Irreversible thermodynamics of Poisson processes with reaction

A kinetic model is derived to study the successive movements of particles, described by a Poisson process, as well as their generation. The irreversible thermodynamics of this system is also studied from the kinetic model. This makes it possible to evaluate the differences between thermodynamical quantities computed exactly and up to second-order. Such differences determine the range of validity of the second-order approximation to extended irreversible thermodynamics

Point-occurrence self-similarity in crackling-noise systems and in other complex systems

It has been recently found that a number of systems displaying crackling noise also show a remarkable behavior regarding the temporal occurrence of successive events versus their size: a scaling law for the probability distributions of waiting times as a function of a minimum size is fulfilled, signaling the existence on those systems of self-similarity in time-size. This property is also present in some non-crackling systems. Here, the uncommon character of the scaling law is illustrated with simple marked renewal processes, built by definition with no correlations. Whereas processes with a finite mean waiting time do not fulfill a scaling law in general and tend towards a Poisson process in the limit of very high sizes, processes without a finite mean tend to another class of distributions, characterized by double power-law waiting-time densities. This is somehow reminiscent of the generalized central limit theorem. A model with short-range correlations is not able to escape from the attraction of those limit distributions. A discussion on open problems in the modeling of these properties is provided.

A fast Bayesian reconstruction algorithm for emission tomography with entropy prior converging to feasible images

The development and tests of an iterative reconstruction algorithm for emission tomography based on Bayesian statistical concepts are described. The algorithm uses the entropy of the generated image as a prior distribution, can be accelerated by the choice of an exponent, and converges uniformly to feasible images by the choice of one adjustable parameter. A feasible image has been defined as one that is consistent with the initial data (i.e. it is an image that, if truly a source of radiation in a patient, could have generated the initial data by the Poisson process that governs radioactive disintegration). The fundamental ideas of Bayesian reconstruction are discussed, along with the use of an entropy prior with an adjustable contrast parameter, the use of likelihood with data increment parameters as conditional probability, and the development of the new fast maximum a posteriori with entropy (FMAPE) Algorithm by the successive substitution method. It is shown that in the maximum likelihood estimator (MLE) and FMAPE algorithms, the only correct choice of initial image for the iterative procedure in the absence of a priori knowledge about the image configuration is a uniform field.

The Effect of a threshold proportional reinsurance strategy on ruin probabilities

[spa] En un modelo de Poisson compuesto, definimos una estrategia de reaseguro proporcional de umbral : se aplica un nivel de retención k1 siempre que las reservas sean inferiores a un determinado umbral b, y un nivel de retención k2 en caso contrario. Obtenemos la ecuación íntegro-diferencial para la función Gerber-Shiu, definida en Gerber-Shiu -1998- en este modelo, que nos permite obtener las expresiones de la probabilidad de ruina y de la transformada de Laplace del momento de ruina para distintas distribuciones de la cuantía individual de los siniestros. Finalmente presentamos algunos resultados numéricos.

The Effect of a threshold proportional reinsurance strategy on ruin probabilities

[spa] En un modelo de Poisson compuesto, definimos una estrategia de reaseguro proporcional de umbral : se aplica un nivel de retención k1 siempre que las reservas sean inferiores a un determinado umbral b, y un nivel de retención k2 en caso contrario. Obtenemos la ecuación íntegro-diferencial para la función Gerber-Shiu, definida en Gerber-Shiu -1998- en este modelo, que nos permite obtener las expresiones de la probabilidad de ruina y de la transformada de Laplace del momento de ruina para distintas distribuciones de la cuantía individual de los siniestros. Finalmente presentamos algunos resultados numéricos.

Scale effect in hazard assessment - application to daily rainfall

Daily precipitation is recorded as the total amount of water collected by a rain-gauge in 24h. Events are modelled as a Poisson process and the 24h precipitation by a Generalized Pareto Distribution (GPD) of excesses. Hazard assessment is complete when estimates of the Poisson rate and the distribution parameters, together with a measure of their uncertainty, are obtained. The shape parameter of the GPD determines the support of the variable: Weibull domain of attraction (DA) corresponds to finite support variables, as should be for natural phenomena. However, Fréchet DA has been reported for daily precipitation, which implies an infinite support and a heavy-tailed distribution. We use the fact that a log-scale is better suited to the type of variable analyzed to overcome this inconsistency, thus showing that using the appropriate natural scale can be extremely important for proper hazard assessment. The approach is illustrated with precipitation data from the Eastern coast of the Iberian Peninsula affected by severe convective precipitation. The estimation is carried out by using Bayesian techniques

The effect of scale in daily precipitation hazard assessment

Daily precipitation is recorded as the total amount of water collected by a rain-gauge in 24 h. Events are modelled as a Poisson process and the 24 h precipitation by a Generalised Pareto Distribution (GPD) of excesses. Hazard assessment is complete when estimates of the Poisson rate and the distribution parameters, together with a measure of their uncertainty, are obtained. The shape parameter of the GPD determines the support of the variable: Weibull domain of attraction (DA) corresponds to finite support variables as should be for natural phenomena. However, Fréchet DA has been reported for daily precipitation, which implies an infinite support and a heavy-tailed distribution. Bayesian techniques are used to estimate the parameters. The approach is illustrated with precipitation data from the Eastern coast of the Iberian Peninsula affected by severe convective precipitation. The estimated GPD is mainly in the Fréchet DA, something incompatible with the common sense assumption of that precipitation is a bounded phenomenon. The bounded character of precipitation is then taken as a priori hypothesis. Consistency of this hypothesis with the data is checked in two cases: using the raw-data (in mm) and using log-transformed data. As expected, a Bayesian model checking clearly rejects the model in the raw-data case. However, log-transformed data seem to be consistent with the model. This fact may be due to the adequacy of the log-scale to represent positive measurements for which differences are better relative than absolute

