相关论文: Growth fluctuation in preferential attachment dyna…

Of basic interest is the quantification of the long term growth of a language's lexicon as it develops to more completely cover both a culture's communication requirements and knowledge space. Here, we explore the usage dynamics of words in…

We study the population profile in a simple discrete time model of population dynamics. Our model, which is closely related to certain ``bit-string'' models of evolution, incorporates competition for resources via a population dependent…

In this work, it is pointed out that in the mean-field version of majority-rule opinion dynamics, the dependence of the consensus time on the population size exhibits two regimes. This is determined by the size distribution of the groups…

Eliciting a high-dimensional probability distribution from an expert via noisy judgments is notoriously challenging, yet useful for many applications, such as prior elicitation and reward modeling. We introduce a method for eliciting the…

The Pitman-Yor process is a random discrete measure. The random weights or masses follow the two-parameter Poisson-Dirichlet distribution with parameters $0<\alpha<1, \theta>-\alpha$. The parameters $\alpha$ and $\theta$ correspond to the…

We investigate the limiting behavior of random tree growth in preferential attachment models. The tree stems from a root, and we add vertices to the system one-by-one at random, according to a rule which depends on the degree distribution…

We show that to explain the growth of the citation network by preferential attachment (PA), one has to accept that individual nodes exhibit heterogeneous fitness values that decay with time. While previous PA-based models assumed either…

Fluctuations of cell state, e.g., abundances of some proteins, have attracted much attention both theoretically and experimentally. The distribution of such state over cells, however, is not only a result of intracellular stochastic…

We consider a component of the word statistics known as clump; starting from a finite set of words, clumps are maximal overlapping sets of these occurrences. This parameter has first been studied by Schbath with the aim of counting the…

It is generally believed that, when a linguistic item acquires a new meaning, its overall frequency of use in the language rises with time with an S-shaped growth curve. Yet, this claim has only been supported by a limited number of case…

We investigate the process of fixation of advantageous mutations in an asexual population. We assume that the effect of each beneficial mutation is exponentially distributed with mean value $\omega_{med}=1/\beta$. The model also considers…

In population genetics, diffusions on the unit interval are often used to model the frequency path of an allele. In this setting we derive approximations for fixation probabilities, expected hitting times and the expected…

This article is a presentation of specific recent results describing scaling limits of individual-based models. Thanks to them, we wish to relate the time-scales typical of demographic dynamics and natural selection to the parameters of the…

We study pattern formation in the bounded confidence model of opinion dynamics. In this random process, opinion is quantified by a single variable. Two agents may interact and reach a fair compromise, but only if their difference of opinion…

Cross-linguistic similarities are reflected by the speech sound systems of languages all over the world. In this work we try to model such similarities observed in the consonant inventories, through a complex bipartite network. We present a…

The estimation of mutation probabilities and relative fitnesses in fluctuation analysis is based on the unrealistic hypothesis that the single-cell times to division are exponentially distributed. Using the classical Luria-Delbr\"{u}ck…

We prove almost sure convergence of the maximum degree in an evolving graph model combining a growing number of local choices with sublinear preferential attachment. At each step in the growth of the graph, a new vertex is introduced. Then…

Free association is a task that requires a subject to express the first word to come to their mind when presented with a certain cue. It is a task which can be used to expose the basic mechanisms by which humans connect memories. In this…

Theoretical ecology has traditionally equated persistence with the stability of a fixed equilibrium point. Here we argue that the primary threat to ecosystem persistence need not be the loss of stability, but instead the escape of the…

We consider a dynamical system which has a stable attractor and which is perturbed by an additive noise. Under some quite typical conditions, the fluctuations from the attractor are intermittent and have a probability distribution with…