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In this work, the method of drawing of nine celebrated Minoan Late Bronze Age wall-paintings, is studied. Four of these frescoes were unearthed at Akrotiri, Thera, while the other five were excavated in Crete; these frescoes have never been thoroughly studied before, concerning their method of drawing. The authors demonstrate that practically all actually drawn contours in these frescoes, optimally fit six geometric stencilsguides, namely, four hyperbolae and two Archimedes' (linear) spirals. It is important to note that the hyperbola and the linear spiral do not exist in nature, definitely not with the precision encountered here. We would like to stress that all wall-paintings the authors have studied so far, i.e. more than twenty-five (25), had been drawn via the use of the same stencils, a fact that renders the eventuality that this was indeed the method of drawing of these frescoes, almost certain. The considered wall-paintings cover a period of at least two centuries, located both before and after the gigantic eruption of Thera volcano. Moreover, here, possible methods of construction of the determined stencils are proposed, as well as the most probable one, according to our opinion. Methodologically, the authors determine couples of the longest contour parts, CP, appearing in the studied frescoes and of a proper sub-curve GPopt of one of the aforementioned stencils; these couples are chosen so as they fit with exceptionally low approximation errors. The latter terms are rigorously defined here, for the first time. Special care is taken, mathematically and programmatically, to ensure the maximum possible smoothness between successive optimally fit stencils' parts GPopt. Next, the authors employed these modern prerequisites, to introduce the more probable sequence of actions taken by the prehistoric artist(s) for drawing the specific frescoes. Finally, crucial queries and conjectures are set, together with a number of plausible answers. [ABSTRACT FROM AUTHOR]

A research team at Akrotiri, Thera, here examine the Bronze Age frescoes and show that the artists were making use of templates of well known geometric curves. Some of the spirals, hyperbolae and ellipses which all feature in the repertoire do not occur in nature and must have their origin in some still unknown human science or aesthetic. Keywords: Aegean, Crete, Thera, Cyclades, Bronze Age, wall-painting, fresco, images, geometry, Introduction The Cycladic islands in the central Aegean were home to a distinctive culture throughout the entire third millennium BC, the hallmark of which are the Early Cycladic figurines, masterpieces […]

A new recursive least squares (RLS) adaptive algorithm is proposed. The suggested computational methodology employs a finite window by means of a lemma for the system matrix inversion that is stated and proven for the first time. The algorithm has excellent tracking capabilities. Also, its particular structure permits stabilization through a simple method. Its stabilized version performs well not only for a white noise input but also for nonstationary inputs as well.

Two finite precision error sources were identified when an algorithm was used to solve LS FIR filtering and l-step ahead prediction problems. The first source was associated with the formulae used in FIR filtering and l-step ahead prediction problems, while the second source was connected with the numerical error produced in the FIR's problem solution. FIR filtering and l-step ahead prediction are crucial to time series analysis, communications, geophysics and system identification.

This paper studies a set of wall-paintings of the Late Bronze Age (c. 1650bc) initially decorating the internal walls of the third floor of the edifice called ‘Xeste 3’, excavated at Akrotiri, Thera, whose restoration is now in progress. It deals with the methods used for the drawing of the geometrical figures appearing in these wall-paintings. It is demonstrated that most of the depicted configurations correspond with accuracy to geometrical prototypes such as linear spirals and canonical polygons. It is pointed out that the steady lines of the figures, their remarkable repeatability, the precision of the geometrical shapes and their even distribution in the wall-paintings indicate a very distinctive use of the ‘Xeste 3’ third floor, which is now investigated. [ABSTRACT FROM AUTHOR]

The exact and actual cause of the failure of the fast-Kalman algorithm due to the generation and propagation of finite-precision or quantization error is presented. It is demonstrated that out of all the formulas that constitute this fast Recursive Least Squares (RLS) scheme only three generate an amount of finite-precision error that consistently propagates in the subsequent iterations and eventually makes the algorithm fail after a certain number of recursions. Moreover, it is shown that there is a very limited number of specific formulas that transmit the generated finite-precision error, while there is another class of formulas that lift or "relax" this error. In addition, a number of general propositions is presented that allow for the calculation of the exact number of erroneous digits with which the various quantities of the fast-Kalman scheme are computed, including the filter coefficients. On the basis of the previous analysis a method of stabilization of the fast-Kalman algorithm is developed and is presented here, a method that allows for the fast-Kalman algorithm to follow very difficult signals such as music, speech, environmental noise, and other nonstationary ones. Finally, a general methodology is pointed out, that allows for the development of new algorithms which, intrinsically, suffer far less of finite-precision problems.

A novel methodology is introduced here that exploits 2D images of arbitrary elastic body deformation instances so as to quantify mechanoelastic characteristics that are deformation invariant. Determination of such characteristics allows for developing methods offering an image of the undeformed body. General assumptions about the mechanoelastic properties of the bodies are stated which lead to two different approaches for obtaining bodies' deformation invariants. One was developed to spot a deformed body's neutral line and its cross sections, while the other solves deformation PDEs by performing a set of equivalent image operations on the deformed body images. Both of these processes may furnish a body-undeformed version from its deformed image. This was confirmed by obtaining the undeformed shape of deformed parasites, cells (protozoa), fibers, and human lips. In addition, the method has been applied to the important problem of parasite automatic classification from their microscopic images. To achieve this, we first apply the previous method to straighten the highly deformed parasites, and then, apply a dedicated curve classification method to the straightened parasite contours. It is demonstrated that essentially different deformations of the same parasite give rise to practically the same undeformed shape, thus confirming the consistency of the introduced methodology. Finally, the developed pattern recognition method classifies the unwrapped parasites into six families, with an accuracy rate of 97.6 percent.