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Multiscale & Integrative compleX Networks: EXperiments & Theories 2023

Vienna, Austria | July 10-14 2023



Network Science for Multidimensional Data Analysis

The coexistence of multiple types of interactions within social, technological and biological networks has moved the focus of the statistical physics of complex systems towards their description as a set of subsystems organized as layers of connectivity. This approach has unveiled that the multilayer nature of complex systems has strong influence in the emergence of collective states and their critical properties, setting a novel paradigm in the past decade.
However, real-world systems are not only multilayer in their nature: they exhibit, simultaneously, a complex organization across multiple scales in their topology, dynamics and function. Recently, many approaches have been proposed to model higher-order interactions different from multiplexity: from simplicial complexes to memory in network flows, from latent topological geometry to multiresolution methods to unravel the hidden geometry of network-driven processes.
All those methods provide powerful tools to analyze complex systems and to unravel the effects of hierarchies from different points of view. However, empirical networks often exhibit multiscale spatio-temporal organization, multilayer relationships and non-trivial geometry.

Aim of MIX-NEXT. The goal of this Satellite meeting is to showcase the latest advancements in the theory of complex networks while keeping an integrated view of different trends in the field, rather than a more specialized one. We want to do so by balancing the contributions of well-established leading experts and rising young researchers that work on frontier problems. We aim at triggering and igniting new discussions on theoretical and computational solutions required to build a more comprehensive set of tools integrating different perspectives into one, coherent and self-consistent, framework for modeling and analysis of complex networks.
In this edition, special emphasis will be given to the following topics:
- Structural/functional robustness and resilience of multiscale, multilayer and (hidden) geometric structures.
- Information-theoretic tools to characterize such interconnected systems.
- Applications of such network models and metrics to biological, social, technological and urban systems.

Previous editions

 2014 Berkeley, California
 2015 Zaragoza, Spain
 2016 Amsterdam, The Netherlands
 2017 Cancun, Mexico
 2018 Paris, France
 2019 Singapore
 2020 Rome, Italy
 2020 Online
 2021 Lyon, France
 2022 Shanghai, China


János Kertész
Central European University, Vienna, Austria
Luis M. Rocha
Binghamton University (SUNY), NY, US


Luca Gallo
Central European University, Vienna, Austria
Arsham Ghavasieh
Trento University and Fondazione Bruno Kessler, Italy

Wout Merbis
Dutch Institute for Emergent Phenomena,University of Amsterdam, Netherlands
Giacomo Barzon
Padova Neuroscience Center, Italy


Contributions are welcome as abstracts about published or unpublished research (one page abstract). Deadline for contributing: June 12th.


May 1, 2023 Early Registration
June 12, 2023 June 21, 2023 Deadline for contributions
July 10 - 11, 2023 Satellites & School
July 12 - 14, 2023 Main Conference
July 10, 2023 MIXNEXT Satellite


Time (CET)    Speaker
9:00    Oriol Artime and Marco Grassia

9:10    János Kertész, Central European University, Vienna, Austria
[keynote talk] Multidimensional political polarization in online social media

Despite their relevance to modern-day politics, the structure and dynamics of political polarization in digital spaces are still poorly understood. We analyze the community structure of a two-layer, interconnected network of French Twitter users, where one layer contains members of Parliament and the other one regular users. We obtain an optimal representation of the network in a four-dimensional political opinion space by combining network embedding methods and political survey data. We find structurally cohesive groups sharing common political attitudes and relate them to the political party landscape in France. The distribution of opinions of professional politicians is narrower than that of regular users, indicating the presence of more extreme attitudes in the general population. We find that politically extreme communities interact less with other groups as compared to more centrist groups. We apply an empirically tested social influence model to the two-layer network to pinpoint interaction mechanisms that can describe the political polarization seen in data.
9:45    Luca Gallo, Central European University, Vienna, Austria
[regular talk] The Master Stability Function for Synchronization in Higher-order Networks

In the past decades, many complex systems, either natural, social, or artificial, have been modeled as networks of coupled dynamical systems, with links describing interactions among pairs of units. However, recent evidence shows that various systems are characterized by many-body, group interactions that cannot be captured by a network description. Here, we introduce a general theory for studying the collective behavior of coupled dynamical systems in the presence of higher-order interactions. We use this framework to analyze the complete synchronization of chaotic oscillators, extending the Master Stability Function approach developed for networks to the case of higher-order systems. With this formalism, we show how the interplay between different orders of interaction determines the onset of synchronization. We analyze the cases of reciprocal and nonreciprocal interactions, showing how the presence of privileged directions in the interactions can affect the stability of the synchronized state.
10:07    Wout Merbis, Dutch Institute for Emergent Phenomena, University of Amsterdam, Netherlands
[regular talk] Quantum methods for complex systems

