更改

删除28,751字节 、 2025年6月27日 (五) 23:36
第282行: 第282行:     
== 参考文献 ==
 
== 参考文献 ==
−
  −
1. Pósfai, M. & Barabási, A.-L. Network Science (Cambridge Univ. Press, 2016).
  −
2. Squartini, T. & Garlaschelli, D. Maximum-Entropy Networks: Pattern Detection, Network Reconstruction and Graph Combinatorics (Springer, 2017).
  −
3. Newman, M. Networks (Oxford Univ. Press, 2018).
  −
4. Cimini, G. The statistical physics of real-world networks. Nat. Rev. Phys. 1 (2019).
  −
5. Radicchi, F., Ramasco, J., Barrat, A. & Fortunato, S. Complex networks renormalization: flows and fixed points. Phys. Rev. Lett. 101 (2008).
  −
6. Radicchi, F., Barrat, A., Fortunato, S. & Ramasco, J. J. Renormalization flows in complex networks. Phys. Rev. E 79 (2009).
  −
7. Chen, D., Su, H., Wang, X., Pan, G.-J. & Chen, G. Finite-size scaling of geometric renormalization flows in complex networks. Phys. Rev. E 104 (2021).
  −
8. Chen, D., Cai, D. & Su, H. Scaling properties of scale-free networks in degree-thresholding renormalization flows. IEEE Trans. Netw. Sci. Eng. 10 (2023).
  −
9. Serafino, M. True scale-free networks hidden by finite size effects. Proc. Natl Acad. Sci. USA 118 (2021).
  −
10. Itzykson, C. & Drouffe, J. M. Statistical Field Theory: Volume 1, From Brownian Motion to Renormalization and Lattice Gauge Theory (Cambridge Univ. Press, 1989).
  −
11. Burgess, C. P. Introduction to Effective Field Theory (Cambridge Univ. Press, 2020).
  −
12. Bardoscia, M. The physics of financial networks. Nat. Rev. Phys. 3 (2021).
  −
13. Soriano-Paños, D. Modeling communicable diseases, human mobility, and epidemics: a review. Ann. Phys. 534 (2022).
  −
14. Song, C., Havlin, S. & Makse, H. A. Self-similarity of complex networks. Nature 433 (2005).
  −
15. Binder, K. & Young, A. P. Spin glasses: experimental facts, theoretical concepts, and open questions. Rev. Mod. Phys. 58 (1986).
  −
16. Bar-Yam, Y. & Patil, S. P. Renormalization of sparse disorder in the Ising model. Preprint at arXiv (2018).
  −
17. Mandelbrot, B. B. The Fractal Geometry of Nature Vol. 2 (Freeman, 1982).
  −
18. Samsel, M., Makulski, K., Łepek, M., Fronczak, A. & Fronczak, P. Towards fractal origins of the community structure in complex networks: a model-based approach. Preprint at arXiv (2023).
  −
19. Goh, K.-I., Salvi, G., Kahng, B. & Kim, D. Skeleton and fractal scaling in complex networks. Phys. Rev. Lett. 96 (2006).
  −
20. Kim, J. S., Goh, K.-I., Kahng, B. & Kim, D. Fractality and self-similarity in scale-free networks. New J. Phys. 9 (2007).
  −
21. Fronczak, A. Scaling theory of fractal complex networks. Sci. Rep. (2024).
  −
22. Song, C., Havlin, S. & Makse, H. A. Origins of fractality in the growth of complex networks. Nat. Phys. 2 (2006).
  −
23. Rozenfeld, H. D., Song, C. & Makse, H. A. Small-world to fractal transition in complex networks: a renormalization group approach. Phys. Rev. Lett. 104 (2010).
  −
24. Newman, M. & Watts, D. Renormalization group analysis of the small-world network model. Phys. Lett. A 263 (1999).
  −
25. Kim, B. J. Geographical coarse graining of complex networks. Phys. Rev. Lett. 93 (2004).
  −
26. Gfeller, D. & Los Rios, P. Spectral coarse graining of complex networks. Phys. Rev. Lett. 99 (2007).
  −
27. Wang, Y., Zeng, A., Di, Z. & Fan, Y. Spectral coarse graining for random walks in bipartite networks. Chaos 23 (2013).
  −
28. Gfeller, D. & Los Rios, P. Spectral coarse graining and synchronization in oscillator networks. Phys. Rev. Lett. 100 (2008).
  −
29. Chen, J., an Lu, J., Lu, X., Wu, X. & Chen, G. Spectral coarse graining of complex clustered networks. Commun. Nonlinear Sci. Numer. Simul. 18 (2013).
