Non-Euclidean geometry in nature

I describe the manifestation of the non-Euclidean geometry in the behavior of collective observables of some complex physical systems. Specifically, I consider the formation of equilibrium shapes of plants and statistics of sparse random graphs. For these systems I discuss the following interlinked questions: (i) the optimal embedding of plants leaves in the three-dimensional space, (ii) the spectral statistics of sparse random matrix ensembles.Comment: 52 pages, 21 figures, last section is rewritten, a reference to chaotic Hamiltonian systems is adde

Covers counting via Feynman Calculus

Let $G$ be a finite group. In this paper we present a tool for counting the number of principle $G$-bundles over a surface. As an application, we express (non-standard) generating functions for double Hurwitz numbers as integrals over commutative Frobenius algebras, associated with symmetric groups.Comment: 15 pages, 5 figure

Magnetic Fields and Afterglows of BdHNe: Inferences from GRB 130427A, GRB 160509A, GRB 160625B, GRB 180728A and GRB 190114C

GRB 190114C is the first binary-driven hypernova (BdHN) fully observed from the initial supernova appearance to the final emergence of the optical SN signal. It offers an unprecedented testing ground for the BdHN theory and it is here determined and further extended to additional gamma-ray bursts (GRBs). BdHNe comprise two subclasses of long GRBs with progenitors a binary system composed of a carbon-oxygen star (CO$_\textrm{core}$) and a neutron star (NS) companion. The CO$_\textrm{core}$ explodes as a SN leaving at its center a newborn NS ($\nu$NS). The SN ejecta hypercritically accretes both on the $\nu$NS and the NS companion. BdHNe I are the tightest binaries where the accretion leads the companion NS to gravitational collapse into a black hole (BH). In BdHN II the accretion onto the NS is lower, so there is no BH formation. We observe the same structure of the afterglow for GRB 190114C and other selected examples of BdHNe I (GRB 130427A, GRB 160509A, GRB 160625B) and for BdHN II (GRB 180728A). In all the cases the explanation of the afterglow is reached via the synchrotron emission powered by the $\nu$NS: their magnetic fields structures and their spin are determined. For BdHNe I, we discuss the properties of the magnetic field embedding the newborn BH, inherited from the collapsed NS and amplified during the gravitational collapse process, and surrounded by the SN ejecta.Comment: 7 figures, 3 tables, submitted to Ap

Local Search for the Resource Constrained Assignment Problem

The resource constrained assignment problem (RCAP) is to find a minimal cost cycle partition in a directed graph such that a resource constraint is fulfilled. The RCAP has its roots in an application that deals with the covering of a railway timetable by rolling stock vehicles. Here, the resource constraint corresponds to maintenance constraints for rail vehicles. Moreover, the RCAP generalizes several variants of vehicle routing problems. We contribute a local search algorithm for this problem that is derived from an exact algorithm which is similar to the Hungarian method for the standard assignment problem. Our algorithm can be summarized as a k-OPT heuristic, exchanging k arcs of an alternating cycle of the incumbent solution in each improvement step. The alternating cycles are found by dual arguments from linear programming. We present computational results for instances from our railway application at Deutsche Bahn Fernverkehr AG as well as for instances of the vehicle routing problem from the literature

The colours of food: final layer in the Palimpsest of Santa Caterina Market in Barcelona

The colours and shapes of food in the decoration of a building were common in traditional architecture, particularly in the Spanish regions of Catalonia and Valencia in the nineteenth century. During the modernist period, we can distinguish both an abstract and a mimetic tendency in these colour transfers. Coloured glazed tiles were often used to cover modernist public buildings in the Spanish Mediterranean coast. The roof of Santa Caterina market in Barcelona follows this abstract modernist tradition and starts from the picture of a food stall as an inspiration. In the same way as some other contemporary architects, Enric Miralles and Benedetta Tagliabue used a computer-aided process of pixilation to design a shiny coloured composition that reminds us of traditional colour transfer techniques from nature and traditional building materials. The result is a market conceived as a palimpsest in which various historical layers from the past can be read. Moreover, it represents in a virtual manner the chromatic experiences that take place in the spaces inside. The building features a type of transparency that is consistent with contemporary perception and which blurs the boundaries between reality and fiction. Food has been a prominent inspiration throughout history for many artistic disciplines and was used as an argument to experiment with colour. The presence of food as a decorative element in architecture goes beyond a simple functional relationship with the use of rooms, and becomes a useful motive for organising a chromatic composition. Examples include coloured cornucopias of classical architecture, biblical food goods in the frescoes of medieval architecture (grapes, bread, fish, etc.), still life paintings in bourgeois housing, or the glazed ceramics used in modernist market buildings.Postprint (published version

On the Spectral Gap of a Quantum Graph

We consider the problem of finding universal bounds of "isoperimetric" or "isodiametric" type on the spectral gap of the Laplacian on a metric graph with natural boundary conditions at the vertices, in terms of various analytical and combinatorial properties of the graph: its total length, diameter, number of vertices and number of edges. We investigate which combinations of parameters are necessary to obtain non-trivial upper and lower bounds and obtain a number of sharp estimates in terms of these parameters. We also show that, in contrast to the Laplacian matrix on a combinatorial graph, no bound depending only on the diameter is possible. As a special case of our results on metric graphs, we deduce estimates for the normalised Laplacian matrix on combinatorial graphs which, surprisingly, are sometimes sharper than the ones obtained by purely combinatorial methods in the graph theoretical literature

