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AbstractThis article describes the limiting distribution of the extremes of observations that arrive in clusters. We start by studying the tail behaviour of an individual cluster, and then we apply the developed theory to determine the limiting distribution of $\max\{X_j\,:\, j=0,\ldots, K(t)\}$ , where K(t) is the number of independent and identically distributed observations $(X_j)$ arriving up to the time taccording to a general marked renewal cluster process. The results are illustrated in the context of some commonly used Poisson cluster models such as the marked Hawkes process.

The study of ultrafast photoinduced dynamics of adsorbates on metal surfaces requires thorough investigation of laser-excited electrons and, in many cases, the highly excited surface lattice. While ab initio molecular dynamics with electronic friction and thermostats (Te, Tl)-AIMDEF addresses such complex modeling, it imposes severe computational costs, hindering quantitative comparison with experimental desorption probabilities. In order to bypass this limitation, we utilize the embedded atom neural network method to construct a potential energy surface (PES) for the coadsorption of CO and O on Ru(0001). Our results demonstrate that this PES not only reproduces the short-time ab initio dynamics but is also able to yield statistically significant data for long lasting trajectories that correlate well with experimental findings. Furthermore, the analysis of the laser-induced dynamics reveals the existence of a dynamic trapping state that acts as a precursor for CO desorption, and it is not observed under thermal conditions. Altogether, our results validate the underlying theoretical framework, providing robust support for the description of not only the photoinduced desorption but also the oxidation of CO in terms of nonequilibrated but thermal hot electrons and phonons.

AbstractWe study the asymptotic distribution of the total claim amount for marked Poisson cluster models. The marks determine the size and other characteristics of the individual claims and potentially influence the arrival rate of future claims. We find sufficient conditions under which the total claim amount satisfies the central limit theorem or, alternatively, tends in distribution to an infinite-variance stable random variable. We discuss several Poisson cluster models in detail, paying special attention to the marked Hawkes process as our key example.

In a three year study (1994-96) reduced soil tillage variants proved satisfactory for winter wheat grown on Humogley soil in Eastern Croatia in the absence of herbicides. During the experiment the conventional tillage (ploughing, disk-harrowing, standard sowing) did not give significantly higher yields compared to the reduced tillage treatments (disk-harrowing; tillage by multitiller with chisels; seedbed preparation (rototiller) + sowing by rotosem; and ploughing, seedbed preparation + sowing by rotosem). Production of weed biomass at the conventional tillage equalled the treatment tillage by rototiller + sowing by rotosem, but was significantly lower than in other tillage treatments. Totally, nitrogen fertilisation had a significant influence upon wheat yield inerease at each N level (140, 170, and 200 kg ha-1), whereas the efficacy of fertilisation upon yields was higher at reduced tillage treatments without ploughing than at the conventional tillage. The correlation between crop yield and weed biomass deereased along with the inerease of N level. Winter wheat had a higher N optimum than its weed component, which points out that for this crop N fertilisation at reduced tillage systems can be used as a measure for weed control. The reduced tillage variant with rototiller + sowing by rotosem turned out to be entirely competitive with the conventional tillage regarding yield and weed biomass, as well as a higher resistance to weather conditions.