An Analytical Technique Implemented in the Fractional Clannish Random Walker’s Parabolic Equation with Nonlinear Physical Phenomena

In this paper, the adapted (G′/G)-expansion scheme is executed to obtain exact solutions to the fractional Clannish Random Walker’s Parabolic (FCRWP) equation. Some innovative results of the FCRWP equation are gained via the scheme. A diverse variety of exact outcomes are obtained. The proposed procedure could also be used to acquire exact solutions for other nonlinear fractional mathematical models (NLFMMs)

Mutation Rate Analysis of RM Y-STRs in Deep-Rooted Multi-Generational Punjabi Pedigrees from Pakistan

Y chromosome short tandem repeat polymorphisms (Y-STRs) are important in many areas of human genetics. Y chromosomal STRs, being normally utilized in the field of forensics, exhibit low haplotype diversity in consanguineous populations and fail to discriminate among male relatives from the same pedigree. Rapidly mutating Y-STRs (RM Y-STRs) have received much attention in the past decade. These 13 RM Y-STRs have high mutation rates (>10−2) and have considerably higher haplotype diversity and discrimination capacity than conventionally used Y-STRs, showing remarkable power when it comes to differentiation in paternal lineages in endogamous populations. Previously, we analyzed two to four generations of 99 pedigrees with 1568 pairs of men covering one to six meioses from all over Pakistan and 216 male relatives from 18 deep-rooted endogamous Sindhi pedigrees covering one to seven meioses. Here, we present 861 pairs of men from 62 endogamous pedigrees covering one to six meioses from the Punjabi population of Punjab, Pakistan. Mutations were frequently observed at DYF399 and DYF403, while no mutation was observed at DYS526a/b. The rate of differentiation ranged from 29.70% (first meiosis) to 80.95% (fifth meiosis), while overall (first to sixth meiosis) differentiation was 59.46%. Combining previously published data with newly generated data, the overall differentiation rate was 38.79% based on 5176 pairs of men related by 1–20 meioses, while Yfiler differentiation was 9.24% based on 3864 pairs. Using father–son pair data from the present and previous studies, we also provide updated RM Y-STR mutation rates