Simplified solutions of the Cox-Thompson inverse scattering method at fixed energy

Simplified solutions of the Cox-Thompson inverse quantum scattering method at fixed energy are derived if a finite number of partial waves with only even or odd angular momenta contribute to the scattering process. Based on new formulae various approximate methods are introduced which also prove applicable to the generic scattering events.Comment: 9 pages, 3 figure

The inverse scattering problem at fixed energy based on the Marchenko equation for an auxiliary Sturm-Liouville operator

A new approach is proposed to the solution of the quantum mechanical inverse scattering problem at fixed energy. The method relates the fixed energy phase shifts to those arising in an auxiliary Sturm-Liouville problem via the interpolation theory of the Weyl-Titchmarsh m-function. Then a Marchenko equation is solved to obtain the potential.Comment: 6 pages, 8 eps figure

Impact of predicted precipitation scenarios on multitrophic interactions

1. Predicted changes in the frequency and intensity of extreme rainfall events in the UK have the potential to disrupt terrestrial ecosystem function. However, responses of different trophic levels to these changes in rainfall patterns, and the underlying mechanisms, are not well characterised. 2. This study aimed to investigate how changes in both the quantity and frequency of rainfall events will affect the outcome of interactions between plants, insect herbivores (above- and below- ground) and natural enemies. 3. Hordeum vulgare L. plants were grown in controlled conditions and in the field, and subjected to three precipitation scenarios: ambient (based on a local 10 year average rainfall); continuous drought (40% reduction compared to ambient); drought/ deluge (40% reduction compared to ambient at a reduced frequency). The effects of these watering regimes and wireworm (Agriotes species) root herbivory on the performance of the plants, aphid herbivores above-ground (Sitobion avenae, Metapolophium dirhodum and Rhopalosiphum padi), and natural enemies of aphids including ladybirds (Harmonia axyridis) were assessed from measurements of plant growth, insect abundance and mass, and assays of feeding behaviour. 4. Continuous drought decreased plant biomass, whereas reducing the frequency of watering events did not affect plant biomass but did alter plant chemical composition. In controlled conditions, continuous drought ameliorated the negative impact of wireworms on plant biomass. 5. Compared to the ambient treatment, aphid mass was increased by 15% when feeding on plants subjected to drought/ deluge; and ladybirds were 66% heavier when feeding on these aphids but this did not affect ladybird prey choice. In field conditions, wireworms feeding below-ground reduced the number of shoot-feeding aphids under ambient and continuous drought conditions but not under drought/ deluge. 6. Predicted changes in both the frequency and intensity of precipitation events under climate change have the potential to limit plant growth, but reduce wireworm herbivory, while simultaneously promoting above-ground aphid numbers and mass, with these effects transferring to the third trophic level. Understanding the effect of future changes in precipitation on species interactions is critical for determining their potential impact on ecosystem functioning and constructing accurate predictions under global change scenarios

Fast Function to Function Regression

Abstract We analyze the problem of regression when both input covariates and output responses are functions from a nonparametric function class. Function to function regression (FFR) covers a large range of interesting applications including timeseries prediction problems, and also more general tasks like studying a mapping between two separate types of distributions. However, previous nonparametric estimators for FFR type problems scale badly computationally with the number of input/output pairs in a data-set. Given the complexity of a mapping between general functions it may be necessary to consider large datasets in order to achieve a low estimation risk. To address this issue, we develop a novel scalable nonparametric estimator, the Triple-Basis Estimator (3BE), which is capable of operating over data-sets with many instances. To the best of our knowledge, the 3BE is the first nonparametric FFR estimator that can scale to massive data-sets. We analyze the 3BE's risk and derive an upperbound rate. Furthermore, we show an improvement of several orders of magnitude in terms of prediction speed and a reduction in error over previous estimators in various real-world datasets

Ammonite stratigraphy of a Toarcian (Lower Jurassic) section on Nagy-Pisznice Hill (Gerecse Mts, Hungary)

Abstract In the Jurassic rocks exposed in a small abandoned quarry on the northwestern edge of Nagy-Pisznice Hill in the Gerecse Mts, fairly well preserved parts of a crocodile skeleton was found in 1996. The bed which yielded the skeletal remains is the uppermost layer of the Kisgerecse Marl Formation exposed here and was determined as belonging to the Upper Toarcian Grammoceras thouarsense Zone. The beds of the sequence above and below were carefully sampled in the late 1990s, and the encountered ammonites were evaluated biostratigraphically. As a result, the Lower Toarcian Harpoceras serpentinum Zone, the Middle Toarcian Hildoceras bifrons and Merlaites gradatus Zones, and the Upper Toarcian Grammoceras thouarsense and Geczyceras speciosum Zones were identified. Within most of these zones the subzones and even the faunal horizons were successfully recognized. The lowermost beds above the underlying Pliensbachian red limestone did not yield any fossils; thus the lowermost Toarcian Dactylioceras tenuicostatum Zone could not be documented. The highest Toarcian ammonite zones also remained unidentified, because the beds of the Tölgyhát Limestone above were not sampled all the way up. This paper presents the lithostratigraphic and biostratigraphic details of the sequence, and the paleontological descriptions of the most important ammonites

Identification of genes preferentially expressed in wheat egg cells and zygotes

Wheat genes differentially expressed in the egg cell before and after fertilization were identified. The data support zygotic gene activation before the first cell division in wheat. To have an insight into fertilization-induced gene expression, cDNA libraries have been prepared from isolated wheat egg cells and one-celled zygotes. Two-hundred and twenty-six egg cell and 253 zygote-expressed EST sequences were determined. Most of the represented transcripts were detected in the wheat egg cell or zygote transcriptome at the first time. Expression analysis of fourteen of the identified genes and three controls was carried out by real-time quantitative PCR. The preferential expression of all investigated genes in the female gametophyte-derived samples (egg cells, zygotes, two-celled proembryos, and basal ovule parts with synergids) in comparison to the anthers, and the leaves were verified. Three genes with putative signaling/regulatory functions were expressed at a low level in the egg cell but exhibited increased (2-to-33-fold) relative expression in the zygote and the proembryo. Genes with high EST abundance in cDNA libraries exhibited strong expression in the egg cell and the zygote, while the ones coding for unknown or hypothetical proteins exhibited differential expression patterns with preferential transcript accumulation in egg cells and/or zygotes. The obtained data support the activation of the zygotic genome before the first cell division in wheat