Breathless Beasts and Stuffed Savages

This chapter takes the reader deep into the nineteenth-century afterlife of the Classical construction of nature, the wild, and the primitive and civilized, foundational to Victorian ideas of progress and to the nascent sciences that claimed the study of humanity as their own. It shows how the Natural History Courts of London’s Crystal Palace presented the marvels of ethnology and natural history, and how these displays were received in the context of nineteenth-century social evolutionist thought, which was itself built upon Classical foundations such as the account of primitive man in Lucretius’ De rerum natura. Against the Courts’ taxidermic dioramas of ‘savage life’, the ethnological casts displayed to the Victorian public prompted comparative questions about the evolutionary status of the non-European Other, while the ‘primitive’ nakedness of the casts created further parallels with the idealized nudity of Greek and Roman sculpture casts, engendering destabilizing dissonance with the connotations of civilization inscribed in the Classical ideal.

On the State Approach Representations of Convolutional Codes over Rings of Modular Integers

In this study, we prove the existence of minimal first-order representations for convolutional codes with the predictable degree property over principal ideal artinian rings. Further, we prove that any such first-order representation leads to an input/state/output representation of the code provided the base ring is local. When the base ring is a finite field, we recover the classical construction, studied in depth by J. Rosenthal and E. V. York. This allows us to construct observable convolutional codes over such rings in the same way as is carried out in classical convolutional coding theory. Furthermore, we prove the minimality of the obtained representations. This completes the study of the existence of input/state/output representations of convolutional codes over rings of modular integers.

Comparison of the New Type Modular Panel for Green Roofs and Classical Construction of Green Roofs by Stormwater Management

Proper stormwater management is one of the main problems cities today face. In order to understand how to properly manage urban stormwater it is first necessary to construct roofs with new construction methods. The first step for controlling urban stormwater is the construction of green roofs. We already know that the construction of green roofs improves water management in cities. But can we make it better? What will happen if we use the same layers for the green roofs but with a different construction method? This article wants to answer these questions. In this article the two green roofs, differing in the construction method, are compared and contrasted in terms of stormwater management. One of the green roofs was built traditionally, while the other has been built using a new type of modular panel. The article then compares their results during laboratory tests. In the conclusion you can read about measured data from tests and possible solutions and development of solutions to improve green roofs in the future.

El Escorial – the Concept, the Image, and the Style of the Royal Residence of King Philip II

The paper explores the architecture of King Philip II royal residence. El Escorial monastery palace represents a system of art treasures of the Spanish Renaissance, manifested in the method of implementing the figurative absolutization of the Classical aesthetics, revealing the ideas of the magnificence of the “Roman spirit” of the Habsburg empire. By reinterpreting the legacy of the theory of architectural rules, El Escorial was the standard of classical construction in late 16th century Spain. The Christian ideas become the cement of the Empire governance. It is symbolic that the year of the completion of Trento Cathedral (1563) was also the year the construction of El Escorial had begun. The first executor of the project was the architect, philosopher, and mathematician Juan Bautista de Toledo, who studied in Rome and Naples under the masters of the Italian Renaissance. He was later replaced by Juan de Herrera, the acclaimed spokesman of the royal architectural style. The paper covers the most controversial issues: problems of the ensemble concept, their interpretations, the role of theoretical sources, biblical semantics, etc.

A non-Archimedean analogue of Teichmüller space and its tropicalization

In this article we use techniques from tropical and logarithmic geometry to construct a non-Archimedean analogue of Teichmüller space$$\overline{{{\mathcal {T}}}}_g$$ T ¯ g whose points are pairs consisting of a stable projective curve over a non-Archimedean field and a Teichmüller marking of the topological fundamental group of its Berkovich analytification. This construction is closely related to and inspired by the classical construction of a non-Archimedean Schottky space for Mumford curves by Gerritzen and Herrlich. We argue that the skeleton of non-Archimedean Teichmüller space is precisely the tropical Teichmüller space introduced by Chan–Melo–Viviani as a simplicial completion of Culler–Vogtmann Outer space. As a consequence, Outer space turns out to be a strong deformation retract of the locus of smooth Mumford curves in $$\overline{{\mathcal {T}}}_g$$ T ¯ g .

UNITY and Büchi automata

UNITY is a model for concurrent specifications with a complete logic for proving progress properties of the form “P leads to Q”. UNITY is generalized to U-specifications by giving more freedom to specify the steps that are to be taken infinitely often. In particular, these steps can correspond to non-total relations. The generalization keeps the logic sound and complete. The paper exploits the generalization in two ways. Firstly, the logic remains sound when the specification is extended with hypotheses of the form “F leads to G”. As the paper shows, this can make the logic incomplete. The generalization is used to show that the logic remains complete, if the added hypotheses “F leads to G” satisfy “F unless G”. The main result extends the applicability and completeness of UNITY logic to proofs that a given concurrent program satisfies any given formula of LTL, linear temporal logic, without the next-operator which is omitted because it is sensitive to stuttering. For this purpose, the program, written as a UNITY program, is extended with a number of boolean variables. The proof method relies on implementing the LTL formula, i.e., restricting the specification in such a way that only those runs remain that satisfy the formula. This result is a variation of the classical construction of a Büchi automatonfor a given LTL formula that accepts precisely those runs that satisfy the formula.

