A parallel and adaptive multigrid solver for the solutions of the optimal control of geometric evolution laws in two and three dimensions

We present a problem concerning the optimal control of geometric evolution laws. This is a minimisation problem that aims to find a control η which minimises the objective functional J subject to some imposed constraints. We apply this methodology to an application of whole cell tracking. Given two sets of data of cell morphologies, we may solve the optimal control problem to dynamically reconstruct the cell movements between the time frame of these two sets of data. This problem is solved in two and three space dimensions, using a state-of-the-art numerical method, namely multigrid, with adaptivity and parallelism

An optimal control approach to cell tracking

Cell tracking is of vital importance in many biological studies, hence robust cell tracking algorithms are needed for inference of dynamic features from (static) in vivo and in vitro experimental imaging data of cells migrating. In recent years much attention has been focused on the modelling of cell motility from physical principles and the development of state-of-the art numerical methods for the simulation of the model equations. Despite this, the vast majority of cell tracking algorithms proposed to date focus solely on the imaging data itself and do not attempt to incorporate any physical knowledge on cell migration into the tracking procedure. In this study, we present a mathematical approach for cell tracking, in which we formulate the cell tracking problem as an inverse problem for fitting a mathematical model for cell motility to experimental imaging data. The novelty of this approach is that the physics underlying the model for cell migration is encoded in the tracking algorithm. To illustrate this we focus on an example of Zebrafish (Danio rerio's larvae) Neutrophil migration and contrast an ad-hoc approach to cell tracking based on interpolation with the model fitting approach we propose in this study

Finite element approximation of a phase field model for void electromigration

We consider a fully practical finite element approximation of the nonlinear degenerate parabolic syste

Building Relationships With Youth in Program Settings: A Study of Big Brothers/Big Sisters

The success of mentoring programs often relies on ensuring that matched adults and youth meet long enough and often enough to establish a relationship that could generate positive changes for youth. This report draws on P/PV's research on program practices from Big Brothers/Big Sisters of America to provide a better understanding of mentoring relationships and their dynamics. Specifically, it provides insight into what helps good mentoring relationships to form, characteristics of good relationships and why they break up

Understanding How Youth and Elders Form Relationships: A Study of Four Linking Lifetimes Programs

This report describes four projects established by the Temple University Center for Intergenerational Learning. It also uses the mentors' and youth's own words to delineate the various stages their relationships go through and the effects of different strategies on the development of positive relationships. The report includes an early attempt to correlate different mentoring approaches with their effects on relationship formation

Multispin correlations and pseudo-thermalization of the transient density matrix in solid-state NMR: free induction decay and magic echo

Quantum unitary evolution typically leads to thermalization of generic interacting many-body systems. There are very few known general methods for reversing this process, and we focus on the magic echo, a radio-frequency pulse sequence known to approximately "rewind" the time evolution of dipolar coupled homonuclear spin systems in a large magnetic field. By combining analytic, numerical, and experimental results we systematically investigate factors leading to the degradation of magic echoes, as observed in reduced revival of mean transverse magnetization. Going beyond the conventional analysis based on mean magnetization we use a phase encoding technique to measure the growth of spin correlations in the density matrix at different points in time following magic echoes of varied durations and compare the results to those obtained during a free induction decay (FID). While considerable differences are documented at short times, the long-time behavior of the density matrix appears to be remarkably universal among the types of initial states considered - simple low order multispin correlations are observed to decay exponentially at the same rate, seeding the onset of increasingly complex high order correlations. This manifestly athermal process is constrained by conservation of the second moment of the spectrum of the density matrix and proceeds indefinitely, assuming unitary dynamics.Comment: 12 Pages, 9 figure

Evaluation of Year 1 of the Tuition Partners Programme: Impact Evaluation Report for Year 11. Evaluation Report: An exploration of impact in Year 11

