Contact ability based topology control for predictable delay-tolerant networks

In predictable delay tolerant networks (PDTNs), the network topology is known a priori or can be predicted over time, such as space planet networks and vehicular networks based on public buses or trains. Due to the intermittent connectivity, network partitioning, and long delays in PDTNs, most of the researchers mainly focuses on routing and data access research. However, topology control can improve energy effectiveness and increase the communication capacity, thus how to maintain the dynamic topology of PDTNs becomes crucial. In this paper, a contact ability based topology control method for PDTNs is proposed. First, the contact ability is calculated using our contact ability calculation model, and then the PDTNs is modeled as an undirected weighted contact graph which includes spatial and contact ability information. The topology control problem is defined as constructing a minimum spanning tree (MST) that the contact ability of the MST is maximized. We propose two algorithms based on undirected weighted contact graph to solve the defined problem, and compare them with the latest method in terms of energy cost and contact ability. Extensive simulation experiments demonstrate that the proposed algorithms can guarantee data transmission effectively, and reduce the network energy consumption significantly.

Pandemic spread in communities via random graphs

Working in the multi-type Galton–Watson branching-process framework we analyse the spread of a pandemic via a general multi-type random contact graph. Our model consists of several communities, and takes, as input, parameters that outline the contacts between individuals in distinct communities. Given these parameters, we determine whether there will be an outbreak and if yes, we calculate the size of the giant-connected-component of the graph, thereby, determining the fraction of the population of each type that would be infected before it ends. We show that the pandemic spread has a natural evolution direction given by the Perron–Frobenius eigenvector of a matrix whose entries encode the average number of individuals of one type expected to be infected by an individual of another type. The corresponding eigenvalue is the basic reproduction number of the pandemic. We perform numerical simulations that compare homogeneous and heterogeneous spread graphs and quantify the difference between them. We elaborate on the difference between herd immunity and the end of the pandemic and the effect of countermeasures on the fraction of infected population.

Temporal Contact Graph Reveals The Evolving Epidemic Situation of COVID-19

Digital contact tracing has been recently advocated by China and many countries as part of digital prevention measures on COVID-19. Controversies have been raised about their effectiveness in practice as it remains open how they can be fully utilized to control COVID-19. In this article, we show that an abundance of information can be extracted from digital contact tracing for COVID-19 prevention and control. Specifically, we construct a temporal contact graph that quantifies the daily contacts between infectious and susceptible individuals by exploiting a large volume of location-related data contributed by 10,527,737 smartphone users in Wuhan, China. The temporal contact graph reveals five time-varying indicators can accurately capture actual contact trends at population level, demonstrating that travel restrictions (e.g., city lockdown) in Wuhan played an important role in containing COVID-19. We reveal a strong correlation between the contacts level and the epidemic size, and estimate several significant epidemiological parameters (e.g., serial interval). We also show that user participation rate exerts higher influence on situation evaluation than user upload rate does. At individual level, however, the temporal contact graph plays a limited role, since the behavior distinction between the infected and uninfected contacted individuals are not substantial. The revealed results can tell the effectiveness of digital contact tracing against COVID-19, providing guidelines for governments to implement interventions using information technology.

Epidemics on hypergraphs: spectral thresholds for extinction

Epidemic spreading is well understood when a disease propagates around a contact graph. In a stochastic susceptible–infected–susceptible setting, spectral conditions characterize whether the disease vanishes. However, modelling human interactions using a graph is a simplification which only considers pairwise relationships. This does not fully represent the more realistic case where people meet in groups. Hyperedges can be used to record higher order interactions, yielding more faithful and flexible models and allowing for the rate of infection of a node to depend on group size and also to vary as a nonlinear function of the number of infectious neighbours. We discuss different types of contagion models in this hypergraph setting and derive spectral conditions that characterize whether the disease vanishes. We study both the exact individual-level stochastic model and a deterministic mean field ODE approximation. Numerical simulations are provided to illustrate the analysis. We also interpret our results and show how the hypergraph model allows us to distinguish between contributions to infectiousness that (i) are inherent in the nature of the pathogen and (ii) arise from behavioural choices (such as social distancing, increased hygiene and use of masks). This raises the possibility of more accurately quantifying the effect of interventions that are designed to contain the spread of a virus.

Contact Ability Based Topology Control for Predictable Delay-tolerant Networks

In predictable delay tolerant networks (PDTNs), the network topology is known a priori or can be predicted over time such as space planet networks and vehicular networks based on public buses or trains. Due to the intermittent connectivity, network partitioning, and long delays in PDTNs, most of the researchers mainly focuses on routing and data access research. However, topology control can improve energy effectiveness and increase the communication capacity, thus how to maintain the dynamic topology of PDTNs becomes crucial. In this paper, a contact ability based topology control method for PDTNs is proposed. First, the contact ability is calculated using our contact ability calculation model, and then the PDTNs is modeled as an undirected weighted contact graph which includes spatial and contact ability information. The topology control problem is defined as constructing a Minimum Spanning Tree(MST) that the contact ability of the MST is maximized. We propose two algorithms based on undirected weighted contact graph to solve the defined problem, and compare them with the latest method in terms of energy cost and contact ability. Extensive simulation experiments demonstrate that the proposed algorithms can guarantee data transmission effectively, and reduce the network energy consumption significantly.

Automorphisms of Contact Graphs of CAT(0) Cube Complexes

We show that, under weak assumptions, the automorphism group of a $\textrm{CAT(0)}$ cube complex $X$ coincides with the automorphism group of Hagen’s contact graph $\mathcal{C}(X)$. The result holds, in particular, for universal covers of Salvetti complexes, where it provides an analogue of Ivanov’s theorem on curve graphs of non-sporadic surfaces. This highlights a contrast between contact graphs and Kim–Koberda extension graphs, which have much larger automorphism group. We also study contact graphs associated with Davis complexes of right-angled Coxeter groups. We show that these contact graphs are less well behaved and describe exactly when they have more automorphisms than the universal cover of the Davis complex.