Simple applications of Noether's first theorem in quantum mechanics and electromagnetism

Internal global symmetries exist for the free non-relativistic Schr\"{o}dinger particle, whose associated Noether charges--the space integrals of the wavefunction and the wavefunction multiplied by the spatial coordinate--are exhibited. Analogous symmetries in classical electromagnetism are also demonstrated.Comment: 12 page

Standard State Space Models of Unawareness

The impossibility theorem of Dekel, Lipman and Rustichini has been thought to demonstrate that standard state-space models cannot be used to represent unawareness. We first show that Dekel, Lipman and Rustichini do not establish this claim. We then distinguish three notions of awareness, and argue that although one of them may not be adequately modeled using standard state spaces, there is no reason to think that standard state spaces cannot provide models of the other two notions. In fact, standard space models of these forms of awareness are attractively simple. They allow us to prove completeness and decidability results with ease, to carry over standard techniques from decision theory, and to add propositional quantifiers straightforwardly

Higher-order signature cocycles for subgroups of mapping class groups and homology cylinders

We define families of invariants for elements of the mapping class group of S, a compact orientable surface. Fix any characteristic subgroup H of pi_1(S) and restrict to J(H), any subgroup of mapping classes that induce the identity modulo H. To any unitary representation, r of pi_1(S)/H we associate a higher-order rho_r-invariant and a signature 2-cocycle sigma_r. These signature cocycles are shown to be generalizations of the Meyer cocycle. In particular each rho_r is a quasimorphism and each sigma_r is a bounded 2-cocycle on J(H). In one of the simplest non-trivial cases, by varying r, we exhibit infinite families of linearly independent quasimorphisms and signature cocycles. We show that the rho_r restrict to homomorphisms on certain interesting subgroups. Many of these invariants extend naturally to the full mapping class group and some extend to the monoid of homology cylinders based on S.Comment: 38 pages. This is final version for publication in IMRN, deleted some material and many references (sorry-at referee's insistence

Preferences Between Continuous Streams of Events

Cost-benefit and health policy studies often model a consequence occurring over time as a continuous stream of events. Such a consequence is measured by the rates at which events occur or by the states that occur, and the value of the consequence is measured by an integral. This paper presents a foundation for such models. It defines conditions on preferences between consequences that are equivalent to an integral value function having a discounting function and an intertemporal equity function.discounting; equity; continuous time; value function; evaluation

Are Class Size Differences Related to Pupils' Educational Progress and Classroom Processes? Findings from the Institute of Education Class Size Study of Children Aged 5-7 Years

Despite evidence from the USA that children in small classes of less than 20 do better academically there is still a vociferous debate about the effects of class size differences in schools, and considerable gaps in our understanding of the effects of class size differences. This article summarises results from the most complete UK analysis to date of the educational consequences of class size differences. The study had two aims: first, to establish whether class size differences affect pupils' academic achievement; and second, to study connections between class size and classroom processes, which might explain any differences found. The study had a number of features that were designed to be an improvement on previous research. It used an 'observational' approach, rather than an interventionist one, in order to capture the nature of the relationship between class size and achievement across the full range of observed classes, and it employed a longitudinal design with baseline assessment to adjust for possible non-random selection of children into classes. The study followed a large sample of over 10,000 children from school entry through the infant stage, i.e. children aged 4-7 years. It used multilevel statistical procedures to model effects of class size differences while controlling for sources of variation that might affect the relationship with academic achievement, and a multimethod research approach, integrating teachers' judgements and experiences with case studies, and also carefully designed time allocation estimates and systematic observation data. Results showed that there was a clear effect of class size differences on children's academic attainment over the (first) Reception year. In the case of literacy, the lowest attainers on entry to school benefited most from small classes, particularly below 25. Connections between class size and classroom processes were examined and a summary model of relationships presented. Effects were multiple, not singular; in largeclasses there are more large groups and this presented teachers with more difficulties, in smaller classes there was more individual teacher contact with pupils and more support for learning, and in larger classes there was more pupil inattentiveness and off-task behaviour. Results support a contextual approach to classroom learning, within which class size differences have effects on both teachers and pupils. It is concluded that much will depend on how teachers adapt their teaching to different class sizes and that more could be done in teacher training and professional development to address contextual features like size of class

How Do Predatory Lending Laws Influence Mortgage Lending in Urban Areas? A Tale of Two Cities

This paper examines the effects of predatory lending laws in the cities of Chicago and Philadelphia. The level of mortgage activity in each of the cities is compared during the pre- and post-legislative periods relative to other parts of the state to assess the impact of localized legislation. In Chicago, where the predatory lending law focused on banks, a subprime origination in the city was found to be more likely to be made by a nonbank after the passage of the law. In Philadelphia, however, where the predatory legislation was aimed at all financial service providers, a decline was observed in the likelihood of a subprime loan being originated in the city during the post-legislation period, with the minority and low-income market segments experiencing the largest reduction.

Integral-Value Models for Outcomes over Continuous Time

Models of preferences between outcomes over continuous time are important for individual, corporate, and social decision making, e.g., medical treatment, infrastructure development, and environmental regulation. This paper presents a foundation for such models. It shows that conditions on preferences between real- or vector-valued outcomes over continuous time are satisfied if and only if the preferences are represented by a value function having an integral form.continuous time; discounting; ordinal utility scale; value function; integral

Cardinal Scales for Public Health Evaluation

Policy studies often evaluate health for a population by summing the individuals’ health as measured by a scale that is ordinal or that depends on risk attitudes. We develop a method using a different type of preferences, called preference intensity or cardinal preferences, to construct scales that measure changes in health. The method is based on a social welfare model that relates preferences between changes in an individual’s health to preferences between changes in health for a population.public health evaluation; social welfare; preference intensity; health state

Discounting Models for Outcomes over Continuous Time

Events that occur over a period of time can be described either as sequences of outcomes at discrete times or as functions of outcomes in an interval of time. This paper presents discounting models for events of the latter type. Conditions on preferences are shown to be satisfied if and only if the preferences are represented by a function that is an integral of a discounting function times a scale defined on outcomes at instants of time.continuous time; integral discounting; integral value or utility function

Sustainable population health : a pressing priority for community wellbeing

Recent developments in primary health care, preventive care, early intervention programs, population health constructs and coordinated care trials in Australia have explored the idea of changing our emphasis in health care from responsive acute care to more integrated, whole population community wellbeing management. This idea accepts that much illness and even trauma experienced by individuals in our communities can be prevented, mitigated or managed in a more constructive and positive manner than has previously been the case. Much disabling illness need not occur at all and can be avoided through better community based management models, education programs, and lifestyle changes that contribute to more healthy communities. As in the wider business world, we are becoming more cognisant of the fact that prevention is not only an appealing idea in terms of health outcomes and quality of life, but that it is good for business also. It can moderate demand for costly health care, assist consumers to understand how to live healthier and fulfilling lives and overall help to sustain a much more dynamic community. This article, based on work in a rural health service in South Australia, points to some elements of sustainable primary care that appear to have potential to take us where we need to go. It asks whether we have the capacity and the will to make the necessary investment in sustainability to ensure our future or whether we are to remain bound in a reactionary model of health care rather than considering the impact of wider social and physical environments as part of the overall community health equation