Motivation Principal Component Analysis is a key tool in the study of population structure in human genetics. As modern datasets become increasingly larger in size, traditional approaches based on loading the entire dataset in the system memory (Random Access Memory) become impractical and out-of-core implementations are the only viable alternative. Results We present TeraPCA, a C++ implementation of the Randomized Subspace Iteration method to perform Principal Component Analysis of large-scale datasets. TeraPCA can be applied both in-core and out-of-core and is able to successfully operate even on commodity hardware with a system memory of just a few gigabytes. Moreover, TeraPCA has minimal dependencies on external libraries and only requires a working installation of the BLAS and LAPACK libraries. When applied to a dataset containing a million individuals genotyped on a million markers, TeraPCA requires <5 h (in multi-threaded mode) to accurately compute the 10 leading principal components. An extensive experimental analysis shows that TeraPCA is both fast and accurate and is competitive with current state-of-the-art software for the same task. Availability and implementation Source code and documentation are both available at https://github.com/aritra90/TeraPCA. Supplementary information Supplementary data are available at Bioinformatics online.

Peloponnese has been one of the cradles of the Classical European civilization and an important contributor to the ancient European history. It has also been the subject of a controversy about the ancestry of its population. In a theory hotly debated by scholars for over 170 years, the German historian Jacob Philipp Fallmerayer proposed that the medieval Peloponneseans were totally extinguished by Slavic and Avar invaders and replaced by Slavic settlers during the 6th century CE. Here we use 2.5 million single-nucleotide polymorphisms to investigate the genetic structure of Peloponnesean populations in a sample of 241 individuals originating from all districts of the peninsula and to examine predictions of the theory of replacement of the medieval Peloponneseans by Slavs. We find considerable heterogeneity of Peloponnesean populations exemplified by genetically distinct subpopulations and by gene flow gradients within Peloponnese. By principal component analysis (PCA) and ADMIXTURE analysis the Peloponneseans are clearly distinguishable from the populations of the Slavic homeland and are very similar to Sicilians and Italians. Using a novel method of quantitative analysis of ADMIXTURE output we find that the Slavic ancestry of Peloponnesean subpopulations ranges from 0.2 to 14.4%. Subpopulations considered by Fallmerayer to be Slavic tribes or to have Near Eastern origin, have no significant ancestry of either. This study rejects the theory of extinction of medieval Peloponneseans and illustrates how genetics can clarify important aspects of the history of a human population.

India represents an intricate tapestry of population substructure shaped by geography, language, culture and social stratification. While geography closely correlates with genetic structure in other parts of the world, the strict endogamy imposed by the Indian caste system and the large number of spoken languages add further levels of complexity to understand Indian population structure. To date, no study has attempted to model and evaluate how these factors have interacted to shape the patterns of genetic diversity within India. We merged all publicly available data from the Indian subcontinent into a dataset of 891 individuals from 90 well-defined groups. Bringing together geography, genetics and demographic factors, we developed COGG (Correlation Optimization of Genetics and Geodemographics) to build a model that explains the observed population genetic substructure. We show that shared language along with social structure have been the most powerful forces in creating paths of gene flow in the subcontinent. Furthermore, we discover the ethnic groups that best capture the diverse genetic substructure using a ridge leverage score statistic. Integrating data from India with a dataset of additional 1,323 individuals from 50 Eurasian populations we find that Indo-European and Dravidian speakers of India show shared genetic drift with Europeans, whereas the Tibeto-Burman speaking tribal groups have maximum shared genetic drift with East Asians.

The effect of a diffusivity edge is studied in a system of scalar active matter confined by a periodic potential and driven by an externally applied force. We find that this system shows qualitatively distinct stationary regimes depending on the amplitude of the driving force with respect to the potential barrier. For small driving, the diffusivity edge induces a transition to a condensed phase analogous to the Bose–Einstein-like condensation reported for the nondriven case, which is characterized by a density-independent steady state current. Conversely, large external forces lead to a qualitatively different phase diagram since in this case condensation is only possible beyond a given density threshold, while the associated transition at higher densities is found to be reentrant.

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