A question of Mazurov on groups of exponent dividing 12

Mazurov asked whether a group of exponent dividing 12, which is generated by x, y and z subject to the relations $$x^3=y^2=z^2=(xy)^3=(yz)^3=1$, has order at most 12. We show that if such a group is finite, then the answer is yes

Effects of modeling errors on trajectory predictions in air traffic control automation

Air traffic control automation synthesizes aircraft trajectories for the generation of advisories. Trajectory computation employs models of aircraft performances and weather conditions. In contrast, actual trajectories are flown in real aircraft under actual conditions. Since synthetic trajectories are used in landing scheduling and conflict probing, it is very important to understand the differences between computed trajectories and actual trajectories. This paper examines the effects of aircraft modeling errors on the accuracy of trajectory predictions in air traffic control automation. Three-dimensional point-mass aircraft equations of motion are assumed to be able to generate actual aircraft flight paths. Modeling errors are described as uncertain parameters or uncertain input functions. Pilot or autopilot feedback actions are expressed as equality constraints to satisfy control objectives. A typical trajectory is defined by a series of flight segments with different control objectives for each flight segment and conditions that define segment transitions. A constrained linearization approach is used to analyze trajectory differences caused by various modeling errors by developing a linear time varying system that describes the trajectory errors, with expressions to transfer the trajectory errors across moving segment transitions. A numerical example is presented for a complete commercial aircraft descent trajectory consisting of several flight segments

FindFoci: a focus detection algorithm with automated parameter training that closely matches human assignments, reduces human inconsistencies and increases speed of analysis

Accurate and reproducible quantification of the accumulation of proteins into foci in cells is essential for data interpretation and for biological inferences. To improve reproducibility, much emphasis has been placed on the preparation of samples, but less attention has been given to reporting and standardizing the quantification of foci. The current standard to quantitate foci in open-source software is to manually determine a range of parameters based on the outcome of one or a few representative images and then apply the parameter combination to the analysis of a larger dataset. Here, we demonstrate the power and utility of using machine learning to train a new algorithm (FindFoci) to determine optimal parameters. FindFoci closely matches human assignments and allows rapid automated exploration of parameter space. Thus, individuals can train the algorithm to mirror their own assignments and then automate focus counting using the same parameters across a large number of images. Using the training algorithm to match human assignments of foci, we demonstrate that applying an optimal parameter combination from a single image is not broadly applicable to analysis of other images scored by the same experimenter or by other experimenters. Our analysis thus reveals wide variation in human assignment of foci and their quantification. To overcome this, we developed training on multiple images, which reduces the inconsistency of using a single or a few images to set parameters for focus detection. FindFoci is provided as an open-source plugin for ImageJ

Development of an observational protocol for reducing and mitigating workload and the risk of Retained Foreign Objects

Retained Foreign Objects are an uncommon but costly problem in today's healthcare. It regards the outcome after an unintended item is left behind in a patient after an invasive procedure. This paper presents the development of an observational protocol used for surgical observations in the FOR_RaM Project. The FOR_RaM or Foreign Object Retention - Reduction and Mitigation project aims to analyze and understand the problem of retained foreign objects in surgery and maternity settings in Ireland, develop hospital specific foreign object management processes and implementation roadmaps, with a focus on reducing and mitigating the risk of foreign object retention. This paper discusses the methodology used for developing an observational protocol as part of a socio-technical multi-methods approach in order to gain a better understanding of the existing practices that take place in these settings, including workload, operational processes and collaboration. Emphasis is placed on the observational template development and design, observational tasks, critical points, procedures and protocols followed throughout. This observation protocol has facilitated the collection of critical data and been successful in identifying good practices and potential areas for improvement

Cerebrospinal fluid in the differential diagnosis of Alzheimer's disease: clinical utility of an extended panel of biomarkers in a specialist cognitive clinic.

