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 a) preprocessing of the wall-paintings contours to properly partition them, according to their curvature, b) choice of prototype curves families, c) analysis and optimization in 4-manifold for a first estimation of the form of these prototypes, d) clustering of the contour parts and the prototypes, to determine a minimal number of potential guides, e) 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 introduced methodology simultaneously deals with two problems: a) the arbitrariness in data-points orientation and b) 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 it is highly probable that these wall-paintings had been 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 0.39mm. Hence, the approach suggests the existence of accurate realizations of complicated geometric entities, more than 1000 years before their axiomatic formulation in Classical Ages

Timing is everything:radiocarbon dating multiple levels in the Mycenaean tholos tomb of Petroto, Achaia, Greece

Reuse in Mycenaean tholoi (bee-hive shaped tombs) has been studied for centuries. Initially, bodies are interred on tomb floors, but moved after decomposition to make space for later burials. Extensive reuse can produce burial levels that are poorly understood often due to a lack of absolute dating. The Petroto tholos is a prime case study for dating multiple burial levels because all eight levels were sequential as later burials did not disturb previous depositions. The initial burial phase has been dated by ceramic chronology to the Late Helladic IIB-IIIA (ca. 1440–1400 BC). Radiocarbon dating of human bone samples yield for Level 7 (middle burial level) 3105 +/− 35 BP (1420–1305 cal BC) and for Level 3 (final burial) 2965 +/− 35 BP (1255–1120 cal BC). The ceramic and radiocarbon dates show that the tomb was used over for approximately 300 years during the Mycenaean period and never used again

16. Human Heads and Crawling Snakes: Ritual Vases in Postpalatial Mycenae

Continuous habitation and extensive fieldwork in the pioneering days of Mycenaean research, plus the splendor of the Shaft Graves and the legend of palatial Mycenae, have left little space for understanding the Postpalatial period. The ritual vessels presented here come from no stratified deposits and it is hard to specify their date and function. Their features however, jugs with human heads and a ring vase with crawling snakes, belong to an idiom known in the Mainland or Crete in LH IIIC. L..

RA-PI-NE-U

This volume, in honour of one of the Odysseuses in Aegean archaeology, Professor Robert Laffineur, comprises a combination of papers presented during a seminar series on recent developments in Mycenaean archaeology at the Université de Louvain during the academic year 2015-2016. These were organised within the frame of the ARC13/18-049 (concerted research action) ’A World in Crisis?’To these are added a series of papers by friends of Robert Laffineur who were keen to offer a contribution to honour him foremost as a friend and scholar in his own right but also as editor of a respected international series founded by him - Aegaeum - and as the driving force and inspiration behind the biannual Aegean meetings that have travelled the world. Several papers within touch scientific domains close to Robert’s heart while others present new excavations or new interpretations of known data