On the number of limit cycles of the Lienard equation

In this paper, we study a Lienard system of the form dot{x}=y-F(x), dot{y}=-x, where F(x) is an odd polynomial. We introduce a method that gives a sequence of algebraic approximations to the equation of each limit cycle of the system. This sequence seems to converge to the exact equation of each limit cycle. We obtain also a sequence of polynomials R_n(x) whose roots of odd multiplicity are related to the number and location of the limit cycles of the system.Comment: 10 pages, 5 figures. Submitted to Physical Review

Variational approach to a class of nonlinear oscillators with several limit cycles

We study limit cycles of nonlinear oscillators described by the equation $\ddot x + \nu F(\dot x) + x =0$. Depending on the nonlinearity this equation may exhibit different number of limit cycles. We show that limit cycles correspond to relative extrema of a certain functional. Analytical results in the limits $\nu ->0$ and $\nu -> \infty$ are in agreement with previously known criteria. For intermediate $\nu$ numerical determination of the limit cycles can be obtained.Comment: 12 pages, 3 figure

Seatbelt use and risk of major injuries sustained by vehicle occupants during motor-vehicle crashes: A systematic review and meta-analysis of cohort studies

BackgroundIn 2004, a World Health Report on road safety called for enforcement of measures such as seatbelt use, effective at minimizing morbidity and mortality caused by road traffic accidents. However, injuries caused by seatbelt use have also been described. Over a decade after publication of the World Health Report on road safety, this study sought to investigate the relationship between seatbelt use and major injuries in belted compared to unbelted passengers.MethodsCohort studies published in English language from 2005 to 2018 were retrieved from seven databases. Critical appraisal of studies was carried out using the Scottish Intercollegiate Guidelines Network (SIGN) checklist. Pooled risk of major injuries was assessed using the random effects meta-analytic model. Heterogeneity was quantified using I-squared and Tau-squared statistics. Funnel plots and Egger's test were used to investigate publication bias. This review is registered in PROSPERO (CRD42015020309).ResultsEleven studies, all carried out in developed countries were included. Overall, the risk of any major injury was significantly lower in belted passengers compared to unbelted passengers (RR 0.47; 95%CI, 0.29 to 0.80; I-2=99.7; P=0.000). When analysed by crash types, belt use significantly reduced the risk of any injury (RR 0.35; 95%CI, 0.24 to 0.52). Seatbelt use reduces the risk of facial injuries (RR=0.56, 95% CI=0.37 to 0.84), abdominal injuries (RR=0.87; 95% CI=0.78 to 0.98) and, spinal injuries (RR=0.56, 95% CI=0.37 to 0.84). However, we found no statistically significant difference in risk of head injuries (RR=0.49; 95% CI=0.22 to 1.08), neck injuries (RR=0.69: 95%CI 0.07 to 6.44), thoracic injuries (RR 0.96, 95%CI, 0.74 to 1.24), upper limb injuries (RR=1.05, 95%CI 0.83 to 1.34) and lower limb injuries (RR=0.77, 95%CI 0.58 to 1.04) between belted and non-belted passengers.ConclusionIn sum, the risk of most major road traffic injuries is lower in seatbelt users. Findings were inconclusive regarding seatbelt use and susceptibility to thoracic, head and neck injuries during road traffic accidents. Awareness should be raised about the dangers of inadequate seatbelt use. Future research should aim to assess the effects of seatbelt use on major injuries by crash type

A Model-Based Analysis of Chemical and Temporal Patterns of Cuticular Hydrocarbons in Male Drosophila melanogaster

Drosophila Cuticular Hydrocarbons (CH) influence courtship behaviour, mating, aggregation, oviposition, and resistance to desiccation. We measured levels of 24 different CH compounds of individual male D. melanogaster hourly under a variety of environmental (LD/DD) conditions. Using a model-based analysis of CH variation, we developed an improved normalization method for CH data, and show that CH compounds have reproducible cyclic within-day temporal patterns of expression which differ between LD and DD conditions. Multivariate clustering of expression patterns identified 5 clusters of co-expressed compounds with common chemical characteristics. Turnover rate estimates suggest CH production may be a significant metabolic cost. Male cuticular hydrocarbon expression is a dynamic trait influenced by light and time of day; since abundant hydrocarbons affect male sexual behavior, males may present different pheromonal profiles at different times and under different conditions

Understanding and using quantitative genetic variation

Quantitative genetics, or the genetics of complex traits, is the study of those characters which are not affected by the action of just a few major genes. Its basis is in statistical models and methodology, albeit based on many strong assumptions. While these are formally unrealistic, methods work. Analyses using dense molecular markers are greatly increasing information about the architecture of these traits, but while some genes of large effect are found, even many dozens of genes do not explain all the variation. Hence, new methods of prediction of merit in breeding programmes are again based on essentially numerical methods, but incorporating genomic information. Long-term selection responses are revealed in laboratory selection experiments, and prospects for continued genetic improvement are high. There is extensive genetic variation in natural populations, but better estimates of covariances among multiple traits and their relation to fitness are needed. Methods based on summary statistics and predictions rather than at the individual gene level seem likely to prevail for some time yet

