Framing Welfare Reform in Affluent Societies: Rendering Retrenchment more Palatable?

social policy; welfare state; Maastricht Social Protocol

Guessing Numbers of Odd Cycles

For a given number of colours, $s$, the guessing number of a graph is the base $s$ logarithm of the size of the largest family of colourings of the vertex set of the graph such that the colour of each vertex can be determined from the colours of the vertices in its neighbourhood. An upper bound for the guessing number of the $n$-vertex cycle graph $C_n$ is $n/2$. It is known that the guessing number equals $n/2$ whenever $n$ is even or $s$ is a perfect square \cite{Christofides2011guessing}. We show that, for any given integer $s\geq 2$, if $a$ is the largest factor of $s$ less than or equal to $\sqrt{s}$, for sufficiently large odd $n$, the guessing number of $C_n$ with $s$ colours is $(n-1)/2 + \log_s(a)$. This answers a question posed by Christofides and Markstr\"{o}m in 2011 \cite{Christofides2011guessing}. We also present an explicit protocol which achieves this bound for every $n$. Linking this to index coding with side information, we deduce that the information defect of $C_n$ with $s$ colours is $(n+1)/2 - \log_s(a)$ for sufficiently large odd $n$. Our results are a generalisation of the $s=2$ case which was proven in \cite{bar2011index}.Comment: 16 page

Raw Life, New Hope

The Cape Flats, a windswept, barren and sandy area which rings Cape Town, is home to more than a million people. Many live here in sprawling shack settlements. The post-apartheid state is attempting to eradicate such settlements by providing formal houses in planned residential estates. Raw Life, New Hope is a longitudinal study of the residents of one such shack settlement, The Park, who moved to new, 'formal' houses in The Village, at the turn of the millennium. It introduces readers to core social science topics and modes of theorising. Over 17 years the author has traced how ordinary people attempt to live in accord with their ideals of decency under almost impossible circumstances, and the effects of material changes in their lives after 1994, including the provision of housing. Photos, maps, anecdotes, recipes and philosophical reflections on subjects that arose during conversations elicit a sense of the everyday and of how people try to solve the problems of poverty

Learning English, and Teaching English – and linking the two together

Degree courses in modern languages, especially those for students wishing to become teachers, tend to consist of different modules with little connection to each other and may have insufficient emphasis on improving language skills. This paper presents the concept and structure of a language course designed to address such issues. It is holistic in approach and focuses on developing students' awareness of language learning processes; the insights acquired by the participants can be applied to any learning or teaching situation.Fremdsprachliche Studiengänge, besonders die für zukünftige Lehrerinnen und Lehrer, bestehen häufig aus verschiedenen Modulen, die nur zum Teil aufeinander bezogen sind und der Verbesserung von Fremdsprachenkenntnissen einen relativ geringen Wert beimessen. Der folgende Artikel stellt einen Sprachkurs vor, der darauf abzielt, sich speziell diesen Themen zu stellen. Der Kurs ist ganzheitlich in seinem Ansatz und konzentriert sich darauf, das Bewusstsein von Studierenden für die Prozesse des Fremdsprachenerwerbs zu schärfen; die von den Teilnehmenden erworbenen Erkenntnisse lassen sich auf jegliche Lern- oder Lehrsituationen anwenden

The Jordan curve theorem is non-trivial

The formal mathematical definition of a Jordan curve (a non-self-intersecting continuous loop in the plane) is so simple that one is often lead to the unimaginative view that a Jordan curve is nothing more than a circle or an ellipse. In this paper, we pursue the theme that a Jordan curve can be quite fantastical in the sense that there are some bizarre properties such a curve might have (jagged at every point, space filling, etc.) or that such a curve can have a difficult to discover inside and outside as promised by the celebrated Jordan Curve Theorem (JCT). We explore the JCT theorem through its history and some hand drawings which not only challenge the viewer\u27s preconceived notions of interior and exterior or that the JCT is a trivial result, but also challenge the reader\u27s notion that a curve is a cold boring object, incapable of telling an interesting story