  −
30. Jia, Z., Zeng, L., Wang, Y.-Y. & Wang, P. Optimization algorithms for spectral coarse-graining of complex networks. Physica A 514 (2019).
  −
31. Zeng, A. & Lü, L. Coarse graining for synchronization in directed networks. Phys. Rev. E 83 (2011).
  −
32. Wang, P. & Xu, S. Spectral coarse grained controllability of complex networks. Physica A 478 (2017).
  −
33. Aygün, E. & Erzan, A. Spectral renormalization group theory on networks. J. Phys. Conf. Ser. 319 (2011).
  −
34. Tuncer, A. & Erzan, A. Spectral renormalization group for the Gaussian model and $Psi$4 theory on nonspatial networks. Phys. Rev. E 92 (2015).
  −
35. Villegas, P., Gili, T., Caldarelli, G. & Gabrielli, A. Laplacian renormalization group for heterogeneous networks. Nat. Phys. 19 (2023).
  −
36. Chen, H., Hou, Z., Xin, H. & Yan, Y. Statistically consistent coarse-grained simulations for critical phenomena in complex networks. Phys. Rev. E 82 (2010).
  −
37. Long, Y.-S., Jia, Z. & Wang, Y.-Y. Coarse graining method based on generalized degree in complex network. Physica A 505 (2018).
  −
38. Wang, Y. Coarse graining method based on node similarity in complex network. Commun. Netw. 10 (2018).
  −
39. Lorrain, F. & White, H. C. Structural equivalence of individuals in social networks. J. Math. Sociol. 1 (1971).
  −
40. Dunne, J. A. Food webs. In textit{Encyclopedia of Complexity and Systems Science (ed. Meyers, R.) 3661–3682 (Springer, 2009).
  −
41. Itzkovitz, S. Coarse-graining and self-dissimilarity of complex networks. Phys. Rev. E 71 (2005).
  −
42. Serrano, M. Á., Krioukov, D. & Boguñá, M. Self-similarity of complex networks and hidden metric spaces. Phys. Rev. Lett. 100 (2008).
  −
43. Alvarez-Hamelin, J., Dall’Asta, L., Barrat, A. & Vespignani, A. K-core decomposition of Internet graphs: hierarchies, self-similarity and measurement biases. Netw. Heterog. Media 3 (2008).
  −
44. Lambiotte, R. Multi-scale modularity in complex networks. In textit{8th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks 546–553 (IEEE, 2010).
  −
45. Karypis, G. & Kumar, V. A fast and high quality multilevel scheme for partitioning irregular graphs. SIAM J. Sci. Comput. 20 (1998).
  −
46. Abou-Rjeili, A. & Karypis, G. Multilevel algorithms for partitioning power-law graphs. In textit{Proc. 20th IEEE International Parallel & Distributed Processing Symposium (IEEE, 2006).
  −
47. Leifer, I., Phillips, D., Sorrentino, F. & Makse, H. A. Symmetry-driven network reconstruction through pseudobalanced coloring optimization. J. Stat. Mech. 2022 (2022).
  −
48. Boldi, P. & Vigna, S. Fibrations of graphs. Discrete Math. 243 (2002).
  −
49. Cardelli, L., Tribastone, M., Tschaikowski, M. & Vandin, A. Maximal aggregation of polynomial dynamical systems. Proc. Natl Acad. Sci. USA 114 (2017).
  −
50. Cardelli, L., Tribastone, M., Tschaikowski, M. & Vandin, A. Erode: a tool for the evaluation and reduction of ordinary differential equations. In textit{Proc. Tools and Algorithms for the Construction and Analysis of Systems: 23rd International Conference, TACAS 2017 Part II 23, 310–328 (Springer, 2017).
  −
51. Argyris, G. A., Lluch Lafuente, A., Tribastone, M., Tschaikowski, M. & Vandin, A. Reducing Boolean networks with backward equivalence. BMC Bioinformatics 24 (2023).
  −
52. Morone, F., Leifer, I. & Makse, H. A. Fibration symmetries uncover the building blocks of biological networks. Proc. Natl Acad. Sci. USA 117 (2020).
  −
53. Gili, T. et al. Fibration symmetry-breaking supports functional transitions in a brain network engaged in language. Preprint at arXiv (2024).
  −
54. Papadopoulos, F., Psounis, K. & Govindan, R. Performance preserving topological downscaling of internet-like networks. IEEE J. Sel. Areas Commun. 24 (2006).
