A combinatorial approach to knot recognition

This is a report on our ongoing research on a combinatorial approach to knot recognition, using coloring of knots by certain algebraic objects called quandles. The aim of the paper is to summarize the mathematical theory of knot coloring in a compact, accessible manner, and to show how to use it for computational purposes. In particular, we address how to determine colorability of a knot, and propose to use SAT solving to search for colorings. The computational complexity of the problem, both in theory and in our implementation, is discussed. In the last part, we explain how coloring can be utilized in knot recognition

On Irrelevance and Algorithmic Equality in Predicative Type Theory

Dependently typed programs contain an excessive amount of static terms which are necessary to please the type checker but irrelevant for computation. To separate static and dynamic code, several static analyses and type systems have been put forward. We consider Pfenning's type theory with irrelevant quantification which is compatible with a type-based notion of equality that respects eta-laws. We extend Pfenning's theory to universes and large eliminations and develop its meta-theory. Subject reduction, normalization and consistency are obtained by a Kripke model over the typed equality judgement. Finally, a type-directed equality algorithm is described whose completeness is proven by a second Kripke model.Comment: 36 pages, superseds the FoSSaCS 2011 paper of the first author, titled "Irrelevance in Type Theory with a Heterogeneous Equality Judgement

Metabolomics demonstrates divergent responses of two Eucalyptus species to water stress

Past studies of water stress in Eucalyptus spp. generally highlighted the role of fewer than five “important” metabolites, whereas recent metabolomic studies on other genera have shown tens of compounds are affected. There are currently no metabolite profiling data for responses of stress-tolerant species to water stress. We used GC–MS metabolite profiling to examine the response of leaf metabolites to a long (2 month) and severe (Ψpredawn < −2 MPa) water stress in two species of the perennial tree genus Eucalyptus (the mesic Eucalyptus pauciflora and the semi-arid Eucalyptus dumosa). Polar metabolites in leaves were analysed by GC–MS and inorganic ions by capillary electrophoresis. Pressure–volume curves and metabolite measurements showed that water stress led to more negative osmotic potential and increased total osmotically active solutes in leaves of both species. Water stress affected around 30–40% of measured metabolites in E. dumosa and 10–15% in E. pauciflora. There were many metabolites that were affected in E. dumosa but not E. pauciflora, and some that had opposite responses in the two species. For example, in E. dumosa there were increases in five acyclic sugar alcohols and four low-abundance carbohydrates that were unaffected by water stress in E. pauciflora. Re-watering increased osmotic potential and decreased total osmotically active solutes in E. pauciflora, whereas in E. dumosa re-watering led to further decreases in osmotic potential and increases in total osmotically active solutes. This experiment has added several extra dimensions to previous targeted analyses of water stress responses in Eucalyptus, and highlights that even species that are closely related (e.g. congeners) may respond differently to water stress and re-waterin

Chlamydial infection among patients attending STD and genitourinary clinics in Taiwan

<p>Abstract</p> <p>Background</p> <p>The main objective of this study is to examine the epidemiology of <it>Chlamydia trachomatis </it>(CT) infection amongst patients (473 men, 180 women) seen two hospitals in Taiwan.</p> <p>Methods</p> <p>Between July 2004 and June 2005, a total of 653 patients provided first-void urine samples for examination of CT using PCR assay.</p> <p>Results</p> <p>The overall prevalence of CT infection was 18.4% (95% confidence interval [CI] 17.3–19.5). Prevalence for men and women were 16.7 % (95% CI 15.3–18.0%) and 22.8% (95% CI 17.5–28.1%), respectively. Age group-specific prevalence was 25.7% (95% CI 22.5–28.9%) in < 20 year olds, 23.5% (95% CI 20.3–26.7%) in 20–24 year olds, 22.3% (95% CI 18.9–25.7%) in 25–30 year olds, and 11.5% (95% CI 10.3–12.7%) in > 30 year olds. Independent risk factors for chlamydial infection included younger age (aged ≤ 30 years) (adjusted odds ratio [AOR] = 2.44; 95% CI 1.52–3.84; <it>p </it>< 0.001), inconsistent condom use (AOR = 2.01; 95% CI 1.32–3.06; <it>p </it>< 0.001), being symptomatic (dysuria, urethral discharge) at the time of testing (AOR = 1.84; 95% CI 1.21–2.80; <it>p </it>< 0.001), and having <it>N. gonorrhoeae </it>infection (AOR = 3.82; 95% CI 2.20–6.58; <it>p </it>< 0.001).</p> <p>Conclusion</p> <p>Genital chlamydial infection is an important sexually transmitted disease in Taiwan. Young Taiwanese persons attending a STD clinic should be screened for CT infection and counselled on condom use.</p

