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3D surfaces based on the Archimedes' spiral are widely used in mechanical engineering, especially in the manufacturing the gear milling cutters. The machining process to create this type of surface is usually performed in specialized machines. In this study, relieving grinding process was conducted to machine the Archimedes surface of HSS P18 workpiece material using a specialized machine (1Б811) to investigate the influence of the grinding wheel graininess (G), hardness of grinding wheel (Hd), grinding wheel velocity (V), and feedrate (s) on surface quality including surface roughness (Ra) and surface hardening (ΔHRC). The experimental plan with 27 experiments (L27) was designed using the Taguchi method. Applying the analysis of variance (ANOVA), the influence of G, V, s, and Hd on Ra and ΔHRC was investigated. G, V, s, and Hd have different influences on Ra and ΔHRC in the relieving grinding process. V has the greatest influence on Ra and ΔHRC with 40.96% for Ra and 26.43% for ΔHRC. The grinding wheel hardness that has the lowest influence on Ra (0.82%), whereas the feedrate has a negligible effect on ΔHRC (7.01%). The interaction effect of the input parameters on Ra is not significant (2.91%). However, for ΔHRC, the interaction influence degree of these parameters on this criterion is quite high (33.77%). From the experimental data, Ra and ΔHRC were presented as a quadratic function of G, V, s, and Hd with high values of determination coefficient (R2 = 92.75% for Ra and R2 = 92.00% for ΔHRC). In the surveyed range of the input parameters, Ra decreases if G and V increase, and s decreases. Also in this survey range, the hardening increases if the values of the input parameters (G, V, and s) increase. This study also determined that there is no clear rule about the relationship between Ra and ΔHRC. Further studies need to be carried out to find the input optimal values ensuring the quality criteria of the relieving grinding process. [ABSTRACT FROM AUTHOR]

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]

Essential tremor (ET) is the most common movement disorder. In fact, its prevalence is about 20 times higher than that of Parkinson's disease. In addition, studies have shown that a high percentage of cases, between 50 and 70%, are estimated to be of genetic origin. The gold standard test for diagnosis, monitoring and to differentiate between both pathologies is based on the drawing of the Archimedes' spiral. Our major challenge is to develop the simplest system able to correctly classify Archimedes' spirals, therefore we will exclusively use the information of the x and y coordinates. This is the minimum information provided by any digitizing device. We explore the use of features from drawings related to the Discrete Cosine Transform as part of a wider cross-study for the diagnosis of essential tremor held at Biodonostia. We compare the performance of these features against other classic and already analyzed ones. We outperform previous results using a very simple system and a reduced set of features. Because the system is simple, it will be possible to implement it in a portable device (microcontroller), which will receive the x and y coordinates and will issue the classification result. This can be done in real time, and therefore without needing any extra job from the medical team. In future works these new drawing-biomarkers will be integrated with the ones obtained in the previous Biodonostia study. Undoubtedly, the use of this technology and user-friendly tools based on indirect measures could provide remarkable social and economic benefits.

Essential tremor (ET) is the most common movement disorder. In fact, its prevalence is about 20 times higher than that of Parkinson's disease. In addition, studies have shown that a high percentage of cases, between 50 and 70%, are estimated to be of genetic origin. The gold standard test for diagnosis, monitoring and to differentiate between both pathologies is based on the drawing of the Archimedes' spiral. Our major challenge is to develop the simplest system able to correctly classify Archimedes' spirals, therefore we will exclusively use the information of the x and y coordinates. This is the minimum information provided by any digitizing device. We explore the use of features from drawings related to the Discrete Cosine Transform as part of a wider cross-study for the diagnosis of essential tremor held at Biodonostia. We compare the performance of these features against other classic and already analyzed ones. We outperform previous results using a very simple system and a reduced set of features. Because the system is simple, it will be possible to implement it in a portable device (microcontroller), which will receive the x and y coordinates and will issue the classification result. This can be done in real time, and therefore without needing any extra job from the medical team. In future works these new drawing-biomarkers will be integrated with the ones obtained in the previous Biodonostia study. Undoubtedly, the use of this technology and user-friendly tools based on indirect measures could provide remarkable social and economic benefits. [ABSTRACT FROM AUTHOR]

Biomedical systems produce biosignals that arise from interaction mechanisms. In a general form, those mechanisms occur across multiple scales, both spatial and temporal, and contain linear and non-linear information. In this framework, entropy measures are good candidates in order provide useful evidence about disorder in the system, lack of information in time-series and/or irregularity of the signals. The most common movement disorder is essential tremor (ET), which occurs 20 times more than Parkinson's disease. Interestingly, about 50%-70% of the cases of ET have a genetic origin. One of the most used standard tests for clinical diagnosis of ET is Archimedes' spiral drawing. This work focuses on the selection of non-linear biomarkers from such drawings and handwriting, and it is part of a wider cross study on the diagnosis of essential tremor, where our piece of research presents the selection of entropy features for early ET diagnosis. Classic entropy features are compared with features based on permutation entropy. Automatic analysis system settled on several Machine Learning paradigms is performed, while automatic features selection is implemented by means of ANOVA (analysis of variance) test. The obtained results for early detection are promising and appear applicable to real environments. [ABSTRACT FROM AUTHOR]

Abstract: Several ways of interleaving, as studied in theoretical computer science, and some subjects from mathematics can be modeled by length-preserving operations on strings, that only permute the symbol positions in strings. Each such operation gives rise to a family of similar permutations. We call an integer -prime if consists of a single cycle of length ( ). For some instances of –such as shuffle, twist, operations based on the Archimedes’ spiral and on the Josephus problem–we investigate the distribution of -primes and of the associated (ordinary) prime numbers, which leads to variations of some well-known conjectures on the density of certain sets of prime numbers. [Copyright &y& Elsevier]

In NC machining of noncircular contours with a rotation table, the cutter is fed along a straight line intersecting perpendicularly the rotation axis of the work piece. In this situation, the cutter path usually consists of a series of Archimedes’ spiral segments. This paper proposes an optimal interpolation approach of Archimedes’ spiral segments to generate the cutter path for machining noncircular contours. The number of segments for the cutter path resulted from the approach is the fewest under the condition that the interpolation accuracy completely satisfies the specified limit value. It has been also evidenced that the profile error of the machined contours corresponding to the cutter path is perfectly controlled within the specified interpolation accuracy limit. The effectiveness of the proposed approach has been sufficiently confirmed by applying it to machining a disc cam and an algebraic spiral type of scroll wrap. [ABSTRACT FROM AUTHOR]

Abstract: We present a simple method for creating artistic space-filling designs based on spiral packings. Connected spiral sets are generated by successively branching child spirals from parent spirals, constrained to fit nearby neighbors in their environment. The underlying geometry is discussed in detail and a number of color examples generated by the algorithm are given. [Copyright &y& Elsevier]