  −
55. Papadopoulos, F. & Psounis, K. Efficient identification of uncongested internet links for topology downscaling. SIGCOMM Comput. Commun. Rev. 37 (2007).
  −
56. Di, X., Zhao, Y., Huang, S. & Liu, H. X. A similitude theory for modeling traffic flow dynamics. IEEE Trans. Intell. Transp. Syst. 20 (2019).
  −
57. Chen, H., Perozzi, B., Hu, Y. & Skiena, S. HARP: hierarchical representation learning for networks. In textit{Proc. 32nd AAAI Conference on Artificial Intelligence/30th Innovative Applications of Artificial Intelligence Conference/8th AAAI Symposium on Educational Advances in Artificial Intelligence (AAAI’18/IAAI’18/EAAI’18) 2127–2134 (AAAI, 2018).
  −
58. Loukas, A. Graph reduction with spectral and cut guarantees. J. Mach. Learn. Res. 20 (2019).
  −
59. Jin, Y., Loukas, A. & JaJa, J. Graph coarsening with preserved spectral properties. In textit{Proc. International Conference on Artificial Intelligence and Statistics 4452–4462 (PMLR, 2020).
  −
60. Fahrbach, M., Goranci, G., Peng, R., Sachdeva, S. & Wang, C. Faster graph embeddings via coarsening. In textit{Proc. International Conference on Machine Learning 2953–2963 (PMLR, 2020).
  −
61. Liang, J., Gurukar, S. & Parthasarathy, S. MILE: A multi-level framework for scalable graph embedding. In textit{Proc. International AAAI Conference on Web and Social Media Vol. 15, 361–372 (AAAI, 2021).
  −
62. Huang, Z., Zhang, S., Xi, C., Liu, T. & Zhou, M. Scaling up graph neural networks via graph coarsening. In textit{Proc. 27th ACM SIGKDD Conference on Knowledge Discovery and Data Mining 675–684 (ACM, 2021).
  −
63. Zhang, Z., Ghavasieh, A., Zhang, J. & De Domenico, M. Coarse-graining network flow through statistical physics and machine learning. Nat. Commun. 16 (2025).
  −
64. Yedidia, J. S. & Bouchaud, J.-P. Renormalization group approach to error-correcting codes. J. Phys. A 36 (2003).
  −
65. Klein, B. & Hoel, E. The emergence of informative higher scales in complex networks. Complexity 2020 (2020).
  −
66. Faccin, M., Schaub, M. T. & Delvenne, J.-C. Entrograms and coarse graining of dynamics on complex networks. J. Complex Netw. 6 (2017).
  −
67. Boguñá, M. Network geometry. Nat. Rev. Phys. 3 (2021).
  −
68. García-Pérez, G., Boguñá, M. & Serrano, M. Á. Multiscale unfolding of real networks by geometric renormalization. Nat. Phys. 14 (2018).
  −
69. Zheng, M., García-Pérez, G., Boguñá, M. & Serrano, M. Á. Scaling up real networks by geometric branching growth. Proc. Natl Acad. Sci. USA (2021).
  −
70. Zheng, M., García-Pérez, G., Boguñá, M. & Serrano, M. Á. Geometric renormalization of weighted networks. Commun. Phys. 7 (2024).
  −
71. Kolk, J., Serrano, M. & Boguñá, M. Renormalization of networks with weak geometric coupling. Phys. Rev. E 110 (2024).
  −
72. Krioukov, D., Papadopoulos, F., Kitsak, M., Vahdat, A. & Boguñá, M. Hyperbolic geometry of complex networks. Phys. Rev. E 82 (2010).
  −
73. Gilbert, E. N. Random plane networks. J. Soc. Indust. Appl. Math. 9 (1961).
  −
74. Penrose, M. Random Geometric Graphs Vol. 5 (Oxford Univ. Press, 2003).
  −
75. Hoff, P. D., Raftery, A. E. & Handcock, M. S. Latent space approaches to social network analysis. J. Am. Stat. Assoc. 97 (2002).
  −
76. Boguñá, M., Krioukov, D., Almagro, P. & Serrano, M. Á. Small worlds and clustering in spatial networks. Phys. Rev. Res. 2 (2020).
  −
77. Kolk, J., Serrano, M. Á. & Boguñá, M. An anomalous topological phase transition in spatial random graphs. Commun. Phys. 5 (2022).
  −
78. Kolk, J., Serrano, M. Á. & Boguñá, M. Random graphs and real networks with weak geometric coupling. Phys. Rev. Res. 6 (2024).
