Convex regions in the plane and their domes

We make a detailed study of the relation of a euclidean convex region $\Omega \subset \mathbb C$ to $\mathrm{Dome} (\Omega)$. The dome is the relative boundary, in the upper halfspace model of hyperbolic space, of the hyperbolic convex hull of the complement of $\Omega$. The first result is to prove that the nearest point retraction $r: \Omega \to \mathrm{Dome} (\Omega)$ is 2-quasiconformal. The second is to establish precise estimates of the distortion of $r$ near $\partial \Omega$

Maps of zeroes of the grand canonical partition function in a statistical model of high energy collisions

Theorems on zeroes of the truncated generating function in the complex plane are reviewed. When examined in the framework of a statistical model of high energy collisions based on the negative binomial (Pascal) multiplicity distribution, these results lead to maps of zeroes of the grand canonical partition function which allow to interpret in a novel way different classes of events in pp collisions at LHC c.m. energies.Comment: 17 pages, figures (ps included); added references, some figures enlarged. To appear in J. Phys.

Singular perturbations and a theorem of Kisynski

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/31989/1/0000031.pd

Modelling of root reinforcement and erosion control by ‘Veronese’ poplar on pastoral hill country in New Zealand

Background The control of erosion processes is an important issue worldwide. In New Zealand, previous studies have shown the benefits of reforestation or bioengineering measures to control erosion. The impetus for this work focuses on linking recent research to the needs of practitioners by formulating quantitative guidelines for planning and evaluation of ground bioengineering stabilisation measures. Methods Two root distribution datasets of ‘Veronese’ poplar (Populus deltoides x nigra) were used to calibrate a root distribution model for application on single root systems and to interacting root systems at the hillslope scale. The root distribution model results were then used for slope stability calculations in order to quantitatively evaluate the mechanical stabilisation effects of spaced trees on pastoral hillslopes. Results This study shows that root distribution data are important inputs for quantifying root reinforcement at the hillslope scale, and that root distribution strongly depends on local environmental conditions and on the tree planting density. The results also show that the combination of soil mechanical properties (soil angle of internal friction and cohesion) and topographic conditions (slope inclination) are the major parameters to define how much root reinforcement is needed to stabilise a specific slope, and thus the spacing of the trees to achieve this. Conclusions For the worst scenarios, effective root reinforcement (>2 kPa) is reached for tree spacing ranging from 2500 stems per hectare (sph) for 0.1 m stem diameter at breast height (DBH) to 300 sph for 0.3 m stem DBH. In ideal growing conditions, tree spacing less than 100 sph is sufficient for stem DBH greater than 0.15 m. New quantitative information gained from this study can provide a basis for evaluating planting strategies using poplar trees for erosion control on pastoral hill country in New Zealand

