Positive semigroups and perturbations of boundary conditions

We present a generation theorem for positive semigroups on an $L^1$ space. It provides sufficient conditions for the existence of positive and integrable solutions of initial-boundary value problems. An application to a two-phase cell cycle model is given

The Gambler's Fallacy and Gender

The “gambler’s fallacy” is the false belief that a random event is less likely to occur if the event has occurred recently. Such beliefs are false if the onset of events is in fact independent of previous events. We study gender differences in the gambler’s fallacy using data from the Danish state lottery. Our data set is unique in that we track individual players over time which allows us to investigate how men and women react with their number picking to outcomes of recent lotto drawings. We find evidence of gambler’s fallacy for men but not for women. On average, men are about 1% less likely to bet on numbers drawn in the previous week than on numbers not drawn. Women do not react significantly to the previous week’s drawing outcome.lottery gambling;gender;gambler’s fallacy

Piecewise deterministic Markov processes in biological models

We present a short introduction into the framework of piecewise deterministic Markov processes. We illustrate the abstract mathematical setting with a series of examples related to dispersal of biological systems, cell cycle models, gene expression, physiologically structured populations, as well as neural activity. General results concerning asymptotic properties of stochastic semigroups induced by such Markov processes are applied to specific examples.Comment: in: Semigroup of Operators - Theory and Applications, J. Banasiak et al. (eds.), Springer Proceedings in Mathematics & Statistics 113, (2015), pp. 235-25

Serving the Public Interest

We present a model of political selection in which voters elect a president from a set of candidates. We assume that some of the candidates are benevolent and that all voters prefer a benevolent president, i.e. a president who serves the public interest. Yet, political selection may fail in our model because voters cannot easily tell benevolent from egoistic candidates by observing their pre-election behavior. Egoistic types may strategically imitate benevolent types in the pre-election stage to extract rents once in office. We show that strategic imitation is less likely if the political system is likely to produce good governance. That is, if benevolent candidates are common, if the president has little discretionary power, and if the public sector is effective. We analyze the role of institutions like investigative media and re-election and show that they can improve or further hamper political selection, depending on the parameters of the political game.Political selection, elections, social preferences, political leadership