Palindromic complexity of trees

We consider finite trees with edges labeled by letters on a finite alphabet $\varSigma$. Each pair of nodes defines a unique labeled path whose trace is a word of the free monoid $\varSigma^*$. The set of all such words defines the language of the tree. In this paper, we investigate the palindromic complexity of trees and provide hints for an upper bound on the number of distinct palindromes in the language of a tree.Comment: Submitted to the conference DLT201

Critical connectedness of thin arithmetical discrete planes

An arithmetical discrete plane is said to have critical connecting thickness if its thickness is equal to the infimum of the set of values that preserve its $2$-connectedness. This infimum thickness can be computed thanks to the fully subtractive algorithm. This multidimensional continued fraction algorithm consists, in its linear form, in subtracting the smallest entry to the other ones. We provide a characterization of the discrete planes with critical thickness that have zero intercept and that are $2$-connected. Our tools rely on the notion of dual substitution which is a geometric version of the usual notion of substitution acting on words. We associate with the fully subtractive algorithm a set of substitutions whose incidence matrix is provided by the matrices of the algorithm, and prove that their geometric counterparts generate arithmetic discrete planes.Comment: 18 pages, v2 includes several corrections and is a long version of the DGCI extended abstrac

Spatial palindromes/palindromic spaces: spatial devices in Vitruvius, Mallarmé, Polieri, Perec and Libeskind

This thesis explores non-linear geometric texts and narratives in literature and architecture and the experience of space that is facilitated by them. The research focuses on the palindrome because it is a non-linear mathematical/geometrical device that is found both in literature and architecture. In language, the palindrome is expressed in the geometrical arrangement of words, letters or concepts in the text or the narrative; and, in architecture, as mirrored symmetries or palindromic proportions, measurements and distributions of elements in drawings and buildings. The primary aim of the thesis is to explore the spatial qualities of palindromes, and the experience of those qualities not only in text but also in architecture. This dissertation thus consists of two parts: the first examines Spatial Palindromes in terms of the spatial structures of selected texts and considers their relation to architecture; and the second examines Palindromic Spaces in terms of the spatial experiences created by and through palindromes in text and architecture. The first part, Spatial Palindromes, constructs an original history of the spatial qualities of palindromes by looking at the theory guiding the use of non-linear devices in texts and architecture. This history moves from the use of palindromes in the work of classical figures and scholars (Orpheus, Pythagoras and Vitruvius), to the Medieval and Renaissance practice of mnemonics (Frances Yates, Mary Carruthers), to early twentieth-century structural linguistics (Ferdinand de Saussure) and the group OuLiPo (Raymond Queneau, Franyois Le Lionnais) and, finally, to late twentieth-century post-structural linguistics (Jean Baudrillard.) The thesis argues that palindromes create spatial experiences both in texts and architecture. For this reason the second part, Palindromic Spaces, studies the nature of spatial experience in the fictions and designs of Stephane Mallarme, Jacques Polieri, Georges Perec, and Daniel Libeskind. According to Baudrillard the poetic space, hidden or revealed by the anagram and palindrome, is where the solid structure of language is "exterminated." This act of extermination, or the poetic space that palindrome reveals in language, opens up perception, memory and recollection to a spatial experience "that incorporates the recession of outcomes ad infinitum;" a self-generated, self-consumed or self-reflective conception of history and space that this thesis aims to explore in architecture

Temporal representations in human computer interaction: Designing for the lived experience of time

Temporal representations in Human Computer Interaction: is a portfolio of peer reviewed papers and media artworks representing several years of investigation, experimental making, and study into the perceptions and representation of time in digital media and Human Computer Interaction (HCI). The lived experience of time is fundamental to our understanding of the world and the work investigates the complex and contradictory nature of time and the powerful effect temporal representations have on health, well-being and perception.The investigation, methodology and outputs are based in the traditions of interdisciplinary electronic arts, technology research and digital culture. Practice-led, research through design techniques, are used as a means to explore alternative framings of temporal processes. I discuss the importance of temporal experience as a concern for contextual design and consider the models and lived experiences of time and how system-centric representations alter our perceptions of time.The papers and works (discussed in chapters 4, 5 and 6 and included in full in appendix a) cover three broad areas:Analysis and discussion of practice and language in HCI related to time;Experimental designs for temporal objects and media artworks;Finally through critical artefacts, media art and publications I discuss a new perspective on temporality in design and representation and present a framework for re-assessing how we include time in interaction design.The framework is designed to be used as a tool to support understanding of the temporality of users, or situations of use, and to assist in translating and re-framing insights into practical outputs for improved design of interactive systems. It contrasts system-centric with user-centric temporal representation, and contributes a new design methodology that is aimed at improving contextual design processes. By increasing awareness of temporal context, and the multi-dimensional nature of user’s temporality, designers can better understand user context when creating truly user centred interactive experiences

Reflections in the Author\u27s Eye: Optics, Involution, and Artifice in the Novels and Short Stories of Vladimir Nabokov

Vladimir Nabokov’s fourth novel, The Eye, is consistently characterized as his most obscure work. Despite comparatively slim critical attention, the work marked a seminal moment in Nabokov’s literary career, as it initiated his experimentation with perceptual distortions such as mirroring, mimicry, optics, and doubling all through the frame of unreliable narration. Going beyond conventionally untrustworthy narration, Nabokov presents an authorial consciousness that manipulates the narratory point of view through incredibly detailed encryptions, requiring the imaginative participation of readers in unmasking Nabokov’s second, “real” authorial plot. Although Nabokov openly dismissed the moral foregrounding associated with the doppelgänger motif, the thesis will explore the ways in which Nabokov frequently utilizes myriads of false doubles to create an imprint of artifice, which the reader must sift through in order to grasp the authorial “texture” beneath the overt text. Utilizing The Eye as well as several of Nabokov’s short stories as introductory prototypes of Lolita and Pale Fire, the thesis will explore the development of Nabokov’s increasingly intricate and deceptive ocular and aesthetic designs, which inculcate the creative participation of an audience, thereby making the perceptive reader a real and conscious double of the author