Structure and dimension of global branches of solutions to multiparameter nonlinear equations

A general study of the dimension and connectivity properties of branches of solutions of equations depending on n-parameters are studied using the homotopy properties of 0-epi maps

Macroeconomic homogeneity within Mercosur: An overview

Similar business fluctuations are considered a necessary condition for the harmonization of economic policies and institutions within countries involved in an economic integration process. This paper deals with the macroeconomic performance of Mercosur countries during the last twenty five years. Its aim is threefold. First, to determine whether the economic fluctuations of Mercosur countries had a similar behavior according to their duration, intensity and timing. Second, to evaluate the reaction of the economies to demand and supply shocks; an exercise which is made only for Argentina and Brazil. Third, to study simultaneously the economic fluctuations of the four countries.

Logical operations with Localized Structures

We show how to exploit excitable regimes mediated by localized structures (LS) to perform AND, OR, and NOT logical operations providing full logical functionality. Our scheme is general and can be implemented in any physical system displaying LS. In particular, LS in nonlinear photonic devices can be used for all-optical computing applications where several reconfigurable logic gates can be implemented in the transverse plane of a single device, allowing for parallel computing.Comment: 11 pages, 6 figure

Black hole entropy quantization

Ever since the pioneer works of Bekenstein and Hawking, black hole entropy has been known to have a quantum origin. Furthermore, it has long been argued by Bekenstein that entropy should be quantized in discrete (equidistant) steps given its identification with horizon area in (semi-)classical general relativity and the properties of area as an adiabatic invariant. This lead to the suggestion that black hole area should also be quantized in equidistant steps to account for the discrete black hole entropy. Here we shall show that loop quantum gravity, in which area is {\it not} quantized in equidistant steps can nevertheless be consistent with Bekenstein's equidistant entropy proposal in a subtle way. For that we perform a detailed analysis of the number of microstates compatible with a given area and show consistency with the Bekenstein framework when an oscillatory behavior in the entropy-area relation is properly interpreted.Comment: 4 pages, 4 figures. Version to be published in PR

Loop quantum gravity and Planck-size black hole entropy

The Loop Quantum Gravity (LQG) program is briefly reviewed and one of its main applications, namely the counting of black hole entropy within the framework is considered. In particular, recent results for Planck size black holes are reviewed. These results are consistent with an asymptotic linear relation (that fixes uniquely a free parameter of the theory) and a logarithmic correction with a coefficient equal to -1/2. The account is tailored as an introduction to the subject for non-experts.Comment: 21 pages, 5 figures. Contribution to the Proceedings of the NEB XII International Conferenc

Precambrian isotopic sources of the Anti-Atlas, Morocco

The isotopic data stored in detrital and magmatic zircons are crucial for assessing magma sources, terrane correlation, paleogeography and plate reconstructions. In many cases the comparison of the zircon age and isotope signature of a terrane of unknown provenance with the signature of possible sources, generally old cratonic areas, can resolve questions of origin and paleoposition. Obviously, a precise knowledge of the zircon characteristics of these old areas is essential for reliable comparisons. One of the major sources of sediments of the peri-Gondwanan terranes and of the European Variscan Belt is the West African craton. The northern boundary of this craton is the Pan- African Anti-Atlas belt, which is therefore an ideal place to better constrain the zircon isotopic features of sediments sourced from it. With that aim, we obtained LA-ICM-MS U-Pb and Hf isotopic data of more than 600 zircons separated from six samples of siliciclastic sedimentary rocks from the main Neoproterozoic stratigraphic units of the Anti-Atlas belt, from the Sirwa and Zenaga inliers. The data suggest that the north part of the West African craton formed during three cycles of juvenile crust formation, with variable amount of reworking of older crust. The youngest group of zircons, with a main population clustering around 610 Ma, has a predominantly juvenile character and evidence of moderate mixing with Paleoproterozoic crust, suggesting that the igneous and metamorphic rocks in which the zircons originally crystallized were formed in an ensialic magmatic arc environment. A group of zircons with ages in the range 1.79–2.3 Ga corresponds to the major crust forming event in the West African craton: the Eburnian- Birimian orogeny. The isotopic data indicate that the provenance area should represent a crustal domain that separated from a mantle reservoir at ∼2050–2300 Ma, and further evolved with a time-integrated 176Lu/177Hf of ∼0.013, characteristic of continental crust. The evolution of the Eburnian orogeny is apparently dominated by new crust formation in a magmatic arc environment. The Lower Paleoproterozoic and Neoarchean evolution (2.3–2.75 Ga) involves a group of detrital zircon ages that has not been identified up to now in the igneous or metamorphic rocks of the north West African craton basement. Their Hf isotopic signature points to reworking of juvenile crust mixed with moderate amounts of Archean crust. The significance of these ages is uncertain: they could represent a tectonothermal event not discovered yet in the Reguibat Shield or the zircons can be far-travelled from an unknown source.Peer Reviewe

Dynamical community structure of populations evolving on genotype networks

Neutral evolutionary dynamics of replicators occurs on large and heterogeneous networks of genotypes. These networks, formed by all genotypes that yield the same phenotype, have a complex architecture that conditions the molecular composition of populations and their movements on genome spaces. Here we consider as an example the case of populations evolving on RNA secondary structure neutral networks and study the community structure of the network revealed through dynamical properties of the population at equilibrium and during adaptive transients. We unveil a rich hierarchical community structure that, eventually, can be traced back to the non-trivial relationship between RNA secondary structure and sequence composition. We demonstrate that usual measures of modularity that only take into account the static, topological structure of networks, cannot identify the community structure disclosed by population dynamics.This study has been supported by project FIS2011-27569 from the Spanish Ministry of Economy and Competitivity.Publicad

Phase-space structure of two-dimensional excitable localized structures

In this work we characterize in detail the bifurcation leading to an excitable regime mediated by localized structures in a dissipative nonlinear Kerr cavity with a homogeneous pump. Here we show how the route can be understood through a planar dynamical system in which a limit cycle becomes the homoclinic orbit of a saddle point (saddle-loop bifurcation). The whole picture is unveiled, and the mechanism by which this reduction occurs from the full infinite-dimensional dynamical system is studied. Finally, it is shown that the bifurcation leads to an excitability regime, under the application of suitable perturbations. Excitability is an emergent property for this system, as it emerges from the spatial dependence since the system does not exhibit any excitable behavior locally.Comment: 10 pages, 9 figure