Problems in the different branches of philosophy, adapted to the course of reading pursued in the University of Cambridge.

Trigonometrical problems.--Hydrostatical problems.--Optical problems.--Problems from Newton's Principia.--Astronomical problems.

Mechanical problems, adapted to the course of reading in the university of Cambridge.

Mode of access: Internet.

Problems and potentialities of e-Learning for regular undergraduate courses in emergency medicine

BACKGROUND: E-learning techniques are spreading at great speed in medicine, raising concerns about the impact of adopting them. Websites especially designed to host courses are becoming more common. There is a lack of evidence that these systems could enhance student knowledge acquisition. GOAL: To evaluate the impact of using dedicated-website tools over cognition of medical students exposed to a first-aid course. METHODS: Prospective study of 184 medical students exposed to a twenty-hour first-aid course. We generated a dedicated-website with several sections (lectures, additional reading material, video and multiple choice exercises). We constructed variables expressing the student's access to each section. The evaluation was composed of fifty multiple-choice tests, based on clinical problems. We used multiple linear regression to adjust for potential confounders. RESULTS: There was no association of website intensity of exposure and the outcome - beta-coeficient 0.27 (95%CI - 0.454 - 1.004). These findings were not altered after adjustment for potential confounders - 0.165 (95%CI -0.628 - 0.960). CONCLUSION: A dedicated website with passive and active capabilities for aiding in person learning had not shown association with a better outcome.

The effectiveness of short-term literacy skills intervention on children at risk of reading and writing difficulties in Tanzania : a study of grade one children with dynamic assessment approach

The aim of the study was to create and evaluate an intervention programme for Tanzanian children from a low-income area who are at risk of reading and writing difficulties. The learning difficulties, including reading and writing difficulties, are likely to be behind many of the common school problems in Tanzania, but they are not well understood, and research is needed. The design of the study included an identification and intervention phase with follow-up. A group based dynamic assessment approach was used in identifying children at risk of difficulties in reading and writing. The same approach was used in the intervention. The study was a randomized experiment with one experimental and two control groups. For the experimental and the control groups, a total of 96 (46 girls and 50 boys) children from grade one were screened out of 301 children from two schools in a low income urban area of Dar-es-Salaam. One third of the children, the experimental group, participated in an intensive training programme in literacy skills for five weeks, six hours per week, aimed at promoting reading and writing ability, while the children in the control groups had a mathematics and art programme. Follow-up was performed five months after the intervention. The intervention programme and the tests were based on the Zambian BASAT (Basic Skill Assessment Tool, Ketonen & Mulenga, 2003), but the content was drawn from the Kiswahili school curriculum in Tanzania. The main components of the training and testing programme were the same, only differing in content. The training process was different from traditional training in Tanzanian schools in that principles of teaching and training in dynamic assessment were followed. Feedback was the cornerstone of the training and the focus was on supporting the children in exploring knowledge and strategies in performing the tasks. The experimental group improved significantly more (p = .000) than the control groups during the intervention from pre-test to follow-up (repeated measures ANOVA). No differences between the control groups were noticed. The effect was significant on all the measures: phonological awareness, reading skills, writing skills and overall literacy skills. A transfer effect on school marks in Kiswahili and English was found. Following a discussion of the results, suggestions for further research and adaptation of the programme are presented.

Assessment of social cognition in schizophrenia through the “Reading the Mind in the Eyes” test. Implications for rehabilitation

Introduction: Schizophrenia is a serious and chronic mental illness that has effect on cognitive and social functioning of a person who suffers it. Recent research points out that social cognition subprocesses, such as Theory of Mind, social perception or emotional processing, have to do with some problems that patients show in their social adjustment. Aim: Assessing ability of recognizing mental states from facial expressions in schizophrenia patients compared to a control group. Subjects and methods: 17 stable schizophrenia patients who are aware of the illness and 17 healthy people, with the same age and sociocultural level, took the “Reading the Mind in the Eyes” Test Revised Version of Baron- Cohen. Results: Compared with the control group, subjects with schizophrenia showed much lower scores. Conclusions: It is confirmed that schizophrenia patients have impairments to understand facial expressions, especially from the eyes. That is typical of this illness, so it is necessary to do interventions at that point. Furthermore, inability to recognize emotions, as a domain of social cognition, contributes to deficit in functional outcome in schizophrenia. Finally, some treatment programs are put forward.

Approximate Gauss-Newton methods for nonlinear least squares problems

The Gauss–Newton algorithm is an iterative method regularly used for solving nonlinear least squares problems. It is particularly well suited to the treatment of very large scale variational data assimilation problems that arise in atmosphere and ocean forecasting. The procedure consists of a sequence of linear least squares approximations to the nonlinear problem, each of which is solved by an “inner” direct or iterative process. In comparison with Newton’s method and its variants, the algorithm is attractive because it does not require the evaluation of second-order derivatives in the Hessian of the objective function. In practice the exact Gauss–Newton method is too expensive to apply operationally in meteorological forecasting, and various approximations are made in order to reduce computational costs and to solve the problems in real time. Here we investigate the effects on the convergence of the Gauss–Newton method of two types of approximation used commonly in data assimilation. First, we examine “truncated” Gauss–Newton methods where the inner linear least squares problem is not solved exactly, and second, we examine “perturbed” Gauss–Newton methods where the true linearized inner problem is approximated by a simplified, or perturbed, linear least squares problem. We give conditions ensuring that the truncated and perturbed Gauss–Newton methods converge and also derive rates of convergence for the iterations. The results are illustrated by a simple numerical example. A practical application to the problem of data assimilation in a typical meteorological system is presented.

