Journal•
MI Preprint Series
About: MI Preprint Series is an academic journal. The journal publishes majorly in the area(s): Restricted isometry property & Space (mathematics). Over the lifetime, 103 publications have been published receiving 1324 citations.
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71 citations
Journal Article•
TL;DR: In this article, the authors exploit recent advances in computational topology to study the compressibility of various proteins found in the Protein Data Bank (PDB), using the persistence diagram, a topological invariant which captures the sizes and robustness of geometric features such as tunnels and cavities in protein molecules.
Abstract: We exploit recent advances in computational topology to study the compressibility of various proteins found in the Protein Data Bank (PDB). Our fundamental tool is the persistence diagram, a topological invariant which captures the sizes and robustness of geometric features such as tunnels and cavities in protein molecules. Based on certain physical and chemical properties conjectured to impact protein compressibility, we propose a topological measurement CP for each protein molecule P . CP can be efficiently computed from the PDB data of P . Our main result establishes a clear linear correlation between CP and the experimentally measured compressibility of most proteins for which both PDB information and experimental compressibility data are available.
62 citations
Journal Article•
TL;DR: In this article, a Galerkin-characteristics finite element scheme of lumped mass type is presented for convection-diffusion problems under the weakly acute triangulation hypothesis, which is proved to be stable and convergent in the L ∞ -norm.
Abstract: A Galerkin-characteristics finite element scheme of lumped mass type is presented for the convection-diffusion problems. Under the weakly acute triangulation hypothesis the scheme is proved to be stable and convergent in the L ∞ -norm. Using the Freefem, we show 2D and 3D numerical examples, which reflect the robustness ot the scheme and the theoretical convergence result.
53 citations
Journal Article•
41 citations
Journal Article•
TL;DR: In this paper, the problem of variable selection for factor analysis models via the L1 regularization procedure is considered and a model selection criterion for evaluating a factor analysis model via the grouped lasso is derived.
Abstract: The L1 regularization such as the lasso has been widely used in regression analysis since it tends to produce some coefficients that are exactly zero, which leads to variable selection. We consider the problem of variable selection for factor analysis models via the L1 regularization procedure. In order to select variables each of which is controlled by multiple parameters, we treat parameters as grouped parameters and then apply the grouped lasso. Crucial issues in this modeling procedure include the selection of the number of factors and regularization parameters. Choosing these parameters can be viewed as a model selection and evaluation problem. We derive a model selection criterion for evaluating a factor analysis model via the grouped lasso. The proposed procedure produces estimates that lead to variable selection and also selects the number of factors objectively. Monte Carlo simulations are conducted to investigate the effectiveness of the proposed procedure. A real data example is also given to illustrate our procedure.
41 citations