Bicomponents and the robustness of networks to failure

A common definition of a robust connection between two nodes in a network such as a communication network is that there should be at least two independent paths connecting them, so that the failure of no single node in the network causes them to become disconnected. This definition leads us naturally to consider bicomponents, subnetworks in which every node has a robust connection of this kind to every other. Here we study bicomponents in both real and model networks using a combination of exact analytic techniques and numerical methods. We show that standard network models predict there to be essentially no small bicomponents in most networks, but there may be a giant bicomponent, whose presence coincides with the presence of the ordinary giant component, and we find that real networks seem by and large to follow this pattern, although there are some interesting exceptions. We study the size of the giant bicomponent as nodes in the network fail, using a specially developed computer algorithm based on data trees, and find in some cases that our networks are quite robust to failure, with large bicomponents persisting until almost all vertices have been removed.Comment: 5 pages, 1 figure, 1 tabl

Random graphs with clustering

We offer a solution to a long-standing problem in the physics of networks, the creation of a plausible, solvable model of a network that displays clustering or transitivity -- the propensity for two neighbors of a network node also to be neighbors of one another. We show how standard random graph models can be generalized to incorporate clustering and give exact solutions for various properties of the resulting networks, including sizes of network components, size of the giant component if there is one, position of the phase transition at which the giant component forms, and position of the phase transition for percolation on the network.Comment: 5 pages, 2 figure

Gathering evidence of benefits: a structured approach from the JISC Managing Research Data Programme

The work of the Jisc Managing Research Data programme is – along with the rest of the UK higher education sector – taking place in an environment of increasing pressure on research funding. In order to justify the investment made by Jisc in this activity – and to help make the case more widely for the value of investing time and money in research data management – projects and the programme as a whole must be able to clearly express the resultant benefits to the host institutions and to the broader sector. This paper describes a structured approach to the measurement and description of benefits provided by the work of these projects for the benefit of funders, institutions and researchers. We outline the context of the programme and its work; discuss the drivers and challenges of gathering evidence of benefits; specify benefits as distinct from aims and outputs; present emerging findings and the types of metrics and other evidence which projects have provided; explain the value of gathering evidence in a structured way to demonstrate benefits generated by work in this field; and share lessons learned from progress to date

Generating random networks with given degree-degree correlations and degree-dependent clustering

Random networks are widely used to model complex networks and research their properties. In order to get a good approximation of complex networks encountered in various disciplines of science, the ability to tune various statistical properties of random networks is very important. In this manuscript we present an algorithm which is able to construct arbitrarily degree-degree correlated networks with adjustable degree-dependent clustering. We verify the algorithm by using empirical networks as input and describe additionally a simple way to fix a degree-dependent clustering function if degree-degree correlations are given.Comment: 4 pages, 3 figure

Dynamics of Epidemics

This article examines how diseases on random networks spread in time. The disease is described by a probability distribution function for the number of infected and recovered individuals, and the probability distribution is described by a generating function. The time development of the disease is obtained by iterating the generating function. In cases where the disease can expand to an epidemic, the probability distribution function is the sum of two parts; one which is static at long times, and another whose mean grows exponentially. The time development of the mean number of infected individuals is obtained analytically. When epidemics occur, the probability distributions are very broad, and the uncertainty in the number of infected individuals at any given time is typically larger than the mean number of infected individuals.Comment: 4 pages and 3 figure

Hierarchical Bayesian analysis reveals complex neural dynamics of inhibitory control

Cognitive control has been of interest to psychologists and neuroscientists because of its contribution to understanding individual differences, impulsivity, addiction, and obsessive-compulsive disorder. Two tasks used to test cognitive control are the Go/No-Go (GNG) and Stop-Signal (SS) tasks. In the GNG task, subjects are given a cue to respond or withhold a response at the beginning of a trial. The SS task extends this basic paradigm by including the possibility that a “Go” cue may switch to a response-withholding cue. Behavioral and functional magnetic resonance imaging (fMRI) data, extracted for twenty- four regions of interest (ROIs), were collected from eleven subjects who completed both the GNG and SS tasks. In this study, blood oxygenation level-dependent (BOLD) responses were fit using a hierarchical Bayesian analysis to five increasingly complex models of the trial-wise neural activation to improve the signal-to-noise ratio and explore differences in neural activation between response (Go trials) and response inhibition (No-Go/Stop trials). We found that constructing a hierarchy, or adding multiple levels to the model, greatly constrained the predicted BOLD signal by systematically removing outliers. Additionally, increasing model complexity elucidated brain regions that played a role solely in carrying out a response (Go trials). We next replicated these results using the more complicated SS task. We found, from adding a hierarchical structure, that some brain areas showed less activation after a stop signal than during either a Go or No-Go trial. Our results suggest hierarchical modeling is a useful tool in interpreting often noisy fMRI data.Air Force Research Lab contract FA8650-16-1-6770No embargoAcademic Major: Neuroscienc

Threshold effects for two pathogens spreading on a network

Diseases spread through host populations over the networks of contacts between individuals, and a number of results about this process have been derived in recent years by exploiting connections between epidemic processes and bond percolation on networks. Here we investigate the case of two pathogens in a single population, which has been the subject of recent interest among epidemiologists. We demonstrate that two pathogens competing for the same hosts can both spread through a population only for intermediate values of the bond occupation probability that lie above the classic epidemic threshold and below a second higher value, which we call the coexistence threshold, corresponding to a distinct topological phase transition in networked systems.Comment: 5 pages, 2 figure

Resilience of Complex Networks to Random Breakdown

Using Monte Carlo simulations we calculate $f_c$, the fraction of nodes which are randomly removed before global connectivity is lost, for networks with scale-free and bimodal degree distributions. Our results differ with the results predicted by an equation for $f_c$ proposed by Cohen, et al. We discuss the reasons for this disagreement and clarify the domain for which the proposed equation is valid

Computer programs for estimating civil aircraft economics

Computer programs for calculating airline direct operating cost, indirect operating cost, and return on investment were developed to provide a means for determining commercial aircraft life cycle cost and economic performance. A representative wide body subsonic jet aircraft was evaluated to illustrate use of the programs

Clustering in complex networks. II. Percolation properties

The percolation properties of clustered networks are analyzed in detail. In the case of weak clustering, we present an analytical approach that allows to find the critical threshold and the size of the giant component. Numerical simulations confirm the accuracy of our results. In more general terms, we show that weak clustering hinders the onset of the giant component whereas strong clustering favors its appearance. This is a direct consequence of the differences in the $k$-core structure of the networks, which are found to be totally different depending on the level of clustering. An empirical analysis of a real social network confirms our predictions.Comment: Updated reference lis