Line Graphs of Weighted Networks for Overlapping Communities

In this paper, we develop the idea to partition the edges of a weighted graph in order to uncover overlapping communities of its nodes. Our approach is based on the construction of different types of weighted line graphs, i.e. graphs whose nodes are the links of the original graph, that encapsulate differently the relations between the edges. Weighted line graphs are argued to provide an alternative, valuable representation of the system's topology, and are shown to have important applications in community detection, as the usual node partition of a line graph naturally leads to an edge partition of the original graph. This identification allows us to use traditional partitioning methods in order to address the long-standing problem of the detection of overlapping communities. We apply it to the analysis of different social and geographical networks.Comment: 8 Pages. New title and text revisions to emphasise differences from earlier paper

Space as a low-temperature regime of graphs

I define a statistical model of graphs in which 2-dimensional spaces arise at low temperature. The configurations are given by graphs with a fixed number of edges and the Hamiltonian is a simple, local function of the graphs. Simulations show that there is a transition between a low-temperature regime in which the graphs form triangulations of 2-dimensional surfaces and a high-temperature regime, where the surfaces disappear. I use data for the specific heat and other observables to discuss whether this is a phase transition. The surface states are analyzed with regard to topology and defects.Comment: 22 pages, 12 figures; v3: published version; J.Stat.Phys. 201

Percolation on two- and three-dimensional lattices

In this work we apply a highly efficient Monte Carlo algorithm recently proposed by Newman and Ziff to treat percolation problems. The site and bond percolation are studied on a number of lattices in two and three dimensions. Quite good results for the wrapping probabilities, correlation length critical exponent and critical concentration are obtained for the square, simple cubic, HCP and hexagonal lattices by using relatively small systems. We also confirm the universal aspect of the wrapping probabilities regarding site and bond dilution.Comment: 15 pages, 6 figures, 3 table

The Strategic Exploitation of Limited Information and Opportunity in Networked Markets

This paper studies the effect of constraining interactions within a market. A model is analysed in which boundedly rational agents trade with and gather information from their neighbours within a trade network. It is demonstrated that a trader’s ability to profit and to identify the equilibrium price is positively correlated with its degree of connectivity within the market. Where traders differ in their number of potential trading partners, well-connected traders are found to benefit from aggressive trading behaviour.Where information propagation is constrained by the topology of the trade network, connectedness affects the nature of the strategies employed

Properties of the random field Ising model in a transverse magnetic field

We consider the effect of a random longitudinal field on the Ising model in a transverse magnetic field. For spatial dimension $d > 2$, there is at low strength of randomness and transverse field, a phase with true long range order which is destroyed at higher values of the randomness or transverse field. The properties of the quantum phase transition at zero temperature are controlled by a fixed point with no quantum fluctuations. This fixed point also controls the classical finite temperature phase transition in this model. Many critical properties of the quantum transition are therefore identical to those of the classical transition. In particular, we argue that the dynamical scaling is activated, i.e, the logarithm of the diverging time scale rises as a power of the diverging length scale

Cosolvent flushing for the remediation of PAHs from former manufactured gas plants

Cosolvent flushing is a technique that has been proposed for the removal of hydrophobic organic contaminants in the subsurface. Cosolvents have been shown to dramatically increase the solubility of such compounds compared to the aqueous solubility; however, limited data are available on the effectiveness of cosolvents for field-contaminated media. In this work, we examine cosolvent flushing for the removal of polycyclic aromatic hydrocarbons (PAHs) in soil from a former manufactured gas plant (FMGP). Batch studies confirmed that the relationship between the soil-cosolvent partitioning coefficient (Ki) and the volume fraction of cosolvent (fc) followed a standard log-linear equation. Using methanol at an fc of 0.95, column studies were conducted at varying length scales, ranging from 11.9 to 110 cm. Removal of PAH compounds was determined as a function of pore volumes (PVs) of cosolvent flushed. Despite using a high fc, rate and chromatographic effects were observed in all the columns. PAH effluent concentrations were modeled using a common two-site sorption model. Model fits were improved by using MeOH breakthrough curves to determine fitted dispersion coefficients. Fitted mass-transfer rates were two to three orders of magnitude lower than predicted values based on published data using artificially contaminated sands

