Singularities of the susceptibility of an SRB measure in the presence of stable-unstable tangencies

Let $\rho$ be an SRB (or "physical"), measure for the discrete time evolution given by a map $f$, and let $\rho(A)$ denote the expectation value of a smooth function $A$. If $f$ depends on a parameter, the derivative $\delta\rho(A)$ of $\rho(A)$ with respect to the parameter is formally given by the value of the so-called susceptibility function $\Psi(z)$ at $z=1$. When $f$ is a uniformly hyperbolic diffeomorphism, it has been proved that the power series $\Psi(z)$ has a radius of convergence $r(\Psi)>1$, and that $\delta\rho(A)=\Psi(1)$, but it is known that $r(\Psi)<1$ in some other cases. One reason why $f$ may fail to be uniformly hyperbolic is if there are tangencies between the stable and unstable manifolds for $(f,\rho)$. The present paper gives a crude, nonrigorous, analysis of this situation in terms of the Hausdorff dimension $d$ of $\rho$ in the stable direction. We find that the tangencies produce singularities of $\Psi(z)$ for $|z|1$ if $d>1/2$. In particular, if $d>1/2$ we may hope that $\Psi(1)$ makes sense, and the derivative $\delta\rho(A)=\Psi(1)$ has thus a chance to be definedComment: 12 page

Using digital representations of practical production work for summative assessment

This paper presents the findings of the first phase of a three-year study investigating the efficacy of the digitisation of creative practical work as digital portfolios for the purposes of high-stakes summative assessment. At the same time the paired comparisons method of scoring was tried as an alternative to analytical rubric-based marking because we believed that it was likely that a more holistic approach to scoring would be more appropriate. Researchers created digital representations of the practical submissions of 75 Visual Arts and 82 Design students graduating from secondary school in Western Australia. These digital portfolios were scored using the two methods, with the scores compared to those officially awarded to the physical forms. It was concluded that the digital representations of the Visual Arts submissions had adequate fidelity for the purpose of awarding high-stakes scores particularly using the paired comparisons method. However, the Visual Arts teachers and students were opposed to digitisation. For the Design portfolios teachers and students were supportive of digital submission, but the structure of the portfolios reduced the reliability and validity of scores, particularly from analytical marking

Simultaneous Continuation of Infinitely Many Sinks Near a Quadratic Homoclinic Tangency

We prove that the $C^3$ diffeomorphisms on surfaces, exhibiting infinitely many sinksnear the generic unfolding of a quadratic homoclinic tangency of a dissipative saddle, can be perturbed along an infinite dimensional manifold of $C^3$ diffeomorphisms such that infinitely many sinks persist simultaneously. On the other hand, if they are perturbed along one-parameter families that unfold generically the quadratic tangencies, then at most a finite number of those sinks have continuation

MONITORING THE ELITE ATHLETE

The application of sports medicine technology to the practical aspect of sport has led to the common belief that the scientific preparation of the athlete is the responsibility of a team -a coach, biomechanist, physician, exercise pysiologist, sport psychologist and others. The advent of sophisticated physiological equipment to determine specific objective measures of performance during activity has allowed the coach to perceive the athlete in precise scientific terms. This monitoring process is a contemporary yet controversial issue. To what extent does applied science impinge of this article is to review the different facets of monitoring with specific emphasis on the overtraining phenomena. The monitoring process can generally be divided into three separate phases: medical, physiological and assessment of overtraining

Using pairwise comparisons in the online social moderation of performance assessment

Assessing the performance of a student involves some form of judgement, and where more than one assessor is involved this usually requires some form of moderation to ensure consistent and fair results. Often this involves meetings or communication between assessors, which is referred to as social moderation. This paper reports on a study that investigated the use of online technologies to support a form of social moderation of artworks submitted for assessment in a senior secondary school course in Western Australia. Online systems were used to facilitate communications and provide access to digital representations of the submissions along with assessment tools. In particular a pairwise comparison judging online tool was used. This approach to social moderation was tested in a realistic context involving a sample of 12 teachers from rural schools for whom face-to-face meetings would be difficult. The aim was to investigate whether the use of these online systems would support good moderation outcomes and valuable professional learning for those involved. The study found that this approach to online social moderation was feasible, and participants perceived that it had improved the consistency of their judgements because they had developed an improved understanding of the assessment criteria and standard of work. However, analysis of scores and reliability data suggested some were not adequately consistent, and it was likely that this was due to their inexperience in assessing such work. Therefore some changes to the processes of this form of online social moderation were recommended

Absence of kinetic effects in reaction-diffusion processes in scale-free networks

We show that the chemical reactions of the model systems of A+A->0 and A+B->0 when performed on scale-free networks exhibit drastically different behavior as compared to the same reactions in normal spaces. The exponents characterizing the density evolution as a function of time are considerably higher than 1, implying that both reactions occur at a much faster rate. This is due to the fact that the discerning effects of the generation of a depletion zone (A+A) and the segregation of the reactants (A+B) do not occur at all as in normal spaces. Instead we observe the formation of clusters of A (A+A reaction) and of mixed A and B (A+B reaction) around the hubs of the network. Only at the limit of very sparse networks is the usual behavior recovered.Comment: 4 pages, 4 figures, to be published in Physical Review Letter

Infinitely Many Stochastically Stable Attractors

Let f be a diffeomorphism of a compact finite dimensional boundaryless manifold M exhibiting infinitely many coexisting attractors. Assume that each attractor supports a stochastically stable probability measure and that the union of the basins of attraction of each attractor covers Lebesgue almost all points of M. We prove that the time averages of almost all orbits under random perturbations are given by a finite number of probability measures. Moreover these probability measures are close to the probability measures supported by the attractors when the perturbations are close to the original map f.Comment: 14 pages, 2 figure

Reflecting on Teaching Practices Using Digital Video Representation in Teacher Education

This paper reports on the perceptions of teacher education student of the value of using digital tools to analyse video-based information on the practice of teachers in classrooms. This strategy was employed to address a dilemma in providing sufficient exposure to real examples of good classroom teaching to link theory with practice. The use of video of teachers in action could augment their practicum experience in schools but this required efficient and effective access to appropriate video material. For this purpose, the use of digital tools in a system called LessonLab was successfully implemented in an introductory unit focussed on learning theories at Edith Cowan University. Data collected using a survey of students and focus group discussion indicated that for almost all the students the experience was valued and the system operated effectively

Can the United States Afford a “No-Fault” System of Compensation for Medical Injury?

One of the key issues separating US critics of a no-fault alternative to the tort system for compensating victims of medical injury from supporters is its anticipated cost. Results from a study are presented that estimate the costs of a no-fault system, one that is similar to the system now in operation in Sweden, within the context of the US health care system

Trends and Issues in Educational Psychology

The review of issues in educational psychology looks at areas of innovation as well as areas of stagnation. The authors challenge researchers to find meaningful information which has utility in the development and improvement of teaching