A family of rotation numbers for discrete random dynamics on the circle

We revisit the problem of well-defining rotation numbers for discrete random dynamical systems on the circle. We show that, contrasting with deterministic systems, the topological (i.e. based on Poincar\'{e} lifts) approach does depend on the choice of lifts (e.g. continuously for nonatomic randomness). Furthermore, the winding orbit rotation number does not agree with the topological rotation number. Existence and conversion formulae between these distinct numbers are presented. Finally, we prove a sampling in time theorem which recover the rotation number of continuous Stratonovich stochastic dynamical systems on $S^1$ out of its time discretisation of the flow.Comment: 15 page

Correlation-based entanglement criterion in bipartite multiboson systems

We describe a criterion for the detection of entanglement between two multi-boson systems. The criterion is based on calculating correlations of Gell-Mann matrices with a fixed boson number on each subsystem. This applies naturally to systems such as two entangled spinor Bose-Einstein condensates. We apply our criterion to several experimentally motivated examples, such as an $S^z S^z$ entangled BECs, ac Stark shift induced two-mode squeezed BECs, and photons under parametric down conversion. We find that entanglement can be detected for all parameter regions for the most general criterion. Alternative criteria based on a similar formalism are also discussed together with their merits.Comment: 8 pages, 4 figures, journal versio

New formats for computing with real-numbers under round-to-nearest

An edited version of this work was accepted in IEEE Transactions on computers, DOI 10.1109/TC.2015.2479623In this paper, a new family of formats to deal with real number for applications requiring round to nearest is proposed. They are based on shifting the set of exactly represented numbers which are used in conventional radix-R number systems. This technique allows performing radix complement and round to nearest without carry propagation with negligible time and hardware cost. Furthermore, the proposed formats have the same storage cost and precision as standard ones. Since conversion to conventional formats simply require appending one extra-digit to the operands, standard circuits may be used to perform arithmetic operations with operands under the new format. We also extend the features of the RN-representation system and carry out a thorough comparison between both representation systems. We conclude that the proposed representation system is generally more adequate to implement systems for computation with real number under round-to-nearest.Ministry of Education and Science of Spain under contracts TIN2013-42253-P

Conversion to Organic Field Vegetable Production (Phase 2)

Introduction, aims and objectives When this project began in 1996 the UK supply of organic vegetables, from 2400 hectares, was insufficient to meet the growing market and the majority of organic vegetables were imported. It was a policy objective to enable UK farmers to meet the demands of this growing market. A farmer converting to organic agriculture is faced with a range of specific agronomic and economic challenges different from those of conventional agriculture and of established organic systems and a lack of knowledge about these challenges was recognised as a major barrier for individual farmers considering conversion. The overall aim of this project was therefore to provide information on the agronomic and economic performance of farming systems which included field vegetables as part of their rotations during the conversion period and in the years immediately afterwards. The project was commissioned in 1996 as Project OF0126T, later continued as OF0191; this report describes the findings from both projects. The projects were led by HDRA with HRI (now Warwick HRI), EFRC (Elm Farm Research Centre), and the Institute of Rural Sciences (University of Wales, Aberystwyth) as subcontractors. The main objectives were: 1. To convert 12 ha (Hunts Mill) of the farm at HRI Wellesbourne to an organic system, with a rotation including field vegetables and arable crops. 2. To assess agronomic and economic performance of the crops grown, soils, weeds, pest and diseases, during conversion and for the first target rotation at Hunts Mill. 3. To assess the overall agronomic and financial performance during the first full cycle of the rotations at Hunts Mill, comparing scenarios where the initial fertility building phase was 29 months, 17 or 7 months. 4. To assess the agronomic and economic performance during conversion at 10 commercial reference farms, representing contrasting scenarios of organic vegetable production. 5. To interpret and evaluate the data and to produce information appropriate to aid farmers who are undergoing, or who are considering undergoing conversion to organic systems, and to aid future policy making on related farming issues. The reference farms were selected to represent three different scenarios of conversion (from conventional arable, from conventional intensive vegetable and from conventional mixed farms with livestock). The farms represented a range of sizes and were located in all the principle vegetable growing areas of England. The assessment period covered the two-year conversion period itself plus at least the first three years of certified organic production. The basic experimental approach was to use all the farms as case studies for monitoring and documenting the performance of the systems undergoing conversion. Comparisons were made between Hunts Mill and the reference farms and also between the reference farms representing the same vegetable production scenario and between the three different scenarios. See main document for a summary of findings. More specific key agronomic and economic findings can also be found in the main report. Conclusions The project has demonstrated that the process of conversion from conventional agriculture to organic vegetables production is often quite complex involving a significant number of innovations and restructuring of the farm systems, including changes in production, the introduction of new enterprises and marketing methods. These have resulted in a number of physical, financial and management changes both during the transition process and on the final organic farm businesses. The project has demonstrated that large-scale organic vegetable production is technically feasible, with soil fertility, weeds and pest and disease problems overcome without too much difficulty. The biggest challenges have been marketing, managing labour and making it financially viable at the farm level. Organic Farming Scheme payments have only made small contributions to the ‘cost of conversion’. Conversions, especially on the larger farms, would seem to be preferable over a 5 to 10 year period, allowing time to make the necessary learning and adjustments. Further research Monitoring at Hunts Mill has been extended until 2006 as part of a new project: Organic field vegetable production – baseline monitoring of systems with different fertility building strategies (OF 0332). Monitoring of some of the reference farms has continued as part of the project The Sustainable Vegetable Systems Network (OF 0340). This project monitors agronomy and economics and aims to assist in the development of established organic vegetable systems. Economic conditions change and the impact of the new CAP reforms beginning in 2005 would merit further research. The models developed within this project could form the basis for this work

