The process of irreversible nucleation in multilayer growth. I. Failure of the mean-field approach

The formation of stable dimers on top of terraces during epitaxial growth is investigated in detail. In this paper we focus on mean-field theory, the standard approach to study nucleation. Such theory is shown to be unsuitable for the present problem, because it is equivalent to considering adatoms as independent diffusing particles. This leads to an overestimate of the correct nucleation rate by a factor N, which has a direct physical meaning: in average, a visited lattice site is visited N times by a diffusing adatom. The dependence of N on the size of the terrace and on the strength of step-edge barriers is derived from well known results for random walks. The spatial distribution of nucleation events is shown to be different from the mean-field prediction, for the same physical reason. In the following paper we develop an exact treatment of the problem.Comment: 19 pages, 3 figures. To appear in Phys. Rev.

Multiscaling to Standard Scaling Crossover in the Bray-Humayun Model for Phase Ordering Kinetics

The Bray-Humayun model for phase ordering dynamics is solved numerically in one and two space dimensions with conserved and non conserved order parameter. The scaling properties are analysed in detail finding the crossover from multiscaling to standard scaling in the conserved case. Both in the nonconserved case and in the conserved case when standard scaling holds the novel feature of an exponential tail in the scaling function is found.Comment: 21 pages, 10 Postscript figure

Steady-State Dynamics of the Forest Fire Model on Complex Networks

Many sociological networks, as well as biological and technological ones, can be represented in terms of complex networks with a heterogeneous connectivity pattern. Dynamical processes taking place on top of them can be very much influenced by this topological fact. In this paper we consider a paradigmatic model of non-equilibrium dynamics, namely the forest fire model, whose relevance lies in its capacity to represent several epidemic processes in a general parametrization. We study the behavior of this model in complex networks by developing the corresponding heterogeneous mean-field theory and solving it in its steady state. We provide exact and approximate expressions for homogeneous networks and several instances of heterogeneous networks. A comparison of our analytical results with extensive numerical simulations allows to draw the region of the parameter space in which heterogeneous mean-field theory provides an accurate description of the dynamics, and enlights the limits of validity of the mean-field theory in situations where dynamical correlations become important.Comment: 13 pages, 9 figure

Personalized monitoring of electrical remodelling during atrial fibrillation progression via remote transmissions from implantable devices

Atrial electrical remodelling (AER) is a transitional period associated with the progression and long-term maintenance of atrial fibrillation (AF). We aimed to study the progression of AER in individual patients with implantable devices and AF episodes. Observational multicentre study (51 centres) including 4618 patients with implantable cardioverter-defibrillator and results þ/resynchronization therapy (ICD/CRT-D) and 352 patients (2 centres) with pacemakers (median follow-up: 3.4 years). Atrial activation rate (AAR) was quantified as the frequency of the dominant peak in the signal spectrum of AF episodes with atrial bipolar electrograms. Patients with complete progression of AER, from paroxysmal AF episodes to electrically remodelled persistent AF, were used to depict patient-specific AER slopes. A total of 34 712 AF tracings from 830 patients (87 with pacemakers) were suitable for the study. Complete progression of AER was documented in 216 patients (16 with pacemakers). Patients with persistent AF after completion of AER showed ∼30% faster AAR than patients with paroxysmal AF. The slope of AAR changes during AF progression revealed patient-specific patterns that correlated with the time-to-completion of AER (R = 0.85). Pacemaker patients were older than patients with ICD/CRT-Ds (78.3 vs. 67.2 year olds, respectively, P < 0.001) and had a shorter median time-to-completion of AER (24.9 vs. 93.5 days, respectively, P = 0.016). Remote transmissions in patients with ICD/CRT-D devices enabled the estimation of the time-to-completion of AER using the predicted slope of AAR changes from initiation to completion of electrical remodelling (R = 0.45). The AF progression shows patient-specific patterns of AER, which can be estimated using available remote-monitoring technology

Personalized monitoring of electrical remodelling during atrial fibrillation progression via remote transmissions from implantable devices

Aims: Atrial electrical remodelling (AER) is a transitional period associated with the progression and long-term maintenance of atrial fibrillation (AF). We aimed to study the progression of AER in individual patients with implantable devices and AF episodes. Methods and results: Observational multicentre study (51 centres) including 4618 patients with implantable cardioverter-defibrillator +/-resynchronization therapy (ICD/CRT-D) and 352 patients (2 centres) with pacemakers (median follow-up: 3.4 years). Atrial activation rate (AAR) was quantified as the frequency of the dominant peak in the signal spectrum of AF episodes with atrial bipolar electrograms. Patients with complete progression of AER, from paroxysmal AF episodes to electrically remodelled persistent AF, were used to depict patient-specific AER slopes. A total of 34 712 AF tracings from 830 patients (87 with pacemakers) were suitable for the study. Complete progression of AER was documented in 216 patients (16 with pacemakers). Patients with persistent AF after completion of AER showed ∼30% faster AAR than patients with paroxysmal AF. The slope of AAR changes during AF progression revealed patient-specific patterns that correlated with the time-to-completion of AER (R2 = 0.85). Pacemaker patients were older than patients with ICD/CRT-Ds (78.3 vs. 67.2 year olds, respectively, P < 0.001) and had a shorter median time-to-completion of AER (24.9 vs. 93.5 days, respectively, P = 0.016). Remote transmissions in patients with ICD/CRT-D devices enabled the estimation of the time-to-completion of AER using the predicted slope of AAR changes from initiation to completion of electrical remodelling (R2 = 0.45). Conclusion: The AF progression shows patient-specific patterns of AER, which can be estimated using available remote-monitoring technology

