Predicting criticality and dynamic range in complex networks: effects of topology

The collective dynamics of a network of coupled excitable systems in response to an external stimulus depends on the topology of the connections in the network. Here we develop a general theoretical approach to study the effects of network topology on dynamic range, which quantifies the range of stimulus intensities resulting in distinguishable network responses. We find that the largest eigenvalue of the weighted network adjacency matrix governs the network dynamic range. Specifically, a largest eigenvalue equal to one corresponds to a critical regime with maximum dynamic range. We gain deeper insight on the effects of network topology using a nonlinear analysis in terms of additional spectral properties of the adjacency matrix. We find that homogeneous networks can reach a higher dynamic range than those with heterogeneous topology. Our analysis, confirmed by numerical simulations, generalizes previous studies in terms of the largest eigenvalue of the adjacency matrix.Comment: 4 pages, 3 figure

Statistical Properties of Avalanches in Networks

We characterize the distributions of size and duration of avalanches propagating in complex networks. By an avalanche we mean the sequence of events initiated by the externally stimulated `excitation' of a network node, which may, with some probability, then stimulate subsequent firings of the nodes to which it is connected, resulting in a cascade of firings. This type of process is relevant to a wide variety of situations, including neuroscience, cascading failures on electrical power grids, and epidemology. We find that the statistics of avalanches can be characterized in terms of the largest eigenvalue and corresponding eigenvector of an appropriate adjacency matrix which encodes the structure of the network. By using mean-field analyses, previous studies of avalanches in networks have not considered the effect of network structure on the distribution of size and duration of avalanches. Our results apply to individual networks (rather than network ensembles) and provide expressions for the distributions of size and duration of avalanches starting at particular nodes in the network. These findings might find application in the analysis of branching processes in networks, such as cascading power grid failures and critical brain dynamics. In particular, our results show that some experimental signatures of critical brain dynamics (i.e., power-law distributions of size and duration of neuronal avalanches), are robust to complex underlying network topologies.Comment: 11 pages, 7 figure

Reductions in commuting mobility correlate with geographic differences in SARS-CoV-2 prevalence in New York City.

SARS-CoV-2-related mortality and hospitalizations differ substantially between New York City neighborhoods. Mitigation efforts require knowing the extent to which these disparities reflect differences in prevalence and understanding the associated drivers. Here, we report the prevalence of SARS-CoV-2 in New York City boroughs inferred using tests administered to 1,746 pregnant women hospitalized for delivery between March 22nd and May 3rd, 2020. We also assess the relationship between prevalence and commuting-style movements into and out of each borough. Prevalence ranged from 11.3% (95% credible interval [8.9%, 13.9%]) in Manhattan to 26.0% (15.3%, 38.9%) in South Queens, with an estimated city-wide prevalence of 15.6% (13.9%, 17.4%). Prevalence was lowest in boroughs with the greatest reductions in morning movements out of and evening movements into the borough (Pearson R = -0.88 [-0.52, -0.99]). Widespread testing is needed to further specify disparities in prevalence and assess the risk of future outbreaks

Failure of adaptive self-organized criticality during epileptic seizure attacks

Critical dynamics are assumed to be an attractive mode for normal brain functioning as information processing and computational capabilities are found to be optimized there. Recent experimental observations of neuronal activity patterns following power-law distributions, a hallmark of systems at a critical state, have led to the hypothesis that human brain dynamics could be poised at a phase transition between ordered and disordered activity. A so far unresolved question concerns the medical significance of critical brain activity and how it relates to pathological conditions. Using data from invasive electroencephalogram recordings from humans we show that during epileptic seizure attacks neuronal activity patterns deviate from the normally observed power-law distribution characterizing critical dynamics. The comparison of these observations to results from a computational model exhibiting self-organized criticality (SOC) based on adaptive networks allows further insights into the underlying dynamics. Together these results suggest that brain dynamics deviates from criticality during seizures caused by the failure of adaptive SOC.Comment: 7 pages, 5 figure

Critical synchronization dynamics of the Kuramoto model on connectome and small world graphs

The hypothesis, that cortical dynamics operates near criticality also suggests, that it exhibits universal critical exponents which marks the Kuramoto equation, a fundamental model for synchronization, as a prime candidate for an underlying universal model. Here, we determined the synchronization behavior of this model by solving it numerically on a large, weighted human connectome network, containing 804092 nodes, in an assumed homeostatic state. Since this graph has a topological dimension $d < 4$, a real synchronization phase transition is not possible in the thermodynamic limit, still we could locate a transition between partially synchronized and desynchronized states. At this crossover point we observe power-law--tailed synchronization durations, with $\tau_t \simeq 1.2(1)$, away from experimental values for the brain. For comparison, on a large two-dimensional lattice, having additional random, long-range links, we obtain a mean-field value: $\tau_t \simeq 1.6(1)$. However, below the transition of the connectome we found global coupling control-parameter dependent exponents $1 < \tau_t \le 2$, overlapping with the range of human brain experiments. We also studied the effects of random flipping of a small portion of link weights, mimicking a network with inhibitory interactions, and found similar results. The control-parameter dependent exponent suggests extended dynamical criticality below the transition point.Comment: 12 pages, 9 figures + Supplemenraty material pdf 2 pages 4 figs, 1 table, accepted version in Scientific Report