  −
79. García-Pérez, G., Allard, A., Serrano, M. Á. & Boguñá, M. Mercator: uncovering faithful hyperbolic embeddings of complex networks. New J. Phys. 21 (2019).
  −
80. Jankowski, R., Allard, A., Boguñá, M. & Serrano, M. Á. The D-Mercator method for the multidimensional hyperbolic embedding of real networks. Nat. Commun. 14 (2023).
  −
81. Boguñá, M., Papadopoulos, F. & Krioukov, D. Sustaining the internet with hyperbolic mapping. Nat. Commun. 1 (2010).
  −
82. Gugelmann, L., Panagiotou, K. & Peter, U. Random hyperbolic graphs: degree sequence and clustering. In textit{Proc. Automata, Languages and Programming, 39th International Colloquium (ICALP 2012) (eds Czumaj, A. et al.) 573–585 (Springer, 2012).
  −
83. Candellero, E. & Fountoulakis, N. Clustering and the hyperbolic geometry of complex networks. Internet Math. 12 (2016).
  −
84. Fountoulakis, N., Hoorn, P., Müller, T. & Schepers, M. Clustering in a hyperbolic model of complex networks. Electron. J. Probab. 26 (2021).
  −
85. Abdullah, M. A., Fountoulakis, N. & Bode, M. Typical distances in a geometric model for complex networks. Internet Math. (2017).
  −
86. Friedrich, T. & Krohmer, A. On the diameter of hyperbolic random graphs. SIAM J. Discrete Math. 32 (2018).
  −
87. Müller, T. & Staps, M. The diameter of KPKVB random graphs. Adv. Appl. Probab. 51 (2019).
  −
88. Serrano, M. Á., Krioukov, D. & Boguñá, M. Percolation in self-similar networks. Phys. Rev. Lett. 106 (2011).
  −
89. Fountoulakis, N. & Müller, T. Law of large numbers for the largest component in a hyperbolic model of complex networks. Ann. Appl. Probab. 28 (2018).
  −
90. Bianconi, G. & Ziff, R. Topological percolation on hyperbolic simplicial complexes. Phys. Rev. E 98 (2018).
  −
91. Kiwi, M. & Mitsche, D. Spectral gap of random hyperbolic graphs and related parameters. Ann. Appl. Probab. 28 (2018).
  −
92. Papadopoulos, F., Kitsak, M., Serrano, M. Á., Boguñá, M. & Krioukov, D. Popularity versus similarity in growing networks. Nature 489 (2012).
  −
93. Allard, A., Serrano, M. Á., García-Pérez, G. & Boguñá, M. The geometric nature of weights in real complex networks. Nat. Commun. 8 (2017).
  −
94. Serrano, M. Á., Boguñá, M. & Sagués, F. Uncovering the hidden geometry behind metabolic networks. Mol. Biosyst. 8 (2012).
  −
95. Kitsak, M., Papadopoulos, F. & Krioukov, D. Latent geometry of bipartite networks. Phys. Rev. E 95 (2017).
  −
96. Budel, G. & Kitsak, M. Complementarity in complex networks. Preprint at arXiv (2023).
  −
97. Kleineberg, K.-K., Boguñá, M., Serrano, M. Á. & Papadopoulos, F. Hidden geometric correlations in real multiplex networks. Nat. Phys. 12 (2016).
  −
98. Kleineberg, K.-K., Buzna, L., Papadopoulos, F., Boguñá, M. & Serrano, M. Á. Geometric correlations mitigate the extreme vulnerability of multiplex networks against targeted attacks. Phys. Rev. Lett. 118 (2017).
  −
99. Zuev, K., Boguñá, M., Bianconi, G. & Krioukov, D. Emergence of soft communities from geometric preferential attachment. Sci. Rep. 5 (2015).
  −
100. García-Pérez, G., Serrano, M. Á. & Boguñá, M. Soft communities in similarity space. J. Stat. Phys. 173 (2018).
  −
101. Muscoloni, A. & Cannistraci, C. V. A nonuniform popularity-similarity optimization (nPSO) model to efficiently generate realistic complex networks with communities. New J. Phys. 20 (2018).
  −
102. Allard, A., Serrano, M. Á. & Boguñá, M. Geometric description of clustering in directed networks. Nat. Phys. 20 (2024).
  −
103. Aliakbarisani, R., Ángeles Serrano, M. & Boguñá, M. Feature-enriched hyperbolic network geometry. Preprint at arXiv (2023).
