Complexity and non-linearity in earth surface processes - concepts, methods and applications

Complexity has long been recognized and is increasingly becoming mainstream in geomorphology. However, the relative novelty of various concepts and techniques associated to it means that ambiguity continues to surround complexity. In this commentary, we present and discuss a variety of recent contributions that have the potential to help clarify issues and advance the use of complexity in geomorphology.

Screening and prediction of erosive potential

The literature on the erosive potential of drinks and other products is summarised, and aspects of the conduct of screening tests as well as possible correlations of the erosive potential with various solution parameters are discussed. The solution parameters that have been suggested as important include pH, acid concentration (with respect to buffer capacity and concentration of undissociated acid), degree of saturation, calcium and phosphate concentrations, and inhibitors of erosion. Based on the available data, it is concluded that the dominant factor in erosion is pH. The effect of buffer capacity seems to be pH dependent. The degree of saturation probably has a non-linear relationship with erosion. While calcium at elevated concentrations is known to reduce erosion effectively, it is not known whether it is important at naturally occurring concentrations. Fluoride at naturally occurring concentrations is inversely correlated with erosive potential, but phosphate is probably not. Natural plant gums, notably pectin, do not inhibit erosion, so they are unlikely to interfere with the prediction of erosive potential. The non-linearity of some solution factors and interactions with pH need to be taken into account when developing multivariate models for predicting the erosive potential of different solutions. Finally, the erosive potential of solutions towards enamel and dentine might differ.

Ar diffusion in K-feldspar: present and absent

The mechanisms of Ar release from K-feldspar samples in laboratory experiments and during their geological history are assessed here. Modern petrology clearly established that the chemical and isotopic record of minerals is normally dominated by aqueous recrystallization. The laboratory critique is trickier, which explains why so many conflicting approaches have been able to survive long past their expiration date. Current models are evaluated for self-consistency; especially Arrhenian non-linearity leads to paradoxes. The models’ testable geological predictions suggest that temperature-based downslope extrapolations often overestimate observed geological Ar mobility substantially. An updated interpretation is based on the unrelatedness of geological behaviour to laboratory experiments. The isotopic record of K-feldspar in geological samples is not a unique function of temperature, as recrystallisation promoted by aqueous fluids is the predominant mechanism controlling isotope transport. K-feldspar should therefore be viewed as a hygrochronometer. Laboratory degassing proceeds from structural rearrangements and phase transitions such as are observed in situ at high temperature in Na and Pb feldspars. These effects violate the mathematics of an inert Fick’s Law matrix and preclude downslope extrapolation. The similar upward-concave, non-linear shapes of Arrhenius trajectories of many silicates, hydrous and anhydrous, are likely common manifestations of structural rearrangements in silicate structures.

Moving forward on facilitation research: response to changing environments and effects on the diversity, functioning and evolution of plant communities

Once seen as anomalous, facilitative interactions among plants and their importance for community structure and functioning are now widely recognized. The growing body of modelling, descriptive and experimental studies on facilitation covers a wide variety of terrestrial and aquatic systems throughout the globe. However, the lack of a general body of theory linking facilitation among different types of organisms and biomes and their responses to environmental changes prevents further advances in our knowledge regarding the evolutionary and ecological implications of facilitation in plant communities. Moreover, insights gathered from alternative lines of inquiry may substantially improve our understanding of facilitation, but these have been largely neglected thus far. Despite over 15 years of research and debate on this topic, there is no consensus on the degree to which plant–plant interactions change predictably along environmental gradients (i.e. the stress-gradient hypothesis), and this hinders our ability to predict how plant–plant interactions may affect the response of plant communities to ongoing global environmental change. The existing controversies regarding the response of plant–plant interactions across environmental gradients can be reconciled when clearly considering and determining the species-specificity of the response, the functional or individual stress type, and the scale of interest (pairwise interactions or community-level response). Here, we introduce a theoretical framework to do this, supported by multiple lines of empirical evidence. We also discuss current gaps in our knowledge regarding how plant–plant interactions change along environmental gradients. These include the existence of thresholds in the amount of species-specific stress that a benefactor can alleviate, the linearity or non-linearity of the response of pairwise interactions across distance from the ecological optimum of the beneficiary, and the need to explore further how frequent interactions among multiple species are and how they change across different environments. We review the latest advances in these topics and provide new approaches to fill current gaps in our knowledge. We also apply our theoretical framework to advance our knowledge on the evolutionary aspects of plant facilitation, and the relative importance of facilitation, in comparison with other ecological processes, for maintaining ecosystem structure, functioning and dynamics. We build links between these topics and related fields, such as ecological restoration, woody encroachment, invasion ecology, ecological modelling and biodiversity–ecosystem-functioning relationships. By identifying commonalities and insights from alternative lines of research, we further advance our understanding of facilitation and provide testable hypotheses regarding the role of (positive) biotic interactions in the maintenance of biodiversity and the response of ecological communities to ongoing environmental changes.

