Workshop on Higher-order Interaction Networks - Schedule

Monday - Networks & Higher-order Interactions

- [1230-1345] Registration

- [1345-1400] Welcome / Organizational remarks

- [1400-1500] Keynote: Heather Harrington

Title: Topological data analysis for investigating dynamics on and of biological networks
Abstract: Topological data analysis (TDA) allows one to examine features in data across multiple scales in a robust and mathematically principled manner, and it is being applied to an increasingly diverse set of applications. We investigate dynamics of biological networks, models and data using topological data analysis with concrete examples from contagions, neuroscience, and cancer. Time permitting, we will present preliminary results using TDA to analyse biological systems indexed by multiple parameters.

- [1500-1530] Coffee

- [1530-1610] Laetitia Gauvin

Title: Representation for temporal networks: Tensor based methods & Embedding techniques

- [1610-1650] Pawel Dlotko

Title: Topology of dynamics and dynamical topology
Abstract: Topology and dynamics are deeply interconnected: topology restrict the shape of the scene on which dynamical process is taking place while dynamics further model that scene. In this talk we will discuss this relation and explore it. Given a finite collection of simulation or observation data we will use topological methods to analyse and understand processess described by mathematical models. In particular, we will show how topology gives description of different phases of the considered dynamics. Later we will give a way of building model and parameter free descriptors of dynamics that allows for prediciton of the system.

- [1650-1730] Santiago Segarra

Title: Signal Processing and Machine Learning for Edge Flows using the Hodge Laplacian

- [1730-1800] Discussion / Breakout

- [1800-1900] Wine + Poster Session

Tuesday - Dynamical Systems & Higher-order Interactions

- [0925-0930] Organizational Updates / Intro

- [0930-1030] Keynote: Lou Pecora

Title: Symmetries and Cluster Synchronization in Undirected Complex Networks
Abstract: Complex networks of oscillators or other dynamical systems can break down into subsets of nodes that are synchronized among each other, but not synchronized to node in other subsets. We call these subsets Clusters. For large networks finding such clusters is difficult to humanly impossible. The solution is to use computational group theory to find the symmetries of the network and, hence, the clusters. In addition, other clusters that are not formed from symmetries are also possible. Such clusters are called equitable clusters or Laplacian clusters. It turns out these are intimately related to the symmetry clusters and we can construct all of them from the original symmetry clusters making the symmetry clusters the building blocks of all synchronized clusters in undirected networks. We can also use group representation theory to derive the variational equations for the stability of the symmetry, equitable, and Laplacian clusters along with their desynchronization bifurcation modes. We have recently extended these findings to multilayered networks, which add some interesting group theory constructs to the analysis. I also show some experimental results that demonstrate the success of our analysis.

- [1030-1100] Coffee

- [1100-1140] Arkady Pikovsky

Title: Dynamics of oscillatory networks with structural and functional high-order interactions

- [1140-1220] Stephen Coombes

Title: Networks of Nonsmooth Oscillators & Applications in Neuroscience 
Abstract: The tools of weakly coupled phase oscillator theory have had a profound impact on the neuroscience community, providing insight into a variety of network behaviours ranging from central pattern generation to synchronisation. However, there are many instances where this theory is expected to break down, say in the presence of strong coupling.  To gain insight into the behaviour of neural networks when phase-oscillator descriptions are not appropriate we turn instead to the study of tractable piece-wise linear (pwl) systems.  There has been an appreciation for some time in the applied sciences, and particularly in electrical engineering, of the benefits of studying caricatures of complex systems built from pwl and possibly discontinuous dynamical systems.  Although a beautifully simplistic modelling perspective the necessary loss of smoothness precludes the use of many results from the standard toolkit of smooth dynamical systems, and one must be careful to correctly determine conditions for existence, uniqueness and stability of solutions.  

In this talk I will describe a variety of pwl neural oscillators and show how to analyse periodic orbits.  Building on this approach I will show how to analyse network states, with a focus on synchrony.  I will make use of an extension of the master stability function (MSF) approach utilising saltation matrices, and show how this framework is very amenable to explicit calculations when considering networks of pwl oscillators.  These can include pwl integrate-and-fire (IF) systems with smooth synaptic interactions, for which synchrony is ubiquitous in the case of a balance between excitation and inhibition.  Moreover, the MSF approach is readily generalised to treat other phase-locked states such as clusters.  For the case of nonsmooth synaptic interactions there is a further mathematical challenge that requires a careful treatment of the order in which perturbations cross the IF threshold.  A similar issue arises in networks of switch-like elements, as exemplified by Glass networks and neural mass models with a Heaviside nonlinearity.  Finally, I will discuss the dynamics of the famous Wilson-Cowan model posed on a realistic large-scale brain atlas and, time permitting, the important role that axonal delays can have on emergent network brain states and rhythms.

- [1220-1300] Jess Enright

Title: An algorithmic look at counting subgraphs in multilayer graphs

- [1300-1500] Lunch / Breakout

- [1500-1540] Peter Ashwin

Title: Oscillator networks with multiway interactions and dead zones
Abstract: Although many common paradigms for the dynamics of phase oscillator networks make an assumption of rather simple pairwise forms of coupling. Firstly, general reductions of nonlinear oscillator networks will result in multi-way coupling in very generic situations. Secondly, the coupling may "disappear" for certain phase configurations, giving rise to a subset of the links actually being part of the "effective" coupling network in some cases. In this talk I, will review recent joint work with Ana Rodrigues, Chris Bick and Camille Poignard that explores some dynamical effects in coupled phase oscillators that break the "simple pairwise" paradigm in one of these two ways.

- [1540-1620] Ana Paula Dias

Title: Coupled cell networks - classification and synchrony patterns
Abstract: In this talk, we consider weighed networks and homogeneous networks of cells with asymmetric inputs. We plan to address some questions concerning their classification and corresponding synchrony patterns. For weighed networks, our emphasis will be on those with feed-forward structure. Ongoing work in collaboration with Manuela Aguiar, Michael Field and Pedro Soares.

- [1620-1700] Tiago Pereira

Title: Reconstructing community structures and predicting critical transitions from data
Abstract: In this talk, we consider weighed networks and homogeneous networks of cells with asymmetric inputs. We plan to address some questions concerning their classification and corresponding synchrony patterns. For weighed networks, our emphasis will be on those with feed-forward structure. Ongoing work in collaboration with Manuela Aguiar, Michael Field and Pedro Soares.

- [1700-1900] Discussion / Breakout

- [1900-2300] Dinner at Somerville

Wednesday - Data & Higher-order Interactions

- [0900-1000] Keynote: Tanya Berger-Wolf

Title: Dynamic networks of animal behavior
Abstract: Why do social animals (including humans) do what they do? How do they make decisions, build coalitions, find resources, and protect themselves from danger? In the age of video and GPS tracking, remote sensing, and digital communications, we are now starting to have the data at high spatio-tempo-individual resolution and sufficient scale to start answering these questions computationally. While network analysis is a convenient tool, much of the methodology for understanding highly dynamic noisy collective interactions is still nascent. In this talk I will show some of the components of the framework of network inference and analysis we have been developing and demonstrate the insight it can provide in understanding social behavior.

- [1000-1030] Coffee

- [1030-1110] Roger Guimera

Title: Using graphs to build a Bayesian machine scientist.

- [1110-1150] Rebecca Hoyle

Title: Social influence on strategic decision-making in networks

- [1150-1230] Marya Bazzi

Title: Generative model for mesoscale structure in multilayer networks

- [1230-1300] Panel / Closing

- [1300-1400] Lunch

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