Universality of explosive percolation under product and sum rule.

We study explosive percolation processes on random graphs for the so-called product rule (PR) and sum rule (SR), in which M candidate edges are randomly selected from all possible ones at each time step, and the edge with the smallest product or sum of the sizes of the two components that would be joined by the edge is added to the graph, while all other M-1 candidate edges are being discarded. These two rules are prototypical "explosive" percolation rules, which exhibit an extremely abrupt yet continuous phase transition in the thermodynamic limit. Recently, it has been demonstrated that PR and SR belong to the same universality class for two competing edges, i.e., M=2. Here we investigate whether the claimed PR-SR universality is valid for higher-order models with M larger than 2. Based on traditional finite-size scaling theory and largest-gap scaling, we obtain the percolation threshold and the critical exponents of the order parameter, susceptibility, and the derivative of entropy for PR and SR for M from 2 to 9. Our results strongly suggest PR-SR universality, for any fixed M.

Structure and function in artificial, zebrafish and human neural networks.

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.

Impact of basic network motifs on the collective response to perturbations.

Many collective phenomena such as epidemic spreading and cascading failures in socioeconomic systems on networks are caused by perturbations of the dynamics. How perturbations propagate through networks, impact and disrupt their functions may depend on the network, the type and location of the perturbation as well as the spreading dynamics. Previous work has analyzed the retardation effects of the nodes along the propagation paths, suggesting a few transient propagation "scaling" regimes as a function of the nodes' degree, but regardless of motifs such as triangles. Yet, empirical networks consist of motifs enabling the proper functioning of the system. Here, we show that basic motifs along the propagation path jointly determine the previously proposed scaling regimes of distance-limited propagation and degree-limited propagation, or even cease their existence. Our results suggest a radical departure from these scaling regimes and provide a deeper understanding of the interplay of self-dynamics, interaction dynamics, and topological properties.

Decisive conditions for strategic vaccination against SARS-CoV-2.

While vaccines against severe acute respiratory syndrome coronavirus (SARS-CoV-2) are being administered, in many countries it may still take months until their supply can meet demand. The majority of available vaccines elicit strong immune responses when administered as prime-boost regimens. Since the immunological response to the first ("prime") dose may provide already a substantial reduction in infectiousness and protection against severe disease, it may be more effective-under certain immunological and epidemiological conditions-to vaccinate as many people as possible with only one dose instead of administering a person a second ("booster") dose. Such a vaccination campaign may help to more effectively slow down the spread of SARS-CoV-2 and reduce hospitalizations and fatalities. The conditions that make prime-first vaccination favorable over prime-boost campaigns, however, are not well understood. By combining epidemiological modeling, random-sampling techniques, and decision tree learning, we find that prime-first vaccination is robustly favored over prime-boost vaccination campaigns even for low single-dose efficacies. For epidemiological parameters that describe the spread of coronavirus disease 2019 (COVID-19), recent data on new variants included, we show that the difference between prime-boost and single-shot waning rates is the only discriminative threshold, falling in the narrow range of 0.01-0.02 day-1 below which prime-first vaccination should be considered.

Decisive Conditions for Strategic Vaccination against SARS-CoV-2.

While vaccines against SARS-CoV-2 are being administered, in most countries it may still take months until their supply can meet demand. The majority of available vaccines elicits strong immune responses when administered as prime-boost regimens. Since the immunological response to the first ("prime") injection may provide already a substantial reduction in infectiousness and protection against severe disease, it may be more effective-under certain immunological and epidemiological conditions-to vaccinate as many people as possible with only one shot, instead of administering a person a second ("boost") shot. Such a vaccination campaign may help to more effectively slow down the spread of SARS-CoV-2, reduce hospitalizations, and reduce fatalities, which is our objective. Yet, the conditions which make single-dose vaccination favorable over prime-boost administrations are not well understood. By combining epidemiological modeling, random sampling techniques, and decision tree learning, we find that single-dose vaccination is robustly favored over prime-boost vaccination campaigns, even for low single-dose efficacies. For realistic scenarios and assumptions for SARS-CoV-2, recent data on new variants included, we show that the difference between prime-boost and single-shot waning rates is the only discriminative threshold, falling in the narrow range of 0.01-0.02 day-1 below which single-dose vaccination should be considered.