BACKGROUND: Cerebrospinal fluid (CSF) biomarkers are increasingly being used to support a diagnosis of Alzheimer's disease (AD). Their clinical utility for differentiating AD from non-AD neurodegenerative dementias, such as dementia with Lewy bodies (DLB) or frontotemporal dementia (FTD), is less well established. We aimed to determine the diagnostic utility of an extended panel of CSF biomarkers to differentiate AD from a range of other neurodegenerative dementias. METHODS: We used immunoassays to measure conventional CSF markers of amyloid and tau pathology (amyloid beta (Aβ)1-42, total tau (T-tau), and phosphorylated tau (P-tau)) as well as amyloid processing (AβX-38, AβX-40, AβX-42, soluble amyloid precursor protein (sAPP)α, and sAPPβ), large fibre axonal degeneration (neurofilament light chain (NFL)), and neuroinflammation (YKL-40) in 245 patients with a variety of dementias and 30 controls. Patients fulfilled consensus criteria for AD (n = 156), DLB (n = 20), behavioural variant frontotemporal dementia (bvFTD; n = 45), progressive non-fluent aphasia (PNFA; n = 17), and semantic dementia (SD; n = 7); approximately 10% were pathology/genetically confirmed (n = 26). Global tests based on generalised least squares regression were used to determine differences between groups. Non-parametric receiver operating characteristic (ROC) curves and area under the curve (AUC) analyses were used to quantify how well each biomarker discriminated AD from each of the other diagnostic groups (or combinations of groups). CSF cut-points for the major biomarkers found to have diagnostic utility were validated using an independent cohort which included causes of AD (n = 104), DLB (n = 5), bvFTD (n = 12), PNFA (n = 3), SD (n = 9), and controls (n = 10). RESULTS: There were significant global differences in Aβ1-42, T-tau, T-tau/Aβ1-42 ratio, P-tau-181, NFL, AβX-42, AβX-42/X-40 ratio, APPα, and APPβ between groups. At a fixed sensitivity of 85%, AβX-42/X-40 could differentiate AD from controls, bvFTD, and SD with specificities of 93%, 85%, and 100%, respectively; for T-tau/Aβ1-42 these specificities were 83%, 70%, and 86%. AβX-42/X-40 had similar or higher specificity than Aβ1-42. No biomarker or ratio could differentiate AD from DLB or PNFA with specificity > 50%. Similar sensitivities and specificities were found in the independent validation cohort for differentiating AD and other dementias and in a pathology/genetically confirmed sub-cohort. CONCLUSIONS: CSF AβX-42/X-40 and T-tau/Aβ1-42 ratios have utility in distinguishing AD from controls, bvFTD, and SD. None of the biomarkers tested had good specificity at distinguishing AD from DLB or PNFA

Postmenopausal Hormone Therapy and Colorectal Cancer Risk by Molecularly Defined Subtypes and Tumor Location

Background: Postmenopausal hormone therapy (HT) is associated with a decreased colorectal cancer (CRC) risk. As CRC is a heterogeneous disease, we evaluated whether the association of HT and CRC differs across etiologically relevant, molecularly defined tumor subtypes and tumor location. Methods: We pooled data on tumor subtypes (microsatellite instability status, CpG island methylator phenotype status, BRAF and KRAS mutations, pathway: adenoma-carcinoma, alternate, serrated), tumor location (proximal colon, distal colon, rectum), and HT use among 8220 postmenopausal women (3898 CRC cases and 4322 controls) from 8 observational studies. We used multinomial logistic regression to estimate odds ratios (OR) and 95% confidence intervals (CIs) for the association of ever vs never HT use with each tumor subtype compared with controls. Models were adjusted for study, age, body mass index, smoking status, and CRC family history. All statistical tests were 2-sided. Results: Among postmenopausal women, ever HT use was associated with a 38% reduction in overall CRC risk (OR =0.62, 95% CI = 0.56 to 0.69). This association was similar according to microsatellite instability, CpG island methylator phenotype and BRAF or KRAS status. However, the association was attenuated for tumors arising through the serrated pathway (OR = 0.81, 95% CI = 0.66 to 1.01) compared with the adenoma-carcinoma pathway (OR = 0.63, 95% CI = 0.55 to 0.73; P het =.04) and alternate pathway (OR = 0.61, 95% CI = 0.51 to 0.72). Additionally, proximal colon tumors had a weaker association (OR = 0.71, 95% CI = 0.62 to 0.80) compared with rectal (OR = 0.54, 95% CI = 0.46 to 0.63) and distal colon (OR = 0.57, 95% CI = 0.49 to 0.66; P het =.01) tumors. Conclusions: We observed a strong inverse association between HT use and overall CRC risk, which may predominantly reflect a benefit of HT use for tumors arising through the adenoma-carcinoma and alternate pathways as well as distal colon and rectal tumors