  −
104. Zheng, M., Allard, A., Hagmann, P., Alemán-Gómez, Y. & Serrano, M. Á. Geometric renormalization unravels self-similarity of the multiscale human connectome. Proc. Natl Acad. Sci. USA 117 (2020).
  −
105. Barrat, A., Barthelemy, M., Pastor-Satorras, R. & Vespignani, A. The architecture of complex weighted networks. Proc. Natl Acad. Sci. USA 101 (2004).
  −
106. Serrano, M. Á., Boguñá, M. & Pastor-Satorras, R. Correlations in weighted networks. Phys. Rev. E 74 (2006).
  −
107. Nolan, J. P. Univariate Stable Distributions: Models for Heavy Tailed Data (Springer Nature, 2019).
  −
108. Caldarelli, G., Gabrielli, A., Gili, T. & Villegas, P. Laplacian renormalization group: an introduction to heterogeneous coarse-graining. J. Stat. Mech. 2024 (2024).
  −
109. Domenico, M. & Biamonte, J. Spectral entropies as information-theoretic tools for complex network comparison. Phys. Rev. X 6 (2016).
  −
110. Masuda, N., Porter, M. A. & Lambiotte, R. Random walks and diffusion on networks. Phys. Rep. 716 (2017).
  −
111. Kadanoff, L. P. Notes on Migdal’s recursion formulas. Ann. Phys. 100 (1976).
  −
112. Migdal, A. A. Phase transitions in gauge and spin-lattice systems. Zh. Eksp. Teor. Fiz. 69 (1975).
  −
113. Wilson, K. G. & Kogut, J. The renormalization group and the $$varepsilo$$ expansion. Phys. Rep. 12 (1974).
  −
114. Newman, M. E. J. Networks: An Introduction (Oxford Univ. Press, 2010).
  −
115. Moretti, P. & Zaiser, M. Network analysis predicts failure of materials and structures. Proc. Natl Acad. Sci. USA 116 (2019).
  −
116. Burioni, R. & Cassi, D. Random walks on graphs: ideas, techniques and results. J. Phys. A 38 (2005).
  −
117. Villegas, P., Gabrielli, A., Poggialini, A. & Gili, T. Multi-scale Laplacian community detection in heterogeneous networks. Phys. Rev. Res. 7 (2025).
  −
118. Kadanoff, L. P. Scaling laws for Ising models near Tc. Phys. Phys. Fiz. 2 (1966).
  −
119. Wilson, K. G. Problems in physics with many scales of length. Sci. Am. 241 (1979).
  −
120. Hinrichsen, H. Non-equilibrium critical phenomena and phase transitions into absorbing states. Adv. Phys. 49 (2000).
  −
121. Dornic, I., Chaté, H. & Muñoz, M. A. Integration of Langevin equations with multiplicative noise and the viability of field theories for absorbing phase transitions. Phys. Rev. Lett. 94 (2005).
  −
122. Burioni, R. & Cassi, D. Geometrical universality in vibrational dynamics. Mod. Phys. Lett. B 11 (1997).
  −
123. Cassi, D. Phase transitions and random walks on graphs: a generalization of the Mermin–Wagner theorem to disordered lattices, fractals, and other discrete structures. Phys. Rev. Lett. 68 (1992).
  −
124. Reitz, M. & Bianconi, G. The higher-order spectrum of simplicial complexes: a renormalization group approach. J. Phys. A 53 (2020).
  −
125. Bianconi, G. & Dorogovstev, S. N. The spectral dimension of simplicial complexes: a renormalization group theory. J. Stat. Mech. 2020 (2020).
  −
126. Nurisso, M. et al. Higher-order Laplacian renormalization. Nat. Phys. (2025).
  −
127. Cheng, A., Xu, Y., Sun, P. & Tian, Y. A simplex path integral and a simplex renormalization group for high-order interactions. Rep. Prog. Phys. 87 (2024).
  −
128. Ghavasieh, A., Nicolini, C. & Domenico, M. Statistical physics of complex information dynamics. Phys. Rev. E 102 (2020).
  −
129. Villegas, P., Gabrielli, A., Santucci, F., Caldarelli, G. & Gili, T. Laplacian paths in complex networks: information core emerges from entropic transitions. Phys. Rev. Res. 4 (2022).
  −
130. Binney, J. J., Dowrick, N. J., Fisher , A. J. & Newman, M. E. The Theory of Critical Phenomena: An Introduction to the Renormalization Group (Oxford Univ. Press, 1992).