The National Tutoring Programme (NTP) Tuition Partners (TP) programme was designed to provide additional support to schools and teachers to supplement classroom teaching through subsidised, high quality tutoring for pupils from an approved list of tutoring organisations, the Tuition Partners. This evaluation covers the TP programme as delivered in its first year by the Education Endowment Foundation (EEF), from November 2020 to August 2021. Tuition Partners was one arm of the NTP. The NTP aimed to support teachers and schools in providing a sustained response to the Covid-19 pandemic and to provide a longer term contribution to closing the attainment gap between disadvantaged pupils and their peers. The NTP was part of a wider government response to the pandemic, funded by the Department for Education and originally developed by the EEF, Nesta, Impetus, The Sutton Trust, and Teach First, and with the support of the KPMG Foundation. The EEF appointed 33 approved ‘Tuition Partners’ that schools could select from to deliver tuition. Schools could access 15 hours of tutoring per selected pupil (with a minimum of 12 hours being considered a completed block of tuition). Tuition was provided online and/or face-to-face; and was 1:1, or in small groups (1:2 or 1:3); and available in English, maths, science, humanities and modern foreign languages. Tuition was expected to be delivered in schools (before, during and after school), in addition to usual teaching; and in certain circumstances, at home. The programme was targeted at disadvantaged pupils attending state-maintained schools in England, including those eligible for Pupil Premium funding (PP-eligible), Free School Meals (FSM), or those identified by schools as having an equivalent need for support. Participating schools had discretion to identify which of their pupils they felt would most benefit from additional tuition support. Pupils in Years 1–11 were eligible (5–16 years old). The programme aimed to reach 215,000 to 265,000 pupils, across 6,000 state-maintained schools in England, and it was expected that approximately 20,000 tutors would be recruited by Tuition Partners. The TP programme was set up and delivered during the Covid-19 pandemic, requiring continued responsiveness to the challenges faced by schools including restricted attendance, remote teaching, and ongoing widespread staff and pupil absences. During school closures to most pupils from January – March 2021, the EEF approved TPs to deliver online tuition at home, however many schools chose to wait to commence tutoring until schools reopened fully, and therefore started tutoring later than planned. The usual summer exams process for Year 11 pupils could not go ahead as planned in summer 2021, and GCSEs were determined by TAGs instead. This evaluation report covers the analysis on the impact of the TP programme on the maths and English attainment outcomes for Year 11 pupils only. Separate reports relate to analysis on a sample of primary schools and an implementation and process evaluation (IPE). The evaluation findings for the TP programme are brought together in a summary and interpretation report that is available here. This evaluation uses a quasi-experimental design (QED), involving a group of intervention schools that participated in the TP programme, and a group of comparison schools that did not receive the programme. The evaluation relies on a propensity score matching approach to ensure that the intervention and comparison schools are similar to each other in important, observable regards. As pupils who would have received TP in comparison schools were difficult to identify, the evaluation focused on pupils eligible for Pupil Premium and on all pupils, as these groups can be identified in both TP and non-TP schools. The analysis is based on 1,464 secondary schools with a total of 62,024 pupils eligible for Pupil Premium. The evaluation assessed impact in English and maths using Teacher Assessed Grades (TAGs) from 2021. Year 11 pupils eligible for Pupil Premium in schools that received TP made similar progress in English and maths compared to pupils eligible for Pupil Premium in comparison schools (there was no evidence of an effect in English or maths). A particular challenge is that, on average, only 12% of pupils eligible for Pupil Premium were selected for tutoring in maths and 9% were selected for tutoring in English, meaning the vast majority of the pupils included in the analysis did not receive tutoring. Therefore, this estimated impact of TP is diluted and it is hard to detect any effect that may (or may not) be present. When looking at all pupils in Year 11, pupils in schools that received TP made, on average, similar progress in English compared to all Year 11 pupils in comparison schools (there was no evidence of an effect). In maths, Year 11 pupils in schools that received TP made slightly less progress than all Year 11 pupils in comparison schools (though this effect was very small and equivalent to zero months ’ additional progress). However, this analysis was subject to even further dilution than the PPeligible analysis: only 7% of Year 11 pupils were selected for tutoring in maths and 6% in English. Given this context, it is unlikely that any of these differences were due to TP. Additional analysis restricted the sample of schools to those that targeted higher proportions of pupils eligible for Pupil Premium to receive tutoring, to reduce the issue of dilution and bring the group of analysed pupils closer to those that were selected for the intervention. In schools that selected over 50% of pupils eligible for Pupil Premium for tutoring, pupils eligible for Pupil Premium made similar progress in TP and comparison schools in English and maths. However, when the sample was restricted to schools that selected over 70% of pupils eligible for Pupil Premium for tutoring (and reducing dilution further), the impact of TP on pupils eligible for Pupil Premium is positive. In these schools, pupils eligible for Pupil Premium made, on average, the equivalent of two months additional progress in English and two months additional progress in maths, compared to pupils eligible for Pupil Premium in comparison schools. This analysis was based on a smaller sample of schools that were rematched to a comparison sample. However, different characteristics to the rest of the TP population of schools remained (more ‘Outstanding’ schools, lower percentage of FSM students), so this finding may not necessarily be generalisable to all TP schools. Within schools that participated in TP, pupils who received more hours of tutoring in maths obtained higher maths TAGs, and pupils who received more hours of tutoring in English obtained higher English TAGs, than pupils who received fewer hours of tutoring in the respective subjects. These results are associations and are not necessarily causal estimates of impact; there may be other explanations for the higher grades among these pupils

