Abstract: Complex systems often undergo abrupt or gradual transitions to dynamical regimes that canbe safe or dangerous for the system functionality. Examples of dangerous transitions includedesertification, population extinctions, financial crashes, cardiac arrhythmia, epileptic seizures,etc. A precise identification of such transitions is important for preventing harmfulconsequences, and a lot of efforts are nowadays focused on developing reliable diagnostictools that can be applied to observed time-series, which are finite and usually stochastic. Inthis presentation I will discuss our recent work aimed at exploiting network theory andnonlinear time-series analysis tools, for characterizing and quantifying regime transitions indifferent systems. Specifically, I will consider synthetic data generated from a vegetationmodel [1] and empirical data recorded from the output of various laser systems [2-4].References[1] G. Tirabassi, J. Viebahn, V. Dakos, H. A. Dijkstra, C. Masoller, M. Rietkerk, and S.C. Dekker,"Interaction network based early-warning indicators of vegetation transitions", EcologicalComplexity 19, 148 (2014).[2] C. Masoller, Y. Hong, S. Ayad, F. Gustave, S. Barland, A. J. Pons, S. Gomez, and A. Arenas,?Quantifying sudden changes in dynamical systems using symbolic networks?, New Journal ofPhysics 17, 023068 (2015).[3] A. Aragoneses, L. Carpi, N. Tarasov, D. V. Churkin, M. C. Torrent, C. Masoller, and S. K.Turitsyn, ?Unveiling temporal correlations characteristic to phase transition in the intensity offibre laser radiation?, Phys. Rev. Lett. 116, 033902 (2016).[4] C. Quintero-Quiroz, J. Tiana-Alsina, J. Roma, M. C. Torrent, and C. Masoller, ?Characterizinghow complex optical signals emerge from noisy intensity fluctuations?, submitted (2016)

Abstract: Human societies depend on the resources ecosystems provide. Particularly since the last century, human activities have transformed the relationship between nature and society at a global scale. We study this coevolutionary relationship by utilizing a stylized model of regional resource use and preference formation on an adaptive social network. The latter process is based on two social key dynamics beyond economic paradigms: boundedly rational imitation of resource use preferences and homophily in the formation of social network ties. The private and logistically growing resources are harvested either with a sustainable (small) or non-sustainable (large) effort. We show that these social processes can have a profound influence on the environmental state, such as determining whether the private renewable resources collapse from overuse or not. Additionally, we demonstrate that heterogeneously distributed regional resource capacities shift the critical social parameters (social-ecological transition regime) where this resource extraction system collapses. We make these points to argue that, in more advanced coevolutionary models of the planetary social-ecological system, such socio-cultural phenomena as well as regional resource heterogeneities should receive attention in addition to the processes represented in established Earth system and integrated assessment models.

Abstract: Critical transitions in nature and society are likely to occur more often and severe as humans increase they pressure on the world ecosystems. Yet it is largely unknown how these transitions will interact, whether the occurrence of one will increase the likelihood of another, and whether these potential teleconnections (social and ecological) correlate critical transition in distant places. Here we present a framework for exploring three types of potential cascading effects of critical transitions: forks, domino effects and inconvenient feedbacks. Drivers and feedback mechanisms are reduced to a network form that allow us to explore drivers co-occurrence (forks). Sharing drivers is likely to increase correlation in time or space among critical transitions but not necessarily interdependence. Random walks on causal networks allow us to detect and compare communities of common drivers and feedback mechanisms across different critical transitions. Domino effects and inconvenient feedbacks were identified by mapping new circular pathways on coupled networks that have not been previously reported. The method serves as a platform for hypothesis exploration of plausible new feedbacks between critical transitions in social-ecological systems; it helps to scope structural interdependence and hence an avenue for future modelling and empirical testing of regime shifts coupling.

Abstract: Transformations to create more sustainable social-ecological are urgently needed. Agency and dynamics are frequently cited as key components for understanding transformational change, but structural change is a third central feature in transformations of social-ecological systems that has received relatively little attention. Here, we propose a framework for conceptualising and modelling sustainability transformations based on adaptive networks. Adaptive networks focus attention on the interplay between the structure of a social-ecological system and the dynamics of individual entities within it. Adaptive networks have the potential to progress transformations research by: 1) focusing research on structure, a neglected aspect of social-ecological transformation; 2) providing quantitative modelling tools in an area of study dominated by qualitative methods; 3) providing a conceptual framework that clarifies the temporal dynamics of social-ecological transformations compared to the most commonly used heuristic in resilience studies, the ball-and-cup diagram. We illustrate the application of adaptive networks to social-ecological transformations using a case study of illegal fishing in the Southern Ocean. Adaptive network modelling could help drive a renaissance of modelling and conceptual work regarding transformations of social-ecological systems. Insights from these studies, in turn, could help society respond to the need for sustainability transformations in today?s era of global social and environmental change.

