Exploring poverty gaps among children in the UK

"The purpose of this paper is to use poverty gap analysis to explore the depth of poverty experienced by children of low-income families in the UK. Measures set out in the Child Poverty Act1 and in the National Child Poverty Strategy2 are based on poverty headcounts, i.e. you are either below or above a certain poverty threshold. The most commonly used measure is the 60 per cent relative poverty measure, defined as individuals living in households with incomes below 60 per cent of the median income. The National Strategy, published in April 2011, introduces a new measure on severe poverty, defined as individuals living in households experiencing material deprivation and with incomes below 50 per cent of the median income. The head count does not distinguish between those with incomes just below the poverty line and those deeper in poverty. Policies which improve incomes for those at the bottom of the income distribution will not lead to a fall in measured income poverty, unless incomes are raised sufficiently to cross the chosen poverty threshold, and yet reducing these families’ depth of poverty is highly likely to improve living standards. This paper supplements the headcount measures with analysis of the ‘poverty gap’ for UK children. The poverty gap measures ‘How poor are the poor’ i.e. the extent of poverty for those who are below the relative poverty threshold. With this measure, an improvement in incomes for those in poverty which is not sufficient for them to escape poverty, is nevertheless captured as a drop in measured poverty. In practice, for each poor individual we measure the poverty gap by calculating the shortfall in their income from the poverty line, and expressing this as a percentage of the poverty line. For example, if the poverty line was 100 and the income was 25 then the poverty gap would be 75 per cent (100 minus 25 equals 75; 75 divided by 100 is 75 per cent). A poverty gap of 75 per cent can be interpreted as an income that is 75 per cent below the poverty line" - page 1

Abelian covers of graphs and maps between outer automorphism groups of free groups

We explore the existence of homomorphisms between outer automorphism groups of free groups Out(F_n) \to Out(F_m). We prove that if n > 8 is even and n \neq m \leq 2n, or n is odd and n \neq m \leq 2n - 2, then all such homomorphisms have finite image; in fact they factor through det: Out(F_n) \to Z/2. In contrast, if m = r^n(n - 1) + 1 with r coprime to (n - 1), then there exists an embedding Out(F_n) \to Out(F_m). In order to prove this last statement, we determine when the action of Out(F_n) by homotopy equivalences on a graph of genus n can be lifted to an action on a normal covering with abelian Galois group.Comment: Final version, to appear in Mathematische Annalen. Minor errors and typos corrected, including range of n in Theorem

Actions of automorphism groups of free groups on homology spheres and acyclic manifolds

For n at least 3, let SAut(F_n) denote the unique subgroup of index two in the automorphism group of a free group. The standard linear action of SL(n,Z) on R^n induces non-trivial actions of SAut(F_n) on R^n and on S^{n-1}. We prove that SAut(F_n) admits no non-trivial actions by homeomorphisms on acyclic manifolds or spheres of smaller dimension. Indeed, SAut(F_n) cannot act non-trivially on any generalized Z_2-homology sphere of dimension less than n-1, nor on any Z_2-acyclic Z_2-homology manifold of dimension less than n. It follows that SL(n,Z) cannot act non-trivially on such spaces either. When n is even, we obtain similar results with Z_3 coefficients.Comment: Typos corrected, reference and thanks added. Final version, to appear in Commetarii. Math. Hel

The Dehn functions of Out(F_n) and Aut(F_n)

For n > 2, the Dehn functions of Aut(F_n) and Out(F_n) are exponential. Hatcher and Vogtmann proved that they are at most exponential, and the complementary lower bound in the case n=3 was established by Bridson and Vogtmann. Handel and Mosher completed the proof by reducing the lower bound for n>4 to the case n=3. In this note we give a shorter, more direct proof of this last reduction.Comment: Final version, to appear in Annales de l'Institut Fourie

Incorporating Problem-Based Learning Strategies to Develop Learner Autonomy and Employability Skills in Sports Science Undergraduates

This study investigated the impact of a 12-week problem-based learning (PBL) intervention on three psychological constructs (motivation, locus of control and self-esteem) linked to learner autonomy. Results indicated that there was a significant increase in the students’ intrinsic motivation (P<0.05) and a non-significant shift towards an internal locus of control after the intervention period. Students perceived the benefits of PBL to be the opportunity to work in teams and to consider a wider knowledge base. A short course of PBL was successful in developing learner autonomy and other key employability skills alongside the application of content knowledge

On Verifying Complex Properties using Symbolic Shape Analysis

One of the main challenges in the verification of software systems is the analysis of unbounded data structures with dynamic memory allocation, such as linked data structures and arrays. We describe Bohne, a new analysis for verifying data structures. Bohne verifies data structure operations and shows that 1) the operations preserve data structure invariants and 2) the operations satisfy their specifications expressed in terms of changes to the set of objects stored in the data structure. During the analysis, Bohne infers loop invariants in the form of disjunctions of universally quantified Boolean combinations of formulas. To synthesize loop invariants of this form, Bohne uses a combination of decision procedures for Monadic Second-Order Logic over trees, SMT-LIB decision procedures (currently CVC Lite), and an automated reasoner within the Isabelle interactive theorem prover. This architecture shows that synthesized loop invariants can serve as a useful communication mechanism between different decision procedures. Using Bohne, we have verified operations on data structures such as linked lists with iterators and back pointers, trees with and without parent pointers, two-level skip lists, array data structures, and sorted lists. We have deployed Bohne in the Hob and Jahob data structure analysis systems, enabling us to combine Bohne with analyses of data structure clients and apply it in the context of larger programs. This report describes the Bohne algorithm as well as techniques that Bohne uses to reduce the ammount of annotations and the running time of the analysis

Limited availability of cardiac rehabilitation for heart failure patients in the United Kingdom: findings from a national survey

Background: Participation of patients with heart failure in cardiac rehabilitation in the UK is low. This study investigated the availability of cardiac rehabilitation services for patients with heart failure in the UK and the views of service coordinators on ideal service models. Design: Our study was a cross-sectional national postal survey that was mailed to 342 service coordinators in the UK between April and June 2009. Methods: We developed a 38-item questionnaire to survey all cardiac rehabilitation service coordinators on theNational Audit of Cardiac Rehabilitation register in the UK in 2009. Results: The survey response rate was 71% (244/342). Forty three per cent (105/244) of coordinators did not accept patients with heart failure to their cardiac rehabilitation services. Most coordinators who did accept patients with heart failure offered their services to patients with a variety of cardiac conditions, though referral criteria and models of care varied widely. Services inconsistently used New York Heart Association classes and left ventricular ejection fraction measures to select patients. Few offered separate dedicated heart failure programmes (14%; 33/244) but where these existed they ran for longer than programmes which included patients with heart failure alongside other cardiac patients (10.9 vs 8.5 weeks; F=4.04; p=0.019). Few offered home-based options for patients with heart failure (11%; 27/244). Coordinators accepting patients with heart failure to their cardiac rehabilitation services tended to agree that patients with heart failure should be included in services alongside other cardiac patients (X2=6.2; p=0.013). Conclusions: There is limited access for patients with heart failure to cardiac rehabilitation in the UK. Local policies on referral and selection criteria differ and reflect coordinators views rather than clinical guidance. © The European Society of Cardiology 2013 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav