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

Nestedness in mutualistic networks

James et al. (2012) presented simulations that apparently falsify the analytical result by Bastolla et al. (2009), who showed that nested mutualistic interactions decrease interspecific competition and increase biodiversity in model ecosystems. This contradiction, however, mainly stems from the incorrect application of formulas derived for fully connected networks to empirical, sparse networks.Comment: 2 pages, 1 figur

A new convergent algorithm to approximate potentials from fixed angle scattering data

We introduce a new iterative method to recover a real compact supported potential of the Schr\"odinger operator from their fixed angle scattering data. The method combines a fixed point argument with a suitable approximation of the resolvent of the Schr\"odinger operator by partial sums associated to its Born series. Convergence is established for potentials with small norm in certain Sobolev spaces. As an application we show some numerical experiments that illustrate this convergence.Comment: 25 pages, 6 figure

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

Symmetry considerations in the empirical k.p Hamiltonian for the study of intermediate band solar cells

With the purpose of assessing the absorption coefficients of quantum dot solar cells, symmetry considerations are introduced into a Hamiltonian whose eigenvalues are empirical. In this way, the proper transformation from the Hamiltonian's diagonalized form to the form that relates it with Γ-point exact solutions through k.p envelope functions is built accounting for symmetry. Forbidden transitions are thus determined reducing the calculation burden and permitting a thoughtful discussion of the possible options for this transformation. The agreement of this model with the measured external quantum efficiency of a prototype solar cell is found to be excellent