Triggering the generation of an iron(IV)-oxo compound and its reactivity toward sulfides by RuII photocatalysis

The preparation of [FeIV(O)(MePy2tacn)]2+ (2, MePy2tacn = N-methyl-N,N-bis(2-picolyl)-1,4,7-triazacyclononane) by reaction of [FeII(MePy2tacn)(solvent)]2+ (1) and PhIO in CH3CN and its full characterization are described. This compound can also be prepared photochemically from its iron(II) precursor by irradiation at 447 nm in the presence of catalytic amounts of [Ru II(bpy)3]2+ as photosensitizer and a sacrificial electron acceptor (Na2S2O8). Remarkably, the rate of the reaction of the photochemically prepared compound 2 toward sulfides increases 150-fold under irradiation, and 2 is partially regenerated after the sulfide has been consumed; hence, the process can be repeated several times. The origin of this rate enhancement has been established by studying the reaction of chemically generated compound 2 with sulfides under different conditions, which demonstrated that both light and [Ru II(bpy)3]2+ are necessary for the observed increase in the reaction rate. A combination of nanosecond time-resolved absorption spectroscopy with laser pulse excitation and other mechanistic studies has led to the conclusion that an electron transfer mechanism is the most plausible explanation for the observed rate enhancement. According to this mechanism, the in-situ-generated [RuIII(bpy)3] 3+ oxidizes the sulfide to form the corresponding radical cation, which is eventually oxidized by 2 to the corresponding sulfoxide

Does bounded rationality lead to individual heterogeneity? The impact of the experimentation process and of memory constraints

In this paper we explore the effect of bounded rationality on the convergence of individual behavior toward equilibrium. In the context of a Cournot game with a unique and symmetric Nash equilibrium, firms are modeled as adaptive economic agents through a genetic algorithm. Computational experiments show that (1) there is remarkable heterogeneity across identical but boundedly rational agents; (2) such individual heterogeneity is not simply a consequence of the random elements contained in the genetic algorithm; (3) the more rational agents are in terms of memory abilities and pre-play evaluation of strategies, the less heterogeneous they are in their actions. At the limit case of full rationality, the outcome converges to the standard result of uniform individual behavior.

Reflected Backward Stochastic Differential Equation with Jumps and RCLL Obstacle

In this paper we study one-dimensional reflected backward stochastic differential equation when the noise is driven by a Brownian motion and an independent Poisson point process when the solution is forced to stay above a right continuous left-hand limited obstacle. We prove existence and uniqueness of the solution by using a penalization method combined with a monotonic limit theorem.

Degradació en planta pilot de colorants reactius mitjançant el procés de foto-Fenton assistit amb llum solar: aplicació del procés com a pre-tractament d'un procés biològic

Estudi elaborat a partir d’una estada a la Plataforma Solar de Almería entre desembre del 2006 i gener del 2007. S’ha dut a terme la degradació en planta pilot dels colorants reactius Procion Red H-E7B i Cibacron Red FN-R mitjançant el procés de foto-Fenton aplicat com a tractament únic i com a pretractament d’un procés biològic. El procés de foto-Fenton, assistit amb llum solar, es va realitzar en un fotoreactor solar tipus Col•lector Parabòlic Compost (CPC) i el tractament biològic en un Reactor de Biomassa Immobilitzada (RBI). Com a punt de partida, i amb l’objectiu d’estudiar la reproductibilitat del sistema, es van prendre resultats obtinguts d’experiments realitzats prèviament a escala de laboratori i amb llum artificial. El paràmetre Carboni Orgànic Total (COT) es va emprar com a indicador de l’eliminació dels colorants i dels seus intermedis. En aplicar únicament el procés de foto-Fenton com a tractament, concentracions de 10 mg•l-1 de Fe (II) i 250 mg•l-1 de H2O2 per degradar 250 mg•l-1 Procion Red H-E7B, i de 20 mg•l-1 de Fe (II) i 500 mg•l-1 de H2O2 per degradar 250 mg•l-1 Cibacron Red FN-R, van reproduir els resultants obtinguts al laboratori, amb uns nivells d’eliminació de COT del 82 i 86%, respectivament. A més, l’ús beneficiós de la llum solar en el procés de foto-Fenton, juntament amb la configuració del CPC, van incrementar la velocitat de degradació respecte als resultats previs, permetent la reducció de la concentració de Fe (II) de 10 a 2 mg•l-1 (Procion Red H-E7B) i de 20 a 5 mg•l-1 (Cibacron Red FN-R) sense pèrdues d’efectivitat. D’altre banda, el sistema combinat foto-Fenton/tractament biològic en planta pilot, unes concentracions d’oxidant de 225 mg•l-1 H2O2 per Cibacron Red FN-R i 65 mg•l-1 H2O2 per Procion Red H-E7B van ser suficients per generar solucions intermèdies biodegradables i alimentar així el RBI, millorant inclús els resultats obtinguts prèviament al laboratori.

Cooperative vs. non-cooperative mechanisms in the EU decision making process

According to the account of the European Union (EU) decision making proposed in this paper, this is a bargaining process during which actors shift their policy positions with a view to reaching agreements on controversial issues.

An extension of the Marsden-Ratiu reduction for Poisson manifolds

We propose a generalization of the reduction of Poisson manifolds by distributions introduced by Marsden and Ratiu. Our proposal overcomes some of the restrictions of the original procedure, and makes the reduced Poisson structure effectively dependent on the distribution. Different applications are discussed, as well as the algebraic interpretation of the procedure and its formulation in terms of Dirac structures.