Periodic Reporting for period 2 - DYNASNET (Dynamics and Structure of Networks)
Período documentado: 2021-03-01 hasta 2022-08-31
Contemporary world, diverse human activities and their effect on the environment, the manyfold impact of technology on society, the global health problems, all these very diverse areas have one latent feature in common: they are all related to particular networks. Such networks can be seemingly unmanageably large and complex. Yet their underlying structure may be modeled as a graph or network, which gives us hope for understanding them.
DYNASNET is an important addition to network science by bringing together a strong group of leading experts in network science, mathematics, physics and computer science. This strong interdisciplinary group attacks some most challenging problems in this very diverse area, contributes to foundations of the emerging theory and brings new paradigm on the cross boundary of individual disciplines.
DYNASNET is an important addition to network science by bringing together a strong group of leading experts in network science, mathematics, physics and computer science. This strong interdisciplinary group attacks some most challenging problems in this very diverse area, contributes to foundations of the emerging theory and brings new paradigm on the cross boundary of individual disciplines.
The project DYNASNET adapted very quickly to the pandemic situation. This of course not only changed our modus operandi but also provided us with new and challenging problems on the mathematical study of epidemic. A successful solutions which resulted in distinguished publications (such as PNAS) showed the relevance of our research tools for epidemic modeling. PI László Lovász gave a keynote talk on some of these results at the Conference on Complex Systems in Lyon.
Novel methodologies include a new paradigm to model very large graphs by infinite structures, in the context of Borel (measurable) combinatorics as well as from an algorithmic point of view, leading into areas of mathematics that are novel to this field, most notably measure theory and mathematical logic. A theory of Markov spaces, representing limits of convergent graph sequences, has been developed, and several papers have been published or are awaiting publication. Extending flow theory to these limit objects and defining subgraph measures in Markov spaces are two groups of results showing the validity of this approach.
Sparsity is a key word here and the interaction with model theory is very active internationally. Another, on the first glance surprising, relevance is Ramsey theory in its structural setting, which allows us to describe canonical patterns (types) of expansions of infinite structures defined from trees.
Physical networks have emerged as an important and active area of collaboration between network scientists at CEU and graph theorists at the Renyi Institute. Physical networks are composed of three-dimensional physical objects embedded in space, examples of such systems include biological networks from molecular networks to nervous systems and man-made systems from computer chips to critical infrastructure. Our work focuses on describing, modeling and predicting these systems and the joint participation of graph theorists and network scientists in the project allows us to tackle these questions by leveraging results of graph combinatorics, group theory and knot theory. Some of the key results of the project were published in Nature Physics (Liu, Yanchen, Nima Dehmamy, and Albert-László Barabási. Nature Physics 17.2 (2021): 216-222.) and presented as a keynote talk by PI Albert-László Barabási at the 3rd Statistical Physics of Complex Systems Conference organized by the European Physical Society.
Novel methodologies include a new paradigm to model very large graphs by infinite structures, in the context of Borel (measurable) combinatorics as well as from an algorithmic point of view, leading into areas of mathematics that are novel to this field, most notably measure theory and mathematical logic. A theory of Markov spaces, representing limits of convergent graph sequences, has been developed, and several papers have been published or are awaiting publication. Extending flow theory to these limit objects and defining subgraph measures in Markov spaces are two groups of results showing the validity of this approach.
Sparsity is a key word here and the interaction with model theory is very active internationally. Another, on the first glance surprising, relevance is Ramsey theory in its structural setting, which allows us to describe canonical patterns (types) of expansions of infinite structures defined from trees.
Physical networks have emerged as an important and active area of collaboration between network scientists at CEU and graph theorists at the Renyi Institute. Physical networks are composed of three-dimensional physical objects embedded in space, examples of such systems include biological networks from molecular networks to nervous systems and man-made systems from computer chips to critical infrastructure. Our work focuses on describing, modeling and predicting these systems and the joint participation of graph theorists and network scientists in the project allows us to tackle these questions by leveraging results of graph combinatorics, group theory and knot theory. Some of the key results of the project were published in Nature Physics (Liu, Yanchen, Nima Dehmamy, and Albert-László Barabási. Nature Physics 17.2 (2021): 216-222.) and presented as a keynote talk by PI Albert-László Barabási at the 3rd Statistical Physics of Complex Systems Conference organized by the European Physical Society.
For basic research novelty is a principal issue. Some DYNASNET research points to new directions, and the results will no doubt have an important impact on further development.
The study of physical networks is an emerging field driven by the newly available data describing the detailed three-dimensional structure of complex networks. The work within DYNASNET contributes to establishing the basic tenets of the field, developing the mathematical language required to describe physical networks and identifying the most important consequences of physicality on the behavior of networks.
In epidemic modeling, besides a better understanding of the "switchover phenomenon", a move from specific randomized network models to general graphs satisfying reasonable conditions should bring in a new perspective.
New probabilistic models for graph limits (which may handle sparse as well as dense setting) and constructive combinatorics as a blend of infinite and finite problems and theories. The connection with measure theory should bring substantial progress not only in network theory, but in measure theory as well. Big Ramsey degrees, for example, present very challenging problems for higher dimensional structures (such as hypergraphs).
The study of physical networks is an emerging field driven by the newly available data describing the detailed three-dimensional structure of complex networks. The work within DYNASNET contributes to establishing the basic tenets of the field, developing the mathematical language required to describe physical networks and identifying the most important consequences of physicality on the behavior of networks.
In epidemic modeling, besides a better understanding of the "switchover phenomenon", a move from specific randomized network models to general graphs satisfying reasonable conditions should bring in a new perspective.
New probabilistic models for graph limits (which may handle sparse as well as dense setting) and constructive combinatorics as a blend of infinite and finite problems and theories. The connection with measure theory should bring substantial progress not only in network theory, but in measure theory as well. Big Ramsey degrees, for example, present very challenging problems for higher dimensional structures (such as hypergraphs).