Beyond clustering: mean-field dynamics on networks with arbitrary subgraph composition

Clustering is the propensity of nodes that share a common neighbour to be connected. It is ubiquitous in many networks but poses many modelling challenges. Clustering typically manifests itself by a higher than expected frequency of triangles, and this has led to the principle of constructing networks from such building blocks. This approach has been generalised to networks being constructed from a set of more exotic subgraphs. As long as these are fully connected, it is then possible to derive mean-field models that approximate epidemic dynamics well. However, there are virtually no results for non-fully connected subgraphs. In this paper, we provide a general and automated approach to deriving a set of ordinary differential equations, or mean-field model, that describes, to a high degree of accuracy, the expected values of system-level quantities, such as the prevalence of infection. Our approach offers a previously unattainable degree of control over the arrangement of subgraphs and network characteristics such as classical node degree, variance and clustering. The combination of these features makes it possible to generate families of networks with different subgraph compositions while keeping classical network metrics constant. Using our approach, we show that higher-order structure realised either through the introduction of loops of different sizes or by generating networks based on different subgraphs but with identical degree distribution and clustering, leads to non-negligible differences in epidemic dynamics

18S rRNA processing requires base pairings of snR30 H/ACA snoRNA to eukaryote-specific 18S sequences

The H/ACA RNAs represent an abundant, evolutionarily conserved and functionally diverse class of non-coding RNAs. Many H/ACA RNAs direct pseudouridylation of rRNAs and snRNAs, while members of the rapidly growing group of ‘orphan' H/ACA RNAs participate in pre-rRNA processing, telomere synthesis and probably, in other nuclear processes. The yeast snR30 ‘orphan' H/ACA snoRNA has long been known to function in the nucleolytic processing of 18S rRNA, but its molecular role remained unknown. Here, we provide biochemical and genetic evidence demonstrating that during pre-rRNA processing, two evolutionarily conserved sequence elements in the 3′-hairpin of snR30 base-pair with short pre-rRNA sequences located in the eukaryote-specific internal region of 18S rRNA. The newly discovered snR30-18S base-pairing interactions are essential for 18S rRNA production and they constitute a complex snoRNA target RNA transient structure that is novel to H/ACA RNAs. We also demonstrate that besides the 18S recognition motifs, the distal part of the 3′-hairpin of snR30 contains an additional snoRNA element that is essential for 18S rRNA processing and that functions most likely as a snoRNP protein-binding site

Salience-based selection: attentional capture by distractors less salient than the target

Current accounts of attentional capture predict the most salient stimulus to be invariably selected first. However, existing salience and visual search models assume noise in the map computation or selection process. Consequently, they predict the first selection to be stochastically dependent on salience, implying that attention could even be captured first by the second most salient (instead of the most salient) stimulus in the field. Yet, capture by less salient distractors has not been reported and salience-based selection accounts claim that the distractor has to be more salient in order to capture attention. We tested this prediction using an empirical and modeling approach of the visual search distractor paradigm. For the empirical part, we manipulated salience of target and distractor parametrically and measured reaction time interference when a distractor was present compared to absent. Reaction time interference was strongly correlated with distractor salience relative to the target. Moreover, even distractors less salient than the target captured attention, as measured by reaction time interference and oculomotor capture. In the modeling part, we simulated first selection in the distractor paradigm using behavioral measures of salience and considering the time course of selection including noise. We were able to replicate the result pattern we obtained in the empirical part. We conclude that each salience value follows a specific selection time distribution and attentional capture occurs when the selection time distributions of target and distractor overlap. Hence, selection is stochastic in nature and attentional capture occurs with a certain probability depending on relative salience

Consistent approximation of epidemic dynamics on degree-heterogeneous clustered networks

Realistic human contact networks capable of spreading infectious disease, for example studied in social contact surveys, exhibit both significant degree heterogeneity and clustering, both of which greatly affect epidemic dynamics. To understand the joint effects of these two network properties on epidemic dynamics, the effective degree model of Lindquist et al. [28] is reformulated with a new moment closure to apply to highly clustered networks. A simulation study comparing alternative ODE models and stochastic simulations is performed for SIR (Susceptible–Infected–Removed) epidemic dynamics, including a test for the conjectured error behaviour in [40], providing evidence that this novel model can be a more accurate approximation to epidemic dynamics on complex networks than existing approaches

Dynamics of multi-stage infections on networks

This paper investigates the dynamics of infectious diseases with a nonexponentially distributed infectious period. This is achieved by considering a multistage infection model on networks. Using pairwise approximation with a standard closure, a number of important characteristics of disease dynamics are derived analytically, including the final size of an epidemic and a threshold for epidemic outbreaks, and it is shown how these quantities depend on disease characteristics, as well as the number of disease stages. Stochastic simulations of dynamics on networks are performed and compared to output of pairwise models for several realistic examples of infectious diseases to illustrate the role played by the number of stages in the disease dynamics. These results show that a higher number of disease stages results in faster epidemic outbreaks with a higher peak prevalence and a larger final size of the epidemic. The agreement between the pairwise and simulation models is excellent in the cases we consider

