Stochastic multiplicative processes with reset events

We study a stochastic multiplicative process with reset events. It is shown that the model develops a stationary power-law probability distribution for the relevant variable, whose exponent depends on the model parameters. Two qualitatively different regimes are observed, corresponding to intermittent and regular behaviour. In the boundary between them, the mean value of the relevant variable is time-independent, and the exponent of the stationary distribution equals -2. The addition of diffusion to the system modifies in a non-trivial way the profile of the stationary distribution. Numerical and analytical results are presented.Comment: 8 pages, 3 figures. To appear in Phys. Rev.

On the genealogy of a population of biparental individuals

If one goes backward in time, the number of ancestors of an individual doubles at each generation. This exponential growth very quickly exceeds the population size, when this size is finite. As a consequence, the ancestors of a given individual cannot be all different and most remote ancestors are repeated many times in any genealogical tree. The statistical properties of these repetitions in genealogical trees of individuals for a panmictic closed population of constant size N can be calculated. We show that the distribution of the repetitions of ancestors reaches a stationary shape after a small number Gc ~ log N of generations in the past, that only about 80% of the ancestral population belongs to the tree (due to coalescence of branches), and that two trees for individuals in the same population become identical after Gc generations have elapsed. Our analysis is easy to extend to the case of exponentially growing population.Comment: 14 pages, 7 figures, to appear in the Journal of Theoretical Biolog

Interacting Individuals Leading to Zipf's Law

We present a general approach to explain the Zipf's law of city distribution. If the simplest interaction (pairwise) is assumed, individuals tend to form cities in agreement with the well-known statisticsComment: 4 pages 2 figure

Maxillary nerve block: A comparison between the greater palatine canal and high tuberosity approaches.

Aim: Analgesia and anxiolysis during dental procedures are important for dental care and patient compliance. This study aims to compare two classical maxillary nerve block (MNB) techniques: the greater palatine canal (GPC) and the high tuberosity (HT) approaches, seldom used in routine dental practice. Methods: The study was conducted on 30 patients, scheduled for sinus lift surgery, who were randomly divided into 2 groups: the GPC approach to the MNB was used in 15 and the HT one in the other 15 patients. Anxiolysis was also used, depending on the results of the pre- preoperative assessment. Patients\u2019 sensations/pain during the procedure, details about anesthesia, and the dentist\u2019s considerations were all recorded. Data are expressed as mean \ub1SD. Statistical tests including ANOVA, \u3c72 following Yates correction and linear regression analysis were carried out. A < 0.05 p value was considered significant. Results: Study results showed that the anesthesia was effective and constant in the molar and premolar area. Additional infiltrations of local anesthetics were necessary for vestibular and palatal areas in the anterior oral cavity, respectively, in the GPC and HT groups. The two techniques were equally difficult to carry out in the dentist\u2019s opinion. There were no differences in pain or unpleasant sensations between the two groups, nor were any anesthesia-related complications reported. Conclusion: The GPC approach ensures effective anesthesia in the posterior maxillary region as far as both the dental pulp and the palatal/vestibular mucous membranes are concerned; the HT approach did not guarantee adequate anesthesia of the pterygopalatine branch of the maxillary nerve. These regional anesthesia techniques were characterized by a low incidence of intra and postoperative pain, no noteworthy complications, and high patient satisfaction

Analysis of scale-free networks based on a threshold graph with intrinsic vertex weights

Many real networks are complex and have power-law vertex degree distribution, short diameter, and high clustering. We analyze the network model based on thresholding of the summed vertex weights, which belongs to the class of networks proposed by Caldarelli et al. (2002). Power-law degree distributions, particularly with the dynamically stable scaling exponent 2, realistic clustering, and short path lengths are produced for many types of weight distributions. Thresholding mechanisms can underlie a family of real complex networks that is characterized by cooperativeness and the baseline scaling exponent 2. It contrasts with the class of growth models with preferential attachment, which is marked by competitiveness and baseline scaling exponent 3.Comment: 5 figure

Propagation of small perturbations in synchronized oscillator networks

We study the propagation of a harmonic perturbation of small amplitude on a network of coupled identical phase oscillators prepared in a state of full synchronization. The perturbation is externally applied to a single oscillator, and is transmitted to the other oscillators through coupling. Numerical results and an approximate analytical treatment, valid for random and ordered networks, show that the response of each oscillator is a rather well-defined function of its distance from the oscillator where the external perturbation is applied. For small distances, the system behaves as a dissipative linear medium: the perturbation amplitude decreases exponentially with the distance, while propagating at constant speed. We suggest that the pattern of interactions may be deduced from measurements of the response of individual oscillators to perturbations applied at different nodes of the network

Global firing induced by network disorder in ensembles of activerotators

Abstract.: We study the influence of repulsive interactions on an ensemble of coupled excitable rotators. We find that a moderate fraction of repulsive interactions can trigger global firing of the ensemble. The regime of global firing, however, is suppressed in sufficiently large systems if the network of repulsive interactions is fully random, due to self-averaging in its degree distribution. We thus introduce a model of partially random networks with a broad degree distribution, where self-averaging due to size growth is absent. In this case, the regime of global firing persists for large sizes. Our results extend previous work on the constructive effects of diversity in the collective dynamics of complex system

Global firing induced by network disorder in ensembles of active rotators

We study the influence of repulsive interactions on an ensemble of coupled excitable rotators. We find that a moderate fraction of repulsive interactions can trigger global firing of the ensemble. The regime of global firing, however, is suppressed in sufficiently large systems if the network of repulsive interactions is fully random, due to self-averaging in its degree distribution. We thus introduce a model of partially random networks with a broad degree distribution, where self-averaging due to size growth is absent. In this case, the regime of global firing persists for large sizes. Our results extend previous work on the constructive effects of diversity in the collective dynamics of complex systems.Comment: 8 pages, 6 figure

Distribution of repetitions of ancestors in genealogical trees

We calculate the probability distribution of repetitions of ancestors in a genealogical tree for simple neutral models of a closed population with sexual reproduction and non-overlapping generations. Each ancestor at generation g in the past has a weight w which is (up to a normalization) the number of times this ancestor appears in the genealogical tree of an individual at present. The distribution P_g(w) of these weights reaches a stationary shape P_\infty(w) for large g, i.e. for a large number of generations back in the past. For small w, P_\infty(w) is a power law with a non-trivial exponent which can be computed exactly using a standard procedure of the renormalization group approach. Some extensions of the model are discussed and the effect of these variants on the shape of P_\infty(w) are analysed.Comment: 20 pages, 5 figures included, to appear in Physica