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Sampling numbers of smoothness classes via 𝓁1-minimization 通过𝓁1-minimization获取平滑度类的采样数
IF 2.1 4区 数学
Journal of complex networks Pub Date : 2022-12-01 DOI: 10.48550/arXiv.2212.00445
Thomas Jahn, T. Ullrich, Felix Voigtländer
{"title":"Sampling numbers of smoothness classes via 𝓁1-minimization","authors":"Thomas Jahn, T. Ullrich, Felix Voigtländer","doi":"10.48550/arXiv.2212.00445","DOIUrl":"https://doi.org/10.48550/arXiv.2212.00445","url":null,"abstract":"Using techniques developed recently in the field of compressed sensing we prove new upper bounds for general (nonlinear) sampling numbers of (quasi-)Banach smoothness spaces in $L^2$. In particular, we show that in relevant cases such as mixed and isotropic weighted Wiener classes or Sobolev spaces with mixed smoothness, sampling numbers in $L^2$ can be upper bounded by best $n$-term trigonometric widths in $L^infty$. We describe a recovery procedure from $m$ function values based on $ell^1$-minimization (basis pursuit denoising). With this method, a significant gain in the rate of convergence compared to recently developed linear recovery methods is achieved. In this deterministic worst-case setting we see an additional speed-up of $m^{-1/2}$ (up to log factors) compared to linear methods in case of weighted Wiener spaces. For their quasi-Banach counterparts even arbitrary polynomial speed-up is possible. Surprisingly, our approach allows to recover mixed smoothness Sobolev functions belonging to $S^r_pW(mathbb{T}^d)$ on the $d$-torus with a logarithmically better rate of convergence than any linear method can achieve when $1","PeriodicalId":15442,"journal":{"name":"Journal of complex networks","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80386334","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 8
Improving mean-field network percolation models with neighbourhood information and their limitations on highly modular, highly dispersed networks 基于邻域信息的平均场网络渗透模型的改进及其在高度模块化、高度分散网络中的局限性
IF 2.1 4区 数学
Journal of complex networks Pub Date : 2022-11-04 DOI: 10.48550/arXiv.2211.02346
Chris Jones, K. Wiesner
{"title":"Improving mean-field network percolation models with neighbourhood information and their limitations on highly modular, highly dispersed networks","authors":"Chris Jones, K. Wiesner","doi":"10.48550/arXiv.2211.02346","DOIUrl":"https://doi.org/10.48550/arXiv.2211.02346","url":null,"abstract":"Mean field theory models of percolation on networks provide analytic estimates of network robustness under node or edge removal. We introduce a new mean field theory model based on generating functions that includes information about the tree-likeness of each node's local neighbourhood. We show that our new model outperforms all other generating function models in prediction accuracy when testing their estimates on a wide range of real-world network data. We compare the new model's performance against the recently introduced message passing models and provide evidence that the standard version is also outperformed, while the `loopy' version is only outperformed on a targeted attack strategy. As we show, however, the computational complexity of our model implementation is much lower than that of message passing algorithms. We provide evidence that all discussed models are poor in predicting networks with highly modular structure with dispersed modules, which are also characterised by high mixing times, identifying this as a general limitation of percolation prediction models.","PeriodicalId":15442,"journal":{"name":"Journal of complex networks","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2022-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75813974","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Hypergraph Artificial Benchmark for Community Detection (h-ABCD) 社区检测的超图人工基准
IF 2.1 4区 数学
Journal of complex networks Pub Date : 2022-10-26 DOI: 10.48550/arXiv.2210.15009
Bogumil Kami'nski, P. Prałat, F. Théberge