Hysteretic Percolation from Locally Optimal Individual Decisions.

The emergence of large-scale connectivity underlies the proper functioning of many networked systems, ranging from social networks and technological infrastructure to global trade networks. Percolation theory characterizes network formation following stochastic local rules, while optimization models of network formation assume a single controlling authority or one global objective function. In socioeconomic networks, however, network formation is often driven by individual, locally optimal decisions. How such decisions impact connectivity is only poorly understood to date. Here, we study how large-scale connectivity emerges from decisions made by rational agents that individually minimize costs for satisfying their demand. We establish that the solution of the resulting nonlinear optimization model is exactly given by the final state of a local percolation process. This allows us to systematically analyze how locally optimal decisions on the microlevel define the structure of networks on the macroscopic scale.

Unfair and Anomalous Evolutionary Dynamics from Fluctuating Payoffs.

Evolution occurs in populations of reproducing individuals. Reproduction depends on the payoff a strategy receives. The payoff depends on the environment that may change over time, on intrinsic uncertainties, and on other sources of randomness. These temporal variations in the payoffs can affect which traits evolve. Understanding evolutionary game dynamics that are affected by varying payoffs remains difficult. Here we study the impact of arbitrary amplitudes and covariances of temporally varying payoffs on the dynamics. The evolutionary dynamics may be "unfair," meaning that, on average, two coexisting strategies may persistently receive different payoffs. This mechanism can induce an anomalous coexistence of cooperators and defectors in the prisoner's dilemma, and an unexpected selection reversal in the hawk-dove game.

Controlling percolation with limited resources.

Connectivity, or the lack thereof, is crucial for the function of many man-made systems, from financial and economic networks over epidemic spreading in social networks to technical infrastructure. Often, connections are deliberately established or removed to induce, maintain, or destroy global connectivity. Thus, there has been a great interest in understanding how to control percolation, the transition to large-scale connectivity. Previous work, however, studied control strategies assuming unlimited resources. Here, we depart from this unrealistic assumption and consider the effect of limited resources on the effectiveness of control. We show that, even for scarce resources, percolation can be controlled with an efficient intervention strategy. We derive such an efficient strategy and study its implications, revealing a discontinuous transition as an unintended side effect of optimal control.

Interaction Control to Synchronize Non-synchronizable Networks.

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.

Gender Gap in the ERASMUS Mobility Program.

Studying abroad has become very popular among students. The ERASMUS mobility program is one of the largest international student exchange programs in the world, which has supported already more than three million participants since 1987. We analyzed the mobility pattern within this program in 2011-12 and found a gender gap across countries and subject areas. Namely, for almost all participating countries, female students are over-represented in the ERASMUS program when compared to the entire population of tertiary students. The same tendency is observed across different subject areas. We also found a gender asymmetry in the geographical distribution of hosting institutions, with a bias of male students in Scandinavian countries. However, a detailed analysis reveals that this latter asymmetry is rather driven by subject and consistent with the distribution of gender ratios among subject areas.

Paradoxical effects of coupling infectious livestock populations and imposing transport restrictions.

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.

How do online social networks grow?

