activities like conversations. Typically, interrupted participants suspend the activity, address the interruption, and then reinstate the activity. In conversation, people jointly commit to interact and to talk about a topic, establishing these commitments sequentially. When a commitment is suspended, face is…

In this article, we discuss the effect of removing the independence assumptions between the residuals in two-level random effect models. We first consider removing the independence between the Level 2 residuals and instead assume that the vector of all residuals at the cluster level follows a general multivariate normal distribution. We…