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  • 1
    Electronic Resource
    Electronic Resource
    The study of quasi wavelets based numerical method applied to Burgers' equations (2000)
    Springer
    Applied mathematics and mechanics 21 (2000), S. 1099-1110 
    Details
    ISSN: 1573-2754
    Keywords: quasi-wavelets ; Runge-Kutta method ; Burgers' equations ; O351.2
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract A quasi-wavelet based numerical method was introduced for solving the evolution of the solutions of nonlinear paritial differential Burgers' equations. The quasi wavelet based numerical method was used to discrete the spatial derivatives, while the fourth-order Runge-Kutta method was adopted to deal with the temporal discretization. The calculations were conducted at a variety of Reynolds numbers ranging from 10 to unlimited large. The comparisons of present results with analytical solutions show that the quasi wavelet based numerical method has distinctive local property, and is efficient and robust for numerically solving Burgers' equations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02458986
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    Paper (German National Licenses)
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  • 2
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    Structure and regeneration dynamics of three forest types at different succession stages of spruce – fir mixed forest in Changbai Mountain, northeastern China (2017)
    Springer
    Details
    Publication Date: 2017-09-01
    Print ISSN: 1672-6316
    Electronic ISSN: 1993-0321
    Topics: Geography
    Published by Springer
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  • 3
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    Generalized flexibility-rigidity index (2016)
    American Institute of Physics (AIP)
    Details
    Publication Date: 2016-06-21
    Description: Flexibility-rigidity index (FRI) has been developed as a robust, accurate, and efficient method for macromolecular thermal fluctuation analysis and B-factor prediction. The performance of FRI depends on its formulations of rigidity index and flexibility index. In this work, we introduce alternative rigidity and flexibility formulations. The structure of the classic Gaussian surface is utilized to construct a new type of rigidity index, which leads to a new class of rigidity densities with the classic Gaussian surface as a special case. Additionally, we introduce a new type of flexibility index based on the domain indicator property of normalized rigidity density. These generalized FRI (gFRI) methods have been extensively validated by the B-factor predictions of 364 proteins. Significantly outperforming the classic Gaussian network model, gFRI is a new generation of methodologies for accurate, robust, and efficient analysis of protein flexibility and fluctuation. Finally, gFRI based molecular surface generation and flexibility visualization are demonstrated.
    Print ISSN: 0021-9606
    Electronic ISSN: 1089-7690
    Topics: Chemistry and Pharmacology , Physics
    Published by American Institute of Physics (AIP)
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  • 4
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    Protein structure prediction beyond AlphaFold (2019)
    Springer Nature
    Details
    Publication Date: 2019
    Electronic ISSN: 2522-5839
    Topics: Computer Science
    Published by Springer Nature
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  • 5
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    Photodynamics of oxybenzone sunscreen: Nonadiabatic dynamics simulations (2016)
    American Institute of Physics
    Details
    Publication Date: 2016-08-21
    Print ISSN: 0021-9606
    Electronic ISSN: 1089-7690
    Topics: Chemistry and Pharmacology , Physics
    Published by American Institute of Physics
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  • 6
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    Communication: Capturing protein multiscale thermal fluctuations (2015)
    American Institute of Physics (AIP)
    Details
    Publication Date: 2015-06-03
    Description: Existing elastic network models are typically parametrized at a given cutoff distance and often fail to properly predict the thermal fluctuation of many macromolecules that involve multiple characteristic length scales. We introduce a multiscale flexibility-rigidity index (mFRI) method to resolve this problem. The proposed mFRI utilizes two or three correlation kernels parametrized at different length scales to capture protein interactions at corresponding scales. It is about 20% more accurate than the Gaussian network model (GNM) in the B-factor prediction of a set of 364 proteins. Additionally, the present method is able to deliver accurate predictions for some large macromolecules on which GNM fails to produce accurate predictions. Finally, for a protein of N residues, mFRI is of linear scaling ( O ( N ) ) in computational complexity, in contrast to the order of O ( N 3 ) for GNM.
    Print ISSN: 0021-9606
    Electronic ISSN: 1089-7690
    Topics: Chemistry and Pharmacology , Physics
    Published by American Institute of Physics (AIP)
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  • 7
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    Communication: Capturing protein multiscale thermal fluctuations (2015)
    American Institute of Physics (AIP)
    Details
    Publication Date: 2015-06-03
    Description: Existing elastic network models are typically parametrized at a given cutoff distance and often fail to properly predict the thermal fluctuation of many macromolecules that involve multiple characteristic length scales. We introduce a multiscale flexibility-rigidity index (mFRI) method to resolve this problem. The proposed mFRI utilizes two or three correlation kernels parametrized at different length scales to capture protein interactions at corresponding scales. It is about 20% more accurate than the Gaussian network model (GNM) in the B-factor prediction of a set of 364 proteins. Additionally, the present method is able to deliver accurate predictions for some large macromolecules on which GNM fails to produce accurate predictions. Finally, for a protein of N residues, mFRI is of linear scaling ( O ( N ) ) in computational complexity, in contrast to the order of O ( N 3 ) for GNM.