Numerical study of circulation on the inner Amazon Shelf

Author Posting. © Springer, 2008. This is the author's version of the work. It is posted here by permission of Springer for personal use, not for redistribution. The definitive version was published in Ocean Dynamics 58 (2008): 187-198, doi:10.1007/s10236-008-0139-4.We studied the circulation on the coastal domain of the Amazon Shelf by applying the hydrodynamic module of the Estuarine and Coastal Ocean Model and Sediment Transport - ECOMSED. The first barotropic experiment aimed to explain the major bathymetric effects on tides and those generated by anisotropy in sediment distribution. We analyzed the continental shelf response of barotropic tides under realistic bottom stress parametrization (Cd), considering sediment granulometry obtained from a faciologic map, where river mud deposits and reworked sediments areas are well distinguished, among others classes of sediments. Very low Cd values were set in the fluid mud regions off the Amapa coast (1.0 10-4 ), in contrast to values around 3:5 10-3 for coarser sediment regions off the Para coast. Three-dimensional experiments represented the Amazon River discharge and trade winds, combined to barotropic tide influences and induced vertical mixing. The quasi-resonant response of the Amazon Shelf to the M2 tide act on the local hydrodynamics by increasing tidal admittance, along with tidal forcing at the shelf break and extensive fluid mud regions. Harmonic analysis of modeled currents agreed well with analysis of the AMASSEDS observational data set. Tidal-induced vertical shear provided strong homogenization of threshold waters, which are subject to a kind of hydraulic control due to the topographic steepness. Ahead of the hydraulic jump, the low-salinity plume is disconnected from the bottom and acquires negative vorticity, turning southeastward. Tides act as a generator mechanism and topography, via hydraulic control, as a maintainer mechanism for the low-salinity frontal zone positioning. Tidally induced southeastward plume fate is overwhelmed by northwestward trade winds so that, along with background circulation, probably play the most important role on the plume fate and variability over the Amazon Shelf

α-Syntrophin Modulates Myogenin Expression in Differentiating Myoblasts

α-Syntrophin is a scaffolding protein linking signaling proteins to the sarcolemmal dystrophin complex in mature muscle. However, α-syntrophin is also expressed in differentiating myoblasts during the early stages of muscle differentiation. In this study, we examined the relationship between the expression of α-syntrophin and myogenin, a key muscle regulatory factor.The absence of α-syntrophin leads to reduced and delayed myogenin expression. This conclusion is based on experiments using muscle cells isolated from α-syntrophin null mice, muscle regeneration studies in α-syntrophin null mice, experiments in Sol8 cells (a cell line that expresses only low levels of α-syntrophin) and siRNA studies in differentiating C2 cells. In primary cultured myocytes isolated from α-syntrophin null mice, the level of myogenin was less than 50% that from wild type myocytes (p<0.005) 40 h after differentiation induction. In regenerating muscle, the expression of myogenin in the α-syntrophin null muscle was reduced to approximately 25% that of wild type muscle (p<0.005). Conversely, myogenin expression is enhanced in primary cultures of myoblasts isolated from a transgenic mouse over-expressing α-syntrophin and in Sol8 cells transfected with a vector to over-express α-syntrophin. Moreover, we find that myogenin mRNA is reduced in the absence of α-syntrophin and increased by α-syntrophin over-expression. Immunofluorescence microscopy shows that α-syntrophin is localized to the nuclei of differentiating myoblasts. Finally, immunoprecipitation experiments demonstrate that α-syntrophin associates with Mixed-Lineage Leukemia 5, a regulator of myogenin expression.We conclude that α-syntrophin plays an important role in regulating myogenesis by modulating myogenin expression

Correlation of omega-3 levels in serum phospholipid from 2053 human blood samples with key fatty acid ratios