{"title":"Hypergraph Artificial Benchmark for Community Detection (h-ABCD)","authors":"Bogumil Kami'nski, P. Prałat, F. Théberge","doi":"10.48550/arXiv.2210.15009","DOIUrl":"https://doi.org/10.48550/arXiv.2210.15009","url":null,"abstract":"\u0000 The Artificial Benchmark for Community Detection (ABCD) graph is a recently introduced random graph model with community structure and power-law distribution for both degrees and community sizes. The model generates graphs with similar properties as the well-known Lancichinetti, Fortunato, Radicchi (LFR) one, and its main parameter ξ can be tuned to mimic its counterpart in the LFR model, the mixing parameter μ. In this article, we introduce hypergraph counterpart of the ABCD model, h–ABCD, which also produces random hypergraph with distributions of ground-truth community sizes and degrees following power-law. As in the original ABCD, the new model h–ABCD can produce hypergraphs with various levels of noise. More importantly, the model is flexible and can mimic any desired level of homogeneity of hyperedges that fall into one community. As a result, it can be used as a suitable, synthetic playground for analyzing and tuning hypergraph community detection algorithms.\u0000 [Received on 22 October 2022; editorial decision on 18 July 2023; accepted on 19 July 2023]","PeriodicalId":15442,"journal":{"name":"Journal of complex networks","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2022-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80601680","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
Controllability of a Class of Swarm Signaling Networks 一类群信令网络的可控性
IF 2.1 4区 数学
Journal of complex networks Pub Date : 2022-09-26 DOI: 10.1093/comnet/cnac054
Peng Sun, R. Kooij, Roland Bouffanais
{"title":"Controllability of a Class of Swarm Signaling Networks","authors":"Peng Sun, R. Kooij, Roland Bouffanais","doi":"10.1093/comnet/cnac054","DOIUrl":"https://doi.org/10.1093/comnet/cnac054","url":null,"abstract":"In this paper, we propose closed-form analytical expressions to determine the minimum number of driver nodes that is needed to control a specific class of networks. We consider swarm signaling networks with regular out-degree distribution where a fraction $p$ of the links is unavailable. We further apply our method to networks with bi-modal out-degree distributions. Our approximations are validated through intensive simulations. Results show that our approximations have high accuracy when compared with simulation results for both types of out-degree distribution.","PeriodicalId":15442,"journal":{"name":"Journal of complex networks","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2022-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80293718","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Analyzing and visualizing polarization and balance with signed networks: the U.S. Congress case study 用签名网络分析和可视化两极分化和平衡:美国国会案例研究
IF 2.1 4区 数学
Journal of complex networks Pub Date : 2022-09-01 DOI: 10.1093/comnet/cnad027
A. Capozzi, Alfonso Semeraro, G. Ruffo
{"title":"Analyzing and visualizing polarization and balance with signed networks: the U.S. Congress case study","authors":"A. Capozzi, Alfonso Semeraro, G. Ruffo","doi":"10.1093/comnet/cnad027","DOIUrl":"https://doi.org/10.1093/comnet/cnad027","url":null,"abstract":"\u0000 Signed networks and balance theory provide a natural setting for real-world scenarios that show polarization dynamics, positive/negative relationships and political partisanship. For example, they have been proven effective in studying the increasing polarization of the votes in the two chambers of the U.S. Congress from World War II on Andris, Lee, Hamilton, Martino, Gunning & Selden (2015, PLoS ONE, 10, 1–14) and Aref & Neal (2020, Sci. Rep., 10, 1–10). To provide further insights into this particular case study, we propose the application of a pipeline to analyze and visualize a signed graphs configuration based on the exploitation of the corresponding Laplacian matrix spectral properties. The overall methodology is comparable with others based on the frustration index, but it has at least two main advantages: first, it requires a much lower computational cost and second, it allows for a quantitative and visual assessment of how arbitrarily small subgraphs (even single nodes) contribute to the overall balance (or unbalance) of the network. The proposed pipeline allows the exploration of polarization dynamics shown by the U.S. Congress from 1945 to 2020 at different resolution scales. In fact, we are able to spot and point out the influence of some (groups of) congressmen in the overall balance, as well as to observe and explore polarizations evolution of both chambers across the years.","PeriodicalId":15442,"journal":{"name":"Journal of complex networks","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2022-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81449196","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
