Automata with Nested Pebbles Capture First-Order Logic with Transitive Closure

String languages recognizable in (deterministic) log-space are characterized either by two-way (deterministic) multi-head automata, or following Immerman, by first-order logic with (deterministic) transitive closure. Here we elaborate this result, and match the number of heads to the arity of the transitive closure. More precisely, first-order logic with k-ary deterministic transitive closure has the same power as deterministic automata walking on their input with k heads, additionally using a finite set of nested pebbles. This result is valid for strings, ordered trees, and in general for families of graphs having a fixed automaton that can be used to traverse the nodes of each of the graphs in the family. Other examples of such families are grids, toruses, and rectangular mazes. For nondeterministic automata, the logic is restricted to positive occurrences of transitive closure. The special case of k=1 for trees, shows that single-head deterministic tree-walking automata with nested pebbles are characterized by first-order logic with unary deterministic transitive closure. This refines our earlier result that placed these automata between first-order and monadic second-order logic on trees.Comment: Paper for Logical Methods in Computer Science, 27 pages, 1 figur

Shape Recognition by a Finite Automaton Robot

Motivated by the problem of shape recognition by nanoscale computing agents, we investigate the problem of detecting the geometric shape of a structure composed of hexagonal tiles by a finite-state automaton robot. In particular, in this paper we consider the question of recognizing whether the tiles are assembled into a parallelogram whose longer side has length l = f(h), for a given function f(*), where h is the length of the shorter side. To determine the computational power of the finite-state automaton robot, we identify functions that can or cannot be decided when the robot is given a certain number of pebbles. We show that the robot can decide whether l = ah+b for constant integers a and b without any pebbles, but cannot detect whether l = f(h) for any function f(x) = omega(x). For a robot with a single pebble, we present an algorithm to decide whether l = p(h) for a given polynomial p(*) of constant degree. We contrast this result by showing that, for any constant k, any function f(x) = omega(x^(6k + 2)) cannot be decided by a robot with k states and a single pebble. We further present exponential functions that can be decided using two pebbles. Finally, we present a family of functions f_n(*) such that the robot needs more than n pebbles to decide whether l = f_n(h)

Quantitative descriptors for a range of visual biologic and synthetic pigmentation patterns

Nature is exuberant in visual patterns: spots on mammals, veins on leaves, maze-like structures in fishes, and many others. Computer Graphics has achieved success in model- ing and rendering many of these patterns. Nevertheless, a fundamental problem remains: how to validate the results beyond visual comparison. Here we propose a set of quantitative descriptors tailored to describe visual biological patterns found in many species of mammals and fishes. We are interested in analyzing the most common pattern structures: spots, labyrinths, and stripes. First, we compute a set of metrics from a dataset of real patterns – curated from scratch from publicly available repositories – and synthetic images generated using reaction-diffusion simulations. We calculate our first four descriptors as ratios of “global” measures. The last eight descriptors are the standard deviation of the average measure of pattern region features, giving us twelve descriptors. We validate the descriptors through two machine learning tasks on an augmented dataset with real and synthetic patterns. First, the descriptors are used as features of a supervised classifier with an overall accuracy of 98.4%, a result better than that obtained with a general state- of-the-art convolutional classification network. Second, we tested the descriptors in an unsupervised clustering task, differentiating natural from artificial patterns and identify- ing species studied in the natural pattern set. Clustering was also used for unsupervised detection of regions of biologic patterns over larger images.A natureza é exuberante em padrões visuais: padrões de manchas em mamíferos, veias em folhas, estruturas labirínticas em peixes e muitos outros. A Computação Gráfica alcançou sucesso na modelagem e renderização de muitos desses padrões. No entanto, um problema fundamental permanece: como validar os resultados além da comparação visual. Neste trabalho, é proposto um conjunto de descritores quantitativos adaptados para descrever padrões biológicos visuais encontrados em várias espécies de mamíferos e peixes. Foram analisadas as estruturas de padrões mais comuns, como padrões de manchas, labirintos e listras. Primeiro, é calculado um conjunto de métricas para uma base de imagens de padrões reais – selecionadas de repositórios disponíveis publicamente – junto com imagens sintéticas, geradas usando simulações de reação-difusão (reaction-diffusion). Os quatro primeiros descritores são calculados a partir de razões entre medidas “globais”. Os oito descritores restantes são definidos como o desvio padrão da média das métricas obtidas a partir das características das regiões do padrão, totalizando doze descritores. Estes descritores são validados em duas tarefas de aprendizado de máquina em um conjunto de dados com padrões reais e sintéticos. Primeiro, os descritores são usados como entradas para um classificador supervisionado, obtendo uma precisão geral de 98,4%, um resultado melhor do que o obtido em rede de classi- ficação convolucional de propósito geral de última geração. Para a segunda validação, os descritores são testados em uma tarefa de agrupamento (clustering) não supervisi- onado, sendo capaz de diferenciar padrões naturais de artificiais e também identificar espécies estudadas no conjunto de padrões naturais. O agrupamento também foi usado para detecção não supervisionada de regiões de padrões biológicos em imagens maiores