  −
131. Pathria, R. K. & Beale, P. D. Statistical Mechanics (Elsevier/Academic, 2011).
  −
132. Holland, P. W., Laskey, K. B. & Leinhardt, S. Stochastic blockmodels: first steps. Soc. Networks 5 (1983).
  −
133. Burioni, R. & Cassi, D. Universal properties of spectral dimension. Phys. Rev. Lett. 76 (1996).
  −
134. Moretti, P. & Muñoz, M. A. Griffiths phases and the stretching of criticality in brain networks. Nat. Commun. 4 (2013).
  −
135. Poggialini, A., Villegas, P., Muñoz, M. A. & Gabrielli, A. Networks with many structural scales: a renormalization group perspective. Phys. Rev. Lett. 134 (2024).
  −
136. de C. Loures, M., Piovesana, A. A. & Brum, J. A. Laplacian coarse graining in complex networks. Preprint at arXiv (2023).
  −
137. Garuccio, E., Lalli, M. & Garlaschelli, D. Multiscale network renormalization: scale-invariance without geometry. Phys. Rev. Res. 5 (2023).
  −
138. Avena, L., Garlaschelli, D., Hazra, R. S. & Lalli, M. Inhomogeneous random graphs with infinite-mean fitness variables. Preprint at arXiv (2022).
  −
139. Lalli, M. & Garlaschelli, D. Geometry-free renormalization of directed networks: scale-invariance and reciprocity. Preprint at arXiv (2024).
  −
140. Uchaikin, V. V. & Zolotarev, V. M. Chance and Stability: Stable Distributions and their Applications (Walter de Gruyter, 2011).
  −
141. Samorodnitsky, G. & Taqqu, M. S. Stable Non-Gaussian Random Processes: Stochastic Models with Infinite Variance (Chapman & Hall, 1994).
  −
142. Lévy, P. L’addition des variables aléatoires définies sur une circonférence. Bull. Soc. Math. Fr. 67 (1939).
  −
143. Balkema, A. A. & Resnick, S. I. Max-infinite divisibility. J. Appl. Probab. 14 (1977).
  −
144. Giné, E., Hahn, M. G. & Vatan, P. Max-infinitely divisible and max-stable sample continuous processes. Probab. Theory Relat. Fields 87 (1990).
  −
145. Verteletskyi, V. Renormalization of Networks with Weighted Links. MSc thesis, Leiden Univ. (2022).
  −
146. Garlaschelli, D. & Loffredo, M. I. Patterns of link reciprocity in directed networks. Phys. Rev. Lett. 93 (2004).
  −
147. Garlaschelli, D. & Loffredo, M. I. Multispecies grand-canonical models for networks with reciprocity. Phys. Rev. E 73 (2006).
  −
148. Squartini, T., Picciolo, F., Ruzzenenti, F. & Garlaschelli, D. Reciprocity of weighted networks. Sci. Rep. 3 (2013).
  −
149. Gallo, A., Saracco, F., Lambiotte, R., Garlaschelli, D. & Squartini, T. Patterns of link reciprocity in directed, signed networks. Phys. Rev. E 111 (2025).
  −
150. Ialongo, L. N., Bangma, S., Jansen, F. & Garlaschelli, D. Multi-scale reconstruction of large supply networks. Preprint at arXiv (2024).
  −
151. Milocco, R., Jansen, F. & Garlaschelli, D. Multi-scale node embeddings for graph modeling and generation. Preprint at arXiv (2024).
  −
152. Caldarelli, G., Capocci, A., Los Rios, P. & Munoz, M. A. Scale-free networks from varying vertex intrinsic fitness. Phys. Rev. Lett. 89 (2002).
  −
153. Dehghan-Kooshkghazi, A., Kamiński, B., Kraiński, Ł., Prałat, P. & Théberge, F. Evaluating node embeddings of complex networks. J. Complex Netw. 10 (2022).
  −
154. van der Hofstad, R. Random Graphs and Complex Networks (Cambridge Univ. Press, 2024).
  −
155. Hattori, K., Hattori, T. & Watanabe, H. Gaussian field theories on general networks and the spectral dimensions. Prog. Theor. Phys. Suppl. 92 (1987).
  −
156. Burioni, R. & Cassi, D. Random walks on graphs: ideas, techniques and results. J. Phys. A 38 (2005).
  −
157. Boettcher, S. & Brunson, C. T. Renormalization group for critical phenomena in complex networks. Front. Physiol. 2 (2011).
  −
158. Dorogovtsev, S. N. Renormalization group for evolving networks. Phys. Rev. E 67 (2003).
  −
159. Meshulam, L., Gauthier, J. L., Brody, C. D., Tank, D. W. & Bialek, W. Coarse graining, fixed points, and scaling in a large population of neurons. Phys. Rev. Lett. 123 (2019).
