Refinement for Probabilistic Systems with Nondeterminism

Before we combine actions and probabilities two very obvious questions should be asked. Firstly, what does "the probability of an action" mean? Secondly, how does probability interact with nondeterminism? Neither question has a single universally agreed upon answer but by considering these questions at the outset we build a novel and hopefully intuitive probabilistic event-based formalism. In previous work we have characterised refinement via the notion of testing. Basically, if one system passes all the tests that another system passes (and maybe more) we say the first system is a refinement of the second. This is, in our view, an important way of characterising refinement, via the question "what sort of refinement should I be using?" We use testing in this paper as the basis for our refinement. We develop tests for probabilistic systems by analogy with the tests developed for non-probabilistic systems. We make sure that our probabilistic tests, when performed on non-probabilistic automata, give us refinement relations which agree with for those non-probabilistic automata. We formalise this property as a vertical refinement.Comment: In Proceedings Refine 2011, arXiv:1106.348

Approaches for modeling magnetic nanoparticle dynamics

Magnetic nanoparticles are useful biological probes as well as therapeutic agents. There have been several approaches used to model nanoparticle magnetization dynamics for both Brownian as well as N\'eel rotation. The magnetizations are often of interest and can be compared with experimental results. Here we summarize these approaches including the Stoner-Wohlfarth approach, and stochastic approaches including thermal fluctuations. Non-equilibrium related temperature effects can be described by a distribution function approach (Fokker-Planck equation) or a stochastic differential equation (Langevin equation). Approximate models in several regimes can be derived from these general approaches to simplify implementation

The Ungraded Primary Department: Centennial Lab School, Decatur, Illinois

During the summer of 1980, this writer became a member of the faculty of Centennial Laboratory School, 1500 East Condit, Decatur, Illinois. The transfer to Centennial occurred in order to take part in the establishment of an Ungraded Primary Department within that school. This paper examines the rationale, planning, and production of such a department as an integral part of the total educational program of Centennial during the first semester of its existence. The Ungraded Primary Department is a valuable educational experience for five, six, and seven year old children. It provides flexibility of grouping according to individual needs, a system of continuous progress and evaluation of children\u27s needs, reduces the problems associated with acceleration and retention, and provides each child with experiences which provide success, self-esteem, and well-rounded growth in all areas. The paper is divided into four main sections. The first section of the paper serves as the introduction, explaining the purpose of the field experience, giving pertinent background information, and reviewing briefly some of the literature consulted in establishing the department. Section II consists of a Log of Activities carried out as a part of the field experience. Both as an observer of the department and a participant in its development, this writer was involved in numerous activities. This log is a weekly record of the activities unique to the establishment and development of the Ungraded Primary Department. Section III is an analyses of the four major activities conducted as a part of the field study. The activities reported include Student Placement, Instructional Program, Communications, and Mainstreaming Students. The Student Placement section outlines both the Initial Placement plan, which includes screening, interviewing, and reviewing past performance, and the Adjustive Placement plan which corrects errors made in initial placement. The Instructional Program section details both the content of the curriculum and the methods used to enhance learning. The curriculum is a balance between teaching and learning experiences. For purposes of this paper Communication activities are reported in two sections---those activities of communication between staff members and communication activities between school and home. Children are mainstreamed into the Ungraded Primary Department from two different sources and for two very different reasons. They come from the Early Childhood (Special Education) Department for exposure to the normal classroom and from the Refugee Classroom to learn English. The summary, Section IV of the paper, contains conclusions and recommendations for the future. The nine appendices to the paper contain forms, communication and evaluation devices, and other information which has been part of the development of the Ungraded Primary Department

Playful exploration and meaning making in and out of school with cross-curricula creative computing

This paper shows how the methods of software development and the art of computer programming can provide meaning in the school's and the wider curriculum, while encouraging a playful exploration and expression of knowledge with young people. The paper provides an analysis of computing's place in the educational world. This includes a focus on creativity in computing as an influence in helping people to explore information, communicate their worldview in an expressive and engaging way, and work well with other people in facilitating the expression of their ideas. The research into the influence of creative computing in the learning of both primary and secondary age pupils is focused on weekly computing clubs in a primary and secondary school. The self-study focuses on a pedagogical approach that is cross-curricula and design based, in keeping with professional practice of software development, and allows each child to uniquely express themselves within the living curriculum, while achieving results that are measureable within the given curriculum. The creative development of 150 children is used to demonstrate how computing can be used to reinforce the educational strands of literacy and numeracy, as well as other cross-curricula activities, such as evidence, environment and sustainability, and constructive self-expression

Average eccentricity values of the human cornea at 7, 8, and 9 mm chords

Eccentricity is a value that describes how much the peripheral curve radius flattens with respect to the apical curve radius. Much of the fitting of RGPs takes place in the periphery; this is why it is important to take into account eccentricity when fitting lenses. 100 subjects had eccentricities measured of their right eye at 7, 8, and 9 mm chords and the data analyzed. The average eccentricities are 0.572, 0.603, and 0.635 for the 7, 8, and 9 mm chords respectively. The average values show greater eccentricities as you move into the periphery of the cornea, demonstration that eccentricity can change a great deal with small changes in chord length. We have shown that there is a large, well distributed range of values at each chord. Very few of those sampled would have eccentricities that would not change the peripheral curve radius by ±1/8th D from the expected peripheral curve radius at a given chord. Furthermore, small changes in eccentricity can change the peripheral curve radius a great deal. Because of this large distribution of values, and because a small change in eccentricity can have great impacts on peripheral steepness, it is important to take into account eccentricity, and the position where the lens fits on the cornea when fitting RGP lenses

Letter from John Collins & John Reeves to James B. Finley

Collins writes that Finley\u27s letter was delayed in reaching him, so he was not able to procure requested places for the Indian boys. He reports that there are seven Indian boys in his district. Brother Waddle has requested that the district supply clothing and other needed items to the boys. Collins has recently seen Finley\u27s father, who appears to be in good health. The latter preached one of his best sermons at a quarterly meeting two weeks ago. Abstract Number - 741https://digitalcommons.owu.edu/finley-letters/2249/thumbnail.jp