A note on the CBC-DBD construction of lattice rules with general positive weights 关于一般正权格规则的CBC-DBD构造的注记
IF 2.1 4区 数学
Journal of complex networks Pub Date : 2022-08-29 DOI: 10.48550/arXiv.2208.13610
P. Kritzer
{"title":"A note on the CBC-DBD construction of lattice rules with general positive weights","authors":"P. Kritzer","doi":"10.48550/arXiv.2208.13610","DOIUrl":"https://doi.org/10.48550/arXiv.2208.13610","url":null,"abstract":"Lattice rules are among the most prominently studied quasi-Monte Carlo methods to approximate multivariate integrals. A rank-$1$ lattice rule to approximate an $s$-dimensional integral is fully specified by its emph{generating vector} $boldsymbol{z} in mathbb{Z}^s$ and its number of points~$N$. While there are many results on the existence of ``good'' rank-$1$ lattice rules, there are no explicit constructions of good generating vectors for dimensions $s ge 3$. This is why one usually resorts to computer search algorithms. In a recent paper by Ebert et al. in the Journal of Complexity, we showed a component-by-component digit-by-digit (CBC-DBD) construction for good generating vectors of rank-1 lattice rules for integration of functions in weighted Korobov classes. However, the result in that paper was limited to product weights. In the present paper, we shall generalize this result to arbitrary positive weights, thereby answering an open question posed in the paper of Ebert et al. We also include a short section on how the algorithm can be implemented in the case of POD weights, by which we see that the CBC-DBD construction is competitive with the classical CBC construction.","PeriodicalId":15442,"journal":{"name":"Journal of complex networks","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2022-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75738677","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Efficient link prediction model for real-world complex networks using matrix-forest metric with local similarity features 基于局部相似特征的矩阵森林度量的复杂网络链路预测模型
IF 2.1 4区 数学
Journal of complex networks Pub Date : 2022-08-23 DOI: 10.1093/comnet/cnac039
Haji Gul, F. Al-Obeidat, Adnan Amin, Muhammad Mohsin Tahir, Kaizhu Huang
{"title":"Efficient link prediction model for real-world complex networks using matrix-forest metric with local similarity features","authors":"Haji Gul, F. Al-Obeidat, Adnan Amin, Muhammad Mohsin Tahir, Kaizhu Huang","doi":"10.1093/comnet/cnac039","DOIUrl":"https://doi.org/10.1093/comnet/cnac039","url":null,"abstract":"\u0000 Link prediction in a complex network is a difficult and challenging issue to address. Link prediction tries to better predict relationships, interactions and friendships based on historical knowledge of the complex network graph. Many link prediction techniques exist, including the common neighbour, Adamic-Adar, Katz and Jaccard coefficient, which use node information, local and global routes, and previous knowledge of a complex network to predict the links. These methods are extensively used in various applications because of their interpretability and convenience of use, irrespective of the fact that the majority of these methods were designed for a specific field. This study offers a unique link prediction approach based on the matrix-forest metric and vertex local structural information in a real-world complex network. We empirically examined the proposed link prediction method over 13 real-world network datasets obtained from various sources. Extensive experiments were performed that demonstrated the superior efficacy of the proposed link prediction method compared to other methods and outperformed the existing state-of-the-art in terms of prediction accuracy.","PeriodicalId":15442,"journal":{"name":"Journal of complex networks","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2022-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85414906","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Efficient eigenvalue counts for tree-like networks 树状网络的有效特征值计数
IF 2.1 4区 数学
Journal of complex networks Pub Date : 2022-08-23 DOI: 10.1093/comnet/cnac040
Grover E. C. Guzman, P. Stadler, André Fujita
