Revealing regional deforestation dynamics in north-eastern Madagascar - Insights from multi-temporal land cover change analysis

The north-eastern escarpment of Madagascar harbours the island’s last remaining large-scale humid forest massifs surrounded by a small-scale agricultural mosaic. There is high deforestation, commonly thought to be caused by shifting cultivation practiced by local land users to produce upland rice. However, little is known about the dynamics between forest and shifting cultivation systems at a regional level. Our study presents a first attempt to quantify changes in the extent of forest and different agricultural land cover classes, and to identify the main dynamics of land cover change for two intervals, 1995–2005 and 2005–2011. Over the 16-year study period, the speed of forest loss increased, the total area of upland rice production remained almost stable, and the area of irrigated rice fields slightly increased. While our findings seem to confirm a general trend of land use intensification, deforestation through shifting cultivation is still on the rise. Deforestation mostly affects the small forest fragments interspersed in the agricultural mosaic and is slowly leading to a homogenization of the landscape. These findings have important implications for future interventions to slow forest loss in the region, as the processes of agricultural expansion through shifting cultivation versus intensified land use cannot per se be considered mutually exclusive.

A Clearer Picture of Total Variation Blind Deconvolution

Blind deconvolution is the problem of recovering a sharp image and a blur kernel from a noisy blurry image. Recently, there has been a significant effort on understanding the basic mechanisms to solve blind deconvolution. While this effort resulted in the deployment of effective algorithms, the theoretical findings generated contrasting views on why these approaches worked. On the one hand, one could observe experimentally that alternating energy minimization algorithms converge to the desired solution. On the other hand, it has been shown that such alternating minimization algorithms should fail to converge and one should instead use a so-called Variational Bayes approach. To clarify this conundrum, recent work showed that a good image and blur prior is instead what makes a blind deconvolution algorithm work. Unfortunately, this analysis did not apply to algorithms based on total variation regularization. In this manuscript, we provide both analysis and experiments to get a clearer picture of blind deconvolution. Our analysis reveals the very reason why an algorithm based on total variation works. We also introduce an implementation of this algorithm and show that, in spite of its extreme simplicity, it is very robust and achieves a performance comparable to the top performing algorithms.

Bifurcation Analysis of Reaction Diffusion Systems on Arbitrary Surfaces

In this article we present a computational framework for isolating spatial patterns arising in the steady states of reaction-diffusion systems. Such systems have been used to model many different phenomena in areas such as developmental and cancer biology, cell motility and material science. Often one is interested in identifying parameters which will lead to a particular pattern. To attempt to answer this, we compute eigenpairs of the Laplacian on a variety of domains and use linear stability analysis to determine parameter values for the system that will lead to spatially inhomogeneous steady states whose patterns correspond to particular eigenfunctions. This method has previously been used on domains and surfaces where the eigenvalues and eigenfunctions are found analytically in closed form. Our contribution to this methodology is that we numerically compute eigenpairs on arbitrary domains and surfaces. Here we present various examples and demonstrate that mode isolation is straightforward especially for low eigenvalues. Additionally we see that if two or more eigenvalues are in a permissible range then the inhomogeneous steady state can be a linear combination of the respective eigenfunctions. Finally we show an example which suggests that pattern formation is robust on similar surfaces in cases that the surface either has or does not have a boundary.