Stochastic Desertification

The process of desertification is usually modeled as a first order transition, where a change of an external parameter (e.g. precipitation) leads to a catastrophic bifurcation followed by an ecological regime shift. However, vegetation elements like shrubs and trees undergo a stochastic birth-death process with an absorbing state; such a process supports a second order continuous transition with no hysteresis. We present a numerical study of a minimal model that supports bistability and catastrophic shift on spatial domain with demographic noise and an absorbing state. When the external parameter varies adiabatically the transition is continuous and the front velocity renormalizes to zero at the extinction transition. Below the transition one may identify three modes of desertification: accumulation of local catastrophes, desert invasion and global collapse. A catastrophic regime shift occurs as a dynamical hysteresis, when the pace of environmental variations is too fast. We present some empirical evidence, suggesting that the mid-holocene desertification of the Sahara was, indeed, continuous

Compact coalgebras, compact quantum groups and the positive antipode

In this article -that has also the intention to survey some known results in the theory of compact quantum groups using methods different from the standard and with a strong algebraic flavor- we consider compact o-coalgebras and Hopf algebras. In the case of a o-Hopf algebra we present a proof of the characterization of the compactness in terms of the existence of a positive definite integral, and use our methods to give an elementary proof of the uniqueness - up to conjugation by an automorphism of Hopf algebras- of the compact involution appearing in [4]. We study the basic properties of the positive square root of the antipode square that is a Hopf algebra automorphism that we call the positive antipode. We use it -as well as the unitary antipode and the Nakayama automorphism- in order to enhance our understanding of the antipode itself

Empirical analysis of vegetation dynamics and the possibility of a catastrophic desertification transition

The process of desertification in the semi-arid climatic zone is considered by many as a catastrophic regime shift, since the positive feedback of vegetation density on growth rates yields a system that admits alternative steady states. Some support to this idea comes from the analysis of static patterns, where peaks of the vegetation density histogram were associated with these alternative states. Here we present a large-scale empirical study of vegetation dynamics, aimed at identifying and quantifying directly the effects of positive feedback. To do that, we have analyzed vegetation density across $~2.5 \times 10^6 \ \rm{km}^2$ of the African Sahel region, with spatial resolution of $30 \times 30$ meters, using three consecutive snapshots. The results are mixed. The local vegetation density (measured at a single pixel) moves towards the average of the corresponding rainfall line, indicating a purely negative feedback. On the other hand, the chance of spatial clusters (of many "green" pixels) to expand in the next census is growing with their size, suggesting some positive feedback. We show that these apparently contradicting results emerge naturally in a model with positive feedback and strong demographic stochasticity, a model that allows for a catastrophic shift only in a certain range of parameters. Static patterns, like the double peak in the histogram of vegetation density, are shown to vary between censuses, with no apparent correlation with the actual dynamical features

Theory of spike timing based neural classifiers

We study the computational capacity of a model neuron, the Tempotron, which classifies sequences of spikes by linear-threshold operations. We use statistical mechanics and extreme value theory to derive the capacity of the system in random classification tasks. In contrast to its static analog, the Perceptron, the Tempotron's solutions space consists of a large number of small clusters of weight vectors. The capacity of the system per synapse is finite in the large size limit and weakly diverges with the stimulus duration relative to the membrane and synaptic time constants.Comment: 4 page, 4 figures, Accepted to Physical Review Letters on 19th Oct. 201

Unique Scanning Electron Microscopic Features of Hairy Cells in Hairy-Cell Leukemia. A Review and Current Status

Past scanning electron microscopy (SEM) reports demonstrated cell surface undulations, ridges, folds, and ruffles to support the monocytic/histiocytic nature of hairy-cell leukemia (HCL) cells. On the other hand, SEM studies illustrating spikes, villi, and microvilli on the cell surfaces favored the lymphocytic nature of hairy cells (HCs). The evidence for the \u27hybrid\u27 nature of the HCs has emerged from the demonstration of concurrent display of monocytic (ruffles) and lymphocytic (microvilli) surface features on each cell. Utilizing improved methods of sampling, fixation, and drying, the current status is that all HCs display microvilli and ruffles simultaneously. However, two distinct morphological types of HCs are acknowledged: cells showing ruffled areas next to clumps of microvilli (type A), and cells displaying microvilli interspersed among ruffles (type B) . Each of the HCL cases reported in our studies had cells with either type A or type B surface features. Amazingly, these unique SEM features correlate well with the prevalent trend to classify HCs as malignant (villous) B-lymphocytes imitating (ruffled) monocytes in some functional respects