Majority versus minority dynamics: Phase transition in an interacting two-state spin system

We introduce a simple model of opinion dynamics in which binary-state agents evolve due to the influence of agents in a local neighborhood. In a single update step, a fixed-size group is defined and all agents in the group adopt the state of the local majority with probability p or that of the local minority with probability 1-p. For group size G=3, there is a phase transition at p_c=2/3 in all spatial dimensions. For p>p_c, the global majority quickly predominates, while for p<p_c, the system is driven to a mixed state in which the densities of agents in each state are equal. For p=p_c, the average magnetization (the difference in the density of agents in the two states) is conserved and the system obeys classical voter model dynamics. In one dimension and within a Kirkwood decoupling scheme, the final magnetization in a finite-length system has a non-trivial dependence on the initial magnetization for all p.ne.p_c, in agreement with numerical results. At p_c, the exact 2-spin correlation functions decay algebraically toward the value 1 and the system coarsens as in the classical voter model.Comment: 11 pages, 3 figures, revtex4 2-column format; minor revisions for publication in PR

A pseudo-spectral method for the Kardar-Parisi-Zhang equation

We discuss a numerical scheme to solve the continuum Kardar-Parisi-Zhang equation in generic spatial dimensions. It is based on a momentum-space discretization of the continuum equation and on a pseudo-spectral approximation of the non-linear term. The method is tested in (1+1)- and (2+1)- dimensions, where it is shown to reproduce the current most reliable estimates of the critical exponents based on Restricted Solid-on-Solid simulations. In particular it allows the computations of various correlation and structure functions with high degree of numerical accuracy. Some deficiencies which are common to all previously used finite-difference schemes are pointed out and the usefulness of the present approach in this respect is discussed.Comment: 12 pages, 13 .eps figures, revetx4. A few equations have been corrected. Erratum sent to Phys. Rev.

A stochastic evolutionary model generating a mixture of exponential distributions

Recent interest in human dynamics has stimulated the investigation of the stochastic processes that explain human behaviour in various contexts, such as mobile phone networks and social media. In this paper, we extend the stochastic urn-based model proposed in \cite{FENN15} so that it can generate mixture models, in particular, a mixture of exponential distributions. The model is designed to capture the dynamics of survival analysis, traditionally employed in clinical trials, reliability analysis in engineering, and more recently in the analysis of large data sets recording human dynamics. The mixture modelling approach, which is relatively simple and well understood, is very effective in capturing heterogeneity in data. We provide empirical evidence for the validity of the model, using a data set of popular search engine queries collected over a period of 114 months. We show that the survival function of these queries is closely matched by the exponential mixture solution for our model

The Drosophila melanogaster Genetic Reference Panel

A major challenge of biology is understanding the relationship between molecular genetic variation and variation in quantitative traits, including fitness. This relationship determines our ability to predict phenotypes from genotypes and to understand how evolutionary forces shape variation within and between species. Previous efforts to dissect the genotype-phenotype map were based on incomplete genotypic information. Here, we describe the Drosophila melanogaster Genetic Reference Panel (DGRP), a community resource for analysis of population genomics and quantitative traits. The DGRP consists of fully sequenced inbred lines derived from a natural population. Population genomic analyses reveal reduced polymorphism in centromeric autosomal regions and the X chromosome, evidence for positive and negative selection, and rapid evolution of the X chromosome. Many variants in novel genes, most at low frequency, are associated with quantitative traits and explain a large fraction of the phenotypic variance. The DGRP facilitates genotype-phenotype mapping using the power of Drosophila genetics

Genome-Wide Meta-Analysis Identifies Variants in DSCAM and PDLIM3 that correlate with efficacy outcomes in metastatic renal cell carcinoma patients treated with sunitinib

Individual response to sunitinib in metastatic renal cell carcinoma (mRCC) patients is highly variable. Earlier, sunitinib outcome was related to single nucleotide polymorphisms (SNPs) in CYP3A5 and ABCB1. Our aim is to provide novel insights into biological mechanisms underlying sunitinib action. We included mRCC patients from the European EuroTARGET consortium (n = 550) and the RIKEN cohort in Japan (n = 204) which were analysed separately and in a meta-analysis of genome-wide association studies (GWAS). SNPs were tested for association with progression-free survival (PFS) and overall survival (OS) using Cox regression. Summary statistics were combined using a fixed effect meta-analysis. SNP rs28520013 in PDLIM3 and the correlated SNPs rs2205096 and rs111356738 both in DSCAM, showed genome-wide significance (p Personalised Therapeutic