Evaluation of Year 1 of the Tuition Partners Programme: Impact Evaluation for Primary Schools. Evaluation Report

The National Tutoring Programme (NTP) Tuition Partners (TP) programme was designed to provide additional support to schools and teachers to supplement classroom teaching through subsidised high-quality tutoring for pupils from an approved list of tutoring organisations, the Tuition Partners. This evaluation covers the TP programme as delivered in its first year by the Education Endowment Foundation (EEF), from November 2020 to August 2021. Tuition Partners was one arm of the NTP. The NTP aimed to support teachers and schools in providing a sustained response to the Covid-19 pandemic and to provide a longer term contribution to closing the attainment gap between disadvantaged pupils and their peers. The NTP was part of a wider government response to the pandemic, funded by the Department for Education and originally developed by the EEF, Nesta, Impetus, The Sutton Trust, and Teach First, and with the support of the KPMG Foundation. The EEF appointed 33 approved ‘Tuition Partners’ that schools could select from to deliver tuition. Schools could access 15 hours of tutoring per selected pupil (with a minimum of 12 hours being considered a completed block of tuition). Tuition was provided online and/or face-to-face; and was 1:1, or in small groups (1:2 or 1:3); and available in English, maths, science, humanities and modern foreign languages. Tuition was expected to be delivered in schools (before, during and after school), in addition to usual teaching; and, in certain circumstances, at home. The programme was targeted at disadvantaged pupils attending state-maintained schools in England, including those eligible for Pupil Premium funding (PP-eligible), Free School Meals (FSM), or those identified by schools as having an equivalent need for support. Participating schools had discretion to identify which of their pupils they felt would most benefit from additional tuition support. Pupils in Years 1–11 were eligible (5–16 years old). The programme aimed to reach 215,000 to 265,000 pupils, across 6000 state-maintained schools in England, and it was expected that approximately 20,000 tutors would be recruited by Tuition Partners. The TP programme was set up and delivered during the Covid-19 pandemic, requiring continued responsiveness to the challenges faced by schools including restricted attendance, remote teaching, and ongoing widespread staff and pupil absences. During the school closures to most pupils from January – March 2021, the EEF approved TPs to deliver online tuition at home, however many schools chose to wait to commence tutoring until schools reopened fully, and therefore started tutoring later than planned. This evaluation report covers the analysis on the impact of the TP programme on the maths and English attainment outcomes for primary school pupils (Years 1–6) using standardised classroom assessments. Separate reports relate to analysis on Year 11 pupils and an implementation and process evaluation (IPE). The evaluation findings for the TP programme are brought together in a summary and interpretation report that is available here. This evaluation uses a quasi-experimental design (QED), involving a group of intervention schools that participated in the TP programme, and a group of comparison schools that did not receive the programme. The evaluation relies on a propensity score matching and re-weighting approach to ensure that the intervention and comparison schools are similar to each other in important, observable regards. As pupils who would have received TP in comparison schools were difficult to identify, the evaluation focused on pupils eligible for Pupil Premium and on all pupils, as these groups can be identified in both TP and comparison schools. For English, the analysis is based on 165 primary schools with 7073 pupils eligible for Pupil Premium and for maths, 126 primary schools with 5102 pupils eligible for Pupil Premium3. An additional instrumental variable (IV) analysis, based on the sample of TP schools only, looked at the impact of TP in schools that signed up to the TP programme earlier (and that delivered more tutoring) compared to schools that signed up later. On average, pupils eligible for Pupil Premium in schools that received TP made similar progress in English and maths compared to pupils eligible for Pupil Premium in comparison schools (no evidence of an effect in English or in maths). This result has a low security rating. A particular challenge is that, on average, only approximately 20% of pupils eligible for Pupil Premium were selected for tutoring, meaning a large proportion of pupils eligible for Pupil Premium were included in the analysis who did not receive tutoring. Therefore, this estimated impact of TP is diluted and it is hard to detect any effect that may (or may not) be present. Similar analysis on all pupils found that pupils in schools that received TP made, on average, similar progress in English compared to all pupils in comparison schools (no evidence of an effect), and an additional one month’s progress in maths compared to pupils in comparison schools. However, there is uncertainty around these estimates, with the positive maths result being consistent with a null (0 months) or slightly larger positive effect (2 months) and the English result being consistent with small positive (1 month) or small negative effect (−1 months). Furthermore, this analysis was subject to even further dilution: on average, only 12% (for maths) and 14% (for English) of pupils in the analysed schools were selected for tutoring. Given this context, it is unlikely that any of these differences were due to TP. In the sample of TP schools, completing a 12-hour block of tutoring (compared to zero hours) was related to higher English scores amongst pupils eligible for Pupil Premium that received more tutoring due to the early sign-up of the school. An equivalent analysis for maths was not able to proceed. A different analysis within TP schools showed that pupils who received more hours of tutoring were associated with higher English scores on average than pupils who received fewer hours of tutoring. However, this was not the case for maths, where receiving more hours of tutoring was not associated with higher maths scores. These results are associations and are not necessarily causal estimates of impact; there may be other explanations for the results

