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Quad-tree Based Finite Volume Method for Diffusion Equations with Application to SAR Imaged Filtering

Zuzana KRIVÁ, Juraj PAPČO, Jakub VANKO (2015)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In this paper we present a method to remove the noise by applying the Perona Malik algorithm working on an irregular computational grid. This grid is obtained with a quad-tree technique and is adapted to the image intensities—pixels with similar intensities can form large elements. We apply this algorithm to remove the speckle noise present in SAR images, i.e., images obtained by radars with a synthetic aperture enabling to increase their resolution in an electronic way. The presence of the speckle...

Quality improvement of rule-based gene group descriptions using information about GO terms importance occurring in premises of determined rules

Marek Sikora, Aleksandra Gruca (2010)

International Journal of Applied Mathematics and Computer Science

In this paper we present a method for evaluating the importance of GO terms which compose multi-attribute rules. The rules are generated for the purpose of biological interpretation of gene groups. Each multi-attribute rule is a combination of GO terms and, based on relationships among them, one can obtain a functional description of gene groups. We present a method which allows evaluating the influence of a given GO term on the quality of a rule and the quality of a whole set of rules. For each...

Quantitative properties of quadratic spline wavelet bases in higher dimensions

Černá, Dana, Finěk, Václav, Šimůnková, Martina (2015)

Programs and Algorithms of Numerical Mathematics

To use wavelets efficiently to solve numerically partial differential equations in higher dimensions, it is necessary to have at one’s disposal suitable wavelet bases. Ideal wavelets should have short supports and vanishing moments, be smooth and known in closed form, and a corresponding wavelet basis should be well-conditioned. In our contribution, we compare condition numbers of different quadratic spline wavelet bases in dimensions d = 1, 2 and 3 on tensor product domains (0,1)^d.

Quantum optimal control using the adjoint method

Alfio Borzì (2012)

Nanoscale Systems: Mathematical Modeling, Theory and Applications

Control of quantum systems is central in a variety of present and perspective applications ranging from quantum optics and quantum chemistry to semiconductor nanostructures, including the emerging fields of quantum computation and quantum communication. In this paper, a review of recent developments in the field of optimal control of quantum systems is given with a focus on adjoint methods and their numerical implementation. In addition, the issues of exact controllability and optimal control are...

Quasi-Interpolation and A Posteriori Error Analysis in Finite Element Methods

Carsten Carstensen (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

One of the main tools in the proof of residual-based a posteriori error estimates is a quasi-interpolation operator due to Clément. We modify this operator in the setting of a partition of unity with the effect that the approximation error has a local average zero. This results in a new residual-based a posteriori error estimate with a volume contribution which is smaller than in the standard estimate. For an elliptic model problem, we discuss applications to conforming, nonconforming and mixed...

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