Research on the human microbiome, the microbiota that live in, on, and around the human person, has revolutionized our understanding of the complex interactions between microbial life and human health and disease. The microbiome may also provide a valuable tool in forensic death investigations by helping to reveal the postmortem interval (PMI) of a decedent that is discovered after an unknown amount of time since death. Current methods of estimating PMI for cadavers discovered in uncontrolled, unstudied environments have substantial limitations, some of which may be overcome through the use of microbial indicators. In this project, we sampled the microbiomes of decomposing human cadavers, focusing on the skin microbiota found in the nasal and ear canals. We then developed several models of statistical regression to establish an algorithm for predicting the PMI of microbial samples. We found that the complete data set, rather than a curated list of indicator species, was preferred for training the regressor. We further found that genus and family, rather than species, are the most informative taxonomic levels. Finally, we developed a k-nearest- neighbor regressor, tuned with the entire data set from all nasal and ear samples, that predicts the PMI of unknown samples with an average error of ±55 accumulated degree days (ADD). This study outlines a machine learning approach for the use of necrobiome data in the prediction of the PMI and thereby provides a successful proof-of- concept that skin microbiota is a promising tool in forensic death investigations.

We show that any family of sets uniformly definable in an o-minimal structure has an extended compression scheme of size equal to the number of parameters in the defining formula.As a consequence, the combinatorial complexity (or density) of any definable family in a structure with a o-minimal theory is bounded by the number of parameters in the defining formula.Extended compression schemes for uniformly definable families corresponding to stable formulas are also shown to exist.

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ABSTRACT. A theory T is shown to have an ICT pattern of depth k in n variables iff it interprets some k-maximum VC class in n parameters.