Alternatives to linear analysis of energy balance data from lactating dairy cows

The current energy requirements system used in the United Kingdom for lactating dairy cows utilizes key parameters such as metabolizable energy intake (MEI) at maintenance (MEm), the efficiency of utilization of MEI for 1) maintenance, 2) milk production (k(l)), 3) growth (k(g)), and the efficiency of utilization of body stores for milk production (k(t)). Traditionally, these have been determined using linear regression methods to analyze energy balance data from calorimetry experiments. Many studies have highlighted a number of concerns over current energy feeding systems particularly in relation to these key parameters, and the linear models used for analyzing. Therefore, a database containing 652 dairy cow observations was assembled from calorimetry studies in the United Kingdom. Five functions for analyzing energy balance data were considered: straight line, two diminishing returns functions, (the Mitscherlich and the rectangular hyperbola), and two sigmoidal functions (the logistic and the Gompertz). Meta-analysis of the data was conducted to estimate k(g) and k(t). Values of 0.83 to 0.86 and 0.66 to 0.69 were obtained for k(g) and k(t) using all the functions (with standard errors of 0.028 and 0.027), respectively, which were considerably different from previous reports of 0.60 to 0.75 for k(g) and 0.82 to 0.84 for k(t). Using the estimated values of k(g) and k(t), the data were corrected to allow for body tissue changes. Based on the definition of k(l) as the derivative of the ratio of milk energy derived from MEI to MEI directed towards milk production, MEm and k(l) were determined. Meta-analysis of the pooled data showed that the average k(l) ranged from 0.50 to 0.58 and MEm ranged between 0.34 and 0.64 MJ/kg of BW0.75 per day. Although the constrained Mitscherlich fitted the data as good as the straight line, more observations at high energy intakes (above 2.4 MJ/kg of BW0.75 per day) are required to determine conclusively whether milk energy is related to MEI linearly or not.

Extending Zelterman’s approach for robust estimation of population size to zero-truncated clustered data

Estimation of population size with missing zero-class is an important problem that is encountered in epidemiological assessment studies. Fitting a Poisson model to the observed data by the method of maximum likelihood and estimation of the population size based on this fit is an approach that has been widely used for this purpose. In practice, however, the Poisson assumption is seldom satisfied. Zelterman (1988) has proposed a robust estimator for unclustered data that works well in a wide class of distributions applicable for count data. In the work presented here, we extend this estimator to clustered data. The estimator requires fitting a zero-truncated homogeneous Poisson model by maximum likelihood and thereby using a Horvitz-Thompson estimator of population size. This was found to work well, when the data follow the hypothesized homogeneous Poisson model. However, when the true distribution deviates from the hypothesized model, the population size was found to be underestimated. In the search of a more robust estimator, we focused on three models that use all clusters with exactly one case, those clusters with exactly two cases and those with exactly three cases to estimate the probability of the zero-class and thereby use data collected on all the clusters in the Horvitz-Thompson estimator of population size. Loss in efficiency associated with gain in robustness was examined based on a simulation study. As a trade-off between gain in robustness and loss in efficiency, the model that uses data collected on clusters with at most three cases to estimate the probability of the zero-class was found to be preferred in general. In applications, we recommend obtaining estimates from all three models and making a choice considering the estimates from the three models, robustness and the loss in efficiency. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

The application of the Hilbert spectrum to the analysis of electromyographic signals

This paper investigates the application of the Hilbert spectrum (HS), which is a recent tool for the analysis of nonlinear and nonstationary time-series, to the study of electromyographic (EMG) signals. The HS allows for the visualization of the energy of signals through a joint time-frequency representation. In this work we illustrate the use of the HS in two distinct applications. The first is for feature extraction from EMG signals. Our results showed that the instantaneous mean frequency (IMNF) estimated from the HS is a relevant feature to clinical practice. We found that the median of the IMNF reduces when the force level of the muscle contraction increases. In the second application we investigated the use of the HS for detection of motor unit action potentials (MUAPs). The detection of MUAPs is a basic step in EMG decomposition tools, which provide relevant information about the neuromuscular system through the morphology and firing time of MUAPs. We compared, visually, how MUAP activity is perceived on the HS with visualizations provided by some traditional (e.g. scalogram, spectrogram, Wigner-Ville) time-frequency distributions. Furthermore, an alternative visualization to the HS, for detection of MUAPs, is proposed and compared to a similar approach based on the continuous wavelet transform (CWT). Our results showed that both the proposed technique and the CWT allowed for a clear visualization of MUAP activity on the time-frequency distributions, whereas results obtained with the HS were the most difficult to interpret as they were extremely affected by spurious energy activity. (c) 2008 Elsevier Inc. All rights reserved.

