Deconvolution by simulation

Given samples (x_1,...,x_m) and (z_1,...,z_n) which we believe are independent realizations of random variables X and Z respectively, where we further believe that Z=X+Y with Y independent of X, the problem is to estimate the distribution of Y. We present a new method for doing this, involving simulation. Experiments suggest that the method provides useful estimates.Comment: Published at http://dx.doi.org/10.1214/074921707000000021 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

Baxter permutations rise again

AbstractBaxter permutations, so named by Boyce, were introduced by Baxter in his study of the fixed points of continuous functions which commute under composition. Recently Chung, Graham, Hoggatt, and Kleiman obtained a sum formula for the number of Baxter permutations of 2n − 1 objects, but admit to having no interpretation of the individual terms of this sum. We show that in fact the kth term of this sum counts the number of (reduced) Baxter permutations that have exactly k − 1 rises

Geophysical Studies of Oceanic Core Complexes: The Mid-Atlantic Ridge, 13 - 14°N

Marine geophysical studies have revealed that crustal accretion processes at mid-ocean ridges are largely dependent on the relative contribution of magmatism and tectonism to plate separation. At high levels of magmatic accretion, the ridge is associated with large amounts of surficial volcanism and the formation of closely spaced, continuous abyssal hills that parallel the ridge axis. In contrast, when magmatic accretion is low, tectonic extension prevails and crustal structure is markedly different. In this latter scenario, long-lived detachment faulting forms oceanic core complexes (OCCs) that expose lower crustal rocks and mantle material at the seafloor. Whilst many of the general features of this ‘magma-poor’ terrain have been identified, there is still widespread debate as to the exact conditions that necessitate and regulate OCC formation. This study presents the results of a deep-towed and shipboard geophysical survey of the Mid-Atlantic Ridge between 13 – 14°N. This area is an ideal place to test and develop models for OCC structure and formation as the ridge axis exhibits multiple core complexes at various evolutionary stages. The data presented here include: deep-towed TOBI sidescan sonar and tri-axial magnetometer data, shipboard gravity and bathymetric data, and detailed seabed sampling results. High resolution sidescan sonar data reveal that active core complexes in this region are associated with a neovolcanic hiatus within the axial valley. In contrast, a recently terminated near-axis OCC is associated with widespread neovolcanism, thus confirming that OCC formation is regulated by variations in melt supply to the ridge axis. Forward modelling of gravity data shows that beneath the domal sections of OCC footwalls (from which serpentinised peridotites were ubiquitously sampled), a low density zone (LDZ) exists. This area is interpreted as comprising predominantly gabbroic material that has been captured by each detachment fault at depth beneath the ridge axis (thus explaining the gap in neovolcanism at the surface). Furthermore, magnetic data suggest that OCC footwalls are highly heterogeneous, reflecting significant compositional and thickness variations of the LDZ. Analyses of sidescan sonar imagery, combined with models of gravity and magnetic anomalies, reveal significant across- and along-axis asymmetry in the region. In general, the quadrants of the survey area within the inside-corners of the non-transform offset at 13°38’N are associated with widespread OCC formation, elevated tectonic strain (Tε = 25 – 30%), thin crust and faster spreading (20 – 40%) compared with conjugate ridge flanks; these areas are characterised by crust that is typically ~0.5 – 1.0 km thicker than OCC-forming areas, and tectonic strain (Tε = 10 – 15%) is partitioned across numerous, small faults. On the basis of these results, a model is presented for the structure of the 13 – 14°N region, and for the life cycle of oceanic core complexes. These models have implications for our current understanding of the magmato-tectonic conditions within which OCCs are expected to operate, and, in a broader sense, for the long wavelength processes that govern crustal accretion at low levels of magmatism

