Predictability and Randomness

Algorithmic theories of randomness can be related to theories of probabilistic sequence prediction through the notion of a predictor, defined as a function which supplies lower bounds on initial-segment probabilities of infinite sequences. An infinite binary sequence $z$ is called unpredictable iff its initial-segment "redundancy" $n+\log p(z(n))$ remains sufficiently low relative to every effective predictor $p$. A predictor which maximizes the initial-segment redundancy of a sequence is called optimal for that sequence. It turns out that a sequence is random iff it is unpredictable. More generally, a sequence is random relative to an arbitrary computable distribution iff the distribution is itself an optimal predictor for the sequence. Here "random" can be taken in the sense of Martin-L\"{o}f by using weak criteria of effectiveness, or in the sense of Schnorr by using stronger criteria of effectiveness. Under the weaker criteria of effectiveness it is possible to construct a universal predictor which is optimal for all infinite sequences. This predictor assigns nonvanishing limit probabilities precisely to the recursive sequences. Under the stronger criteria of effectiveness it is possible to establish a law of large numbers for sequences random relative to a computable distribution, which may be useful as a criterion of "rationality" for methods of probabilistic prediction. A remarkable feature of effective predictors is the fact that they are expressible in the special form first proposed by Solomonoff. In this form sequence prediction reduces to assigning high probabilities to initial segments with short and/or numerous encodings. This fact provides the link between theories of randomness and Solomonoff's theory of prediction.Comment: 30 pages + refs. A re-typeset University of Alberta Technical Report, no longer available as suc

Community shifts and carbon translocation within metabolically-active rhizosphere microorganisms in grasslands under elevated CO₂

International audienceThe aim of this study was to identify the microbial communities that are actively involved in the assimilation of rhizosphere-C and are most sensitive in their activity to elevated atmospheric CO2 in a temperate semi-natural low-input grassland ecosystem. For this, we analyzed 13C signatures in microbial biomarker phospholipid fatty acids (PLFA) from an in-situ 13CO2 pulse-labeling experiment in the Giessen Free Air Carbon dioxide Enrichment grasslands (GiFACE, Germany) exposed to ambient and elevated (i.e. 50% above ambient) CO2 concentrations. Short-term 13C PLFA measurements at 3 h and 10 h after the pulse-labeling revealed very little to no 13C enrichment after 3 h in biomarker PLFAs and a much greater incorporation of new plant-C into fungal compared to bacterial PLFAs after 10 h. After a period of 11 months following the pulse-labeling experiment, the 13C enrichment of fungal PLFAs was still largely present but had decreased, while bacterial PLFAs were much more enriched in 13C compared to a few hours after the pulse-labeling. These results imply that new rhizodeposit-C is rapidly processed by fungal communities and only much later by the bacterial communities, which we attributed to either a fungal-mediated translocation of rhizosphere-C from the fungal to bacterial biomass or a preferential bacterial use of dead root or fungal necromass materials as C source over the direct utilization of fresh root-exudate C in these N-limited grassland ecosystems. Elevated CO2 caused an increase in the proportional 13C enrichment (relative to the universal biomarker 16:0) of the arbuscular mycorrhizal fungal biomarker PLFA 16:1?5 and one gram-positive bacterial biomarker PLFA i16:0, but a decrease in the proportional 13C enrichment of 18:1?9c, a commonly used though questionable fungal biomarker PLFA. This suggests enhanced fungal rhizodeposit-C assimilation only by arbuscular mycorrhizal fungal species under elevated CO2

Optimal control strategies for tuberculosis treatment: a case study in Angola

We apply optimal control theory to a tuberculosis model given by a system of ordinary differential equations. Optimal control strategies are proposed to minimize the cost of interventions. Numerical simulations are given using data from Angola.Comment: This is a preprint of a paper whose final and definite form will appear in the international journal Numerical Algebra, Control and Optimization (NACO). Paper accepted for publication 15-March-201

Stable Carbon Isotope Signature of Methane Released From Phytoplankton

Unidad de excelencia María de Maeztu CEX2019-000940-MAquatic ecosystems play an important role in global methane cycling and many field studies have reported methane supersaturation in the oxic surface mixed layer (SML) of the ocean and in the epilimnion of lakes. The origin of methane formed under oxic condition is hotly debated and several pathways have recently been offered to explain the "methane paradox." In this context, stable isotope measurements have been applied to constrain methane sources in supersaturated oxygenated waters. Here we present stable carbon isotope signatures for six widespread marine phytoplankton species, three haptophyte algae and three cyanobacteria, incubated under laboratory conditions. The observed isotopic patterns implicate that methane formed by phytoplankton might be clearly distinguished from methane produced by methanogenic archaea. Comparing results from phytoplankton experiments with isotopic data from field measurements, suggests that algal and cyanobacterial populations may contribute substantially to methane formationobserved in the SML of oceans and lakes