Factors determining the growth curve of the foliose lichen Parmelia conspersa

Growth curves of the foliose lichen Parmelia conspersa (Ehrh. Ex Ach.)Ach. Were obtained by plotting radial growth (RGR, mm yr-1) of the fastest measured lobe, the slowest measured lobe, a randomly selected lobe, and by averaging a sample of lobes from each thallus against thallus diameter. Growth curves derived from the fastest-growing lobe and by averaging lobes were asymptotic and could be fitted by the growth model of Aplin and Hill. Mean lobe width increased with thallus size, reaching a maximum at approx. 4.5 cm thallus diameter. In four out of six thalli, radial growth of lobes over four months was positively correlated with initial lobe width or area. The RGR of isolated lobes was unaffected until the base of the lobe was removed to within 1-2 mm of the tip. The concentration (micrograms mg-1 biomass) of ribitol, arabitol and mannitol was greater in the marginal lobes of large than in small thalli. The results suggested that the growth curve of P. conspersa is determined by processes that occur within individual marginal lobes and can be explained by the Aplin and Hill model. Changes in lobe width and in the productive capacity of individual lobes with thallus size are likely to be more important factors than the degree of translocation within the lobe in determining the growth curve.

Growth curve of the lichen Rhizocarpon geographicum

Data on the growth curve of the lichen Rhizocarpon geographicum were obtained by measuring the radial growth rates (mm per 1.5 years) of 39 thalli from 2 to 65 mm in diameter growing in the same environment. An Aplin and Hill plot (r2 – r1 against ln r2 – ln r1) of the data and regression analyses suggested an initial phase of growth (up to a diameter of about 7 mm) in which the relative growth rate increased rapidly. This was followed by a phase in which the relative growth rate fell but the radial growth rate continued to rise (7 to 20 mm in diameter). Radial growth was then relatively constant until about 45 mm diameter and then declined. The Aplin and Hill model did not fit the data as a whole but may apply for a transient period in thalli between about 7 and 16 mm in diameter. The curve shows some similarities to that suggested by lichenometric studies but differs in showing a less steep decline in growth rate after the ‘great’ period.

Radial growth of Rhizocarpon section Rhizocarpon lichen thalli over six years at snoqualmie pass in the Cascade Range, Washington State

This article describes a 6-yr study of the radial growth rates (RGR, mm yr-1) of Rhizocarpon section Rhizocarpon thalli on a talus slope at Snoqualmie Pass in the Cascade Range, Washington State, United States (47°27'N; 121°26'W). At the end of the growth period, 32 of a total of 39 thalli had exhibited a positive RGR, and 7 of a total of 39 thalli showed no measurable growth. Mean RGR of all thalli was 0.07 mm yr-1 (range, 0-0.19 mm, SD = 0.06). Analysis of variance suggested no significant variation in RGR in successive growth periods, but significant differences were present both within and between thalli. The slope of a boulder facet did not influence RGR, but growth was affected by aspect, the least growth being observed on north-northwest facets. A plot of RGR against thallus diameter revealed a wide scatter of data points with little evidence for a significant change in growth with thallus size. Hence, the study showed that the RGR of Rhizocarpon thalli at Snoqualmie is extremely slow and highly variable and significantly less than estimates based on lichenometry. To determine the growth curve of a yellow-green Rhizocarpon by direct measurement at such a site would require a large sample of thalli and careful standardization of the species studied, the aspect conditions under which the thalli were measured, and the initial hypothallus width of the thalli. © 2005 Regents of the University of Colorado.

Experimental studies of lobe growth in the lichen Parmelia conspersa (Ehrh. Ex Ach.) Ach.

The radial growth of individual lobes of the foliose lichen, Parmelia conspersa (Ehrh. Ex Ach.) Ach. was studied to determine whether (1) adjacent lobes exchange carbohydrate and (2) marginal competition between lobes influences radial growth. In a survey of thalli of different size, the number of marginal lobes was linearly related to thallus circumference. However, the relationship between mean lobe width and thallus circumference was fitted by a second order polynomial. Hence, mean lobe width may reach a maximum in thalli approx. 3 cm in diameter. The interactions between marginal lobes were studied by either painting single lobes with acrylic paint or by removing lobes from the thallus. Painting the whole lobe virtually stopped its radial growth while partially painted lobes grew less than control lobes. The radial growth of a lobe was unaffected by either completely painting or removing its neighbour. Removal of both neighbouring lobes did not influence the radial growth of a lobe but severing the lobe from the thallus reduced its radial growth. In addition, lobe width increased significantly when both neighbouring lobes were removed. These results suggest that adjacent lobes have a considerable degree of independence and that there is little exchange of carbohydrate between them. In addition, marginal competition between adjacent lobes may restrict the lateral extension of the lobe and this may maintain a more constant mean lobe width in larger thalli. It is possible that the intensity of marginal competition between adjacent lobes may vary with thallus size and this could be a factor determining the growth curve of a foliose lichen throughout its life.