  −
160. Griffiths, R. B. Nonanalytic behavior above the critical point in a random Ising ferromagnet. Phys. Rev. Lett. 23 (1969).
  −
161. Munoz, M. A., Juhász, R., Castellano, C. & Ódor, G. Griffiths phases on complex networks. Phys. Rev. Lett. 105 (2010).
  −
162. Amari, S.-i. Information Geometry and Its Applications (Springer, 2016).
  −
163. Berman, D. S., Klinger, M. S. & Stapleton, A. G. Bayesian renormalization. Mach. Learn. Sci. Tech. 4 (2023).
  −
164. Raju, A., Machta, B. B. & Sethna, J. P. Information loss under coarse graining: a geometric approach. Phys. Rev. E 98 (2018).
  −
165. Machta, B. B., Chachra, R., Transtrum, M. K. & Sethna, J. P. Parameter space compression underlies emergent theories and predictive models. Science 342 (2013).
  −
166. Har-Shemesh, O., Quax, R., Hoekstra, A. G. & Sloot, P. M. A. Information geometric analysis of phase transitions in complex patterns: the case of the Gray-Scott reaction–diffusion model. J. Stat. Mech. 4 (2016).
  −
167. Ehrenfest, P. & Ehrenfest, T. Begriffliche Grundlagen der statistischen Auffassung in der Mechanik (Springer, 1907).
  −
168. Niemeijer, T. & Leeuwen, J. M. J. Wilson theory for spin systems on a triangular lattice. Phys. Rev. Lett. 31 (1973).
  −
169. Kadanoff, L. P. Variational principles and approximate renormalization group calculations. Phys. Rev. Lett. 34 (1975).
  −
170. Southern, B. W. Kadanoff’s variational renormalisation group method: the Ising model on the square and triangular lattices. J. Phys. A 11 (1978).
  −
171. Jan, N. & Glazer, A. Kadanoff’s approximate renormalization group transformation applied to the triangular Ising lattice. Physica A 91 (1978).
  −
172. Nijs, M. & Knops, H. Variational renormalization method and the Potts model. Physica A 93 (1978).
  −
173. Castro, C. & Jona-Lasinio, G. On the microscopic foundation of scaling laws. Phys. Lett. A 29 (1969).
  −
174. Gell-Mann, M. & Low, F. E. Quantum electrodynamics at small distances. Phys. Rev. 95 (1954).
  −
175. Zinn-Justin, J. Quantum Field Theory and Critical Phenomena (Oxford Univ. Press, 2021).
  −
176. Amit, D. J. & Martin-Mayor, V. Field Theory, the Renormalization Group and Critical Phenomena (World Scientific, 2005).
  −
177. Täuber, U. C. Renormalization group: applications in statistical physics. Nucl. Phys. B 228 (2012).
  −
178. Pelissetto, A. & Vicari, E. Critical phenomena and renormalization-group theory. Phys. Rep. 368 (2002).
  −
179. Efrati, E., Wang, Z., Kolan, A. & Kadanoff, L. P. Real-space renormalization in statistical mechanics. Rev. Mod. Phys. 86 (2014).
  −
180. Gefen, Y., Mandelbrot, B. B. & Aharony, A. Critical phenomena on fractal lattices. Phys. Rev. Lett. 45 (1980).
  −
181. Gefen, Y., Aharony, A., Mandelbrot, B. B. & Kirkpatrick, S. Solvable fractal family, and its possible relation to the backbone at percolation. Phys. Rev. Lett. 47 (1981).
  −
182. Phani, M. K. & Dhar, D. Real-space renormalisation group: application to directed percolation. J. Phys. C 15 (1982).
  −
183. Gefen, Y., Aharony, A. & Mandelbrot, B. B. Phase transitions on fractals. I. Quasi-linear lattices. J. Phys. A 16 (1983).
  −
184. Gefen, Y., Aharony, A., Shapir, Y. & Mandelbrot, B. B. Phase transitions on fractals. II. Sierpinski gaskets. J. Phys. A 17 (1984).
  −
185. Gefen, Y., Aharony, A. & Mandelbrot, B. B. Phase transitions on fractals. III. Infinitely ramified lattices. J. Phys. A 17 (1984).
  −
186. Das, D., Dey, S., Jacobsen, J. L. & Dhar, D. Critical behavior of loops and biconnected clusters on fractals of dimension d < 2. J. Phys. A 41 (2008).
