Coding-theorem Like Behaviour and Emergence of the Universal Distribution from Resource-bounded Algorithmic Probability

Previously referred to as `miraculous' in the scientific literature because of its powerful properties and its wide application as optimal solution to the problem of induction/inference, (approximations to) Algorithmic Probability (AP) and the associated Universal Distribution are (or should be) of the greatest importance in science. Here we investigate the emergence, the rates of emergence and convergence, and the Coding-theorem like behaviour of AP in Turing-subuniversal models of computation. We investigate empirical distributions of computing models in the Chomsky hierarchy. We introduce measures of algorithmic probability and algorithmic complexity based upon resource-bounded computation, in contrast to previously thoroughly investigated distributions produced from the output distribution of Turing machines. This approach allows for numerical approximations to algorithmic (Kolmogorov-Chaitin) complexity-based estimations at each of the levels of a computational hierarchy. We demonstrate that all these estimations are correlated in rank and that they converge both in rank and values as a function of computational power, despite fundamental differences between computational models. In the context of natural processes that operate below the Turing universal level because of finite resources and physical degradation, the investigation of natural biases stemming from algorithmic rules may shed light on the distribution of outcomes. We show that up to 60\% of the simplicity/complexity bias in distributions produced even by the weakest of the computational models can be accounted for by Algorithmic Probability in its approximation to the Universal Distribution.Comment: 27 pages main text, 39 pages including supplement. Online complexity calculator: http://complexitycalculator.com

Effect of stevia supplementation of kale juice spheres on their quality changes during refrigerated shelf life

Kale is a vegetable with high contents of health–promoting compounds although its consumption as a beverage is highly limited due to its bitter flavour. Nonetheless, the bitter flavour of Brassicas may be masked by sweetening. Then, the effects of different stevia extracts (CTRL, S0.5 (g L–1), S1.25 and S2.5), added to an innovative kale beverage presentation, were studied on the kale juice spheres quality during 7 days at 5ºC. Kale juice spheres were produced with a double spherification technique, which allowed to obtain hydrogel spheres with high mechanical resistance.The authors express their gratitude to CNPq (Council for Scientific and Technological Development, Brazil) for a doctoral grant (232758/2014−0) made to Tâmmila Venzke Klug. The authorsare grateful to S.G. Hasa for her skillful technical assistance. The authors are also grateful to Sakata Seeds Ibérica SLU and to Sacoje SCL for providing the plant material

Disjointly homogeneous Banach lattices and applications

This is a survey on disjointly homogeneous Banach lattices and their applicactions. Several structural properties of this class are analyzed. In addition we show how these spaces provide a natural framework for studying the compactness of powers of operators allowing for a unified treatment of well-known results.Comment: 20 pages, to appear in Proceedings Positivity VII Conference (2013

Microeconomic Effects of Capital Controls: The Chilean Experience During the 1990s.

This paper studies the experience with the use of capital controls in Chile during the 1990s. Rather than revisiting previous studies, it complements previous research by providing, for the first time, empirical evidence on some of the microeconomic effects of capital controls, in particular, the unremunerated reserve requirement (URR). By looking at financial statements for a group of 73 Chilean firms during 1986-2001, the paper attempts to identify the effects of the URR on the firms’ costs and ways of financing. Chilean firms are grouped by economic sector, size and access to international capital markets. Results show that the effects of the URR are firm specific; forinstance, there are striking differences in the response to the URR among firms of different size and those with or without access to international capital markets.