A Baseline Wander Tracking System for Artifact Rejection in Long-Term Electrocardiography

Long-term electrocardiogram (ECG) signals might suffer from relevant baseline disturbances during physical activity. Motion artifacts in particular are more pronounced with dry surface or esophageal electrodes which are dedicated to prolonged ECG recording. In this paper we present a method called baseline wander tracking (BWT) that tracks and rejects strong baseline disturbances and avoids concurrent saturation of the analog front-end. The proposed algorithm shifts the baseline level of the ECG signal to the middle of the dynamic input range. Due to the fast offset shifts, that produce much steeper signal portions than the normal ECG waves, the true ECG signal can be reconstructed offline and filtered using computationally intensive algorithms. Based on Monte Carlo simulations we observed reconstruction errors mainly caused by the non-linearity inaccuracies of the DAC. However, the signal to error ratio of the BWT is higher compared to an analog front-end featuring a dynamic input ranges above 15 mV if a synthetic ECG signal was used. The BWT is additionally able to suppress (electrode) offset potentials without introducing long transients. Due to its structural simplicity, memory efficiency and the DC coupling capability, the BWT is dedicated to high integration required in long-term and low-power ECG recording systems.

Fine particulate matter measurements in Swiss restaurants, cafés and bars: what is the effect of spatial separation between smoking and non-smoking areas?

We performed 124 measurements of particulate matter (PM(2.5)) in 95 hospitality venues such as restaurants, bars, cafés, and a disco, which had differing smoking regulations. We evaluated the impact of spatial separation between smoking and non-smoking areas on mean PM(2.5) concentration, taking relevant characteristics of the venue, such as the type of ventilation or the presence of additional PM(2.5) sources, into account. We differentiated five smoking environments: (i) completely smoke-free location, (ii) non-smoking room spatially separated from a smoking room, (iii) non-smoking area with a smoking area located in the same room, (iv) smoking area with a non-smoking area located in the same room, and (v) smoking location which could be either a room where smoking was allowed that was spatially separated from non-smoking room or a hospitality venue without smoking restriction. In these five groups, the geometric mean PM(2.5) levels were (i) 20.4, (ii) 43.9, (iii) 71.9, (iv) 110.4, and (v) 110.3 microg/m(3), respectively. This study showed that even if non-smoking and smoking areas were spatially separated into two rooms, geometric mean PM(2.5) levels in non-smoking rooms were considerably higher than in completely smoke-free hospitality venues. PRACTICAL IMPLICATIONS: PM(2.5) levels are considerably increased in the non-smoking area if smoking is allowed anywhere in the same location. Even locating the smoking area in another room resulted in a more than doubling of the PM(2.5) levels in the non-smoking room compared with venues where smoking was not allowed at all. In practice, spatial separation of rooms where smoking is allowed does not prevent exposure to environmental tobacco smoke in nearby non-smoking areas.

