Bootstrap Percolation on Complex Networks

We consider bootstrap percolation on uncorrelated complex networks. We obtain the phase diagram for this process with respect to two parameters: $f$, the fraction of vertices initially activated, and $p$, the fraction of undamaged vertices in the graph. We observe two transitions: the giant active component appears continuously at a first threshold. There may also be a second, discontinuous, hybrid transition at a higher threshold. Avalanches of activations increase in size as this second critical point is approached, finally diverging at this threshold. We describe the existence of a special critical point at which this second transition first appears. In networks with degree distributions whose second moment diverges (but whose first moment does not), we find a qualitatively different behavior. In this case the giant active component appears for any $f>0$ and $p>0$, and the discontinuous transition is absent. This means that the giant active component is robust to damage, and also is very easily activated. We also formulate a generalized bootstrap process in which each vertex can have an arbitrary threshold.Comment: 9 pages, 3 figure

Percolation in invariant Poisson graphs with i.i.d. degrees

Let each point of a homogeneous Poisson process in R^d independently be equipped with a random number of stubs (half-edges) according to a given probability distribution mu on the positive integers. We consider translation-invariant schemes for perfectly matching the stubs to obtain a simple graph with degree distribution mu. Leaving aside degenerate cases, we prove that for any mu there exist schemes that give only finite components as well as schemes that give infinite components. For a particular matching scheme that is a natural extension of Gale-Shapley stable marriage, we give sufficient conditions on mu for the absence and presence of infinite components

Heterogeneous-k-core versus Bootstrap Percolation on Complex Networks

We introduce the heterogeneous-$k$-core, which generalizes the $k$-core, and contrast it with bootstrap percolation. Vertices have a threshold $k_i$ which may be different at each vertex. If a vertex has less than $k_i$ neighbors it is pruned from the network. The heterogeneous-$k$-core is the sub-graph remaining after no further vertices can be pruned. If the thresholds $k_i$ are $1$ with probability $f$ or $k \geq 3$ with probability $(1-f)$, the process forms one branch of an activation-pruning process which demonstrates hysteresis. The other branch is formed by ordinary bootstrap percolation. We show that there are two types of transitions in this heterogeneous-$k$-core process: the giant heterogeneous-$k$-core may appear with a continuous transition and there may be a second, discontinuous, hybrid transition. We compare critical phenomena, critical clusters and avalanches at the heterogeneous-$k$-core and bootstrap percolation transitions. We also show that network structure has a crucial effect on these processes, with the giant heterogeneous-$k$-core appearing immediately at a finite value for any $f > 0$ when the degree distribution tends to a power law $P(q) \sim q^{-\gamma}$ with $\gamma < 3$.Comment: 10 pages, 4 figure

Initiation and final failure via environmentally assisted cracking in high strength aluminium

Environmentally assisted cracking (EAC) is particularly important to understand and control in high strength aluminium used in engineering applications as moist air provides a suitable environment to assist cracking in these materials. Propagation of EAC has been widely investigated but initiation has been difficult to follow due to it’s stochastic nature. We show that time-lapse 3D imaging using X-ray computed tomography offers a way to survey large surface areas whilst maintaining site specific high resolution information giving new insights into this process. In addition the final failure of these materials occurs when the environmentally assisted cracks of intergranular or transgranular type grow to a critical length from the initiation sites. We show through mechanical testing assessment and high resolution fractography that the rapid fracture that follows is also assisted by the environment leading to reduced ductility during the final failure. Examples from AA5083-H131 and AA7085-T7651 are shown which appear to show the same general behaviour. Round dog bone specimens prepared in the Short Transverse direction were subjected to slow strain rate testing (SSRT) at different strain rates and in different environments. Samples were also pre-exposed to different environments to introduce small corrosion sites to act as ‘realistic’ stress raisers in the specimens

Activity in human reward-sensitive brain areas is strongly context dependent.

