The Role of the Greco-Roman Practice as a Progenitor of the Armenian and Eastern Roman Ornamental Art

We investigate two-dimensional, periodic ornaments of the Late Hellenistic (some centuries before the Common Era, the Classical Period) and Early Roman (Common Era) classical periods found at different locations in Asia Minor in Turkey and classify them into mathematical wallpaper groups based on their symmetry properties. The source material comes from Terrace Houses in Ephesus, Izmir, from Zeugma, now in the Zeugma Museum, Gaziantep, and from the recently released bathing pool in Antiochia ad Cragum near Gazipa\c{s}a, Antalya. Using the artifacts we first determine the occurrence of each symmetry group. Then we compare this distribution with those of the medieval cultures of the Middle East, namely the Armenian, Byzantine, Arab and Seljuk Turks, calculating in pairs the Euclidean distances of the wallpaper distributions. The subsequent multi-dimensional scaling and hierarchical cluster analysis of the results confirm that the Armenian and Byzantine artworks are strongly inspired by the classical masterpieces, as is the Seljuk creation by the Arabs.Comment: 13 pages, 5 figure

Tracking tumor evolution via prostate-specific antigen: an individual post-operative study

<p>Abstract</p> <p>Background</p> <p>The progress of the prostate-specific antigen (PSA) level after radical prostatectomy is observed for a patient in order to extract information about the mode of tumor cell growth. Although PSA values are determined routinely to find the doubling time of the prostate marker, to our knowledge, this analysis is the first in the literature.</p> <p>Results</p> <p>The prostate tumor marker values were determined regularly after the surgery and plotted on a logarithmic scale against time. An initial rapid-growth mode changed to a slower power-law regime within two years of surgery. Our analysis associates this observation with a transition in the growth mode from unrestricted growth of dispersed cells to their clumping into macroscopic structures.</p> <p>Conclusions</p> <p>Such studies may help determine the appropriate time window for postoperative therapies in order to increase the life expectancy of the patient.</p

Mathematical Determination of the Cultural Interaction between Medieval Groups

A mathematical classification of two-dimensional ornaments into 17 plane symmetry groups is presented, which were created by five medieval cultural groups of Middle East. The data are considered representative for the cultural groups. By applying a correlation algorithm on the individual use of symmetry classes by each cultural group, the strength of the interaction between the pairs of groups are quantitatively determined. The analysis shows that the strongest similarity in the creation of periodic ornaments is between Rum Seljuks and Arab Muslims. It is also found that the Rum Seljuks, followed by Armenians, are the most interactive cultures. This report is the first attempt to quantify cultural communication by mathematical means.ISSN:2636-869

Bezemelerin simetrilerinde saklı olan ortaçağ kültür ilişkileri

We trace the culture on the mosaics of seven medieval civilizations by taking the symmetry of the ornaments found on the mosaics as characteristic evidence for the cultural group in which the artwork is created. We classify the ornaments into 17 wallpaper groups according to their symmetry. Applying the cosine law to the frequency of each symmetry group we calculate the pairwise correlation of the cultural interactions. Finally, a hierarchical cluster analysis is performed on the correlations to find cultural groups that are closely related to each other. The results show the formation of two clusters: The Islamic cluster includes the Arabs and the Seljuk dynasties. The Hellenistic group inspired other Anatolian civilizations and even influenced the Umayyads in Andalusia. These results are consistent with the calculations based on multidimensional scaling. Our work demonstrates the possibility of applying symmetry analysis and statistical methods to the visual arts to reveal valuable details such as the hidden influences in art practice.Mozaiklerde bulunan bezemelerin simetrilerini kullanarak, yedi Ortaçağ uygarlığının kültürel izlerini gözlemliyoruz. Simetrileri, sanat eserinin yaratıldığı kültürün bir özelliği olarak değerlendiriyoruz. Öncelikle iki boyutlu periyodik bezemeleri simetrilerine göre 17 Wallpaper grubuna ayırıyor ve her uygarlık için simerti gruplarının kullanım sıklığını sayısal olarak belirliyoruz. Bu değerlere kosinüs yöntemini uygulayarak, her bir topluluk çifti için bir tane olmak üzere, uygarlıklar arasındaki ilişkileri gösteren toplam 21 korelasyon sayısı elde ediyoruz. Bu korelasyon sayılarına uygulanan hiyerarşik kümeleme tekniği, uygarlıkların birbirlerine yakınlaştıkları iki ana kümeyi ortaya çıkarıyor: Birincisi Araplar ve Selçukluların yer aldığı İslam kümesi, ikincisi ise etkisini Anadolu’da olduğu kadar ilginç olarak Endülüs’te de belli eden HelenRoma grubu. Uyguladığımız çok boyutlu ölçekleme yöntemi sonuçları desteklemektedir. Böylece matematiğin değişik dallarından esinlenen simetri analizi ve istatistiksel yöntemler yardımıyla, farklı uygarlıkların sanat eserlerindeki simetrileri incelemiş ve uygarlıklar arasındaki sanatsal etkileşmeleri bulma yolunda yenilikçi bir adım atmış oluyoru

Cultural Interactions of Medieval Societies Hidden in The Symmetry of Ornaments

We trace the culture on the mosaics of seven medieval civilizations by taking the symmetry of the ornaments found on the mosaics as characteristic evidence for the cultural group in which the artwork is created. We classify the ornaments into 17 wallpaper groups according to their symmetry. Applying the cosine law to the frequency of each symmetry group we calculate the pairwise correlation of the cultural interactions. Finally, a hierarchical cluster analysis is performed on the correlations to find cultural groups that are closely related to each other. The results show the formation of two clusters: The Islamic cluster includes the Arabs and the Seljuk dynasties. The Hellenistic group inspired other Anatolian civilizations and even influenced the Umayyads in Andalusia. These results are consistent with the calculations based on multidimensional scaling. Our work demonstrates the possibility of applying symmetry analysis and statistical methods to the visual arts to reveal valuable details such as the hidden influences in art practice.ISSN:1309-047XISSN:2619-916

Symmetry of planar ornaments in hellenic through seljuk ages

Planar ornaments of medieval civilizations are classified in terms of 17 wallpaper groups. The calculated correlations place the civilizations in two main clusters.ISSN:0865-4824ISSN:2226-187

Mathematical Determination of the Cultural Interaction between Medieval Groups

A mathematical classification of two-dimensional ornaments into 17 plane symmetry groups is presented, which were created by five medieval cultural groups of Middle East. The data are considered representative for the cultural groups. By applying a correlation algorithm on the individual use of symmetry classes by each cultural group, the strength of the interaction between the pairs of groups are quantitatively determined. The analysis shows that the strongest similarity in the creation of periodic ornaments is between Rum Seljuks and Arab Muslims. It is also found that the Rum Seljuks, followed by Armenians, are the most interactive cultures. This report is the first attempt to quantify cultural communication by mathematical means.ISSN:2636-869

The Origins of Seljuk Ornamental Art in Anatolia

The Seljuks, who came from the Central Asian prairies, invaded Asia Minor towards the end of the 11th century. The land had been settled by then mainly by the Christian Eastern Romans and Armenian peoples. Seljuks were Moslems; they built monumental structures, some of which have survived the natural disasters of several centuries to the present day. Most of these architectural marvels contain extraordinary decorations in the form of ornaments, friezes and rosettes. I have studied periodic ornaments and classified them into 17 mathematical wallpaper groups according to their symmetry properties that reveal their global structure. On the other hand, the local details of the ornaments, the motifs, show a clear variation from simple geometric patterns to complicated and refined forms. Seljuk art was originally influenced by Persian styles, later influenced by the Christian population in Asia Minor, and finally represents the impact of Islamic culture

Similarity in Symmetry Groups of Ornaments as a Measure for Cultural Interactions in Medieval Times

The symmetry properties of an ornament contain information about its civilisation and its interactions with other cultural sources. Two-dimensional periodic ornaments can be strictly classified into a limited set of 17 mathematical symmetry groups, also known as wallpaper groups. The collection of ornaments thus classified for a civilisation is characteristic of the cultural group and serves as a fingerprint to identify that group. If the distribution of wallpaper groups is available for several societies, mathematical methods can be applied to determine similarities and differences between the art practices of these communities. This method allows a systematic approach to the general ornamental practices within a culture and their interactions in the form of similarity of fingerprints. We test the feasibility of the method on examples of medieval Armenians, Byzantium, Seljuks first in Persia and then in Anatolia and among Arabs in the Middle East. For this purpose we present the distribution of the planar ornaments and calculate the Euclidean distances in pairs. We tested to what extend geographical and religious factors could account for the observed similarity of ornamental groups between cultures. The results suggest an intensive interaction between the Seljuk Turks and Arab craftsmen who produced the ornaments. Therefore the cultural interactions are religiously motivated