A metric property of umbilic points

In the space $\mathbb U^4$ of cubic forms of surfaces, regarded as a $G$-space and endowed with a natural invariant metric, the ratio of the volumes of those representing umbilic points with negative to those with positive indexes is evaluated in terms of the asymmetry of the metric, defined here. A connection of this ratio with that reported by Berry and Hannay (1977) in the domain of Statistical Physics, is discussed.Comment: 8 pages, 1 figur

The Minimal Geometric Deformation Approach: a brief introduction

We review the basic elements of the Minimal Geometric Deformation approach in details. This method has been successfully used to generate brane-world configurations from general relativistic perfect fluid solutions.Comment: Brief review; minor corrections; references adde

Seeds banks of desert annuals in an aridity gradient in the southern Atacama Desert

*Background/Question/Methods*
Annual plant communities are important components of the biodiversity found in the coastal southern Atacama Desert in Chile. Moreover, they are an important economic resource for the human communities living in that area. These plant communities develop, after heavy rainfall episodes, a phenomenon locally known as the “blooming of the desert”. Although the minimum rainfall thresholds for these plants to emerge are relatively well known, little is known about their seed banks, its composition, dynamics and variation across the latitudinal aridity gradient from south to north. This system is interesting to study species coexistence, as well as, to look for exotic plants invasion, since previous studies have shown that exotic annual plants decreases in importance northwards. We hypothesize that, as a result of the gradient, we should find more seeds of annuals in the southern part because of the increase of exotic species. The lowest diversity will be found in the northern limit, while the highest in the middle part of the gradient, coincident with a natural protected area, and less influence of exotics. In terms of seed size and viability, we should find larger and more viable seeds in the southern limit of the gradient, probably contrasting with smaller and more dormant seeds to the north. To test these hypotheses we selected 8 sites along the gradient and collected soil samples after seed set in December 2008 for seed bank determination. 

*Results/Conclusions*
According to our hypothesis we found more seeds in the southern part of the gradient. The northern seed banks (Rodillo and Cisne) are characterized by their low number of seeds and low species richness, according with their more extreme aridity. The central and southern seed banks have more than two times higher number and species richness than the northern ones. Southern seed banks (Lagunillas, Romeral and Punta Choros) contain more exotics’ seeds; meanwhile central seed banks (Pajonales, Carrizal Bajo and Los Bronces) have less seeds, and less exotics’ seeds. These results suggest that the increased seed number in the southern portion of the gradient could be due to an increased number of exotic species, rather than an increased diversity of native annuals. More viable and larger seeds were found in the southern sites, meanwhile, smaller seeds were found to the north indicating the use of a cautious opportunism strategy by these species. This is the first report on seed banks composition of this Atacama Desert area

Anisotropic solutions by gravitational decoupling

We investigate the extension of isotropic interior solutions for static self-gravitating systems to include the effects of anisotropic spherically symmetric gravitational sources by means of the gravitational decoupling realised via the minimal geometric deformation approach. In particular, the matching conditions at the star surface with the outer Schwarzschild space-time are studied in great details, and we describe how to generate, from a single physically acceptable isotropic solution, new families of anisotropic solutions whose physical acceptability is also inherited from their isotropic parent.Comment: 20 pages, 4 figures; references and typos corrected; final version to match the EPJC versio

A causal Schwarzschild-de Sitter interior solution by gravitational decoupling

We employ the minimal geometric deformation approach to gravitational decoupling (MGD- decoupling) in order to build an exact anisotropic version of the Schwarzschild interior solution in a space-time with cosmological constant. Contrary to the well-known Schwarzschild interior, the matter density in the new solution is not uniform and possesses subluminal sound speed. It therefore satisfies all standard physical requirements for a candidate astrophysical object.Comment: 15 pages, 6 figure

Translating Global Nature: Territoriality, Environmental Discourses, and Ecocultural Identities

In this study, I explore environmental discourses circulating among Indigenous transboundary organizations working on environmental initiatives at the border between Ecuador and Colombia. I focus on three global environmental discourses –sustainability, development, and climate change– as they are at the core of the global environmental governance vernacular. La Gran Familia Awá Binacional (GFAB), one of the few transboundary Indigenous organizations working along the binational border, utilizes these global concepts to frame their environmental initiatives and projects. I use a critical and interpretive qualitative approach to investigate, deconstruct, and rearticulate global environmental discourses circulating among and translated by two of the organizations forming the GFAB: Federación de Centros Awá del Ecuador (FCAE) and Unidad Indígena del Pueblo Awá (UNIPA) from Colombia. I conducted in-depth interviews with cultural and political elites working in, or related to, these Awá organizations. I analyze interview texts, Awá organizations’ community-based plans, official government documents, and NGOs reports to understand (1) How does the GFAB understand, construct, and reproduce their relationships with their territories?; (2) How does the GFAB translate the global environmental discourses of development, sustainability, and climate change at the level of the communities with which this organization works?; and (3) What are the politics of identity, ecocultural identities and positionings, that emerge from Awá’s translation of and engagement with development, sustainability, and climate change within Awá’s territoriality? To answer these questions, I investigate how transboundary Indigenous communities construct a sense of territory, navigate global environmental discourses, and negotiate multiple ecocultural identities. I describe the articulations among relationships and principles that configure Awá’s territoriality. Then, I situate the notion of translation in relation to Awá’s territory, katza su, to explore the system of meanings implicated in Awá’s translation of the global environmental discourses of development, sustainability, and climate change. I illustrate how Awá recontextualize and emplace these discourses once they enter the material and discursive realm of Awá’s territoriality. Finally, I further the notion of territory and territoriality to investigate the formation of Awá, mestizos, and Afros’ ecocultural identities. I illustrate how two dialectics, insider-outsider and respect-disrespect, work in the discursive positioning of these populations as restorative or unwholesome ecocultural identities. In closing, I propose a rhizomatic situational analysis framework to map factors, forces, and processes, and demonstrate its applicability by presenting a situational analysis of the Awá binational Indigenous people. The rhizome illuminates Awá’s translation of development, sustainability, and climate change, and the ecocultural identities that emerge through processes of translation. I end with some recommendations to rethink identity-based mediation in environmental conflicts, explore transversal forms of communication, agency, and dissent, and further processes of environmental peacebuilding at the border between Ecuador and Colombia

Canard Cycles and Poincar\'e Index of Non-Smooth Vector Fields on the Plane

This paper is concerned with closed orbits of non-smooth vector fields on the plane. For a subclass of non-smooth vector fields we provide necessary and sufficient conditions for the existence of canard kind solutions. By means of a regularization we prove that the canard cycles are singular orbits of singular perturbation problems which are limit periodic sets of a sequence of limit cycles. Moreover, we generalize the Poincar\'e Index for non-smooth vector fields.Comment: 20 pages, 25 figure