Constant Curvature Coefficients and Exact Solutions in Fractional Gravity and Geometric Mechanics

We study fractional configurations in gravity theories and Lagrange mechanics. The approach is based on Caputo fractional derivative which gives zero for actions on constants. We elaborate fractional geometric models of physical interactions and we formulate a method of nonholonomic deformations to other types of fractional derivatives. The main result of this paper consists in a proof that for corresponding classes of nonholonomic distributions a large class of physical theories are modelled as nonholonomic manifolds with constant matrix curvature. This allows us to encode the fractional dynamics of interactions and constraints into the geometry of curve flows and solitonic hierarchies.Comment: latex2e, 11pt, 27 pages, the variant accepted to CEJP; added and up-dated reference

Evaluation of DNA methylation biomarkers ASCL1 and LHX8 on HPV-positive self-collected samples from primary HPV-based screening

Background: Host-cell DNA methylation analysis can be used to triage women with high-risk human papillomavirus (HPV)-positive self-collected cervicovaginal samples, but current data are restricted to under-/never-screened women and referral populations. This study evaluated triage performance in women who were offered primary HPV self-sampling for cervical cancer screening. Methods: Self-collected samples from 593 HPV-positive women who participated in a primary HPV self-sampling trial (IMPROVE study; NTR5078), were tested for the DNA methylation markers ASCL1 and LHX8 using quantitative multiplex methylation-specific PCR (qMSP). The diagnostic performance for CIN3 and cervical cancer (CIN3 +) was evaluated and compared with that of paired HPV-positive clinician-collected cervical samples. Results: Significantly higher methylation levels were found in HPV-positive self-collected samples of women with CIN3 + than control women with no evidence of disease (P values <0.0001). The marker panel ASCL1/LHX8 yielded a sensitivity for CIN3 + detection of 73.3% (63/86; 95% CI 63.9–82.6%), with a corresponding specificity of 61.1% (310/507; 95% CI 56.9–65.4%). The relative sensitivity for detecting CIN3+ was 0.95 (95% CI 0.82–1.10) for self-collection versus clinician-collection, and the relative specificity was 0.82 (95% CI 0.75–0.90). Conclusions: The ASCL1/LHX8 methylation marker panel constitutes a feasible direct triage method for the detection of CIN3 + in HPV-positive women participating in routine screening by self-sampling