Harmonic sets and the harmonic prime number theorem

We restrict primes and prime powers to sets H(x)= U∞n=1 (x/2n, x/(2n-1)). Let θH(x)= ∑ pεH(x)log p. Then the error in θH(x) has, unconditionally, the expected order of magnitude θH (x)= xlog2 + O(√x). However, if ψH(x)= ∑pmε H(x) log p then ψH(x)= xlog2+ O(log x). Some reasons for and consequences of these sharp results are explored. A proof is given of the “harmonic prime number theorem” π H(x)/ π(x) → log2

Brachial vein transposition arteriovenous fistulas for hemodialysis access

BackgroundAn arteriovenous fistula (AVF) is the preferred vascular access for hemodialysis, offering lower morbidity, mortality, and cost compared with grafts or catheters. Patients with a difficult access extremity have often lost all superficial veins, and even basilic veins may be obliterated. We have used brachial vein transposition AVFs (BVT-AVFs) in these challenging patients and review our experience in this report.MethodsThe study reviewed consecutive patients in whom BVT-AVFs were created from September 2006 to March 2009. Most BVT-AVFs were created in staged procedures, with the second-stage transposition operations completed 4 to 6 weeks after the first-stage AVF operation. A single-stage BVT-AVF was created when the brachial vein diameter was ≥6 mm.ResultsWe identified 58 BVT-AVF procedures, comprising 41 women (71.0%), 28 diabetic patients (48.3%), and 29 (50.0%) had previous access surgery. The operation was completed in two stages in 45 operations (77.6%) and was a primary transposition in 13 patients. However, five of these were secondary AVFs with previous distal AV grafts or AVFs placed elsewhere; effectively, late staged procedures. Follow-up was a mean of 11 months (range, 2.0-31.7 months). Primary patency, primary-assisted patency, and cumulative (secondary) patency were 52.0%, 84.9%, and 92.4% at 12 months and 46.2%, 75.5%, and 92.4% at 24 months, respectively. Harvesting the brachial vein was tedious and more difficult than harvesting other superficial veins. No prosthetic grafts were used.ConclusionBVT-AVFs provide a suitable option for autogenous access when the basilic vein is absent in patients with difficult access extremities. Most patients required intervention for access maturation or maintenance. Most BVT-AVFs were created with staged procedures. Cumulative (secondary) patency was 92.4% at 24 months

There are no multiply-perfect Fibonacci numbers

Here, we show that no Fibonacci number (larger than 1) divides the sum of its divisors

Brachial vein transposition arteriovenous fistulas for hemodialysis access

BackgroundAn arteriovenous fistula (AVF) is the preferred vascular access for hemodialysis, offering lower morbidity, mortality, and cost compared with grafts or catheters. Patients with a difficult access extremity have often lost all superficial veins, and even basilic veins may be obliterated. We have used brachial vein transposition AVFs (BVT-AVFs) in these challenging patients and review our experience in this report.MethodsThe study reviewed consecutive patients in whom BVT-AVFs were created from September 2006 to March 2009. Most BVT-AVFs were created in staged procedures, with the second-stage transposition operations completed 4 to 6 weeks after the first-stage AVF operation. A single-stage BVT-AVF was created when the brachial vein diameter was ≥6 mm.ResultsWe identified 58 BVT-AVF procedures, comprising 41 women (71.0%), 28 diabetic patients (48.3%), and 29 (50.0%) had previous access surgery. The operation was completed in two stages in 45 operations (77.6%) and was a primary transposition in 13 patients. However, five of these were secondary AVFs with previous distal AV grafts or AVFs placed elsewhere; effectively, late staged procedures. Follow-up was a mean of 11 months (range, 2.0-31.7 months). Primary patency, primary-assisted patency, and cumulative (secondary) patency were 52.0%, 84.9%, and 92.4% at 12 months and 46.2%, 75.5%, and 92.4% at 24 months, respectively. Harvesting the brachial vein was tedious and more difficult than harvesting other superficial veins. No prosthetic grafts were used.ConclusionBVT-AVFs provide a suitable option for autogenous access when the basilic vein is absent in patients with difficult access extremities. Most patients required intervention for access maturation or maintenance. Most BVT-AVFs were created with staged procedures. Cumulative (secondary) patency was 92.4% at 24 months

