Algebraic Approaches

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

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, Linnea Schmidt, Naser Monsefi, Teresia Kling, Rebecka Jornsten, Sven Nelander
    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.

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.

  • 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.

  • On the Essence of Parallel Independence for the Double-Pushout and Sesqui-Pushout Approaches
    2016
    Co-Authors: Andrea Corradini, Michael Lowe, Dominique Duval, Leila Ribeiro, 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.

  • on the definition of parallel independence in the Algebraic Approaches to graph transformation
    International Workshop Software Engineering Methods Spreadsheets, 2016
    Co-Authors: Andrea Corradini
    Abstract:

    Parallel independence between transformation steps is a basic and well-understood notion of the Algebraic Approaches to graph transformation, and typically guarantees that the two steps can be applied in any order obtaining the same resulting graph, up to isomorphism. The concept has been redefined for several Algebraic Approaches as variations of a classical “Algebraic” condition, requiring that each matching morphism factorizes through the context graphs of the other transformation step. However, looking at some classical papers on the double-pushout approach, one finds that the original definition of parallel independence was formulated in set-theoretical terms, requiring that the intersection of the images of the two left-hand sides in the host graph is contained in the intersection of the two interface graphs. The relationship between this definition and the standard Algebraic one is discussed in this position paper, both in the case of left-linear and non-left-linear rules.

  • AGREE - Algebraic Graph Rewriting with Controlled Embedding
    2015
    Co-Authors: Andrea Corradini, Dominique Duval, Rachid Echahed, Frederic Prost, Leila Ribeiro
    Abstract:

    The several Algebraic Approaches to graph transformation proposed in the literature all ensure that if an item is preserved by a rule, so are its connections with the context 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 conservative extension of classical Algebraic Approaches to graph transformation, for the case of monic matches, where rules allow one to specify how the embedding of preserved items should be carried out.

Gregory Ward - One of the best experts on this subject based on the ideXlab platform.

  • modeling the direct sun component in buildings using matrix Algebraic Approaches methods and validation
    Solar Energy, 2018
    Co-Authors: David Geislermoroder, Gregory Ward
    Abstract:

    Abstract Simulation tools that enable annual energy performance analysis of optically-complex fenestration systems have been widely adopted by the building industry for use in building design, code development, and the development of rating and certification programs for commercially-available shading and daylighting products. The tools rely on a three-phase matrix operation to compute solar heat gains, using as input low-resolution bidirectional scattering distribution function (BSDF) data (10–15° angular resolution; BSDF data define the angle-dependent behavior of light-scattering materials and systems). Measurement standards and product libraries for BSDF data are undergoing development to support solar heat gain calculations. Simulation of other metrics such as discomfort glare, annual solar exposure, and potentially thermal discomfort, however, require algorithms and BSDF input data that more accurately model the spatial distribution of transmitted and reflected irradiance or illuminance from the sun (0.5° resolution). This study describes such algorithms and input data, then validates the tools (i.e., an interpolation tool for measured BSDF data and the five-phase method) through comparisons with ray-tracing simulations and field monitored data from a full-scale testbed. Simulations of daylight-redirecting films, a micro-louvered screen, and venetian blinds using variable resolution, tensor tree BSDF input data derived from interpolated scanning goniophotometer measurements were shown to agree with field monitored data to within 20% for greater than 75% of the measurement period for illuminance-based performance parameters. The three-phase method delivered significantly less accurate results. We discuss the ramifications of these findings on industry and provide recommendations to increase end user awareness of the current limitations of existing software tools and BSDF product libraries.

Pascal Morin - One of the best experts on this subject based on the ideXlab platform.

  • Nonlinear observer design on SL(3) for homography estimation by exploiting point and line correspondences with application to image stabilization
    Automatica, 2020
    Co-Authors: Minh-duc Hua, Jochen Trumpf, Tarek Hamel, Robert Mahony, Pascal Morin
    Abstract:

    Although homography estimation from correspondences of mixed-type features, namely points and lines, has been relatively well studied with Algebraic Approaches by the computer vision community, this problem has never been addressed with nonlinear observer paradigms. In this paper, a novel nonlinear observer on the Special Linear group SL(3) applied to homography estimation is developed. The key advance with respect to similar works on the topic is the formulation of observer innovation that exploits directly point and line correspondences as input without requiring prior Algebraic reconstruction of individual homographies. Rigourous observability and stability analysis is provided. A potential application to image stabilization in presence of very fast camera motion, severe occlusion, specular reflection, image blur, and light saturation is demonstrated with very encouraging results.