Feasibility of large-scale population testing for SARS-CoV-2 detection by self-testing at home

The simplicity and low cost of rapid point-of-care tests greatly facilitate large-scale population testing, which can contribute to controlling the spread of the COVID-19 virus. We evaluated the applicability of a self-testing strategy for SARS-CoV2 in a population-based, cross-sectional study in Cantabria, Spain, between April and May 2020. For the self-testing strategy, participants received the necessary material for the self-collection of blood and performance of a rapid antibody test using lateral flow immunoassay at home without the supervision of healthcare personnel. A total of 1,022 participants were enrolled. Most participants correctly performed the COVID-19 self-test the first time (91.3% [95% CI 89.4-92.9]). Only a minority of the participants (0.7%) needed the help of healthcare personnel, while 6.9% required a second kit delivery, for a total valid test result in 96.9% of the participants. Incorrect use of the self-test was not associated with the educational level, age over 65, or housing area. Prevalence of IgG antibodies against SARS-CoV2 for subjects with a valid rapid test result was 3.1% (95% CI 2.2-4.4), similar to the seroprevalence result obtained using a conventional approach carried out by healthcare professionals. In conclusion, COVID-19 self-testing should be considered as a screening tool.Acknowledgements: We would like to acknowledge the participation of all the individuals in this study. JVL acknowledges support to ISGlobal from the Spanish Ministry of Science, Innovation and Universities through the “Centro de Excelencia Severo Ochoa 2019-2023” Programme (CEX2018-000806-S), and from the Government of Catalonia through the CERCA Programme

A unified data representation theory for network visualization, ordering and coarse-graining

Representation of large data sets became a key question of many scientific disciplines in the last decade. Several approaches for network visualization, data ordering and coarse-graining accomplished this goal. However, there was no underlying theoretical framework linking these problems. Here we show an elegant, information theoretic data representation approach as a unified solution of network visualization, data ordering and coarse-graining. The optimal representation is the hardest to distinguish from the original data matrix, measured by the relative entropy. The representation of network nodes as probability distributions provides an efficient visualization method and, in one dimension, an ordering of network nodes and edges. Coarse-grained representations of the input network enable both efficient data compression and hierarchical visualization to achieve high quality representations of larger data sets. Our unified data representation theory will help the analysis of extensive data sets, by revealing the large-scale structure of complex networks in a comprehensible form.Comment: 13 pages, 5 figure

Ape parasite origins of human malaria virulence genes

Antigens encoded by the var gene family are major virulence factors of the human malaria parasite Plasmodium falciparum, exhibiting enormous intra- and interstrain diversity. Here we use network analysis to show that var architecture and mosaicism are conserved at multiple levels across the Laverania subgenus, based on var-like sequences from eight single-species and three multi-species Plasmodium infections of wild-living or sanctuary African apes. Using select whole-genome amplification, we also find evidence of multi-domain var structure and synteny in Plasmodium gaboni, one of the ape Laverania species most distantly related to P. falciparum, as well as a new class of Duffy-binding-like domains. These findings indicate that the modular genetic architecture and sequence diversity underlying var-mediated host-parasite interactions evolved before the radiation of the Laverania subgenus, long before the emergence of P. falciparum

Genomes of cryptic chimpanzee Plasmodium species reveal key evolutionary events leading to human malaria

African apes harbour at least six Plasmodium species of the subgenus Laverania, one of which gave rise to human Plasmodium falciparum. Here we use a selective amplification strategy to sequence the genome of chimpanzee parasites classified as Plasmodium reichenowi and Plasmodium gaboni based on the subgenomic fragments. Genome-wide analyses show that these parasites indeed represent distinct species, with no evidence of cross-species mating. Both P. reichenowi and P. gaboni are 10-fold more diverse than P. falciparum, indicating a very recent origin of the human parasite. We also find a remarkable Laverania-specific expansion of a multigene family involved in erythrocyte remodelling, and show that a short region on chromosome 4, which encodes two essential invasion genes, was horizontally transferred into a recent P. falciparum ancestor. Our results validate the selective amplification strategy for characterizing cryptic pathogen species, and reveal evolutionary events that likely predisposed the precursor of P. falciparum to colonize humans