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.

A meta-analysis of cambium phenology and growth: linear and non-linear patterns in conifers of the northern hemisphere

Background and Aims Ongoing global warming has been implicated in shifting phenological patterns such as the timing and duration of the growing season across a wide variety of ecosystems. Linear models are routinely used to extrapolate these observed shifts in phenology into the future and to estimate changes in associated ecosystem properties such as net primary productivity. Yet, in nature, linear relationships may be special cases. Biological processes frequently follow more complex, non-linear patterns according to limiting factors that generate shifts and discontinuities, or contain thresholds beyond which responses change abruptly. This study investigates to what extent cambium phenology is associated with xylem growth and differentiation across conifer species of the northern hemisphere. Methods Xylem cell production is compared with the periods of cambial activity and cell differentiation assessed on a weekly time scale on histological sections of cambium and wood tissue collected from the stems of nine species in Canada and Europe over 1–9 years per site from 1998 to 2011. Key Results The dynamics of xylogenesis were surprisingly homogeneous among conifer species, although dispersions from the average were obviously observed. Within the range analysed, the relationships between the phenological timings were linear, with several slopes showing values close to or not statistically different from 1. The relationships between the phenological timings and cell production were distinctly non-linear, and involved an exponential pattern. Conclusions The trees adjust their phenological timings according to linear patterns. Thus, shifts of one phenological phase are associated with synchronous and comparable shifts of the successive phases. However, small increases in the duration of xylogenesis could correspond to a substantial increase in cell production. The findings suggest that the length of the growing season and the resulting amount of growth could respond differently to changes in environmental conditions.

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.

Making Research Relevant to Development - Experience from the NCCR North-South

Making research relevant to development is a complex, non-linear and often unpredictable process which requires very particular skills and strategies on the part of researchers. The National Centre of Competence in Research (NCCR) North-South provides financial and technical support for researchers so that they can effectively cooperate with policy-makers and practitioners. An analysis of 10 years of experience translating research into development practise in the NCCR North-South revealed the following four strategies as particularly relevant: a) research orientation towards the needs and interests of partners; b) implementation of promising methods and approaches; c) communication and dissemination of research results; and d) careful analysis of the political context through monitoring and learning approaches. The NCCR North-South experience shows that “doing excellent research” is just one piece of the mosaic. It is equally important to join hands with non-academic partners from the very beginning of a research project, in order to develop and test new pathways for sustainable development. Capacity building – in the North and South – enables researchers to do both: To do excellent research and to make it relevant for development.

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.

Quantitative 3D strain analysis in analogue experiments: Integration of X-ray computed tomography and digital volume correlation techniques

The combination of scaled analogue experiments, material mechanics, X-ray computed tomography (XRCT) and Digital Volume Correlation techniques (DVC) is a powerful new tool not only to examine the 3 dimensional structure and kinematic evolution of complex deformation structures in scaled analogue experiments, but also to fully quantify their spatial strain distribution and complete strain history. Digital image correlation (DIC) is an important advance in quantitative physical modelling and helps to understand non-linear deformation processes. Optical non-intrusive (DIC) techniques enable the quantification of localised and distributed deformation in analogue experiments based either on images taken through transparent sidewalls (2D DIC) or on surface views (3D DIC). X-ray computed tomography (XRCT) analysis permits the non-destructive visualisation of the internal structure and kinematic evolution of scaled analogue experiments simulating tectonic evolution of complex geological structures. The combination of XRCT sectional image data of analogue experiments with 2D DIC only allows quantification of 2D displacement and strain components in section direction. This completely omits the potential of CT experiments for full 3D strain analysis of complex, non-cylindrical deformation structures. In this study, we apply digital volume correlation (DVC) techniques on XRCT scan data of “solid” analogue experiments to fully quantify the internal displacement and strain in 3 dimensions over time. Our first results indicate that the application of DVC techniques on XRCT volume data can successfully be used to quantify the 3D spatial and temporal strain patterns inside analogue experiments. We demonstrate the potential of combining DVC techniques and XRCT volume imaging for 3D strain analysis of a contractional experiment simulating the development of a non-cylindrical pop-up structure. Furthermore, we discuss various options for optimisation of granular materials, pattern generation, and data acquisition for increased resolution and accuracy of the strain results. Three-dimensional strain analysis of analogue models is of particular interest for geological and seismic interpretations of complex, non-cylindrical geological structures. The volume strain data enable the analysis of the large-scale and small-scale strain history of geological 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.

Cochrane and non-Cochrane systematic reviews in leading orthodontic journals: a quality paradigm?

The aims of this study were to assess and compare the methodological quality of Cochrane and non-Cochrane systematic reviews (SRs) published in leading orthodontic journals and the Cochrane Database of Systematic Reviews (CDSR) using AMSTAR and to compare the prevalence of meta-analysis in both review types. A literature search was undertaken to identify SRs that consisted of hand-searching five major orthodontic journals [American Journal of Orthodontics and Dentofacial Orthopedics, Angle Orthodontist, European Journal of Orthodontics, Journal of Orthodontics and Orthodontics and Craniofacial Research (February 2002 to July 2011)] and the Cochrane Database of Systematic Reviews from January 2000 to July 2011. Methodological quality of the included reviews was gauged using the AMSTAR tool involving 11 key methodological criteria with a score of 0 or 1 given for each criterion. A cumulative grade was given for the paper overall (0-11); an overall score of 4 or less represented poor methodological quality, 5-8 was considered fair and 9 or greater was deemed to be good. In total, 109 SRs were identified in the five major journals and on the CDSR. Of these, 26 (23.9%) were in the CDSR. The mean overall AMSTAR score was 6.2 with 21.1% of reviews satisfying 9 or more of the 11 criteria; a similar prevalence of poor reviews (22%) was also noted. Multiple linear regression indicated that reviews published in the CDSR (P < 0.01); and involving meta-analysis (β = 0.50, 95% confidence interval 0.72, 2.07, P < 0.001) showed greater concordance with AMSTAR.

Initial cord blood unit volume affects mononuclear cell and CD34+ cell-processing efficiency in a non-linear fashion

Umbilical cord blood (UCB) is a source of hematopoietic stem cells that initially was used exclusively for the hematopoietic reconstitution of pediatric patients. It is now suggested for use for adults as well, a fact that increases the pressure to obtain units with high cellularity. Therefore, the optimization of UCB processing is a priority.

An integrative transcranial magnetic stimulation mapping technique using non-linear curve fitting

The aim of this study is to develop a new simple method for analyzing one-dimensional transcranial magnetic stimulation (TMS) mapping studies in humans. Motor evoked potentials (MEP) were recorded from the abductor pollicis brevis (APB) muscle during stimulation at nine different positions on the scalp along a line passing through the APB hot spot and the vertex. Non-linear curve fitting according to the Levenberg-Marquardt algorithm was performed on the averaged amplitude values obtained at all points to find the best-fitting symmetrical and asymmetrical peak functions. Several peak functions could be fitted to the experimental data. Across all subjects, a symmetric, bell-shaped curve, the complementary error function (erfc) gave the best results. This function is characterized by three parameters giving its amplitude, position, and width. None of the mathematical functions tested with less or more than three parameters fitted better. The amplitude and position parameters of the erfc were highly correlated with the amplitude at the hot spot and with the location of the center of gravity of the TMS curve. In conclusion, non-linear curve fitting is an accurate method for the mathematical characterization of one-dimensional TMS curves. This is the first method that provides information on amplitude, position and width simultaneously.