The first algorithm for linear programming: An analysis of Kantorovich's method

An analysis is given of Kantorovich's method of resolving multipliers. It is shown that the method is equivalent to a parametric method but that it is also equivalent with the simplex method with a special rule for the choice of the new basic variable.     

PENDULUM--a guideline-based approach to the interpretation of STR mixtures

Several years ago, a theory to interpret mixed DNA profiles was proposed that included a consideration of peak area using the method of least squares. This method of mixture interpretation has not been widely adopted because of the complexity of the associated calculations. Most reporting officers (RO) employ an experience and judgement based approach to the interpretation of mixed DNA profiles. Here we present an approach that has formalised the thinking behind this experience and judgement. This has been written into a computer program package called PENDULUM. The program uses a least squares method to estimate the pre-amplification mixture proportion for two potential contributors. It then calculates the heterozygous balance for all of the potential sets of genotypes. A list of "possible" genotypes is generated using a set of heuristic rules. External to the programme the candidate genotypes may then be used to formulate likelihood ratios (LR) that are based on alternative casework propositions. The system does not represent a black box approach; rather it has been integrated into the method currently used by the reporting officers at the Forensic Science Service (FSS). The time saved in automating routine calculations associated with mixtures analysis is significant. In addition, the computer program assists in unifying reporting processes, thereby improving the consistency of reporting.     

Medicaid reform: programming solutions to the equity problem

This paper demonstrates the application of a mathematical programming model to a longstanding policy issue in the Medicaid reform debate: the redistribution of program funds necessary to achieve equity in eligibility and benefit coverage across states. The model is used to estimate the potential degree of equity achievable in the current Medicaid system given various budgetary and political constraints. Two model simulations, based on a 1979 data set for aged recipients of Supplementary Security Income, are presented. The results indicate that half or more of the interstate differences in spending for this population group are due to actuarial and efficiency factors rather than deviations from equity potential. The implications of eliminating the remaining differences are discussed.     

股东派生诉讼的程序设计对公司治理结构的影响

股东派生诉讼制度的产生溯源于通过公司的最终所有者(股东)对其代理人(主要是董事)的有效监督来完善公司治理结构的初衷.本文主要对美国的判例法、成文法和美国法律协会的建议在股东派生诉讼程序设计方面的做法和规定及其对公司治理结构的影响进行介绍和评析,以期得出对中国立法有借鉴意义的结论.     

Using FastID to analyze complex SNP mixtures from indoor dust

Forensically relevant single nucleotide polymorphisms (SNPs) can provide valuable supplemental information to short tandem repeats (STRs) for investigative leads, and genotyping can now be streamlined using massively parallel sequencing (MPS). Dust is an attractive evidence source, as it accumulates on undisturbed surfaces, often is overlooked by perpetrators, and contains sufficient human DNA for analysis. To assess whether SNPs genotyped from indoor dust using MPS could be used to detect known household occupants, 13 households were recruited and provided buccal samples from each occupant and dust from five predefined indoor locations. Thermo Fisher Scientific Precision ID Identity and Ancestry Panels were utilized for SNP genotyping, and sequencing was completed using Illumina^® chemistry. FastID, a software developed to permit mixture analysis and identity searching, was used to assess whether known occupants could be detected from associated household dust samples. A modified “subtraction” method was also used in FastID to estimate the percentage of alleles in each dust sample contributed by known and unknown occupants. On average, 72% of autosomal SNPs were recovered from dust samples. When using FastID, (a) 93% of known occupants were detected in at least one indoor dust sample and could not be excluded as contributors to the mixture, and (b) non-contributor alleles were detected in 54% of dust samples (29 ± 11 alleles per dust sample). Overall, this study highlights the potential of analyzing human DNA present in indoor dust to detect known household occupants, which could be valuable for investigative leads.     