Online social networks such as Facebook, Twitter and Gowalla allow people to communicate and interact across borders. In past years online social networks have become increasingly important for studying the behavior of individuals, group formation, and the emergence of online societies. Here we focus on the characterization of the average growth of online social networks and try to understand which are possible processes behind seemingly long-range temporal correlated collective behavior. In agreement with recent findings, but in contrast to Gibrat's law of proportionate growth, we find scaling in the average growth rate and its standard deviation. In contrast, Renren and Twitter deviate, however, in certain important aspects significantly from those found in many social and economic systems. Whereas independent methods suggest no significance for temporally long-range correlated behavior for Renren and Twitter, a scaling analysis of the standard deviation does suggest long-range temporal correlated growth in Gowalla. However, we demonstrate that seemingly long-range temporal correlations in the growth of online social networks, such as in Gowalla, can be explained by a decomposition into temporally and spatially independent growth processes with a large variety of entry rates. Our analysis thus suggests that temporally or spatially correlated behavior does not play a major role in the growth of online social networks.

Possible origin of stagnation and variability of earth's biodiversity.

The magnitude and variability of Earth's biodiversity have puzzled scientists ever since paleontologic fossil databases became available. We identify and study a model of interdependent species where both endogenous and exogenous impacts determine the nonstationary extinction dynamics. The framework provides an explanation for the qualitative difference of marine and continental biodiversity growth. In particular, the stagnation of marine biodiversity may result from a global transition from an imbalanced to a balanced state of the species dependency network. The predictions of our framework are in agreement with paleontologic databases.

Microtransition cascades to percolation.

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.

Unstable supercritical discontinuous percolation transitions.

The location and nature of the percolation transition in random networks is a subject of intense interest. Recently, a series of graph evolution processes have been introduced that lead to discontinuous percolation transitions where the addition of a single edge causes the size of the largest component to exhibit a significant macroscopic jump in the thermodynamic limit. These processes can have additional exotic behaviors, such as displaying a "Devil's staircase" of discrete jumps in the supercritical regime. Here we investigate whether the location of the largest jump coincides with the percolation threshold for a range of processes, such as Erdos-Rényipercolation, percolation via edge competition and via growth by overtaking. We find that the largest jump asymptotically occurs at the percolation transition for Erdos-Rényiand other processes exhibiting global continuity, including models exhibiting an "explosive" transition. However, for percolation processes exhibiting genuine discontinuities, the behavior is substantially richer. In percolation models where the order parameter exhibits a staircase, the largest discontinuity generically does not coincide with the percolation transition. For the generalized Bohman-Frieze-Wormald model, it depends on the model parameter. Distinct parameter regimes well in the supercritical regime feature unstable discontinuous transitions-a novel and unexpected phenomenon in percolation. We thus demonstrate that seemingly and genuinely discontinuous percolation transitions can involve a rich behavior in supercriticality, a regime that has been largely ignored in percolation.

Crackling noise in fractional percolation.

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.

Phase transitions in supercritical explosive percolation.

Percolation describes the sudden emergence of large-scale connectivity as edges are added to a lattice or random network. In the Bohman-Frieze-Wormald model (BFW) of percolation, edges sampled from a random graph are considered individually and either added to the graph or rejected provided that the fraction of accepted edges is never smaller than a decreasing function with asymptotic value of α, a constant. The BFW process has been studied as a model system for investigating the underlying mechanisms leading to discontinuous phase transitions in percolation. Here we focus on the regime αε[0.6,0.95] where it is known that only one giant component, denoted C(1) , initially appears at the discontinuous phase transition. We show that at some point in the supercritical regime C(1) stops growing and eventually a second giant component, denoted C(2), emerges in a continuous percolation transition. The delay between the emergence of C(1) and C(2) and their asymptotic sizes both depend on the value of α and we establish by several techniques that there exists a bifurcation point α(c)=0.763±0.002. For αε[0.6,α(c)), C(1) stops growing the instant it emerges and the delay between the emergence of C(1) and C(2) decreases with increasing α. For αε(α(c),0.95], in contrast, C(1) continues growing into the supercritical regime and the delay between the emergence of C(1) and C(2) increases with increasing α. As we show, α(c) marks the minimal delay possible between the emergence of C(1) and C(2) (i.e., the smallest edge density for which C(2) can exist). We also establish many features of the continuous percolation of C(2) including scaling exponents and relations.

