Geometric singular perturbation theory for stochastic differential equations

We consider slow-fast systems of differential equations, in which both the slow and fast variables are perturbed by noise. When the deterministic system admits a uniformly asymptotically stable slow manifold, we show that the sample paths of the stochastic system are concentrated in a neighbourhood of the slow manifold, which we construct explicitly. Depending on the dynamics of the reduced system, the results cover time spans which can be exponentially long in the noise intensity squared (that is, up to Kramers' time). We obtain exponentially small upper and lower bounds on the probability of exceptional paths. If the slow manifold contains bifurcation points, we show similar concentration properties for the fast variables corresponding to non-bifurcating modes. We also give conditions under which the system can be approximated by a lower-dimensional one, in which the fast variables contain only bifurcating modes.Comment: 43 pages. Published version. Remarks added, minor correction

A Method for Evaluation and Equation of Test Forms

Notwithstanding the pioneer work of Spearman (1927 (and numerous studies by Thurstone on problems of intelligence, most testing programs seem to postulate only one type of intelligence. Division of the total score may be made into arbitrary categories for use in advising students but the program itself does not seem to conform to accepted theory on the subject. There has been little change in the administration of the program. This is partly due to the elaborate nature of test materials used. To save labor in developing a test it has been customary to build a long one to cover a given area most comprehensively. In many fields it has been found that less material carefully selected will do the job as well or better, thus affording notable economy in time and effort. Further, there is a limit to the measurement of human capacities by the longer methods used in the past. In order to sample human traits adequately it is necessary to reduce the length of conventional tests without doing violence to the reliability of scores. This problem was studied by Rostron and Lauer (1939) and the ground work laid for a testing program of diversified nature possible of administration within limits of time normally available in crowded orientation programs. The present study is an extension of the above paper designed to facilitate the development of parallel forms of tests. It is presented as a method of approach when limited time and energy are available to spend on the construction and application of measuring instruments

On the noise-induced passage through an unstable periodic orbit II: General case

Consider a dynamical system given by a planar differential equation, which exhibits an unstable periodic orbit surrounding a stable periodic orbit. It is known that under random perturbations, the distribution of locations where the system's first exit from the interior of the unstable orbit occurs, typically displays the phenomenon of cycling: The distribution of first-exit locations is translated along the unstable periodic orbit proportionally to the logarithm of the noise intensity as the noise intensity goes to zero. We show that for a large class of such systems, the cycling profile is given, up to a model-dependent change of coordinates, by a universal function given by a periodicised Gumbel distribution. Our techniques combine action-functional or large-deviation results with properties of random Poincar\'e maps described by continuous-space discrete-time Markov chains.Comment: 44 pages, 4 figure

Which Classes of Structures Are Both Pseudo-elementary and Definable by an Infinitary Sentence?

When classes of structures are not first-order definable, we might still try to find a nice description. There are two common ways for doing this. One is to expand the language, leading to notions of pseudo-elementary classes, and the other is to allow infinite conjuncts and disjuncts. In this paper we examine the intersection. Namely, we address the question: Which classes of structures are both pseudo-elementary and $\mathcal{L}_{\omega_1 \omega}$-elementary? We find that these are exactly the classes that can be defined by an infinitary formula that has no infinitary disjunctions

A regulation-based classification system for marine protected areas: A response to Dudley et al. [9]

Dudley et al. [9] commented on our paper [11], arguing that the current IUCN objective-based categorization of protected areas, which is also used in marine protected areas (MPAs), should not be abandoned and replaced by the new regulation-based classification system [11]. Here we clarify that we do not advocate replacing the current IUCN categories, but highlight the benefits of using both the objective-based IUCN categories and the new regulation-based classification when applied to MPAs. With an increasing number of MPA types being implemented, most of them multiple-use areas zoned for various purposes, assessing ecological and socio-economic benefits is key for advancing conservation targets and policy objectives. Although the IUCN categories can be used both in terrestrial and marine systems, they were not designed to follow a gradient of impacts and there is often a mismatch between stated objectives and implemented regulations. The new regulation-based classification system addresses these problems by linking impacts of activities in marine systems with MPA and zone classes in a simple and globally applicable way. Applying both the IUCN categories and the regulation based classes will increase transparency when assessing marine conservation goals.ERA-Net BiodivERsA project "BUFFER Partially protected areas as buffers to increase the linked social ecological resilience"; national funders ANR (France); FCT (Portugal); FOR-MAS (Sweden); SEPA (Sweden); RCN (Norway); project BUFFER; Fernand Braudel IFER fellowship (Fondation Maison des Sciences de l'Homme); Fundacao para a Ciencia e a Tecnologia (FCT) [UID/MAR/04292/2013

Population data

This chapter of Beginning Population Studies (3rd edition) discusses sources of data for population studies, and their relative use and value. There are separate chapters in the book in which data sources for specific topics (eg. Mortality, Marriage) are discussed

The construction of early career teachers’ identities: coping or managing?

This paper examines how early career teachers cope with or manage the challenges that they experience during the transition from pre-service to the first and then the second year of teaching as they seek to establish stable, positive, professional identities and teach effectively in various school and policy contexts. Findings from three waves of interviews conducted with six elementary and secondary school teachers showed that, for these teachers in the early years of teaching, the construction of positive or negative, stable or unstable professional identities was closely related to whether they coped with or managed various tensions and to their perceived effectiveness. The findings also revealed that their ability to cope or manage was not only influenced by the relative strength of commitment with which they entered teaching, but also by the kinds of school-level support which they experienced

Canonical explorations of 'Tel' environments for computer programming

This paper applies a novel technique of canonical gradient analysis, pioneered in ecological sciences, with the aim of exploring student performance and behaviours (such as communication and collaboration) while undertaking formative and summative tasks in technology enhanced learning (TEL) environments for computer programming. The research emphasis is, therefore, on revealing complex patterns, trends, tacit communications and technology interactions associated with a particular type of learning environment, rather than the testing of discrete hypotheses. The study is based on observations of first year programming modules in BSc Computing and closely related joint-honours with software engineering, web and game development courses. This research extends earlier work, and evaluates the suitability of canonical approaches for exploring complex dimensional gradients represented by multivariate and technology-enhanced learning environments. The advancements represented here are: (1) an extended context, beyond the use of the ‘Ceebot’ learning platform, to include learning-achievement following advanced instruction using an industrystandard integrated development environment, or IDE, for engineering software; and (2) longitudinal comparison of consistency of findings across cohort years. Direct findings (from analyses based on code tests, module assessment and questionnaire surveys) reveal overall engagement with and high acceptance of collaborative working and of the TEL environments used, but an inconsistent relationship between deeply learned programming skills and module performance. The paper also discusses research findings in the contexts of established and emerging teaching practices for computer programming, as well as government policies and commercial requirements for improved capacity in computer-science related industries