The Experts below are selected from a list of 66 Experts worldwide ranked by ideXlab platform

Uli Wagner - One of the best experts on this subject based on the ideXlab platform.

  • eliminating higher multiplicity intersections ii the deleted Product Criterion in the r metastable range
    Symposium on Computational Geometry, 2016
    Co-Authors: Isaac Mabillard, Uli Wagner
    Abstract:

    Motivated by Tverberg-type problems in topological combinatorics and by classical results about embeddings (maps without double points), we study the question whether a finite simplicial complex K can be mapped into R^d without higher-multiplicity intersections. We focus on conditions for the existence of almost r-embeddings, i.e., maps f: K -> R^d such that the intersection of f(sigma_1), ..., f(sigma_r) is empty whenever sigma_1,...,sigma_r are pairwise disjoint simplices of K. Generalizing the classical Haefliger-Weber embeddability Criterion, we show that a well-known necessary deleted Product condition for the existence of almost r-embeddings is sufficient in a suitable r-metastable range of dimensions: If r d > (r+1) dim K + 2 then there exists an almost r-embedding K-> R^d if and only if there exists an equivariant map of the r-fold deleted Product of K to the sphere S^(d(r-1)-1). This significantly extends one of the main results of our previous paper (which treated the special case where d=rk and dim K=(r-1)k, for some k> 2), and settles an open question raised there.

  • eliminating higher multiplicity intersections ii the deleted Product Criterion in the r metastable range
    arXiv: Geometric Topology, 2016
    Co-Authors: Isaac Mabillard, Uli Wagner
    Abstract:

    Motivated by Tverberg-type problems in topological combinatorics and by classical results about embeddings (maps without double points), we study the question whether a finite simplicial complex K can be mapped into R^d without higher-multiplicity intersections. We focus on conditions for the existence of almost r-embeddings, i.e., maps from K to R^d without r-intersection points among any set of r pairwise disjoint simplices of K. Generalizing the classical Haefliger-Weber embeddability Criterion, we show that a well-known necessary deleted Product condition for the existence of almost r-embeddings is sufficient in a suitable r-metastable range of dimensions (r d > (r+1) dim K +2). This significantly extends one of the main results of our previous paper (which treated the special case where d=rk and dim K=(r-1)k, for some k> 3).

Isaac Mabillard - One of the best experts on this subject based on the ideXlab platform.

  • eliminating higher multiplicity intersections ii the deleted Product Criterion in the r metastable range
    Symposium on Computational Geometry, 2016
    Co-Authors: Isaac Mabillard, Uli Wagner
    Abstract:

    Motivated by Tverberg-type problems in topological combinatorics and by classical results about embeddings (maps without double points), we study the question whether a finite simplicial complex K can be mapped into R^d without higher-multiplicity intersections. We focus on conditions for the existence of almost r-embeddings, i.e., maps f: K -> R^d such that the intersection of f(sigma_1), ..., f(sigma_r) is empty whenever sigma_1,...,sigma_r are pairwise disjoint simplices of K. Generalizing the classical Haefliger-Weber embeddability Criterion, we show that a well-known necessary deleted Product condition for the existence of almost r-embeddings is sufficient in a suitable r-metastable range of dimensions: If r d > (r+1) dim K + 2 then there exists an almost r-embedding K-> R^d if and only if there exists an equivariant map of the r-fold deleted Product of K to the sphere S^(d(r-1)-1). This significantly extends one of the main results of our previous paper (which treated the special case where d=rk and dim K=(r-1)k, for some k> 2), and settles an open question raised there.

  • eliminating higher multiplicity intersections ii the deleted Product Criterion in the r metastable range
    arXiv: Geometric Topology, 2016
    Co-Authors: Isaac Mabillard, Uli Wagner
    Abstract:

    Motivated by Tverberg-type problems in topological combinatorics and by classical results about embeddings (maps without double points), we study the question whether a finite simplicial complex K can be mapped into R^d without higher-multiplicity intersections. We focus on conditions for the existence of almost r-embeddings, i.e., maps from K to R^d without r-intersection points among any set of r pairwise disjoint simplices of K. Generalizing the classical Haefliger-Weber embeddability Criterion, we show that a well-known necessary deleted Product condition for the existence of almost r-embeddings is sufficient in a suitable r-metastable range of dimensions (r d > (r+1) dim K +2). This significantly extends one of the main results of our previous paper (which treated the special case where d=rk and dim K=(r-1)k, for some k> 3).

