Convergence of matrices under random conjugation: wave packet scattering without kinematic entanglement

In previous work, it was shown numerically that under successive scattering events, a collection of particles with Gaussian wavefunctions retains the Gaussian property, with the spread of the Gaussian ('Δx') tending to a value inversely proportional to the square root of each particle's mass. We prove this convergence in all dimensions ≥3

Policy Barriers to School Improvement: What's Real and What's Imagined?

Some of the most promising reforms are happening where school leaders are thinking differently about how to get the strongest student outcomes from the limited resources available. But even principals who use their autonomy to aggressively reallocate resources say that persistent district, state, and federal barriers prohibit them from doing more.What are these barriers? What do they block principals from doing? Is there a way around them?CRPE researchers probed these questions with principals in three states (NH, CT, MD). These principals cited numerous district, state, and federal barriers standing in the way of school improvement. The barriers, 128 in all, fell into three categories: 1) barriers to instructional innovations, 2) barriers to allocating resources differently, and 3) barriers to improving teacher quality.Upon investigation, researchers found that principals have far more authority than they think. Only 31% of the barriers cited were "real" -- immovable statutes, policies, or managerial directives that bring the threat of real consequences if broken.The report recommends educating principals on the authority they already possess, to help them find workarounds to onerous rules. The report also outlines a number of specific state and district policy changes to grant schools the autonomy they need to improve student outcomes

Wave-packet scattering without kinematic entanglement: convergence of expectation values

The wave packet spread of a particle in a collection of different mass particles, all with Gaussian wave functions, evolves to a value that is inversely proportional to the mass of the particle. The assumptions underlying this result and its derivation are reviewed. A mathematical demonstration of the convergence of an iteration central to this assertion is presented. Finally, the question of in-principle measurement of wave packet spread is taken up

A study of current practice in liaison between primary and secondary schools in physical education

The purpose of this study was to investigate current practice in liaison between primary and secondary schools to promote continuity and progression in physical education during the transfer of pupils from Key Stage 2 to Key Stage 3 and to identify constraints to engaging in liaison activities. A questionnaire was completed by the head of the physical education department in secondary schools in five local education authorities in England that received pupils from primary schools in year 7 (n = 80) and by the physical education coordinator of the primary feeder schools of those secondary schools that responded to the questionnaire (n = 299). Results showed that 32 (43.8%) secondary teachers and 157 (53.4%) primary teachers identified that they had established contacts with their primary feeder schools or associated secondary schools respectively; and 49 (64.5%) secondary teachers but 114 (39.6%) primary teachers identified that currently they were engaged in liaison activities. There was a discrepancy between the percentages of teachers who indicated they had contacts with their primary feeder schools or associated secondary schools respectively, and who indicated they were engaged in liaison activities with them. These results suggested that contacts with and/or engagement in liaison activities between primary and secondary schools were not consistent across schools. A range of constraints for developing effective contacts/liaison activities were identified, with time being identified as the major constraint by both primary and secondary teachers. A range of suggestions for overcoming the constraints were also identified. These results are discussed in relation to findings from studies looking at liaison in other subjects and also in relation to the implications for schools

Exchange of information about physical education to support the transition of pupils from primary and secondary school

The purpose of this study was to identify how information about physical education is exchanged between secondary schools and their respective feeder primary schools, what information is exchanged and how this information is used. A secondary purpose was to look at whether there is any relationship between schools engaging in liaison activities and exchanging information about physical education, and between exchanging information and the number of associated secondary schools to which pupils are sent or feeder primary schools from which pupils are received. Questionnaires were sent to 177 secondary and 538 feeder primary schools. Responses from 80 secondary schools and 299 primary schools showed that the highest percentage of teachers exchanged information through written documentation, followed by discussion at cross phase liaison meetings. The type of information exchanged by the highest percentage of teachers was identified as generic information about key stage 2 and 3 of the National Curriculum for Physical Education (NCPE) areas of activity and schemes of work, rather than information about the specific physical education content covered or information about individual pupils, such as levels of attainment or ability. Further, results suggest that information may be used for pastoral purposes and that only a small percentage of teachers used the information exchanged to plan for continuity and progression in the physical education curriculum. There was a significant positive relationship between engagement in liaison activities and information received about the physical education curriculum followed by pupils, but a significant negative relationship for primary teachers between the number of different secondary schools to which pupils' progress and knowledge about the key stage 3 schemes of work that Year 6 pupils will follow in their associated secondary schools. These results are discussed in relation to continuity and progression in physical education in the transfer of pupils from primary to secondary schools