The biology of the crustose lichen Rhizocarpon geographicum

The crustose lichen Rhizocarpon geographicum (L.) DC. comprises yellow-green lichenized areolae which develop and grow on the surface of a non-lichenized fungal hypothallus, the latter extending beyond the edge of the areolae to form a marginal ring. The hypothallus advances very slowly and the considerable longevity of R. geographicum, especially in Arctic and Alpine environments, has been exploited by geologists in dating the exposure age of rock surfaces (lichenometry). This review explores various aspects of the biology of R. geographicum including: (1) structure and symbionts, (2) lichenization, (3) development of areolae, (4) radial growth rates (RaGR), (5) growth physiology, (6) changes in RaGR with thallus size (growth ratesize curve), (7) maturity and senescence, and (8) aspects of ecology. Lichenization occurs when fungal hyphae become associated with a compatible species of the alga Trebouxia, commonly found free-living on the substratum. Similarly, 'primary' areolae develop from free-living algal cells trapped by the advancing hypothallus. The shape of the growth rate-size curve of R. geographicum is controversial but may exhibit a phase of decreasing growth in larger thalli. Low rates of translocation of carbohydrate to the hypothallus together with allocation for stress resistance results in very slow RaGR, a low demand for nutrients, hence, the ability of R. geographicum to colonize more extreme environments. Several aspects of the biology of R. geographicum have implications for lichenometry including early development, mortality rates, the shape of the growth-rate size curve, and competition. © The Author(s) 2012.

Size distribution curves of senile plaques in patients with Alzheimer’s disease: do plaques grow according to the log-normal model?

The size frequency distributions of diffuse, primitive and cored senile plaques (SP) were studied in single sections of the temporal lobe from 10 patients with Alzheimer’s disease (AD). The size distribution curves were unimodal and positively skewed. The size distribution curve of the diffuse plaques was shifted towards larger plaques while those of the neuritic and cored plaques were shifted towards smaller plaques. The neuritic/diffuse plaque ratio was maximal in the 11 – 30 micron size class and the cored/ diffuse plaque ratio in the 21 – 30 micron size class. The size distribution curves of the three types of plaque deviated significantly from a log-normal distribution. Distributions expressed on a logarithmic scale were ‘leptokurtic’, i.e. with excess of observations near the mean. These results suggest that SP in AD grow to within a more restricted size range than predicted from a log-normal model. In addition, there appear to be differences in the patterns of growth of diffuse, primitive and cored plaques. If neuritic and cored plaques develop from earlier diffuse plaques, then smaller diffuse plaques are more likely to be converted to mature plaques.

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.

Nonlinear dynamics of a periodically driven Duffing resonator coupled to a Van der Pol oscillator

We explore the dynamics of a periodically driven Duffing resonator coupled elastically to a van der Pol oscillator in the case of 1?:?1 internal resonance in the cases of weak and strong coupling. Whilst strong coupling leads to dominating synchronization, the weak coupling case leads to a multitude of complex behaviours. A two-time scales method is used to obtain the frequency-amplitude modulation. The internal resonance leads to an antiresonance response of the Duffing resonator and a stagnant response (a small shoulder in the curve) of the van der Pol oscillator. The stability of the dynamic motions is also analyzed. The coupled system shows a hysteretic response pattern and symmetry-breaking facets. Chaotic behaviour of the coupled system is also observed and the dependence of the system dynamics on the parameters are also studied using bifurcation analysis.

Studies on the generalisation of Gaussian processes and Bayesian neural networks

The assessment of the reliability of systems which learn from data is a key issue to investigate thoroughly before the actual application of information processing techniques to real-world problems. Over the recent years Gaussian processes and Bayesian neural networks have come to the fore and in this thesis their generalisation capabilities are analysed from theoretical and empirical perspectives. Upper and lower bounds on the learning curve of Gaussian processes are investigated in order to estimate the amount of data required to guarantee a certain level of generalisation performance. In this thesis we analyse the effects on the bounds and the learning curve induced by the smoothness of stochastic processes described by four different covariance functions. We also explain the early, linearly-decreasing behaviour of the curves and we investigate the asymptotic behaviour of the upper bounds. The effect of the noise and the characteristic lengthscale of the stochastic process on the tightness of the bounds are also discussed. The analysis is supported by several numerical simulations. The generalisation error of a Gaussian process is affected by the dimension of the input vector and may be decreased by input-variable reduction techniques. In conventional approaches to Gaussian process regression, the positive definite matrix estimating the distance between input points is often taken diagonal. In this thesis we show that a general distance matrix is able to estimate the effective dimensionality of the regression problem as well as to discover the linear transformation from the manifest variables to the hidden-feature space, with a significant reduction of the input dimension. Numerical simulations confirm the significant superiority of the general distance matrix with respect to the diagonal one.In the thesis we also present an empirical investigation of the generalisation errors of neural networks trained by two Bayesian algorithms, the Markov Chain Monte Carlo method and the evidence framework; the neural networks have been trained on the task of labelling segmented outdoor images.

Growth of foliose lichens: a review

This review considers various aspects of the growth of foliose lichens including early growth and development, variation in radial growth rate (RaGR) of different species, growth to maturity, lobe growth variation, senescence and fragmentation, growth models, the influence of environmental variables, and the maintenance of thallus symmetry. The data suggest that a foliose lichen thallus is essentially a ‘colony’ in which the individual lobes exhibit a considerable degree of autonomy in their growth processes. During development, recognisable juvenile thalli are usually formed by 15 months to 4 years while most mature thalli exhibit RaGR between 1 and 5 mm yr-1. RaGR within a species is highly variable. The growth rate-size curve of a foliose lichen thallus may result from growth processes that take place at the tips of individual lobes together with size-related changes in the intensity of competition for space between the marginal lobes. Radial growth and growth in mass is influenced by climatic and microclimatic factors and also by substratum factors such as rock and bark texture, chemistry, and nutrient enrichment. Possible future research topics include: (1) measuring fast growing foliose species through life, (2) the three dimensional changes that occur during lobe growth, (3) the cellular changes that occur during regeneration, growth, and division of lobes, and (4) the distribution and allocation of the major lichen carbohydrates within lobes.

A tree-based decision model to support prediction of the severity of asthma exacerbations in children

This paper describes the development of a tree-based decision model to predict the severity of pediatric asthma exacerbations in the emergency department (ED) at 2 h following triage. The model was constructed from retrospective patient data abstracted from the ED charts. The original data was preprocessed to eliminate questionable patient records and to normalize values of age-dependent clinical attributes. The model uses attributes routinely collected in the ED and provides predictions even for incomplete observations. Its performance was verified on independent validating data (split-sample validation) where it demonstrated AUC (area under ROC curve) of 0.83, sensitivity of 84%, specificity of 71% and the Brier score of 0.18. The model is intended to supplement an asthma clinical practice guideline, however, it can be also used as a stand-alone decision tool.

Regression analysis of ranked segment parameters for optic nerve head classification:a pilot study

Purpose: To determine whether curve-fitting analysis of the ranked segment distributions of topographic optic nerve head (ONH) parameters, derived using the Heidelberg Retina Tomograph (HRT), provide a more effective statistical descriptor to differentiate the normal from the glaucomatous ONH. Methods: The sample comprised of 22 normal control subjects (mean age 66.9 years; S.D. 7.8) and 22 glaucoma patients (mean age 72.1 years; S.D. 6.9) confirmed by reproducible visual field defects on the Humphrey Field Analyser. Three 10°-images of the ONH were obtained using the HRT. The mean topography image was determined and the HRT software was used to calculate the rim volume, rim area to disc area ratio, normalised rim area to disc area ratio and retinal nerve fibre cross-sectional area for each patient at 10°-sectoral intervals. The values were ranked in descending order, and each ranked-segment curve of ordered values was fitted using the least squares method. Results: There was no difference in disc area between the groups. The group mean cup-disc area ratio was significantly lower in the normal group (0.204 ± 0.16) compared with the glaucoma group (0.533 ± 0.083) (p < 0.001). The visual field indices, mean deviation and corrected pattern S.D., were significantly greater (p < 0.001) in the glaucoma group (-9.09 dB ± 3.3 and 7.91 ± 3.4, respectively) compared with the normal group (-0.15 dB ± 0.9 and 0.95 dB ± 0.8, respectively). Univariate linear regression provided the best overall fit to the ranked segment data. The equation parameters of the regression line manually applied to the normalised rim area-disc area and the rim area-disc area ratio data, correctly classified 100% of normal subjects and glaucoma patients. In this study sample, the regression analysis of ranked segment parameters method was more effective than conventional ranked segment analysis, in which glaucoma patients were misclassified in approximately 50% of cases. Further investigation in larger samples will enable the calculation of confidence intervals for normality. These reference standards will then need to be investigated for an independent sample to fully validate the technique. Conclusions: Using a curve-fitting approach to fit ranked segment curves retains information relating to the topographic nature of neural loss. Such methodology appears to overcome some of the deficiencies of conventional ranked segment analysis, and subject to validation in larger scale studies, may potentially be of clinical utility for detecting and monitoring glaucomatous damage. © 2007 The College of Optometrists.

Anisotropic viscoelastic properties of undamaged asphalt mixtures

A test protocol and a data analysis method are developed in this paper on the basis of linear viscoelastic theory to characterize the anisotropic viscoelastic properties of undamaged asphalt mixtures. The test protocol includes three nondestructive tests: (1) uniaxial compressive creep test, (2) indirect tensile creep test, and (3) the uniaxial tensile creep test. All three tests are conducted on asphalt mixture specimens at three temperatures (10, 20, and 30°C) to determine the tensile and compressive properties at each temperature and then to construct the master curve of each property. The determined properties include magnitude and phase angle of the compressive complex modulus in the vertical direction, magnitude and phase angle of the tensile complex modulus, and the magnitude and phase angle of the compressive complex modulus in the horizontal plane. The test results indicate that all tested asphalt mixtures have significantly different tensile properties from compressive properties. The peak value of the master curve of the tensile complex modulus phase angle is within a range from 65 to 85°, whereas the peak value of the compressive moduli phase angle in both directions ranges from 35 to 55°. In addition, the undamaged asphalt mixtures exhibit distinctively anisotropic properties in compression. The magnitude of the compressive modulus in the vertical direction is approximately 1.2 to ̃2 times of the magnitude of the compressive modulus in the horizontal plane. Dynamic modulus tests are performed to verify the results of the proposed test protocol. The test results from the proposed test protocol match well with those from the dynamic tests. © 2012 American Society of Civil Engineers.

Regularity analysis of nocturnal oximetry recordings to assist in the diagnosis of sleep apnoea syndrome

The relationship between sleep apnoea–hypopnoea syndrome (SAHS) severity and the regularity of nocturnal oxygen saturation (SaO2) recordings was analysed. Three different methods were proposed to quantify regularity: approximate entropy (AEn), sample entropy (SEn) and kernel entropy (KEn). A total of 240 subjects suspected of suffering from SAHS took part in the study. They were randomly divided into a training set (96 subjects) and a test set (144 subjects) for the adjustment and assessment of the proposed methods, respectively. According to the measurements provided by AEn, SEn and KEn, higher irregularity of oximetry signals is associated with SAHS-positive patients. Receiver operating characteristic (ROC) and Pearson correlation analyses showed that KEn was the most reliable predictor of SAHS. It provided an area under the ROC curve of 0.91 in two-class classification of subjects as SAHS-negative or SAHS-positive. Moreover, KEn measurements from oximetry data exhibited a linear dependence on the apnoea–hypopnoea index, as shown by a correlation coefficient of 0.87. Therefore, these measurements could be used for the development of simplified diagnostic techniques in order to reduce the demand for polysomnographies. Furthermore, KEn represents a convincing alternative to AEn and SEn for the diagnostic analysis of noisy biomedical signals.

Protection issue discussion of DC network development:circuit breaker or fault-tolerant converter

This paper provides a discussion on future direct current (DC) network development in terms of system protection under DC-side fault scenarios. The argument between appropriate DC circuit breaker and new DC fault-tolerant converters is discussed after a review on DC technology development and bottleneck issues that require proper solutions. The overcurrent/cost curve of power-electronic DC circuit breakers (CB) superimposed to voltage-source converter (VSC) systems is derived and compared with other possible fault-tolerant power conversion options. This in-advance planning of protection capability is essential for the future development of DC networks.