  −
187. Della Morte, M. & Sannino, F. Renormalization group approach to pandemics as a time-dependent SIR model. Front. Phys. (2021).
  −
188. Cavagna, A. Dynamic scaling in natural swarms. Nat. Phys. 13 (2017).
  −
189. Cavagna, A. Dynamical renormalization group approach to the collective behavior of swarms. Phys. Rev. Lett. (2019).
  −
190. Cavagna, A. Natural swarms in 3.99 dimensions. Nat. Phys. 19 (2023).
  −
191. Koch-Janusz, M. & Ringel, Z. Mutual information, neural networks and the renormalization group. Nat. Phys. 14 (2018).
  −
192. Li, S.-H. & Wang, L. Neural network renormalization group. Phys. Rev. Lett. (2018).
  −
193. Hu, H.-Y., Li, S.-H., Wang, L. & You, Y.-Z. Machine learning holographic mapping by neural network renormalization group. Phys. Rev. Res. 2 (2020).
  −
194. Caso, F., Trappolini, G., Bacciu, A., Liò, P. & Silvestri, F. Renormalized graph neural networks. Preprint at arXiv (2023).
  −
195. Young, A. P. & Stinchcombe, R. B. A renormalization group theory for percolation problems. J. Phys. C 8 (1975).
  −
196. Reynolds, P. J., Stanley, H. E. & Klein, W. A real-space renormalization group for site and bond percolation. J. Phys. C 10 (1977).
  −
197. Galam, S. Real space renormalization group and totalitarian paradox of majority rule voting. Physica A 285 (2000).
  −
198. Kogan, O., Rogers, J. L., Cross, M. C. & Refael, G. Renormalization group approach to oscillator synchronization. Phys. Rev. E 80 (2009).
  −
199. Östborn, P. Renormalization of oscillator lattices with disorder. Phys. Rev. E 79 (2009).
  −
200. Garlaschelli, D., Hollander, F., Meylahn, J. & Zeegers, B. Synchronization of phase oscillators on the hierarchical lattice. J. Stat. Phys. 174 (2019).
  −
201. Levin, M. & Nave, C. P. Tensor renormalization group approach to two-dimensional classical lattice models. Phys. Rev. Lett. (2007).
  −
202. Evenbly, G. & Vidal, G. Tensor network renormalization. Phys. Rev. Lett. (2015).
  −
203. Bal, M., Mariën, M., Haegeman, J. & Verstraete, F. Renormalization group flows of Hamiltonians using tensor networks. Phys. Rev. Lett. (2017).
  −
204. Lenggenhager, P. M., Gökmen, D. E., Ringel, Z., Huber, S. D. & Koch-Janusz, M. Optimal renormalization group transformation from information theory. Phys. Rev. X 10 (2020).
  −
205. Gökmen, D. E., Ringel, Z., Huber, S. D. & Koch-Janusz, M. Statistical physics through the lens of real-space mutual information. Phys. Rev. Lett. 127 (2021).
  −
206. Gordon, A., Banerjee, A., Koch-Janusz, M. & Ringel, Z. Relevance in the renormalization group and in information theory. Phys. Rev. Lett. 126 (2021).
  −
207. Sarra, L., Aiello, A. & Marquardt, F. Renormalized mutual information for artificial scientific discovery. Phys. Rev. Lett. 126 (2021).
  −
208. Gökmen, D. E., Ringel, Z., Huber, S. D. & Koch-Janusz, M. Symmetries and phase diagrams with real-space mutual information neural estimation. Phys. Rev. E 104 (2021).
  −
209. Canet, L., Delamotte, B., Deloubrière, O. & Wschebor, N. Nonperturbative renormalization-group study of reaction–diffusion processes. Phys. Rev. Lett. 92 (2004).
  −
210. Canet, L., Chaté, H. & Delamotte, B. Quantitative phase diagrams of branching and annihilating random walks. Phys. Rev. Lett. 92 (2004).
  −
211. Canet, L., Chaté, H., Delamotte, B., Dornic, I. & Muñoz, M. A. Nonperturbative fixed point in a nonequilibrium phase transition. Phys. Rev. Lett. 95 (2005).
  −
212. Canet, L., Chaté, H. & Delamotte, B. General framework of the non-perturbative renormalization group for non-equilibrium steady states. J. Phys. A 44 (2011).
  −
213. Tarpin, M., Benitez, F., Canet, L. & Wschebor, N. Nonperturbative renormalization group for the diffusive epidemic process. Phys. Rev. E 96 (2017).
 
5,443

个编辑