Elliptic Reciprocity

The paper introduces the notions of an elliptic pair, an elliptic cycle and an elliptic list over a square free positive integer d. These concepts are related to the notions of amicable pairs of primes and aliquot cycles that were introduced by Silverman and Stange. Settling a matter left open by Silverman and Stange it is shown that for d=3 there are elliptic cycles of length 6. For d not equal to 3 the question of the existence of proper elliptic lists of length n over d is reduced to the the theory of prime producing quadratic polynomials. For d=163 a proper elliptic list of length 40 is exhibited. It is shown that for each d there is an upper bound on the length of a proper elliptic list over d. The final section of the paper contains heuristic arguments supporting conjectured asymptotics for the number of elliptic pairs below integer X. Finally, for d congruent to 3 modulo 8 the existence of infinitely many anomalous prime numbers is derived from Bunyakowski's Conjecture for quadratic polynomials.Comment: 17 pages, including one figure and two table

Algebraic properties of generalized Rijndael-like ciphers

We provide conditions under which the set of Rijndael functions considered as permutations of the state space and based on operations of the finite field \GF (p^k) ($p\geq 2$ a prime number) is not closed under functional composition. These conditions justify using a sequential multiple encryption to strengthen the AES (Rijndael block cipher with specific block sizes) in case AES became practically insecure. In Sparr and Wernsdorf (2008), R. Sparr and R. Wernsdorf provided conditions under which the group generated by the Rijndael-like round functions based on operations of the finite field \GF (2^k) is equal to the alternating group on the state space. In this paper we provide conditions under which the group generated by the Rijndael-like round functions based on operations of the finite field \GF (p^k) ($p\geq 2$) is equal to the symmetric group or the alternating group on the state space.Comment: 22 pages; Prelim0

Prevalence of suicidal behaviour following traumatic brain injury: Longitudinal follow-up data from the NIDRR Traumatic Brain Injury Model Systems

Objective: This study utilized the Traumatic Brain Injury Model Systems (TBIMS) National Database to examine the prevalence of depression and suicidal behaviour in a large cohort of patients who sustained moderate-to-severe TBI. Method: Participants presented to a TBIMS acute care hospital within 72 hours of injury and received acute care and comprehensive rehabilitation in a TBIMS designated brain injury inpatient rehabilitation programme. Depression and suicidal ideation were measured with the Patient Health Questionnaire (PHQ-9). Self-reported suicide attempts during the past year were recorded at each follow-up examination, at 1, 2, 3, 10, 15 and 20 years post-injury. Results: Throughout the 20 years of follow-up, rates of depression ranged from 24.8–28.1%, suicidal ideation ranged from 7.0–10.1% and suicide attempts (past year) ranged from 0.8–1.7%. Participants who endorsed depression and/or suicidal behaviour at year 1 demonstrated consistently elevated rates of depression and suicidal behaviour 5 years after TBI. Conclusion: Compared to the general population, individuals with TBI are at greater risk for depression and suicidal behaviour many years after TBI. The significant psychiatric symptoms evidenced by individuals with TBI highlight the need for routine screening and mental health treatment in this population

IMPLEmenting a clinical practice guideline for acute low back pain evidence-based manageMENT in general practice (IMPLEMENT) : cluster randomised controlled trial study protocol

