3,911,690 research outputs found

    A record-driven growth process

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    We introduce a novel stochastic growth process, the record-driven growth process, which originates from the analysis of a class of growing networks in a universal limiting regime. Nodes are added one by one to a network, each node possessing a quality. The new incoming node connects to the preexisting node with best quality, that is, with record value for the quality. The emergent structure is that of a growing network, where groups are formed around record nodes (nodes endowed with the best intrinsic qualities). Special emphasis is put on the statistics of leaders (nodes whose degrees are the largest). The asymptotic probability for a node to be a leader is equal to the Golomb-Dickman constant omega=0.624329... which arises in problems of combinatorical nature. This outcome solves the problem of the determination of the record breaking rate for the sequence of correlated inter-record intervals. The process exhibits temporal self-similarity in the late-time regime. Connections with the statistics of the cycles of random permutations, the statistical properties of randomly broken intervals, and the Kesten variable are given.Comment: 30 pages,5 figures. Minor update

    The branching process with logistic growth

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    In order to model random density-dependence in population dynamics, we construct the random analogue of the well-known logistic process in the branching process' framework. This density-dependence corresponds to intraspecific competition pressure, which is ubiquitous in ecology, and translates mathematically into a quadratic death rate. The logistic branching process, or LB-process, can thus be seen as (the mass of) a fragmentation process (corresponding to the branching mechanism) combined with constant coagulation rate (the death rate is proportional to the number of possible coalescing pairs). In the continuous state-space setting, the LB-process is a time-changed (in Lamperti's fashion) Ornstein-Uhlenbeck type process. We obtain similar results for both constructions: when natural deaths do not occur, the LB-process converges to a specified distribution; otherwise, it goes extinct a.s. In the latter case, we provide the expectation and the Laplace transform of the absorption time, as a functional of the solution of a Riccati differential equation. We also show that the quadratic regulatory term allows the LB-process to start at infinity, despite the fact that births occur infinitely often as the initial state goes to \infty. This result can be viewed as an extension of the pure-death process starting from infinity associated to Kingman's coalescent, when some independent fragmentation is added.Comment: Published at http://dx.doi.org/10.1214/105051605000000098 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

    Obtaining Communities with a Fitness Growth Process

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    The study of community structure has been a hot topic of research over the last years. But, while successfully applied in several areas, the concept lacks of a general and precise notion. Facts like the hierarchical structure and heterogeneity of complex networks make it difficult to unify the idea of community and its evaluation. The global functional known as modularity is probably the most used technique in this area. Nevertheless, its limits have been deeply studied. Local techniques as the ones by Lancichinetti et al. and Palla et al. arose as an answer to the resolution limit and degeneracies that modularity has. Here we start from the algorithm by Lancichinetti et al. and propose a unique growth process for a fitness function that, while being local, finds a community partition that covers the whole network, updating the scale parameter dynamically. We test the quality of our results by using a set of benchmarks of heterogeneous graphs. We discuss alternative measures for evaluating the community structure and, in the light of them, infer possible explanations for the better performance of local methods compared to global ones in these cases

    Coarsening process in one-dimensional surface growth models

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    Surface growth models may give rise to unstable growth with mound formation whose tipical linear size L increases in time. In one dimensional systems coarsening is generally driven by an attractive interaction between domain walls or kinks. This picture applies to growth models for which the largest surface slope remains constant in time (model B): coarsening is known to be logarithmic in the absence of noise (L(t)=log t) and to follow a power law (L(t)=t^{1/3}) when noise is present. If surface slope increases indefinitely, the deterministic equation looks like a modified Cahn-Hilliard equation: here we study the late stage of coarsening through a linear stability analysis of the stationary periodic configurations and through a direct numerical integration. Analytical and numerical results agree with regard to the conclusion that steepening of mounds makes deterministic coarsening faster: if alpha is the exponent describing the steepening of the maximal slope M of mounds (M^alpha = L) we find that L(t)=t^n: n is equal to 1/4 for 1<alpha<2 and it decreases from 1/4 to 1/5 for alpha>2, according to n=alpha/(5*alpha -2). On the other side, the numerical solution of the corresponding stochastic equation clearly shows that in the presence of shot noise steepening of mounds makes coarsening slower than in model B: L(t)=t^{1/4}, irrespectively of alpha. Finally, the presence of a symmetry breaking term is shown not to modify the coarsening law of model alpha=1, both in the absence and in the presence of noise.Comment: One figure and relative discussion changed. To be published in Eur. Phys. J.

