Lehmer's conjecture for Hermitian matrices over the Eisenstein and Gaussian integers

We solve Lehmer's problem for a class of polynomials arising from Hermitian matrices over the Eisenstein and Gaussian integers, that is, we show that all such polynomials have Mahler measure at least Lehmer's number \tau_0 = 1.17628...

Detecting energy dependent neutron capture distributions in a liquid scintillator

A novel technique is being developed to estimate the effective dose of a neutron field based on the distribution of neutron captures in a scintillator. Using Monte Carlo techniques, a number of monoenergetic neutron source energies and locations were modelled and their neutron capture response was recorded. Using back propagation Artificial Neural Networks (ANN) the energy and incident direction of the neutron field was predicted from the distribution of neutron captures within a 6Li-loaded liquid scintillator. Using this proposed technique, the effective dose of 252Cf, 241AmBe and 241AmLi neutron fields was estimated to within 30% for four perpendicular angles in the horizontal plane. Initial theoretical investigations show that this technique holds some promise for real-time estimation of the effective dose of a neutron field

A novel approach to neutron dosimetry

Purpose: Having been overlooked for many years, research is now starting to take into account the directional distribution of neutron workplace fields. Existing neutron dosimetry instrumentation does not account for this directional distribution, resulting in conservative estimates of dose in neutron workplace fields (by around a factor of 2, although this is heavily dependent on the type of field). This conservatism could influence epidemiological studies on the health effects of radiation exposure. This paper reports on the development of an instrument which can estimate the effective dose of a neutron field, accounting for both the direction and the energy distribution. Methods: A 6Li-loaded scintillator was used to perform neutron assays at a number of locations in a 20 × 20 × 17.5 cm3 water phantom. The variation in thermal and fast neutron response to different energies and field directions was exploited. The modeled response of the instrument to various neutron fields was used to train an artificial neural network (ANN) to learn the effective dose and ambient dose equivalent of these fields. All experimental data published in this work were measured at the National Physical Laboratory (UK). Results: Experimental results were obtained for a number of radionuclide source based neutron fields to test the performance of the system. The results of experimental neutron assays at 25 locations in a water phantom were fed into the trained ANN. A correlation between neutron counting rates in the phantom and neutron fluence rates was experimentally found to provide dose rate estimates. A radionuclide source behind shadow cone was used to create a more complex field in terms of energy and direction. For all fields, the resulting estimates of effective dose rate were within 45% or better of their calculated values, regardless of energy distribution or direction for measurement times greater than 25 min. Conclusions: This work presents a novel, real-time, approach to workplace neutron dosimetry. It is believed that in the research presented in this paper, for the first time, a single instrument has been able to estimate effective dose

Neutron assay in mixed radiation fields with a 6Li-loaded plastic scintillator

A novel technique for assay of thermal and fast neutrons in a 6Li-loaded plastic scintillator is presented. Existing capture-gated thermal neutron detection techniques were evaluated with the 6Li-loaded plastic scintillator studied in this work. Using simulations and experimental work, shortcomings in its performance were highlighted. As a result, it was proposed that by separating the combined fast and thermal neutron events from gamma events, using established pulse shape discrimination techniques, the thermal neutron events could then be assayed. Experiments were conducted at the National Physical Laboratory, Teddington, performing neutron assays with seven different neutron fields using the proposed technique. For each field, thermal and fast neutron content was estimated and were shown to corroborate with the seven synthesised fields

Persistent Pain: Physiotherapy Student Experiences of Person-Centred Care in Musculoskeletal Outpatient Departments

Person-centred care is championed throughout healthcare and emphasised in the management of persistent pain. Research reports that physiotherapists and physiotherapy students have struggled to integrate person-centred care into their practice and clinical work with people experiencing persistent pain. The aim of the study was to explore physiotherapy students’ experiences of person-centred care with people with persistent pain in a musculoskeletal outpatients’ placement setting, and to understand what affects physiotherapy students’ ability to implement person-centred practice. An interpretive qualitative method was used with data being collected by semi-structured focus groups of a purposive sample of undergraduate final-year physiotherapy students. A thematic approach to data analysis was completed using a cyclical immersive process. Three themes emerged: understanding of person-centred care, learning, and influences on clinical practice. The students showed an understanding of person-centred care in line with current literature. Person-centred care was generally deemed ‘well taught’ at university however this did not translate into their practice in a placement setting. Several factors influenced their ability to implement person-centred care, and this impacted upon their learning and their management of people presenting with persistent pain. In conclusion, physiotherapy students struggled to integrate learning of person-centred care from university into their practice on a musculoskeletal outpatient’s placement. It is recommended that physiotherapy course teams consider their curricula so that university and placement teaching facilitate person-centred learning and improve the management of persistent pain

Toward a transformed system to address child abuse and family violence in New Zealand

Executive Summary Introduction The Glenn Inquiry (TGI) has contracted Institute of Environmental Science and Research Limited (ESR) to bring together the relevant experience and expertise to collaboratively model a transformed system to address child abuse and neglect (CAN) and family violence (FV) in New Zealand. Our approach We have treated the task of reducing FV and CAN as a ‘wicked problem’1; that is, reducing FV and CAN is a problem that cannot be solved once and for all, and is not a matter of simply applying expert knowledge. The methods used in this project have been chosen because they are appropriate for working with wicked problems: stakeholder engagement, systems thinking and inter-disciplinary analysis. In this report, we refer to both CAN and FV. We recognise that, for some purposes, dealing with CAN requires particular strategies and treatment; however, the purpose of this report is to develop a transformed system that will reduce both CAN and other forms of FV. While the underlying causes of CAN and other FV may be considered independently, and some responses to each form of abuse will need to be particular, this report proposes a wider system of responses that will enable targeted interventions for each form of abuse. We use the term ‘family violence’ in this report in the sense it has come to be understood in Aotearoa, and is used in Te Rito: New Zealand Family Violence Prevention Strategy. In this use, FV includes intimate partner violence, child abuse and neglect, elder abuse, inter-sibling abuse and parental abuse. The project consisted of four work-streams: A review of the international and national literature on what would constitute a high performing system to address CAN and FV, including a review of New Zealand’s current approach with a focus on government legalisation, policies and initiatives; Qualitative modelling of the system dynamics associated with the existing way in which New Zealand has responded to CAN and FV; A secondary (sociological) analysis of suggestions for system improvement from the People’s Report; and, Developing a systemic model of a transformed system through collaborative workshops with sector experts

Cyclotomic matrices and graphs

We generalise the study of cyclotomic matrices - those with all eigenvalues in the interval [-2; 2] - from symmetric rational integer matrices to Hermitian matrices with entries from rings of integers of imaginary quadratic fields. As in the rational integer case, a corresponding graph-like structure is defined. We introduce the notion of `4-cyclotomic' matrices and graphs, prove that they are necessarily maximal cyclotomic, and classify all such objects up to equivalence. Six rings OQ( p d) for d = -1;-2;-3;-7;-11;-15 give rise to examples not found in the rational-integer case; in four (d = -1;-2;-3;-7) we recover infinite families as well as sporadic cases. For d = -15;-11;-7;-2, we demonstrate that a maximal cyclotomic graph is necessarily 4- cyclotomic and thus the presented classification determines all cyclotomic matrices/graphs for those fields. For the same values of d we then identify the minimal noncyclotomic graphs and determine their Mahler measures; no such graph has Mahler measure less than 1.35 unless it admits a rational-integer representative