A method to enable forensic genetic genealogy investigations from DNA mixtures

The presence of more than one DNA contributor in an evidentiary sample may preclude attempts to use forensic genetic genealogy to develop an investigative lead. To address this issue, we developed a workflow for deconvolution of SNP mixtures into single source profiles that are suitable for matching against a genealogical database. Using the method, two-contributor DNA mixtures assayed using a commercial SNP typing kit can produce informative match results for both major and minor contributors.     

On the selection of capital juries

Death qualification may bias capital juries not only because it alters the composition of the group “qualified” to sit, but also because it exposes them to an unusual and suggestive legal process. This study examined some of the effects of that process. Subjects were randomly assigned to one of two conditions in which they were exposed to standard criminalvoir dire that either included death qualification or did not. Subjects who were exposed to death qualification were significantly more conviction prone, more likely to believe that other trial participants thought the defendant was guilty, were more likely to sentence him to death, and believed that the law disapproves of death penalty opposition. Several psychological features of the death-qualification process are suggested to account for the biasing effects.     

Forensic interpretation of Y-chromosomal DNA mixtures

The mathematical concept previously introduced for the forensic interpretation of DNA mixtures using non-associated genetic markers has been adapted to the assessment of haplotypes. Such calculus is required, for example, when Y-chromosomal markers are used in forensics. In addition to outlining the general mathematical framework, we devise two approaches to its practical computational implementation, involving either the inclusion-exclusion principle of probability theory or a recursion in the number of unknown contributors invoked. The two approaches scale differently, depending upon the complexity of the case and the diversity of the markers used. The performance of Y-chromosomal microsatellites (Y-STRs) as a means of trace donor discrimination has been assessed by simulation, using the derived formulas. Based upon data from the Y-chromosomal Haplotype Reference Database (YHRD), the exclusion chance of a non-contributor is shown to vary between 95% in the case of two contributors, and 70% for five contributors. With only one additional contributor, half of all contributing suspects would yield a log-likelihood ratio in favour of donorship of 1.61 or higher, although the median drops to 0.66 with four additional contributors. It must be emphasised that these estimates of the discriminatory power of Y-STRs are likely to be conservative since the simulations involved only haplotypes known to occur in YHRD.     

Empirical analysis of the STR profiles resulting from conceptual mixtures

Samples containing DNA from two or more individuals can be difficult to interpret. Even ascertaining the number of contributors can be challenging and associated uncertainties can have dramatic effects on the interpretation of testing results. Using an FBI genotypes dataset, containing complete genotype information from the 13 Combined DNA Index System (CODIS) loci for 959 individuals, all possible mixtures of three individuals were exhaustively and empirically computed. Allele sharing between pairs of individuals in the original dataset, a randomized dataset and datasets of generated cousins and siblings was evaluated as were the number of loci that were necessary to reliably deduce the number of contributors present in simulated mixtures of four or less contributors. The relatively small number of alleles detectable at most CODIS loci and the fact that some alleles are likely to be shared between individuals within a population can make the maximum number of different alleles observed at any tested loci an unreliable indicator of the maximum number of contributors to a mixed DNA sample. This analysis does not use other data available from the electropherograms (such as peak height or peak area) to estimate the number of contributors to each mixture. As a result, the study represents a worst case analysis of mixture characterization. Within this dataset, approximately 3% of three-person mixtures would be mischaracterized as two-person mixtures and more than 70% of four-person mixtures would be mischaracterized as two- or three-person mixtures using only the maximum number of alleles observed at any tested locus.     

A guide to interpreting single locus profiles of DNA mixtures in forensic cases.

Analysis of a mixed body fluid crime sample by means of a single locus DNA probe may give rise to several bands. If a suspect is found to have a profile which matches two of the bands, then the evaluation of the evidential strength requires careful analysis. This paper describes the analysis of two relatively simple case examples. It is intended that the principles of the interpretative process will provide a guide to caseworkers who may encounter similar cases. The extension of the treatment to more complex cases should be clear.