Can hierarchical predictive coding explain binocular rivalry?

Hohwy et al.’s (2008) model of binocular rivalry (BR) is taken as a classic illustration of predictive coding’s explanatory power. I revisit the account and show that it cannot explain the role of reward in BR. I then consider a more recent version of Bayesian model averaging, which recasts the role of reward in (BR) in terms of optimism bias. If we accept this account, however, then we must reconsider our conception of perception. On this latter view, I argue, organisms engage in what amounts to policy-driven, motivated perception

Sovereign debt: Do we need an EU solution? Bertelsmann Stiftung EUROPA Briefing 2017

High levels of sovereign debt have become a serious issue in the Eurozone. This does not just affect the individual member states: The European debt crisis has shown that difficulties in one euro-area country can spread to the entire currency union. What strategies are being discussed for reducing sovereign debt? Would a stronger role for the EU help to reduce debt over the long term or should this be left solely to the member states

Asymptotic behavior of solutions of the fragmentation equation with shattering: An approach via self-similar Markov processes

The subject of this paper is a fragmentation equation with nonconservative solutions, some mass being lost to a dust of zero-mass particles as a consequence of an intensive splitting. Under some assumptions of regular variation on the fragmentation rate, we describe the large time behavior of solutions. Our approach is based on probabilistic tools: the solutions to the fragmentation equation are constructed via nonincreasing self-similar Markov processes that continuously reach 0 in finite time. Our main probabilistic result describes the asymptotic behavior of these processes conditioned on nonextinction and is then used for the solutions to the fragmentation equation. We note that two parameters significantly influence these large time behaviors: the rate of formation of "nearly-1 relative masses" (this rate is related to the behavior near 0 of the L\'evy measure associated with the corresponding self-similar Markov process) and the distribution of large initial particles. Correctly rescaled, the solutions then converge to a nontrivial limit which is related to the quasi-stationary solutions of the equation. Besides, these quasi-stationary solutions, or, equivalently, the quasi-stationary distributions of the self-similar Markov processes, are fully described.Comment: Published in at http://dx.doi.org/10.1214/09-AAP622 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org