Optimized Gillespie algorithms for the simulation of Markovian epidemic processes on large and heterogeneous networks

Numerical simulation of continuous-time Markovian processes is an essential and widely applied tool in the investigation of epidemic spreading on complex networks. Due to the high heterogeneity of the connectivity structure through which epidemics is transmitted, efficient and accurate implementations of generic epidemic processes are not trivial and deviations from statistically exact prescriptions can lead to uncontrolled biases. Based on the Gillespie algorithm (GA), in which only steps that change the state are considered, we develop numerical recipes and describe their computer implementations for statistically exact and computationally efficient simulations of generic Markovian epidemic processes aiming at highly heterogeneous and large networks. The central point of the recipes investigated here is to include phantom processes, that do not change the states but do count for time increments. We compare the efficiencies for the susceptible-infected-susceptible, contact process and susceptible-infected-recovered models, that are particular cases of a generic model considered here. We numerically confirm that the simulation outcomes of the optimized algorithms are statistically indistinguishable from the original GA and can be several orders of magnitude more efficient.Comment: 12 pages, 9 figure

Griffiths effects of the susceptible-infected-susceptible epidemic model on random power-law networks

We provide numerical evidence for slow dynamics of the susceptible-infected-susceptible model evolving on finite-size random networks with power-law degree distributions. Extensive simulations were done by averaging the activity density over many realizations of networks. We investigated the effects of outliers in both highly fluctuating (natural cutoff) and non-fluctuating (hard cutoff) most connected vertices. Logarithmic and power-law decays in time were found for natural and hard cutoffs, respectively. This happens in extended regions of the control parameter space $\lambda_1<\lambda<\lambda_2$, suggesting Griffiths effects, induced by the topological inhomogeneities. Optimal fluctuation theory considering sample-to-sample fluctuations of the pseudo thresholds is presented to explain the observed slow dynamics. A quasistationary analysis shows that response functions remain bounded at $\lambda_2$. We argue these to be signals of a smeared transition. However, in the thermodynamic limit the Griffiths effects loose their relevancy and have a conventional critical point at $\lambda_c=0$. Since many real networks are composed by heterogeneous and weakly connected modules, the slow dynamics found in our analysis of independent and finite networks can play an important role for the deeper understanding of such systems.Comment: 10 pages, 8 figure

Griffiths phases in infinite-dimensional, non-hierarchical modular networks

Griffiths phases (GPs), generated by the heterogeneities on modular networks, have recently been suggested to provide a mechanism, rid of fine parameter tuning, to explain the critical behavior of complex systems. One conjectured requirement for systems with modular structures was that the network of modules must be hierarchically organized and possess finite dimension. We investigate the dynamical behavior of an activity spreading model, evolving on heterogeneous random networks with highly modular structure and organized non-hierarchically. We observe that loosely coupled modules act as effective rare-regions, slowing down the extinction of activation. As a consequence, we find extended control parameter regions with continuously changing dynamical exponents for single network realizations, preserved after finite size analyses, as in a real GP. The avalanche size distributions of spreading events exhibit robust power-law tails. Our findings relax the requirement of hierarchical organization of the modular structure, which can help to rationalize the criticality of modular systems in the framework of GPs.Comment: 14 pages, 8 figure

A geochemical study of the Riddle Peaks gabbro, North Cascades: evidence for amphibole accumulation in the mid-crust of an arc

Mid-crustal arc rocks are not commonly exposed, hampering our understanding of magma differentiation processes and mineral crystallization in the mid-crust of arc systems. This thesis presents results of the study of one exposed mid-crustal arc pluton, which is a unique laboratory to understand the geochemical effects of crystallization in this type of system. I report on the major and trace element characteristics of amphibole, plagioclase, and apatite in hornblendite and hornblende gabbro cumulates from the ~44 km2 Riddle Peaks pluton (~77 Ma) in the North Cascades Crystalline Core (NCCC), Washington. Electron microprobe and laser ablation-induced mass spectrometry (LA-ICP-MS), coupled with whole rock major and trace element data, show that the Riddle Peaks contains low Mg# cumulates with 40.7-47.2 wt.% SiO2; Mg# 33-67, where Mg# is defined as 100*[(Mg/(Mg+Fe2+)]. The two rock types present in the pluton are a rhythmically layered gabbro, consisting of hornblendite and hornblende gabbro layered with anorthite to plagioclase-rich gabbro, and a massive hornblende gabbro. The layered gabbro has higher Mg# amphibole (60-70, with the majority 66-70) than massive gabbro (60-63) and more anorthitic plagioclase (layered gabbro = An81-85; massive gabbro = An71-77), suggesting that it was formed by a more primitive liquid. This is supported by modeling that shows that equilibrium liquids from the massive gabbros could have been produced by 40% crystallization of a hornblende gabbro lithology from the parent, calculated liquids in equilibrium with the layered gabbros. Equilibrium liquid calculations also allow for calculation of new apatite partition coefficients for 16 trace elements and REE in a mid-crustal, basaltic andesite system. This study finds that cumulate amphiboles crystallized from a basaltic andesite parent are responsible for increasing La/Yb ratios in derivative melts, such as arc magmas, continental crust and NCCC magmas (NCCC magmas approximated by liquid compositions from the Cardinal Peak and Tenpeak plutons). Amphibole crystallization decreases Dy/Yb in derivative melts; these results are in accordance with predictions from observed arc magmas. Other observed ratios in arc and crustal magmas, such as high Sr/Y (16-20), low Nb/Ta (10-17) and Ti/Zr (30) relative to primitive mantle/chondritic values (Sr/Y = 4.6; Nb/Ta = 18-20; Ti/Zr = 115) are not explained by amphibole crystallization. It has been suggested that amphibole-rich plutons could fractionate certain incompatible trace element pairs to explain the differing ratios in arc magmas and continental crust versus primitive mantle values. With the exception of REE, the Riddle Peaks pluton does not fractionate these ratios sufficiently to explain the differing ratios. If mineral fractionation is occurring, another mineral partitions these elements; or, another process occurs