<p>Abstract</p> <p>Background</p> <p>This research was conducted to explore the relationships between the levels of omega-3 fatty acids in serum phospholipid and key fatty acid ratios including potential cut-offs for risk factor assessment with respect to coronary heart disease and fatal ischemic heart disease.</p> <p>Methods</p> <p>Blood samples (n = 2053) were obtained from free-living subjects in North America and processed for determining the levels of total fatty acids in serum phospholipid as omega-3 fatty acids including EPA (eicosapentaenoic acid, 20:5 n-3) and DHA (docosahexaenoic acid, 22:6 n-3) by combined thin-layer and gas-liquid chromatographic analyses. The omega-3 levels were correlated with selected omega-6: omega-3 ratios including AA (arachidonic acid, 20:4n-6): EPA and AA:(EPA+DHA). Based on previously-published levels of omega-3 fatty acids considered to be in a 'lower risk' category for heart disease and related fatality, 'lower risk' categories for selected fatty acid ratios were estimated.</p> <p>Results</p> <p>Strong inverse correlations between the summed total of omega-3 fatty acids in serum phospholipid and all four ratios (omega-6:omega-3 (n-6:n-3), AA:EPA, AA:DHA, and AA:(EPA+DHA)) were found with the most potent correlation being with the omega-6:omega-3 ratio (R²= 0.96). The strongest inverse relation for the EPA+DHA levels in serum phospholipid was found with the omega-6: omega-3 ratio (R²= 0.94) followed closely by the AA:(EPA+DHA) ratio at R²= 0.88. It was estimated that 95% of the subjects would be in the 'lower risk' category for coronary heart disease (based on total omega-3 ≥ 7.2%) with omega-6:omega-3 ratios <4.5 and AA:(EPA+DHA) ratios <1.4. The corresponding ratio cut-offs for a 'lower risk' category for fatal ischemic heart disease (EPA+DHA ≥ 4.6%) were estimated at < 5.8 and < 2.1, respectively.</p> <p>Conclusions</p> <p>Strong inverse correlations between the levels of omega-3 fatty acids in serum (or plasma) phospholipid and omega-6: omega-3 ratios are apparent based on this large database of 2053 samples. Certain fatty acid ratios may aid in cardiovascular disease-related risk assessment if/when complete profiles are not available.</p

The systematic guideline review: method, rationale, and test on chronic heart failure

Background: Evidence-based guidelines have the potential to improve healthcare. However, their de-novo-development requires substantial resources-especially for complex conditions, and adaptation may be biased by contextually influenced recommendations in source guidelines. In this paper we describe a new approach to guideline development-the systematic guideline review method (SGR), and its application in the development of an evidence-based guideline for family physicians on chronic heart failure (CHF). Methods: A systematic search for guidelines was carried out. Evidence-based guidelines on CHF management in adults in ambulatory care published in English or German between the years 2000 and 2004 were included. Guidelines on acute or right heart failure were excluded. Eligibility was assessed by two reviewers, methodological quality of selected guidelines was appraised using the AGREE instrument, and a framework of relevant clinical questions for diagnostics and treatment was derived. Data were extracted into evidence tables, systematically compared by means of a consistency analysis and synthesized in a preliminary draft. Most relevant primary sources were re-assessed to verify the cited evidence. Evidence and recommendations were summarized in a draft guideline. Results: Of 16 included guidelines five were of good quality. A total of 35 recommendations were systematically compared: 25/35 were consistent, 9/35 inconsistent, and 1/35 un-rateable (derived from a single guideline). Of the 25 consistencies, 14 were based on consensus, seven on evidence and four differed in grading. Major inconsistencies were found in 3/9 of the inconsistent recommendations. We re-evaluated the evidence for 17 recommendations (evidence-based, differing evidence levels and minor inconsistencies) - the majority was congruent. Incongruity was found where the stated evidence could not be verified in the cited primary sources, or where the evaluation in the source guidelines focused on treatment benefits and underestimated the risks. The draft guideline was completed in 8.5 man-months. The main limitation to this study was the lack of a second reviewer. Conclusion: The systematic guideline review including framework development, consistency analysis and validation is an effective, valid, and resource saving-approach to the development of evidence-based guidelines

How robust are the natural history parameters used in chlamydia transmission dynamic models? A systematic review

Transmission dynamic models linked to economic analyses often form part of the decision making process when introducing new chlamydia screening interventions. Outputs from these transmission dynamic models can vary depending on the values of the parameters used to describe the infection. Therefore these values can have an important influence on policy and resource allocation. The risk of progression from infection to pelvic inflammatory disease has been extensively studied but the parameters which govern the transmission dynamics are frequently neglected. We conducted a systematic review of transmission dynamic models linked to economic analyses of chlamydia screening interventions to critically assess the source and variability of the proportion of infections that are asymptomatic, the duration of infection and the transmission probability. We identified nine relevant studies in Pubmed, Embase and the Cochrane database. We found that there is a wide variation in their natural history parameters, including an absolute difference in the proportion of asymptomatic infections of 25% in women and 75% in men, a six-fold difference in the duration of asymptomatic infection and a four-fold difference in the per act transmission probability. We consider that much of this variation can be explained by a lack of consensus in the literature. We found that a significant proportion of parameter values were referenced back to the early chlamydia literature, before the introduction of nucleic acid modes of diagnosis and the widespread testing of asymptomatic individuals. In conclusion, authors should use high quality contemporary evidence to inform their parameter values, clearly document their assumptions and make appropriate use of sensitivity analysis. This will help to make models more transparent and increase their utility to policy makers