Some thoughts on pseudoprimes

We consider several problems about pseudoprimes. First, we look at the issue of their distribution in residue classes. There is a literature on this topic in the case that the residue class is coprime to the modulus. Here we provide some robust statistics in both these cases and the general case. In particular we tabulate all even pseudoprimes to $10^{16}$. Second, we prove a recent conjecture of Ordowski: the set of integers $n$ which are a pseudoprime to some base which is a proper divisor of $n$ has an asymptotic density

Strengthening the Baillie-PSW primality test

The Baillie-PSW primality test combines Fermat and Lucas probable prime tests. It reports that a number is either composite or probably prime. No odd composite integer has been reported to pass this combination of primality tests if the parameters are chosen in an appropriate way. Here, we describe a significant strengthening of this test that comes at almost no additional computational cost. This is achieved by including in the test what we call Lucas-V pseudoprimes, of which there are only five less than $10^{15}$.Comment: 25 page

Protection of alodine coatings from thermal aging by removable polymer coatings.

Removable polymer coatings were evaluated as a means to suppress dehydration of Alodine chromate conversion coatings during thermal aging and thereby retain the corrosion protection afforded by Alodine. Two types of polymer coatings were applied to Alodine-treated panels of aluminum alloys 7075-T73 and 6061-T6 that were subsequently aged for 15 to 50 hours at temperatures between 135 F to 200 F. The corrosion resistance of the thermally aged panels was evaluated, after stripping the polymer coatings, by exposure to a standard salt-fog corrosion test and the extent of pitting of the polymer-coated and untreated panels compared. Removable polymer coatings mitigated the loss of corrosion resistance due to thermal aging experienced by the untreated alloys. An epoxide coating was more effective than a fluorosilicone coating as a dehydration barrier

Creating an environment for thriving: An ethnographic exploration of a British decentralised Olympic and Paralympic Sport Organisation

Objectives The aims of this study were to explore the features of the athletic environment that influence thriving within a British Olympic and Paralympic sport organisation and to understand the interconnectedness of these factors across a range of individuals and contexts. These aims were pursued within a decentralised organisation that was undergoing a leader-led cultural change strategy. Method To develop an understanding of the environmental factors that facilitate athlete thriving, a 16-month ethnography was conducted. Data analysis consisted of reflexive thematic analysis of observational notes, reflexive diaries, and interview transcripts. The findings are presented in an ethnographic tale. Results Alongside the complexities of implementing a culture change strategy across a decentralised organisation, the ethnographic tale details three key features of the athletic environment targeted by senior leadership to successfully influence the athletes’ ability to thrive within their silos. Underpinning these factors are three interconnected themes of understanding, openness, and trust. Conclusions This study demonstrates how empowering devolved leadership was impactful for organisational culture by reducing the homogeneity of leader-centric change initiatives. Further, harnessing an organisation-wide commitment to promoting relationships founded on understanding, openness, and trust can create athletic environments that facilitate thriving. Therefore, while a decentralised structure may present challenges for promoting a duty of care, it is possible to create an environment that supports athletes to thrive

How Mistimed and Unwanted Pregnancies Affect Timing of Antenatal Care Initiation in three Districts in Tanzania

Early antenatal care (ANC) initiation is a doorway to early detection and management of potential complications associated with pregnancy. Although the literature reports various factors associated with ANC initiation such as parity and age, pregnancy intentions is yet to be recognized as a possible predictor of timing of ANC initiation. Data originate from a cross-sectional household survey on health behaviour and service utilization patterns. The survey was conducted in 2011 in Rufiji, Kilombero and Ulanga districts in Tanzania on 910 women of reproductive age who had given birth in the past two years. ANC initiation was considered to be early only if it occurred in the first trimester of pregnancy gestation. A recently completed pregnancy was defined as mistimed if a woman wanted it later, and if she did not want it at all the pregnancy was termed as unwanted. Chisquare was used to test for associations and multinomial logistic regression was conducted to examine how mistimed and unwanted pregnancies affect timing of ANC initiation. Although 49.3% of the women intended to become pregnant, 50.7% (34.9% mistimed and 15.8% unwanted) became pregnant unintentionally. While ANC initiation in the 1st trimester was 18.5%, so was 71.7% and 9.9% in the 2nd and 3rd trimesters respectively. Multivariate analysis revealed that ANC initiation in the 2nd trimester was 1.68 (95% CI 1.10‒2.58) and 2.00 (95% CI 1.05‒3.82) times more likely for mistimed and unwanted pregnancies respectively compared to intended pregnancies. These estimates rose to 2.81 (95% CI 1.41‒5.59) and 4.10 (95% CI 1.68‒10.00) respectively in the 3rd trimester. We controlled for gravidity, age, education, household wealth, marital status, religion, district of residence and travel time to a health facility. Late ANC initiation is a significant maternal and child health consequence of mistimed and unwanted pregnancies in Tanzania. Women should be empowered to delay or avoid pregnancies whenever they need to do so. Appropriate counseling to women, especially those who happen to conceive unintentionally is needed to minimize the possibility of delaying ANC initiation.\u

Cosmology of a Scalar Field Coupled to Matter and an Isotropy-Violating Maxwell Field