Complex systems are often composed of large collections of like constituents (spins, bits, agents, etc..) with locally defined interaction rules. They are ubiquitous in Nature and often dynamical, out of equilibrium and of high complexity. In stochastic modeling of complex systems, the state of the system is described by a high-dimensional probability vector (i.e. exponential in system size), which complicates any exact analytical treatment. This situation is very similar to that in quantum many-body systems, where macroscopic properties of materials emerge from quantum mechanical interaction between many atoms and/or electrons. In this talk, we will discuss the implementation of state-of-the-art techniques from quantum many-body systems based on tensor networks to obtain an efficient and accurate compression of the high dimensional probability vector describing the dynamical behavior of stochastic models. As an example, we will look at the one-dimensional contact process (known as the SIS model to epidemiologists). We use these techniques to obtain accurate distributions over rare events and study large deviations in the dynamical activity, which is extremely hard to obtain using Monte Carlo sampling methods. We conclude with ideas for further research, and possible applications of these methods to study information dynamics on complex networks.
10:30    Break

11:00    Luis M. Rocha, Binghamton University (SUNY), NY, US
[keynote talk] Redundancy in the Structure and Dynamics of Complex Networks

Many advances in network science derive from the study of patterns of connectivity (network structure), which provides many insights into the organization of complex systems. Yet, a critical gap remains in understanding how the structure of networks affects the dynamics of complex systems. We have been addressing this gap from a complementary angle: in addition to patterns of connectivity and patterns of dynamics, there are important patterns of redundancy which dictate how interaction structure and logic shape network dynamics. We first characterize structural redundancy via the concept of distance backbone of a weighted graph: the sub-graph formed by all edges that obey a generalized triangle inequality for a given path length measure. We show that distance backbones are a parameter-free, principled method to obtain typically very small subgraphs in networks across domains. We illustrate the relationship to dynamics on networks by showing that the metric backbone is a primary subgraph for epidemic transmission based on pure diffusion processes. The study of experimentally-validated systems biology models of biochemical regulation and signaling has revealed another form of redundancy which is involved in the canalization of biochemical dynamics towards robust phenotypes— where the focus is the macro dynamics of networks. To study this form of dynamical redundancy, we measure the effective connectivity of micro-level causal interactions and demonstrate that redundant pathways are prevalent in biochemical regulation. Indeed, the redundancy found in biological models is much more pronounced than what is expected from random networks, and a major reason for them being much more ordered than what the current criticality hypothesis, or “edge-of-chaos” theory, predicts.
11:35    Arsham Ghavasieh, Trento University and Fondazione Bruno Kessler, Italy
[regular talk] Diversity of information pathways drives scaling and sparsity in real-world networks

Empirical complex systems must differentially respond to external perturbations and, at the same time, internally distribute information to coordinate their components. While networked backbones help with the latter, they limit the components' individual degrees of freedom and reduce their collective dynamical range. Here, we show that real-world networks are formed to optimize the gain in information flow and loss in response diversity. Encoding network states as density matrices, we demonstrate that such a trade-off mathematically resembles the thermodynamic efficiency characterized by heat and work in physical systems. Our findings explain, analytically and numerically, the sparsity and the empirical scaling law observed in hundreds of real-world networks across multiple domains. We show, through numerical experiments in synthetic and biological networks, that ubiquitous topological features such as modularity and small-worldness emerge to optimize the above trade-off for middle- to large-scale information exchange between system's units. Our results highlight that the emergence of some of the most prevalent topological features of real-world networks have a thermodynamic origin.
11:57    Giacomo Barzon, Padova Neuroscience Center, Italy
[regular talk] Structural Foundations of Brain Criticality: Unraveling the Influence of the Human Connectome

Understanding the complex dynamics of the brain is a fascinating and challenging endeavor. In recent years, the brain criticality hypothesis has emerged as a promising framework to shed light on the relationship between brain structure and function. Computational models tuned at criticality have played a crucial role in bridging this gap. In this talk, our focus is on a cellular automata model proposed to explain criticality in the brain. We analytically characterize the model and reveal that in the mean field limit, it exhibits a bistability. This finding underscores the significance of the underlying empirical connectome as a key ingredient for the emergence of criticality. Furthermore, we explore the practical implications of this model by applying it to stroke patients. Previous results have demonstrated a correlation between the loss of cognitive features and the decline in criticality. Interestingly, we observe that the topological dimension of the connectome serves as a predictive factor for such loss of criticality. This finding suggests that the organization and structure of the brain's connectivity play a pivotal role in maintaining critical dynamics and cognitive function.
12:20    Open discussion

12:30    Closing



Manlio De Domenico
University of Padua


Oriol Artime
University of Barcelona


Valeria d'Andrea
Fondazione Bruno Kessler

Marco Grassia
University of Catania



Alex Arenas Univ. Rovira i Virgili (Spain)
Dirk Brockmann Humboldt Univ. (Germany)
Albert Diaz-Guilera Univ. Barcelona (Spain)
Sergio Gómez Univ. Rovira i Virgili (Spain)