Forest and Labyrinth. Toward an Ecology of the Subject

The concept of the subject is articulated here as a correlation between two terms — movements and actions. Classical theories of action presupposed the subject as a unique way to correlate movements and actions and to translate the one into the other. The “soul,” i.e., a natural complex of cognitive and volitional abilities, was a reliable tool for that translation. However, the modern period faces the problem of “the failure of the soul,” which brings about the concept of the subject. Different ways of translating movements into actions do not always permit stable subjectification, which indicates that “transport” is a mediating term in the opposition of movements and actions. There is an intermediary region between the “physics” of movement and the “ethics” of action, and that region is the “logic” of transport which is to be understood as an open-ended collection of ways to correlate movements with actions. The problematic function of transport becomes clear when it is impossible to rely on the soul as a black box that is responsible for the stability in the translation of movements into actions. The solution to the problem of the failure of the soul appears particularly in Henry David Thoreau’s “forest,” which is constructed as a way to restore a classical ecology of the subject in the face of a proliferation of different modes of transport that threaten the uniformity of subjective experience. According to Roland Barthes’ seminar, the opposite of Thoreau’s “forest” would be the “labyrinth” as an anti-subject machine. The labyrinth is not merely a place of loss, but the production of loss that turns any movement into action or decision while at the same time cancelling any action and drawing the subject out of its own structure. Labyrinth and forest as alternatives to the classical construction of the subject delineate a general space for subjectification, which has problems that cannot be encompassed by theories of praxis.

PROJECTIVE LOOPS GENERATE RATIONAL LOOP GROUPS

We generalize Uhlenbeck’s generator theorem of ${\mathcal{L}}^{-}\operatorname{U}_{n}$ to the full rational loop group ${\mathcal{L}}^{-}\operatorname{GL}_{n}\mathbb{C}$ and its subgroups ${\mathcal{L}}^{-}\operatorname{GL}_{n}\mathbb{R}$ , ${\mathcal{L}}^{-}\operatorname{U}_{p,q}$ : they are all generated by just simple projective loops. Recall that Terng–Uhlenbeck studied the dressing actions of such projective loops as generalized Bäcklund transformations for integrable systems. Our result makes a nice supplement: any rational dressing is the composition of these Bäcklund transformations. This conclusion is surprising in the sense that Lie theory suggests the indispensable role of nilpotent loops in the case of noncompact reality conditions, and nilpotent dressings appear quite complicated and mysterious. The sacrifice is to introduce some extra fake singularities. So we also propose a set of generators if fake singularities are forbidden. A very geometric and physical construction of $\operatorname{U}_{p,q}$ is obtained as a by-product, generalizing the classical construction of unitary groups.

The Trace Field of Hyperbolic Gluings

We determine the adjoint trace field of gluings of general hyperbolic manifolds. This provides a new method to prove the nonarithmeticity of gluings, which can be applied to the classical construction of Gromov and Piatetski-Shapiro (and generalizations) as well as certain gluings of pieces of commensurable arithmetic manifolds. As an application, we give many new examples of nonarithmetic gluings and prove that the unique nonarithmetic Coxeter 5-simplex is not commensurable to any gluing of arithmetic pieces.

Computer Algorithm for Creation Classic Mosaic Fillings Based on the Vector Guide Lines

The article suggests algorithms for filling mosaic surfaces. Today, there are a number of algorithms that use the software design environment to automate the creation of images that correspond to mosaic compositions based on raster images. However, they do not allow realizing the principles of the classical construction of mosaic works, which guide professional mosaics. In this case, the main task is the problem of optimizing the filling of space from a mathematical point of view. From the point of view of the artist, this is not the main problem, moreover, the distance between the parts of the mosaic can vary, act as an artistic element. Much more important is the organization of the structure of the mosaic surface. This article is dedicated to this problem. The sequence of actions is given - algorithms that allow the artist to achieve the desired effect and gain full control when filling mosaic surfaces. These algorithms allow you to create mosaic fillings based on linear patterns without color and tonal design, which is impossible for existing algorithms. The authors proposed the construction of the topology of classical mosaics using vector guides. When forming the algorithm, vector guide lines or “power lines” are taken as a basis, on which mosaic elements (tesserae) are subsequently placed. Variants of using existing algorithms at each stage of the solution of the problem are proposed. Algorithms and results of filling a mosaic panel with a line-by-line and equidistant method are presented. This technology will allow not only creating mosaic surfaces, but also using it as a tool for creating real art projects for implementation in design and art. The possibility of using existing technologies in this technique is commented.