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Spectral Techniques to Explore Point Clouds in Euclidean Space, with Applications to Collective Coordinates in Structural Biology

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Nonlinear Computational Geometry

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 151))

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Abstract

Life sciences, engineering, or telecommunications provide numerous systems whose description requires a large number of variables. Developing insights into such systems, forecasting their evolution, or monitoring them is often based on the inference of correlations between these variables. Given a collection of points describing states of the system, questions such as inferring the effective number of independent parameters of the system (its intrinsic dimensionality) and the way these are coupled are paramount to develop models. In this context, this paper makes two contributions.

First, we review recent work on spectral techniques to organize point clouds in Euclidean space, with emphasis on the main difficulties faced. Second, after a careful presentation of the bio-physical context, we present applications of dimensionality reduction techniques to a core problem in structural biology, namely protein folding.

Both from the computer science and the structural biology perspective, we expect this survey to shed new light on the importance of non linear computational geometry in geometric data analysis in general, and for protein folding in particular.

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Authors and Affiliations

  1. INRIA Sophia-Antipolis, 2004 route des Lucioles, BP 93, 06902, Valbonne, Sophia Antipolis, France

    Frédéric Cazals

  2. INRIA Saclay, Parc Orsay Université, 4 rue Jacques Monod, 91893, Orsay Cedex, France

    Frédéric Chazal

  3. Institut fuer Informatik, Ernst-Abbe-Platz 2, D-07743, Jena, Germany

    Joachim Giesen

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  1. Frédéric Cazals
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  2. Frédéric Chazal
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  3. Joachim Giesen
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Correspondence to Frédéric Cazals .

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Editors and Affiliations

  1. Dept. Informatics & Telecommunications, National University of Athens, Panepistimiopolis, Athens, 157 84, Greece

    Ioannis Z. Emiris

  2. Dept. Mathematics, Texas A & M University, Blocker Hall 608K, College Station, 77843, U.S.A.

    Frank Sottile

  3. Zentrum Mathematik (M10), TU München, Boltzmannstr. 3, Garching, 85748, Germany

    Thorsten Theobald

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Cazals, F., Chazal, F., Giesen, J. (2009). Spectral Techniques to Explore Point Clouds in Euclidean Space, with Applications to Collective Coordinates in Structural Biology. In: Emiris, I., Sottile, F., Theobald, T. (eds) Nonlinear Computational Geometry. The IMA Volumes in Mathematics and its Applications, vol 151. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-0999-2_1

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