Exact solution of a stochastic protein dynamics model with delayed degradation

We study a stochastic model of protein dynamics that explicitly includes delay in the degradation. We rigorously derive the master equation for the processes and solve it exactly. We show that the equations for the mean values obtained differ from others intuitively proposed and that oscillatory behavior is not possible in this system. We discuss the calculation of correlation functions in stochastic systems with delay, stressing the differences with Markovian processes. The exact results allow to clarify the interplay between stochasticity and delay

On the effect of heterogeneity in stochastic interacting-particle systems

We study stochastic particle systems made up of heterogeneous units. We introduce a general framework suitable to analytically study this kind of systems and apply it to two particular models of interest in economy and epidemiology. We show that particle heterogeneity can enhance or decrease the collective fluctuations depending on the system, and that it is possible to infer the degree and the form of the heterogeneity distribution in the system by measuring only global variables and their fluctuations

On the Gaussian approximation for master equations

We analyze the Gaussian approximation as a method to obtain the first and second moments of a stochastic process described by a master equation. We justify the use of this approximation with ideas coming from van Kampen's expansion approach (the fact that the probability distribution is Gaussian at first order). We analyze the scaling of the error with a large parameter of the system and compare it with van Kampen's method. Our theoretical analysis and the study of several examples shows that the Gaussian approximation turns out to be more accurate. This could be specially important for problems involving stochastic processes in systems with a small number of particles

Non-universal results induced by diversity distribution in coupled excitable systems

We consider a system of globally coupled active rotators near the excitable regime. The system displays a transition to a state of collective firing induced by disorder. We show that this transition is found generically for any diversity distribution with well defined moments. Singularly, for the Lorentzian distribution (widely used in Kuramoto-like systems) the transition is not present. This warns about the use of Lorentzian distributions to understand the generic properties of coupled oscillators.We acknowledge financial support by the MICINN (Spain) and FEDER (EU) through project FIS2007-60327. L.F.L. is supported by the JAEPredoc program of CSIC.Peer reviewe

Non-universal results induced by diversity distribution in coupled excitable systems

We consider a system of globally coupled active rotators near the excitable regime. The system displays a transition to a state of collective firing induced by disorder. We show that this transition is found generically for any diversity distribution with well defined moments. Singularly, for the Lorentzian distribution (widely used in Kuramoto-like systems) the transition is not present. This warns about the use of Lorentzian distributions to understand the generic properties of coupled oscillators

Evolution of surname distribution under gender-equality measurements

We consider a model for the evolution of the surnames distribution under a gender-equality measurement presently discussed in the Spanish parliament (the children take the surname of the father or the mother according to alphabetical order). We quantify how this would bias the alphabetical distribution of surnames, and analyze its effect on the present distribution of the surnames in Spain

Simulating non-Markovian stochastic processes

We present a simple and general framework to simulate statistically correct realizations of a system of non-Markovian discrete stochastic processes. We give the exact analytical solution and a practical an efficient algorithm alike the Gillespie algorithm for Markovian processes, with the difference that now the occurrence rates of the events depend on the time elapsed since the event last took place. We use our non-Markovian generalized Gillespie stochastic simulation methodology to investigate the effects of non-exponential inter-event time distributions in the susceptible-infected-susceptible model of epidemic spreading. Strikingly, our results unveil the drastic effects that very subtle differences in the modeling of non-Markovian processes have on the global behavior of complex systems, with important implications for their understanding and prediction. We also assess our generalized Gillespie algorithm on a system of biochemical reactions with time delays. As compared to other existing methods, we find that the generalized Gillespie algorithm is the most general as it can be implemented very easily in cases, like for delays coupled to the evolution of the system, where other algorithms do not work or need adapted versions, less efficient in computational terms.Comment: Improvement of the algorithm, new results, and a major reorganization of the paper thanks to our coauthors L. Lafuerza and R. Tora

Triggering Mechanisms of Tsunamis in the Gulf of Cadiz and the Alboran Sea: An Overview

The Gulf of Cadiz and the Alboran Sea are characterized by tectonic activity due to oblique convergence at the boundary between the Eurasian and Nubian plates. This activity has favoured a variety of tsunamigenic sources: basically, seismogenic faults and submarine landslides. The main tsunamigenic faults in the Gulf of Cadiz would comprise the thrust systems of Gorringe Ridge, Marquês de Pombal, São Vicente Canyon, and Horseshoe faults with a high susceptibility; meanwhile in the Alboran Sea would be the thrust system of the northern Alboran Ridge with high susceptibility, and the thrust systems of north Xauen and Adra margin, the transpressive segment of Al Idrissi fault, and the Yusuf-Habibas and Averroes faults, with moderate to high susceptibility. The areas with the greatest potential to generate tsunamigenic submarine landslides are in the Gulf of Cadiz, the São Vicente Canyon, Hirondelle Seamount, and Gorringe Ridge; and in the Alboran Sea are the southern and northern flanks of Alboran Ridge. Both sources are likely to generate destructive tsunamis in the Gulf of Cadiz, given its history of bigger earthquakes (>7 Mw) and larger landslides. To fully assess tsunamigenic sources, further work needs to be performed. In the case of seismogenic faults, research focuses on geometry, offsets, timing, paleoearthquakes, and recurrence, and in landslides on early post-failure evolution, age, events, and recurrence. In situ measurements, paleotsunami records, and long-term monitoring, in addition to major modelling developments, will be also necessary.Versión del edito