Hopf algebras and Markov chains: Two examples and a theory

The operation of squaring (coproduct followed by product) in a combinatorial Hopf algebra is shown to induce a Markov chain in natural bases. Chains constructed in this way include widely studied methods of card shuffling, a natural "rock-breaking" process, and Markov chains on simplicial complexes. Many of these chains can be explictly diagonalized using the primitive elements of the algebra and the combinatorics of the free Lie algebra. For card shuffling, this gives an explicit description of the eigenvectors. For rock-breaking, an explicit description of the quasi-stationary distribution and sharp rates to absorption follow.Comment: 51 pages, 17 figures. (Typographical errors corrected. Further fixes will only appear on the version on Amy Pang's website, the arXiv version will not be updated.

Voiceless but empowered farmers in corporate supply chains: contradictory imagery and instrumental approach to empowerment

There have been calls for a shift of focus towards the political and power-laden aspects of transitioning towards socially equitable global supply chains. This paper offers an empirically grounded response to these calls from a critical realist stance in the context of global food supply chains. We examine how an imaginary for sustainable farming structured around an instrumental construction of empowerment limits what is viewed as permissible, desirable and possible in global food supply chains. We adopt a multimodal Critical Discourse Analysis (CDA) to examine the sustainable farming imaginary for smallholder farmers constructed by one large organization, Unilever, in a series of videos produced and disseminated on YouTube. We expose the underlying mechanisms of power and marginalization at work within the sustainability imaginary and show how “empowerment” has the potential to create of new dependencies for these farmers. We recontextualize the representations to show that while the imaginary may be commercially feasible, it is less achievable in terms of empowering smallholder farmers

Lost in the sauce: the effects of alcohol on mind wandering

Alcohol consumption alters consciousness in ways that make drinking both alluring and hazardous. Recent advances in the study of consciousness using a mind-wandering paradigm permit a rigorous examination of the effects of alcohol on experiential consciousness and metaconsciousness. Fifty-four male social drinkers consumed alcohol (0.82 g/kg) or a placebo beverage and then performed a mind-wandering reading task. This task indexed both self-caught and probe-caught zone-outs to distinguish between mind wandering inside and outside of awareness. Compared with participants who drank the placebo, those who drank alcohol were significantly more likely to report that they were zoning out when probed. After this increase in mind wandering was accounted for, alcohol also lowered the probability of catching oneself zoning out. The results suggest that alcohol increases mind wandering while simultaneously reducing the likelihood of noticing one's mind wandering. Findings are discussed with regard to theories of alcohol and theories of consciousness