Quantifying long-range correlations in complex networks beyond nearest neighbors

We propose a fluctuation analysis to quantify spatial correlations in complex networks. The approach considers the sequences of degrees along shortest paths in the networks and quantifies the fluctuations in analogy to time series. In this work, the Barabasi-Albert (BA) model, the Cayley tree at the percolation transition, a fractal network model, and examples of real-world networks are studied. While the fluctuation functions for the BA model show exponential decay, in the case of the Cayley tree and the fractal network model the fluctuation functions display a power-law behavior. The fractal network model comprises long-range anti-correlations. The results suggest that the fluctuation exponent provides complementary information to the fractal dimension

Dynamic Critical approach to Self-Organized Criticality

A dynamic scaling Ansatz for the approach to the Self-Organized Critical (SOC) regime is proposed and tested by means of extensive simulations applied to the Bak-Sneppen model (BS), which exhibits robust SOC behavior. Considering the short-time scaling behavior of the density of sites ($\rho(t)$) below the critical value, it is shown that i) starting the dynamics with configurations such that $\rho(t=0) \to 0$ one observes an {\it initial increase} of the density with exponent $\theta = 0.12(2)$; ii) using initial configurations with $\rho(t=0) \to 1$, the density decays with exponent $\delta = 0.47(2)$. It is also shown that he temporal autocorrelation decays with exponent $C_a = 0.35(2)$. Using these, dynamically determined, critical exponents and suitable scaling relationships, all known exponents of the BS model can be obtained, e.g. the dynamical exponent $z = 2.10(5)$, the mass dimension exponent $D = 2.42(5)$, and the exponent of all returns of the activity $\tau_{ALL} = 0.39(2)$, in excellent agreement with values already accepted and obtained within the SOC regime.Comment: Rapid Communication Physical Review E in press (4 pages, 5 figures

Irreversible phase transitions induced by an oscillatory input

A novel kind of irreversible phase transitions (IPT's) driven by an oscillatory input parameter is studied by means of computer simulations. Second order IPT's showing scale invariance in relevant dynamic critical properties are found to belong to the universality class of directed percolation. In contrast, the absence of universality is observed for first order IPT's.Comment: 18 pages (Revtex); 8 figures (.ps); submitted to Europhysics Letters, December 9th, 199

Vertex routing models

A class of models describing the flow of information within networks via routing processes is proposed and investigated, concentrating on the effects of memory traces on the global properties. The long-term flow of information is governed by cyclic attractors, allowing to define a measure for the information centrality of a vertex given by the number of attractors passing through this vertex. We find the number of vertices having a non-zero information centrality to be extensive/sub-extensive for models with/without a memory trace in the thermodynamic limit. We evaluate the distribution of the number of cycles, of the cycle length and of the maximal basins of attraction, finding a complete scaling collapse in the thermodynamic limit for the latter. Possible implications of our results on the information flow in social networks are discussed.Comment: 12 pages, 6 figure

Crispr/cas9 editing for gaucher disease modelling

Gaucher disease (GD) is an autosomal recessive lysosomal storage disorder caused by mutations in the acid \u3b2-glucosidase gene (GBA1). Besides causing GD, GBA1 mutations constitute the main genetic risk factor for developing Parkinson\u2019s disease. The molecular basis of neurological manifestations in GD remain elusive. However, neuroinflammation has been proposed as a key player in this process. We exploited CRISPR/Cas9 technology to edit GBA1 in the human monocytic THP-1 cell line to develop an isogenic GD model of monocytes and in glioblastoma U87 cell lines to generate an isogenic GD model of glial cells. Both edited (GBA1 mutant) cell lines presented low levels of mutant acid \u3b2-glucosidase expression, less than 1% of residual activity and massive accumulation of substrate. Moreover, U87 GBA1 mutant cells showed that the mutant enzyme was retained in the ER and subjected to proteasomal degradation, triggering unfolded protein response (UPR). U87 GBA1 mutant cells displayed an increased production of interleukin-1\u3b2, both with and without inflammosome activation, \u3b1-syn accumulation and a higher rate of cell death in comparison with wild-type cells. In conclusion, we developed reliable, isogenic, and easy-to-handle cellular models of GD obtained from commercially accessible cells to be employed in GD pathophysiology studies and high-throughput drug screenings

Statistics of Cycles: How Loopy is your Network?

