The geometry and construction of Byzantine vaults: the fundamental contribution of Auguste Choisy

In 1883 Auguste Choisy published his book L=art de bâtir chez les Byzantins. In it he explained, for the first time, all the details of the geometry and construction of byzantine vaults. The main source was the direct study of the monuments, interpreting his observations in the light of traditional vaulting techniques. He is explicit about this: *ma seule ressource était d'interroger les monuments eux mêmes, ou mieux encore de rapprocher les uns des autres les faits anciens et les traditions contemporaines+ (Choisy 1883, 3). Choisy concentrated his attention on the vaults, as he was convinced that the vault governs the whole architectural system: *Toutes les circonstances de la construction découlent ainsi de la nature de la voûte byzantine; et j'ai cru qu'il convenait de ranger les faits autour de cet élément fondamental du système+ (4). The other fundamental principle is the economy of construction, as the vaults *. . .s'y subordonnent dans l'économie générale des édifices+. The observations were made during a six month mission of the Adminiatration des des Ponts et Chaussées the year 1875 (Mandoul 2008, 29). The next year he published a *Note sur la construction des voûtes sans cintrage pendant la période byzantine+ (Choisy 1876), were he resumed the main results concerning the technique of vaulting without centring. The book had an enormous impact on contemporary historians of byzantine architecture. It was cited and praised by the new light it threw to the constructive aspects, for its clarity and rigour of exposition, and for their superb plates. Eventually, his theories were incorporated in the manuals and histories of Byzantine architecture. The book of Choisy concentrated on *l=art de bâtir+. The interest on the technical aspects of architecture almost disappeared after the First World War, maybe due to the coming of the modern architecture and the new materials (iron, steel and reinforced concrete). As a concequence Choisy=s works on *l=art de bâtir+ were almost systematically ignored. The first specifical study of Byzantine construction after the Second World Ward was written by Ward-Perkins (1958) and it has been considered, since then, the standard reference for Byzantine construction. Ward-Perkins ignore the work of Choisy making a passing criticism of his geometrical theories of Byzantine vaults. However, the detailed description of wall construction made by Ward-perkins coincides pretty well with that of Choisy (7-13). He apparently was unaware that the whole theory of Byzantine vaulting without theory centring is Choisy=s. Besides, he attributes to Giovanonni the detailed description of the use brick ribs in vaults construction. In all, it appears that Ward-Perkins did not read carefully Choisy=s book on Byzantine construction nor was familiar with the history of vault construction. The consquence was that subsequent authors didn=t take seriously Choisy=s work or simply ignored. Sanpaolesi (1971) in a work with the suggestive title *Strutture a cupola autoportanti+ simply ignore him. To Mango (1975), author of one of the standard manuals on Byzantine architecture, Choisy is superseded; Krautheimer (1984) did not consider Choisy in treating, summarily, the vaulting problems. Robert Ousterhout author of a book on the Master Builders of Byzantium (1998) considers Choisy *outdated+, being *more than a century old+. Even in detailed archeological studies of vaulted structures his work is ignored (Deichmann 1979). There are some exceptions in specialised studies on vault construction: Besenval (1984), Cejka (1978) and Storz (1994). It must be said from the beginning, that Choisy=s L=art de bâtir chez les Byzantins is still the best source for anyone interested in understanding the geometry, construction and structural behaviour of Byzantine vaulted buildings. In what follows, we will try to demonstrate that this assertion is true

RSA: Byzantine-Robust Stochastic Aggregation Methods for Distributed Learning from Heterogeneous Datasets

In this paper, we propose a class of robust stochastic subgradient methods for distributed learning from heterogeneous datasets at presence of an unknown number of Byzantine workers. The Byzantine workers, during the learning process, may send arbitrary incorrect messages to the master due to data corruptions, communication failures or malicious attacks, and consequently bias the learned model. The key to the proposed methods is a regularization term incorporated with the objective function so as to robustify the learning task and mitigate the negative effects of Byzantine attacks. The resultant subgradient-based algorithms are termed Byzantine-Robust Stochastic Aggregation methods, justifying our acronym RSA used henceforth. In contrast to most of the existing algorithms, RSA does not rely on the assumption that the data are independent and identically distributed (i.i.d.) on the workers, and hence fits for a wider class of applications. Theoretically, we show that: i) RSA converges to a near-optimal solution with the learning error dependent on the number of Byzantine workers; ii) the convergence rate of RSA under Byzantine attacks is the same as that of the stochastic gradient descent method, which is free of Byzantine attacks. Numerically, experiments on real dataset corroborate the competitive performance of RSA and a complexity reduction compared to the state-of-the-art alternatives.Comment: To appear in AAAI 201

Byzantine Attack and Defense in Cognitive Radio Networks: A Survey

The Byzantine attack in cooperative spectrum sensing (CSS), also known as the spectrum sensing data falsification (SSDF) attack in the literature, is one of the key adversaries to the success of cognitive radio networks (CRNs). In the past couple of years, the research on the Byzantine attack and defense strategies has gained worldwide increasing attention. In this paper, we provide a comprehensive survey and tutorial on the recent advances in the Byzantine attack and defense for CSS in CRNs. Specifically, we first briefly present the preliminaries of CSS for general readers, including signal detection techniques, hypothesis testing, and data fusion. Second, we analyze the spear and shield relation between Byzantine attack and defense from three aspects: the vulnerability of CSS to attack, the obstacles in CSS to defense, and the games between attack and defense. Then, we propose a taxonomy of the existing Byzantine attack behaviors and elaborate on the corresponding attack parameters, which determine where, who, how, and when to launch attacks. Next, from the perspectives of homogeneous or heterogeneous scenarios, we classify the existing defense algorithms, and provide an in-depth tutorial on the state-of-the-art Byzantine defense schemes, commonly known as robust or secure CSS in the literature. Furthermore, we highlight the unsolved research challenges and depict the future research directions.Comment: Accepted by IEEE Communications Surveys and Tutoiral

Bloomsbury\u27s Byzantium and the Writing of Modern Art

“Bloomsbury’s Byzantium and the Writing of Modern Art” examines the role of Byzantine art in Bloomsbury art critics Roger Fry’s and Clive Bell’s narratives of aesthetic Modernism. Fry, in his pre-World War I and interwar writings and teachings on art, and Bell, in seminal texts such as Art (1914), have been branded by art historiography as the prime movers in a Formalist, teleological narrative of Modern art still prevalent in textbooks today. Fry’s and Bell’s ideas were later adopted by important Modernist authors and cultural figures, such as Alfred H. Barr, Jr., first director of New York’s Museum of Modern Art, and critic Clement Greenberg. Yet, less known is the integral role Byzantine art played in delimiting both Fry’s and Bell’s ideas of Modernism, and the art works they valued. Consistent with the international nineteenth- and twentieth-century interest in Byzantium, Fry and Bell each crafted an ahistorical idea of Byzantium. The Bloomsbury critics’ highly subjective definitions of Byzantine art and the Byzantine era allowed both Fry and Bell to project onto Byzantium qualities that aligned with their own intellectual interests. My dissertation uses these varied characterizations of Byzantium to reinterpret both authors’ writings on Modern art and subsequently to challenge canonical understanding of Western aesthetic Modernism. For instance, in my analysis of Fry’s and Bell’s idea of Byzantine art, I point to parallel qualities the critics’ valued in Modern pieces; and suggest that they used their concept of Byzantium to define a more secular, universalized spiritual conception of art as an alternative and counterpart to mainstream religions. I also explain how the critics relied on their definition of Byzantium to each advocate for non-Western art’s aesthetic value, and I demonstrate how the authors utilized their characterization of Byzantine art to contest the precedent of both John Ruskin and establishment, Western art history. This dissertation unravels the myriad personal, intellectual, and contextual circumstances which led to Fry’s and Bell’s interpretation of Byzantine art, and, as a result, illustrates how art-world politics and world politics of the late-nineteenth and early-twentieth centuries impacted the writing of formative texts in Western Modern art

Hesychasm and Art

“Although many of the iconographic traditions in Byzantine art formed in the early centuries of Christianity, they were not petrified within a time warp. Subtle changes and refinements in Byzantine theology did find reflection in changes to the iconographic and stylistic conventions of Byzantine art. This is a brilliant and innovative book in which Dr Anita Strezova argues that a religious movement called Hesychasm, especially as espoused by the great Athonite monk St Gregory Palamas, had a profound impact on the iconography and style of Byzantine art, including that of the Slav diaspora, of the late Byzantine period. While many have been attracted to speculate on such a connection, none until now has embarked on proving such a nexus. The main stumbling blocks have included the need for a comprehensive knowledge of Byzantine theology; a training in art history, especially iconological, semiotic and formalist methodologies; extensive fieldwork in Macedonia, Bulgaria, Serbia, Greece, Turkey and Russia, and a working knowledge of Greek, Old Church Slavonic, Macedonian, Russian, Serbian, Latin as well as several modern European languages, French, German, Russian and Italian. These are some of the skills which Dr Strezova has brought to her topic.” Professor Sasha Grishin AM, FAHA Adjunct Professor of Art History School of Literature, Languages and Linguistics The Australian National Universit

James, Liz. Light and Color in Byzantine Art

James\u27 title coupled with the generous number of color illustrations in her text led me to assume that she would survey Byzantine art in more traditional terms of light and color. Instead, the book pursues the perceptual repercussions of color in Byzantine art and is based on James\u27 dissertation, Colour Perception in Byzantium (University of London, 1989)

Byzantine Muse

Colors, such as gold, turquoise, brass and black, found in Byzantine art were the inspiration for Byzantine Muse. The primary goal was to design an evening gown that exuded the aesthetics, color wise of the time period