SeisMath

Mathematical Models in Seismology
August 27 - September 7, 2012
L'Aquila, ITALY
 
 

Abstracts

First week August 27 - 31, 2012:
  • Jochen Garcke: "Classification and Regression for Data Analysis"

    The main focus of the course will be on supervised learning for classification and regression. Attention will be given to generalisability and predictive accuracy and the practical contexts in which methods are applied. Relevant statistical theory will mostly be assumed and described rather than derived mathematically. There will be more attention to the mathematical derivation and description of the algorithms.
    Topics to be covered include linear and additive models, support vector machines, Gaussian processes, Bayesian Classifiers, training/test approach to assessing accuracy, and covariance shift.

  • Mijail Guillemard: "Modern Methods in Dimensionality Reduction and Persistent Homology for Signal and Data Analysis"

    Over the last decade, new advances in signal and data analysis have been achieved with the application of geometrical and topological concepts. In this lecture, we will learn about modern developments in dimensionality reduction and manifold learning by studying important algorithms such as Kernel PCA, Isomap, Laplacian Eigenmanps, Local Tangent Space Alignment, etc. Additionally, we study important trends for data analysis based on powerful methods of persistent homology which has emerged as an important subfield of computational topology. Concrete applications in audio and image analysis will be covered both from a theoretical and computational point of view.

  • Holger Rauhut: "An Introduction to Compressive Sensing"

    Compressive sensing is a recent area in mathematical signal processing that predicts that certain signals (vectors, functions) can be recovered from what was previously believed to be incomplete information. The key observation is that many real-world signals are sparse in the sense that they can be well-represented by an expansion with only a small number of non-zero terms. Sparse signals can be accurately reconstructed from a small number of linear measurements via efficient algorithms such as l1-minimization. Remarkably, all known provably optimal measurement matrices in this context are random matrices. Of particular interest for applications are structured random matrices such as random partial Fourier matrices, or partial random circulant matrices. Applications of compressed sensing include medical imaging, geophysical imaging, analog to digital conversion, statistics and more.

Second week September 3 - 7, 2012:
  • Name: "Title"

    Description

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