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

The National Tutoring Programme (NTP) Academic Mentoring (AM) programme (2020/21) was designed to help disadvantaged pupils ‘catch up’ on missed learning by providing trained academic mentors to deliver one to one and small group tutoring in schools. This evaluation covers year 1 of the AM programme as delivered by Teach First from November 2020 to July 2021 (delivery was in three waves starting 26th October 2020, 15th January 2021 and 22nd February 2021). AM 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 (DfE) and was originally developed by the Education Endowment Foundation (EEF), Nesta, Impetus, The Sutton Trust, Teach First, and with the support of the KPMG Foundation. The DfE appointed Teach First to manage the provision of mentors (referred to as ‘academic mentors’) to schools; recruiting, training and placing them in schools. The mentor worked in the school setting as an employee of the school. It was expected that each academic mentor would work with at least 50 pupils between the date they started in school and the end of the academic year. Mentoring was provided online and/or face-to-face; and was one to one, or in groups of 2-4 pupils; and available in English/literacy, maths, science, humanities, and modern foreign languages. Mentoring was expected to be delivered in schools during normal teaching time, as well as before or after school. In certain circumstances, mentoring could be delivered online with pupil(s) at home. The AM programme was targeted at state-maintained primary and secondary schools serving disadvantaged populations. 89% of the schools met Teach First’s priority criteria, which is based on the proportion of children living in income deprived families (IDACI) and whether the school is in an area of chronic and persistent underperformance (AEA). The remaining 11% of schools had an above average proportion of pupils eligible for Pupil Premium (Teach First, 2021). Participating schools could decide which pupils received support from academic mentors. However, the programme encouraged them to select pupils from disadvantaged households or those whose education had been disproportionately impacted by Covid-19. Pupils in Years 1–11 were eligible (5–16 years old). The programme aimed to reach a minimum of 900 schools and 50,000 children, with 1,000 academic mentors. By the end of February 2021, it had surpassed targets having trained and placed 1,124 academic mentors in 946 schools and delivered mentoring sessions to 103,862 pupils, 49% of whom were identified by mentors as being eligible for Pupil Premium of Free School Meals (FSM), and 23% of whom were identified as having a special educational need or disability. The AM programme was initiated and delivered at a time of great pressure for schools when the education system had been disrupted by a series of school closures to most pupils and was contending with ongoing widespread pupil and staff absences. Covid-19 related issues disrupted the anticipated operation of academic mentoring during the year. The AM programme involved initial training and ongoing support from Teach First as intended but there was greater variation in schools’ deployment of mentors during the latter stages of the Autumn Term 2020/21, and during the January to March 2021 period of school closures to most pupils. This evaluation report presents the analysis of the impact of the AM programme on maths and English attainment outcomes for Year 11 pupils only—who represent a very small proportion of individuals targeted by the AM programme. Originally, it was planned to evaluate impact across all year groups (Years 1 – 11) at primary and secondary level using schools’ standardised assessment data from Renaissance Learning (RL) assessments and, in addition, to evaluate the impact for Year 6 pupils using Key Stage (KS) 2 data. However, these analyses could not go ahead as KS2 assessments were cancelled in summer 2021 (related to the ongoing Covid-19 pandemic) and because the number of schools providing agreement to use their RL data was insufficient to warrant impact analyses. Data was only available for pupils in Year 11. Since GCSEs could not go ahead as planned in 2021, the data was in the form of Teacher Assessed Grades (TAGs), which had not previously been used as an outcome measurement tool. Checks were therefore undertaken to explore if TAGs would be suitable as an outcome measure. The only analysis that could proceed was therefore exploratory. The evaluation uses a quasi-experimental design (QED), in which a group of secondary schools and Year 11 pupils who did not receive the AM programme were selected for comparison with schools and pupils who received the AM programme. Comparison schools were selected by matching schools that were similar in important, observable regards to the schools that participated in AM. The evaluation included analysis on the availability of AM for pupils who were eligible for Pupil Premium (a key focus of the overall NTP), and all pupils, as these groups could be identified for both the AM and non-AM schools. In addition, the evaluation aimed to analyse the impact on pupils who received AM by predicting their participation and identifying a comparison group of pupils with similar characteristics. Analysis was based on data about Year 11 pupils’ attainment and characteristics from the National Pupil Database (NPD) merged with data provided by Teach First about pupils’ participation in AM. In total, 159 