Abstract: Study of phase transition and the structure of equilibrium phases plays the central role in statistical mechanics of condensed systems. Indeed, often understanding the symmetries of the phases and proper choice of an order parameter is a crucial step allowing one to get an insight into what is actually going on in the system under consideration. Large equilibrium random networks are, clearly, an object very well suitable to be studied by the methods of statistical mechanics, and importing our insights into phase transition theory can be very instructive. In my talk I will give an overview of several examples where such import of the ideas from the theory of phase transitions turned out to be useful, and then concentrate on a particular example which we have been studying at length lately. Consider a large annealed network with a frozen degree distribution of nodes (that is to say, links between nodes can rewire, but the degree of each node always stays the same), and introduce a three-node interaction in this system which favours creation of closed triangles of bonds. We show that with increasing strength of the interaction, this system undergoes a first order phase transition from a homogeneous phase with locally almost tree-like structure and small concentration of triangles to a "triangle condensate" where the concentration of closed triangles drastically increases. Moreover, the condensed phase has a beautiful microstructure consisting: it is a set of almost fully-connected clicks with very small number of links between them. Such a microstructure formation can be easily understood and is akin to formation of microstructured phases in soft condensed matter.

Abstract: The synchronization between power-grid nodes is one of the essential conditions for the stable electric power system. The synchronization stability changes according to various network parameters corresponding to the amount of power input at each node, damping coefficient, and transmission strength between nodes. Previously, studies have revealed that the synchronization is more stable with smaller power input or larger damping coefficient. In this study we investigate the synchronization stability as a function of the transmission strength. We particularly focus on the transition phenomenon of the synchronization stability measured by basin stability that is numerical Monte Carlo simulation. In order to overcome the computationally costly process, we introduce some techniques to detect and classify various transition patterns. In this talk, we cover the dynamical transition phenomenon of synchronization stability and introduce useful techniques to overcome practical difficulties.

Abstract: In various context, high-dimensional data reside on the vertices of networks, so that the network is the ?natural space? for such systems. Therefore techniques, as Graph Signal Transform, levering the structure of the network, to grasp the main features of the dynamical process upon it are drawing increasing attention. Graph Signal Transform is, by design, well-suited to treat signals in very irregular domains and it allows applications that span from image compression to uncovering network communities [1]. In a nutshell, this technique is reminiscent of Fourier transform, but at the same time it embeds the inhomogeneities of the underlying graph: the time series on the network nodes, i.e. the graph signal, is decomposed in a sum of components on the Laplacian eigenvectors and this decomposition allows to finger the ones which have an high weight, i.e. that are resonant with the dynamics. In this work, we apply Graph Signal Transform to a classical model for magnetized materials, the XY spin model of which we consider the phenomenology on networks. Remarkably, there is recent evidence that a variety of collective responses can be ignited if a complex network connects the spins [2-3]. In particular, we observe the same collective state on different networks through a fine tuning of the network topological parameters: a magnetized regime, displaying a second order phase transition to a non-magnetized phase and, furthermore, a peculiar oscillating phase has been observed where the order parameter is affected by persistent global oscillations. We thus focus on the Graph Signal Transform to benchmark the time series produced by the model in the three aforementioned macroscopic states at equilibrium[4]. Through this benchmarking phase, we retrieve the ?selected network modes? for each macroscopic state on different topologies and this selection points to the sub-structures of the graph relevant for the dynamics. [1]D. Shuman, S. K. Narang, P. Frossard et al., Signal Processing Magazine, IEEE 30, 83 (2013). [2]S. De Nigris and X. Leoncini, Phys. Rev. E 88, 012131 (2013). [3]S. de Nigris and X. Leoncini, Phys. Rev. E 91, 042809 (2015). [4]S. de Nigris, P. Expert, T. Takaguchi and R. Lambiotte, to be submitted.

Abstract: In many complex systems, it may be desirable or even essential to avoid classes of nodes by utilizing multiple paths. The need to avoid a certain set of nodes may be because they are tapped by the same eavesdropper or liable to fail collectively. Thus, secure connectivity is limited to a subset of nodes which can be connected with multiple paths, each avoiding nodes of a given vulnerability. To analyze this secure connectivity, we describe each vulnerable class as a color and develop a ``color-avoiding percolation'' framework. We present an analytic theory for random networks and a numerical algorithm for all networks. Applying our physics-based theory to the Internet, we show how color-avoiding percolation can be used as the basis for new topologically aware secure communication protocols. Beyond applications to cybersecurity, our framework reveals a new layer of hidden structure in a wide range of natural and technological systems. The transition from fully connected system to partially connected system and to a completely disconnected system is systematically analyzed.

Abstract: In recent years much research activity has focused on the application of complex network techniques to problems in climate variability. This has been particularly successful in climate transition problems, where relatively simple topological properties of reconstructed interaction or recurrence networks have provided useful early warning indicators of transitions in the ocean circulation, vegetation patterns and El Nino. In this presentation, a critical evaluation will be given on recent results on such transition problems, with a focus on El Nino occurrences and the collapse of the Atlantic Ocean circulation.