Using geographically weighted regression to explore the spatially heterogeneous spread of bovine tuberculosis in England and Wales

An understanding of the factors that affect the spread of endemic bovine tuberculosis (bTB) is critical for the development of measures to stop and reverse this spread. Analyses of spatial data need to account for the inherent spatial heterogeneity within the data, or else spatial autocorrelation can lead to an overestimate of the significance of variables. This study used three methods of analysis—least-squares linear regression with a spatial autocorrelation term, geographically weighted regression (GWR) and boosted regression tree (BRT) analysis—to identify the factors that influence the spread of endemic bTB at a local level in England and Wales. The linear regression and GWR methods demonstrated the importance of accounting for spatial differences in risk factors for bTB, and showed some consistency in the identification of certain factors related to flooding, disease history and the presence of multiple genotypes of bTB. This is the first attempt to explore the factors associated with the spread of endemic bTB in England and Wales using GWR. This technique improves on least-squares linear regression approaches by identifying regional differences in the factors associated with bTB spread. However, interpretation of these complex regional differences is difficult and the approach does not lend itself to predictive models which are likely to be of more value to policy makers. Methods such as BRT may be more suited to such a task. Here we have demonstrated that GWR and BRT can produce comparable outputs

Farming on the edge: farmer attitudes to bovine tuberculosis in newly endemic areas

Defra's recent strategy to eradicate bovine tuberculosis (bTB) establishes three spatial zones: high-risk areas (HRAs) and low-risk areas, and an area referred to as ‘the edge’, which marks the areas where infection is spreading outwards from the HRA. Little is known about farmers in the edge area, their attitudes towards bTB and their farming practices. This paper examines farmers’ practices and attitudes towards bTB in standardised epidemiologically defined areas. A survey was developed to collect data on farmer attitudes, behaviours, practices and environmental conditions as part of an interdisciplinary analysis of bTB risk factors. Survey items were developed from a literature review and focus groups with vets and farmers in different locations within the edge area. A case-control sampling framework was adopted with farms sampled from areas identified as recently endemic for bTB. 347 farmers participated in the survey including 117 with bTB, representing a 70 percent response rate. Results show that farmers believe they are unable to do anything about bTB but are keen for the government intervention to help control the spread of bTB

Evaluation of the methodological quality of studies of the performance of diagnostic tests for bovine tuberculosis using QUADAS

There has been little assessment of the methodological quality of studies measuring the performance (sensitivity and/or specificity) of diagnostic tests for animal diseases. In a systematic review, 190 studies of tests for bovine tuberculosis (bTB) in cattle (published 1934-2009) were assessed by at least one of 18 reviewers using the QUADAS (Quality Assessment of Diagnostic Accuracy Studies) checklist adapted for animal disease tests. VETQUADAS (VQ) included items measuring clarity in reporting (n = 3), internal validity (n = 9) and external validity (n = 2). A similar pattern for compliance was observed in studies of different diagnostic test types. Compliance significantly improved with year of publication for all items measuring clarity in reporting and external validity but only improved in four of the nine items measuring internal validity (p < 0.05). 107 references, of which 83 had performance data eligible for inclusion in a meta-analysis were reviewed by two reviewers. In these references, agreement between reviewers' responses was 71% for compliance, 32% for unsure and 29% for non-compliance. Mean compliance with reporting items was 2, 5.2 for internal validity and 1.5 for external validity. The index test result was described in sufficient detail in 80.1% of studies and was interpreted without knowledge of the reference standard test result in only 33.1%. Loss to follow-up was adequately explained in only 31.1% of studies. The prevalence of deficiencies observed may be due to inadequate reporting but may also reflect lack of attention to methodological issues that could bias the results of diagnostic test performance estimates. QUADAS was a useful tool for assessing and comparing the quality of studies measuring the performance of diagnostic tests but might be improved further by including explicit assessment of population sampling strategy.The SE3238 project “Meta-analysis of diagnostic tests and modelling to identify appropriate testing strategies to reduce M. bovis infection in GB herds” was funded by the UK Department for Environment, Food and Rural Affairs (Defra).http://www.elsevier.com/locate/prevetmedam2018Veterinary Tropical Disease