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Dynamics and Structure of Networks

Objective

Networks define our life, being essential to cell biology, communications, social and economic systems, and impacting virtually all areas of science and technology. The aim of this proposal is to engage leading experts in network science and graph theory to build a mathematically sound theory of dynamical networks, which will be transformative to our understanding of complex systems, with applications in multiple disciplines.
Both fields have made major conceptual advances in the past decade: network science has offered a data-based basic topological description of complex networks, and has started to address the inherently dynamical nature of real networks, their reconstruction and control; in mathematics we have seen major advances in graph limit theory, the local-global dichotomy in observation, and promising steps in the theory of graphs with intermediate degrees, that capture real networks. While these concepts offer different formalisms to capture the same underlying reality, there has been no conversation between the two communities, limiting our understanding of real networks.
The proposed research aims to build on these advances to construct a coherent theory of dynamical networks, and to exploit its applications and predictive power to various real systems. We plan to offer a sound mathematical foundation of network science, helping us better analyze, predict and control the behavior of real networks. It will benefit mathematics in leading to an enriched, robust graph limit theory, with exciting applications in multiple areas of mathematics. To enhance the wider impact of the proposed mathematical advances, we plan to conduct a permanent conversation with experts from different domains that encounter and explore real networks, from cell biology to brain science and transportation and communication networks, inspiring with novel questions and helping the application of our advances in these domains.

Field of science

  • /natural sciences/biological sciences/cell biology
  • /natural sciences/mathematics/pure mathematics/discrete mathematics/graph theory
  • /natural sciences/mathematics

Call for proposal

ERC-2018-SyG
See other projects for this call

Funding Scheme

ERC-SyG - Synergy grant

Host institution

RENYI ALFRED MATEMATIKAI KUTATOINTEZET
Address
Realtanoda Street 13-15
1053 Budapest
Hungary
Activity type
Other
EU contribution
€ 3 484 324

Beneficiaries (3)

RENYI ALFRED MATEMATIKAI KUTATOINTEZET
Hungary
EU contribution
€ 3 484 324
Address
Realtanoda Street 13-15
1053 Budapest
Activity type
Other
KOZEP-EUROPAI EGYETEM
Hungary
EU contribution
€ 3 799 850
Address
Nador Utca 9
1051 Budapest
Activity type
Higher or Secondary Education Establishments
UNIVERZITA KARLOVA
Czechia
EU contribution
€ 2 031 250
Address
Ovocny Trh 560/5
116 36 Praha 1
Activity type
Higher or Secondary Education Establishments