    Roughening Transition in a One-Dimensional Growth Process

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    A class of nonequilibrium models with short-range interactions and sequential updates is presented. The models describe one dimensional growth processes which display a roughening transition between a smooth and a rough phase. This transition is accompanied by spontaneous symmetry breaking, which is described by an order parameter whose dynamics is non-conserving. Some aspects of models in this class are related to directed percolation in 1+1 dimensions, although unlike directed percolation the models have no absorbing states. Scaling relations are derived and compared with Monte Carlo simulations.Comment: 4 pages, 3 Postscript figures, 1 Postscript formula, uses RevTe

    The random growth of interfaces as a subordinated process

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    We study the random growth of surfaces from within the perspective of a single column, namely, the fluctuation of the column height around the mean value, y(t)= h(t)-, which is depicted as being subordinated to a standard fluctuation-dissipation process with friction gamma. We argue that the main properties of Kardar-Parisi-Zhang theory, in one dimension, are derived by identifying the distribution of return times to y(0) = 0, which is a truncated inverse power law, with the distribution of subordination times. The agreement of the theoretical prediction with the numerical treatment of the 1 + 1 dimensional model of ballistic deposition is remarkably good, in spite of the finite size effects affecting this model.Comment: LaTeX, 4 pages, 3 figure

    A set-valued framework for birth-and-growth process

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    We propose a set-valued framework for the well-posedness of birth-and-growth process. Our birth-and-growth model is rigorously defined as a suitable combination, involving Minkowski sum and Aumann integral, of two very general set-valued processes representing nucleation and growth respectively. The simplicity of the used geometrical approach leads us to avoid problems arising by an analytical definition of the front growth such as boundary regularities. In this framework, growth is generally anisotropic and, according to a mesoscale point of view, it is not local, i.e. for a fixed time instant, growth is the same at each space point

    Do process innovations boost SMEs productivity growth?

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    In this paper we explore in depth the effect of process innovations on total factor productivity growth for small and medium enterprises (SMEs), taking into account the potential endogeneity problem that may be caused by self selection into these activities. First, we analyse whether the ex-ante most productive SMEs are those that start introducing process innovations; then, we test whether process innovations boost SMEs productivity growth using matching techniques to control for the possibility that selection into introducing process innovations may not be a random process. We use a sample of Spanish manufacturing SMEs for the period 1991-2002, drawn from the Encuesta sobre Estrategias Empresariales. Our results show that the introduction of process innovations by a first-time process innovator yields an extra productivity growth as compared to a non-process innovator, and that the life span of this extra productivity growth has an inverted U-shaped form. En este artículo se exploran los posibles efectos de la introducción de innovaciones de proceso en el crecimiento de la productividad de las pequeñas y medianas empresas (PYMES). Para ello se presta especial atención a la existencia de un problema de selección no aleatorio en la implementación de tales innovaciones. En primer lugar, se analiza si son aquellas empresas ex-ante más productivas las que introducen innovaciones de proceso. A continuación, se utilizan técnicas de matching para contrastar si la implementación de innovaciones de proceso acelera el crecimiento de la productividad de las PYMES. La utilización de técnicas de matching permite controlar la posible existencia de un proceso de selección no aleatorio en la implementación de innovaciones de proceso. El análisis empírico se lleva cabo usando una muestra de PYMES manufactureras españolas extraída de la Encuesta sobre Estrategias Empresariales. Nuestros resultados muestran que la implementación de innovaciones de proceso por parte de PYMES sin experiencia previa en la introducción de tales innovaciones, produce un crecimiento extra de la productividad de estas PYMES en comparación con el de aquellas PYMES que no implementan innovaciones de proceso. Adicionalmente, nuestros resultados sugieren la existencia de una relación en forma de U invertida entre el crecimiento extra de la productividad y el tiempo transcurrido desde la introducción de la innovación de proceso.innovaciones de proceso, PTF, dominancia estocástica, técnicas de matching. process innovations, TFP, stochastic dominance, matching techniques.
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