AM schools (8,977 Year 11 pupils eligible for Pupil Premium) and an equal number of comparison schools (8,419 Year 11 pupils eligible for Pupil Premium) were included in the final analysis. The evaluation assessed impact in English and maths using Teacher Assessed Grades (TAGs) from 2021. Where appropriate, this impact evaluation refers to important implementation features from the implementation and process evaluation (IPE) conducted by Teach First themselves. However, there is no independent IPE data to draw on in the interpretation of the impact results. Of the Year 11 pupils selected for Academic Mentoring in this evaluation, 46% of them were eligible for Pupil Premium, however, despite this it is important to note that the number of Year 11 Pupil Premium-eligible pupils selected for AM in AM schools was small as a proportion of all Year 11 Pupil Premium-eligible pupils, and the number of these Year 11 Pupil Premium-eligible pupils receiving AM in maths and/or English (as opposed to other subjects), was smaller still. The same is the case when considering the whole year group of Year 11 pupils – the number receiving AM was small as a proportion of all Year 11 pupils. This means that in the analysis, the number of Year 11 pupils who actually received AM in maths and/or English was heavily ‘diluted’ by the number of pupils who did not. The primary impact findings must be therefore treated with a high degree of caution. The analysis was subject to very high dilution; a large proportion of the pupils eligible for Pupil Premium included in the analysis in AM schools were not selected for AM. This was due to limited programme reach and a tendency for teachers to allocate both non-Pupil Premium and Pupil Premium eligible pupils to the programme. This dilution means that, in order to detect an effect, either the effect would need to be very strong amongst the very small proportion of Year 11 pupils eligible for Pupil Premium who were selected for mentoring (and there was no indication that this was the case elsewhere in our analysis), and/or there would need to be strong spillover effects amongst the rest of the Year 11 pupils eligible for Pupil Premium. Although the programme Theory of Change includes such a mechanism, it is unlikely to be relevant at the dilution levels seen. With such high dilution, it is hard to detect whether AM had an effect on those who received mentoring in the analyses focusing on pupils eligible for Pupil Premium and on all pupils. It is not possible to conclude whether a lack of observed impact is due to the small proportion of disadvantaged pupils who received mentoring, or because AM did not work for those who received it. An additional challenge was that it was not possible to construct a comparison group of similar Year 11 pupils in nonAM to schools to those who received mentoring in AM schools, based on observable, pupil-level characteristics, and this impact analysis did not go ahead. Schools used information such as classroom assessments to select pupils into the programme that was not observable in the available datasets, suggesting that pupil-level selection was driven by unobserved dimensions. These constraints, both of very high dilution and not being able to identify a comparison group with similar pupil characteristics, mean that the evaluation is unable to conclude, with any certainty, whether or not AM had an impact on the English or mathematics attainment outcomes of those pupils who received it. The report must be considered in the light of these caveats. Year 11 pupils eligible for Pupil Premium in schools that received AM made, on average, similar progress in English compared to Year 11 pupils eligible for Pupil Premium in comparison schools (there was no evidence of an effect). In maths, Year 11 pupils eligible for Pupil Premium in schools that received AM made, on average, slightly more progress (equivalent to 1 months’ additional progress) compared to Year 11 pupils eligible for Pupil Premium in comparison schools. However, there is uncertainty around this result; it is also consistent with a null (0 months) effect or an effect of slightly larger than 1 month’s additional progress. A particular challenge in interpretation is that, on average, only 13% of Year 11 pupils eligible for Pupil Premium were selected for mentoring by schools, and only 4.2% of Year 11 pupils eligible for Pupil Premium were selected for mentoring in maths and 2.9% in English, meaning that the vast majority of pupils eligible for Pupil Premium included in the analysis did not receive mentoring. Therefore, this estimated impact of AM is severely diluted and it is unlikely any of these differences were due to AM. When looking at all Year 11 pupils, pupils in schools that received AM made, on average, similar progress in English and maths compared to all Year 11 pupils in comparison schools (there was no evidence of an effect). However, this finding was similarly subject to severe dilution: on average only 10% of Year 11 pupils in the analysed schools were selected for mentoring, with 3.4% in maths and 2.1% in English, and therefore it is hard to detect any effect that may (or may not) have been present. Within schools that offered AM to Year 11 pupils, there was no association between the number of completed mentoring sessions in maths and Year 11 outcomes in maths, or between the number of completed mentoring sessions in English and Year 11 outcomes in English. These results are associations and not necessarily causal