The malignant phenotype in breast cancer is driven by eIF4A1-mediated changes in the translational landscape

Human mRNA DeXD/H-box helicases are ubiquitous molecular motors that are required for the majority of cellular processes that involve RNA metabolism. One of the most abundant is eIF4A, which is required during the initiation phase of protein synthesis to unwind regions of highly structured mRNA that would otherwise impede the scanning ribosome. Dysregulation of protein synthesis is associated with tumorigenesis, but little is known about the detailed relationships between RNA helicase function and the malignant phenotype in solid malignancies. Therefore, immunohistochemical analysis was performed on over 3000 breast tumors to investigate the relationship among expression of eIF4A1, the helicase-modulating proteins eIF4B, eIF4E and PDCD4, and clinical outcome. We found eIF4A1, eIF4B and eIF4E to be independent predictors of poor outcome in ER-negative disease, while in contrast, the eIF4A1 inhibitor PDCD4 was related to improved outcome in ER-positive breast cancer. Consistent with these data, modulation of eIF4A1, eIF4B and PCDC4 expression in cultured MCF7 cells all restricted breast cancer cell growth and cycling. The eIF4A1-dependent translatome of MCF7 cells was defined by polysome profiling, and was shown to be highly enriched for several classes of oncogenic genes, including G-protein constituents, cyclins and protein kinases, and for mRNAs with G/C-rich 5′UTRs with potential to form G-quadruplexes and with 3′UTRs containing microRNA target sites. Overall, our data show that dysregulation of mRNA unwinding contributes to the malignant phenotype in breast cancer via preferential translation of a class of genes involved in pro-oncogenic signaling at numerous levels. Furthermore, immunohistochemical tests are promising biomarkers for tumors sensitive to anti-helicase therapies

Crowdsourcing the General Public for Large Scale Molecular Pathology Studies in Cancer

Background: Citizen science, scientific research conducted by non-specialists, has the potential to facilitate biomedical research using available large-scale data, however validating the results is challenging. The Cell Slider is a citizen science project that intends to share images from tumors with the general public, enabling them to score tumor markers independently through an internet-based interface. Methods: From October 2012 to June 2014, 98,293 Citizen Scientists accessed the Cell Slider web page and scored 180,172 sub-images derived from images of 12,326 tissue microarray cores labeled for estrogen receptor (ER). We evaluated the accuracy of Citizen Scientist's ER classification, and the association between ER status and prognosis by comparing their test performance against trained pathologists. Findings: The area under ROC curve was 0.95 (95% CI 0.94 to 0.96) for cancer cell identification and 0.97 (95% CI 0.96 to 0.97) for ER status. ER positive tumors scored by Citizen Scientists were associated with survival in a similar way to that scored by trained pathologists. Survival probability at 15 years were 0.78 (95% CI 0.76 to 0.80) for ER-positive and 0.72 (95% CI 0.68 to 0.77) for ER-negative tumors based on Citizen Scientists classification. Based on pathologist classification, survival probability was 0.79 (95% CI 0.77 to 0.81) for ER-positive and 0.71 (95% CI 0.67 to 0.74) for ER-negative tumors. The hazard ratio for death was 0.26 (95% CI 0.18 to 0.37) at diagnosis and became greater than one after 6.5 years of follow-up for ER scored by Citizen Scientists, and 0.24 (95% CI 0.18 to 0.33) at diagnosis increasing thereafter to one after 6.7 (95% CI 4.1 to 10.9) years of follow-up for ER scored by pathologists. Interpretation: Crowdsourcing of the general public to classify cancer pathology data for research is viable, engages the public and provides accurate ER data. Crowdsourced classification of research data may offer a valid solution to problems of throughput requiring human input

Evolutionary Consequences of Altered Atmospheric Oxygen in Drosophila melanogaster

Twelve replicate populations of Drosophila melanogaster, all derived from a common ancestor, were independently evolved for 34+ generations in one of three treatment environments of varying PO2: hypoxia (5.0–10.1 kPa), normoxia (21.3 kPa), and hyperoxia (40.5 kPa). Several traits related to whole animal performance and metabolism were assayed at various stages via “common garden” and reciprocal transplant assays to directly compare evolved and acclimatory differences among treatments. Results clearly demonstrate the evolution of a greater tolerance to acute hypoxia in the hypoxia-evolved populations, consistent with adaptation to this environment. Greater hypoxia tolerance was associated with an increase in citrate synthase activity in fly homogenate when compared to normoxic (control) populations, suggesting an increase in mitochondrial volume density in these populations. In contrast, no direct evidence of increased performance of the hyperoxia-evolved populations was detected, although a significant decrease in the tolerance of these populations to acute hypoxia suggests a cost to adaptation to hyperoxia. Hyperoxia-evolved populations had lower productivity overall (i.e., across treatment environments) and there was no evidence that hypoxia or hyperoxia-evolved populations had greatest productivity or longevity in their respective treatment environments, suggesting that these assays failed to capture the components of fitness relevant to adaptation