Iterative Processes Related to Riordan Arrays: The Reciprocation and the Inversion of Power Series

We point out how Banach Fixed Point Theorem, and the Picard successive approximation methods induced by it, allows us to treat some mathematical methods in Combinatorics. In particular we get, by this way, a proof and an iterative algorithm for the Lagrange Inversion Formula.Comment: 17 pages. We extend the results in the previuous version proving finally the Lagrange Inversion Formula via Banach Fixed Point Theore

Finite entanglement entropy from the zero-point-area of spacetime

The calculation of entanglement entropy S of quantum fields in spacetimes with horizon shows that, quite generically, S (a) is proportional to the area A of the horizon and (b) is divergent. I argue that this divergence, which arises even in the case of Rindler horizon in flat spacetime, is yet another indication of a deep connection between horizon thermodynamics and gravitational dynamics. In an emergent perspective of gravity, which accommodates this connection, the fluctuations around the equipartition value in the area elements will lead to a minimal quantum of area, of the order of L_P^2, which will act as a regulator for this divergence. In a particular prescription for incorporating L_P^2 as zero-point-area of spacetime, this does happen and the divergence in entanglement entropy is regularized, leading to S proportional to (A/L_P^2) in Einstein gravity. In more general models of gravity, the surface density of microscopic degrees of freedom is different which leads to a modified regularisation procedure and the possibility that the entanglement entropy - when appropriately regularised - matches the Wald entropy.Comment: ver 2: minor clarifications added; reformatted with Sections; 11 page

Searching the solution space in constructive geometric constraint solving with genetic algorithms

Geometric problems defined by constraints have an exponential number of solution instances in the number of geometric elements involved. Generally, the user is only interested in one instance such that besides fulfilling the geometric constraints, exhibits some additional properties. Selecting a solution instance amounts to selecting a given root every time the geometric constraint solver needs to compute the zeros of a multi valuated function. The problem of selecting a given root is known as the Root Identification Problem. In this paper we present a new technique to solve the root identification problem. The technique is based on an automatic search in the space of solutions performed by a genetic algorithm. The user specifies the solution of interest by defining a set of additional constraints on the geometric elements which drive the search of the genetic algorithm. The method is extended with a sequential niche technique to compute multiple solutions. A number of case studies illustrate the performance of the method.Postprint (published version

Features of ELF interactions in travel blogs: Travelers doing interactional work

Travel blogs constitute a new platform where travelers can tell about their travel experiences and share information and impressions with their readers. Most travel blogs incorporate commenting capabilities, which enable social interaction among members of communities with shared traveling interests. English is most often used as a Lingua Franca, facilitating interaction among people with different L1 backgrounds and transcending the native/non-native distinction. The purpose of this research is to analyze the features of English as a Lingua Franca (ELF) interactions in travel blogs and explore some strategies used by participants in blog discussions to achieve shared understanding and show belonging to an ELF community. The small corpus consists of 36 blog discussions taken from 12 blogs where the commenters belong to different L1 backgrounds. The corpus was analyzed qualitatively to determine whether some strategies used in ELF interactions (make it normal, backchanneling, codeswitching, and metacomments) occur in travel blogs and, if so, how they contribute to identity and community construction

Constructing academic identities online: Identity performance in research group blogs written by multilingual scholars

Blogs provide an open space for research groups to publicise their research and activities, become more visible both to the local and international disciplinary communities, and conduct self-promotion. Research groups harness the affordances of the medium to weave a narrative about the group, presented through various modalities, and thus construct their online identity. The purpose of this research is to analyse how identity is constructed in research group blogs written in English by groups affiliated to Spanish institutions. In this study I address the following questions: (i) which are the facets of the group''s identities created by multilingual scholars in research group blogs?; (ii) which textual and multimodal practices are adopted by researchers to construct the group''s identity? To answer these questions I conducted a content analysis (focusing on written language, visuals, hyperlinks) of posts taken from 12 research group blogs. The study provides insight on how these research groups mesh different semiotic modes in their blogs to project a multifaceted identity and reveals that blogging may be a powerful instrument for research groups’ identity performance and visibility

Academic Republicanism

Reseña de: Suárez Cortina, Manuel: Los caballeros de la razón. Cultura institucionista y democracia parlamentaria en la España liberal, Santander, Genueve Ediciones, 201