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Population pharmacokinetic (PK) modeling has become a cornerstone of drug development and optimal patient dosing. This approach offers great benefits for datasets with sparse sampling, such as in pediatric patients, and can describe between-patient variability. While most current algorithms assume normal or log-normal distributions for PK parameters, we present a mathematically consistent nonparametric maximum likelihood (NPML) method for estimating multivariate mixing distributions without any assumption about the shape of the distribution. This approach can handle distributions with any shape for all PK parameters. It is shown in convexity theory that the NPML estimator is discrete, meaning that it has finite number of points with nonzero probability. In fact, there are at most N points where N is the number of observed subjects. The original infinite NPML problem then becomes the finite dimensional problem of finding the location and probability of the support points. In the simplest case, each point essentially represents the set of PK parameters for one patient. The probability of the points is found by a primal-dual interior-point method; the location of the support points is found by an adaptive grid method. Our method is able to handle high-dimensional and complex multivariate mixture models. An important application is discussed for the problem of population pharmacokinetics and a nontrivial example is treated. Our algorithm has been successfully applied in hundreds of published pharmacometric studies. In addition to population pharmacokinetics, this research also applies to empirical Bayes estimation and many other areas of applied mathematics. Thereby, this approach presents an important addition to the pharmacometric toolbox for drug development and optimal patient dosing. 

The term “ancient DNA” (aDNA) is coming of age, with over 1200 hits in the PubMed database, beginning in the early 1980s with the studies of “molecular paleontology.” Rooted in cloning and limited sequencing of DNA from ancient remains during the pre-PCR era, the field has made incredible progress since the introduction of PCR and next-generation sequencing. Over the last decade, aDNA analysis ushered in a new era in genomics and became the method of choice for reconstructing the history of organisms, their biogeography, and migration routes, with applications in evolutionary biology, population genetics, archaeo-genetics, paleo-epidemiology, and many other areas. This change was brought by development of new strategies for coping with the challenges in studying aDNA due to damage and fragmentation, scarce samples, significant historical gaps, and limited applicability of population genetics methods. In this review, we describe the state-of-the-art achievements in aDNA studies, with particular focus on human evolution and demographic history. We present the current experimental and theoretical procedures for handling and analyzing highly degraded aDNA. We also review the challenges in the rapidly growing field of ancient epigenomics. Advancement of ancient DNA tools and methods signifies a new era in population genetics and evolutionary medicine research.