Akaraphon Jantaraphum

arXiv2026

Simulations of dislocation dynamics on an atomic lattice: the effect of collision rules

The stochastic dynamics of dislocations on a one-dimensional periodic lattice domain are considered. Two models are studied: one without a collision rule, and one which annihilates colliding dislocations if they have opposite orientation. The behaviour of both models is investigated by means of a series of numerical simulations exploring the asymptotic behaviour of these models as the number of dislocations increases. From these simulations, evidence is obtained that the discrete model with annihilation tends to a PDE for the dislocation density that accounts for annihilation. However, the discrete model without a collision rule does not appear to exhibit consistent convergence behaviour; instead, it appears that the expected PDE with conserved dislocation density appears in the limit for some parameters, but that for other parameters the density appears to follow to the evolution of the PDE with annihilation. These findings provide evidence that a careful treatment of dislocation collisions is important in discrete dislocation dynamics models.

cond-mat.mtrl-sci↗

arXiv2025

Incorporating Naive Bayes Classification to Address Subpopulation Structure in Familial DNA Search

Familial DNA search evaluates the genetic relatedness of two individuals by comparing the likelihood of their observed DNA profiles under two competing hypotheses-the null hypothesis that the individuals are unrelated and the alternative hypothesis that they are related-most commonly through the likelihood ratio (LR). Standard LR-based approaches typically assume a uniform genetic background; however, this assumption is rarely valid due to population substructure, where allele frequencies vary among subpopulations and can bias relationship inference. Existing modifications-such as LR calculations based on average allele frequencies (LRLAF) and strategies using maximum, minimum, or average likelihood ratios (LRMAX, LRMIN, LRAVG)-help mitigate these challenges but remain limited in their ability to fully address subpopulation differences. This study introduces a new LR-based statistic, LRCLASS, which incorporates a classification step using the Naive Bayes classifier to account for nuisance parameters associated with unknown subpopulation origins. In LRCLASS, the two DNA profiles being compared are jointly assigned to a subpopulation group via Naive Bayes before LR computation. Empirical evaluations using Thai population data show that LRCLASS achieves higher statistical power for detecting full-sibling relationships than existing LR-based methods. We further assessed multinomial logistic regression as an alternative classifier and found its performance comparable to that of Naive Bayes, suggesting flexibility in classifier choice. Overall, integrating the Naive Bayes classifier with LR computation offers a robust strategy for addressing population substructure in familial DNA search and highlights the broader potential of combining supervised learning techniques with forensic statistical methodologies to enhance the accuracy and reliability of genetic relationship testing.

stat.AP↗