This series of webinars, organized by the CoMuNe Lab, has the aim to explore the multiple aspects of Complexity and Network Science. Leading experts from biochemistry to theoretical physics, from quantum information theory to quantitative social sciences, are invited to discuss about their research line and engaged in discussions about complexity and its application to understanding realworld challenges, from the origin of life to intelligence, cooperation and other emergent phenomena.
Dr. J. Xavier UCL/OoLEN 09/06/2021 
Metabolic networks and the origin of life
A living cell performs billions of reactions and billions of exchanges with the environment each second. Such is metabolism, a vast autocatalytic network of chemical flux towards biomass and energy, shaped by the genetic code triad—DNARNAprotein—but also by an active membrane, nonencoded small molecules, and physicalchemical constraints that apply to nonliving systems alike. In this talk, we will see how metabolic flux models predict essential genes, reactions, and metabolites, which are also ancient and prospective antibiotic targets. We will then explore how both those hubs of modern encoded networks and smaller nonencoded autocatalytic networks can explain the origin of selforganisation before (yet towards) the genetic code. Finally, we will examine the inference of the core metabolic network of the last bacterial common ancestor, predicted to have emerged shortly after the origin of cells. 
Dr. M. Walschaerts Laboratoire Kastler Brossel 19/05/2021 
Emergent complex networks in continuousvariable quantum systems
Once systems reach a sufficiently large scale, they can often be described by some kind of network. In nature such networks often do not show any regularity, nor are they completely random. Throughout the decades, many toy models have been proposed for such complex networks to study some specific properties such as the formation of hubs and the appearance of small world effects. In our work, we analyse how complex networks can appear in continuousvariable (CV) quantum optics. To explain these results, we start with a brief introduction to the terminology of modes and quantum states of light. In particular, we will learn how CV cluster states allow us to directly imprint a network into a quantum state. As we can implement such networks in a highly versatile way, we focus on the case where the imprinted networks are complex (either Barabási–Albert or Watts–Strogatz). Even though we build cluster states by using an imprinted network as blueprint, there are other natural ways to associate networks to multimode quantum states. In our case, we focus on weighted networks that characterise the correlations between pairs of modes in our system. These emergent networks allow us to analyse cluster states in a new manner. First we explore how the statistics of the degree of these weighted emergent networks depends on the structure of the imprinted network. Then, we implement nonGaussian operations on one node of the cluster state and show that the emergent networks changes profoundly, a change which we can also link to the structure of the imprinted network. NonGaussian multimode states are notoriously hard to characterise, but they are also necessary for the development of quantum technologies. Our work shows that techniques of network science may provide a gateway to understand these systems on a scale where thus far all other methods have failed. 
Prof. A. Cavagna Institute for Complex Systems, Rome 12/05/2021 
Equilibrium to offequilibrium crossover in homogeneous active matter near its ordering transition
In active matter systems as flocks and swarms, offequilibrium effects are due to the interplay between the effective alignment interaction and the dynamical rewiring of the interaction network, which gives rise to a nonHamiltonian coupling between density and velocity, as a consequence of which heterogeneous density structures may emerge. It therefore seems that the coupling between density and velocity stays at the very core of offequilibrium active matter. In fact, active motion and densityvelocity coupling are related but distinct phenomena. The fact that particles continuously enter and exit the alignment interaction range of any given particle can violate detail balance also in a system with homogeneous density. We may therefore ask: Can activity lead to relevant offequilibrium dynamics even without any significant coupling between velocity and density, and therefore in absence of heterogeneous density structures? To address this question I will consider the crossover between equilibrium and offequilibrium dynamical universality classes in homogeneous active matter near its ordering transition. Starting from the incompressible hydrodynamic theory of swarms, I will show that increasing the activity leads to a renormalization group (RG) crossover between the equilibrium ferromagnetic fixed point, with dynamical critical exponent z~2, and the offequilibrium active fixed point, with z~1.7. I will present simulations of the compressible Vicsek model in the homogeneous nearordering regime and find that critical slowing down indeed changes with activity, displaying two exponents that are in good agreement with the RG prediction. The equilibriumtooffequilibrium crossover is ruled by a characteristic length scale beyond which active dynamics takes over. Such length scale is smaller the larger the activity, suggesting the existence of a general tradeoff between activity and system's size in determining the dynamical universality class of active matter. 
Dr. C. Marletto University of Oxford 05/05/2021 
Beyond quantum computation: the Science of Can and Can't
The theory of the quantum computer has brought us rapid technological developments, together with remarkable improvements in how we understand quantum theory. There are, however, reasons to believe that quantum theory may ultimately have to be modified into a new theory: for instance, it will have to be merged with general relativity, to incorporate gravity; and some claim that it may be impossible to have quantum effects beyond a certain macroscopic scale. So what lies ahead of quantum theory, and of the universal quantum computer? To shed some light into these questions, we need a shift of logic in the way things are explained. Specifically, one can adopt the approach where the basic assumptions are general principles about possible/impossible transformations, rather than dynamical laws and initial conditions. This ‘Physics of Can and Can’t’ may be the first step towards the ultimate generalization of the universal quantum computer, which von Neumann called the 'universal constructor’. I will describe its foundations and tell you about the latest applications. 
