A Nonparametric Bayesian Approach to the Rare Type Match Problem

The “rare type match problem” is the situation in which, in a criminal case, the suspect’s DNA profile, matching the DNA profile of the crime stain, is not in the database of reference. Ideally, the evaluation of this observed match in the light of the two competing hypotheses (the crime stain has been left by the suspect or by another person) should be based on the calculation of the likelihood ratio and depends on the population proportions of the DNA profiles that are unknown. We propose a Bayesian nonparametric method that uses a two-parameter Poisson Dirichlet distribution as a prior over the ranked population proportions and discards the information about the names of the different DNA profiles. This model is validated using data coming from European Y-STR DNA profiles, and the calculation of the likelihood ratio becomes quite simple thanks to an Empirical Bayes approach for which we provided a motivation.

Value of evidence in the rare type match problem: common source versus specific source

In the so-called rare type match problem, the discrete characteristics of a crime stain have not been observed in the set of background material. To assess the strength of evidence, two competing statistical hypotheses need to be considered. The formulation of the hypotheses depends on which identification of source question is of interest (Ommen, 2017, Approximate statistical solutions to the forensic identification of source problem. (Phd thesis). South Dakota State University). Assuming that the evidence has been generated according to the beta-binomial model, two quantifications of the value of evidence can be found in the literature, but no clear indication is given when to use either of these. When the likelihood ratio is used to quantify the value of evidence, an estimate is needed for the frequency of the discrete characteristics. The central discussion is about whether or not one of the traces needs to be added to the background material when determining this estimate. In this article it is shown, using fully Bayesian methods, that one of the values of evidence from the literature corresponds to the so-called ‘identification of common source’ problem and the other to the ‘identification of specific source’ problem (Ommen, 2017, Approximate statistical solutions to the forensic identification of source problem. (Phd thesis). South Dakota State University). This means that the question whether or not one of the traces needs to be added to the background material reduces to the question whether a common source or specific source problem is under consideration. The distinction between the two values is especially important for the rare type match problem, since the values of evidence differ most in this situation.

Order-disorder Twinning of Malachite

Malachite has a layered structure composed of triangular CO3 groups and CuO2(OH)2 coordination squares of two types. In 2D projection, each layer can be decomposed into two OD strips: the A strip, containing CO3 groups and square co-ordinations of Cu2, with idealized symmetry pgm2, and the B strip, without CO3 groups, with symmetry p2 (the b axis of malachite is the infinite strip direction). In the 3D structure, these strips form the ‘A' OD-layers with symmetry reduced by coordination requirements to approximately p2212, which alternate with the ‘B' OD-layers with layer symmetry . The B-layer can assume two positions, which are related by a 180° rotation axis running through the C1 and O1 atoms of the CO3 group in the A-layer. This axis is oriented close to [100]*. The fit of the A-layer and of the coplanar rotated B-layer is hindered by the presence of important partial gaps and overlaps at the boundary. Inclining these two structure portions towards one another, together with small positional adjustments, appears to alleviate the misfit problems; the two layer portions so related form an angle of about 124°, i.e., they form a twin relationship. This desymmetrization of the malachite structure away from the ideal model results in occasional twinning instead of the fully developed monoclinic polytype structure which is derived in this paper. In the structure of the Cu-Zn analogue, rosasite, the above-described match problem is solved in a different way, by shifting a Zn coordination octahedron (which replaces Cu2 in malachite) into the interlayer space. Malachite polytypes 1 and 2 and rosasite illustrate three different orientations of P21/a symmetry elements with respect to the structural layers, resulting in three different structure configurations.

Exploration of Learning Service Discovery Algorithm based on Ontology

To study the learning service discovery algorithm based on ontology, the introduction of bipartite graph theory is focused on. Based on the undergraduate technology, a learning service discovery algorithm based on the basic bipartite graph theory (eLSDA-BG) is proposed. The algorithm mainly converts the problem of learning service match into the optimal complete match problem of bipartite graphs. Through the optimal complete match problem, the learning service match is realized and the learning service discovery is finally reached. The eLSDA-BG algorithm is compared with the greedy algorithm, the UDDI (Universal Description, Discovery, and Integration) algorithm, and OWL-S (Web Ontology Language for Service) algorithm. The comparison of results shows that the eLSDA-BG algorithm proposed can improve recall ratio, accuracy rate and efficiency of learning service discovery in situation of certain sample size.

Research of Image Matching Based on Evolutionary Algorithm

In image matching research, how to ensure that best match’s accuracy of the premise and a significant reduction in the amount of computing is the focus of concern by researchers. Search strategy to find the best match location of the image matching process to determine the amount of computing of image matching, in the existing image matching method are used to traverse search strategy, it is difficult to reduce the amount of computing. This is a common defect of the existing image matching algorithm. Traditional evolutionary algorithm trapped into the local minimum easily. Therefore, based on a simple evolutionary algorithm and combine the base ideology of orthogonal test then applied it to the population initialization, to prevent local convergence to form a new evolutionary algorithm. Compared the traditional evolutionary algorithm, the new algorithm enlarges the searching space and the complexity is not high. We use this new algorithm in image matching; from the results we reach the conclusion: in the optimization precision and the optimization speed, the new algorithm is efficiency for the image match problem.