Geometrical regular languages and linear Diophantine equations: The strongly connected case

AbstractGiven an arbitrarily large alphabet Σ, we consider the family of regular languages over Σ for which the deterministic minimal automaton has a strongly connected state diagram. We present a new method for checking whether such a language is semi-geometrical or not and whether it is geometrical or not. This method makes use of the enumeration of the simple cycles of the state diagram. It is based on the construction of systems of linear Diophantine equations, where the coefficients are deduced from the set of simple cycles

Entailment systems for stably locally compact locales

The category SCFrU of stably continuous frames and preframe ho-momorphisms (preserving ¯nite meets and directed joins) is dual to the Karoubi envelope of a category Ent whose objects are sets and whose morphisms X ! Y are upper closed relations between the ¯nite powersets FX and FY . Composition of these morphisms is the \cut composition" of Jung et al. that interfaces disjunction in the codomains with conjunctions in the domains, and thereby relates to their multi-lingual sequent calculus. Thus stably locally compact locales are represented by \entailment systems" (X; `) in which `, a generalization of entailment relations,is idempotent for cut composition. Some constructions on stably locally compact locales are represented in terms of entailment systems: products, duality and powerlocales. Relational converse provides Ent with an involution, and this gives a simple treatment of the duality of stably locally compact locales. If A and B are stably continuous frames, then the internal preframe hom A t B is isomorphic to e A ­ B where e A is the Hofmann-Lawson dual. For a stably locally compact locale X, the lower powerlocale of X is shown to be the dual of the upper powerlocale of the dual of X

Publication of an Internet-accessible database resource for Arts et Metiers graphiques

Arts et Metiers graphiques (AMG) was a prominent French graphic arts magazine that was published in 68 issues from 1927 to 1939. Charles Peignot, head of the French typefoundry Deberny et Peignot, created the publication. Deberny et Peignot was the leading company of its kind in France. It manufactured not only thousands of metal type designs, but also machinery, furniture, and accessories for sale to the typesetting and printing industries. Charles Peignot, a young visionary with presses, metal type, and personal connections at his disposal secured his legacy in graphic arts history with the publication of Arts et Metiers graphiques. In it, he wanted to cover all the subjects near or far from printing, of its history, and its diverse contemporary manifestations. In over ten years of publication Peignot\u27s wide editorial goal encompassed subjects ranging from illustration, the history of the book and printing techniques and the then-expanding disciplines of advertising design and modern art photography. The magazine also featured regular reviews of fine limited-edition books and reprints of classical literature excerpts in typographically innovative layouts. Each edition was printed on high-quality papers with frequent tipped-in plates and inserts. Until the Second World War forced the magazine to cease production, Arts et Metiers graphiques was one of the highest standards for graphic arts magazines of its time. This thesis describes the creation and implementation of a web-based database providing access to the digitized content of Arts et Metiers graphiques

A logical study of some 2-categorical aspects of topos theory

There are two well-known topos-theoretic models of point-free generalized spaces: the original Grothendieck toposes (relative to classical sets), and a relativized version (relative to a chosen elementary topos $S$ with a natural number object) in which the generalized spaces are the bounded geometric morphisms from an elementary topos $E$ to $S$, and they form a 2-category $BTop/S$. However, often it is not clear what a preferred choice for the base $S$ should be. In this work, we review and further investigate a third model of generalized spaces, based on the 2-category $Con$ of ‘contexts for Arithmetic Universes (AUs)’ presented by AU-sketches which originally appeared in Vickers’ work in [Vic19] and [Vic17]. We show how to use the AU techniques to get simple proofs of conceptually stronger, base-independent, and predicative (op)fibration results in $ETop$, the 2-category of elementary toposes equipped with a natural number object, and arbitrary geometric morphisms. In particular, we relate the strict Chevalley fibrations, used to define fibrations of AU-contexts, to non-strict Johnstone fibrations, used to define fibrations of toposes. Our approach brings to light the close connection of (op)fibration of toposes, conceived as generalized spaces, with topological properties. For example, every local homeomorphism is an opfibration and every entire map (i.e. fibrewise Stone) is a fibration