Insights – What research has to tell us about ESOL

This is a review of NRDC research in ESOL from 2002 to 2006. It draws on the findings of 18 different research projects to provide insight into the ESOL provision, its learners and its teachers in that period. ESOL was part of Skills for Life from its launch in 2001 and benefited from equivalent investment and the development of curricula, assessment and professional practice, recognising ESOL, alongside numeracy and literacy, as a distinct area of teaching and learning. Consultation with ESOL practitioners identified a number of teaching and learning challenges: The extraordinary diversity of the backgrounds, previous education and current circumstances of learners in the same class. Learners’ strong motivation to learn English as a route to employment or further study. The fact that learners often have little access to interaction with English-speakers outside the classroom. There was an ESOL focus in NRDC research on workforce basic skills, embedded learning, rural provision, adult learners’ lives, and teacher education. There were two large studies: the ESOL effective practice project (EEPP) and a set of case studies. NRDC also commissioned two reviews, one on pedagogy, the other on applied linguistics. This review does not attempt to offer a total picture of ESOL in the period: for example NRDC did not carry out any large-scale surveys of ESOL learners. However, it does contribute to our understanding of ESOL provision, and its learners and teachers, in the first period of the Skills for Life Strategy

Designed-in and contingent scaffolding in the Teaching Practice Groups model

The focus of this paper is the teacher learning of trainee teachers of English as a second, other or foreign language to adults, within a particular model of initial teacher training: Teaching Practice Groups. It draws on socio-constructive theories of teacher learning to explore the learning of trainees within the model. Teaching Practice Groups are highly social; trainees on courses using the model interact a great deal with each other, with their peers, with the learners in the teaching practice classroom, and also with the course documentation and activities. This paper suggests that these interactions, and the consequent development of trainees’ knowledge and understanding of teaching, are scaffolded in both ‘designed-in’ and ‘contingent’ ways (Hammond Gibbons 2005: 12). Designed-in scaffolding can be seen in the way the course is structured, in the activities that learners are expected to engage with, and in the documents and processes through which these processes are managed. Contingent scaffolding on the other hand, the spontaneous actions and guidance of the trainer in response to the immediate learning needs of the trainee teacher, is unplanned. While the findings from this study are specific to the context of Teaching Practice Groups, this paper also offers a contribution to more general knowledge about initial teacher training for English language teachers

Teaching Practice Groups: a case study of social constructive learning

The focus of this thesis is the teacher learning of trainee teachers of English as a second, other or foreign language to adults, within a particular model of initial teacher training: Teaching Practice Groups. It contributes to knowledge in the field by centering on the mechanisms by which the Teaching Practice Group model supports prospective English language teachers in learning to teach. To do so it draws on sodio-construcivist and cognitive theories of teacher learning to explore the learning of trainees within the model, through their interaction with their fellow trainees, the trainers, and the activities of the course. It suggests that within the Teaching Practice Group model the classroom is both the focus and the place of learning about how to teach. The Teaching Practice Group model provides contextually meaningful experiences for trainees, engaging them in situational decision-making, both in advance of teaching in the form of lesson planning, and on their feet in front of a group of learners. The study identifies ways in which both subjective and objective understandings of knowledge impact on the judgments trainees make about how to act in the classroom. It shows how objective descriptions of teacher knowledge are used in order to help trainees to name elements of the teaching and learning process - the classroom and its moves, while subjective knowledge is foregrounded in the focused reflection that Teaching Practice Group model provides on the experience of teaching. The thesis uses concepts from social constructivist theories of learning. Teaching Practice Groups are highly social; trainees on courses using the model interact a great deal with each other, with their peers, with the learners in the teaching practice classroom, and also with the course documentation and activities. I suggest that the development of trainees’ knowledge and understanding of teaching within the model is highly scaffolded, allowing trainers to progress trainees’ attention beyond their own actions, to the learners and their learning. The teacher learning examined in this thesis is driven by engagement with concepts of teaching and learning, with other players (peers, students and trainers), in the specific cultural environment of the shared language classroom

The Nola Green memorial lecture: Wednesday 25 May 1988 - The next hundred years: A planner's viewpoint

The somewhat provocative title to this talk was chosen deliberately. It seems to me that planning is meaningless unless it attempts to deal with the future and therefore the minimum duty of any physical planner is to attempt to forecast future trends, and like any good navi­gator, advise clients - including the authorities at any level - of the way these trends can best be optimized and in what direction they should be guided