Application of a hybrid tracking algorithm to motion analysis

An algorithm for tracking multiple feature positions in a dynamic image sequence is presented. This is achieved using a combination of two trajectory-based methods, with the resulting hybrid algorithm exhibiting the advantages of both. An optimizing exchange algorithm is described which enables short feature paths to be tracked without prior knowledge of the motion being studied. The resulting partial trajectories are then used to initialize a fast predictor algorithm which is capable of rapidly tracking multiple feature paths. As this predictor algorithm becomes tuned to the feature positions being tracked, it is shown how the location of occluded or poorly detected features can be predicted. The results of applying this tracking algorithm to data obtained from real-world scenes are then presented.

Experimental separation of the coherent component of X-ray scattering prior to RDF analysis of non-crystalline polymers

An experimental method is described which enables the inelastically scattered X-ray component to be removed from diffractometer data prior to radial density function analysis. At each scattering angle an energy spectrum is generated from a Si(Li) detector combined with a multi-channel analyser from which the coherently scattered component is separated. The data obtained from organic polymers has an improved signal/noise ratio at high values of scattering angle, and a commensurate enhancement of resolution of the RDF at low r is demonstrated for the case of PMMA (ICI `Perspex'). The method obviates the need for the complicated correction for multiple scattering.

Spatial covariation of Azotobacter abundance and soil properties: A case study using the wavelet transform

The soil microflora is very heterogeneous in its spatial distribution. The origins of this heterogeneity and its significance for soil function are not well understood. A problem for understanding spatial variation better is the assumption of statistical stationarity that is made in most of the statistical methods used to assess it. These assumptions are made explicit in geostatistical methods that have been increasingly used by soil biologists in recent years. Geostatistical methods are powerful, particularly for local prediction, but they require the assumption that the variability of a property of interest is spatially uniform, which is not always plausible given what is known about the complexity of the soil microflora and the soil environment. We have used the wavelet transform, a relatively new innovation in mathematical analysis, to investigate the spatial variation of abundance of Azotobacter in the soil of a typical agricultural landscape. The wavelet transform entails no assumptions of stationarity and is well suited to the analysis of variables that show intermittent or transient features at different spatial scales. In this study, we computed cross-variograms of Azotobacter abundance with the pH, water content and loss on ignition of the soil. These revealed scale-dependent covariation in all cases. The wavelet transform also showed that the correlation of Azotobacter abundance with all three soil properties depended on spatial scale, the correlation generally increased with spatial scale and was only significantly different from zero at some scales. However, the wavelet analysis also allowed us to show how the correlation changed across the landscape. For example, at one scale Azotobacter abundance was strongly correlated with pH in part of the transect, and not with soil water content, but this was reversed elsewhere on the transect. The results show how scale-dependent variation of potentially limiting environmental factors can induce a complex spatial pattern of abundance in a soil organism. The geostatistical methods that we used here make assumptions that are not consistent with the spatial changes in the covariation of these properties that our wavelet analysis has shown. This suggests that the wavelet transform is a powerful tool for future investigation of the spatial structure and function of soil biota. (c) 2006 Elsevier Ltd. All rights reserved.

Calibration and sensitivity analysis of a river water quality model under unsteady flow conditions

Water quality models generally require a relatively large number of parameters to define their functional relationships, and since prior information on parameter values is limited, these are commonly defined by fitting the model to observed data. In this paper, the identifiability of water quality parameters and the associated uncertainty in model simulations are investigated. A modification to the water quality model `Quality Simulation Along River Systems' is presented in which an improved flow component is used within the existing water quality model framework. The performance of the model is evaluated in an application to the Bedford Ouse river, UK, using a Monte-Carlo analysis toolbox. The essential framework of the model proved to be sound, and calibration and validation performance was generally good. However some supposedly important water quality parameters associated with algal activity were found to be completely insensitive, and hence non-identifiable, within the model structure, while others (nitrification and sedimentation) had optimum values at or close to zero, indicating that those processes were not detectable from the data set examined. (C) 2003 Elsevier Science B.V. All rights reserved.

