Ancient DNA reveals admixture history and endogamy in the prehistoric Aegean.

The Neolithic and Bronze Ages were highly transformative periods for the genetic history of Europe but for the Aegean-a region fundamental to Europe's prehistory-the biological dimensions of cultural transitions have been elucidated only to a limited extent so far. We have analysed newly generated genome-wide data from 102 ancient individuals from Crete, the Greek mainland and the Aegean Islands, spanning from the Neolithic to the Iron Age. We found that the early farmers from Crete shared the same ancestry as other contemporaneous Neolithic Aegeans. In contrast, the end of the Neolithic period and the following Early Bronze Age were marked by 'eastern' gene flow, which was predominantly of Anatolian origin in Crete. Confirming previous findings for additional Central/Eastern European ancestry in the Greek mainland by the Middle Bronze Age, we additionally show that such genetic signatures appeared in Crete gradually from the seventeenth to twelfth centuries BC, a period when the influence of the mainland over the island intensified. Biological and cultural connectedness within the Aegean is also supported by the finding of consanguineous endogamy practiced at high frequencies, unprecedented in the global ancient DNA record. Our results highlight the potential of archaeogenomic approaches in the Aegean for unravelling the interplay of genetic admixture, marital and other cultural practices.

Optimization in differentiable manifolds in order to determine the method of construction of prehistoric wall paintings.

In this paper, a general methodology is introduced for the determination of potential prototype curves used for the drawing of prehistoric wall paintings. The approach includes 1) preprocessing of the wall-paintings contours to properly partition them, according to their curvature, 2) choice of prototype curves families, 3) analysis and optimization in 4-manifold for a first estimation of the form of these prototypes, 4) clustering of the contour parts and the prototypes to determine a minimal number of potential guides, and 5) further optimization in 4-manifold, applied to each cluster separately, in order to determine the exact functional form of the potential guides, together with the corresponding drawn contour parts. The methodology introduced simultaneously deals with two problems: 1) the arbitrariness in data-points orientation and 2) the determination of one proper form for a prototype curve that optimally fits the corresponding contour data. Arbitrariness in orientation has been dealt with a novel curvature based error, while the proper forms of curve prototypes have been exhaustively determined by embedding curvature deformations of the prototypes into 4-manifolds. Application of this methodology to celebrated wall paintings excavated at Tyrins, Greece, and the Greek island of Thera manifests that it is highly probable that these wall paintings were drawn by means of geometric guides that correspond to linear spirals and hyperbolae. These geometric forms fit the drawings' lines with an exceptionally low average error, less than 0.39 mm. Hence, the approach suggests the existence of accurate realizations of complicated geometric entities more than 1,000 years before their axiomatic formulation in the Classical Ages.