Motivated by the couplings of the dilaton in four-dimensional effective actions, we investigate the cosmological consequences of a scalar field coupled both to matter and a Maxwell-type vector field. The vector field has a background isotropy-violating component. New anisotropic scaling solutions which can be responsible for the matter and dark energy dominated epochs are identified and explored. For a large parameter region the universe expands almost isotropically. Using that the CMB quadrupole is extremely sensitive to shear, we constrain the ratio of the matter coupling to the vector coupling to be less than 10^(-5). Moreover, we identify a large parameter region, corresponding to a strong vector coupling regime, yielding exciting and viable cosmologies close to the LCDM limit.Comment: Refs. added, some clarifications. Published in JHEP10(2012)06

Properties of a short questionnaire for assessing Primary Care experiences for children in a population survey

<p>Abstract</p> <p>Background</p> <p>The Primary Care Assessment Tool (PCAT) is an interesting set of tools for primary care research. A very short version could inform policy makers about consumer experiences with primary care (PC) through health surveys. This work aimed to investigate the validity and reliability of a selection of items from the child short edition (CS) of the PCAT.</p> <p>Methods</p> <p>A 24 item questionnaire permitted the identification of a regular source of care and the assessment of the key attributes of first contact, ongoing care over time, coordination, services available and services received (comprehensiveness), and cultural competence. Structural validity, reliability, and construct validity were assessed using responses from 2,200 parents of a representative sample of the population aged 0 to 14 years in Catalonia (Spain) who participated in the 2006 Health Survey. Structural validity was analyzed using exploratory and confirmatory factor analyses and reliability was assessed using Cronbach's alpha. Construct validity was assessed using linear regression analysis between PC experience scores and a measure of overall user satisfaction with healthcare services.</p> <p>Results</p> <p>A total of 2,095 (95.2%) parents provided useable responses on PC. After Confirmatory Factor Analysis (CFA), the best fitting model was a 5-factor model in which the original dimensions of first contact and ongoing care were collapsed into one. The CFA also showed a second order factor onto which all domains except services available loaded (root mean square error of approximation = 0.000; comparative fit index = 1.00). Cronbach's alpha values for one of the original scales (first-contact) was poor (alpha < 0.50), but improved using the modified factor structure (alpha > 0.70). Scores on the scales were correlated with satisfaction with healthcare services (p < 0.01), thereby providing some preliminary evidence of construct validity.</p> <p>Conclusions</p> <p>This very short questionnaire obtained from the PCAT-CE yields information about five attributes of PC and a summary score. It has shown evidence of validity and reliability for judgments about experiences with primary care overall. If space on surveys is at a premium, the instrument could be useful as a measure of PC experiences.</p

A phase II study of active specific immunotherapy and5-FU/Leucovorin as adjuvant therapy for stage III colon carcinoma

Active specific immunotherapy, using vaccines with autologous tumour cells and BCG, significantly reduces the rate of tumour recurrence in stage II colon cancer patients, while no clinical benefit has yet been observed in stage III patients. Adjuvant treatment with 5-Fluorouracil/Leucovorin is now considered standard therapy for stage III colon carcinoma and results in an absolute survival benefit of approximately 10%. Yet, the 5-year overall survival rate of stage III colon cancer patients is only 40–50%. Combining chemotherapy and immunotherapy might improve prognosis for stage III patients, especially when considering that active specific immunotherapy and chemotherapy have shown synergistic effects in pre-clinical tumour models. We performed a phase II study with 56 patients, using the combination of active specific immunotherapy and chemotherapy as an adjuvant therapy in stage III colon cancer patients to assess the influence of 5-Fluorouracil/Leucovorin on anti-tumour immunity induced by autologous tumour cell vaccinations. Anti-tumour immunity was measured before and after chemotherapy by means of delayed type hypersensitivity reactions, taken 48 h after the third and the fourth vaccination. We also investigated the toxicity of this combined immuno-chemotherapy treatment. Delayed type hypersensitivity reactions before chemotherapy had a median size of 20.3 mm, while after chemotherapy delayed type hypersensitivity size was 18.4 mm (P=0.01), indicating that chemotherapy hardly affected anti-tumour immunity. The severity of ulcers at the BCG vaccination sites was comparable to previous studies. In 30% of the patients grade III or grade IV chemotherapy related toxicity was seen; this is comparable to what is normally observed after adjuvant chemotherapy alone. This study shows that the active specific immunotherapy-induced anti-tumour immune response is only minimally impaired by consecutive chemotherapy and that the combined treatment of stage III colon cancer patients with active specific immunotherapy and 5-Fluorouracil/Leucovorin does not cause unexpected toxicity

Growth Dynamics of Australia's Polar Dinosaurs

Analysis of bone microstructure in ornithopod and theropod dinosaurs from Victoria, Australia, documents ontogenetic changes, providing insight into the dinosaurs' successful habitation of Cretaceous Antarctic environments. Woven-fibered bone tissue in the smallest specimens indicates rapid growth rates during early ontogeny. Later ontogeny is marked by parallel-fibered tissue, suggesting reduced growth rates approaching skeletal maturity. Bone microstructure similarities between the ornithopods and theropods, including the presence of LAGs in each group, suggest there is no osteohistologic evidence supporting the hypothesis that polar theropods hibernated seasonally. Results instead suggest high-latitude dinosaurs had growth trajectories similar to their lower-latitude relatives and thus, rapid early ontogenetic growth and the cyclical suspensions of growth inherent in the theropod and ornithopod lineages enabled them to successfully exploit polar regions