Filtering Statistics on Networks
Compression, filtering, and cryptography, as well as the sampling of complex systems, can be seen as processing information. A large initial configuration or input space is nontrivially mapped to a smaller set of output or final states. We explored the statistics of filtering of simple patterns on a...
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doaj-0f2815890693406f9b2b1b2d508c96052020-11-25T03:54:16ZengMDPI AGEntropy1099-43002020-10-01221149114910.3390/e22101149Filtering Statistics on NetworksG. J. Baxter0R. A. da Costa1S. N. Dorogovtsev2J. F. F. Mendes3Department of Physics, University of Aveiro de & I3N, Campus Universitário de Santiago, 3810-193 Aveiro, PortugalDepartment of Physics, University of Aveiro de & I3N, Campus Universitário de Santiago, 3810-193 Aveiro, PortugalDepartment of Physics, University of Aveiro de & I3N, Campus Universitário de Santiago, 3810-193 Aveiro, PortugalDepartment of Physics, University of Aveiro de & I3N, Campus Universitário de Santiago, 3810-193 Aveiro, PortugalCompression, filtering, and cryptography, as well as the sampling of complex systems, can be seen as processing information. A large initial configuration or input space is nontrivially mapped to a smaller set of output or final states. We explored the statistics of filtering of simple patterns on a number of deterministic and random graphs as a tractable example of such information processing in complex systems. In this problem, multiple inputs map to the same output, and the statistics of filtering is represented by the distribution of this degeneracy. For a few simple filter patterns on a ring, we obtained an exact solution of the problem and numerically described more difficult filter setups. For each of the filter patterns and networks, we found three key numbers that essentially describe the statistics of filtering and compared them for different networks. Our results for networks with diverse architectures are essentially determined by two factors: whether the graphs structure is deterministic or random and the vertex degree. We find that filtering in random graphs produces much richer statistics than in deterministic graphs, reflecting the greater complexity of such graphs. Increasing the graph’s degree reduces this statistical richness, while being at its maximum at the smallest degree not equal to two. A filter pattern with a strong dependence on the neighbourhood of a node is much more sensitive to these effects.https://www.mdpi.com/1099-4300/22/10/1149filteringinformationdegeneracyentropyrelevanceresolution |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
G. J. Baxter R. A. da Costa S. N. Dorogovtsev J. F. F. Mendes |
spellingShingle |
G. J. Baxter R. A. da Costa S. N. Dorogovtsev J. F. F. Mendes Filtering Statistics on Networks Entropy filtering information degeneracy entropy relevance resolution |
author_facet |
G. J. Baxter R. A. da Costa S. N. Dorogovtsev J. F. F. Mendes |
author_sort |
G. J. Baxter |
title |
Filtering Statistics on Networks |
title_short |
Filtering Statistics on Networks |
title_full |
Filtering Statistics on Networks |
title_fullStr |
Filtering Statistics on Networks |
title_full_unstemmed |
Filtering Statistics on Networks |
title_sort |
filtering statistics on networks |
publisher |
MDPI AG |
series |
Entropy |
issn |
1099-4300 |
publishDate |
2020-10-01 |
description |
Compression, filtering, and cryptography, as well as the sampling of complex systems, can be seen as processing information. A large initial configuration or input space is nontrivially mapped to a smaller set of output or final states. We explored the statistics of filtering of simple patterns on a number of deterministic and random graphs as a tractable example of such information processing in complex systems. In this problem, multiple inputs map to the same output, and the statistics of filtering is represented by the distribution of this degeneracy. For a few simple filter patterns on a ring, we obtained an exact solution of the problem and numerically described more difficult filter setups. For each of the filter patterns and networks, we found three key numbers that essentially describe the statistics of filtering and compared them for different networks. Our results for networks with diverse architectures are essentially determined by two factors: whether the graphs structure is deterministic or random and the vertex degree. We find that filtering in random graphs produces much richer statistics than in deterministic graphs, reflecting the greater complexity of such graphs. Increasing the graph’s degree reduces this statistical richness, while being at its maximum at the smallest degree not equal to two. A filter pattern with a strong dependence on the neighbourhood of a node is much more sensitive to these effects. |
topic |
filtering information degeneracy entropy relevance resolution |
url |
https://www.mdpi.com/1099-4300/22/10/1149 |
work_keys_str_mv |
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