The application of Prony’s method to time-domain waveform data modeling in the presence of noise

In this paper,the Prony's method is applied to the time-domain waveform data modelling in the presence of noise.The following three problems encountered in this work are studied:(1)determination of the order of waveform;(2)de-termination of numbers of multiple roots;(3)determination of the residues.The methods of solving these problems are given and simulated on the computer.Finally,an output pulse of model PG-10N signal generator and the distorted waveform obtained by transmitting the pulse above mentioned through a piece of coaxial cable are modelled,and satisfactory results are obtained.So the effectiveness of Prony's method in waveform data modelling in the presence of noise is confirmed.

Ensemble data assimilation in the presence of cloud

In numerical weather prediction (NWP) data assimilation (DA) methods are used to combine available observations with numerical model estimates. This is done by minimising measures of error on both observations and model estimates with more weight given to data that can be more trusted. For any DA method an estimate of the initial forecast error covariance matrix is required. For convective scale data assimilation, however, the properties of the error covariances are not well understood. An effective way to investigate covariance properties in the presence of convection is to use an ensemble-based method for which an estimate of the error covariance is readily available at each time step. In this work, we investigate the performance of the ensemble square root filter (EnSRF) in the presence of cloud growth applied to an idealised 1D convective column model of the atmosphere. We show that the EnSRF performs well in capturing cloud growth, but the ensemble does not cope well with discontinuities introduced into the system by parameterised rain. The state estimates lose accuracy, and more importantly the ensemble is unable to capture the spread (variance) of the estimates correctly. We also find, counter-intuitively, that by reducing the spatial frequency of observations and/or the accuracy of the observations, the ensemble is able to capture the states and their variability successfully across all regimes.

Resolution of sharp fronts in the presence of model error in variational data assimilation

We show that the four-dimensional variational data assimilation method (4DVar) can be interpreted as a form of Tikhonov regularization, a very familiar method for solving ill-posed inverse problems. It is known from image restoration problems that L1-norm penalty regularization recovers sharp edges in the image more accurately than Tikhonov, or L2-norm, penalty regularization. We apply this idea from stationary inverse problems to 4DVar, a dynamical inverse problem, and give examples for an L1-norm penalty approach and a mixed total variation (TV) L1–L2-norm penalty approach. For problems with model error where sharp fronts are present and the background and observation error covariances are known, the mixed TV L1–L2-norm penalty performs better than either the L1-norm method or the strong constraint 4DVar (L2-norm)method. A strength of the mixed TV L1–L2-norm regularization is that in the case where a simplified form of the background error covariance matrix is used it produces a much more accurate analysis than 4DVar. The method thus has the potential in numerical weather prediction to overcome operational problems with poorly tuned background error covariance matrices.

Phytoplankton–zooplankton dynamics in the ‘presence’ or ‘absence’ of toxic phytoplankton

The inhibitory effects of toxin-producing phytoplankton (TPP) on zooplankton modulate the dynamics of marine plankton. In this article, we employ simple mathematical models to compare theoretically the dynamics of phytoplankton–zooplankton interaction in situations where the TPP are present with those where TPP are absent. We consider two sets of three-component interaction models: one that does not include the effect of TPP and the other that does. The negative effects of TPP on zooplankton is described by a non-linear interaction term. Extensive theoretical analyses of the models have been performed to understand the qualitative behaviour of the model systems around every possible equilibria. The results of local-stability analysis and numerical simulations demonstrate that the two model-systems differ qualitatively with regard to oscillations and stability. The model system that does not include TPP is asymptotically stable around the coexisting equilibria, whereas, the system that includes TPP oscillates for a range of parametric values associated with toxin-inhibition rate and competition coefficients. Our analysis suggests that the qualitative dynamics of the plankton–zooplankton interactions are very likely to alter due to the presence of TPP species, and therefore the effects of TPP should be considered carefully while modelling plankton dynamics.

Using airborne laser altimetry to improve river flood extents delineated from SAR data

Flood extent maps derived from SAR images are a useful source of data for validating hydraulic models of river flood flow. The accuracy of such maps is reduced by a number of factors, including changes in returns from the water surface caused by different meteorological conditions and the presence of emergent vegetation. The paper describes how improved accuracy can be achieved by modifying an existing flood extent delineation algorithm to use airborne laser altimetry (LiDAR) as well as SAR data. The LiDAR data provide an additional constraint that waterline (land-water boundary) heights should vary smoothly along the flooded reach. The method was tested on a SAR image of a flood for which contemporaneous aerial photography existed, together with LiDAR data of the un-flooded reach. Waterline heights of the SAR flood extent conditioned on both SAR and LiDAR data matched the corresponding heights from the aerial photo waterline significantly more closely than those from the SAR flood extent conditioned only on SAR data.

