Efficiency and Equity in Schools around the World

Attention to the quality of human capital in different countries naturally leads to concerns about how school policies relate to student performance. The data from the Third International Mathematics and Science Study (TIMSS) provide a way of comparing performance in different schooling systems. The results of analyses of educational production functions within a range of developed and developing countries show general problems with the efficiency of resource usage similar to those found previously in the United States. These effects do not appear to be dictated by variations related to income level of the country or level of resources in the schools. Neither do they appear to be determined by school policies that involve compensatory application of resources. The conventional view that school resources are relatively more important in poor countries also fails to be supported.

Tauberian conditions, Muckenhoupt weights, and differentiation properties of weighted bases

We give an alternative characterization of the class of Muckenhoupt weights $A_{\infty, \mathfrak B}$ for homothecy invariant Muckenhoupt bases $\mathfrak B$ consisting of convex sets. In particular we show that $w\in A_{\infty, \mathfrak B}$ if and only if there exists a constant $c>0$ such that for all measurable sets $E\subset \mathbb R^n$ we have $$w({x\in \mathbb R^n: M_{\mathfrak B} (\mathbf {1}_E)(x)>1/2}) < c w(E).$$ This applies for example to the collection $\mathfrak R$ of rectangles with sides parallel to the coordinate axes, giving a new characterization of strong (multiparameter) Muckenhoupt weights. We also show versions of these results under the presence of a doubling measure. Thus the strong maximal function $M_{\mathfrak R,\mu}$, defined with respect to a product-doubling measure $\mu$, is bounded on $L^p(\mu)$ for some $p>1$ if and only if $$\mu({x\in \mathbb R^n: M_{\mathfrak R,\mu} (\mathbf{1}_E)(x)>1/2}) < c \mu(E)$$ for all measurable sets $E\subset \mathbb R^n$. Finally we discuss applications in differentiation theory, proving among other things that Tauberian conditions as above imply that the corresponding bases differentiate $L^\infty(\mu)$, with respect to the measure $\mu$.Comment: 35 pages, 1 figure, minor typos corrected, one reference added, incorporates referee's report; to appear in Trans. Amer. Math. So

A robust motion estimation and segmentation approach to represent moving images with layers

The paper provides a robust representation of moving images based on layers. To that goal, we have designed efficient motion estimation and segmentation techniques by affine model fitting suitable for the construction of layers. Layered representations, originally introduced by Wang and Adelson (see IEEE Transactions on Image Processing, vol.3, no.5, p.625-38, 1994) are important in several applications. In particular they are very appropriate for object tracking, object manipulation and content-based scalability which are among the main functionalities of the future MPEG-4 standard. In addition a variety of examples are provided that give a deep insight into the performance bounds of the representation of moving images using layers.Peer ReviewedPostprint (published version

Ultra-high efficiency solar cells: the path for mass penetration of solar electricity

For achieving a photovoltaic penetration above one-third of the world demand for electricity in the first half of this century, the importance of a fast manufacturing learning curve that is linked to the capacity of developing cells of increasing efficiency is stressed. Progress in multijunction cells is described as well as three novel concepts promising very high efficiency. It is explained why these concepts will probably be used in concentrator systems

Quasiperiodic graphs: structural design, scaling and entropic properties

A novel class of graphs, here named quasiperiodic, are constructed via application of the Horizontal Visibility algorithm to the time series generated along the quasiperiodic route to chaos. We show how the hierarchy of mode-locked regions represented by the Farey tree is inherited by their associated graphs. We are able to establish, via Renormalization Group (RG) theory, the architecture of the quasiperiodic graphs produced by irrational winding numbers with pure periodic continued fraction. And finally, we demonstrate that the RG fixed-point degree distributions are recovered via optimization of a suitably defined graph entropy