Non-parametric resampling of random walks for spectral network clustering

Parametric resampling schemes have been recently introduced in complex network analysis with the aim of assessing the statistical significance of graph clustering and the robustness of community partitions. We propose here a method to replicate structural features of complex networks based on the non-parametric resampling of the transition matrix associated with an unbiased random walk on the graph. We test this bootstrapping technique on synthetic and real-world modular networks and we show that the ensemble of replicates obtained through resampling can be used to improve the performance of standard spectral algorithms for community detection.Comment: 5 pages, 2 figure

Galaxy Alignments in Very X-ray Luminous Clusters at z>0.5

We present the results of a search for galaxy alignments in 12 galaxy clusters at z>0.5, a statistically complete subset of the very X-ray luminous clusters from the MAssive Cluster Survey (MACS). Using high-quality images taken with the Hubble Space Telescope (HST) that render measurement errors negligible, we find no radial galaxy alignments within 500 kpc of the cluster centres for a sample of 545 spectroscopically confirmed cluster members. A mild, but statistically insignificant trend favouring radial alignments is observed within a radius of 200 kpc and traced to galaxies on the cluster red sequence. Our results for massive clusters at z>0.5 are in stark contrast to the findings of previous studies which find highly significant radial alignments of galaxies in nearby clusters at z~0.1 out to at least half the virial radius using imaging data from the SDSS. The discrepancy becomes even more startling if radial alignment becomes more prevalent at decreasing clustercentric distance, as suggested by both our and previous work. We investigate and discuss potential causes for the disparity between our findings based on HST images of clusters at z>0.5 and those obtained using groundbased images of systems at z~0.1. We conclude that the most likely explanation is either dramatic evolution with redshift (in the sense that radial alignments are less pronounced in dynamically younger systems) or the presence of systematic biases in the analysis of SDSS imaging data that cause at least partly spurious alignment signals.Comment: 10 pages, 11 figures, and 1 table. Accepted for publication in MNRA

Individualization as driving force of clustering phenomena in humans

One of the most intriguing dynamics in biological systems is the emergence of clustering, the self-organization into separated agglomerations of individuals. Several theories have been developed to explain clustering in, for instance, multi-cellular organisms, ant colonies, bee hives, flocks of birds, schools of fish, and animal herds. A persistent puzzle, however, is clustering of opinions in human populations. The puzzle is particularly pressing if opinions vary continuously, such as the degree to which citizens are in favor of or against a vaccination program. Existing opinion formation models suggest that "monoculture" is unavoidable in the long run, unless subsets of the population are perfectly separated from each other. Yet, social diversity is a robust empirical phenomenon, although perfect separation is hardly possible in an increasingly connected world. Considering randomness did not overcome the theoretical shortcomings so far. Small perturbations of individual opinions trigger social influence cascades that inevitably lead to monoculture, while larger noise disrupts opinion clusters and results in rampant individualism without any social structure. Our solution of the puzzle builds on recent empirical research, combining the integrative tendencies of social influence with the disintegrative effects of individualization. A key element of the new computational model is an adaptive kind of noise. We conduct simulation experiments to demonstrate that with this kind of noise, a third phase besides individualism and monoculture becomes possible, characterized by the formation of metastable clusters with diversity between and consensus within clusters. When clusters are small, individualization tendencies are too weak to prohibit a fusion of clusters. When clusters grow too large, however, individualization increases in strength, which promotes their splitting.Comment: 12 pages, 4 figure

Competitive effects between stationary chemical reaction centres: a theory based on off-center monopoles.

The subject of this paper is competitive effects between multiple reaction sinks. A theory based on off-center monopoles is developed for the steady-state diffusion equation and for the convection-diffusion equation with a constant flow field. The dipolar approximation for the diffusion equation with two equal reaction centres is compared with the exact solution. The former turns out to be remarkably accurate, even for two touching spheres. Numerical evidence is presented to show that the same holds for larger clusters (with more than two spheres). The theory is extended to the convection-diffusion equation with a constant flow field. As one increases the convective velocity, the competitive effects between the reactive centres gradually become less significant. This is demonstrated for a number of cluster configurations. At high flow velocities, the current methodology breaks down. Fixing this problem will be the subject of future research. The current method is useful as an easy-to-use tool for the calibration of other more complicated models in mass and/or heat transfer

The influence of the cosmological expansion on local systems

Following renewed interest, the problem of whether the cosmological expansion affects the dynamics of local systems is reconsidered. The cosmological correction to the equations of motion in the locally inertial Fermi normal frame (the relevant frame for astronomical observations) is computed. The evolution equations for the cosmological perturbation of the two--body problem are solved in this frame. The effect on the orbit is insignificant as are the effects on the galactic and galactic--cluster scales.Comment: To appear in the Astrophysical Journal, Late

Continuous image distortion by astrophysical thick lenses

Image distortion due to weak gravitational lensing is examined using a non-perturbative method of integrating the geodesic deviation and optical scalar equations along the null geodesics connecting the observer to a distant source. The method we develop continuously changes the shape of the pencil of rays from the source to the observer with no reference to lens planes in astrophysically relevant scenarios. We compare the projected area and the ratio of semi-major to semi-minor axes of the observed elliptical image shape for circular sources from the continuous, thick-lens method with the commonly assumed thin-lens approximation. We find that for truncated singular isothermal sphere and NFW models of realistic galaxy clusters, the commonly used thin-lens approximation is accurate to better than 1 part in 10^4 in predicting the image area and axes ratios. For asymmetric thick lenses consisting of two massive clusters separated along the line of sight in redshift up to \Delta z = 0.2, we find that modeling the image distortion as two clusters in a single lens plane does not produce relative errors in image area or axes ratio more than 0.5%Comment: accepted to GR

Micro-Environment Causes Reversible Changes in DNA Methylation and mRNA Expression Profiles in Patient-Derived Glioma Stem Cells

In vitro and in vivo models are widely used in cancer research. Characterizing the similarities and differences between a patient\u27s tumor and corresponding in vitro and in vivo models is important for understanding the potential clinical relevance of experimental data generated with these models. Towards this aim, we analyzed the genomic aberrations, DNA methylation and transcriptome profiles of five parental tumors and their matched in vitro isolated glioma stem cell (GSC) lines and xenografts generated from these same GSCs using high-resolution platforms. We observed that the methylation and transcriptome profiles of in vitro GSCs were significantly different from their corresponding xenografts, which were actually more similar to their original parental tumors. This points to the potentially critical role of the brain microenvironment in influencing methylation and transcriptional patterns of GSCs. Consistent with this possibility, ex vivo cultured GSCs isolated from xenografts showed a tendency to return to their initial in vitro states even after a short time in culture, supporting a rapid dynamic adaptation to the in vitro microenvironment. These results show that methylation and transcriptome profiles are highly dependent on the microenvironment and growth in orthotopic sites partially reverse the changes caused by in vitro culturing