Self-diffusivity of a large tracer ring polymer, D r , immersed in a matrix of linear polymers with N l monomers each shows unusual length dependence. D r initially increases, and then decreases with increasing N l . To understand the relationship between the nonmonotonic variation in D r and threading by matrix chains, we perform equilibrium Monte Carlo simulations of ring-linear blends in which the uncrossability of ring and linear polymer contours is switched on (non-crossing), or artificially turned off (crossing). The D r ≈ 6.2 × 10 −7 N 2/3 l obtained from the crossing simulations, provides an upper bound for the D r obtained for the regular, non-crossing simulations. The center-of-mass mean-squared displacement (g 3 (t)) curves for the crossing simulations are consistent with the Rouse model; we find g 3 (t) = 6D r t. Analysis of the polymer structure indicates that the smaller matrix chains are able to infiltrate the space occupied by the ring probe more effectively, which is dynamically manifested as a larger frictional drag per ring monomer.

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The scale of genetic methods are presently being expanded: forensic genetic assays previously were limited to tens of loci, but now technologies allow for a transition to forensic genomic approaches that assess thousands to millions of loci. However, there are subtle distinctions between genetic assays and their genomic counterparts (especially in the context of forensics). For instance, forensic genetic approaches tend to describe a locus as a haplotype, be it a microhaplotype or a short tandem repeat with its accompanying flanking information. In contrast, genomic assays tend to provide not haplotypes but sequence variants or differences, variants which in turn describe how the alleles apparently differ from the reference sequence. By the given construction, mitochondrial genetic assays can be thought of as genomic as they often describe genetic differences in a similar way. The mitochondrial genetics literature makes clear that sequence differences, unlike the haplotypes they encode, are not comparable to each other. Different alignment algorithms and different variant calling conventions may cause the same haplotype to be encoded in multiple ways. This ambiguity can affect evidence and reference profile comparisons as well as how “match” statistics are computed. In this study, a graph algorithm is described (and implemented in the MMDIT (Mitochondrial Mixture Database and Interpretation Tool) R package) that permits the assessment of forensic match statistics on mitochondrial DNA mixtures in a way that is invariant to both the variant calling conventions followed and the alignment parameters considered. The algorithm described, given a few modest constraints, can be used to compute the “random man not excluded” statistic or the likelihood ratio. The performance of the approach is assessed in in silico mitochondrial DNA mixtures.

Y chromosome Short Tandem Repeat (STR) haplotypes have been used in assisting forensic investigations primarily for identification and male lineage determination. The current SWGDAM interpretation guidelines for Y-STR typing provide helpful guidance on those purposes but do not address the issue of kinship analysis with Y-STR haplotypes. Because of the high mutation rate of Y-STRs, there are complex missing person cases in which inconsistent Y-STR haplotypes between true paternal lineage relatives will arise and cases with two or more male references in the same lineage and yet differ in their haplotypes. Therefore, more useful methods are needed for interpreting the Y-STR haplotype data. Computational methods and interpretation guidelines have been developed specifically addressing this issue, either using a mismatch-based counting method or a pedigree likelihood ratio method. In this study, a software program, MPKin-YSTR, was developed by implementing those more sophisticated methods. This software should be able to improve the interpretation of complex cases with Y-STR haplotype evidence. Thus, more biological evidence will be interpreted, which in turn will result in more investigation leads to help solve crimes.

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