Characterization of optical systems for the ALPS II experiment

ALPS II is a light shining through a wall style experiment that will use the principle of resonant enhancement to boost the conversion and reconversion probabilities of photons to relativistic WISPs. This will require the use of long baseline low-loss optical cavities. Very high power build up factors in the cavities must be achieved in order to reach the design sensitivity of ALPS II. This necessitates a number of different sophisticated optical and control systems to maintain the resonance and ensure maximal coupling between the laser and the cavity. In this paper we report on the results of the characterization of these optical systems with a 20 m cavity and discuss the results in the context of ALPS II

Phase diagram of heavy fermion systems

The Meccano of heavy fermion systems is shown on different cases going from anomalous monochalcogenides to cerium intermetallic compounds with special focus on the ideal case of the CeRu2Si2 series. Discussion is made in the frame of the interplay between valence, electronic structure (Fermi surface), and magnetism. The nice tools given by the temperature, the pressure, and the magnetic field allow to explore different ground states as well as the slow downhill ''race'' before reaching a Fermi liquid finish line at very low temperature. Experimentally, the Gr"uneisen parameter i.e. the ratio of the thermal expansion by the specific heat is a coloured magic number; its temperature, pressure, and magnetic field dependence is a deep disclosure of competing hierarchies and the conversion of this adaptive matter to external responses.Comment: submitted ICM200

Arbuscular mycorrhizal fungi in organic systems

Arbuscular mycorrhizal fungi (AMF) are potential contributors to plant nutrition and pathogen suppression in low input agricultural systems, although individual species of AMF vary widely in their functional attributes. Recent studies at HRI and elsewhere have suggested that in some agricultural systems inoculum of AMF is substantially lower under conventional management relative to that under organic management. Further studies have suggested that conventional management selects AMF communities with limited benefits to their plant hosts relative to those in organic systems. There is a need to investigate the generality of these findings, and their implications for the productivity of organic systems, particularly during the period following conversion to organic management. The current project was designed to pull together existing understanding of the role, and potential role, of AMF in organic systems, and to identify sites and develop methods for use in a subsequent research programme. The project had three objectives: 01 To deliver a literature review covering current knowledge of the role of AMF in conventional and organic agricultural systems. The review considered the ways in which management influences the structure and functioning of AMF communities, including their contributions under conventional and organic management, and recommendations for future research needs. 02 To establish the extent of differences in AMF inoculum between organic and conventional systems, covering a range of management practices. Paired organic and conventional fields at 12 sites from across England were selected to investigate the relationships between management, AMF communities and soil chemistry. Organic and conventionally managed soils showed no significant difference in soil chemical properties (Organic C, total N, total P, extractable P, K, Mg). However, organically managed soils had greater AMF spore numbers and root colonisation potential, and therefore higher AMF inoculum potential, than conventionally managed soil. The relative difference in AMF spore numbers between organic and conventionally managed fields increased with time since conversion. Differences in AMF inoculum potential between organic and conventionally managed fields, and between farm sites, could not be related to differences in soil chemistry. 03 To develop a method suitable for characterising AM fungus communities in soil libraries, based on 18S rRNA terminal restriction fragment length polymorphism (T-RFLP) T-RFLP was shown to provide a rapid semi-quantitative method for analysis of AMF community diversity. However it was clear that primers currently used to amplify AMF are selective and do not allow diversity of the whole AMF community to be determined. Additionally these primers amplify contaminant fungi which need to be removed from the T-RFLP profile prior to analysis. However, contaminant diversity was shown to be low. The project has identified sites and techniques which could be valuable in future research to study the role of AMF under organic management. The study has also highlighted a number of key areas in which further research is needed in order to harness AMF to improve sustainability and productivity of organic and other agricultural systems. In particular, there is a need to determine the extent to which AMF diversity varies between organic and conventional management, the rate and mechanisms by which AMF diversity increases following conversion to organic production, the relationships between AMF diversity and crop nutrition/ pathogen control, and the soil factors controlling the effectiveness of AMF inoculum