A General Model of Dynamics on Networks with Graph Automorphism Lumping

In this paper we introduce a general Markov chain model of dynamical processes on networks. In this model, nodes in the network can adopt a finite number of states and transitions can occur that involve multiple nodes changing state at once. The rules that govern transitions only depend on measures related to the state and structure of the network and not on the particular nodes involved. We prove that symmetries of the network can be used to lump equivalent states in state-space. We illustrate how several examples of well-known dynamical processes on networks correspond to particular cases of our general model. This work connects a wide range of models specified in terms of node-based dynamical rules to their exact continuous-time Markov chain formulation

Asteroseismology

Asteroseismology is the determination of the interior structures of stars by using their oscillations as seismic waves. Simple explanations of the astrophysical background and some basic theoretical considerations needed in this rapidly evolving field are followed by introductions to the most important concepts and methods on the basis of example. Previous and potential applications of asteroseismology are reviewed and future trends are attempted to be foreseen.Comment: 38 pages, 13 figures, to appear in: "Planets, Stars and Stellar Systems", eds. T. D. Oswalt et al., Springer Verla

Exact analysis of summary statistics for continuous-time discrete-state Markov processes on networks using graph-automorphism lumping

We propose a unified framework to represent a wide range of continuous-time discrete-state Markov processes on networks, and show how many network dynamics models in the literature can be represented in this unified framework. We show how a particular sub-set of these models, referred to here as single-vertex-transition (SVT) processes, lead to the analysis of quasi-birth-and-death (QBD) processes in the theory of continuous-time Markov chains. We illustrate how to analyse a number of summary statistics for these processes, such as absorption probabilities and first-passage times. We extend the graph-automorphism lumping approach [Kiss, Miller, Simon, Mathematics of Epidemics on Networks, 2017; Simon, Taylor, Kiss, J. Math. Bio. 62(4), 2011], by providing a matrix-oriented representation of this technique, and show how it can be applied to a very wide range of dynamical processes on networks. This approach can be used not only to solve the master equation of the system, but also to analyse the summary statistics of interest. We also show the interplay between the graph-automorphism lumping approach and the QBD structures when dealing with SVT processes. Finally, we illustrate our theoretical results with examples from the areas of opinion dynamics and mathematical epidemiology

A search for new members of the β Pictoris, Tucana–Horologium and ε Cha moving groups in the RAVE data base

We report on the discovery of new members of nearby young moving groups, exploiting the full power of combining the Radial Velocity Experiment (RAVE) survey with several stellar age diagnostic methods and follow-up high-resolution optical spectroscopy. The results include the identification of one new and five likely members of the β Pictoris moving group, ranging from spectral types F9 to M4 with the majority being M dwarfs, one K7 likely member of the ε Cha group and two stars in the Tucana–Horologium association. Based on the positive identifications, we foreshadow a great potential of the RAVE data base in progressing towards a full census of young moving groups in the solar neighbourhood

Stability, Entrapment and Variant Formation of Salmonella Genomic Island 1

<div><h3>Background</h3><p>The <em>Salmonella</em> genomic island 1 (SGI1) is a 42.4 kb integrative mobilizable element containing several antibiotic resistance determinants embedded in a complex integron segment In104. The numerous SGI1 variants identified so far, differ mainly in this segment and the explanations of their emergence were mostly based on comparative structure analyses. Here we provide experimental studies on the stability, entrapment and variant formation of this peculiar gene cluster originally found in <em>S</em>. Typhimurium.</p> <h3>Methodology/Principal Findings</h3><p>Segregation and conjugation tests and various molecular techniques were used to detect the emerging SGI1 variants in <em>Salmonella</em> populations of 17 <em>Salmonella enterica</em> serovar Typhimurium DT104 isolates from Hungary. The SGI1s in these isolates proved to be fully competent in excision, conjugal transfer by the IncA/C helper plasmid R55, and integration into the <em>E. coli</em> chromosome. A trap vector has been constructed and successfully applied to capture the island on a plasmid. Monitoring of segregation of SGI1 indicated high stability of the island. SGI1-free segregants did not accumulate during long-term propagation, but several SGI1 variants could be obtained. Most of them appeared to be identical to SGI1-B and SGI1-C, but two new variants caused by deletions via a short-homology-dependent recombination process have also been detected. We have also noticed that the presence of the conjugation helper plasmid increased the formation of these deletion variants considerably.</p> <h3>Conclusions/Significance</h3><p>Despite that excision of SGI1 from the chromosome was proven in SGI1⁺<em>Salmonella</em> populations, its complete loss could not be observed. On the other hand, we demonstrated that several variants, among them two newly identified ones, arose with detectable frequencies in these populations in a short timescale and their formation was promoted by the helper plasmid. This reflects that IncA/C helper plasmids are not only involved in the horizontal spreading of SGI1, but may also contribute to its evolution.</p> </div