An extensive English language bibliography on graph theory and its applications

Bibliography on graph theory and its application

With dark, rose-coloured glasses: gothic, queer and intertextual labyrinths in the novels by Louise Welsh

Tesis doctoral inédita leída en la Universidad Autónoma de Madrid, Facultad de Filosofía y Letras, Departamento de Lingüística, Lenguas Modernas, Lógica y Fª de la Ciencia y Tª de la Literatura Comparada. Fecha de lectura: 05-05-201

Ideas of Time in Music : A Philosophico-logical Investigation Applied to Works of Alberto Ginastera (1916 - 1983)

This thesis proposes temporal conceptions that stem from philosophical inquiry, such as linear time, cyclical time and branching time, to then find a connection with the way music is structured and with musical meaning. I consider ontological and phenomenological approaches to the problem of time and music in order to demonstrate this. The central aim of this investigation is to build bridges and dissolve the opposition between time taken (clock time) vs. time evoked (conceptual time) in studies on time and music. Lewis Rowell, Jonathan Kramer, Jos Kunst and Alan Marsden s contributions are going to be taken as the main references. I consider the ontological approach as extremely literal since linearity, circularity and branching time are not explored there as concepts defining the meaning of music, but as abstract orders in time for music being processed, viewed from an exclusively technical point of view. In turn, the phenomenological approach does not generally link music to philosophical developments, it just describes general cultural conceptions of time. This thesis interprets the temporal modes of the phenomenological approach as highly coincident with the temporal ontologies in the ontological approach, as seen through developments in temporal logic. Temporal logic, a branch of the classical logic, is used as a methodological trigger. Here the work of Arthur Prior is going to be taken as reference. Temporal logic first formalises, then clarifies, and finally validates assertions expressing temporal beliefs. The hypothesis of this thesis, that temporal conceptions are expressed through music, having in this case the power to explain at least its primary meaning, uses temporal logic as a bridging symbolism. In this sense, a comparison between music and language within a broader analysis is undertaken, before developing ideas of logic and temporal logic within musical practice. In particular, in my study of some works by the Argentinian composer Alberto Ginastera (1916 1983), I illustrate the idea of a multi-temporality, i.e. the same composer works with several time structures already available by a cumulative process in the history of ideas. The thesis finds there is a special type of time in music─neither an exclusive musical time as a totally separate time species; nor Time in music, in an abstract de-subjectified view. Thus, a cooperative, synthetic position is defended. Secondly, music represents by means of its distinct elements something inherent to itself, which links with concepts of time (ideas), and by using these elements in certain conventional ways, displays culturally conditioned temporal meanings. Thirdly, music displays a kind of temporal logic, although an extended view comparing it with the exclusively linear logic of music as conceived by the formalist tradition in musicology. It is also an aesthetically oriented approach different from the temporal logic as applied in literal representations of music in computing areas. Finally, I argue for a new musical temporal mode, the actual branched time in music (in the sense of parallel times), through the addition of a theoretical background for this mode in musicological studies.Ideas of Time in Music states that music is not only a source of pleasure but also a source of knowledge. We learn something about time with music, not only in the primal sense of understanding dimensions, but in the profound sense that music meditates, through sound, ideas about time. Linear, cyclical, and branching time conceptions external to music find a connection with music s internal structure and meaning. In order to demonstrate this, issues of musical ontology, musical language, and musical logic are developed. In addition, the main philosophical perspectives on time, ontological and phenomenological, are combined for a more comprehensive account of time in music. Alberto Ginastera s music is analysed at the end as an example of how the time of music helps in constructing its meaning