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

Erratum to: Methods for evaluating medical tests and biomarkers

[This corrects the article DOI: 10.1186/s41512-016-0001-y.]

Evidence synthesis to inform model-based cost-effectiveness evaluations of diagnostic tests: a methodological systematic review of health technology assessments

Background: Evaluations of diagnostic tests are challenging because of the indirect nature of their impact on patient outcomes. Model-based health economic evaluations of tests allow different types of evidence from various sources to be incorporated and enable cost-effectiveness estimates to be made beyond the duration of available study data. To parameterize a health-economic model fully, all the ways a test impacts on patient health must be quantified, including but not limited to diagnostic test accuracy. Methods: We assessed all UK NIHR HTA reports published May 2009-July 2015. Reports were included if they evaluated a diagnostic test, included a model-based health economic evaluation and included a systematic review and meta-analysis of test accuracy. From each eligible report we extracted information on the following topics: 1) what evidence aside from test accuracy was searched for and synthesised, 2) which methods were used to synthesise test accuracy evidence and how did the results inform the economic model, 3) how/whether threshold effects were explored, 4) how the potential dependency between multiple tests in a pathway was accounted for, and 5) for evaluations of tests targeted at the primary care setting, how evidence from differing healthcare settings was incorporated. Results: The bivariate or HSROC model was implemented in 20/22 reports that met all inclusion criteria. Test accuracy data for health economic modelling was obtained from meta-analyses completely in four reports, partially in fourteen reports and not at all in four reports. Only 2/7 reports that used a quantitative test gave clear threshold recommendations. All 22 reports explored the effect of uncertainty in accuracy parameters but most of those that used multiple tests did not allow for dependence between test results. 7/22 tests were potentially suitable for primary care but the majority found limited evidence on test accuracy in primary care settings. Conclusions: The uptake of appropriate meta-analysis methods for synthesising evidence on diagnostic test accuracy in UK NIHR HTAs has improved in recent years. Future research should focus on other evidence requirements for cost-effectiveness assessment, threshold effects for quantitative tests and the impact of multiple diagnostic tests

Erratum to: Methods for evaluating medical tests and biomarkers

[This corrects the article DOI: 10.1186/s41512-016-0001-y.]

Algebraic Properties of Generalized Rijndael-Like Ciphers

We provide conditions under which the set of Rijndael-like functions considered as permutations of the state space and based on operations of the finite field GF(pk) (p ≥ 2) is not closed under functional composition. These conditions justify using a sequential multiple encryption to strengthen generalized Rijnadael like ciphers. In 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(2k) is equal to the alternating group on the state space. In [39], this paper we provide conditions under which the group generated by the Rijndael-like round functions based on operations of the finite field GF(pk) (p ≥ 2) is equal to the symmetric group or the alternating group on the state space

Quality of life in individuals newly diagnosed with multiple sclerosis or clinically isolated syndrome.

BACKGROUND: Little is known about quality of life (QOL) at the time of multiple sclerosis (MS) or clinically isolated syndrome (CIS) diagnosis and how it evolves in the critical adjustment period immediately following a new diagnosis. OBJECTIVES: To (1) describe QOL trajectory in the first year post-MS/CIS diagnosis and (2) examine associations of demographic and biopsychosocial factors with QOL at baseline and as it evolves over the first year post-MS/CIS diagnosis. METHODS: Participants were N = 250 individuals newly diagnosed with MS or CIS. Participants completed self-report assessments of QOL, demographics, and biopsychosocial factors at 1, 2, 3, 6, 9, and 12 months post-diagnosis using validated measures. RESULTS: At 1-month post-diagnosis, QOL M = 75.2/100 with subsequent assessments revealing consistent ratings on average. Modelling revealed a small number of variables that were predictive of QOL at baseline and/or change in QOL over time. CONCLUSION: QOL in the first year post-MS/CIS diagnosis was, on average, high and stable. A subset of modifiable factors across the biopsychosocial spectrum was associated with baseline level of QOL and change in QOL over time. The stability in QOL suggests that patients can be assessed early after diagnosis for key variables that are predictive of both current and future QOL

2012 Update of the 2008 American College of Rheumatology Recommendations for the Use of Disease‐Modifying Antirheumatic Drugs and Biologic Agents in the Treatment of Rheumatoid Arthritis

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/90529/1/21641_ftp.pd