Derivation and solution of effective-medium equations for bulk heterojunction organic solar cells

A drift-diffusion model for charge transport in an organic bulk-heterojunction solar cell, formed by conjoined acceptor and donor materials sandwiched between two electrodes, is formulated. The model accounts for (i) bulk photogeneration of excitons, (ii) exciton drift and recombination, (iii) exciton dissociation (into polarons) on the acceptor-donor interface, (iv) polaron recombination, (v) polaron dissociation into a free electron (in the acceptor) and a hole (in the donor), (vi) electron/hole transport and (vii) electron-hole recombination on the acceptor-donor interface. A finite element method is employed to solve the model in a cell with a highly convoluted acceptor/donor interface. The solutions show that, with physically realistic parameters, and in the power generating regime, the solution varies little on the scale of the microstructure. This motivates us to homogenise over the microstructure; a process that yields a far simpler one-dimensional effective medium model on the cell scale. The comparison between the solution of the full model and the effective medium (homogenised) model is very favourable for the applied voltages that are less than the built-in voltage (the power generating regime) but breaks down as the applied voltages increases above it. Furthermore, it is noted that the homogenisation technique provides a systematic way to relate effective medium modelling of bulk heterojunctions [19, 25, 36, 37, 42, 59] to a more fundamental approach that explicitly models the full microstructure [8, 38, 39, 58] and that it allows the parameters in the effective medium model to be derived in terms of the geometry of the microstructure. Finally, the effective medium model is used to investigate the effects of modifying the microstructure geometry, of a device with an interdigitated acceptor/donor interface, on its current-voltage curve

Improving the economic value of photographic screening for optical coherence tomography-detectable macular oedema : a prospective, multicentre, UK study

Peer reviewedPublisher PD