Properties of Random Graphs with Hidden Color

We investigate in some detail a recently suggested general class of ensembles of sparse undirected random graphs based on a hidden stub-coloring, with or without the restriction to nondegenerate graphs. The calculability of local and global structural properties of graphs from the resulting ensembles is demonstrated. Cluster size statistics are derived with generating function techniques, yielding a well-defined percolation threshold. Explicit rules are derived for the enumeration of small subgraphs. Duality and redundancy is discussed, and subclasses corresponding to commonly studied models are identified.Comment: 14 pages, LaTeX, no figure

Correlations in Scale-Free Networks: Tomography and Percolation

We discuss three related models of scale-free networks with the same degree distribution but different correlation properties. Starting from the Barabasi-Albert construction based on growth and preferential attachment we discuss two other networks emerging when randomizing it with respect to links or nodes. We point out that the Barabasi-Albert model displays dissortative behavior with respect to the nodes' degrees, while the node-randomized network shows assortative mixing. These kinds of correlations are visualized by discussig the shell structure of the networks around their arbitrary node. In spite of different correlation behavior, all three constructions exhibit similar percolation properties.Comment: 6 pages, 2 figures; added reference

Universality in percolation of arbitrary Uncorrelated Nested Subgraphs

The study of percolation in so-called {\em nested subgraphs} implies a generalization of the concept of percolation since the results are not linked to specific graph process. Here the behavior of such graphs at criticallity is studied for the case where the nesting operation is performed in an uncorrelated way. Specifically, I provide an analyitic derivation for the percolation inequality showing that the cluster size distribution under a generalized process of uncorrelated nesting at criticality follows a power law with universal exponent $\gamma=3/2$. The relevance of the result comes from the wide variety of processes responsible for the emergence of the giant component that fall within the category of nesting operations, whose outcome is a family of nested subgraphs.Comment: 5 pages, no figures. Mistakes found in early manuscript have been remove

CO oxidation activity of Pt/CeO2 catalysts below 0ºC: Platinum loading effects

Reducing the operating temperature of oxidation catalysts is important for designing energy efficient processes, extending catalyst lifetime, and abating pollutants, especially in cold climates. Herein, high CO oxidation activity at sub-ambient temperatures is reported for Pt/CeO2 catalysts with high content of Pt in the form of dispersed Pt2+ and Pt4+ centers. Whereas the reference 1 wt%Pt catalyst was active for CO oxidation only above 100ᵒC, the 8 and 20 wt%Pt catalysts converted 60 and 90 % of CO, respectively, below 0ᵒC. Ionic platinum was shown to facilitate oxygen release from ceria and lower the light-off temperature of the reaction occurring through the Mars-van-Krevelen mechanism. However, the remarkable activity observed at sub-ambient temperatures for the ≥8 wt%Pt catalysts is proposed to involve O2 and CO reactants weakly adsorbed on PtOx clusters. The synergies between ionic platinum and nanostructured ceria reported in this work advance the knowledge-driven design of catalysts for low-temperature oxidation reactions

The spread of epidemic disease on networks

The study of social networks, and in particular the spread of disease on networks, has attracted considerable recent attention in the physics community. In this paper, we show that a large class of standard epidemiological models, the so-called susceptible/infective/removed (SIR) models can be solved exactly on a wide variety of networks. In addition to the standard but unrealistic case of fixed infectiveness time and fixed and uncorrelated probability of transmission between all pairs of individuals, we solve cases in which times and probabilities are non-uniform and correlated. We also consider one simple case of an epidemic in a structured population, that of a sexually transmitted disease in a population divided into men and women. We confirm the correctness of our exact solutions with numerical simulations of SIR epidemics on networks.Comment: 12 pages, 3 figure

First-line palliative HER2-targeted therapy in HER2-positive metastatic breast cancer is less effective after previous adjuvant trastuzumab-based therapy