The nature and perception of fluctuations in human musical rhythms.

Although human musical performances represent one of the most valuable achievements of mankind, the best musicians perform imperfectly. Musical rhythms are not entirely accurate and thus inevitably deviate from the ideal beat pattern. Nevertheless, computer generated perfect beat patterns are frequently devalued by listeners due to a perceived lack of human touch. Professional audio editing software therefore offers a humanizing feature which artificially generates rhythmic fluctuations. However, the built-in humanizing units are essentially random number generators producing only simple uncorrelated fluctuations. Here, for the first time, we establish long-range fluctuations as an inevitable natural companion of both simple and complex human rhythmic performances. Moreover, we demonstrate that listeners strongly prefer long-range correlated fluctuations in musical rhythms. Thus, the favorable fluctuation type for humanizing interbeat intervals coincides with the one generically inherent in human musical performances.

Impact of microscopic motility on the swimming behavior of parasites: straighter trypanosomes are more directional.

Microorganisms, particularly parasites, have developed sophisticated swimming mechanisms to cope with a varied range of environments. African Trypanosomes, causative agents of fatal illness in humans and animals, use an insect vector (the Tsetse fly) to infect mammals, involving many developmental changes in which cell motility is of prime importance. Our studies reveal that differences in cell body shape are correlated with a diverse range of cell behaviors contributing to the directional motion of the cell. Straighter cells swim more directionally while cells that exhibit little net displacement appear to be more bent. Initiation of cell division, beginning with the emergence of a second flagellum at the base, correlates to directional persistence. Cell trajectory and rapid body fluctuation correlation analysis uncovers two characteristic relaxation times: a short relaxation time due to strong body distortions in the range of 20 to 80 ms and a longer time associated with the persistence in average swimming direction in the order of 15 seconds. Different motility modes, possibly resulting from varying body stiffness, could be of consequence for host invasion during distinct infective stages.

Clinical impact of antimicrobial resistance in European hospitals: excess mortality and length of hospital stay related to methicillin-resistant Staphylococcus aureus bloodstream infections.

Antimicrobial resistance is threatening the successful management of nosocomial infections worldwide. Despite the therapeutic limitations imposed by methicillin-resistant Staphylococcus aureus (MRSA), its clinical impact is still debated. The objective of this study was to estimate the excess mortality and length of hospital stay (LOS) associated with MRSA bloodstream infections (BSI) in European hospitals. Between July 2007 and June 2008, a multicenter, prospective, parallel matched-cohort study was carried out in 13 tertiary care hospitals in as many European countries. Cohort I consisted of patients with MRSA BSI and cohort II of patients with methicillin-susceptible S. aureus (MSSA) BSI. The patients in both cohorts were matched for LOS prior to the onset of BSI with patients free of the respective BSI. Cohort I consisted of 248 MRSA patients and 453 controls and cohort II of 618 MSSA patients and 1,170 controls. Compared to the controls, MRSA patients had higher 30-day mortality (adjusted odds ratio [aOR] = 4.4) and higher hospital mortality (adjusted hazard ratio [aHR] = 3.5). Their excess LOS was 9.2 days. MSSA patients also had higher 30-day (aOR = 2.4) and hospital (aHR = 3.1) mortality and an excess LOS of 8.6 days. When the outcomes from the two cohorts were compared, an effect attributable to methicillin resistance was found for 30-day mortality (OR = 1.8; P = 0.04), but not for hospital mortality (HR = 1.1; P = 0.63) or LOS (difference = 0.6 days; P = 0.96). Irrespective of methicillin susceptibility, S. aureus BSI has a significant impact on morbidity and mortality. In addition, MRSA BSI leads to a fatal outcome more frequently than MSSA BSI. Infection control efforts in hospitals should aim to contain infections caused by both resistant and susceptible S. aureus.