Storage conditions influence the integrity of the recoverable DNA from forensic evidence in terms of yield and quality. FTA cards are widely used in the forensic practice as their chemically-treated matrix provides protection from the moment of collection to the point of analysis with current STR typing technology. In this study we assess the recoverability and the integrity of DNA from eleven years old saliva on FTA cards using a forensic quantitative real-time polymerase chain reaction (qPCR) commercial assay. The quality after long-term storage was investigated in order to evaluate if the FTA device could assure enough stability over time, applying some internally validated quality criteria of the STR profile. Furthermore, we used a 3D interpolation model to combine the quantitative and qualitative data from qPCR to calculate the Minimum Optimal DNA Input (MODI) to add to the downstream PCR reaction based on the quantitative and qualitative data of a sample. According to our results, when saliva sample is properly transferred onto FTA cards and then correctly stored according to the manufacturer's instructions, it's possible to recover sufficient amounts of DNA for human identification even after more than a decade of storage at ambient temperature. Degradation affected the quality of results especially when the Degradation Index exceeds the value of 2.12, requiring modifications of the standard internal workflow to improve the genotyping quality. Above this value, the application of a "corrective factor" to the PCR normalization process was necessary in order to adjust the recommended manufacturer's PCR DNA input taking into account the degradation level. Our results demonstrated the importance to consider in predictive terms the parameters obtained with the real-time quantification assay, both in terms of quantity (DNA concentration) and of quality (DI, Inhibition). Informatics predictive tools including qPCR data together with the variables of storage duration and conditions should be developed in order to optimize the DNA analysis process.
We consider the edge-triangle model, a two-parameter family of exponential random graphs in which dependence between edges is introduced through triangles. In the so-called replica symmetric regime, the limiting free energy exists together with a complete characterization of the phase diagram of the model. We borrow tools from statistical mechanics to obtain limit theorems for the edge density. First, we determine the asymptotic distribution of this quantity, as the graph size tends to infinity, in the various phases. Then we study the fluctuations of the edge density around its average value off the critical curve and formulate conjectures about the behavior at criticality based on the analysis of a meanfield approximation of the model. Some of our results can be extended with no substantial changes to more general classes of exponential random graphs.
We study the pressure of the "edge-triangle model", which is equivalent to the cumulant generating function of triangles in the Erdös-Rényi random graph. The investigation involves a population dynamics method on finite graphs of increasing volume, as well as a discretization of the graphon variational problem arising in the infinite volume limit. As a result, we locate a curve in the parameter space where a one-step replica symmetry breaking transition occurs. Sampling a large graph in the broken symmetry phase is well described by a graphon with a structure very close to the one of an equi-bipartite graph.
We study the pressure of the 'edge-triangle model', which is equivalent to the cumulant generating function of triangles in the Erdös-Rényi random graph. By analyzing finite graphs of increasing volume, as well as the graphon variational problem in the infinite volume limit, we locate a curve in the parameter space where a one-step replica symmetry breaking transition occurs. Sampling a large graph in the broken symmetry phase is well described by a graphon with a structure very close to the one of an equi-bipartite graph.
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