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

To blame? The effects of moralized feedback on implicit racial bias

Implicit bias training (IBT) is now frequently provided by employers, in order to raise awareness of the problems related to implicit biases, and of how to safeguard against discrimination that may result. However, as Atewologun et al (2018) have noted, there is very little systematicity in IBT, and there are many unknowns about what constitutes good IBT. One important issue concerns the tone of information provided regarding implicit bias. This paper engages this question, focusing in particular on the observation that much bias training is delivered in exculpatory tone, emphasising that individuals are not to blame for possessing implicit biases. Normative guidance around IBT exhorts practitioners to adopt this strategy (Moss-Racusin et al 2014). However, existing evidence about the effects of moralized feedback about implicit bias is equivocal (Legault et al 2011; Czopp et al 2006). Through a series of studies, culminating in an experiment with a pre-registered analysis plan, we develop a paradigm for evaluating the impact of moralized feedback on participants’ implicit racial bias scores. We also conducted exploratory analyses of the impact on their moods, and behavioural intentions. Our results indicated that an exculpatory tone, rather than a blaming or neutral tone, did not make participants less resistant to changing their attitudes and behaviours. In fact, participants in the blame condition had significantly stronger explicit intentions to change future behaviour than those in the ‘no feedback’ condition (see experiment 3). These results indicate that considerations of efficacy do not support the need for implicit bias feedback to be exculpatory. We tease out the implications of these findings, and directions for future research

Phylogenetic relationships of the Wolbachia of nematodes and arthropods

Wolbachia are well known as bacterial symbionts of arthropods, where they are reproductive parasites, but have also been described from nematode hosts, where the symbiotic interaction has features of mutualism. The majority of arthropod Wolbachia belong to clades A and B, while nematode Wolbachia mostly belong to clades C and D, but these relationships have been based on analysis of a small number of genes. To investigate the evolution and relationships of Wolbachia symbionts we have sequenced over 70 kb of the genome of wOvo, a Wolbachia from the human-parasitic nematode Onchocerca volvulus, and compared the genes identified to orthologues in other sequenced Wolbachia genomes. In comparisons of conserved local synteny, we find that wBm, from the nematode Brugia malayi, and wMel, from Drosophila melanogaster, are more similar to each other than either is to wOvo. Phylogenetic analysis of the protein-coding and ribosomal RNA genes on the sequenced fragments supports reciprocal monophyly of nematode and arthropod Wolbachia. The nematode Wolbachia did not arise from within the A clade of arthropod Wolbachia, and the root of the Wolbachia clade lies between the nematode and arthropod symbionts. Using the wOvo sequence, we identified a lateral transfer event whereby segments of the Wolbachia genome were inserted into the Onchocerca nuclear genome. This event predated the separation of the human parasite O. volvulus from its cattle-parasitic sister species, O. ochengi. The long association between filarial nematodes and Wolbachia symbionts may permit more frequent genetic exchange between their genomes

Textiles as Material Gestalt: Cloth as a Catalyst in the Co-designing Process

Textiles is the common language within Emotional Fit, a collaborative research project investigating a person-centred, sustainable approach to fashion for an ageing female demographic (55+). Through the co-designing of a collection of research tools, textiles have acted as a material gestalt for exploring our research participants' identities by tracing their embodied knowledge of fashionable dress. The methodology merges Interpretative Phenomenological Analysis, co-design and a simultaneous approach to textile and garment design. Based on an enhanced understanding of our participants textile preferences, particular fabric qualities have catalysed silhouettes, through live draping and geometric pattern cutting to accommodate multiple body shapes and customisation. Printedtextiles have also been digitally crafted in response to the contours of the garment and body and personal narratives of wear. Sensorial and tactile interactions have informed the engineering and scaling of patterns within zero-waste volumes. The article considers the functional and aesthetic role of textiles

Finite-size effects for anisotropic bootstrap percolation: logarithmic corrections

In this note we analyze an anisotropic, two-dimensional bootstrap percolation model introduced by Gravner and Griffeath. We present upper and lower bounds on the finite-size effects. We discuss the similarities with the semi-oriented model introduced by Duarte.Comment: Key words: Bootstrap percolation, anisotropy, finite-size effect

Risk factors for dementia development, frailty, and mortality in older adults with epilepsy – A population-based analysis

Objective: Although the prevalence of comorbid epilepsy and dementia is expected to increase, the impact is not well understood. Our objectives were to examine risk factors associated with incident dementia and the impact of frailty and dementia on mortality in older adults with epilepsy. Methods: The CALIBER scientific platform was used. People with incident epilepsy at or after age 65 were identified using Read codes and matched by age, sex, and general practitioner to a cohort without epilepsy (10:1). Baseline cohort characteristics were compared using conditional logistic regression models. Multivariate Cox proportional hazard regression models were used to examine the impact of frailty and dementia on mortality, and to assess risk factors for dementia development. Results: One thousand forty eight older adults with incident epilepsy were identified. The odds of having dementia at baseline were 7.39 [95% CI 5.21–10.50] times higher in older adults with epilepsy (n = 62, 5.92%) compared to older adults without epilepsy (n = 88, 0.86%). In the final multivariate Cox model (n = 326), age [HR: 1.20, 95% CI 1.09–1.32], Charlson comorbidity index score [HR: 1.26, 95% CI 1.10–1.44], and sleep disturbances [HR: 2.41, 95% CI 1.07–5.43] at baseline epilepsy diagnosis were significantly associated with an increased hazard of dementia development over the follow-up period. In a multivariate Cox model (n = 1047), age [HR: 1.07, 95% CI 1.03–1.11], baseline dementia [HR: 2.66, 95% CI 1.65–4.27] and baseline e-frailty index score [HR: 11.55, 95% CI 2.09–63.84] were significantly associated with a higher hazard of death among those with epilepsy. Female sex [HR: 0.77, 95% CI 0.59–0.99] was associated with a lower hazard of death. Significance: The odds of having dementia were higher in older adults with incident epilepsy. A higher comorbidity burden acts as a risk factor for dementia, while prevalent dementia and increasing frailty were associated with mortality

Rate-controlling processes during environment-sensitive crack propagation in aluminum

Recent experimental findings are challenging today’s conventional view on the rate-controlling processes during environment-sensitive crack growth in aluminum alloys when exposed to moist air and aqueous environments. X-ray computed tomography has revealed the detailed crack morphology of several stress corrosion cracks in 7000 series alloys and this has shown that the complexity of the mesoscale is incredibly important to understand the links between the gross morphology of the crack and the crack front/tip. We will show the large local variation that exists in the crack morphology. At the same time we will show how average measurements of crack velocity and crack opening displacement remain surprisingly uniform across the width of the crack. Discussion will follow in an effort to quantify the effect of Keffective compared to Kapplied and to provide a rationalization of these findings with respect to previously published theories

Metastability threshold for anisotropic bootstrap percolation in three dimensions

In this paper we analyze several anisotropic bootstrap percolation models in three dimensions. We present the order of magnitude for the metastability threshold for a fairly general class of models. In our proofs we use an adaptation of the technique of dimensional reduction. We find that the order of the metastability threshold is generally determined by the "easiest growth direction" in the model. In contrast to the anisotropic bootstrap percolation in two dimensions, in three dimensions the order of the metatstability threshold for anisotropic bootstrap percolation can be equal to that of isotropic bootstrap percolation.Comment: 19 page