Phytochemical characterization and antioxidant activity of Opuntia microdasys (Lehm.) Pfeiff flowers in different stages of maturity

Chemical composition and antioxidant activity of Opuntia microdasys flowers in different maturity stages was evaluated. Fructose, glucose, sucrose and trehalose were found; oxalic, quinic, malic, and citric acids were also detected; five hydroxycinnamoyl, two kaempferol and six isorhamnetin derivatives; 23 fatty acids were quantified in all stages, except C20:2, which was only found in post flowering stage (F3); alpha-, beta-, gamma-, and delta-tocopherols were quantified in all samples. The highest contents in soluble sugars and phenolic compounds were detected in full flowering stage (F2), while organic acids and tocopherols were predominant in vegetative stage (F1). The highest levels of saturated, monounsaturated and polyunsaturated fatty acids were found in F3, F2 and F1, respectively. F1 gave the highest antioxidant activity. Principal components analysis showed clearly individualized groups corresponding to each flowering stage, identifying the most distinctive features, which might be useful to select a flowering stage for incorporation in functional foods. (C) 2014Fundação para a Ciência e a Tecnologia (FCT, Portugal) for financial support to CIMO (strategic project PEst-OE/AGR/UI0690/2011), João C.M. Barreira (SFRH/BPD/72802/2010 grant) and L. Barros (“Compromisso para a Ciência 2008” contract). The GIP-USAL is financially supported by the Spanish Government through the Consolider-Ingenio 2010 Programme (FUN-C-FOOD, CSD2007-00063)

Environmental Values (2-MEV) and Appreciation of Nature

When monitoring the long history of empirical instruments for environmental attitude measurement, the Two Major Environmental Value model (2-MEV) with its two higher order factors: Preservation (PRE) and Utilization (UTL) has repeatedly and independently been confirmed. PRE assesses preferences towards conservation of nature and the environment, whilst UTL measures preferences towards utilization/exploitation of nature. The latter, however, does not yet include the positive aspects of benefitting from the (enjoyable) use of nature. Consequently, besides the established 2-MEV-battery, additional items from an “Appreciation of Nature” (APR) scale were applied to an Irish sample of 289 secondary school students (age: M = 14.3 years). Responses to the altogether 30-item battery were applied on an oblique rotation by using the Promax procedure: UTL and PRE appeared as orthogonally related factors, APR correlated to PRE with 0.283. Based on loading scores, the item number for each subscale was further reduced to make the analysis more manageable in educational outreach sites; on those sites, where completing questionnaires may well be quite unpopular, they are very much needed for planning and fine-tuning educational programs. Therefore, extending the 2-MEV scale with an added scale for Appreciation may help: (i) to judge participants’ feedback for adjusting/balancing program contents better; and (ii) to promote appreciation as a successful strategy for shifting individuals away from their individual exploitative preferences

The use of landscape units as a methodology tool for the open space system analysis

This paper presents a study on the urban form, landscape and open spaces of Patos de Minas, an average city of Minas Gerais, Brazil. Searching to understand the configuration of the Open Spaces System by applying the methodology of Landscape Units. The Landscape Units in this paper are used as identification tools and analysis of different territorial portions formed by the prevalence of morphological characteristics, landscape and interaction between open and built spaces, aiming to highlight the strengths and weaknesses of each unit that can be applied to urban and environmental planning. This approach allows to develop a systemic view of the urban structure in which it is observed, not only the sets of open spaces, but also their interactions and connections with the buildings, with society, with the physical support and urban form.Este trabalho apresenta um estudo sobre a forma urbana, a paisagem e os espaços livres de Patos de Minas, uma cidade média do estado de Minas Gerais, Brasil. Buscando compreender a configuração do Sistema de Espaços Livres por meio da aplicação da metodologia das Unidades de Paisagem, que neste trabalho são utilizadas como ferramentas de identificação e análise das diferentes porções territoriais formadas pela predominância de características morfológicas, de paisagem e de interação entre os espaços livres e edificados, objetivando ressaltar as potencialidades e fragilidades de cada unidade que podem ser aplicadas ao planejamento urbano e ambiental. Essa abordagem permite elaborar uma visão sistêmica da estrutura urbana, na qual se observa não apenas os conjuntos de espaços livres, mas também suas interações e articulações com o edificado, com a sociedade, com o suporte físico e com a forma urbana.Este artículo presenta un estudio sobre la forma urbana, el paisaje y los espacios abiertos de Patos de Minas, una ciudad media de Minas Gerais – Brasil, tratando de entender la configuración del Sistema de Espacios libres mediante la aplicación de la metodología de Unidades Paisaje. Las Unidades de Paisaje en este trabajo se utilizan como herramientas y análisis de porciones territoriales formadas por la asociación individual o sistémica de los diferentes tipos de espacios abiertos, características morfológicas y el espacio construido de identificación. Este documento tiene como objetivo presentar esta aplicación metodológica, sus resultados y las preguntas que surgieron en medio del proceso de análisis. Este enfoque permite desarrollar una visión sistémica de la estructura urbana en la que se observa, no sólo los conjuntos de espacios abiertos, sino también sus interacciones y conexiones con los edificios, con la sociedad, con el hardware y la forma urbana