Enhanced flight performance by genetic manipulation of wing shape in Drosophila

Insect wing shapes are remarkably diverse and the combination of shape and kinematics determines both aerial capabilities and power requirements. However, the contribution of any specific morphological feature to performance is not known. Using targeted RNA interference to modify wing shape far beyond the natural variation found within the population of a single species, we show a direct effect on flight performance that can be explained by physical modelling of the novel wing geometry. Our data show that altering the expression of a single gene can significantly enhance aerial agility and that the Drosophila wing shape is not, therefore, optimized for certain flight performance characteristics that are known to be important. Our technique points in a new direction for experiments on the evolution of performance specialities in animals

Tunneling and the Band Structure of Chaotic Systems

We compute the dispersion laws of chaotic periodic systems using the semiclassical periodic orbit theory to approximate the trace of the powers of the evolution operator. Aside from the usual real trajectories, we also include complex orbits. These turn out to be fundamental for a proper description of the band structure since they incorporate conduction processes through tunneling mechanisms. The results obtained, illustrated with the kicked-Harper model, are in excellent agreement with numerical simulations, even in the extreme quantum regime.Comment: 11 pages, Latex, figures on request to the author (to be sent by fax

Flows and Decompositions of Games: Harmonic and Potential Games

In this paper we introduce a novel flow representation for finite games in strategic form. This representation allows us to develop a canonical direct sum decomposition of an arbitrary game into three components, which we refer to as the potential, harmonic and nonstrategic components. We analyze natural classes of games that are induced by this decomposition, and in particular, focus on games with no harmonic component and games with no potential component. We show that the first class corresponds to the well-known potential games. We refer to the second class of games as harmonic games, and study the structural and equilibrium properties of this new class of games. Intuitively, the potential component of a game captures interactions that can equivalently be represented as a common interest game, while the harmonic part represents the conflicts between the interests of the players. We make this intuition precise, by studying the properties of these two classes, and show that indeed they have quite distinct and remarkable characteristics. For instance, while finite potential games always have pure Nash equilibria, harmonic games generically never do. Moreover, we show that the nonstrategic component does not affect the equilibria of a game, but plays a fundamental role in their efficiency properties, thus decoupling the location of equilibria and their payoff-related properties. Exploiting the properties of the decomposition framework, we obtain explicit expressions for the projections of games onto the subspaces of potential and harmonic games. This enables an extension of the properties of potential and harmonic games to "nearby" games. We exemplify this point by showing that the set of approximate equilibria of an arbitrary game can be characterized through the equilibria of its projection onto the set of potential games

Reproducibility of Dietary Intake Measurement From Diet Diaries, Photographic Food Records, and a Novel Sensor Method

Objective: No data currently exist on the reproducibility of photographic food records compared to diet diaries, two commonly used methods to measure dietary intake. Our aim was to examine the reproducibility of diet diaries, photographic food records, and a novel electronic sensor, consisting of counts of chews and swallows using wearable sensors and video analysis, for estimating energy intake. Method: This was a retrospective analysis of data from a previous study, in which 30 participants (15 female), aged 29 ± 12 y and having a BMI of 27.9 ± 5.5, consumed three identical meals on different days. Four different methods were used to estimate total mass and energy intake on each day: (1) weighed food record; (2) photographic food record; (3) diet diary; and (4) novel mathematical model based on counts of chews and swallows (CCS models) obtained via the use of electronic sensors and video monitoring system. The study staff conducted weighed food records for all meals, took pre- and post-meal photographs, and ensured that diet diaries were completed by participants at the end of each meal. All methods were compared against the weighed food record, which was used as the reference method. Results: Reproducibility was significantly different between the diet diary and photographic food record for total energy intake (p = 0.004). The photographic record had greater reproducibility vs. the diet diary for all parameters measured. For total energy intake, the novel sensor method exhibited good reproducibility (repeatability coefficient (RC) of 59.9 (45.9, 70.4), which was better than that for the diet diary [RC = 79.6 (55.5, 103.3)] but not as repeatable as the photographic method [RC = 43.4 (32.1, 53.9)]. Conclusion: Photographic food records offer superior precision to the diet diary and, therefore, would be valuable for longitudinal studies with repeated measures of dietary intake. A novel electronic sensor also shows promise for the collection of longitudinal dietary intake data.Fil: Fontana, Juan Manuel. Universidad Nacional de Río Cuarto. Instituto para el Desarrollo Agroindustrial y de la Salud. - Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto para el Desarrollo Agroindustrial y de la Salud; ArgentinaFil: Pan, Zhaoxing. University of Colorado; Estados UnidosFil: Sazonov, Edward S.. University of Alabama; Estados UnidosFil: McCrory, Megan A.. Boston University; Estados UnidosFil: Thomas, J. Graham. University Brown; Estados UnidosFil: McGrane, Kelli S.. University of Colorado; Estados UnidosFil: Marden, Tyson. University of Colorado; Estados UnidosFil: Higgins, Janine A.. University of Colorado; Estados Unido

The Asymptotic distribution of circles in the orbits of Kleinian groups

Let P be a locally finite circle packing in the plane invariant under a non-elementary Kleinian group Gamma and with finitely many Gamma-orbits. When Gamma is geometrically finite, we construct an explicit Borel measure on the plane which describes the asymptotic distribution of small circles in P, assuming that either the critical exponent of Gamma is strictly bigger than 1 or P does not contain an infinite bouquet of tangent circles glued at a parabolic fixed point of Gamma. Our construction also works for P invariant under a geometrically infinite group Gamma, provided Gamma admits a finite Bowen-Margulis-Sullivan measure and the Gamma-skinning size of P is finite. Some concrete circle packings to which our result applies include Apollonian circle packings, Sierpinski curves, Schottky dances, etc.Comment: 31 pages, 8 figures. Final version. To appear in Inventiones Mat