PageRank and rank-reversal dependence on the damping factor

PageRank (PR) is an algorithm originally developed by Google to evaluate the importance of web pages. Considering how deeply rooted Google's PR algorithm is to gathering relevant information or to the success of modern businesses, the question of rank-stability and choice of the damping factor (a parameter in the algorithm) is clearly important. We investigate PR as a function of the damping factor d on a network obtained from a domain of the World Wide Web, finding that rank-reversal happens frequently over a broad range of PR (and of d). We use three different correlation measures, Pearson, Spearman, and Kendall, to study rank-reversal as d changes, and show that the correlation of PR vectors drops rapidly as d changes from its frequently cited value, $d_0=0.85$. Rank-reversal is also observed by measuring the Spearman and Kendall rank correlation, which evaluate relative ranks rather than absolute PR. Rank-reversal happens not only in directed networks containing rank-sinks but also in a single strongly connected component, which by definition does not contain any sinks. We relate rank-reversals to rank-pockets and bottlenecks in the directed network structure. For the network studied, the relative rank is more stable by our measures around $d=0.65$ than at $d=d_0$.Comment: 14 pages, 9 figure

Explosive Percolation is Continuous, but with Unusual Finite Size Behavior

We study four Achlioptas type processes with "explosive" percolation transitions. All transitions are clearly continuous, but their finite size scaling functions are not entire holomorphic. The distributions of the order parameter, the relative size $s_{\rm max}/N$ of the largest cluster, are double-humped. But -- in contrast to first order phase transitions -- the distance between the two peaks decreases with system size $N$ as $N^{-\eta}$ with $\eta > 0$. We find different positive values of $\beta$ (defined via $< s_{\rm max}/N > \sim (p-p_c)^\beta$ for infinite systems) for each model, showing that they are all in different universality classes. In contrast, the exponent $\Theta$ (defined such that observables are homogeneous functions of $(p-p_c)N^\Theta$) is close to -- or even equal to -- 1/2 for all models.Comment: 4 pages (including 4 figures), plus 7 pages of supplementary materia

Agglomerative Percolation in Two Dimensions

We study a process termed "agglomerative percolation" (AP) in two dimensions. Instead of adding sites or bonds at random, in AP randomly chosen clusters are linked to all their neighbors. As a result the growth process involves a diverging length scale near a critical point. Picking target clusters with probability proportional to their mass leads to a runaway compact cluster. Choosing all clusters equally leads to a continuous transition in a new universality class for the square lattice, while the transition on the triangular lattice has the same critical exponents as ordinary percolation.Comment: Paper and supplementary figures and discussio

Percolation Theory on Interdependent Networks Based on Epidemic Spreading

We consider percolation on interdependent locally treelike networks, recently introduced by Buldyrev et al., Nature 464, 1025 (2010), and demonstrate that the problem can be simplified conceptually by deleting all references to cascades of failures. Such cascades do exist, but their explicit treatment just complicates the theory -- which is a straightforward extension of the usual epidemic spreading theory on a single network. Our method has the added benefits that it is directly formulated in terms of an order parameter and its modular structure can be easily extended to other problems, e.g. to any number of interdependent networks, or to networks with dependency links.Comment: 6 pages, 5 figure

Irreversible Aggregation and Network Renormalization

Irreversible aggregation is revisited in view of recent work on renormalization of complex networks. Its scaling laws and phase transitions are related to percolation transitions seen in the latter. We illustrate our points by giving the complete solution for the probability to find any given state in an aggregation process $(k+1)X\to X$, given a fixed number of unit mass particles in the initial state. Exactly the same probability distributions and scaling are found in one dimensional systems (a trivial network) and well-mixed solutions. This reveals that scaling laws found in renormalization of complex networks do not prove that they are self-similar.Comment: 4 pages, 2 figure

Protocol for a randomised controlled trial investigating the effectiveness of an online e health application for the prevention of Generalised Anxiety Disorder

BACKGROUND Generalised Anxiety Disorder (GAD) is a highly prevalent psychiatric disorder. Effective prevention in young adulthood has the potential to reduce the prevalence of the disorder, to reduce disability and lower the costs of the disorder to the community. The present trial (the WebGAD trial) aims to evaluate the effectiveness of an evidence-based online prevention website for GAD. METHODS/DESIGN The principal clinical question under investigation is the effectiveness of an online GAD intervention (E-couch) using a community-based sample. We examine whether the effect of the intervention can be maximised by either human support, in the form of telephone calls, or by automated support through emails. The primary outcome will be a reduction in symptoms on the GAD-7 in the active arms relative to the non active intervention arms. DISCUSSION The WebGAD trial will be the first to evaluate the use of an internet-based cognitive behavioural therapy (CBT) program contrasted with a credible control condition for the prevention of GAD and the first formal RCT evaluation of a web-based program for GAD using community recruitment. In general, internet-based CBT programs have been shown to be effective for the treatment of other anxiety disorders such as Post Traumatic Stress Disorder, Social Phobia, Panic Disorder and stress in clinical trials; however there is no evidence for the use of internet CBT in the prevention of GAD. Given the severe shortage of therapists identified in Australia and overseas, and the low rates of treatment seeking in those with a mental illness, the successful implementation of this protocol has important practical outcomes. If found to be effective, WebGAD will provide those experiencing GAD with an easily accessible, free, evidence-based prevention tool which can be promoted and disseminated immediately

Ante-Autobiography and the Archive of Childhood

This essay examines the concept of children’s autobiography via several autobiographical extracts written by the author as a child. Although only a small proportion of people will compose and publish a full-length autobiography, almost everyone will, inadvertently, produce an archive of the self, made from public records and private documents. Here, such works are seen as providing access to writing both about and by children. The essay explores the ethics and poetics of children’s writing via the key debates in life writing; in particular, the dynamic relationship between adults and children, both as distinct stages of life and dual parts of one autobiographical identity. The term “ante-autobiography” is coined to refer to these texts which come before or instead of a full-length narrative. They are not read as less than or inadequate versions of autobiography, but rather as transgressive and challenging to chronological notions of the genre

Site-Specific DC Surface Signatures Influence CD4⁺ T Cell Co-stimulation and Lung-Homing

Dendritic cells (DCs) that drain the gut and skin are known to favor the establishment of T cell populations that home to the original site of DC-antigen (Ag) encounter by providing soluble "imprinting" signals to T cells in the lymph node (LN). To study the induction of lung T cell-trafficking, we used a protein-adjuvant murine intranasal and intramuscular immunization model to compare in vivo-activated Ag+ DCs in the lung and muscle-draining LNs. Higher frequencies of Ag+ CD11b+ DCs were observed in lung-draining mediastinal LNs (MedLN) compared to muscle-draining inguinal LNs (ILN). Ag+ CD11b+ MedLN DCs were qualitatively superior at priming CD4+ T cells, which then expressed CD49a and CXCR3, and preferentially trafficked into the lung parenchyma. CD11b+ DCs from the MedLN expressed higher levels of surface podoplanin, Trem4, GL7, and the known co-stimulatory molecules CD80, CD86, and CD24. Blockade of specific MedLN DC molecules or the use of sorted DC and T cell co-cultures demonstrated that DC surface phenotype influences the ability to prime T cells that then home to the lung. Thus, the density of dLN Ag+ DCs, and DC surface molecule signatures are factors that can influence the output and differentiation of lung-homing CD4+ T cells