Background. Survival of patients with human epidermal growth receptor 2 (HER2)-positive metastatic breast cancer (MBC) has improved dramatically since trastuzumab has become available, although the disease eventually progresses in most patients. This study investigates the outcome (overall survival [OS] and time to next treatment [TNT]) in MBC patients pretreated with trastuzumab in the adjuvant setting (TP-group) compared with trastuzumab-näive patients (TN-group) in order to investigate the possibility of trastuzumab resistance. Patients and Methods. Patients treated with first-line HER2-targeted- containing chemotherapy were eligible for the study. A power analysis was performed to estimate the minimum size of the TP-group. OS and TNT were estimated using Kaplan-Meier curves andmultivariable Cox proportional hazards models. Results. Between January 1, 2000, and June 1, 2014, 469 patients were included, of whom 82 were in the TP-group and 387 were in the TN-group. Median OS and TNT were significantly worse in the TP-group compared with the TN-group (17 vs. 30 months, adjusted hazard ratio [HR] 1.84 [1.15-2.96], p5.01 and 7 vs. 13 months, adjusted HR 1.65 [1.06-2.58], p5.03) after adjustment for age, year of diagnosis, diseasefree interval, hormone receptor status, metastatic site, and cytotoxic regimens. Conclusion. First-line trastuzumab-containing treatment regimens are less effective in patients with failure of adjuvant trastuzumab compared with trastuzumab-näive patients and might be due to trastuzumab resistance. The impact of trastuzumab resistance on the response on dual HER2 blockade with trastuzumab and pertuzumab and how resistance mechanisms can be used in the optimization of HER2-targeted treatment lines need further investigation.</p

Generating correlated networks from uncorrelated ones

In this paper we consider a transformation which converts uncorrelated networks to correlated ones(here by correlation we mean that coordination numbers of two neighbors are not independent). We show that this transformation, which converts edges to nodes and connects them according to a deterministic rule, nearly preserves the degree distribution of the network and significantly increases the clustering coefficient. This transformation also enables us to relate percolation properties of the two networks.Comment: 14 pages, 6 figures, Revtex

Spectra of complex networks

We propose a general approach to the description of spectra of complex networks. For the spectra of networks with uncorrelated vertices (and a local tree-like structure), exact equations are derived. These equations are generalized to the case of networks with correlations between neighboring vertices. The tail of the density of eigenvalues $\rho(\lambda)$ at large $|\lambda|$ is related to the behavior of the vertex degree distribution $P(k)$ at large $k$. In particular, as $P(k) \sim k^{-\gamma}$, $\rho(\lambda) \sim |\lambda|^{1-2\gamma}$. We propose a simple approximation, which enables us to calculate spectra of various graphs analytically. We analyse spectra of various complex networks and discuss the role of vertices of low degree. We show that spectra of locally tree-like random graphs may serve as a starting point in the analysis of spectral properties of real-world networks, e.g., of the Internet.Comment: 10 pages, 4 figure

Magnetic fields in cosmic particle acceleration sources

We review here some magnetic phenomena in astrophysical particle accelerators associated with collisionless shocks in supernova remnants, radio galaxies and clusters of galaxies. A specific feature is that the accelerated particles can play an important role in magnetic field evolution in the objects. We discuss a number of CR-driven, magnetic field amplification processes that are likely to operate when diffusive shock acceleration (DSA) becomes efficient and nonlinear. The turbulent magnetic fields produced by these processes determine the maximum energies of accelerated particles and result in specific features in the observed photon radiation of the sources. Equally important, magnetic field amplification by the CR currents and pressure anisotropies may affect the shocked gas temperatures and compression, both in the shock precursor and in the downstream flow, if the shock is an efficient CR accelerator. Strong fluctuations of the magnetic field on scales above the radiation formation length in the shock vicinity result in intermittent structures observable in synchrotron emission images. Resonant and non-resonant CR streaming instabilities in the shock precursor can generate mesoscale magnetic fields with scale-sizes comparable to supernova remnants and even superbubbles. This opens the possibility that magnetic fields in the earliest galaxies were produced by the first generation Population III supernova remnants and by clustered supernovae in star forming regions.Comment: 30 pages, Space Science Review

Mesoscopics and fluctuations in networks

We describe fluctuations in finite-size networks with a complex distribution of connections, $P(k)$. We show that the spectrum of fluctuations of the number of vertices with a given degree is Poissonian. These mesoscopic fluctuations are strong in the large-degree region, where $P(k) \lesssim 1/N$ ($N$ is the total number of vertices in a network), and are important in networks with fat-tailed degree distributions.Comment: 3 pages, 1 figur