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

Arctic Science and the Nuclear Submarine

... The entire Arctic Ocean has now ceased to be remote and is open to study on a year-round basis by nuclear submarines (Strong 1961). Admittedly, there are limitations to the use of a nuclear submarine for arctic research, but the advantages heavily out-weigh the disadvantages. First among the advantages to be gained through the use of this type of vehicle is mobility (Lyon and Boyle 1962). The nuclear submarine is a self-contained community capable of operating under all arctic conditions for extended periods of time. Its mobility is not a function of pre-determined drift patterns, for the submarine can be directed to any desired place, at a wide range of speed and depth. With its special equipment, such as underwater television and SONAR, it can "see" and "hear" below the surface (Steele 1962). There is adequate space for modest laboratory facilities, a controlled atmosphere, and accommodation for a scientific staff, who are comfortable and have every incentive for conducting research (Molloy 1961). Another advantage, and an equally important one, is the natural protection that the arctic environment offers to the submarine. The polar ice pack that presents such serious obstacles to the conduct of oceanographic research from the surface can be used to advantage by the nuclear submarine. It provides a nearly homogeneous environment free from disturbances of weather and other factors that the oceanographer encounters in the open ocean. The advantages of submarine research in the Arctic are even more readily apparent after evaluating the accomplishments of the U.S. Navy's arctic submarine cruises during the past few years. The floor of the Arctic Ocean was sounded continuously during each cruise (Lyon and Boyle 1962). As a result of this, there is now more information available on the bathymetry of the Arctic Ocean than had been obtained during the previous 75 years of arctic exploration. We have now more data relating to the ice pack over broad areas and under various seasonal conditions than ever before. Ice and water samples, as well as bathythermograph observations, also have been obtained at various points in the arctic basin (LaFond 1960). In addition the submarine itself has been a prime research tool whose advantages have not been limited to being a vehicle for transportation (Lyon and Boyle 1962). For example, surfacings through the ice have answered some of the questions relating to the ice cover. In many respects the Arctic has been the laboratory and the submarine the instrument with which the research was carried out (Lyon 1961). The arctic cruises of the U.S. Navy submarines have not been conducted as purely oceanographic ventures, but diversified scientific programs have been carried out during each of the cruises (Strong 1961). It is manifest from these modest beginnings that the nuclear submarine is an ideal platform from which to launch a research program of rather large dimensions. ..

Rethinking models of feedback for learning: The challenge of design

Student feedback is a contentious and confusing issue throughout higher education institutions. This paper develops and analyses two models of feedback: the first is based on the origins of the term in the disciplines of engineering and biology. It positions teachers as the drivers of feedback. The second draws on ideas of sustainable assessment. This positions learners as having a key role in driving learning, and thus generating and soliciting their own feedback. It suggests that the second model equips students beyond the immediate task and does not lead to false expectations that courses cannot deliver. It identifies the importance of curriculum design in creating opportunities for students to develop the capabilities to operate as judges of their own learning. © 2013 Copyright Taylor and Francis Group, LLC

Developing a learning-centred framework for feedback literacy

There is an increasing focus on notions of feedback in which students are positioned as active players rather than recipients of information. These discussions have been either conceptual in character or have an empirical focus on designs to support learners in feedback processes. There has been little emphasis on learners’ perspectives on, and experiences of, the role they play in such processes and what they need in order to benefit from feedback. This study therefore seeks to identify the characteristics of feedback literacy – that is, how students understand and can utilise feedback for their own learning – by analysing students’ views of feedback processes drawing on a substantial data set derived from a study of feedback in two large universities. The analysis revealed seven groupings of learner feedback literacy, including understanding feedback purposes and roles, seeking information, making judgements about work quality, working with emotions, and processing and using information for the benefit of their future work (31 categories in total). By identifying these realised components of feedback literacy, in the form of illustrative examples, the emergent set of competencies can enable investigations of the development of feedback literacy and improve feedback designs in courses through alignment to these standards

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

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

Seeking a different angle on feedback in clinical education: the learner as seeker, judge and user of performance information

Seeking a different angle on feedback in clinical education: the learner as seeker, judge and user of performance information Seeking a different angle on feedback in clinical education: the learner as seeker, judge and user of performance informatio

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Single-molecule force spectroscopy reveals binding and bridging dynamics of PARP1 and PARP2 at DNA double-strand breaks

Poly(ADP-ribose) polymerases (PARPs) play key roles in DNA damage repair pathways in eukaryotic cells. Human PARPs 1 and 2 are catalytically activated by damage in the form of both double-strand and single-strand DNA breaks. Recent structural work indicates that PARP2 can also bridge two DNA double-strand breaks (DSBs), revealing a potential role in stabilizing broken DNA ends. In this paper, we have developed a magnetic tweezers–based assay in order to measure the mechanical stability and interaction kinetics of proteins bridging across the two ends of a DNA DSB. We find that PARP2 forms a remarkably stable mechanical link (rupture force ~85 pN) across blunt-end 5′-phosphorylated DSBs and restores torsional continuity allowing DNA supercoiling. We characterize the rupture force for different overhang types and show that PARP2 switches between bridging and end-binding modes depending on whether the break is blunt-ended or has a short 5′ or 3′ overhang. In contrast, PARP1 was not observed to form a bridging interaction across blunt or short overhang DSBs and competed away PARP2 bridge formation, indicating that it binds stably but without linking together the two broken DNA ends. Our work gives insights into the fundamental mechanisms of PARP1 and PARP2 interactions at double-strand DNA breaks and presents a unique experimental approach to studying DNA DSB repair pathways