{"title":"Efficient eigenvalue counts for tree-like networks","authors":"Grover E. C. Guzman, P. Stadler, André Fujita","doi":"10.1093/comnet/cnac040","DOIUrl":"https://doi.org/10.1093/comnet/cnac040","url":null,"abstract":"\u0000 Estimating the number of eigenvalues $mu_{[a,b]}$ of a network’s adjacency matrix in a given interval $[a,b]$ is essential in several fields. The straightforward approach consists of calculating all the eigenvalues in $O(n^3)$ (where $n$ is the number of nodes in the network) and then counting the ones that belong to the interval $[a,b]$. Another approach is to use Sylvester’s law of inertia, which also requires $O(n^3)$. Although both methods provide the exact number of eigenvalues in $[a,b]$, their application for large networks is computationally infeasible. Sometimes, an approximation of $mu_{[a,b]}$ is enough. In this case, Chebyshev’s method approximates $mu_{[a,b]}$ in $O(|E|)$ (where $|E|$ is the number of edges). This study presents two alternatives to compute $mu_{[a,b]}$ for locally tree-like networks: edge- and degree-based algorithms. The former presented a better accuracy than Chebyshev’s method. It runs in $O(d|E|)$, where $d$ is the number of iterations. The latter presented slightly lower accuracy but ran linearly ($O(n)$).","PeriodicalId":15442,"journal":{"name":"Journal of complex networks","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2022-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84515635","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Estimating the number of communities in the stochastic block model with outliers 带离群值的随机块模型中群落数量的估计
IF 2.1 4区 数学
Journal of complex networks Pub Date : 2022-08-23 DOI: 10.1093/comnet/cnac042
Jingsong Xiao, Fei Ye, Weidong Ma, Ying Yang
{"title":"Estimating the number of communities in the stochastic block model with outliers","authors":"Jingsong Xiao, Fei Ye, Weidong Ma, Ying Yang","doi":"10.1093/comnet/cnac042","DOIUrl":"https://doi.org/10.1093/comnet/cnac042","url":null,"abstract":"\u0000 The stochastic block model (SBM) is a popular model for community detecting problems. Many community detecting approaches have been proposed, and most of them assume that the number of communities is given previously. However, in practice, the number of communities is often unknown. Plenty of approaches were proposed to estimate the number of communities, but most of them were computationally intensive. Moreover, when outliers exist, there are no approaches to consistently estimate the number of communities. In this article, we propose a fast method based on the eigenvalues of the regularized and normalized adjacency matrix to estimate the number of communities under the SBM with outliers. We show that our method can consistently estimate the number of communities when outliers exist. Moreover, we extend our method to the degree-corrected SBM. We show that our approach is comparable to the other existing approaches in simulations. We also illustrate our approach on four real-world networks.","PeriodicalId":15442,"journal":{"name":"Journal of complex networks","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2022-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84026306","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Numerical weighted integration of functions having mixed smoothness 混合光滑函数的数值加权积分
IF 2.1 4区 数学
Journal of complex networks Pub Date : 2022-08-19 DOI: 10.48550/arXiv.2208.09108
D. Dung
{"title":"Numerical weighted integration of functions having mixed smoothness","authors":"D. Dung","doi":"10.48550/arXiv.2208.09108","DOIUrl":"https://doi.org/10.48550/arXiv.2208.09108","url":null,"abstract":"We investigate the approximation of weighted integrals over $mathbb{R}^d$ for integrands from weighted Sobolev spaces of mixed smoothness. We prove upper and lower bounds of the convergence rate of optimal quadratures with respect to $n$ integration nodes for functions from these spaces. In the one-dimensional case $(d=1)$, we obtain the right convergence rate of optimal quadratures. For $d ge 2$, the upper bound is performed by sparse-grid quadratures with integration nodes on step hyperbolic crosses in the function domain $mathbb{R}^d$.","PeriodicalId":15442,"journal":{"name":"Journal of complex networks","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2022-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79655330","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
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