The intrinsic torsion of almost quaternion-Hermitian manifolds

We study the intrinsic torsion of almost quaternion-Hermitian manifolds via the exterior algebra. In particular, we show how it is determined by particular three-forms formed from simple combinations of the exterior derivatives of the local Kaehler forms. This gives a practical method to compute the intrinsic torsion and is applied in a number of examples. In addition we find simple characterisations of HKT and QKT geometries entirely in the exterior algebra and compute how the intrinsic torsion changes under a twist construction.Comment: 38 page

Almost Hermitian Structures and Quaternionic Geometries

Gray & Hervella gave a classification of almost Hermitian structures (g,I) into 16 classes. We systematically study the interaction between these classes when one has an almost hyper-Hermitian structure (g,I,J,K). In general dimension we find at most 167 different almost hyper-Hermitian structures. In particular, we obtain a number of relations that give hyperK\"aher or locally conformal hyperK\"ahler structures, thus generalising a result of Hitchin. We also study the types of almost quaternion-Hermitian geometries that arise and tabulate the results.Comment: 22 pages, 5 table

The kissing polynomials and their Hankel determinants

We study a family of polynomials that are orthogonal with respect to the weight function $e^{i\omega x}$ in $[-1,1]$, where $\omega\geq 0$. Since this weight function is complex-valued and, for large $\omega$, highly oscillatory, many results in the classical theory of orthogonal polynomials do not apply. In particular, the polynomials need not exist for all values of the parameter $\omega$, and, once they do, their roots lie in the complex plane. Our results are based on analysing the Hankel determinants of these polynomials, reformulated in terms of high-dimensional oscillatory integrals which are amenable to asymptotic analysis. This analysis yields existence of the even-degree polynomials for large values of $\omega$, an asymptotic expansion of the polynomials in terms of rescaled Laguerre polynomials near $\pm 1$ and a description of the intricate structure of the roots of the Hankel determinants in the complex plane. This work is motivated by the design of efficient quadrature schemes for highly oscillatory integrals.Comment: 31 pages, 11 figures. Revised version, Section 8 edite

Cohomogeneity-one G2-structures

G2-manifolds with a cohomogeneity-one action of a compact Lie group G are studied. For G simple, all solutions with holonomy G2 and weak holonomy G2 are classified. The holonomy G2 solutions are necessarily Ricci-flat and there is a one-parameter family with SU(3)-symmetry. The weak holonomy G2 solutions are Einstein of positive scalar curvature and are uniquely determined by the simple symmetry group. During the proof the equations for G2-symplectic and G2-cosymplectic structures are studied and the topological types of the manifolds admitting such structures are determined. New examples of compact G2-cosymplectic manifolds and complete G2-symplectic structures are found.Comment: 23 page

Detecting the sensitive spots of the African interurban transport network

Transport systems are vulnerable to events that create disruptions. This situation is particularly sensitive in parts of Africa with a low density of highways and an increasing level of violence. Here, we measure the risk of the African transport network based on two separate indices: the intensity of future events $\mu$ and the impact $\nu$ of one event on the flow that travels through the network. To estimate the intensity of future events happening in city $i$, we construct a self-exciting point process. To estimate the impact of an event, we consider a network of all highways in the continent and a modelled flow between any pair of cities. Based on both indicators, we construct the $\mu-\nu$ diagram and classify cities based on their combined impact and intensity. Results show that certain cities in the network have a high risk and increase the vulnerability of Africa's infrastructure. These cities have a high propensity for suffering subsequent violence against their civilians, and given their connectivity structure, they also substantially affect the overall regional functioning. Removing just ten edges would require rerouting 32% of trips according to our model. The top 100 edges where violence might happen account for 17% of the trips. We find that cities with the highest $\mu-\nu$ risk are those characterised by small and medium size and large degree, meaning they act as hubs. Vulnerable areas tend to be characterised by the presence of terrorist groups like Boko Haram in Nigeria

Prevalencia de neofobia alimentaria en comedores escolares en la isla de La Palma

La neofobia alimentaria hace referencia al miedo o rechazo que presenta un niño de cara a probar alimentos nuevos. Este comportamiento se considera una etapa normal del desarrollo infantil y afecta entre el 50% y el 75% de los niños. Este trastorno es bajamente diagnosticado en la población pediátrica a pesar del gran conflicto que causa en desarrollar una dieta equilibrada y variada. El comedor escolar es uno de los lugares de referencia para adquirir hábitos de vida saludable, por lo que este diagnóstico y su posterior tratamiento, deberían estar integrados dentro de la coordinación del propio colegio. El presente proyecto tiene como objetivo principal establecer la prevalencia de neofobia alimentaria en niños que cursan segundo de primaria y que asisten a comedor escolar. Se diseña un estudio observacional, descriptivo de corte transversal, que abarcará distintos colegios de educación primaria de La Palma. La recogida de datos será mediante dos cuestionarios, uno sobre los alimentos más consumidos y, por otro lado, se realizará la Escala de Neofobia Alimentaria (FNS). Complementariamente, se hará una encuesta a los padres mediante llamada telefónica para obtener información acerca de aspectos personales, familiares y sociales que pudieran estar relacionados con la neofobia. Debido a la gran repercusión de este problema en el ámbito escolar, se desarrollará un díptico informativo para el personal y para los padres.Food neophobia refers to the fear or rejection of a child with a view to trying new foods. This behavior is considered a normal stage of child development and affects between 50 and 75 per cent of children. This disorder is poorly diagnosed in the pediatric population despite the great conflict it causes in developing a balanced and varied diet. The school canteen is one of the reference points for acquiring healthy lifestyle habits, so this diagnosis and its subsequent treatment should be integrated into the coordination of the school itself. The main objective of this project is establishing the prevalence of food neophobia in children in the second year of primary school who attend school meals. An observational, cross-sectional descriptive study was designed to cover different primary schools in La Palma. The data will be collected through two questionnaires, one on the most consumed foods and, on the other hand, the Food Neophobia Scale (FNS) will be carried out. In addition, parents will be surveyed by telephone to obtain information about personal, family and social aspects that may be related to neophobia. Due to the great impact of this problem on the school environment, an information leaflet for staff and parents will be developed

Effect of different drying systems for the conservation of olive leaves on their nutritive value for ruminants

Leaves obtained from olive trees (Olea europaea L.) were stored under various conditions for periods up to 42 months. Duration of storage had a marked effect on crude protein digestibility of leaves when fed to sheep. Protein appeared to be unavailable to animals fed leaves stored for 24 months or longer. The effect of storage on organic matter digestibility was less dramatic and due largely to the loss of soluble cell contents (r = 0.97). As a result, the proportion of water-insoluble dry matter and lignin present in leaves increased with duration of storage while the proportion of water or acetone-water (60:30 v/v) soluble material decreased. Despite being unavailable in vivo, cellulase digestion released protein from the water-insoluble residues of stored leaves in greater amounts than that released from freshly-dried leaves. It appears likely that protein released from stored leaves was in the form of a complex and remained unavailable to the animal. Hydrolysable and condensed tannins were not detected in fresh or dried leaves and could not have acted as complexing agents. The seco-iridoid glycoside oleuropein was found in fresh tissue (69.9 g kg(-1)) but concentrations decreased on storage in parallel with the observed decrease in crude protein digestibility (r = 0.80). ((C) Elsevier/Inra)