Non-equilibrium mean-field theories on scale-free networks

Many non-equilibrium processes on scale-free networks present anomalous critical behavior that is not explained by standard mean-field theories. We propose a systematic method to derive stochastic equations for mean-field order parameters that implicitly account for the degree heterogeneity. The method is used to correctly predict the dynamical critical behavior of some binary spin models and reaction-diffusion processes. The validity of our non-equilibrium theory is furtherly supported by showing its relation with the generalized Landau theory of equilibrium critical phenomena on networks.Comment: 4 pages, no figures, major changes in the structure of the pape

Solution of the 2-star model of a network

The p-star model or exponential random graph is among the oldest and best-known of network models. Here we give an analytic solution for the particular case of the 2-star model, which is one of the most fundamental of exponential random graphs. We derive expressions for a number of quantities of interest in the model and show that the degenerate region of the parameter space observed in computer simulations is a spontaneously symmetry broken phase separated from the normal phase of the model by a conventional continuous phase transition.Comment: 5 pages, 3 figure

Percolation in invariant Poisson graphs with i.i.d. degrees

Let each point of a homogeneous Poisson process in R^d independently be equipped with a random number of stubs (half-edges) according to a given probability distribution mu on the positive integers. We consider translation-invariant schemes for perfectly matching the stubs to obtain a simple graph with degree distribution mu. Leaving aside degenerate cases, we prove that for any mu there exist schemes that give only finite components as well as schemes that give infinite components. For a particular matching scheme that is a natural extension of Gale-Shapley stable marriage, we give sufficient conditions on mu for the absence and presence of infinite components

Dynamic ploidy changes drive fluconazole resistance in human cryptococcal meningitis.

BACKGROUND: Cryptococcal meningitis (CM) causes an estimated 180,000 deaths annually, predominantly in sub-Saharan Africa, where most patients receive fluconazole (FLC) monotherapy. While relapse after FLC monotherapy with resistant strains is frequently observed, the mechanisms and impact of emergence of FLC resistance in human CM are poorly understood. Heteroresistance (HetR) - a resistant subpopulation within a susceptible strain - is a recently described phenomenon in Cryptococcus neoformans (Cn) and Cryptococcus gattii (Cg), the significance of which has not previously been studied in humans. METHODS: A cohort of 20 patients with HIV-associated CM in Tanzania was prospectively observed during therapy with either FLC monotherapy or in combination with flucytosine (5FC). Total and resistant subpopulations of Cryptococcus spp. were quantified directly from patient cerebrospinal fluid (CSF). Stored isolates underwent whole genome sequencing and phenotypic characterization. RESULTS: Heteroresistance was detectable in Cryptococcus spp. in the CSF of all patients at baseline (i.e., prior to initiation of therapy). During FLC monotherapy, the proportion of resistant colonies in the CSF increased during the first 2 weeks of treatment. In contrast, no resistant subpopulation was detectable in CSF by day 14 in those receiving a combination of FLC and 5FC. Genomic analysis revealed high rates of aneuploidy in heteroresistant colonies as well as in relapse isolates, with chromosome 1 (Chr1) disomy predominating. This is apparently due to the presence on Chr1 of ERG11, which is the FLC drug target, and AFR1, which encodes a drug efflux pump. In vitro efflux levels positively correlated with the level of heteroresistance. CONCLUSION: Our findings demonstrate for what we believe is the first time the presence and emergence of aneuploidy-driven FLC heteroresistance in human CM, association of efflux levels with heteroresistance, and the successful suppression of heteroresistance with 5FC/FLC combination therapy. FUNDING: This work was supported by the Wellcome Trust Strategic Award for Medical Mycology and Fungal Immunology 097377/Z/11/Z and the Daniel Turnberg Travel Fellowship

The Donegal Mackerel Fishery

Irish Mackerel landings have increased dramatically, from less than 2,000 tonnes in 1970 to nearly 30,000 tonnes in 1978. The development of this fishery can be ensured only if a satisfactory management plan is drawn up. To provide the basis for such a plan a major investigation of the Donegal stocks was launched by the Department of Fisheries in 1978 and will continue for some years. At the same time the fishery scientists of other countries are studying other parts of the same mackerel stock and their results are discussed at an annual meeting in Copenhagen. These results are the basis for the total allowable catch imposed by the EEC

Statistical ensemble of scale-free random graphs

A thorough discussion of the statistical ensemble of scale-free connected random tree graphs is presented. Methods borrowed from field theory are used to define the ensemble and to study analytically its properties. The ensemble is characterized by two global parameters, the fractal and the spectral dimensions, which are explicitly calculated. It is discussed in detail how the geometry of the graphs varies when the weights of the nodes are modified. The stability of the scale-free regime is also considered: when it breaks down, either a scale is spontaneously generated or else, a "singular" node appears and the graphs become crumpled. A new computer algorithm to generate these random graphs is proposed. Possible generalizations are also discussed. In particular, more general ensembles are defined along the same lines and the computer algorithm is extended to arbitrary (degenerate) scale-free random graphs.Comment: 10 pages, 6 eps figures, 2-column revtex format, minor correction

The structure of typical clusters in large sparse random configurations

The initial purpose of this work is to provide a probabilistic explanation of a recent result on a version of Smoluchowski's coagulation equations in which the number of aggregations is limited. The latter models the deterministic evolution of concentrations of particles in a medium where particles coalesce pairwise as time passes and each particle can only perform a given number of aggregations. Under appropriate assumptions, the concentrations of particles converge as time tends to infinity to some measure which bears a striking resemblance with the distribution of the total population of a Galton-Watson process started from two ancestors. Roughly speaking, the configuration model is a stochastic construction which aims at producing a typical graph on a set of vertices with pre-described degrees. Specifically, one attaches to each vertex a certain number of stubs, and then join pairwise the stubs uniformly at random to create edges between vertices. In this work, we use the configuration model as the stochastic counterpart of Smoluchowski's coagulation equations with limited aggregations. We establish a hydrodynamical type limit theorem for the empirical measure of the shapes of clusters in the configuration model when the number of vertices tends to $\infty$. The limit is given in terms of the distribution of a Galton-Watson process started with two ancestors

Effect of jet exit vanes on flow pulsations in an open-jet wind tunnel

An investigation was conducted of various jet exit vane configurations in the open test section of the Langley 4- by 7-Meter Tunnel to determine their effectiveness in reducing flow pulsations. The data consist of the instantaneous velocity fluctuations measured with hot-wire anemometers located at the tunnel centerline, 39.5 ft (12.0) downstream of the jet exit. The data are presented in the form of measured root-mean-square turbulence levels in the test section and a time series analysis for the baseline jet exit configuration (without vanes) and forthe most effective vane configuration, which consisted of triangular vanes alternating into and out of the flow around the jet exit

Exact Solution for the Time Evolution of Network Rewiring Models

We consider the rewiring of a bipartite graph using a mixture of random and preferential attachment. The full mean field equations for the degree distribution and its generating function are given. The exact solution of these equations for all finite parameter values at any time is found in terms of standard functions. It is demonstrated that these solutions are an excellent fit to numerical simulations of the model. We discuss the relationship between our model and several others in the literature including examples of Urn, Backgammon, and Balls-in-Boxes models, the Watts and Strogatz rewiring problem and some models of zero range processes. Our model is also equivalent to those used in various applications including cultural transmission, family name and gene frequencies, glasses, and wealth distributions. Finally some Voter models and an example of a Minority game also show features described by our model.Comment: This version contains a few footnotes not in published Phys.Rev.E versio