Background: Evidence generated from reliable research is not frequently implemented into clinical practice. Evidence-based clinical practice guidelines are a potential vehicle to achieve this. A recent systematic review of implementation strategies of guideline dissemination concluded that there was a lack of evidence regarding effective strategies to promote the uptake of guidelines. Recommendations from this review, and other studies, have suggested the use of interventions that are theoretically based because these may be more effective than those that are not. An evidencebased clinical practice guideline for the management of acute low back pain was recently developed in Australia. This provides an opportunity to develop and test a theory-based implementation intervention for a condition which is common, has a high burden, and for which there is an evidence-practice gap in the primary care setting. Aim: This study aims to test the effectiveness of a theory-based intervention for implementing a clinical practice guideline for acute low back pain in general practice in Victoria, Australia. Specifically, our primary objectives are to establish if the intervention is effective in reducing the percentage of patients who are referred for a plain x-ray, and improving mean level of disability for patients three months post-consultation. Methods/Design: This study protocol describes the details of a cluster randomised controlled trial. Ninety-two general practices (clusters), which include at least one consenting general practitioner, will be randomised to an intervention or control arm using restricted randomisation. Patients aged 18 years or older who visit a participating practitioner for acute non-specific low back pain of less than three months duration will be eligible for inclusion. An average of twenty-five patients per general practice will be recruited, providing a total of 2,300 patient participants. General practitioners in the control arm will receive access to the guideline using the existing dissemination strategy. Practitioners in the intervention arm will be invited to participate in facilitated face-to-face workshops that have been underpinned by behavioural theory. Investigators (not involved in the delivery of the intervention), patients, outcome assessors and the study statistician will be blinded to group allocation. Trial registration: Australian New Zealand Clinical Trials Registry ACTRN012606000098538 (date registered 14/03/2006).The trial is funded by the NHMRC by way of a Primary Health Care Project Grant (334060). JF has 50% of her time funded by the Chief Scientist Office3/2006). of the Scottish Government Health Directorate and 50% by the University of Aberdeen. PK is supported by a NHMRC Health Professional Fellowship (384366) and RB by a NHMRC Practitioner Fellowship (334010). JG holds a Canada Research Chair in Health Knowledge Transfer and Uptake. All other authors are funded by their own institutions

A systematic review and meta-synthesis of the impact of low back pain on people's lives

Copyright @ 2014 Froud et al.; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited.Background - Low back pain (LBP) is a common and costly problem that many interpret within a biopsychosocial model. There is renewed concern that core-sets of outcome measures do not capture what is important. To inform debate about the coverage of back pain outcome measure core-sets, and to suggest areas worthy of exploration within healthcare consultations, we have synthesised the qualitative literature on the impact of low back pain on people’s lives. Methods - Two reviewers searched CINAHL, Embase, PsycINFO, PEDro, and Medline, identifying qualitative studies of people’s experiences of non-specific LBP. Abstracted data were thematic coded and synthesised using a meta-ethnographic, and a meta-narrative approach. Results - We included 49 papers describing 42 studies. Patients are concerned with engagement in meaningful activities; but they also want to be believed and have their experiences and identity, as someone ‘doing battle’ with pain, validated. Patients seek diagnosis, treatment, and cure, but also reassurance of the absence of pathology. Some struggle to meet social expectations and obligations. When these are achieved, the credibility of their pain/disability claims can be jeopardised. Others withdraw, fearful of disapproval, or unable or unwilling to accommodate social demands. Patients generally seek to regain their pre-pain levels of health, and physical and emotional stability. After time, this can be perceived to become unrealistic and some adjust their expectations accordingly. Conclusions - The social component of the biopsychosocial model is not well represented in current core-sets of outcome measures. Clinicians should appreciate that the broader impact of low back pain includes social factors; this may be crucial to improving patients’ experiences of health care. Researchers should consider social factors to help develop a portfolio of more relevant outcome measures.Arthritis Research U

Exploring differential item functioning in the SF-36 by demographic, clinical, psychological and social factors in an osteoarthritis population