Nongenetic Determinants of Risk for Early-Onset Colorectal Cancer

Background: Incidence of early-onset (younger than 50 years of age) colorectal cancer (CRC) is increasing in many countries. Thus, elucidating the role of traditional CRC risk factors in early-onset CRC is a high priority. We sought to determine whether risk factors associated with late-onset CRC were also linked to early-onset CRC and whether association patterns differed by anatomic subsite. Methods: Using data pooled from 13 population-based studies, we studied 3767 CRC cases and 4049 controls aged younger than 50 years and 23 437 CRC cases and 35 311 controls aged 50 years and older. Using multivariable and multinomial logistic regression, we estimated odds ratios (ORs) and 95% confidence intervals (CIs) to assess the association between risk factors and early-onset CRC and by anatomic subsite. Results: Early-onset CRC was associated with not regularly using nonsteroidal anti-inflammatory drugs (OR = 1.43, 95% CI = 1.21 to 1.68), greater red meat intake (OR = 1.10, 95% CI = 1.04 to 1.16), lower educational attainment (OR = 1.10, 95% CI = 1.04 to 1.16), alcohol abstinence (OR = 1.23, 95% CI = 1.08 to 1.39), and heavier alcohol use (OR = 1.25, 95% CI = 1.04 to 1.50). No factors exhibited a greater excess in early-onset compared with late-onset CRC. Evaluating risks by anatomic subsite, we found that lower total fiber intake was linked more strongly to rectal (OR = 1.30, 95% CI = 1.14 to 1.48) than colon cancer (OR = 1.14, 95% CI = 1.02 to 1.27; P = .04). Conclusion: In this large study, we identified several nongenetic risk factors associated with early-onset CRC, providing a basis for targeted identification of those most at risk, which is imperative in mitigating the rising burden of this disease

Association Between Smoking and Molecular Subtypes of Colorectal Cancer

Background: Smoking is associated with colorectal cancer (CRC) risk. Previous studies suggested this association may be restricted to certain molecular subtypes of CRC, but large-scale comprehensive analysis is lacking. Methods: A total of 9789 CRC cases and 11 231 controls of European ancestry from 11 observational studies were included. We harmonized smoking variables across studies and derived sex study-specific quartiles of pack-years of smoking for analysis. Four somatic colorectal tumor markers were assessed individually and in combination, including BRAF mutation, KRAS mutation, CpG island methylator phenotype (CIMP), and microsatellite instability (MSI) status. A multinomial logistic regression analysis was used to assess the association between smoking and risk of CRC subtypes by molecular characteristics, adjusting for age, sex, and study. All statistical tests were 2-sided and adjusted for Bonferroni correction. Results: Heavier smoking was associated with higher risk of CRC overall and stratified by individual markers (P-trend <.001). The associations differed statistically significantly between all molecular subtypes, which was the most statistically significant for CIMP and BRAF. Compared with never-smokers, smokers in the fourth quartile of pack-years had a 90% higher risk of CIMP-positive CRC (odds ratio = 1.90, 95% confidence interval = 1.60 to 2.26) but only 35% higher risk for CIMP-negative CRC (odds ratio = 1.35, 95% confidence interval = 1.22 to 1.49; P-difference = 2.1 x 10(-6)). The association was also stronger in tumors that were CIMP positive, MSI high, or KRAS wild type when combined (P-difference <.001). Conclusion: Smoking was associated with differential risk of CRC subtypes defined by molecular characteristics. Heavier smokers had particularly higher risk of CRC subtypes that were CIMP positive and MSI high in combination, suggesting that smoking may be involved in the development of colorectal tumors via the serrated pathway