The hole in the wall: self organising systems in education

Transcript of a keynote speech by Sugata Mitra at “Into something rich and strange” – making sense of the sea-change, the 2010 Association for Learning Technology Conference in Nottingham, England. In the chair, Richard Noss, Co-director of the London Knowledge Lab. This text transcript is at http://repository.alt.ac.uk/855/ [82 kB PDF]. A one hour video of the talk is on the ALT-C 2010 web site at http://www.alt.ac.uk/altc2010/ and on the ALT YouTube channel at http://youtube.com/ClipsFromALT/. Alongside this there will be an experimental version of the video that includes the #altc2010 twitter stream at the time of Sugata’s talk. Made publicly available by ALT in November 2010 under a Creative Commons Attribution-Non-Commercial 2.0 UK: England & Wale

On topological upper-bounds on the number of small cuspidal eigenvalues

Let $S$ be a noncompact, finite area hyperbolic surface of type $(g, n)$. Let $\Delta_S$ denote the Laplace operator on $S$. As $S$ varies over the {\it moduli space} ${\mathcal{M}_{g, n}}$ of finite area hyperbolic surfaces of type $(g, n)$, we study, adapting methods of Lizhen Ji \cite{Ji} and Scott Wolpert \cite{Wo}, the behavior of {\it small cuspidal eigenpairs} of $\Delta_S$. In Theorem 2 we describe limiting behavior of these eigenpairs on surfaces ${S_m} \in {\mathcal{M}_{g, n}}$ when $({S_m})$ converges to a point in $\overline{\mathcal{M}_{g, n}}$. Then we consider the $i$-th {\it cuspidal eigenvalue}, ${\lambda^c_i}(S)$, of $S \in {\mathcal{M}_{g, n}}$. Since {\it non-cuspidal} eigenfunctions ({\it residual eigenfunctions} or {\it generalized eigenfunctions}) may converge to cuspidal eigenfunctions, it is not known if ${\lambda^c_i}(S)$ is a continuous function. However, applying Theorem 2 we prove that, for all $k \geq 2g-2$, the sets $${{\mathcal{C}_{g, n}^{\frac{1}{4}}}}(k)= \{ S \in {\mathcal{M}_{g, n}}: {\lambda_k^c}(S) > \frac{1}{4} \}$$ are open and contain a neighborhood of ${\cup_{i=1}^n}{\mathcal{M}_{0, 3}} \cup {\mathcal{M}_{g-1, 2}}$ in $\overline{\mathcal{M}_{g, n}}$. Moreover, using topological properties of nodal sets of {\it small eigenfunctions} from \cite{O}, we show that ${{\mathcal{C}_{g, n}^{\frac{1}{4}}}}(2g-1)$ contains a neighborhood of ${\mathcal{M}_{0, n+1}} \cup {\mathcal{M}_{g, 1}}$ in $\overline{\mathcal{M}_{g, n}}$. These results provide evidence in support of a conjecture of Otal-Rosas \cite{O-R}.Comment: 24 pages, 1 figur

International Trade and Local Organization of Production - Two Elementary Propositions

This paper argues that international trade should affect local organization of production in a systematic way. By using the standard Heckscher-Ohlin-Samuelson model we show that the export sector is more likely to demonstrate fragmentation, entrepreneurship and outsourcing compared to the import-competing sector in a typical labor abundant country. Liberal trade regime will promote entrepreneurship in general. This is the first elementary proposition. Local outsourcing also establishes a clear link between trade and productivity. This is the second elementary proposition.Trade, outsourcing, entrepreneurship, productivity