A cognitive exploration of the “non-visual” nature of geometric proofs

Why are Geometric Proofs (Usually) “Non-Visual”? We asked this question as a way to explore the similarities and differences between diagrams and text (visual thinking versus language thinking). Traditional text-based proofs are considered (by many to be) more rigorous than diagrams alone. In this paper we focus on human perceptual-cognitive characteristics that may encourage textual modes for proofs because of the ergonomic affordances of text relative to diagrams. We suggest that visual-spatial perception of physical objects, where an object is perceived with greater acuity through foveal vision rather than peripheral vision, is similar to attention navigating a conceptual visual-spatial structure. We suggest that attention has foveal-like and peripheral-like characteristics and that textual modes appeal to what we refer to here as foveal-focal attention, an extension of prior work in focused attention

Hypergraph simplification: Linking the path-sum approach to the ZH-calculus

The ZH-calculus is a complete graphical calculus for linear maps between qubits that admits, for example, a straightforward encoding of hypergraph states and circuits arising from the Toffoli+Hadamard gate set. In this paper, we establish a correspondence between the ZH-calculus and the path-sum formalism, a technique recently introduced by Amy to verify quantum circuits. In particular, we find a bijection between certain canonical forms of ZH-diagrams and path-sum expressions. We then introduce and prove several new simplification rules for the ZH-calculus, which are in direct correspondence to the simplification rules of the path-sum formalism. The relatively opaque path-sum rules are shown to arise naturally as the convergence of two consequences of the ZH-calculus. The first is the extension of the familiar graph-theoretic simplifications based on local complementation and pivoting to their hypergraph-theoretic analogues: hyper-local complementation and hyper-pivoting. The second is the graphical Fourier transform introduced by Kuijpers et al., which enables effective simplification of ZH-diagrams encoding multi-linear phase polynomials with arbitrary real coefficients.Comment: 12 pages + 11 pages appendi

The Semiotics of Spider Diagrams

Spider diagrams are based on Euler and Venn/Peirce diagrams, forming a system which is as expressive as monadic first orderlogic with equality. Rather than being primarily intended for logicians,spider diagrams were developed at the end of the 1990s in the context of visual modelling and software specification. We examine the original goals of the designers, the ways in which the notation has evolved and itsconnection with the philosophical origins of the logical diagrams of Euler, Venn and Peirce on which spider diagrams are based. Using Peirce's concepts and classification of signs, we analyse the ways in which different sign types are exploited in the notation. Our hope is that this analysis may be of interest beyond those readers particularly interested in spider diagrams, and act as a case study in deconstructing a simple visual logic. Along the way, we discuss the need for a deeper semiotic engagement in visual modelling

Web Data Extraction, Applications and Techniques: A Survey

Web Data Extraction is an important problem that has been studied by means of different scientific tools and in a broad range of applications. Many approaches to extracting data from the Web have been designed to solve specific problems and operate in ad-hoc domains. Other approaches, instead, heavily reuse techniques and algorithms developed in the field of Information Extraction. This survey aims at providing a structured and comprehensive overview of the literature in the field of Web Data Extraction. We provided a simple classification framework in which existing Web Data Extraction applications are grouped into two main classes, namely applications at the Enterprise level and at the Social Web level. At the Enterprise level, Web Data Extraction techniques emerge as a key tool to perform data analysis in Business and Competitive Intelligence systems as well as for business process re-engineering. At the Social Web level, Web Data Extraction techniques allow to gather a large amount of structured data continuously generated and disseminated by Web 2.0, Social Media and Online Social Network users and this offers unprecedented opportunities to analyze human behavior at a very large scale. We discuss also the potential of cross-fertilization, i.e., on the possibility of re-using Web Data Extraction techniques originally designed to work in a given domain, in other domains.Comment: Knowledge-based System

An Introduction to String Diagrams for Computer Scientists

This document is an elementary introduction to string diagrams. It takes a computer science perspective: rather than using category theory as a starting point, we build on intuitions from formal language theory, treating string diagrams as a syntax with its semantics. After the basic theory, pointers are provided to contemporary applications of string diagrams in various fields of science

BlogForever D2.6: Data Extraction Methodology

This report outlines an inquiry into the area of web data extraction, conducted within the context of blog preservation. The report reviews theoretical advances and practical developments for implementing data extraction. The inquiry is extended through an experiment that demonstrates the effectiveness and feasibility of implementing some of the suggested approaches. More specifically, the report discusses an approach based on unsupervised machine learning that employs the RSS feeds and HTML representations of blogs. It outlines the possibilities of extracting semantics available in blogs and demonstrates the benefits of exploiting available standards such as microformats and microdata. The report proceeds to propose a methodology for extracting and processing blog data to further inform the design and development of the BlogForever platform

