Embeddings of SL(2,Z) into the Cremona group

Geometric and dynamic properties of embeddings of SL(2,Z) into the Cremona group are studied. Infinitely many non-conjugate embeddings which preserve the type (i.e. which send elliptic, parabolic and hyperbolic elements onto elements of the same type) are provided. The existence of infinitely many non-conjugate elliptic, parabolic and hyperbolic embeddings is also shown. In particular, a group G of automorphisms of a smooth surface S obtained by blowing-up 10 points of the complex projective plane is given. The group G is isomorphic to SL(2,Z), preserves an elliptic curve and all its elements of infinite order are hyperbolic.Comment: to appear in Transformation Group

Reaction to spatial novelty and exploratory strategies in baboons

Exploratory activity was examined in 4 young baboons with the aim of investigating the type of spatial coding (purely geometric and/or by taking into account the identity of the object) used for the configuration of objects. Animals were individually tested in an outdoor enclosure for their exploratory reactions (contact time and order of spontaneous visits) to changes brought about to a configuration of different objects. Two kinds of spatial changes were made: a modification (1) of the shape of the configuration (by displacement of one object) and (2) of the spatial arrangement without changing the initial shape (exchanging the location of two objects). In the second experiment, the effect of a spatial modification of the global geometry constituted by four identical objects was investigated. Finally, in the third experiment, a substitution of a familiar object with a novel one was performed without changing the objects' configuration. The baboons strongly reacted to geometrical modifications of the configuration. In contrast, they were less sensitive to modifications of local features that did not affect the initial spatial configuration. Analyses of spontaneous exploratory activities revealed two types of exploratory strategies (cyclic and back-and-forth). These data are discussed in relation to (1) the distinction between the encoding of geometric versus local spatial features and (2) the spatial function of exploratory activity

Rhesus monkeys use geometric and non geometric during a reorientation task

Rhesus monkeys (Macaca mulata) were subjected to a place finding task in a rectangular room perfectly homogeneous and without distinctive featural information. Results of Experiment 1 show that monkeys rely on the large-scale geometry of the room to retrieve a food reward. Experiments 2 and 3 indicate that subjects use also nongeometric information (colored wall) to reorient. Data of Experiments 4 and 5 suggest that monkeys do not use small angular cues but that they are sensitive to the size of the cues (Experiments 6, 7, and 8). Our findings strengthen the idea that a mechanism based on the geometry of the environment is at work in several mammalian species. In addition, the present data offer new perspectives on spatial cognition in animals that are phylogenetically close to humans. Specifically, the joint use of both geometric and landmark-based cues by rhesus monkeys tends to demonstrate that spatial processing became more flexible with evolutio

Organic sheep breeding on the Causse Méjan: challenges and drawbacks of organic breeding in a national park in France

This work highlights the ecological stakes and the drawbacks associated with the development of organic lamb production on the Causse Méjan, a calcareous plateau, part of which is included in the Cévennes National Park (PnC). It analyses the tensions underlying a valorisation project for organic lambs by a small group of stockbreeders that is supported by the national park because of the ecological quality of their practices. On the one hand, since breeders are highly dependent on the ecological characteristics of the environment, they are forced to multiply their marketing channels and to invest a great deal of energy to obtain good prices for their meat whose characteristics do not match the current standards of quality (homogeneity, clear meat). On the other hand, the Pac can neither fully support these stockbreeders whose practices are marginal at the local level without straining its relationships with mainstream local breeders, nor overstep its role as the protector of nature. Considering this unattractive context and the interesting economic outlooks offered by the mainstream breeding system, which options will the young breeders of the future choose? Supporting a microexperiment like this one appears to be an important step for the development of new production models that combine economic profitability and ecological effectiveness

Compressive Pattern Matching on Multispectral Data

We introduce a new constrained minimization problem that performs template and pattern detection on a multispectral image in a compressive sensing context. We use an original minimization problem from Guo and Osher that uses $L_1$ minimization techniques to perform template detection in a multispectral image. We first adapt this minimization problem to work with compressive sensing data. Then we extend it to perform pattern detection using a formal transform called the spectralization along a pattern. That extension brings out the problem of measurement reconstruction. We introduce shifted measurements that allow us to reconstruct all the measurement with a small overhead and we give an optimality constraint for simple patterns. We present numerical results showing the performances of the original minimization problem and the compressed ones with different measurement rates and applied on remotely sensed data.Comment: Published in IEEE Transactions on Geoscience and Remote Sensin

Resistive Switching Assisted by Noise

We extend results by Stotland and Di Ventra on the phenomenon of resistive switching aided by noise. We further the analysis of the mechanism underlying the beneficial role of noise and study the EPIR (Electrical Pulse Induced Resistance) ratio dependence with noise power. In the case of internal noise we find an optimal range where the EPIR ratio is both maximized and independent of the preceding resistive state. However, when external noise is considered no beneficial effect is observed.Comment: To be published in "Theory and Applications of Nonlinear Dynamics: Model and Design of Complex Systems", Proceedings of ICAND 2012 (Springer, 2013