Universality is a principle that fundamentally underlies many critical phenomena, ranging from epidemic spreading to the emergence or breakdown of global connectivity in networks. Percolation, the ...transition to global connectedness on gradual addition of links, may exhibit substantial gaps in the size of the largest connected network component. We uncover that the largest gap statistics is governed by extreme-value theory. This allows us to unify continuous and discontinuous percolation by virtue of universal critical scaling functions, obtained from normal and extreme-value statistics. Specifically, we show that the universal scaling function of the size of the largest gap is given by the extreme-value Gumbel distribution. This links extreme-value statistics to universality and criticality in percolation.Percolation transitions underpin a generic class of phenomena associated with the degree of connectedness in networks. A detailed numerical study now uncovers a universal scaling in the size of the largest cluster identified in such percolation models.
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FZAB, GEOZS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
Network science provides a set of tools for the characterization of the structure and functional behavior of complex systems. Yet a major problem is to quantify how the structural domain is related ...to the dynamical one. In other words, how the diversity of dynamical states of a system can be predicted from the static network structure? Or the reverse problem: starting from a set of signals derived from experimental recordings, how can one discover the network connections or the causal relations behind the observed dynamics? Despite the advances achieved over the last two decades, many challenges remain concerning the study of the structure-dynamics interplay of complex systems. In neuroscience, progress is typically constrained by the low spatio-temporal resolution of experiments and by the lack of a universal inferring framework for empirical systems. To address these issues, applications of network science and artificial intelligence to neural data have been rapidly growing. In this article, we review important recent applications of methods from those fields to the study of the interplay between structure and functional dynamics of human and zebrafish brain. We cover the selection of topological features for the characterization of brain networks, inference of functional connections, dynamical modeling, and close with applications to both the human and zebrafish brain. This review is intended to neuroscientists who want to become acquainted with techniques from network science, as well as to researchers from the latter field who are interested in exploring novel application scenarios in neuroscience.
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IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
The character of motion for the three-dimensional circular restricted three-body problem with oblate primaries is investigated. The orbits of the test particle are classified into four types: ...non-escaping regular orbits around the primaries, trapped chaotic (or sticky) orbits, escaping orbits that pass over the Lagrange saddle points L2 and L3, and orbits that lead the test particle to collide with one of the primary bodies. We numerically explore the motion of the test particle by presenting color-coded diagrams, where the initial conditions are mapped to the orbit type and studied as a function of the total orbital energy, the initial value of the z-coordinate and the oblateness coefficient. The fraction of the collision orbits, measured on the color-coded diagrams, show an algebraic dependence on the oblateness coefficient, which can be derived by simple arguments.
•The spatial version of the restricted three-body problem is numerically investigated.•The orbital properties of the system are revealed through a systematic orbit classification.•The influence of the energy as well as of the oblateness coefficient on the nature of motion is determined.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
Synchronization constitutes one of the most fundamental collective dynamics across networked systems and often underlies their function. Whether a system may synchronize depends on the internal unit ...dynamics as well as the topology and strength of their interactions. For chaotic units with certain interaction topologies synchronization might be impossible across all interaction strengths, meaning that these networks are non-synchronizable. Here we propose the concept of interaction control, generalizing transient uncoupling, to induce desired collective dynamics in complex networks and apply it to synchronize even such non-synchronizable systems. After highlighting that non-synchronizability prevails for a wide range of networks of arbitrary size, we explain how a simple binary control may localize interactions in state space and thereby synchronize networks. Intriguingly, localizing interactions by a fixed control scheme enables stable synchronization across all connected networks regardless of topological constraints. Interaction control may thus ease the design of desired collective dynamics even without knowledge of the networks' exact interaction topology and consequently have implications for biological and self-organizing technical systems.
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IZUM, KILJ, NUK, PILJ, PNG, SAZU, UL, UM, UPUK
We report the discovery of a discrete hierarchy of microtransitions occurring in models of continuous and discontinuous percolation. The precursory microtransitions allow us to target almost ...deterministically the location of the transition point to global connectivity. This extends to the class of intrinsically stochastic processes the possibility to use warning signals anticipating phase transitions in complex systems.
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CMK, CTK, FMFMET, IJS, NUK, PNG, UM
Spatial heterogeneity of a host population of mobile agents has been shown to be a crucial determinant of many aspects of disease dynamics, ranging from the proliferation of diseases to their ...persistence and to vaccination strategies. In addition, the importance of regional and structural differences grows in our modern world. Little is known, though, about the consequences when traits of a disease vary regionally. In this paper, we study the effect of a spatially varying per capita infection rate on the behaviour of livestock diseases. We show that the prevalence of an infectious livestock disease in a community of animals can paradoxically decrease owing to transport connections to other communities in which the risk of infection is higher. We study the consequences for the design of livestock transportation restriction measures and establish exact criteria to discriminate those connections that increase the level of infection in the community from those that decrease it.
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BFBNIB, NMLJ, NUK, PNG, SAZU, UL, UM, UPUK
Crackling noise is a common feature in many systems that are pushed slowly, the most familiar instance of which is the sound made by a sheet of paper when crumpled. In percolation and regular ...aggregation, clusters of any size merge until a giant component dominates the entire system. Here we establish 'fractional percolation', in which the coalescence of clusters that substantially differ in size is systematically suppressed. We identify and study percolation models that exhibit multiple jumps in the order parameter where the position and magnitude of the jumps are randomly distributed--characteristic of crackling noise. This enables us to express crackling noise as a result of the simple concept of fractional percolation. In particular, the framework allows us to link percolation with phenomena exhibiting non-self-averaging and power law fluctuations such as Barkhausen noise in ferromagnets.
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