Prof. S. Walker Arizona State University 21/04/2021 
Life is What?
In 1943 Erwin Schrodinger famously delivered a set of lectures at the Dublin Institute for Advanced Studies aiming to tackle the question “What is Life?” from the firstprinciples approach of a theoretical physicist. Over 70 years later, we’ve still made little headway in coming up with a general theory for what life is. While many definitions for life do exist, these are primarily descriptive, not predictive, and they have so far proved insufficient to explain the origins of life from nonliving matter, or to provide rigorous constraints on what properties are universal to all life, even that on other worlds. Yet, as NASA and other space agencies are setting sights on life detection as a goal of upcoming robotic missions and space observatories, more rigorous understanding of the universal properties of living matter are becoming increasingly vital to uncover. In this talk I discuss new approaches to understanding what universal principles might underlie living matter and how to generate it, based on studying biochemical networks on Earth from the scale of individual organisms to the planetary scale. 
Dr. A. Kolchinsky Santa Fe Institute 07/04/2021 
Stochastic thermodynamics from a complex networks point of view
I will give a brief tutorial on the recentlydeveloping field of stochastic thermodynamics, which has uncovered a set of fundamental relationships between energy, information, and stochastic dynamics. I will also discuss connections to the field of complex networks, as well as an application to a problem in biophysics. 
Prof. C. Gershenson Universidad Autonoma de Mexico 24/03/2021 
SelfOrganization and Artificial Life
Selforganization can be broadly defined as the ability of a system to display ordered spatiotemporal patterns solely as the result of the interactions among the system components. Processes of this kind characterize both living and artificial systems, making selforganization a concept that is at the basis of several disciplines, from physics to biology and engineering. Placed at the frontiers between disciplines, artificial life (ALife) has heavily borrowed concepts and tools from the study of selforganization, providing mechanistic interpretations of lifelike phenomena as well as useful constructivist approaches to artificial system design. Despite its broad usage within ALife, the concept of selforganization has been often excessively stretched or misinterpreted, calling for a clarification that could help with tracing the borders between what can and cannot be considered selforganization. In this review, we discuss the fundamental aspects of selforganization and list the main usages within three primary ALife domains, namely “soft” (mathematical/computational modeling), “hard” (physical robots), and “wet” (chemical/biological systems) ALife. We also provide a classification to locate this research. Finally, we discuss the usefulness of selforganization and related concepts within ALife studies, point to perspectives and challenges for future research, and list open questions. We hope that this work will motivate discussions related to selforganization in ALife and related fields. 
Prof. G. De Las Cuevas University of Innsbruck 03/03/2021 
Universality everywhere: from spin models to automata, neural networks and beyond
Why is it so easy to generate complexity? I will suggest that this is due to the phenomenon of universality — essentially every nontrivial system is universal, and thus able to explore all complexity in its domain. We understand the phenomenon of universality in spin models, automata and neural networks. I will explain the first step toward rigorously linking the first two, as well as perspectives of extending this study to other fields. I will also talk about one of the consequences of universality, namely undecidability. 
Prof. P. Sacco IULM University  Milan 03/03/2021 
Culture 3.0 and science: towards a research agenda
The seminar will explore how the Culture 3.0 paradigm may be a useful conceptual reference to understand the current models of social engagement with science and suggest strategies to tackle future societal challenges related to the public reception of, and trust building around, science, as in the case of pandemic shocks and vaccine hesitancy. This approach also sheds light on how to interpret fake news and conspiracy theories in the context of a more general view of the role of active participation and citizenship in knowledgeintensive societies, and to design better strategies for the construction and maintenance of future knowledge commons in a variety of spheres of public interest. 
Prof. R. Sole Universitat Pompeu Fabra 23/06/2020 
Liquid brains, solid brains
Collective computations take place in nature in two major classes of architecture, which we can roughly classify as "solid" (the standard, synaptic connectivity picture) versus those that are performed by "liquid" networks, such as the Immune system or ant colonies. Additionally, other solutions (or constraints) associated with plant and fungal communication, or the potential of unicellular systems such as Physarum emerged as relevant actors. Finally, synthetic systems such as robot swarms and engineered communicating cells offer additional avenues for inquiry.There are many questions that we need to address, in particular: What are the computational limits associated with the physical state displayed by the collective? Are there a limited number of possibilities (as those already observed) or many others? What can or cannot be computed? How do we define a proper evolutionary framework to understand the origins of different solutions? What are the tradeoffs involved here? Can we evolve other solutions using artificial life models? Can a statistical physics approach to computa8on including physical phases help finding universality classes? What is the impact of fluid versus solid on the values and meaning of integrated information theory? Answering these questions will help to define a theoretical framework for the emergence and design of cognitive networks. 
Prof. A. Vulpiani Università di Roma  La Sapienza 17/06/2020 
Levels of Reality in Weather Forecasting: the Lesson by Richardson and Von Neumann
At first glance weather forecasting appears just a topic of practical relevance. An analysis of its main aspects shows the presence of conceptual topics which are rather interesting in complex systems:
