Growth rates of Rhizocarpon geographicum lichens:A review with new data from Iceland

This paper reviews evidence from previous growth-rate studies on lichens of the yellow-green species of Subgenus Rhizocarpon - the family most commonly used in lichenometric dating. New data are presented from Rhizocarpon section Rhizocarpon thalli growing on a moraine in southern Iceland over a period of 4.33yr. Measurements of 38 lichen thalli, between 2001 and 2005, show that diametral growth rate (DGR, mmyr-1) is a function of thallus size. Growth rates increase rapidly in small thalli (<10 mm diameter), remain high (ca. 0.8 mm yr-1) and then decrease gradually in larger thalli (>50 mm diameter). Mean DGR in southern Iceland, between 2001 and 2005, was 0.64 mm yr-1 (SD = 0.24). The resultant growth-rate curve is parabolic and is best described by a third-order polynomial function. The striking similarity between these findings in Iceland and those of Armstrong (1983) in Wales implies that the shape of the growth-rate curve may be characteristic of Rhizocarpon geographicum lichens. The difference between the absolute growth rate in southern Iceland and Wales (ca. 66% faster) is probably a function of climate and micro-environment between the two sites. These findings have implications for previous lichenometric-dating studies, namely, that those studies which assume constant lichen growth rates over many decades are probably unreliable. © British Geological Survey/ Natural Environment Research Council copyright 2006.

Growth curves of four crustose lichens

The growth curves of four common species of crustose lichens, viz., Buellia aethalea (Ach.) Th. Fr., Lecidea tumida Massai., Rhizocarpon geographicum (L.) DC., and Rhizocarpon reductum Th. Fr. were studied at a site in south Gwynedd, north Wales, UK. Radial growth rates (RGR, mm 1.5 yr-1) were greatest in thalli of R. reductum and least in R. geographicum. Variation in RGR between thalli was greater in B. aethalea and L. tumida than in the species of Rhizocarpon. The relationship between growth rate and thallus diameter was not asymptotic; RGR increasing in smaller thalli to a maximum and then declining in larger diameter thalli. A polynomial curve was fitted to the data; the growth curves being fitted best by a second-order (quadratic) curve, the best fit to this model being shown by B. aethalea. A significant linear regression with a negative slope was also fitted to the growth of the larger thalli of each species. The data suggest that the growth curves of the four crustose lichens differ significantly from the asymptotic curves of foliose lichen species. A phase of declining RGR in larger thalli appears to be characteristic of crustose lichens and is consistent with data from lichenometric studies.

Statnote 20: non-linear regression: fitting a general polynomial curve

In some circumstances, there may be no scientific model of the relationship between X and Y that can be specified in advance and indeed the objective of the investigation may be to provide a ‘curve of best fit’ for predictive purposes. In such an example, the fitting of successive polynomials may be the best approach. There are various strategies to decide on the polynomial of best fit depending on the objectives of the investigation.

The propensity to disrupt and the disruption nucleolus of a characteristic function game

Gately [1974] recently introduced the concept of an individual player's “propensity to disrupt” a payoff vector in a three-person characteristic function game. As a generalisation of this concept we propose the “disruption nucleolus” of ann-person game. The properties and computational possibilities of this concept are analogous to those of the nucleolus itself. Two numerical examples are given.

Laminar distribution of the pathological changes in sporadic frontotemporal lobar degeneration with transactive response (TAR) DNA-binding protein of 43kDa (TDP-43) proteinopathy:a quantitative study using polynomial curve fitting

Aims: Previous data suggest heterogeneity in laminar distribution of the pathology in the molecular disorder frontotemporal lobar degeneration (FTLD) with transactive response (TAR) DNA-binding protein of 43kDa (TDP-43) proteinopathy (FTLD-TDP). To study this heterogeneity, we quantified the changes in density across the cortical laminae of neuronal cytoplasmic inclusions, glial inclusions, neuronal intranuclear inclusions, dystrophic neurites, surviving neurones, abnormally enlarged neurones, and vacuoles in regions of the frontal and temporal lobe. Methods: Changes in density of histological features across cortical gyri were studied in 10 sporadic cases of FTLD-TDP using quantitative methods and polynomial curve fitting. Results: Our data suggest that laminar neuropathology in sporadic FTLD-TDP is highly variable. Most commonly, neuronal cytoplasmic inclusions, dystrophic neurites and vacuolation were abundant in the upper laminae and glial inclusions, neuronal intranuclear inclusions, abnormally enlarged neurones, and glial cell nuclei in the lower laminae. TDP-43-immunoreactive inclusions affected more of the cortical profile in longer duration cases; their distribution varied with disease subtype, but was unrelated to Braak tangle score. Different TDP-43-immunoreactive inclusions were not spatially correlated. Conclusions: Laminar distribution of pathological features in 10 sporadic cases of FTLD-TDP is heterogeneous and may be accounted for, in part, by disease subtype and disease duration. In addition, the feedforward and feedback cortico-cortical connections may be compromised in FTLD-TDP. © 2012 The Authors. Neuropathology and Applied Neurobiology © 2012 British Neuropathological Society.

Polynomial function intervals for floating-point software verification

The focus of our work is the verification of tight functional properties of numerical programs, such as showing that a floating-point implementation of Riemann integration computes a close approximation of the exact integral. Programmers and engineers writing such programs will benefit from verification tools that support an expressive specification language and that are highly automated. Our work provides a new method for verification of numerical software, supporting a substantially more expressive language for specifications than other publicly available automated tools. The additional expressivity in the specification language is provided by two constructs. First, the specification can feature inclusions between interval arithmetic expressions. Second, the integral operator from classical analysis can be used in the specifications, where the integration bounds can be arbitrary expressions over real variables. To support our claim of expressivity, we outline the verification of four example programs, including the integration example mentioned earlier. A key component of our method is an algorithm for proving numerical theorems. This algorithm is based on automatic polynomial approximation of non-linear real and real-interval functions defined by expressions. The PolyPaver tool is our implementation of the algorithm and its source code is publicly available. In this paper we report on experiments using PolyPaver that indicate that the additional expressivity does not come at a performance cost when comparing with other publicly available state-of-the-art provers. We also include a scalability study that explores the limits of PolyPaver in proving tight functional specifications of progressively larger randomly generated programs. © 2014 Springer International Publishing Switzerland.

Element characteristic tolerance for semi-batch fixed bed biomass pyrolysis

Biomass pyrolysis to bio-oil is one of the promising sustainable fuels. In this work, relation between biomass feedstock element characteristic and crude bio-oil production yield and lower heating value was explored. The element characteristics considered in this study include moisture, ash, fix carbon, volatile matter, C, H, N, O, S, cellulose, hemicellulose, and lignin content. A semi-batch fixed bed reactor was used for biomass pyrolysis with heating rate of 30 °C/min from room temperature to 600 °C and the reactor was held at 600 °C for 1 h before cooling down. Constant nitrogen flow (1bar) was provided for anaerobic condition. Sago and Napier glass were used in the study to create different element characteristic of feedstock by altering mixing ratio. Comparison between each element characteristic to crude bio-oil yield and low heating value was conducted. The result suggested potential key element characteristic for pyrolysis and provide a platform to access the feedstock element acceptance range.

Unveiling temporal correlations characteristic of a phase transition in the output intensity of a fiber laser

We use advanced statistical tools of time-series analysis to characterize the dynamical complexity of the transition to optical wave turbulence in a fiber laser. Ordinal analysis and the horizontal visibility graph applied to the experimentally measured laser output intensity reveal the presence of temporal correlations during the transition from the laminar to the turbulent lasing regimes. Both methods unveil coherent structures with well-defined time scales and strong correlations both, in the timing of the laser pulses and in their peak intensities. Our approach is generic and may be used in other complex systems that undergo similar transitions involving the generation of extreme fluctuations.

Pyrolysis of Napier grass in a fixed bed reactor:effect of operating conditions on product yields and characteristic

This study presents a report on pyrolysis of Napier grass stem in a fixed bed reactor. The effects of nitrogen flow (20 to 60 mL/min), and reaction temperature (450 to 650 degrees C) were investigated. Increasing the nitrogen flow from 20 to 30 mL/min increased the bio-oil yield and decreased both bio-char and non-condensable gas. 30 mL/min nitrogen flow resulted in optimum bio-oil yield and was used in the subsequent experiments. Reaction temperatures between 450 and 600 degrees C increased the bio-oil yield, with maximum yield of 32.26 wt% at 600 degrees C and a decrease in the corresponding bio-char and non-condensable gas. At 650 degrees C, reductions in the bio-oil and bio-char yields were recorded while the non-condensable gas increased. Water content of the bio-oil decreased with increasing reaction temperature, while density and viscosity increased. The observed pH and higher heating values were between 2.43 to 2.97, and 25.25 to 28.88 MJ/kg, respectively. GC-MS analysis revealed that the oil was made up of highly oxygenated compounds and requires upgrading. The bio-char and non-condensable gas were characterized, and the effect of reaction temperature on the properties was evaluated. Napier grass represents a good source of renewable energy when all pyrolysis products are efficiently utilized.