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Algebraic Approaches

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Edward Witten – One of the best experts on this subject based on the ideXlab platform.

  • aps medal for exceptional achievement in research invited article on entanglement properties of quantum field theory
    Reviews of Modern Physics, 2018
    Co-Authors: Edward Witten

    Abstract:

    The 2016 APS Medal for Excellence in Physics was given to Edward Witten. This contribution was invited in conjunction with this award. These original notes contain concise explanations of some key results in the axiomatic and Algebraic Approaches to quantum field theory, which are relevant to quantum entanglement. They serve to put the connection between quantum field theory and quantum information theory on a precise and rigorous footing.

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  • aps medal for exceptional achievement in research invited article on entanglement properties of quantum field theory
    Reviews of Modern Physics, 2018
    Co-Authors: Edward Witten

    Abstract:

    The 2016 APS Medal for Excellence in Physics was given to Edward Witten. This contribution was invited in conjunction with this award. These original notes contain concise explanations of some key results in the axiomatic and Algebraic Approaches to quantum field theory, which are relevant to quantum entanglement. They serve to put the connection between quantum field theory and quantum information theory on a precise and rigorous footing.

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Sven Nelander – One of the best experts on this subject based on the ideXlab platform.

  • searching for synergies matrix Algebraic Approaches for efficient pair screening
    PLOS ONE, 2013
    Co-Authors: Philip Gerlee, Sven Nelander, Linnea Schmidt, Naser Monsefi, Teresia Kling, Rebecka Jornsten

    Abstract:

    Functionally interacting perturbations, such as synergistic drugs pairs or synthetic lethal gene pairs, are of key interest in both pharmacology and functional genomics. However, to find such pairs by traditional screening methods is both time consuming and costly. We present a novel computational-experimental framework for efficient identification of synergistic target pairs, applicable for screening of systems with sizes on the order of current drug, small RNA or SGA (Synthetic Genetic Array) libraries (>1000 targets). This framework exploits the fact that the response of a drug pair in a given system, or a pair of genes’ propensity to interact functionally, can be partly predicted by computational means from (i) a small set of experimentally determined target pairs, and (ii) pre-existing data (e.g. gene ontology, PPI) on the similarities between targets. Predictions are obtained by a novel matrix Algebraic technique, based on cyclical projections onto convex sets. We demonstrate the efficiency of the proposed method using drug-drug interaction data from seven cancer cell lines and gene-gene interaction data from yeast SGA screens. Our protocol increases the rate of synergism discovery significantly over traditional screening, by up to 7-fold. Our method is easy to implement and could be applied to accelerate pair screening for both animal and microbial systems.

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Andrea Corradini – One of the best experts on this subject based on the ideXlab platform.

  • Algebraic graph rewriting with controlled embedding
    Theoretical Computer Science, 2020
    Co-Authors: Andrea Corradini, Dominique Duval, Rachid Echahed, Frederic Prost, Leila Ribeiro

    Abstract:

    Graph transformation is a specification technique suitable for a wide range of applications, specially the ones that require a sophisticated notion of state. In graph transformation, states are represented by graphs and actions are specified by rules. Most Algebraic Approaches to graph transformation proposed in the literature ensure that if an item is preserved by a rule, so are its connections with the graph where it is embedded. But there are applications in which it is desirable to specify different embeddings. For example when cloning an item, there may be a need to handle the original and the copy in different ways. We propose a new Algebraic approach to graph transformation, AGREE: Algebraic Graph Rewriting with controllEd Embedding, where rules allow one to specify how the embedding should be carried out. We define this approach in the framework of classified categories which are categories endowed with partial map classifiers. This new approach leads to graph transformations in which effects may be non-local, e.g. a rewrite step may alter a node of the host graph which is outside the image of the left-hand side of the considered rule. We propose a syntactic condition on AGREE rules which guarantees the locality of transformations. We also compare AGREE with other Algebraic Approaches to graph transformation.

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  • The Pullback-Pushout Approach to Algebraic Graph Transformation
    , 2017
    Co-Authors: Andrea Corradini, Dominique Duval, Rachid Echahed, Frederic Prost, Leila Ribeiro

    Abstract:

    Some recent Algebraic Approaches to graph transformation include a pullback construction involving the match, that allows one to specify the cloning of items of the host graph. We pursue further this trend by proposing the Pullback-Pushout (pb-po) Approach, where we combine smoothly the classical modifications to a host graph specified by a rule (a span of graph morphisms) with the cloning of structures specified by another rule. The approach is shown to be a conservative extension of agree (and thus of the sqpo approach), and we show that it can be extended with standard techniques to attributed graphs. We discuss conditions to ensure a form of locality of transformations, and conditions to ensure that the attribution of transformed graphs is total.

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  • On the Essence of Parallel Independence for the Double-Pushout and Sesqui-Pushout Approaches
    , 2016
    Co-Authors: Andrea Corradini, Michael Lowe, Leila Ribeiro, Dominique Duval, Rodrigo Machado, Andrei Costa, Guilherme Grochau Azzi, Jonas Santos Bezerra, Leonardo Marques Rodrigues

    Abstract:

    Parallel independence between transformation steps is a basic notion in the Algebraic Approaches to graph transformation, which is at the core of some static analysis techniques like Critical Pair Analysis. We propose a new categorical condition of parallel independence and show its equivalence with two other conditions proposed in the literature, for both left-linear and non-left-linear rules. Next we present some preliminary experimental results aimed at comparing the three conditions with respect to computational efficiency. To this aim, we implemented the three conditions, for left-linear rules only, in the Verigraph system, and used them to check parallel independence of pairs of overlapping redexes generated from some sample graph transformation systems over categories of typed graphs.

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