The segmentation of visual form

The argument of this work is that, despite the massive body of literature that has accumulated in the decades since the discovery of 'gestalt' as the ruling principle of perception, little genuine progress in solving the problem posed by the visual perception of form has been made. This state of affairs is attributed, moreover, to a fundementally inadequate formulation of this problem. It is not enough merely to revise this or that theory, or this or that experimental design, if the argument is correct; rather, it is necessary to revise the formulation of the form problem upon which theory and experimental design rest. Thus, the reformulation suggested is that (a) form is the unit which segments space, and consequently that (b) the problem posed by this unit is essentially that of its segmentation/formation of space, rather than that of its recognition/conservation through change in space; the former is the primary, the latter the secondary, (psycho-physical) problem posed by the visual perception of form. This work also contains a segmentation (spatial/holistic) theory of form, and five experiments designed to test this theory against current recognition (dimensional/analytic) theories of form (for example, see Corcoran, 1971); these experiments are all concerned with different facets of the role played by contour in visual perception, and they provide some evidence for the former, and against the latter, type of theory. It should be pointed out that both in the main body of the text, and in an appendix, it is argued that segmentation is primarily two-dimensional rather than three-dimensional: two-dimensional 'figure'form is primary over three-dimensional 'object' form in perceptual development, and indeed, the latter is constructed from the former. (This hypothesis is part of a more general point of view about cognition, namely that there is an a priori spatial system which is used to process perceptual input, and establish in it the spatial structure of perceptual experience, but one whose conceptual implications and properties become available for symbolisation and thinking when it is freed from the task of perceptual processing by being lifted out of perception into a visual form of representation which Bruner terms 'ikonic' (See Bruner et al., 1966).)<p

The Aesthetics of Censorship and the Russian Avant-Garde: Abstraction Beyond Art

Volume I contains the text of the thesis. Volume II contains the illustrations relating to the thesis, but it is not publicly available for copyright reasons.This thesis reconsiders the art of the Russian avant-garde by exploring its engagement with, influence from and contribution towards an unconventional area of culture: censorship. Although extensive research has already considered the way artists such as Malevich, Rodchenko and Stepanova blurred the binaries between art and vandalism, construction and deconstruction in their work, this analysis has not yet extended to consider their engagement with institutions of censorship to its full extent. This disinclination is informed by a long-standing and resilient assumption that censorship and creativity are antithetical, mutually oppositional forces. My thesis uses extensive new archival findings to problematise this position. By questioning these binary distinctions, and searching for commonalties between art and expurgation, this project offers a new understanding of how at different points in their careers, across different media, artists borrowed, adapted or referenced the censor’s strike in complex ways. Whilst extensive research has been devoted to the ideology and institutional mechanisms of Russian censorship, its aesthetic dimensions have been largely disregarded. As a corrective to this, this project will consider case studies of visibly altered and amended works in three different media: typography, photography and painting. Case studies range from redacted texts, censored manuscripts, excised details in print journals and defaced photographs. In each case, it will be argued that the very surface and texture of censorship itself warrants a formal reading, as placeholders of enforced negations which contain a rich semantic complexity. This project adds to a growing field of research which reconsiders the interactions between avant-garde artist and institutional apparatus. Covering a chronological period from the First to the Second World War, it charts the artists’ transition from anti-establishment cultural agitators to employees of the Soviet state’s expanding art administration network. It explores the tense entente that ensued as their art was adapted and appropriated to accommodate these changing institutional allegiances. Ultimately, it illuminates a new facet of the relationship between art and its destruction during this period, and provides a new understanding of the role of the artist as a willing or willed iconoclast.Full scholarship from CEELBAS (Centre for East European Language-Based Area Studies), funded by the Arts and Humanities Research Council (AHRC