Mean first-passage time for random walks on undirected networks

In this paper, by using two different techniques we derive an explicit formula for the mean first-passage time (MFPT) between any pair of nodes on a general undirected network, which is expressed in terms of eigenvalues and eigenvectors of an associated matrix similar to the transition matrix. We then apply the formula to derive a lower bound for the MFPT to arrive at a given node with the starting point chosen from the stationary distribution over the set of nodes. We show that for a correlated scale-free network of size $N$ with a degree distribution $P(d)\sim d^{-\gamma}$, the scaling of the lower bound is $N^{1-1/\gamma}$. Also, we provide a simple derivation for an eigentime identity. Our work leads to a comprehensive understanding of recent results about random walks on complex networks, especially on scale-free networks.Comment: 7 pages, no figures; definitive version published in European Physical Journal

General Requirements on Matter Power Spectrum Predictions for Cosmology with Weak Lensing Tomography

Forthcoming projects such as DES, LSST, WFIRST, and Euclid aim to measure weak lensing shear correlations with unprecedented precision, constraining the dark energy equation of state at the percent level. Reliance on photometrically-determined redshifts constitutes a major source of uncertainty for these surveys. Additionally, interpreting the weak lensing signal requires a detailed understanding of the nonlinear physics of gravitational collapse. We present a new analysis of the stringent calibration requirements for weak lensing analyses of future imaging surveys that addresses both photo-z uncertainty and errors in the calibration of the matter power spectrum. We find that when photo-z uncertainty is taken into account the requirements on the level of precision in the prediction for the matter power spectrum are more stringent than previously thought. Including degree-scale galaxy clustering statistics in a joint analysis with weak lensing not only strengthens the survey's constraining power by ~20%, but can also have a profound impact on the calibration demands, decreasing the degradation in dark energy constraints with matter power spectrum uncertainty by a factor of 2-5. Similarly, using galaxy clustering information significantly relaxes the demands on photo-z calibration. We compare these calibration requirements to the contemporary state-of-the-art in photometric redshift estimation and predictions of the power spectrum and suggest strategies to utilize forthcoming data optimally.Comment: 3 new figures; new section added on multipole-dependence of calibration requirements; references added; version accepted by JCA

Critical exponents and equation of state of the three-dimensional Heisenberg universality class

We improve the theoretical estimates of the critical exponents for the three-dimensional Heisenberg universality class. We find gamma=1.3960(9), nu=0.7112(5), eta=0.0375(5), alpha=-0.1336(15), beta=0.3689(3), and delta=4.783(3). We consider an improved lattice phi^4 Hamiltonian with suppressed leading scaling corrections. Our results are obtained by combining Monte Carlo simulations based on finite-size scaling methods and high-temperature expansions. The critical exponents are computed from high-temperature expansions specialized to the phi^4 improved model. By the same technique we determine the coefficients of the small-magnetization expansion of the equation of state. This expansion is extended analytically by means of approximate parametric representations, obtaining the equation of state in the whole critical region. We also determine a number of universal amplitude ratios.Comment: 40 pages, final version. In publication in Phys. Rev.

The role of the European Society of Human Genetics in delivering genomic education

The European Society of Human Genetics (ESHG) was founded in 1967 as a professional organisation for members working in genetics in clinical practice, research and education. The Society seeks the integration of scientific research and its implementation into clinical practice and the education of specialists and the public in all areas of medical and human genetics. The Society works to do this through many approaches, including educational sessions at the annual conference; training courses in general and specialist areas of genetics; an online resource of educational materials (EuroGEMS); and a mentorship scheme. The ESHG Education Committee is implementing new approaches to expand the reach of its educational activities and portfolio. With changes in technology, appreciation of the utility of genomics in healthcare and the public's and patients' increased awareness of the role of genomics, this review will summarise how the ESHG is adapting to deliver innovative educational activity.Molecular Technology and Informatics for Personalised Medicine and Healt