The potential to narrow uncertainty in projections of regional precipitation change

We separate and quantify the sources of uncertainty in projections of regional (*2,500 km) precipitation changes for the twenty-first century using the CMIP3 multi-model ensemble, allowing a direct comparison with a similar analysis for regional temperature changes. For decadal means of seasonal mean precipitation, internal variability is the dominant uncertainty for predictions of the first decade everywhere, and for many regions until the third decade ahead. Model uncertainty is generally the dominant source of uncertainty for longer lead times. Scenario uncertainty is found to be small or negligible for all regions and lead times, apart from close to the poles at the end of the century. For the global mean, model uncertainty dominates at all lead times. The signal-to-noise ratio (S/N) of the precipitation projections is highest at the poles but less than 1 almost everywhere else, and is far lower than for temperature projections. In particular, the tropics have the highest S/N for temperature, but the lowest for precipitation. We also estimate a ‘potential S/N’ by assuming that model uncertainty could be reduced to zero, and show that, for regional precipitation, the gains in S/N are fairly modest, especially for predictions of the next few decades. This finding suggests that adaptation decisions will need to be made in the context of high uncertainty concerning regional changes in precipitation. The potential to narrow uncertainty in regional temperature projections is far greater. These conclusions on S/N are for the current generation of models; the real signal may be larger or smaller than the CMIP3 multi-model mean. Also note that the S/N for extreme precipitation, which is more relevant for many climate impacts, may be larger than for the seasonal mean precipitation considered here.

Who owned Earls Colne in 1798....or how to squeeze more from the Land Tax

In this important article Richard Hoyle, one of the country’s leading historians of the early modern period, introduces new perspectives on the Land Tax and its use in the analysis of local communities in the late eighteenth and early nineteenth centuries. He uses as his case study the parish of Earls Colne in Essex, on which he has already written extensively with Professor Henry French. The article begins with an overview of the tax itself, explaining its history and the procedures for the collection of revenues – including the numerous changes which took place. The sizeable problems confronting any would-be analyst of the data are clearly identified, and Hoyle observes that because of these apparently insoluble difficulties the potential of the tax returns has never been fully realised. He then considers the surviving documentation in The National Archives, providing an accessible introduction to the sources and their arrangement, and describing the particularly important question o f the redemption of the tax by payment of a lump sum. The extent of redemption (in the years around 1800-1804) is discussed. Hoyle draws attention to the potential for linking the tax returns themselves with the redemption certificates (which have never been subjected to historical analysis and thereby proposes new ways of exploiting the evidence of the taxation as a whole. The article then discusses in detail the specific case of Earls Colne, with tabulated data showing the research potential. Topics analysed include the ownership of property ranked by size of payment, and calculations whereby the amount paid may be used to determine the worth of land and the structure of individual estates. The important question of absentee owners is investigated, and there is a very valuable consideration of the potential for looking at portfolio estate ownership, whereby owners held land in varying proportions in a number of parishes. It is suggested that such studies will allow us to be more aware of the entirety of property ownership, which a focus on a single community does not permit. In the concluding paragraph it is argued that using these sources we may see the rise and fall of estates, gain new information on landownership, landholding and farm size, and even approach the challenging topic of the distribution of wealth.

A spatio-temporal structure-based approach to drought characterisation

Drought characterisation is an intrinsically spatio-temporal problem. A limitation of previous approaches to characterisation is that they discard much of the spatio-temporal information by reducing events to a lower-order subspace. To address this, an explicit 3-dimensional (longitude, latitude, time) structure-based method is described in which drought events are defined by a spatially and temporarily coherent set of points displaying standardised precipitation below a given threshold. Geometric methods can then be used to measure similarity between individual drought structures. Groupings of these similarities provide an alternative to traditional methods for extracting recurrent space-time signals from geophysical data. The explicit consideration of structure encourages the construction of summary statistics which relate to the event geometry. Example measures considered are the event volume, centroid, and aspect ratio. The utility of a 3-dimensional approach is demonstrated by application to the analysis of European droughts (15 °W to 35°E, and 35 °N to 70°N) for the period 1901–2006. Large-scale structure is found to be abundant with 75 events identified lasting for more than 3 months and spanning at least 0.5 × 106 km2. Near-complete dissimilarity is seen between the individual drought structures, and little or no regularity is found in the time evolution of even the most spatially similar drought events. The spatial distribution of the event centroids and the time evolution of the geographic cross-sectional areas strongly suggest that large area, sustained droughts result from the combination of multiple small area (∼106 km2) short duration (∼3 months) events. The small events are not found to occur independently in space. This leads to the hypothesis that local water feedbacks play an important role in the aggregation process.