Davey L Jones - One of the best experts on this subject based on the ideXlab platform.

  • e coli is a poor end Product Criterion for assessing the general microbial risk posed from consuming norovirus contaminated shellfish
    Frontiers in Microbiology, 2021
    Co-Authors: Jasmine H Sharp, Katie Clements, Mallory Diggens, James E Mcdonald, Shelagh K Malham, Davey L Jones
    Abstract:

    The fecal indicator organism (FIO) Escherichia coli is frequently used as a general indicator of sewage contamination and for evaluating the success of shellfish cleaning (depuration) processes. To evaluate the robustness of this approach, the accumulation, retention, and depuration of non-pathogenic E. coli, pathogenic E. coli O157:H7 and norovirus GII (NoV GII) RNA were evaluated using a combination of culture-based (E. coli) and molecular methods (E. coli, NoV GII) after exposure of mussels (Mytilus edulis) to water contaminated with human feces. We simulated water contamination after a point-source release from a combined sewer overflow (CSO) where untreated wastewater is released directly into the coastal zone. All three microbiological indicators accumulated rapidly in the mussels, reaching close to maximum concentration within 3 h of exposure, demonstrating that short CSO discharges pose an immediate threat to shellfish harvesting areas. Depuration (72 h) in clean water proved partially successful at removing both pathogenic and non-pathogenic E. coli from shellfish tissue, but failed to eradicate NoV GII RNA. We conclude that current EU standards for evaluating microbiological risk in shellfish are inadequate for protecting consumers against exposure to human norovirus GII found in polluted marine waters.

George Pelekanos - One of the best experts on this subject based on the ideXlab platform.

  • on an application of the improved maximum Product Criterion to inverse acoustic scattering in a layered medium
    Journal of Applied Mathematics and Physics, 2021
    Co-Authors: Fermin S V Bazan, Juliano B Francisco, Koung Hee Leem, George Pelekanos, V Sevroglou
    Abstract:

    In this paper, we consider the numerical treatment of an inverse acoustic scattering problem that involves an impenetrable obstacle embedded in a layered medium. We begin by employing a modified version of the well known factorization method, in which a computationally effective numerical scheme for the reconstruction of the shape of the scatterer is presented. This is possible, due to a mixed reciprocity principle, which renders the computation of the Green function at the background medium unnecessary. Moreover, to further refine our inversion algorithm, an efficient Tikhonov parameter choice technique, called Improved Maximum Product Criterion (IMPC) is exploited. Our regularization parameter is computed via a fast iterative algorithm which requires no a priori knowledge of the noise level in the far-field data. Finally, the effectiveness of IMPC is illustrated with various numerical examples.

  • an improved maximum Product Criterion for three dimensional reconstructions in electromagnetics
    PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2014 (ICNAAM-2014), 2015
    Co-Authors: Fermin S V Bazan, Juliano B Francisco, Koung Hee Leem, George Pelekanos
    Abstract:

    We present a Tikhonov parameter choice approach for three-dimensional reconstructions based on a maximum Product Criterion (MPC) which provides a regularization parameter located in the concave part of the L-curve in log-log scale. Our method, baptised Improved Maximum Product Criterion (IMPC), is an extension of the MPC method developed by Bazan et al for two-dimensional reconstructions. In the 3D framework, IMPC computes the regularization parameter via a fast iterative algorithm and requires no a priori knowledge of the noise level in the data. It is applied on the linear sampling method for the reconstruction of two objects one of which is a perfect conductor whereas the other is an imperfect conductor.

  • using the linear sampling method and an improved maximum Product Criterion for the solution of the electromagnetic inverse medium problem
    Journal of Computational and Applied Mathematics, 2015
    Co-Authors: Fermin S V Bazan, Juliano B Francisco, Koung Hee Leem, George Pelekanos
    Abstract:

    We present a Tikhonov parameter choice approach for three-dimensional reconstructions based on a maximum Product Criterion (MPC) which provides a regularization parameter located in the concave part of the L-curve in log-log scale. Our method, baptized Improved Maximum Product Criterion (IMPC), is an extension of the MPC method developed by Bazan et al. for two-dimensional reconstructions. In the 3D framework, IMPC computes the regularization parameter via a fast iterative algorithm and requires no a priori knowledge of the noise level in the data. It is applied on the linear sampling method for solving the electromagnetic inverse medium problem in the 3D framework. The effectiveness of IMPC is illustrated with numerical examples involving more than one scatterer.

