Average Continuous Control of Piecewise Deterministic Markov Processes

This paper deals with the long run average continuous control problem of piecewise deterministic Markov processes (PDMP's) taking values in a general Borel space and with compact action space depending on the state variable. The control variable acts on the jump rate and transition measure of the PDMP, and the running and boundary costs are assumed to be positive but not necessarily bounded. Our first main result is to obtain an optimality equation for the long run average cost in terms of a discrete-time optimality equation related to the embedded Markov chain given by the post-jump location of the PDMP. Our second main result guarantees the existence of a feedback measurable selector for the discrete-time optimality equation by establishing a connection between this equation and an integro-differential equation. Our final main result is to obtain some sufficient conditions for the existence of a solution for a discrete-time optimality inequality and an ordinary optimal feedback control for the long run average cost using the so-called vanishing discount approach.Comment: 34 page

Broad distribution effects in sums of lognormal random variables

The lognormal distribution describing, e.g., exponentials of Gaussian random variables is one of the most common statistical distributions in physics. It can exhibit features of broad distributions that imply qualitative departure from the usual statistical scaling associated to narrow distributions. Approximate formulae are derived for the typical sums of lognormal random variables. The validity of these formulae is numerically checked and the physical consequences, e.g., for the current flowing through small tunnel junctions, are pointed out.Comment: 14 pages, 9 figures. Minor changes + Gini coefficient and 4 refs. adde

Stellar populations in superclusters of galaxies

A catalogue of superclusters of galaxies is used to investigate the influence of the supercluster environment on galaxy populations, considering galaxies brighter than M$_r<$-21+5$\log$ h. Empirical spectral synthesis techniques are applied to obtain the stellar population properties of galaxies which belong to superclusters and representative values of stellar population parameters are attributed to each supercluster. We show that richer superclusters present denser environments and older stellar populations. The galaxy populations of superclusters classified as filaments and pancakes are statistically similar, indicating that the morphology of superclusters does not have a significative influence on the stellar populations. Clusters of galaxies within superclusters are also examined in order to evaluate the influence of the supercluster environment on their galaxy properties. Our results suggest that the environment affects galaxy properties but its influence should operate on scales of groups and clusters, more than on the scale of superclusters.Comment: 7 pages, 4 figures; accepted to MNRA

On the Potential of the Excluded Volume and Auto-Correlation as Neuromorphometric Descriptors

This work investigates at what degree two neuromorphometric measurements, namely the autocorrelation and the excluded volume of a neuronal cell can influence the characterization and classification of such a type of cells. While the autocorrelation function presents good potential for quantifying the dendrite-dendrite connectivity of cells in mosaic tilings, the excluded volume, i.e. the amount of the surround space which is geometrically not accessible to an axon or dendrite, provides a complementary characterization of the cell connectivity. The potential of such approaches is illustrated with respect to real neuronal cells.Comment: 15 pages, 6 figure