k-core (bootstrap) percolation on complex networks: Critical phenomena and nonlocal effects

We develop the theory of the k-core (bootstrap) percolation on uncorrelated random networks with arbitrary degree distributions. We show that the k-core percolation is an unusual, hybrid phase transition with a jump emergence of the k-core as at a first order phase transition but also with a critical singularity as at a continuous transition. We describe the properties of the k-core, explain the meaning of the order parameter for the k-core percolation, and reveal the origin of the specific critical phenomena. We demonstrate that a so-called ``corona'' of the k-core plays a crucial role (corona is a subset of vertices in the k-core which have exactly k neighbors in the k-core). It turns out that the k-core percolation threshold is at the same time the percolation threshold of finite corona clusters. The mean separation of vertices in corona clusters plays the role of the correlation length and diverges at the critical point. We show that a random removal of even one vertex from the k-core may result in the collapse of a vast region of the k-core around the removed vertex. The mean size of this region diverges at the critical point. We find an exact mapping of the k-core percolation to a model of cooperative relaxation. This model undergoes critical relaxation with a divergent rate at some critical moment.Comment: 11 pages, 8 figure

k-core organization of complex networks

We analytically describe the architecture of randomly damaged uncorrelated networks as a set of successively enclosed substructures -- k-cores. The k-core is the largest subgraph where vertices have at least k interconnections. We find the structure of k-cores, their sizes, and their birth points -- the bootstrap percolation thresholds. We show that in networks with a finite mean number z_2 of the second-nearest neighbors, the emergence of a k-core is a hybrid phase transition. In contrast, if z_2 diverges, the networks contain an infinite sequence of k-cores which are ultra-robust against random damage.Comment: 5 pages, 3 figure

Controlling the uncontrolled: Are there incidental experimenter effects on physiologic responding?

The degree to which experimenters shape participant behavior has long been of interest in experimental social science research. Here, we extend this question to the domain of peripheral psychophysiology, where experimenters often have direct, physical contact with participants, yet researchers do not consistently test for their influence. We describe analytic tools for examining experimenter effects in peripheral physiology. Using these tools, we investigate nine data sets totaling 1,341 participants and 160 experimenters across different roles (e.g., lead research assistants, evaluators, confederates) to demonstrate how researchers can test for experimenter effects in participant autonomic nervous system activity during baseline recordings and reactivity to study tasks. Our results showed (a) little to no significant variance in participants' physiological reactivity due to their experimenters, and (b) little to no evidence that three characteristics of experimenters that are well known to shape interpersonal interactions-status (using five studies with 682 total participants), gender (using two studies with 359 total participants), and race (in two studies with 554 total participants)-influenced participants' physiology. We highlight several reasons that experimenter effects in physiological data are still cause for concern, including the fact that experimenters in these studies were already restricted on a number of characteristics (e.g., age, education). We present recommendations for examining and reducing experimenter effects in physiological data and discuss implications for replication

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

The Near Infrared NaI Doublet Feature in M Stars

The NaI near-infrared doublet has been used to indicate the dwarf/giant population in composite systems, but its interpretation is still a contentious issue. In order to understand the behaviour of this controversial feature, we study the observed and synthetic spectra of cool stars. We conclude that the NaI infrared feature can be used as a dwarf/giant discriminator. We propose a modified definition of the NaI index by locating the red continuum at 8234 angstrons and by measuring the equivalent width in the range 8172-8197 angstrons, avoiding the region at lambda > 8197 angstrons, which contains VI, ZrI, FeI and TiO lines. We also study the dependence of this feature on stellar atmospheric parameters.Comment: 9 pages, (TeX file) + 7 Figures in Postscript format. Accepted for publication in The Astrophysical Journa

The interplay of university and industry through the FP5 network

To improve the quality of life in a modern society it is essential to reduce the distance between basic research and applications, whose crucial roles in shaping today's society prompt us to seek their understanding. Existing studies on this subject, however, have neglected the network character of the interaction between university and industry. Here we use state-of-the-art network theory methods to analyze this interplay in the so-called Framework Programme--an initiative which sets out the priorities for the European Union's research and technological development. In particular we study in the 5th Framework Programme (FP5) the role played by companies and scientific institutions and how they contribute to enhance the relationship between research and industry. Our approach provides quantitative evidence that while firms are size hierarchically organized, universities and research organizations keep the network from falling into pieces, paving the way for an effective knowledge transfer.Comment: 21 pages (including Appendix), 8 figures. Published online at http://stacks.iop.org/1367-2630/9/18