The Projective Line Over the Finite Quotient Ring GF(2)[xx]/<x3−x>< x^{3} - x> and Quantum Entanglement I. Theoretical Background

The paper deals with the projective line over the finite factor ring $R\_{\clubsuit} \equiv$ GF(2)[$x$]/$$. The line is endowed with 18 points, spanning the neighbourhoods of three pairwise distant points. As $R\_{\clubsuit}$ is not a local ring, the neighbour (or parallel) relation is not an equivalence relation so that the sets of neighbour points to two distant points overlap. There are nine neighbour points to any point of the line, forming three disjoint families under the reduction modulo either of two maximal ideals of the ring. Two of the families contain four points each and they swap their roles when switching from one ideal to the other; the points of the one family merge with (the image of) the point in question, while the points of the other family go in pairs into the remaining two points of the associated ordinary projective line of order two. The single point of the remaining family is sent to the reference point under both the mappings and its existence stems from a non-trivial character of the Jacobson radical, ${\cal J}\_{\clubsuit}$, of the ring. The factor ring $\widetilde{R}\_{\clubsuit} \equiv R\_{\clubsuit}/ {\cal J}\_{\clubsuit}$ is isomorphic to GF(2) $\otimes$ GF(2). The projective line over $\widetilde{R}\_{\clubsuit}$ features nine points, each of them being surrounded by four neighbour and the same number of distant points, and any two distant points share two neighbours. These remarkable ring geometries are surmised to be of relevance for modelling entangled qubit states, to be discussed in detail in Part II of the paper.Comment: 8 pages, 2 figure

Terrace reconstruction and long profile projection: a case study from the Solent river system near Southampton, England

River terrace sequences are important frameworks for archaeological evidence and as such it is important to produce robust correlations between what are often fragmentary remnants of ancient terraces. This paper examines both conceptual and practical issues related to such correlations, using a case study from the eastern part of the former Solent River system near Southampton, England. In this region two recent terrace schemes have been constructed using different data to describe the terrace deposits: one based mainly on terrace surfaces; the other on gravel thicknesses, often not recording the terrace surface itself. The utility of each of these types of data in terrace correlation is discussed in relation to the complexity of the record, the probability of post-depositional alteration of surface sediments and comparison of straight-line projections with modern river long profiles. Correlation using age estimates is also discussed, in relation to optically-stimulated luminescence dating of sand lenses within terrace gravels in this region during the PASHCC project. It is concluded that the need for replication at single sites means that this approach has limited use for correlative purposes, although dating of sediments is important for understanding wider landscape evolution and patterns of human occupation

Human impact parameterizations in global hydrological models improves estimates of monthly discharges and hydrological extremes: a multi-model validation study

Human activities have a profound influence on river discharge, hydrological extremes, and water-related hazards. In this study, we compare the results of five state-of-the-art global hydrological models (GHMs) with observations to examine the role of human impact parameterizations (HIP) in the simulation of the mean, high, and low flows. The analysis is performed for 471 gauging stations across the globe and for the period 1971-2010. We find that the inclusion of HIP improves the performance of GHMs, both in managed and near-natural catchments. For near-natural catchments, the improvement in performance results from improvements in incoming discharges from upstream managed catchments. This finding is robust across GHMs, although the level of improvement and reasons for improvement vary greatly by GHM. The inclusion of HIP leads to a significant decrease in the bias of long-term mean monthly discharge in 36-73% of the studied catchments, and an improvement in modelled hydrological variability in 31-74% of the studied catchments. Including HIP in the GHMs also leads to an improvement in the simulation of hydrological extremes, compared to when HIP is excluded. Whilst the inclusion of HIP leads to decreases in simulated high-flows, it can lead to either increases or decreases in low-flows. This is due to the relative importance of the timing of return flows and reservoir operations and their associated uncertainties. Even with the inclusion of HIP, we find that model performance still not optimal. This highlights the need for further research linking the human management and hydrological domains, especially in those areas with a dominant human impact. The large variation in performance between GHMs, regions, and performance indicators, calls for a careful selection of GHMs, model components, and evaluation metrics in future model applications

Exploring subtle land use and land cover changes: a framework for future landscape studies

UMR AMAP, équipe 3International audienceLand cover and land use changes can have a wide variety of ecological effects, including significant impacts on soils and water quality. In rural areas, even subtle changes in farming practices can affect landscape features and functions, and consequently the environment. Fine-scale analyses have to be performed to better understand the land cover change processes. At the same time, models of land cover change have to be developed in order to anticipate where changes are more likely to occur next. Such predictive information is essential to propose and implement sustainable and efficient environmental policies. Future landscape studies can provide a framework to forecast how land use and land cover changes is likely to react differently to subtle changes. This paper proposes a four step framework to forecast landscape futures at fine scales by coupling scenarios and landscape modelling approaches. This methodology has been tested on two contrasting agricultural landscapes located in the United States and France, to identify possible landscape changes based on forecasting and backcasting agriculture intensification scenarios. Both examples demonstrate that relatively subtle land cover and land use changes can have a large impact on future landscapes. Results highlight how such subtle changes have to be considered in term of quantity, location, and frequency of land use and land cover to appropriately assess environmental impacts on water pollution (France) and soil erosion (US). The results highlight opportunities for improvements in landscape modelling

Measuring femoral lesions despite CT metal artefacts: a cadaveric study

Objective Computed tomography is the modality of choice for measuring osteolysis but suffers from metal-induced artefacts obscuring periprosthetic tissues. Previous papers on metal artefact reduction (MAR) show qualitative improvements, but their algorithms have not found acceptance for clinical applications. We investigated to what extent metal artefacts interfere with the segmentation of lesions adjacent to a metal femoral implant and whether metal artefact reduction improves the manual segmentation of such lesions. Materials and methods We manually created 27 periprosthetic lesions in 10 human cadaver femora. We filled the lesions with a fibrotic interface tissue substitute. Each femur was fitted with a polished tapered cobalt-chrome prosthesis and imaged twice—once with the metal, and once with a substitute resin prosthesis inserted. Metalaffected CTs were processed using standard back-projection as well as projection interpolation (PI) MAR. Two experienced users segmented all lesions and compared segmentation accuracy. Results We achieved accurate delineation of periprosthetic lesions in the metal-free images. The presence of a metal implant led us to underestimate lesion volume and introduced geometrical errors in segmentation boundaries.MediamaticsElectrical Engineering, Mathematics and Computer Scienc