A bioeconomic model for Mediterranean fisherires, the hake off Catalonia (western Mediterranean) as a case study

The theoretical aspects and the associated software of a bioeconomic model for Mediterranean fisheries are presented. The first objective of the model is to reproduce the bioeconomic conditions in which the fisheries occur. The model is, perforce, multispecies and multigear. The main management procedure is effort limitation. The model also incorporates the usual fishermen strategy of increasing efficiency to obtain increased fishing mortality while maintaining the nominal effort. This is modelled by means of a function relating the efficiency (or technological progress) with the capital invested in the fishery and time. A second objective is to simulate alternative management strategies. The model allows the operation of technical and economic management measures in the presence of different kind of events. Both deterministic and stochastic simulations can be performed. An application of this tool to the hake fishery off Catalonia is presented, considering the other species caught and the different gears used. Several alternative management measures are tested and their consequences for the stock and economy of fishermen are analysed.

Stochastic resonance in a dipole

We show that the dipole, a system usually proposed to model relaxation phenomena, exhibits a maximum in the signal-to-noise ratio at a nonzero noise level, thus indicating the appearance of stochastic resonance. The phenomenon occurs in two different situations, i.e., when the minimum of the potential of the dipole remains fixed in time and when it switches periodically between two equilibrium points. We have also found that the signal-to-noise ratio has a maximum for a certain value of the amplitude of the oscillating field.

Weber's law in decision making: integrating behavioral data in humans with a neurophysiological model

Recent single-cell studies in monkeys (Romo et al., 2004) show that the activity of neurons in the ventral premotor cortex covaries with the animal's decisions in a perceptual comparison task regarding the frequency of vibrotactile events. The firing rate response of these neurons was dependent only on the frequency differences between the two applied vibrations, the sign of that difference being the determining factor for correct task performance. We present a biophysically realistic neurodynamical model that can account for the most relevant characteristics of this decision-making-related neural activity. One of the nontrivial predictions of this model is that Weber's law will underlie the perceptual discrimination behavior. We confirmed this prediction in behavioral tests of vibrotactile discrimination in humans and propose a computational explanation of perceptual discrimination that accounts naturally for the emergence of Weber's law. We conclude that the neurodynamical mechanisms and computational principles underlying the decision-making processes in this perceptual discrimination task are consistent with a fluctuation-driven scenario in a multistable regime.

Monotonic continuous-time random walks with drift and stochastic reset events

In this paper we consider a stochastic process that may experience random reset events which suddenly bring the system to the starting value and analyze the relevant statistical magnitudes. We focus our attention on monotonic continuous-time random walks with a constant drift: The process increases between the reset events, either by the effect of the random jumps, or by the action of the deterministic drift. As a result of all these combined factors interesting properties emerge, like the existence (for any drift strength) of a stationary transition probability density function, or the faculty of the model to reproduce power-law-like behavior. General formulas for two extreme statistics, the survival probability, and the mean exit time, are also derived. To corroborate in an independent way the results of the paper, Monte Carlo methods were used. These numerical estimations are in full agreement with the analytical predictions.

Asymptotic analysis of stock price densities and implied volatilities in mixed stochastic models

In this paper, we obtain sharp asymptotic formulas with error estimates for the Mellin con- volution of functions de ned on (0;1), and use these formulas to characterize the asymptotic behavior of marginal distribution densities of stock price processes in mixed stochastic models. Special examples of mixed models are jump-di usion models and stochastic volatility models with jumps. We apply our general results to the Heston model with double exponential jumps, and make a detailed analysis of the asymptotic behavior of the stock price density, the call option pricing function, and the implied volatility in this model. We also obtain similar results for the Heston model with jumps distributed according to the NIG law.