dorsal/arxiv
View SchemaDesigning Complex Networks
| Authors | Raoul-Martin Memmesheimer, Marc Timme |
|---|---|
| Categories | |
| ArXiv ID | q-bio/0606041 |
| URL | https://arxiv.org/abs/q-bio/0606041 |
| DOI | 10.1016/j.physd.2006.09.037 |
| Journal | Physica D 224:182 (2006) |
Abstract
We suggest a new perspective of research towards understanding the relations between structure and dynamics of a complex network: Can we design a network, e.g. by modifying the features of units or interactions, such that it exhibits a desired dynamics? Here we present a case study where we positively answer this question analytically for networks of spiking neural oscillators. First, we present a method of finding the set of all networks (defined by all mutual coupling strengths) that exhibit an arbitrary given periodic pattern of spikes as an invariant solution. In such a pattern all the spike times of all the neurons are exactly predefined. The method is very general as it covers networks of different types of neurons, excitatory and inhibitory couplings, interaction delays that may be heterogeneously distributed, and arbitrary network connectivities. Second, we show how to design networks if further restrictions are imposed, for instance by predefining the detailed network connectivity. We illustrate the applicability of the method by examples of Erd\"{o}s-R\'{e}nyi and power-law random networks. Third, the method can be used to design networks that optimize network properties. To illustrate this idea, we design networks that exhibit a predefined pattern dynamics while at the same time minimizing the networks' wiring costs.
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"abstract": "We suggest a new perspective of research towards understanding the relations\nbetween structure and dynamics of a complex network: Can we design a network,\ne.g. by modifying the features of units or interactions, such that it exhibits\na desired dynamics? Here we present a case study where we positively answer\nthis question analytically for networks of spiking neural oscillators. First,\nwe present a method of finding the set of all networks (defined by all mutual\ncoupling strengths) that exhibit an arbitrary given periodic pattern of spikes\nas an invariant solution. In such a pattern all the spike times of all the\nneurons are exactly predefined. The method is very general as it covers\nnetworks of different types of neurons, excitatory and inhibitory couplings,\ninteraction delays that may be heterogeneously distributed, and arbitrary\nnetwork connectivities. Second, we show how to design networks if further\nrestrictions are imposed, for instance by predefining the detailed network\nconnectivity. We illustrate the applicability of the method by examples of\nErd\\\"{o}s-R\\\u0027{e}nyi and power-law random networks. Third, the method can be\nused to design networks that optimize network properties. To illustrate this\nidea, we design networks that exhibit a predefined pattern dynamics while at\nthe same time minimizing the networks\u0027 wiring costs.",
"arxiv_id": "q-bio/0606041",
"authors": [
"Raoul-Martin Memmesheimer",
"Marc Timme"
],
"categories": [
"q-bio.NC",
"cond-mat.dis-nn",
"q-bio.QM"
],
"doi": "10.1016/j.physd.2006.09.037",
"journal_ref": "Physica D 224:182 (2006)",
"title": "Designing Complex Networks",
"url": "https://arxiv.org/abs/q-bio/0606041"
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