This paper attempts to develop a theory of sufficiency in the setting of non-commutative algebras parallel to the ideas in classical mathematical statistics. Sufficiency of a coarse-graining means that all information is extracted about the mutual relation of a given family of states. In the paper sufficient coarse-grainings are characterized in several equivalent ways and the non-commutative a...

This study investigated the effects of price transparency on consumers’price perceptions. Our two-dimensional information transparency framework (sufficiency and diagnosticity of pricing information) is grounded in the Heuristic-Systematic Model of Persuasion. Real-life online hotel booking sites were used for hypothesis testing. Our results show that consumers’ price fairness perceptions and w...

We derive necessary and sufficient conditions under which a set of variables is informationally sufficient, i.e. it contains enough information to estimate the structural shocks with a VAR model. Based on such conditions, we suggest a procedure to test for informational sufficiency. Moreover, we show how to amend the VAR if informational sufficiency is rejected. We apply our procedure to a VAR ...

We study the section conjecture of anabelian geometry and the sufficiency of the finite descent obstruction to the Hasse principle for the moduli spaces of principally polarized abelian varieties and of curves over number fields. For the former we show that both the section conjecture and the finite descent obstruction fail in a very controlled way. For the latter, we prove some partial results...

International trade plays a fundamental role in today's globalized food system, however, trade-related disruptions to national supply have become increasingly prevalent. Although self-sufficiency and the resilience of domestic production are both discussed, they rarely investigated tandem. This hinders our understanding diversity risks supply. In this article we investigate contribution these r...

Monte-Carlo Tree Search (MCTS) has proved a remarkably effective decision mechanism in many different game domains, including computer Go and general game playing (GGP). However, in GGP, where many disparate games are played, certain type of games have proved to be particularly problematic for MCTS. One of the problems are game trees with so-called optimistic moves, that is, bad moves that supe...

optimization problem in a Banach space. The assumption that the strengthened Legendre– Clebsch condition holds is crucial. In particular, we refer the reader to Milyutin & Osmolovskiı̌ (1998) where the importance of this condition is fully explained. In this paper, we consider a fixed-endpoint optimal control problem with equality control constraints and provide a new set of sufficient condition...

Ultraviolet radiation is a carcinogen that also compromises skin appearance and function. Because the ultraviolet action spectra for DNA damage, skin cancer, and vitamin D(3) photosynthesis are identical and vitamin D is readily available from oral supplements, why has sun protection become controversial? First, the media and, apparently, some researchers are hungry for a new message. Second, t...

We propose a deenition of \regular synthesis," more general than those suggested by other authors such as Boltyanskii and Brunovsk y, and an even more general notion of \regular presynthesis." We give a complete proof of the corresponding suuciency theorem, a slightly weaker version of which had been stated in an earlier article, with only a rough outline of the proof. We illustrate the strengt...

The plethora of vitamin D studies over the recent years highlight the pleomorphic effects of vitamin D outside its conventional role in calcium and bone homeostasis. Vitamin D deficiency, though common and known, still faces several challenges among the medical community in terms of proper diagnosis and correction. In this review, the different levels of vitamin D and its clinical implications ...