  • a maximum Product Criterion as a tikhonov parameter choice rule for kirsch s factorization method
    Journal of Computational and Applied Mathematics, 2012
    Co-Authors: Fermin S V Bazan, Juliano B Francisco, Koung Hee Leem, George Pelekanos
    Abstract:

    Kirsch's factorization method is a fast inversion technique for visualizing the profile of a scatterer from measurements of the far-field pattern. We present a Tikhonov parameter choice approach based on a maximum Product Criterion (MPC) which provides a regularization parameter located in the concave part of the L-curve on a log-log scale. The performance of the method is evaluated by comparing our reconstructions with those obtained via the L-curve, Morozov's discrepancy principle and the SVD-tail. Numerical results that illustrate the effectiveness of the MPC in reconstruction problems involving both simulated and real data are reported and analyzed.

Fermin S V Bazan - One of the best experts on this subject based on the ideXlab platform.

  • on an application of the improved maximum Product Criterion to inverse acoustic scattering in a layered medium
    Journal of Applied Mathematics and Physics, 2021
    Co-Authors: Fermin S V Bazan, Juliano B Francisco, Koung Hee Leem, George Pelekanos, V Sevroglou
    Abstract:

    In this paper, we consider the numerical treatment of an inverse acoustic scattering problem that involves an impenetrable obstacle embedded in a layered medium. We begin by employing a modified version of the well known factorization method, in which a computationally effective numerical scheme for the reconstruction of the shape of the scatterer is presented. This is possible, due to a mixed reciprocity principle, which renders the computation of the Green function at the background medium unnecessary. Moreover, to further refine our inversion algorithm, an efficient Tikhonov parameter choice technique, called Improved Maximum Product Criterion (IMPC) is exploited. Our regularization parameter is computed via a fast iterative algorithm which requires no a priori knowledge of the noise level in the far-field data. Finally, the effectiveness of IMPC is illustrated with various numerical examples.

  • an improved maximum Product Criterion for three dimensional reconstructions in electromagnetics
    PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2014 (ICNAAM-2014), 2015
    Co-Authors: Fermin S V Bazan, Juliano B Francisco, Koung Hee Leem, George Pelekanos
    Abstract:

    We present a Tikhonov parameter choice approach for three-dimensional reconstructions based on a maximum Product Criterion (MPC) which provides a regularization parameter located in the concave part of the L-curve in log-log scale. Our method, baptised Improved Maximum Product Criterion (IMPC), is an extension of the MPC method developed by Bazan et al for two-dimensional reconstructions. In the 3D framework, IMPC computes the regularization parameter via a fast iterative algorithm and requires no a priori knowledge of the noise level in the data. It is applied on the linear sampling method for the reconstruction of two objects one of which is a perfect conductor whereas the other is an imperfect conductor.

  • using the linear sampling method and an improved maximum Product Criterion for the solution of the electromagnetic inverse medium problem
    Journal of Computational and Applied Mathematics, 2015
    Co-Authors: Fermin S V Bazan, Juliano B Francisco, Koung Hee Leem, George Pelekanos
    Abstract:

    We present a Tikhonov parameter choice approach for three-dimensional reconstructions based on a maximum Product Criterion (MPC) which provides a regularization parameter located in the concave part of the L-curve in log-log scale. Our method, baptized Improved Maximum Product Criterion (IMPC), is an extension of the MPC method developed by Bazan et al. for two-dimensional reconstructions. In the 3D framework, IMPC computes the regularization parameter via a fast iterative algorithm and requires no a priori knowledge of the noise level in the data. It is applied on the linear sampling method for solving the electromagnetic inverse medium problem in the 3D framework. The effectiveness of IMPC is illustrated with numerical examples involving more than one scatterer.

  • a maximum Product Criterion as a tikhonov parameter choice rule for kirsch s factorization method
    Journal of Computational and Applied Mathematics, 2012
    Co-Authors: Fermin S V Bazan, Juliano B Francisco, Koung Hee Leem, George Pelekanos
    Abstract:

    Kirsch's factorization method is a fast inversion technique for visualizing the profile of a scatterer from measurements of the far-field pattern. We present a Tikhonov parameter choice approach based on a maximum Product Criterion (MPC) which provides a regularization parameter located in the concave part of the L-curve on a log-log scale. The performance of the method is evaluated by comparing our reconstructions with those obtained via the L-curve, Morozov's discrepancy principle and the SVD-tail. Numerical results that illustrate the effectiveness of the MPC in reconstruction problems involving both simulated and real data are reported and analyzed.