We study the distribution of cycles of length h in large networks (of size N>>1) and find it to be an excellent ergodic estimator, even in the extreme inhomogeneous case of scale-free networks. The distribution is sharply peaked around a characteristic cycle length, h* ~ N^a. Our results suggest that h* and the exponent a might usefully characterize broad families of networks. In addition to an exact counting of cycles in hierarchical nets, we present a Monte-Carlo sampling algorithm for approximately locating h* and reliably determining a. Our empirical results indicate that for small random scale-free nets of degree exponent g, a=1/(g-1), and a grows as the nets become larger.Comment: Further work presented and conclusions revised, following referee report

Portraits of Complex Networks

We propose a method for characterizing large complex networks by introducing a new matrix structure, unique for a given network, which encodes structural information; provides useful visualization, even for very large networks; and allows for rigorous statistical comparison between networks. Dynamic processes such as percolation can be visualized using animations. Applications to graph theory are discussed, as are generalizations to weighted networks, real-world network similarity testing, and applicability to the graph isomorphism problem.Comment: 6 pages, 9 figure

High incidence of autoantibodies in Fabry disease patients

Fabry disease (FD) is an X-linked disorder of glycosphingolipid catabolism that results from a deficiency of the lysosomal enzyme α-galactosidase A. This defect leads to the accumulation of its substrates, mainly globotriaosylceramide, in lysosomes of cells of different tissues. Different studies have shown the involvement of immunopathologies in different sphingolipidoses. The coexistence of FD and immune disorders such as systemic lupus erythematosus, rheumatoid arthritis and IgA nephropathy, has been described in the literature. The aim of this study was to evaluate the prevalence of a group of autoantibodies in a series of Argentine FD patients. Autoantibodies against extractable nuclear antigens (ENAs), double-stranded DNA, anticardiolipin and phosphatidylserine were assayed by ELISA. Lupus anticoagulants were also tested. Fifty-seven per cent of the samples showed reactivity with at least one autoantigen. Such reactivities were more frequent among males than among females. Antiphospholipid autoantibodies were detected in 45% of our patients. The high rate of thrombosis associated with FD could be related, at least in part, to the presence of antiphospholipid autoantibodies in Fabry patients. We found the presence of ENAs, which are a characteristic finding of rheumatological diseases, previous a frequent misdiagnosis of FD, in around 39% of the cases. The detection of a high level of autoantibodies must be correlated clinically to determine the existence of an underlying autoimmune disease. With the recent development of therapy, the life expectancy in FD will increase and autoimmune diseases might play an important role in the morbidity of FD.Facultad de Ciencias ExactasLaboratorio de Investigaciones del Sistema Inmun

Anomalous behavior of trapping on a fractal scale-free network

It is known that the heterogeneity of scale-free networks helps enhancing the efficiency of trapping processes performed on them. In this paper, we show that transport efficiency is much lower in a fractal scale-free network than in non-fractal networks. To this end, we examine a simple random walk with a fixed trap at a given position on a fractal scale-free network. We calculate analytically the mean first-passage time (MFPT) as a measure of the efficiency for the trapping process, and obtain a closed-form expression for MFPT, which agrees with direct numerical calculations. We find that, in the limit of a large network order $V$, the MFPT $$ behaves superlinearly as $\sim V^{{3/2}}$ with an exponent 3/2 much larger than 1, which is in sharp contrast to the scaling $\sim V^{\theta}$ with $\theta \leq 1$, previously obtained for non-fractal scale-free networks. Our results indicate that the degree distribution of scale-free networks is not sufficient to characterize trapping processes taking place on them. Since various real-world networks are simultaneously scale-free and fractal, our results may shed light on the understanding of trapping processes running on real-life systems.Comment: 6 pages, 5 figures; Definitive version accepted for publication in EPL (Europhysics Letters

High Dimensional Apollonian Networks

We propose a simple algorithm which produces high dimensional Apollonian networks with both small-world and scale-free characteristics. We derive analytical expressions for the degree distribution, the clustering coefficient and the diameter of the networks, which are determined by their dimension