An Optimal Family of Exponentially Accurate One-Bit Sigma-Delta Quantization Schemes

Sigma-Delta modulation is a popular method for analog-to-digital conversion of bandlimited signals that employs coarse quantization coupled with oversampling. The standard mathematical model for the error analysis of the method measures the performance of a given scheme by the rate at which the associated reconstruction error decays as a function of the oversampling ratio $\lambda$. It was recently shown that exponential accuracy of the form $O(2^{-r\lambda})$ can be achieved by appropriate one-bit Sigma-Delta modulation schemes. By general information-entropy arguments $r$ must be less than 1. The current best known value for $r$ is approximately 0.088. The schemes that were designed to achieve this accuracy employ the "greedy" quantization rule coupled with feedback filters that fall into a class we call "minimally supported". In this paper, we study the minimization problem that corresponds to optimizing the error decay rate for this class of feedback filters. We solve a relaxed version of this problem exactly and provide explicit asymptotics of the solutions. From these relaxed solutions, we find asymptotically optimal solutions of the original problem, which improve the best known exponential error decay rate to $r \approx 0.102$. Our method draws from the theory of orthogonal polynomials; in particular, it relates the optimal filters to the zero sets of Chebyshev polynomials of the second kind.Comment: 35 pages, 3 figure

Quantifying the economic impact of career guidance in secondary education

Career guidance in secondary education has the potential to play a role in several related areas of government policy, including: youth unemployment prevention or re-engagement; education course choices, transitions, and motivation; skill shortages, regional economic development, and labour mobility; lifelong learning, mental health, and wellbeing. Experts have long identified a need for a more robust, quantitative understanding of medium-term and long-term benefits, to engage policymakers and gain adequate funding for career guidance. Some government officials, particularly those responding to pressure from finance ministries, further request that the economic impact be monetised and contrasted against costs, to support analysis such as return on investment (ROI). This can be challenging because school-based career guidance often, and especially in England, refers to a diverse range of interventions that are small scale compared to the curriculum as a whole, theorised to have correspondingly modest average effects that can be hard to isolate statistically. Nonetheless, small effects from low-cost interventions can still translate into attractive policies from an ROI perspective. This critical appraisal reviews the contributions and limitations of a selection of the author’s work from 2008 to 2022 in improving our understanding of the economic impact of career guidance in secondary education, drawing primarily on new empirical work in Great Britain and the international literature. The corpus is grouped into three themes: (i) Measuring impact: strengthening the quantitative evidence base for the medium-term impact of career guidance on education progression or labour market outcomes, drawing on historical longitudinal surveys, school-level data, administrative data, and contemporary surveys of young adults. (ii) Monetising impact: applying a pragmatic ROI estimation framework to personal guidance conversations for students in English secondary education. The methodology, well-suited to interventions with few large-scale evaluations, was then re-applied and extended in a study for Careers Wales which addressed school-age and adult career guidance, the latter selected for a Cedefop collection which sets out a formalisation of this “linked ROI” methodology. (iii) Interpreting impact: exploring particular limitations and nuances of this evidence and the ROI method as applied to date, such that results might be appropriately used by policymakers, sector leaders, and the research community. A broad range of career guidance activities are in scope, reflecting The Gatsby Benchmarks framework, which became government policy in England at end 2017. Example quantitative insights from the corpus include 0.8% higher average earnings for those in full-time employment associated with each extra career talk received aged 14-15 and an estimated 4.4x fiscal ROI for the provision of two personal guidance interviews. A future research agenda is outlined to enhance the breadth and usefulness of available evidence and ROI analyses. A synthesis view of these contributions identifies a future opportunity to adopt a stronger systems perspective. Such an approach would address key limitations in the corpus: the limited statistical accounting for causality and displacement and the limited consideration of systemic factors, specific mechanisms, and innovative, future-focused approaches to guidance

Evidence for the reliability and validity, and some support for the practical utility of the two-factor Consideration of Future Consequences Scale-14

Researchers have proposed 1-factor, 2-factor, and bifactor solutions to the 12-item Consideration of Future Consequences Scale (CFCS-12). In order to overcome some measurement problems and to create a robust and conceptually useful two-factor scale the CFCS-12 was recently modified to include two new items and to become the CFCS-14. Using a University sample, we tested four competing models for the CFCS-14: (a) a 12-item unidimensional model, (b) a model fitted for two uncorrelated factors (CFC-Immediate and CFC-Future), (c) a model fitted for two correlated factors (CFC-I and CFC-F), and (d) a bifactor model. Results suggested that the addition of the two new items has strengthened the viability of a two factor solution of the CFCS-14. Results of linear regression models suggest that the CFC-F factor is redundant. Further studies using alcohol and mental health indicators are required to test this redundancy

