On classification of intrinsic localized modes for the Discrete Nonlinear Schr\"{o}dinger Equation

We consider localized modes (discrete breathers) of the discrete nonlinear Schr\"{o}dinger equation $i\frac{d\psi_n}{dt}=\psi_{n+1}+\psi_{n-1}-2\psi_n+\sigma|\psi_n|^2\psi_n$, $\sigma=\pm1$, $n\in \mathbb{Z}$. We study the diversity of the steady-state solutions of the form $\psi_n(t)=e^{i\omega t}v_n$ and the intervals of the frequency, $\omega$, of their existence. The base for the analysis is provided by the anticontinuous limit ($\omega$ negative and large enough) where all the solutions can be coded by the sequences of three symbols "-", "0" and "+". Using dynamical systems approach we show that this coding is valid for $\omega<\omega^*\approx -3.4533$ and the point $\omega^*$ is a point of accumulation of saddle-node bifurcations. Also we study other bifurcations of intrinsic localized modes which take place for $\omega>\omega^*$ and give the complete table of them for the solutions with codes consisting of less than four symbols.Comment: 33 pages, 14 figures. To appear in Physica

Reducing the environmental impact of surgery on a global scale: systematic review and co-prioritization with healthcare workers in 132 countries

Background Healthcare cannot achieve net-zero carbon without addressing operating theatres. The aim of this study was to prioritize feasible interventions to reduce the environmental impact of operating theatres. Methods This study adopted a four-phase Delphi consensus co-prioritization methodology. In phase 1, a systematic review of published interventions and global consultation of perioperative healthcare professionals were used to longlist interventions. In phase 2, iterative thematic analysis consolidated comparable interventions into a shortlist. In phase 3, the shortlist was co-prioritized based on patient and clinician views on acceptability, feasibility, and safety. In phase 4, ranked lists of interventions were presented by their relevance to high-income countries and low–middle-income countries. Results In phase 1, 43 interventions were identified, which had low uptake in practice according to 3042 professionals globally. In phase 2, a shortlist of 15 intervention domains was generated. In phase 3, interventions were deemed acceptable for more than 90 per cent of patients except for reducing general anaesthesia (84 per cent) and re-sterilization of ‘single-use’ consumables (86 per cent). In phase 4, the top three shortlisted interventions for high-income countries were: introducing recycling; reducing use of anaesthetic gases; and appropriate clinical waste processing. In phase 4, the top three shortlisted interventions for low–middle-income countries were: introducing reusable surgical devices; reducing use of consumables; and reducing the use of general anaesthesia. Conclusion This is a step toward environmentally sustainable operating environments with actionable interventions applicable to both high– and low–middle–income countries

Large deviations for M-estimators

M-estimators, Maximum likelihood estimators, Large deviations, Empirical processes, Kullback–Leibler information,

Measurement of diffractive photoproduction of vector mesons at large momentum transfer at HERA

Elastic and proton-dissociative photoproduction of rho /sup 0/, phi and J/ psi vector mesons ( gamma p to Vp, gamma p to VN, respectively) have been measured in e/sup +/p interactions at HERA up to -t=3 GeV/sup 2/, where t is the four-momentum transfer squared at the photon-vector-meson vertex. The analysis is based on a data sample in which photoproduction reactions were tagged by detection of the scattered positron in a special-purpose calorimeter. This limits the photon virtuality, Q/sup 2/, to values less than 0.01 GeV/sup 2/, and selects a gamma p average center-of-mass energy of [W]=94 GeV. Results for the differential cross sections, d sigma /dt, for rho /sup 0/, phi and J/ psi mesons are presented and compared to the results of recent QCD calculations. Results are also presented for the t-dependence of the pion-pair invariant-mass distribution in the rho /sup 0/ mass region and of the spin-density matrix elements determined from the decay-angle distributions. The Pomeron trajectory has been derived from measurements of the W dependence of the elastic differential cross sections d sigma /dt for both rho /sup 0/ and phi mesons