Translated Poisson approximation to equilibrium distributions of Markov population processes

The paper is concerned with the equilibrium distributions of continuous-time density dependent Markov processes on the integers. These distributions are known typically to be approximately normal, and the approximation error, as measured in Kolmogorov distance, is of the smallest order that is compatible with their having integer support. Here, an approximation in the much stronger total variation norm is established, without any loss in the asymptotic order of accuracy; the approximating distribution is a translated Poisson distribution having the same variance and (almost) the same mean. Our arguments are based on the Stein-Chen method and Dynkin's formula.Comment: 18 page

Connecting deterministic and stochastic metapopulation models

In this paper, we study the relationship between certain stochastic and deterministic versions of Hanski's incidence function model and the spatially realistic Levins model. We show that the stochastic version can be well approximated in a certain sense by the deterministic version when the number of habitat patches is large, provided that the presence or absence of individuals in a given patch is influenced by a large number of other patches. Explicit bounds on the deviation between the stochastic and deterministic models are given.Comment: The final publication is available at Springer via http://dx.doi.org/10.1007/s00285-015-0865-

Local approximation of a metapopulation's equilibrium

We consider the approximation of the equilibrium of a metapopulation model, in which a finite number of patches are randomly distributed over a bounded subset $\Omega$ of Euclidean space. The approximation is good when a large number of patches contribute to the colonization pressure on any given unoccupied patch, and when the quality of the patches varies little over the length scale determined by the colonization radius. If this is the case, the equilibrium probability of a patch at $z$ being occupied is shown to be close to $q_1(z)$, the equilibrium occupation probability in Levins's model, at any point $z \in \Omega$ not too close to the boundary, if the local colonization pressure and extinction rates appropriate to $z$ are assumed. The approximation is justified by giving explicit upper and lower bounds for the occupation probabilities, expressed in terms of the model parameters. Since the patches are distributed randomly, the occupation probabilities are also random, and we complement our bounds with explicit bounds on the probability that they are satisfied at all patches simultaneously

State of the Nation: K–12 Online Learning in Canada

A variety of initiatives are driving online and blended learning in each of Canada’s provinces and territories. From teachers’ unions in Nova Scotia fighting to ensure online learning is an accepted method of educational delivery, to Ontario’s College of Teachers creating an e-learning endorsement for teachers or the British Columbia government creating policies to expand the growth and opportunities online learning provides, there are multiple, isolated initiatives happening across the country. State of the Nation: K-12 Online Learning in Canada is now in its fourth year of publication and can be seen as a national guide for understanding the field and the state of online learning across all provinces and territories. The report can also provide guidance, resources, and ideas for how to improve both policy barriers and teacher practice in the nation’s schools in order to provide access to high quality educational opportunities for all students through online and blended learning

Introducing In-Service Teachers to Virtual Schooling Through the Lens of the Three Teacher Roles

This study will examine the third and fourth rounds of data collection from an action research project designed to help in-service teachers become better virtual school facilitators (currently being analyzed). The data included blog entries and comments from five of the seven graduate students in an instructional technology course related to K-12 online learning. The specific discussion prompts relate to virtual school readings and the Teacher Education Goes into Virtual Schooling (TEGIVS) curriculum. Based upon initial analysis, the TEGIVS curriculum was effective for providing these graduate students some experience with how K-12 online learning opportunities were delivered, along with some of the possibilities and challenges associated with K-12 online learning. The analysis of this data is continuing, and there are plans to continue this line of inquiry with additional students in future offerings as we continue to improve upon the course design

Book Review - The Publish or Perish Book: Your Guide to Effective and Responsible Citation Analysis

Book review by Michael K. Barbour. Harzing, Anne-Wil. The Publish or Perish Book: Your Guide to Effective and Responsible Citation Analysis. Melbourne, Australia: Tarma Software Research Pty Ltd., 2011

Principles of Effective Web-Based Content for Secondary School Students: Teacher and Developer Perceptions

In this article, I describe findings from a study of the perceptions of course developers and electronic teachers on the principles of effective asynchronous web-based content design for secondary school students. Through interviews, participants\u27 perceptions of various web-based components and instructional strategies, and the effectiveness of both based upon the experiences of the participants were investigated in a virtual high school context for the purpose of generating a list of guidelines that future course developers might utilize

Review of Virtual Schooling and Student Learning

A new report compares the performance of Florida Virtual School (FLVS) students with students in traditional brick-and-mortar schools and concludes the FLVS students perform about the same or somewhat better on state tests and at a lower cost. The report claims to be the first empirical study of K-12 student performance in virtual education. This is not correct, and the report in fact confirms the findings and repeats the methodological flaws and limitations of previous research. The report’s findings fail to account for the potential bias of student selectivity in the FLVS sample, the potential impact of regression effects, differential mortality in the two groups, and the fact that the virtual environment is simply a delivery medium. Given the limitations of research such as this new study, researchers have moved beyond simply investigating whether one medium is better than the other and begun—and need to continue—investigating under what conditions K-12 online and blended learning can be effectively designed, delivered, and supported

Portrait of Rural Virtual Schooling

Over the past two decades, distance education has become a reality of rural schooling in Newfoundland and Labrador. In this article, I provide historical background into the challenges facing rural schools in the province and how distance education was introduced to address that challenge. I also describe how that system of distance education evolved from a system that used the telephone lines and bridging technology to one that uses a combination synchronous and asynchronous system delivered over the Internet. Finally, I examine recent literature concerning the nature of today’s secondary students that would need to avail of this system and relate how this may not be an applicable portrait of youth in rural areas, such as Newfoundland and Labrador

Who’s Researching Virtual Schools?: A Case for Instructional Technologists

Over the past 11 years, virtual schooling has gone from isolated experiments to a reliable alternative to a brick and mortar education. However, during this time, little research has been conducted into how these learning opportunities are and should be provided to their adolescent audiences. Even more troubling is that very few of these researchers are from the field of instructional technology. In this article, I discuss those who have been involved in this early research and then make a case for the value that instructional technologists can bring to this emerging field