Modulus and Poincaré Inequalities on Non-Self-Similar Sierpiński Carpets

A carpet is a metric space homeomorphic to the Sierpiński carpet. We characterize, within a certain class of examples, non-self-similar carpets supporting curve families of nontrivial modulus and supporting Poincaré inequalities. Our results yield new examples of compact doubling metric measure spaces supporting Poincaré inequalities: these examples have no manifold points, yet embed isometrically as subsets of Euclidean space.

The coupling of non-linear supersymmetry to supergravity

We study the coupling of non-linear supersymmetry to supergravity. The goldstino nilpotent superfield of global supersymmetry coupled to supergravity is described by a geometric action of the chiral curvature superfield R subject to the constraint (R−λ)2=0 with an appropriate constant λ. This constraint can be found as the decoupling limit of the scalar partner of the goldstino in a class of f(R) supergravity theories.

Effectiveness of non-steroidal anti-inflammatory drugs for the treatment of pain in knee and hip osteoarthritis: a network meta-analysis.

BACKGROUND Non-steroidal anti-inflammatory drugs (NSAIDs) are the backbone of osteoarthritis pain management. We aimed to assess the effectiveness of different preparations and doses of NSAIDs on osteoarthritis pain in a network meta-analysis. METHODS For this network meta-analysis, we considered randomised trials comparing any of the following interventions: NSAIDs, paracetamol, or placebo, for the treatment of osteoarthritis pain. We searched the Cochrane Central Register of Controlled Trials (CENTRAL) and the reference lists of relevant articles for trials published between Jan 1, 1980, and Feb 24, 2015, with at least 100 patients per group. The prespecified primary and secondary outcomes were pain and physical function, and were extracted in duplicate for up to seven timepoints after the start of treatment. We used an extension of multivariable Bayesian random effects models for mixed multiple treatment comparisons with a random effect at the level of trials. For the primary analysis, a random walk of first order was used to account for multiple follow-up outcome data within a trial. Preparations that used different total daily dose were considered separately in the analysis. To assess a potential dose-response relation, we used preparation-specific covariates assuming linearity on log relative dose. FINDINGS We identified 8973 manuscripts from our search, of which 74 randomised trials with a total of 58 556 patients were included in this analysis. 23 nodes concerning seven different NSAIDs or paracetamol with specific daily dose of administration or placebo were considered. All preparations, irrespective of dose, improved point estimates of pain symptoms when compared with placebo. For six interventions (diclofenac 150 mg/day, etoricoxib 30 mg/day, 60 mg/day, and 90 mg/day, and rofecoxib 25 mg/day and 50 mg/day), the probability that the difference to placebo is at or below a prespecified minimum clinically important effect for pain reduction (effect size [ES] -0·37) was at least 95%. Among maximally approved daily doses, diclofenac 150 mg/day (ES -0·57, 95% credibility interval [CrI] -0·69 to -0·46) and etoricoxib 60 mg/day (ES -0·58, -0·73 to -0·43) had the highest probability to be the best intervention, both with 100% probability to reach the minimum clinically important difference. Treatment effects increased as drug dose increased, but corresponding tests for a linear dose effect were significant only for celecoxib (p=0·030), diclofenac (p=0·031), and naproxen (p=0·026). We found no evidence that treatment effects varied over the duration of treatment. Model fit was good, and between-trial heterogeneity and inconsistency were low in all analyses. All trials were deemed to have a low risk of bias for blinding of patients. Effect estimates did not change in sensitivity analyses with two additional statistical models and accounting for methodological quality criteria in meta-regression analysis. INTERPRETATION On the basis of the available data, we see no role for single-agent paracetamol for the treatment of patients with osteoarthritis irrespective of dose. We provide sound evidence that diclofenac 150 mg/day is the most effective NSAID available at present, in terms of improving both pain and function. Nevertheless, in view of the safety profile of these drugs, physicians need to consider our results together with all known safety information when selecting the preparation and dose for individual patients. FUNDING Swiss National Science Foundation (grant number 405340-104762) and Arco Foundation, Switzerland.