1,683 research outputs found

    Labelled transition systems as a Stone space

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    A fully abstract and universal domain model for modal transition systems and refinement is shown to be a maximal-points space model for the bisimulation quotient of labelled transition systems over a finite set of events. In this domain model we prove that this quotient is a Stone space whose compact, zero-dimensional, and ultra-metrizable Hausdorff topology measures the degree of bisimilarity such that image-finite labelled transition systems are dense. Using this compactness we show that the set of labelled transition systems that refine a modal transition system, its ''set of implementations'', is compact and derive a compactness theorem for Hennessy-Milner logic on such implementation sets. These results extend to systems that also have partially specified state propositions, unify existing denotational, operational, and metric semantics on partial processes, render robust consistency measures for modal transition systems, and yield an abstract interpretation of compact sets of labelled transition systems as Scott-closed sets of modal transition systems.Comment: Changes since v2: Metadata updat

    Operational theories and Categorical quantum mechanics

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    A central theme in current work in quantum information and quantum foundations is to see quantum mechanics as occupying one point in a space of possible theories, and to use this perspective to understand the special features and properties which single it out, and the possibilities for alternative theories. Two formalisms which have been used in this context are operational theories, and categorical quantum mechanics. The aim of the present paper is to establish strong connections between these two formalisms. We show how models of categorical quantum mechanics have representations as operational theories. We then show how nonlocality can be formulated at this level of generality, and study a number of examples from this point of view, including Hilbert spaces, sets and relations, and stochastic maps. The local, quantum, and no-signalling models are characterized in these terms.Comment: 37 pages, updated bibliograph

    A behavioural pseudometric for probabilistic transition systems

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    AbstractDiscrete notions of behavioural equivalence sit uneasily with semantic models featuring quantitative data, like probabilistic transition systems. In this paper, we present a pseudometric on a class of probabilistic transition systems yielding a quantitative notion of behavioural equivalence. The pseudometric is defined via the terminal coalgebra of a functor based on a metric on the space of Borel probability measures on a metric space. States of a probabilistic transition system have distance 0 if and only if they are probabilistic bisimilar. We also characterize our distance function in terms of a real-valued modal logic

    Renewing the respect for similarity

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    In psychology, the concept of similarity has traditionally evoked a mixture of respect, stemming from its ubiquity and intuitive appeal, and concern, due to its dependence on the framing of the problem at hand and on its context. We argue for a renewed focus on similarity as an explanatory concept, by surveying established results and new developments in the theory and methods of similarity-preserving associative lookup and dimensionality reduction—critical components of many cognitive functions, as well as of intelligent data management in computer vision. We focus in particular on the growing family of algorithms that support associative memory by performing hashing that respects local similarity, and on the uses of similarity in representing structured objects and scenes. Insofar as these similarity-based ideas and methods are useful in cognitive modeling and in AI applications, they should be included in the core conceptual toolkit of computational neuroscience. In support of this stance, the present paper (1) offers a discussion of conceptual, mathematical, computational, and empirical aspects of similarity, as applied to the problems of visual object and scene representation, recognition, and interpretation, (2) mentions some key computational problems arising in attempts to put similarity to use, along with their possible solutions, (3) briefly states a previously developed similarity-based framework for visual object representation, the Chorus of Prototypes, along with the empirical support it enjoys, (4) presents new mathematical insights into the effectiveness of this framework, derived from its relationship to locality-sensitive hashing (LSH) and to concomitant statistics, (5) introduces a new model, the Chorus of Relational Descriptors (ChoRD), that extends this framework to scene representation and interpretation, (6) describes its implementation and testing, and finally (7) suggests possible directions in which the present research program can be extended in the future

    Categorical Ontology of Complex Systems, Meta-Systems and Theory of Levels: The Emergence of Life, Human Consciousness and Society

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    Single cell interactomics in simpler organisms, as well as somatic cell interactomics in multicellular organisms, involve biomolecular interactions in complex signalling pathways that were recently represented in modular terms by quantum automata with ‘reversible behavior’ representing normal cell cycling and division. Other implications of such quantum automata, modular modeling of signaling pathways and cell differentiation during development are in the fields of neural plasticity and brain development leading to quantum-weave dynamic patterns and specific molecular processes underlying extensive memory, learning, anticipation mechanisms and the emergence of human consciousness during the early brain development in children. Cell interactomics is here represented for the first time as a mixture of ‘classical’ states that determine molecular dynamics subject to Boltzmann statistics and ‘steady-state’, metabolic (multi-stable) manifolds, together with ‘configuration’ spaces of metastable quantum states emerging from complex quantum dynamics of interacting networks of biomolecules, such as proteins and nucleic acids that are now collectively defined as quantum interactomics. On the other hand, the time dependent evolution over several generations of cancer cells --that are generally known to undergo frequent and extensive genetic mutations and, indeed, suffer genomic transformations at the chromosome level (such as extensive chromosomal aberrations found in many colon cancers)-- cannot be correctly represented in the ‘standard’ terms of quantum automaton modules, as the normal somatic cells can. This significant difference at the cancer cell genomic level is therefore reflected in major changes in cancer cell interactomics often from one cancer cell ‘cycle’ to the next, and thus it requires substantial changes in the modeling strategies, mathematical tools and experimental designs aimed at understanding cancer mechanisms. Novel solutions to this important problem in carcinogenesis are proposed and experimental validation procedures are suggested. From a medical research and clinical standpoint, this approach has important consequences for addressing and preventing the development of cancer resistance to medical therapy in ongoing clinical trials involving stage III cancer patients, as well as improving the designs of future clinical trials for cancer treatments.\ud \ud \ud KEYWORDS: Emergence of Life and Human Consciousness;\ud Proteomics; Artificial Intelligence; Complex Systems Dynamics; Quantum Automata models and Quantum Interactomics; quantum-weave dynamic patterns underlying human consciousness; specific molecular processes underlying extensive memory, learning, anticipation mechanisms and human consciousness; emergence of human consciousness during the early brain development in children; Cancer cell ‘cycling’; interacting networks of proteins and nucleic acids; genetic mutations and chromosomal aberrations in cancers, such as colon cancer; development of cancer resistance to therapy; ongoing clinical trials involving stage III cancer patients’ possible improvements of the designs for future clinical trials and cancer treatments. \ud \u

    COMPOSITIONAL EXPLORATIONS OF PLASTIC SOUND

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    Each piece of music in this research is meant to explore a different aspect of music as a plastic art. Conclusions reached in the review of each new work were used to guide the development of the next. The notions of plasticity in sound, and sound as a plastic material were used to give the overall research a focal point. In exploring different types of composition, reciprocal plasticity between the materials and the developing ideas of the music are discussed in the context of ecological and biological psychology. By restricting all these works within the genre of 'plastic arts' it became necessary to introduce a new technique for instrumental composition. An aural model is used to replace the traditional written score. These instrumental works were developed entirely within an auditory situation.Funded by De Montfort Universit
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