Quantifying echo chamber effects in information spreading over political communication networks

Echo chambers in online social networks, in which users prefer to interact only with ideologically-aligned peers, are believed to facilitate misinformation spreading and contribute to radicalize political discourse. In this paper, we gauge the effects of echo chambers in information spreading phenomena over political communication networks. Mining 12 million Twitter messages, we reconstruct a network in which users interchange opinions related to the impeachment of the former Brazilian President Dilma Rousseff. We define a continuous {political position} parameter, independent of the network's structure, that allows to quantify the presence of echo chambers in the strongly connected component of the network, reflected in two well-separated communities of similar sizes with opposite views of the impeachment process. By means of simple spreading models, we show that the capability of users in propagating the content they produce, measured by the associated spreadability, strongly depends on their attitude. Users expressing pro-impeachment sentiments are capable to transmit information, on average, to a larger audience than users expressing anti-impeachment sentiments. Furthermore, the users' spreadability is correlated to the diversity, in terms of political position, of the audience reached. Our method can be exploited to identify the presence of echo chambers and their effects across different contexts and shed light upon the mechanisms allowing to break echo chambers.Comment: 9 pages, 4 figures. Supplementary Information available as ancillary fil

Fibronectin Contributes To Notochord Intercalation In The Invertebrate Chordate, Ciona Intestinalis

Background: Genomic analysis has upended chordate phylogeny, placing the tunicates as the sister group to the vertebrates. This taxonomic rearrangement raises questions about the emergence of a tunicate/vertebrate ancestor. Results: Characterization of developmental genes uniquely shared by tunicates and vertebrates is one promising approach for deciphering developmental shifts underlying acquisition of novel, ancestral traits. The matrix glycoprotein Fibronectin (FN) has long been considered a vertebrate-specific gene, playing a major instructive role in vertebrate embryonic development. However, the recent computational prediction of an orthologous “vertebrate-like” Fn gene in the genome of a tunicate, Ciona savignyi, challenges this viewpoint suggesting that Fn may have arisen in the shared tunicate/vertebrate ancestor. Here we verify the presence of a tunicate Fn ortholog. Transgenic reporter analysis was used to characterize a Ciona Fn enhancer driving expression in the notochord. Targeted knockdown in the notochord lineage indicates that FN is required for proper convergent extension. Conclusions: These findings suggest that acquisition of Fn was associated with altered notochord morphogenesis in the vertebrate/tunicate ancestor

Matrix Adhesion Polarizes Heart Progenitor Induction In The Invertebrate Chordate Ciona Intestinalis

Cell-matrix adhesion strongly influences developmental signaling. Resulting impacts on cell migration and tissue morphogenesis are well characterized. However, the in vivo impact of adhesion on fate induction remains ambiguous. Here, we employ the invertebrate chordate Ciona intestinalis to delineate an essential in vivo role for matrix adhesion in heart progenitor induction. In Ciona pre-cardiac founder cells, invasion of the underlying epidermis promotes localized induction of the heart progenitor lineage. We found that these epidermal invasions are associated with matrix adhesion along the pre-cardiac cell/epidermal boundary. Through targeted manipulations of RAP GTPase activity, we were able to manipulate pre-cardiac cell-matrix adhesion. Targeted disruption of pre-cardiac cell-matrix adhesion blocked heart progenitor induction. Conversely, increased matrix adhesion generated expanded induction. We were also able to selectively restore cell-matrix adhesion and heart progenitor induction through targeted expression of Ci-Integrin β2. These results indicate that matrix adhesion functions as a necessary and sufficient extrinsic cue for regional heart progenitor induction. Furthermore, time-lapse imaging suggests that cytokinesis acts as an intrinsic temporal regulator of heart progenitor adhesion and induction. Our findings highlight a potentially conserved role for matrix adhesion in early steps of vertebrate heart progenitor specification

Isotropization of Bianchi type models and a new FRW solution in Brans-Dicke theory

Using scaled variables we are able to integrate an equation valid for isotropic and anisotropic Bianchi type I, V, IX models in Brans-Dicke (BD) theory. We analyze known and new solutions for these models in relation with the possibility that anisotropic models asymptotically isotropize, and/or possess inflationary properties. In particular, a new solution of curve ($k\neq0$) Friedmann-Robertson-Walker (FRW) cosmologies in Brans-Dicke theory is analyzed.Comment: 15 pages, 4 postscript figures, to appear in Gen. Rel. Grav., special issue dedicated in honour of Prof. H. Dehne

Griffiths phases in infinite-dimensional, non-hierarchical modular networks

Griffiths phases (GPs), generated by the heterogeneities on modular networks, have recently been suggested to provide a mechanism, rid of fine parameter tuning, to explain the critical behavior of complex systems. One conjectured requirement for systems with modular structures was that the network of modules must be hierarchically organized and possess finite dimension. We investigate the dynamical behavior of an activity spreading model, evolving on heterogeneous random networks with highly modular structure and organized non-hierarchically. We observe that loosely coupled modules act as effective rare-regions, slowing down the extinction of activation. As a consequence, we find extended control parameter regions with continuously changing dynamical exponents for single network realizations, preserved after finite size analyses, as in a real GP. The avalanche size distributions of spreading events exhibit robust power-law tails. Our findings relax the requirement of hierarchical organization of the modular structure, which can help to rationalize the criticality of modular systems in the framework of GPs