Stress and Coping in IAPT Staff: A Mixed Methods Study

Background: Research indicates National Health Service (NHS) mental health workers have particularly high levels of stress. Improving Access to Psychological Therapies (IAPT) is an NHS mental health service with new ways of working. Aims: This exploratory study sought to investigate whether IAPT staff experience high levels of stress and, moreover, identify sources of stress and ways of coping. Method: A mixed methods design was utilised. Forty four IAPT workers completed a quantitative survey in which prevalence of stress (GHQ-12) and dispositional coping styles (COPE) were measured. Qualitative interviews were conducted with 6 staff and analysed using thematic analysis. Results: Almost 30% of IAPT staff reached criteria for minor psychiatric morbidity. Identified stressors included high volume and target orientated work, constant change, resource issues, team dynamics, demands of high stakes in-service training, managing and holding distress and risk, and home-work conflict. Greater engagement in acceptance and active coping styles related to lower stress, whereas focusing on and venting emotions related to higher stress. Conclusions: Stress is an issue for IAPT staff, with newly reported stressors including emphasis on targets and high stakes in-service training. Interventions aimed at promoting acceptance and active coping may be beneficial

Ecocantando: actividades lúdico-musicales para fortalecer la conciencia ambiental

En la actualidad, la contaminación de nuestro medio ambiente está acabando con la vida de muchas especies. Es contradictorio pensar que cada día los avances científicos y tecnológicos producto de la inteligencia humana,exploran y conquistan los más inimaginables campos del saber y sin embargo es el mismo hombre el responsable de la destrucción de nuestro planeta. La escuela es, por excelencia, la institución depositaria del saber humano. En ella los niños y las niñas, desde los primeros años de su vida, adquieren y desarrollan un conjunto de competencias que los convertirán en hombres y mujeres responsables de las grandes decisiones que transformarán el mundo. El ambiente escolar es propicio para despertar en los estudiantes la necesidad de velar por una convivencia pacífica y armónica con el medio ambiente. Las propuestas curriculares que abordan esta problemática deben constituirse en temas transversales que, desde las diversas áreas o asignaturas, estén orientados a propiciar en los estudiantes esa conciencia ambientalista que nos asegure personas responsables y conscientes de la vital necesidad que tiene el cuidado del planeta Tierra. Este programa emplea actividades musicales y lúdicas para abordar aspectos básicos que están relacionados con el medio ambiente, presentado de manera creativa y original las estrategias seleccionadas y cuyo único propósito es asumir una actitud favorable hacia la preservación y cuidado de todas las maravillas que el planeta tiene como son la fauna, flora, clima, atmósfera, ríos,mares, bosques y nosotros mismos

The Water holes at Ijara

Volume: XXI

Evaluation of the impact of the STEM Ambassadors programme upon STEM Ambassadors

STEM Learning is the largest provider of STEM education and careers support to schools, colleges and community groups in the UK providing training, CPD sessions, free resources and governor support. The STEM Ambassador programme is one of STEM Learning’s ways of building young people’s awareness and interest in STEM careers. The programme is in its 20th year of being run by STEM Learning and with this, they have amassed over 25,000 STEM Ambassador volunteers from over 7,000 employers, who work with young people in schools and the community to provide the vital connection between STEM employers and young people. As long as you have experience within industry and/or STEM subjects you can be a STEM Ambassador, providing support in the form of workshops, mentoring, careers talks and enrichment days. The purpose of the evaluation that we undertook was to explore the Ambassadors’ experiences of the programme, the impact of the programme both on their volunteering and those they engage with and the effect of COVID-19 on the programme and shifts to virtual engagement. The evaluation found that motivations to participate in the programme were borne from wanting to raise awareness of STEM amongst young people and inspire the next generation. Young STEM Ambassadors in particular were seen to gain most skills from their volunteering roles and believed that volunteering was particularly important for their career progression. The STEM Ambassador programme was generally very well received by its volunteers who had adapted well to a virtual and hybrid version of their role during COVID-19, and it was expressed that many believed that their role had a positive impact on engaging schools and young people in STEM activities and careers