B-spline tight frame based force matching method

Yang, Jianbin; Zhu, Guang; Tong, Dudu; Lu, Lanyuan; Shen, Zuowei

doi:10.1016/j.jcp.2018.02.024

Cited by 12 publications

(9 citation statements)

References 37 publications

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“…50 By first parameterizing the two-body potential and then introducing three-body terms as a correction, these authors have demonstrated that three-body interactions are essential to reproduce structural properties of liquid water. 50 Four-body terms have also been taken into account in a CG model energy, by considering dihedral potentials between sets of four atoms, 51,52 and higher-body terms have been built by means of statistical contact potentials. [53][54][55] Many-body terms can also be included in a CG potential by using kernel-based machine learning methods, such the Gaussian approximation potentials pioneered by Csańyi and coworkers.…”

Section: Introductionmentioning

confidence: 99%

Multi-body effects in a coarse-grained protein force field

Wang

Charron

Husic

et al. 2021

The Journal of Chemical Physics

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The use of coarse-grained (CG) models is a popular approach to study complex biomolecular systems. By reducing the number of degrees of freedom, a CG model can explore long time-and length-scales inaccessible to computational models at higher resolution. If a CG model is designed by formally integrating out some of the system's degrees of freedom, one expects multi-body interactions to emerge in the effective CG model's energy function. In practice, it has been shown that the inclusion of multi-body terms indeed improves the accuracy of a CG model. However, no general approach has been proposed to systematically construct a CG effective energy that includes arbitrary orders of multi-body terms. In this work, we propose a neural network based approach to address this point and construct a CG model as a multibody expansion. By applying this approach to a small protein, we evaluate the relative importance of the different multi-body terms in the definition of an accurate model. We observe a slow convergence in the multi-body expansion, where up to five-body interactions are needed to reproduce the free energy of an atomistic model.

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Section: Introductionmentioning

confidence: 99%

Multi-body effects in a coarse-grained protein force field

Wang

Charron

Husic

et al. 2021

The Journal of Chemical Physics

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“…Frame theory is a relatively emerging area in pure as well as applied mathematics research and approximation. It has been applied in a wide range of applications in signal processing [13], image denoising [14], and computational physics and biology [15]. Interested readers should consult the references therein to get a complete picture.…”

Section: Preliminary Resultsmentioning

confidence: 99%

“…Let X 0 (Ψ) be a quasi-tight framelet system generated using the OEP from the compactly supported function φ. Assume that f satisfies the condition (15). Then,…”

Section: Error Analysismentioning

confidence: 99%

A Numerical Solution of Fredholm Integral Equations of the Second Kind Based on Tight Framelets Generated by the Oblique Extension Principle

Mohammad

2019

Symmetry

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In this paper, we present a new computational method for solving linear Fredholm integral equations of the second kind, which is based on the use of B-spline quasi-affine tight framelet systems generated by the unitary and oblique extension principles. We convert the integral equation to a system of linear equations. We provide an example of the construction of quasi-affine tight framelet systems. We also give some numerical evidence to illustrate our method. The numerical results confirm that the method is efficient, very effective and accurate.

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“…After weighted sum image ĝ is obtained, we generate its feature set by using a tight wavelet frame system. Due to its simplicity and practicability, a piecewise linear B-spline tight frame system [35], [37] is popular for feature extraction and redundant representations of images. We choose this system in which three one-dimensional filters are discretized as…”

Section: B Feature Extraction Via Wavelet Framesmentioning

confidence: 99%

Sparse Regularization-Based Fuzzy C-Means Clustering Incorporating Morphological Grayscale Reconstruction and Wavelet Frames

Wang

Pedrycz

Zhou

et al. 2021

IEEE Trans. Fuzzy Syst.

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Instead of directly utilizing an observed image including some outliers, noise or intensity inhomogeneity, the use of its ideal value (e.g. noise-free image) has a favorable impact on clustering. Hence, the accurate estimation of the residual (e.g. unknown noise) between the observed image and its ideal value is an important task. To do so, we propose an ℓ0 regularization-based Fuzzy C-Means (FCM) algorithm incorporating a morphological reconstruction operation and a tight wavelet frame transform. To achieve a sound trade-off between detail preservation and noise suppression, morphological reconstruction is used to filter an observed image. By combining the observed and filtered images, a weighted sum image is generated. Since a tight wavelet frame system has sparse representations of an image, it is employed to decompose the weighted sum image, thus forming its corresponding feature set. Taking it as data for clustering, we present an improved FCM algorithm by imposing an ℓ0 regularization term on the residual between the feature set and its ideal value, which implies that the favorable estimation of the residual is obtained and the ideal value participates in clustering. Spatial information is also introduced into clustering since it is naturally encountered in image segmentation. Furthermore, it makes the estimation of the residual more reliable. To further enhance the segmentation effects of the improved FCM algorithm, we also employ the morphological reconstruction to smoothen the labels generated by clustering. Finally, based on the prototypes and smoothed labels, the segmented image is reconstructed by using a tight wavelet frame reconstruction operation. Experimental results reported for synthetic, medical, and color images show that the proposed algorithm is effective and efficient, and outperforms other algorithms.

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B-spline tight frame based force matching method

Cited by 12 publications

References 37 publications

Multi-body effects in a coarse-grained protein force field

Multi-body effects in a coarse-grained protein force field

A Numerical Solution of Fredholm Integral Equations of the Second Kind Based on Tight Framelets Generated by the Oblique Extension Principle

Sparse Regularization-Based Fuzzy C-Means Clustering Incorporating Morphological Grayscale Reconstruction and Wavelet Frames

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