Contains fulltext : 55984.pdf (Publisher’s version ) (Closed access)Functional neuroimaging research in humans has identified a number of brain areas that are activated by the delivery of primary and secondary reinforcers. The present study investigated how activity in these reward-sensitive regions is modulated by the context in which rewards and punishments are experienced. Fourteen healthy volunteers were scanned during the performance of a simple monetary gambling task that involved a "win" condition (in which the possible outcomes were a large monetary gain, a small gain, or no gain of money) and a "lose" condition (in which the possible outcomes were a large monetary loss, a small loss, or no loss of money). We observed reward-sensitive activity in a number of brain areas previously implicated in reward processing, including the striatum, prefrontal cortex, posterior cingulate, and inferior parietal lobule. Critically, activity in these reward-sensitive areas was highly sensitive to the range of possible outcomes from which an outcome was selected. In particular, these regions were activated to a comparable degree by the best outcomes in each condition-a large gain in the win condition and no loss of money in the lose condition-despite the large difference in the objective value of these outcomes. In addition, some reward-sensitive brain areas showed a binary instead of graded sensitivity to the magnitude of the outcomes from each distribution. These results provide important evidence regarding the way in which the brain scales the motivational value of events by the context in which these events occur

Neural dynamics of error processing in medial frontal cortex.

Contains fulltext : 56338.pdf (publisher's version ) (Closed access)Adaptive behavior requires an organism to evaluate the outcome of its actions, such that future behavior can be adjusted accordingly and the appropriate response selected. During associative learning, the time at which such evaluative information is available changes as learning progresses, from the delivery of performance feedback early in learning to the execution of the response itself during learned performance. Here, we report a learning-dependent shift in the timing of activation in the rostral cingulate zone of the anterior cingulate cortex from external error feedback to internal error detection. This pattern of activity is seen only in the anterior cingulate, not in the presupplementary motor area. The dynamics of these reciprocal changes are consistent with the claim that the rostral cingulate zone is involved in response selection on the basis of the expected outcome of an action. Specifically, these data illustrate how the anterior cingulate receives evaluative information, indicating that an action has not produced the desired result

On Bootstrap Percolation in Living Neural Networks

Recent experimental studies of living neural networks reveal that their global activation induced by electrical stimulation can be explained using the concept of bootstrap percolation on a directed random network. The experiment consists in activating externally an initial random fraction of the neurons and observe the process of firing until its equilibrium. The final portion of neurons that are active depends in a non linear way on the initial fraction. The main result of this paper is a theorem which enables us to find the asymptotic of final proportion of the fired neurons in the case of random directed graphs with given node degrees as the model for interacting network. This gives a rigorous mathematical proof of a phenomena observed by physicists in neural networks

Meningococcal genetic variation mechanisms viewed through comparative analysis of Serogroup C strain FAM18

Copyright @ 2007 Public Library of ScienceThe bacterium Neisseria meningitidis is commonly found harmlessly colonising the mucosal surfaces of the human nasopharynx. Occasionally strains can invade host tissues causing septicaemia and meningitis, making the bacterium a major cause of morbidity and mortality in both the developed and developing world. The species is known to be diverse in many ways, as a product of its natural transformability and of a range of recombination and mutation-based systems. Previous work on pathogenic Neisseria has identified several mechanisms for the generation of diversity of surface structures, including phase variation based on slippage-like mechanisms and sequence conversion of expressed genes using information from silent loci. Comparison of the genome sequences of two N. meningitidis strains, serogroup B MC58 and serogroup A Z2491, suggested further mechanisms of variation, including C-terminal exchange in specific genes and enhanced localised recombination and variation related to repeat arrays. We have sequenced the genome of N. meningitidis strain FAM18, a representative of the ST-11/ET-37 complex, providing the first genome sequence for the disease-causing serogroup C meningococci; it has 1,976 predicted genes, of which 60 do not have orthologues in the previously sequenced serogroup A or B strains. Through genome comparison with Z2491 and MC58 we have further characterised specific mechanisms of genetic variation in N. meningitidis, describing specialised loci for generation of cell surface protein variants and measuring the association between noncoding repeat arrays and sequence variation in flanking genes. Here we provide a detailed view of novel genetic diversification mechanisms in N. meningitidis. Our analysis provides evidence for the hypothesis that the noncoding repeat arrays in neisserial genomes (neisserial intergenic mosaic elements) provide a crucial mechanism for the generation of surface antigen variants. Such variation will have an impact on the interaction with the host tissues, and understanding these mechanisms is important to aid our understanding of the intimate and complex relationship between the human nasopharynx and the meningococcus.This work was supported by the Wellcome Trust through the Beowulf Genomics Initiative