The transfer of pupils from primary to secondary school: A case study of a foundation subject - physical education

A series of transitions, from class to class, year to year and school to school, are integral to the education system in England. The transfer of pupils from primary to secondary education is an important stage of transition. Models for managing this transfer highlight different aspects of the experience, including social/pastoral integration and curriculum continuity and progression of individual pupils. The purpose of this study was to investigate the transfer of pupils from primary to secondary school in relation to physical education. Semi-structured interviews were conducted with 14 secondary school physical education heads of department. Results showed that although all of the heads of department reported the transfer of pupils from primary to secondary school to be very important in relation to physical education, this was not translated into practice. There was limited involvement in activities supporting the transfer from primary to secondary school, and what involvement there was placed greater emphasis on activities to support social/pastoral integration than to support continuity and progression of individual pupils during transfer. Some possible reasons for these results are considered, along with some suggestions for further research

Temporal Aggregation and Structural Inference in Macroeconomics

This paper examines the quantitative importance of temporal aggregation bias in distorting parameter estimates and hypothesis tests. Our strategy is to consider two empirical examples in which temporal aggregation bias has the potential to account for results which are widely viewed as being anomalous from the perspective of particular economic models. Our first example investigates the possibility that temporal aggregation bias can lead to spurious Granger causality relationships. The quantitative importance of this possibility is examined in the context of Granger causal relations between the growth rates of money and various measures of aggregate output. Our second example investigates the possibility that temporal aggregation bias can account for the slow speeds of adjustment typically obtained with stock adjustment models. The quantitative importance of this possibility is examined in the context of a particular class of continuous and discrete time equilibriurn models of inventories and sales. The different models are compared on the basis of the behavioral implications of the estimated values of the structural parameters which we obtain and their overall statistical performance. The empirical results from both examples provide support for the view that temporal aggregation bias can be quantitatively important in the sense of Significantly distorting inference.

Evidence for the Multiverse in the Standard Model and Beyond

In any theory it is unnatural if the observed parameters lie very close to special values that determine the existence of complex structures necessary for observers. A naturalness probability, P, is introduced to numerically evaluate the unnaturalness. If P is small in all known theories, there is an observer naturalness problem. In addition to the well-known case of the cosmological constant, we argue that nuclear stability and electroweak symmetry breaking (EWSB) represent significant observer naturalness problems. The naturalness probability associated with nuclear stability is conservatively estimated as P_nuc < 10^{-(3-2)}, and for simple EWSB theories P_EWSB < 10^{-(2-1)}. This pattern of unnaturalness in three different arenas, cosmology, nuclear physics, and EWSB, provides evidence for the multiverse. In the nuclear case the problem is largely solved even with a flat multiverse distribution, and with nontrivial distributions it is possible to understand both the proximity to neutron stability and the values of m_e and m_d - m_u in terms of the electromagnetic contribution to the proton mass. It is reasonable that multiverse distributions are strong functions of Lagrangian parameters due to their dependence on various factors. In any EWSB theory, strongly varying distributions typically lead to a little or large hierarchy, and in certain multiverses the size of the little hierarchy is enhanced by a loop factor. Since the correct theory of EWSB is unknown, our estimate for P_EWSB is theoretical. The LHC will determine P_EWSB more robustly, which may remove or strengthen the observer naturalness problem of EWSB. For each of the three arenas, the discovery of a natural theory would eliminate the evidence for the multiverse; but in the absence of such a theory, the multiverse provides a provisional understanding of the data.Comment: 79 pages, 23 figure