Space, Territory, Occupy: Towards a Non-Phenomenological Dwelling

This thesis analyzes the relationship between the body and space through the works of Henri Lefebvre, and Gilles Deleuze and Félix Guattari. The aim of the project is to move beyond Lefebvre’s theory of the production of space, which relies on a phenomenological understanding of the body and space. In order to do so, it will find in Deleuze and Guattari’s concept of ‘territory’ a non-phenomenological and constructivist concept of space that does not posit the ‘lived body’ as a transcendent ground. As a result, it will also attempt to trace out a non-phenomenological concept of ‘dwelling’ that is not based on a concept of the subject, but is ‘involuntary’ and constructive, and emphasizes the spatio-temporal dynamisms or rhythms that a ‘space without world’ consists of. Finally, by being loosely guided by the global Occupy movement, it seeks to invoke a politics ‘of’ space, where the concept of ‘occupy’ emphasizes a being-in-space that is primarily political and only secondarily ontological

Bringing Model Checking Closer To Practical Software Engineering

Bal, H.E. [Promotor]Templon, J.A. [Copromotor]Willemse, T.A.C. [Copromotor

Quantum Theory from Principles, Quantum Software from Diagrams

This thesis consists of two parts. The first part is about how quantum theory can be recovered from first principles, while the second part is about the application of diagrammatic reasoning, specifically the ZX-calculus, to practical problems in quantum computing. The main results of the first part include a reconstruction of quantum theory from principles related to properties of sequential measurement and a reconstruction based on properties of pure maps and the mathematics of effectus theory. It also includes a detailed study of JBW-algebras, a type of infinite-dimensional Jordan algebra motivated by von Neumann algebras. In the second part we find a new model for measurement-based quantum computing, study how measurement patterns in the one-way model can be simplified and find a new algorithm for extracting a unitary circuit from such patterns. We use these results to develop a circuit optimisation strategy that leads to a new normal form for Clifford circuits and reductions in the T-count of Clifford+T circuits.Comment: PhD Thesis. Part A is 135 pages. Part B is 95 page

Psychoanalytic aesthetics: the case of Miró and the 'child-like'

Miró's art is regularly characterised as 'child-like' in art historical literature. That is, his work is taken visually to resemble, or as sharing some of the characteristics (freshness of vision, spontaneity, emotional expressiveness, freedom from traditional illusionistic techniques) attributed to, the artistic productions of children. This analogy with child art (exploited by Expressionists and others in the early years of the twentieth-century) dates in Miró's case to his involvement with Surrealism in the 1920s. It was understood as a more or less conscious intention to exploit the visual characteristics of the successive stages in a child's artistic development. In other words, it was one aspect of Surrealism's engagement with 'primitivist' forms of expression, in which artists appropriated the aesthetic of children's drawings, tribal and folk artifacts, and the artistic productions of the mentally ill. My discussion of Miró is supported by comparison with the work of two other artists, Klee and Chagall, who also borrowed from child art and whose production was likewise associated with childhood by critical literature. Klee's work supports my contention that although Mirós painting bears a passing resemblance to children's drawings, a more sustained analysis demonstrates that it is unlike anything that a child would actually produce. 'Child-likeness', generally a comment on form, becomes in Miró's case question of artistic content, relating to the development and constant recycling of a vocabulary of shapes largely derived from childhood memories. Comparison with Chagall, whose oeuvre was also thematically indebted to childhood memories, allows one to put forward a psychoanalytically informed explanation of the infantile origins of the content that finds expression in art. Miró's thematic 'child-like' content, from this point onwards, is used as a case study to effect the comparison between the theories of Freud (a major influence on Surrealism), and those of the Kleinian tradition within the British Object-Relations School of psychoanalysis, insofar as these have lent themselves to the discussion of art. Both approaches are developmental (Freud and Klein theorised adult psychology as a development of the thought processes of infancy and childhood), and for this reason have been preferred to the topographical and Lacanian orientation adopted in recent applied psychoanalytic literature. \Vhereas Freud's psychoanalysis of art concentrates on the unconscious processes and mechanisms by means of which the fantasy-distorted derivatives of repressed infantile material emerge into consciousness and become the material of art, the Kleinian psychoanalytic aesthetic developed by Segal and Stokes focuses on the unconscious revelations underlying creativity and the phantasy content that finds expression at the level of the medium. Winnicott provides a (poetic) description of the experiences, rooted in childhood perceptual patterns, to which the production of art and its reception give rise. Miró's own accounts of his creative procedures confirm that the unconscious infantile-derived thought processes, motivations and contents theorised by these authors are in .... [?] operative in the production of art, whilst also making clear that creativity is determined by socio-cultural, therefore conscious (and, as such, psychoanalytically unaccounted for) factors. Both the explanatory value and the principal methodological limitation of psychoanalytic aesthetics centre on these two final considerations