    Electronic ISSN: 1931-9223
    Topics: Chemistry and Pharmacology , Physics
    Published by American Institute of Physics (AIP)
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  • 8
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    Multiresolution persistent homology for excessively large biomolecular datasets (2015)
    American Institute of Physics (AIP)
    Details
    Publication Date: 2015-10-02
    Description: Although persistent homology has emerged as a promising tool for the topological simplification of complex data, it is computationally intractable for large datasets. We introduce multiresolution persistent homology to handle excessively large datasets. We match the resolution with the scale of interest so as to represent large scale datasets with appropriate resolution. We utilize flexibility-rigidity index to access the topological connectivity of the data set and define a rigidity density for the filtration analysis. By appropriately tuning the resolution of the rigidity density, we are able to focus the topological lens on the scale of interest. The proposed multiresolution topological analysis is validated by a hexagonal fractal image which has three distinct scales. We further demonstrate the proposed method for extracting topological fingerprints from DNA molecules. In particular, the topological persistence of a virus capsid with 273 780 atoms is successfully analyzed which would otherwise be inaccessible to the normal point cloud method and unreliable by using coarse-grained multiscale persistent homology. The proposed method has also been successfully applied to the protein domain classification, which is the first time that persistent homology is used for practical protein domain analysis, to our knowledge. The proposed multiresolution topological method has potential applications in arbitrary data sets, such as social networks, biological networks, and graphs.
    Electronic ISSN: 1931-9223
    Topics: Chemistry and Pharmacology , Physics
    Published by American Institute of Physics (AIP)
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  • 9
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    Multiresolution persistent homology for excessively large biomolecular datasets (2015)
    American Institute of Physics (AIP)
    Details
    Publication Date: 2015-10-02
    Description: Although persistent homology has emerged as a promising tool for the topological simplification of complex data, it is computationally intractable for large datasets. We introduce multiresolution persistent homology to handle excessively large datasets. We match the resolution with the scale of interest so as to represent large scale datasets with appropriate resolution. We utilize flexibility-rigidity index to access the topological connectivity of the data set and define a rigidity density for the filtration analysis. By appropriately tuning the resolution of the rigidity density, we are able to focus the topological lens on the scale of interest. The proposed multiresolution topological analysis is validated by a hexagonal fractal image which has three distinct scales. We further demonstrate the proposed method for extracting topological fingerprints from DNA molecules. In particular, the topological persistence of a virus capsid with 273 780 atoms is successfully analyzed which would otherwise be inaccessible to the normal point cloud method and unreliable by using coarse-grained multiscale persistent homology. The proposed method has also been successfully applied to the protein domain classification, which is the first time that persistent homology is used for practical protein domain analysis, to our knowledge. The proposed multiresolution topological method has potential applications in arbitrary data sets, such as social networks, biological networks, and graphs.
    Print ISSN: 0021-9606
    Electronic ISSN: 1089-7690
    Topics: Chemistry and Pharmacology , Physics
    Published by American Institute of Physics (AIP)
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  • 10
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    Multiscale Gaussian network model (mGNM) and multiscale anisotropic network model (mANM) (2015)
    American Institute of Physics (AIP)
    Details
    Publication Date: 2015-12-01
    Description: Gaussian network model (GNM) and anisotropic network model (ANM) are some of the most popular methods for the study of protein flexibility and related functions. In this work, we propose generalized GNM (gGNM) and ANM methods and show that the GNM Kirchhoff matrix can be built from the ideal low-pass filter, which is a special case of a wide class of correlation functions underpinning the linear scaling flexibility-rigidity index (FRI) method. Based on the mathematical structure of correlation functions, we propose a unified framework to construct generalized Kirchhoff matrices whose matrix inverse leads to gGNMs, whereas, the direct inverse of its diagonal elements gives rise to FRI method. With this connection, we further introduce two multiscale elastic network models, namely, multiscale GNM (mGNM) and multiscale ANM (mANM), which are able to incorporate different scales into the generalized Kirchhoff matrices or generalized Hessian matrices. We validate our new multiscale methods with extensive numerical experiments. We illustrate that gGNMs outperform the original GNM method in the B-factor prediction of a set of 364 proteins. We demonstrate that for a given correlation function, FRI and gGNM methods provide essentially identical B-factor predictions when the scale value in the correlation function is sufficiently large. More importantly, we reveal intrinsic multiscale behavior in protein structures. The proposed mGNM and mANM are able to capture this multiscale behavior and thus give rise to a significant improvement of more than 11% in B-factor predictions over the original GNM and ANM methods. We further demonstrate the benefits of our mGNM through the B-factor predictions of many proteins that fail the original GNM method. We show that the proposed mGNM can also be used to analyze protein domain separations. Finally, we showcase the ability of our mANM for the analysis of protein collective motions.
    Electronic ISSN: 1931-9223
    Topics: Chemistry and Pharmacology , Physics
    Published by American Institute of Physics (AIP)
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