Evolution equation for a model of surface relaxation in complex networks

In this paper we derive analytically the evolution equation of the interface for a model of surface growth with relaxation to the minimum (SRM) in complex networks. We were inspired by the disagreement between the scaling results of the steady state of the fluctuations between the discrete SRM model and the Edward-Wilkinson process found in scale-free networks with degree distribution $P(k) \sim k^{-\lambda}$ for $\lambda <3$ [Pastore y Piontti {\it et al.}, Phys. Rev. E {\bf 76}, 046117 (2007)]. Even though for Euclidean lattices the evolution equation is linear, we find that in complex heterogeneous networks non-linear terms appear due to the heterogeneity and the lack of symmetry of the network; they produce a logarithmic divergency of the saturation roughness with the system size as found by Pastore y Piontti {\it et al.} for $\lambda <3$.Comment: 9 pages, 2 figure

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

Laplacian spectra of complex networks and random walks on them: Are scale-free architectures really important?

We study the Laplacian operator of an uncorrelated random network and, as an application, consider hopping processes (diffusion, random walks, signal propagation, etc.) on networks. We develop a strict approach to these problems. We derive an exact closed set of integral equations, which provide the averages of the Laplacian operator's resolvent. This enables us to describe the propagation of a signal and random walks on the network. We show that the determining parameter in this problem is the minimum degree $q_m$ of vertices in the network and that the high-degree part of the degree distribution is not that essential. The position of the lower edge of the Laplacian spectrum $\lambda_c$ appears to be the same as in the regular Bethe lattice with the coordination number $q_m$. Namely, $\lambda_c>0$ if $q_m>2$, and $\lambda_c=0$ if $q_m\leq2$. In both these cases the density of eigenvalues $\rho(\lambda)\to0$ as $\lambda\to\lambda_c+0$, but the limiting behaviors near $\lambda_c$ are very different. In terms of a distance from a starting vertex, the hopping propagator is a steady moving Gaussian, broadening with time. This picture qualitatively coincides with that for a regular Bethe lattice. Our analytical results include the spectral density $\rho(\lambda)$ near $\lambda_c$ and the long-time asymptotics of the autocorrelator and the propagator.Comment: 25 pages, 4 figure

Cortisol levels and history of depression in acute coronary syndrome patients

Background Depressed mood following an acute coronary syndrome (ACS) is a risk factor for future cardiac morbidity. Hypothalamic-pituitary-adrenal (HPA) axis dysregulation is associated with depression, and may be a process through which depressive symptoms influence later cardiac health. Additionally, a history of depression predicts depressive symptoms in the weeks following ACS. The purpose of this study was to determine whether a history of depression and/or current depression are associated with the HPA axis dysregulation following ACS. Method A total of 152 cardiac patients completed a structured diagnostic interview, a standardized depression questionnaire and a cortisol profile over the day, 3 weeks after an ACS. Cortisol was analysed using: the cortisol awakening response (CAR), total cortisol output estimated using the area under the curve method, and the slope of cortisol decline over the day. Results Total cortisol output was positively associated with history of depression, after adjustment for age, gender, marital status, ethnicity, smoking status, body mass index (BMI), Global Registry of Acute Cardiac Events (GRACE) risk score, days in hospital, medication with statins and antiplatelet compounds, and current depression score. Men with clinically diagnosed depression after ACS showed a blunted CAR, but the CAR was not related to a history of depression. Conclusions Patients with a history of depression showed increased total cortisol output, but this is unlikely to be responsible for associations between depression after ACS and later cardiac morbidity. However, the blunted CAR in patients with severe depression following ACS indicates that HPA dysregulation is presen

Emotional triggering and low socio-economic status as determinants of depression following acute coronary syndrome

Background The determinants of depression following acute coronary syndrome (ACS) are poorly understood. Triggering of ACS by emotional stress and low socio-economic status (SES) are predictors of adverse outcomes. We therefore investigated whether emotional triggering and low SES predict depression and anxiety following ACS. Method This prospective observational clinical cohort study involved 298 patients with clinically verified ACS. Emotional stress was assessed for the 2 h before symptom onset and compared with the equivalent period 24 h earlier using case-crossover methods. SES was defined by household income and education. Depression was measured with the Beck Depression Inventory and the Hamilton Rating Scale for Depression and anxiety with the Hospital Anxiety and Depression Scale 3 weeks after ACS and again at 6 and 12 months. Age, gender, ethnicity, marital status, the Global Registry of Acute Coronary Events risk score, duration of hospital stay and history of depression were included as covariates. Results Emotional stress during the 2-h hazard period was associated with increased risk of ACS (odds ratio 1.88, 95% confidence interval 1.01-3.61). Both low income and emotional triggering predicted depression and anxiety at 3 weeks and 6/12 months independently of covariates. The two factors interacted, with the greatest depression and anxiety in lower income patients who experienced acute emotional stress. Education was not related to depression. Conclusions Patients who experience acute emotional stress during their ACS and are lower SES as defined by current affluence and access to resources are particularly vulnerable to subsequent depression and anxiet