An integral equation method for a boundary value problem arising in unsteady water wave problems

In this paper we consider the 2D Dirichlet boundary value problem for Laplace’s equation in a non-locally perturbed half-plane, with data in the space of bounded and continuous functions. We show uniqueness of solution, using standard Phragmen-Lindelof arguments. The main result is to propose a boundary integral equation formulation, to prove equivalence with the boundary value problem, and to show that the integral equation is well posed by applying a recent partial generalisation of the Fredholm alternative in Arens et al [J. Int. Equ. Appl. 15 (2003) pp. 1-35]. This then leads to an existence proof for the boundary value problem. Keywords. Boundary integral equation method, Water waves, Laplace’s

Consistent Dirichlet Boundary Conditions for Numerical Solution of Moving Boundary Problems

We consider the imposition of Dirichlet boundary conditions in the finite element modelling of moving boundary problems in one and two dimensions for which the total mass is prescribed. A modification of the standard linear finite element test space allows the boundary conditions to be imposed strongly whilst simultaneously conserving a discrete mass. The validity of the technique is assessed for a specific moving mesh finite element method, although the approach is more general. Numerical comparisons are carried out for mass-conserving solutions of the porous medium equation with Dirichlet boundary conditions and for a moving boundary problem with a source term and time-varying mass.

Boundary value problems for third-order linear PDEs in time-dependent domains

We present the extension of a methodology to solve moving boundary value problems from the second-order case to the case of the third-order linear evolution PDE qt + qxxx = 0. This extension is the crucial step needed to generalize this methodology to PDEs of arbitrary order. The methodology is based on the derivation of inversion formulae for a class of integral transforms that generalize the Fourier transform and on the analysis of the global relation associated with the PDE. The study of this relation and its inversion using the appropriate generalized transform are the main elements of the proof of our results.

An interpretation of baroclinic initial value problems: results for simple basic states with nonzero interior PV gradients

In the Eady model, where the meridional potential vorticity (PV) gradient is zero, perturbation energy growth can be partitioned cleanly into three mechanisms: (i) shear instability, (ii) resonance, and (iii) the Orr mechanism. Shear instability involves two-way interaction between Rossby edge waves on the ground and lid, resonance occurs as interior PV anomalies excite the edge waves, and the Orr mechanism involves only interior PV anomalies. These mechanisms have distinct implications for the structural and temporal linear evolution of perturbations. Here, a new framework is developed in which the same mechanisms can be distinguished for growth on basic states with nonzero interior PV gradients. It is further shown that the evolution from quite general initial conditions can be accurately described (peak error in perturbation total energy typically less than 10%) by a reduced system that involves only three Rossby wave components. Two of these are counterpropagating Rossby waves—that is, generalizations of the Rossby edge waves when the interior PV gradient is nonzero—whereas the other component depends on the structure of the initial condition and its PV is advected passively with the shear flow. In the cases considered, the three-component model outperforms approximate solutions based on truncating a modal or singular vector basis.

Evolving graphs: dynamical models, inverse problems and propagation

Applications such as neuroscience, telecommunication, online social networking, transport and retail trading give rise to connectivity patterns that change over time. In this work, we address the resulting need for network models and computational algorithms that deal with dynamic links. We introduce a new class of evolving range-dependent random graphs that gives a tractable framework for modelling and simulation. We develop a spectral algorithm for calibrating a set of edge ranges from a sequence of network snapshots and give a proof of principle illustration on some neuroscience data. We also show how the model can be used computationally and analytically to investigate the scenario where an evolutionary process, such as an epidemic, takes place on an evolving network. This allows us to study the cumulative effect of two distinct types of dynamics.

Problems with determining the particle size distribution of chalk soil and some of their implications

Particle size distribution (psd) is one of the most important features of the soil because it affects many of its other properties, and it determines how soil should be managed. To understand the properties of chalk soil, psd analyses should be based on the original material (including carbonates), and not just the acid-resistant fraction. Laser-based methods rather than traditional sedimentation methods are being used increasingly to determine particle size to reduce the cost of analysis. We give an overview of both approaches and the problems associated with them for analyzing the psd of chalk soil. In particular, we show that it is not appropriate to use the widely adopted 8 pm boundary between the clay and silt size fractions for samples determined by laser to estimate proportions of these size fractions that are equivalent to those based on sedimentation. We present data from field and national-scale surveys of soil derived from chalk in England. Results from both types of survey showed that laser methods tend to over-estimate the clay-size fraction compared to sedimentation for the 8 mu m clay/silt boundary, and we suggest reasons for this. For soil derived from chalk, either the sedimentation methods need to be modified or it would be more appropriate to use a 4 pm threshold as an interim solution for laser methods. Correlations between the proportions of sand- and clay-sized fractions, and other properties such as organic matter and volumetric water content, were the opposite of what one would expect for soil dominated by silicate minerals. For water content, this appeared to be due to the predominance of porous, chalk fragments in the sand-sized fraction rather than quartz grains, and the abundance of fine (<2 mu m) calcite crystals rather than phyllosilicates in the clay-sized fraction. This was confirmed by scanning electron microscope (SEM) analyses. "Of all the rocks with which 1 am acquainted, there is none whose formation seems to tax the ingenuity of theorists so severely, as the chalk, in whatever respect we may think fit to consider it". Thomas Allan, FRS Edinburgh 1823, Transactions of the Royal Society of Edinburgh. (C) 2009 Natural Environment Research Council (NERC) Published by Elsevier B.V. All rights reserved.