Weyl law for fat fractals

It has been conjectured that for a class of piecewise linear maps the closure of the set of images of the discontinuity has the structure of a fat fractal, that is, a fractal with positive measure. An example of such maps is the sawtooth map in the elliptic regime. In this work we analyze this problem quantum mechanically in the semiclassical regime. We find that the fraction of states localized on the unstable set satisfies a modified fractal Weyl law, where the exponent is given by the exterior dimension of the fat fractal.Comment: 8 pages, 4 figures, IOP forma

Winter Grazing in a Grass-Fed System: Effect of Stocking Density and Sequential Use of Autumn-Stockpiled Grassland on Performance of Yearling Steers

Winter grazing can help reduce the need for purchased feeds in livestock production systems, when finishing cattle on pasture. Our objective was to evaluate the influence of stocking density and grazing stockpiled forage on performance of yearling steers during winter. Three grasslands were winter grazed for two years: I, naturalized pastureland, and II and III, sown and managed for hay production during the growing season but grazed in winter. Two stocking densities were used: low 7.41 and high 12.35 steers ha−1. Herbage mass was estimated before and after each grazing event, and disappearance (consumption, weathering, and trampling) was the difference between both. Forage mass and residual differed by stocking density (SD), year (YR), and grazing interval (GI), and disappearance differed by YR and GI. Grass and dead constituents of botanical composition differed by YR and GI. No differences were found for legumes and forbs. CP differed by YR and GI, and NDF and ADF differed only by YR. Steer average daily gain was 0.15 kg d−1 in 2011 and 0.68 kg d−1 in 2012 and varied by YR and GI. Acceptable gains in 2012 may be a product of environmental conditions that influenced herbage mass and nutritive value during stockpile and animal behavior during winter

Semiclassical approach to fidelity amplitude

The fidelity amplitude is a quantity of paramount importance in echo type experiments. We use semiclassical theory to study the average fidelity amplitude for quantum chaotic systems under external perturbation. We explain analytically two extreme cases: the random dynamics limit --attained approximately by strongly chaotic systems-- and the random perturbation limit, which shows a Lyapunov decay. Numerical simulations help us bridge the gap between both extreme cases.Comment: 10 pages, 9 figures. Version closest to published versio

Desarrollo de un algoritmo de solución directa para el cálculo de distribuciones óptimas de cultivos bajo riego deficitario controlado

La adecuada gestión de un recurso natural cada vez más escaso, como es el agua, implica maximizar la eficiencia en su uso. Desde el punto de vista de una explotación agraria, es de la máxima importancia encontrar la distribución óptima de cultivos que maximice el margen bruto obtenido con el agua de riego disponible. Actualmente, los métodos de optimización disponibles para resolver este problema no lineal, recurren a métodos de optimización heurísticos de propósito general mucho más lentos y menos eficientes de lo que sería un algoritmo de optimización de solución directa, donde se conocen los mecanismos involucrados y las sinergias existentes entre los cultivos para la obtención de la solución óptima del problema. El objetivo del presente trabajo es desarrollar un algoritmo de solución directa capaz de determinar la distribución óptima de cultivos que sea compatible con el modelo MOPECO (Modelo de Optimización Económica del agua de riego). La solución óptima se consigue con sólo uno o dos cultivos, pero esta solución no es la más adecuada desde el punto de vista agronómico (p.e. rotación de cultivos, PAC, etc.), por lo que ha sido necesario adaptar el algoritmo desarrollado para manejar este tipo de situaciones. Para una hipotética explotación de 100 ha, considerando 10 cultivos diferentes y 11 escenarios de volumen de agua total disponible, se han comparado los resultados del algoritmo desarrollado con las soluciones ofrecidas por el software de optimización LINGO y los algoritmos genéticos. El algoritmo desarrollado consigue márgenes brutos un 0,5% inferiores a los de LINGO, y un 1,1% mayores que los algoritmos genéticos, reduciendo el tiempo de cálculo entre 50-100 y 2000 veces, respectivamente

SpheroidJ: An Open-Source Set of Tools for Spheroid Segmentation

Background and objectives: Spheroids are the most widely used 3D models for studying the effects of different micro-environmental characteristics on tumour behaviour, and for testing different preclinical and clinical treatments. In order to speed up the study of spheroids, imaging methods that automatically segment and measure spheroids are instrumental; and, several approaches for automatic segmentation of spheroid images exist in the literature. However, those methods fail to generalise to a diversity of experimental conditions. The aim of this work is the development of a set of tools for spheroid segmentation that works in a diversity of settings. Methods: In this work, we have tackled the spheroid segmentation task by first developing a generic segmentation algorithm that can be easily adapted to different scenarios. This generic algorithm has been employed to reduce the burden of annotating a dataset of images that, in turn, has been employed to train several deep learning architectures for semantic segmentation. Both our generic algorithm and the constructed deep learning models have been tested with several datasets of spheroid images where the spheroids were grown under several experimental conditions, and the images acquired using different equipment. Results: The developed generic algorithm can be particularised to different scenarios; however, those particular algorithms fail to generalise to different conditions. By contrast, the best deep learning model, constructed using the HRNet-Seg architecture, generalises properly to a diversity of scenarios. In order to facilitate the dissemination and use of our algorithms and models, we present SpheroidJ, a set of open-source tools for spheroid segmentation. Conclusions: In this work, we have developed an algorithm and trained several models for spheroid segmentation that can be employed with images acquired under different conditions. Thanks to this work, the analysis of spheroids acquired under different conditions will be more reliable and comparable; and, the developed tools will help to advance our understanding of tumour behaviour

Assembly in G1 phase and long-term stability are unique intrinsic features of CENP-A nucleosomes

Centromeres are the site of kinetochore formation during mitosis. Centromere protein A (CENP-A), the centromere-specific histone H3 variant, is essential for the epigenetic maintenance of centromere position. Previously we showed that newly synthesized CENP-A is targeted to centromeres exclusively during early G1 phase and is subsequently maintained across mitotic divisions. Using SNAP-based fluorescent pulse labeling, we now demonstrate that cell cycle-restricted chromatin assembly at centromeres is unique to CENP-A nucleosomes and does not involve assembly of other H3 variants. Strikingly, stable retention is restricted to the CENP-A/H4 core of the nucleosome, which we find to outlast general chromatin across several cell divisions. We further show that cell cycle timing of CENP-A assembly is independent of centromeric DNA sequences and instead is mediated by the CENP-A targeting domain. Unexpectedly, this domain also induces stable transmission of centromeric nucleosomes, independent of the CENP-A deposition factor HJURP. This demonstrates that intrinsic properties of the CENP-A protein direct its cell cycle-restricted assembly and induces quantitative mitotic transmission of the CENP-A/H4 nucleosome core, ensuring long-term stability and epigenetic maintenance of centromere position.FCT fellpwships: (SFRH/BD/74284/2010, SFRH/BPD/69115/2010), National Institutes of Health grant: (GM082989), Burroughs Wellcome Fund (Career Award in the Biomedical Sciences), Rita Allen Foundation Scholar Award, Instituto Gulbenkian de Ciência, European Commission FP7 Program, EMBO