The goal of the research workshop "Higher-order interaction networks: dynamics, structure, data" is to bring together researchers from these different communities with distinct perspectives on network dynamics —- from network science, dynamical systems, and data science/machine learning -- to develop novel approaches to understand networked systems. By cutting across different mathematical communities, this will allow to develop new tools, for example by exploring links between data driven methods (such as machine learning) and dynamics. A particular focus of this workshop will be on the role of non-dyadic dynamical interactions (joint interactions between more than two nodes) whose importance for the modeling, analysis, and control of such networked systems have recently been highlighted.

Expressions of interest are now open with an initial deadline of June 1, 2019, with notification of acceptance no later than June 15, 2019.

Participation in the workshop will cost a nominal fee of £50 which will be used to cover catering during the workshop. Participants will also have the chance to attend the workshop dinner on Wednesday 10th September at the nearby Somerville College, the cost of which will be £30.  

Thanks to generous funding from EU and the London Mathematical Society, there is limited travel support for UK-based early career researchers available. Please indicate whether you wish to apply for support during registration.

For further information including registration please click here.

Confirmed Speakers:

Lou Pecora (Naval Research Labs)
Tanya Berger-Wolf (Illinois)
Santiago Segarra (Rice)
Tiago Pereira (USP Sao Carlos)
Marta Sales-Pardo (Barcelona)
Jacopo Grilli (Santa Fe Institute/ICTP Trieste)
Marya Bazzi (ATI)
Rebecca Hoyle (Southampton)
Ana Paula Dias (Porto)
Laetitia Gauvin (ISI Torino)
Heather Harrington (Oxford)
Rodolphe Sepulchre (Cambridge)
Jess Enright (Stirling)
Peter Ashwin (Exeter)
Pawel Dlotko (Swansea)

The Hales–Jewett Theorem states that any r–colouring of [m]^n contains a monochromatic combinatorial line if n is large enough. Shelah’s proof of the theorem implies that for m = 3 there always exists a monochromatic combinatorial line whose set of active coordinates is the union of at most r intervals. I will present some recent findings relating to this observation. This is joint work with Nina Kamcev.

Expander graphs play a key role in modern mathematics and computer science. Random d-regular graphs are good expanders. Recent developments in PCP theory require families of graphs that are expanders both globally and locally. The meaning of “globally" is the usual one of expansion in graphs, and locally means that for every vertex the subgraph induced by its neighbors is also an expander graph. These requirements are significantly harder to satisfy and no good random model for such (bounded degree) graphs is presently known. In this talk we discuss two new combinatorial constructions of such graphs. We also say something about the limitations of such constructions and provide an Alon-Bopanna type bound for the (global) spectral gap of such a graph. In addition we discuss other notions of high dimensional expansion that our constructions do and do not satisfy, such as coboundary expansion, geometric overlap and mixing of the edge-triangle-edge random walk. This is a joint work with Nati Linial and Yuval Peled.
 

We study problems that share an important common feature: they can all be solved by exploiting the spectrum of their corresponding graph Laplacian. We first consider a classic problem in data analysis and machine learning, of establishing a statistical ranking of a set of items given a set of inconsistent and incomplete pairwise comparisons. We formulate the above problem of ranking with incomplete noisy information as an instance of the group synchronization problem over the group SO(2) of planar rotations, whose least-squares solution can be approximated by either a spectral or a semidefinite programming relaxation, and consider an application to detecting leaders and laggers in financial multivariate time series data. An instance of the group synchronization problem over Z_2 with anchor information is broadly applicable to settings where one has available a sparse signal such as positive or negative news sentiment for a subset of nodes, and would like to understand how the available measurements propagate to the remaining nodes of the network. We also present a simple spectral approach to the well-studied constrained clustering problem, which captures constrained clustering as a generalized eigenvalue problem with graph Laplacians. This line of work extends to the setting of clustering signed networks and correlation clustering, where the edge weights between the nodes of the graph may take either positive or negative values, for which we provide theoretical guarantees in the setting of a signed stochastic block model and numerical experiments for financial correlation matrices. Finally, we discuss a spectral clustering algorithm for directed graphs based on a complex-valued representation of the adjacency matrix, motivated by the application of extracting cluster-based lead-lag relationships in time series data.