The SF-36 is a very commonly used generic measure of health outcome in osteoarthritis (OA). An important, but frequently overlooked, aspect of validating health outcome measures is to establish if items work in the same way across subgroup of a population. That is, if respondents have the same 'true' level of outcome, does the item give the same score in different subgroups or is it biased towards one subgroup or another. Differential item functioning (DIF) can identify items that may be biased for one group or another and has been applied to measuring patient reported outcomes. Items may show DIF for different conditions and between cultures, however the SF-36 has not been specifically examined in an osteoarthritis population nor in a UK population. Hence, the aim of the study was to apply the DIF method to the SF-36 for a UK OA population. The sample comprised a community sample of 763 people with OA who participated in the Somerset and Avon Survey of Health. The SF-36 was explored for DIF with respect to demographic, social, clinical and psychological factors. Well developed ordinal regression models were used to identify DIF items. Results: DIF items were found by age (6 items), employment status (6 items), social class (2 items), mood (2 items), hip v knee (2 items), social deprivation (1 item) and body mass index (1 item). Although the impact of the DIF items rarely had a significant effect on the conclusions of group comparisons, in most cases there was a significant change in effect size. Overall, the SF-36 performed well with only a small number of DIF items identified, a reassuring finding in view of the frequent use of the SF-36 in OA. Nevertheless, where DIF items were identified it would be advisable to analyse data taking account of DIF items, especially when age effects are the focus of interest

Overstating the evidence - double counting in meta-analysis and related problems

Background: The problem of missing studies in meta-analysis has received much attention. Less attention has been paid to the more serious problem of double counting of evidence. Methods: Various problems in overstating the precision of results from meta-analyses are described and illustrated with examples, including papers from leading medical journals. These problems include, but are not limited to, simple double-counting of the same studies, double counting of some aspects of the studies, inappropriate imputation of results, and assigning spurious precision to individual studies. Results: Some suggestions are made as to how the quality and reliability of meta-analysis can be improved. It is proposed that the key to quality in meta-analysis lies in the results being transparent and checkable. Conclusions: Existing quality check lists for meta-analysis do little to encourage an appropriate attitude to combining evidence and to statistical analysis. Journals and other relevant organisations should encourage authors to make data available and make methods explicit. They should also act promptly to withdraw meta-analyses when mistakes are found

Fatigue Intervention by Nurses Evaluation - The FINE Trial. A randomised controlled trial of nurse led self-help treatment for patients in primary care with chronic fatigue syndrome: study protocol. [ISRCTN74156610]

Background: Chronic fatigue syndrome, also known as ME (CFS/ME), is a condition characterised primarily by severe, disabling fatigue, of unknown origin, which has a poor prognosis and serious personal and economic consequences. Evidence for the effectiveness of any treatment for CFS/ME in primary care, where most patients are seen, is sparse. Recently, a brief, pragmatic treatment for CFS/ME, based on a physiological dysregulation model of the condition, was shown to be successful in improving fatigue and physical functioning in patients in secondary care. The treatment involves providing patients with a readily understandable explanation of their symptoms, from which flows the rationale for a graded rehabilitative plan, developed collaboratively with the therapist. The present trial will test the effectiveness and cost-effectiveness of pragmatic rehabilitation when delivered by specially trained general nurses in primary care. We selected a client-centred counselling intervention, called supportive listening, as a comparison treatment. Counselling has been shown to be as effective as cognitive behaviour therapy for treating fatigue in primary care, is more readily available, and controls for supportive therapist contact time. Our control condition is treatment as usual by the general practitioner (GP). Methods and design: This study protocol describes the design of an ongoing, single-blind, pragmatic randomized controlled trial of a brief (18 week) self-help treatment, pragmatic rehabilitation, delivered by specially trained nurse-therapists in patients' homes, compared with nurse-therapist delivered supportive listening and treatment as usual by the GP. An economic evaluation, taking a societal viewpoint, is being carried out alongside the clinical trial. Three adult general nurses were trained over a six month period to deliver the two interventions. Patients aged over 18 and fulfilling the Oxford criteria for CFS are assessed at baseline, after the intervention, and again one year later. Primary outcomes are self-reported physical functioning and fatigue at one year, and will be analysed on an intention-to-treat basis. A qualitative study will examine the interventions' mechanisms of change, and also GPs' drivers and barriers towards referral