Diffusion-annihilation processes in complex networks

We present a detailed analytical study of the $A+A\to\emptyset$ diffusion-annihilation process in complex networks. By means of microscopic arguments, we derive a set of rate equations for the density of $A$ particles in vertices of a given degree, valid for any generic degree distribution, and which we solve for uncorrelated networks. For homogeneous networks (with bounded fluctuations), we recover the standard mean-field solution, i.e. a particle density decreasing as the inverse of time. For heterogeneous (scale-free networks) in the infinite network size limit, we obtain instead a density decreasing as a power-law, with an exponent depending on the degree distribution. We also analyze the role of finite size effects, showing that any finite scale-free network leads to the mean-field behavior, with a prefactor depending on the network size. We check our analytical predictions with extensive numerical simulations on homogeneous networks with Poisson degree distribution and scale-free networks with different degree exponents.Comment: 9 pages, 5 EPS figure

Diffusion-annihilation processes in complex networks

We present a detailed analytical study of the $A+A\to\emptyset$ diffusion-annihilation process in complex networks. By means of microscopic arguments, we derive a set of rate equations for the density of $A$ particles in vertices of a given degree, valid for any generic degree distribution, and which we solve for uncorrelated networks. For homogeneous networks (with bounded fluctuations), we recover the standard mean-field solution, i.e. a particle density decreasing as the inverse of time. For heterogeneous (scale-free networks) in the infinite network size limit, we obtain instead a density decreasing as a power-law, with an exponent depending on the degree distribution. We also analyze the role of finite size effects, showing that any finite scale-free network leads to the mean-field behavior, with a prefactor depending on the network size. We check our analytical predictions with extensive numerical simulations on homogeneous networks with Poisson degree distribution and scale-free networks with different degree exponents.Comment: 9 pages, 5 EPS figure

Kinetic growth walks on complex networks

Kinetically grown self-avoiding walks on various types of generalized random networks have been studied. Networks with short- and long-tailed degree distributions $P(k)$ were considered ($k$, degree or connectivity), including scale-free networks with $P(k) \sim k^{-\gamma}$. The long-range behaviour of self-avoiding walks on random networks is found to be determined by finite-size effects. The mean self-intersection length of non-reversal random walks, , scales as a power of the system size $N$: $ \sim N^{\beta}$, with an exponent $\beta = 0.5$ for short-tailed degree distributions and $\beta < 0.5$ for scale-free networks with $\gamma < 3$. The mean attrition length of kinetic growth walks, , scales as $\sim N^{\alpha}$, with an exponent $\alpha$ which depends on the lowest degree in the network. Results of approximate probabilistic calculations are supported by those derived from simulations of various kinds of networks. The efficiency of kinetic growth walks to explore networks is largely reduced by inhomogeneity in the degree distribution, as happens for scale-free networks.Comment: 10 pages, 8 figure

Hypergraph topological quantities for tagged social networks

Recent years have witnessed the emergence of a new class of social networks, that require us to move beyond previously employed representations of complex graph structures. A notable example is that of the folksonomy, an online process where users collaboratively employ tags to resources to impart structure to an otherwise undifferentiated database. In a recent paper[1] we proposed a mathematical model that represents these structures as tripartite hypergraphs and defined basic topological quantities of interest. In this paper we extend our model by defining additional quantities such as edge distributions, vertex similarity and correlations as well as clustering. We then empirically measure these quantities on two real life folksonomies, the popular online photo sharing site Flickr and the bookmarking site CiteULike. We find that these systems share similar qualitative features with the majority of complex networks that have been previously studied. We propose that the quantities and methodology described here can be used as a standard tool in measuring the structure of tagged networks.Comment: 8 pages, 9 figures, revte

Genomic epidemiology of Cryptococcus yeasts identifies adaptation to environmental niches underpinning infection across an African HIV/AIDS cohort

Emerging infections caused by fungi have become a widely recognized global phenomenon and are causing an increasing burden of disease. Genomic techniques are providing new insights into the structure of fungal populations, revealing hitherto undescribed fine-scale adaptations to environments and hosts that govern their emergence as infections. Cryptococcal meningitis is a neglected tropical disease that is responsible for a large proportion of AIDS-related deaths across Africa; however, the ecological determinants that underlie a patient's risk of infection remain largely unexplored. Here, we use genome sequencing and ecological genomics to decipher the evolutionary ecology of the aetiological agents of cryptococcal meningitis, Cryptococcus neoformans and Cryptococcus gattii, across the central African country of Zambia. We show that the occurrence of these two pathogens is differentially associated with biotic (macroecological) and abiotic (physical) factors across two key African ecoregions, Central Miombo woodlands and Zambezi Mopane woodlands. We show that speciation of Cryptococcus has resulted in adaptation to occupy different ecological niches, with C. neoformans found to occupy Zambezi Mopane woodlands and C. gattii primarily recovered from Central Miombo woodlands. Genome sequencing shows that C. neoformans causes 95% of human infections in this region, of which over three-quarters belonged to the globalized lineage VNI. We show that VNI infections are largely associated with urbanized populations in Zambia. Conversely, the majority of C. neoformans isolates recovered in the environment belong to the genetically diverse African-endemic lineage VNB, and we show hitherto unmapped levels of genomic diversity within this lineage. Our results reveal the complex evolutionary ecology that underpins the reservoirs of infection for this, and likely other, deadly pathogenic fungi