scholarly journals Synchronization under matrix-weighted Laplacian

Automatica ◽  
2016 ◽  
Vol 73 ◽  
pp. 76-81 ◽  
Author(s):  
S. Emre Tuna
Keyword(s):  
Weighted Laplacian

scholarly journals Weighted Laplacian Method and Its Theoretical Applications

2020 ◽  
Vol 768 ◽  
pp. 072032
Author(s):  
Shijie Xu ◽  
Jiayan Fang ◽  
Xiangyang Li
Keyword(s):  
Weighted Laplacian

scholarly journals Generalized network dismantling

2019 ◽  
Vol 116 (14) ◽  
pp. 6554-6559 ◽  
Author(s):  
Xiao-Long Ren ◽  
Niels Gleinig ◽  
Dirk Helbing ◽  
Nino Antulov-Fantulin
Keyword(s):  
Large Scale ◽  
Vertex Cover ◽  
Criminal Organization ◽  
Fine Tuning ◽  
Laplacian Operator ◽  
Optimal Subset ◽  
Current State ◽  
Weighted Laplacian ◽  
Weighted Vertex ◽  
Large Scale Networks

Finding an optimal subset of nodes in a network that is able to efficiently disrupt the functioning of a corrupt or criminal organization or contain an epidemic or the spread of misinformation is a highly relevant problem of network science. In this paper, we address the generalized network-dismantling problem, which aims at finding a set of nodes whose removal from the network results in the fragmentation of the network into subcritical network components at minimal overall cost. Compared with previous formulations, we allow the costs of node removals to take arbitrary nonnegative real values, which may depend on topological properties such as node centrality or on nontopological features such as the price or protection level of a node. Interestingly, we show that nonunit costs imply a significantly different dismantling strategy. To solve this optimization problem, we propose a method which is based on the spectral properties of a node-weighted Laplacian operator and combine it with a fine-tuning mechanism related to the weighted vertex cover problem. The proposed method is applicable to large-scale networks with millions of nodes. It outperforms current state-of-the-art methods and opens more directions for understanding the vulnerability and robustness of complex systems.

Isoperimetric properties of weighted graphs related to the Laplacian spectrum and canonical correlations

2002 ◽  
Vol 39 (3-4) ◽  
pp. 425-441 ◽  
Author(s):  
M. Bolla ◽  
G. Molnár-Sáska
Keyword(s):  
Volume Ratio ◽  
Weighted Graph ◽  
Weighted Graphs ◽  
Laplacian Spectrum ◽  
Minimum Requirement ◽  
Cheeger Constant ◽  
Canonical Correlations ◽  
Laplacian Spectra ◽  
Weighted Laplacian ◽  
Similar Cluster

The relation between isoperimetric properties and Laplacian spectra of weighted graphs is investigated. The vertices are classified into k clusters with „few" inter-cluster edges of „small" weights (area) and „similar" cluster sizes (volumes). For k=2 the Cheeger constant represents the minimum requirement for the area/volume ratio and it is estimated from above by v?1(2-?1), where ?1 is the smallest positive eigenvalue of the weighted Laplacian. For k?2 we define the k-density of a weighted graph that is a generalization of the Cheeger constant and estimated from below by Si=1k-1?i and from above by c2 Si=1k-1 ?i, where 0<?1=…=Sk-1 are the smallest Laplacian eigenvalues and the constant c?1 depends on the metric classification properties of the corresponding eigenvectors. Laplacian spectra are also related to canonical correlations in a probabilistic setup.

scholarly journals Kriging-Weighted Laplacian Kernels

2021 ◽  
Author(s):  
Tuan Pham
Keyword(s):  
Neural Networks ◽  
Image Processing ◽  
Convolutional Neural Networks ◽  
Sharp Discontinuity ◽  
Weighted Laplacian ◽  
New Type

<div>Laplacian kernels, which are widely used as sharpening filters in image processing, are isotropic and tend to over-highlight fine details with a sharp discontinuity in images. To address this issue, this paper introduces a method that integrates anisotropic averaging with the Laplacian kernels. </div><div>The proposed method can also be useful as a new type of image convolution for designing convolutional neural networks. </div>

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