Analysis of the seasonal cycle within the first international urban land-surface model comparison

A number of urban land-surface models have been developed in recent years to satisfy the growing requirements for urban weather and climate interactions and prediction. These models vary considerably in their complexity and the processes that they represent. Although the models have been evaluated, the observational datasets have typically been of short duration and so are not suitable to assess the performance over the seasonal cycle. The First International Urban Land-Surface Model comparison used an observational dataset that spanned a period greater than a year, which enables an analysis over the seasonal cycle, whilst the variety of models that took part in the comparison allows the analysis to include a full range of model complexity. The results show that, in general, urban models do capture the seasonal cycle for each of the surface fluxes, but have larger errors in the summer months than in the winter. The net all-wave radiation has the smallest errors at all times of the year but with a negative bias. The latent heat flux and the net storage heat flux are also underestimated, whereas the sensible heat flux generally has a positive bias throughout the seasonal cycle. A representation of vegetation is a necessary, but not sufficient, condition for modelling the latent heat flux and associated sensible heat flux at all times of the year. Models that include a temporal variation in anthropogenic heat flux show some increased skill in the sensible heat flux at night during the winter, although their daytime values are consistently overestimated at all times of the year. Models that use the net all-wave radiation to determine the net storage heat flux have the best agreement with observed values of this flux during the daytime in summer, but perform worse during the winter months. The latter could result from a bias of summer periods in the observational datasets used to derive the relations with net all-wave radiation. Apart from these models, all of the other model categories considered in the analysis result in a mean net storage heat flux that is close to zero throughout the seasonal cycle, which is not seen in the observations. Models with a simple treatment of the physical processes generally perform at least as well as models with greater complexity.

Meta-analysis of the INSIG2 association with obesity including 74,345 individuals: does heterogeneity of estimates relate to study design?

The INSIG2 rs7566605 polymorphism was identified for obesity (BMI> or =30 kg/m(2)) in one of the first genome-wide association studies, but replications were inconsistent. We collected statistics from 34 studies (n = 74,345), including general population (GP) studies, population-based studies with subjects selected for conditions related to a better health status ('healthy population', HP), and obesity studies (OB). We tested five hypotheses to explore potential sources of heterogeneity. The meta-analysis of 27 studies on Caucasian adults (n = 66,213) combining the different study designs did not support overall association of the CC-genotype with obesity, yielding an odds ratio (OR) of 1.05 (p-value = 0.27). The I(2) measure of 41% (p-value = 0.015) indicated between-study heterogeneity. Restricting to GP studies resulted in a declined I(2) measure of 11% (p-value = 0.33) and an OR of 1.10 (p-value = 0.015). Regarding the five hypotheses, our data showed (a) some difference between GP and HP studies (p-value = 0.012) and (b) an association in extreme comparisons (BMI> or =32.5, 35.0, 37.5, 40.0 kg/m(2) versus BMI<25 kg/m(2)) yielding ORs of 1.16, 1.18, 1.22, or 1.27 (p-values 0.001 to 0.003), which was also underscored by significantly increased CC-genotype frequencies across BMI categories (10.4% to 12.5%, p-value for trend = 0.0002). We did not find evidence for differential ORs (c) among studies with higher than average obesity prevalence compared to lower, (d) among studies with BMI assessment after the year 2000 compared to those before, or (e) among studies from older populations compared to younger. Analysis of non-Caucasian adults (n = 4889) or children (n = 3243) yielded ORs of 1.01 (p-value = 0.94) or 1.15 (p-value = 0.22), respectively. There was no evidence for overall association of the rs7566605 polymorphism with obesity. Our data suggested an association with extreme degrees of obesity, and consequently heterogeneous effects from different study designs may mask an underlying association when unaccounted for. The importance of study design might be under-recognized in gene discovery and association replication so far.