Impact of sewage sludge applications on the biogeochemistry of soils

This report describes an investigation into the bioavailability and fate of trace metals and their subsequent impact on important soil microbiological functions such as nitrification, denitrification and methane oxidation in low and high Cu containing soils in the presence and absence of residual organic matter from sewage sludge additions made 10 years earlier. The soils being studied are part of long term sewage sludge trials and include a low Cu soil ( 13.3mg Cu/ kg soil, 4.18 LOI %), left un- amended to serve as a control soil, soil amended with a high Cu sewage sludge ( 278.3mg Cu/ kg soil, 6.52 LOI %) and soil amended with a low Cu sewage sludge ( 46.3mg Cu/ kg soil, 6.18 LOI %). Soil was also amended with inorganic metal salts ( 273.4mg Cu/ kg soil, 4.52 LOI %) to further investigate the impact of Cu in the absence of additional organic matter contained in applied sewage sludge. Data from the first two years of a project are presented which has included field- based studies at long term sewage sludge trials based in Watlington, Oxford, UK and laboratory based studies at the Institute of Grassland & Environmental Research, North Wyke, Devon, UK.

Determining nugget: sill ratios of standardized variograms from aerial photographs to krige sparse soil data

Maps of kriged soil properties for precision agriculture are often based on a variogram estimated from too few data because the costs of sampling and analysis are often prohibitive. If the variogram has been computed by the usual method of moments, it is likely to be unstable when there are fewer than 100 data. The scale of variation in soil properties should be investigated prior to sampling by computing a variogram from ancillary data, such as an aerial photograph of the bare soil. If the sampling interval suggested by this is large in relation to the size of the field there will be too few data to estimate a reliable variogram for kriging. Standardized variograms from aerial photographs can be used with standardized soil data that are sparse, provided the data are spatially structured and the nugget:sill ratio is similar to that of a reliable variogram of the property. The problem remains of how to set this ratio in the absence of an accurate variogram. Several methods of estimating the nugget:sill ratio for selected soil properties are proposed and evaluated. Standardized variograms with nugget:sill ratios set by these methods are more similar to those computed from intensive soil data than are variograms computed from sparse soil data. The results of cross-validation and mapping show that the standardized variograms provide more accurate estimates, and preserve the main patterns of variation better than those computed from sparse data.

An extension of an over-dispersion test for count data

While over-dispersion in capture–recapture studies is well known to lead to poor estimation of population size, current diagnostic tools to detect the presence of heterogeneity have not been specifically developed for capture–recapture studies. To address this, a simple and efficient method of testing for over-dispersion in zero-truncated count data is developed and evaluated. The proposed method generalizes an over-dispersion test previously suggested for un-truncated count data and may also be used for testing residual over-dispersion in zero-inflation data. Simulations suggest that the asymptotic distribution of the test statistic is standard normal and that this approximation is also reasonable for small sample sizes. The method is also shown to be more efficient than an existing test for over-dispersion adapted for the capture–recapture setting. Studies with zero-truncated and zero-inflated count data are used to illustrate the test procedures.

A revised Tobit procedure for mitigating bias in the presence of non-zero censoring with an application to milk-market participation in the Ethiopian highlands

Fixed transactions costs that prohibit exchange engender bias in supply analysis due to censoring of the sample observations. The associated bias in conventional regression procedures applied to censored data and the construction of robust methods for mitigating bias have been preoccupations of applied economists since Tobin [Econometrica 26 (1958) 24]. This literature assumes that the true point of censoring in the data is zero and, when this is not the case, imparts a bias to parameter estimates of the censored regression model. We conjecture that this bias can be significant; affirm this from experiments; and suggest techniques for mitigating this bias using Bayesian procedures. The bias-mitigating procedures are based on modifications of the key step that facilitates Bayesian estimation of the censored regression model; are easy to implement; work well in both small and large samples; and lead to significantly improved inference in the censored regression model. These findings are important in light of the widespread use of the zero-censored Tobit regression and we investigate their consequences using data on milk-market participation in the Ethiopian highlands. (C) 2004 Elsevier B.V. All rights reserved.

Genetic parameters and evaluations from single- and multiple-trait analysis of dairy cow fertility and milk production

Genetic parameters and breeding values for dairy cow fertility were estimated from 62 443 lactation records. Two-trait analysis of fertility and milk yield was investigated as a method to estimate fertility breeding values when culling or selection based on milk yield in early lactation determines presence or absence of fertility observations in later lactations. Fertility traits were calving interval, intervals from calving to first service, calving to conception and first to last service, conception success to first service and number of services per conception. Milk production traits were 305-day milk, fat and protein yield. For fertility traits, range of estimates of heritability (h(2)) was 0.012 to 0.028 and of permanent environmental variance (c(2)) was 0.016 to 0.032. Genetic correlations (r(g)) among fertility traits were generally high ( > 0.70). Genetic correlations of fertility with milk production traits were unfavourable (range -0.11 to 0.46). Single and two-trait analyses of fertility were compared using the same data set. The estimates of h(2) and c(2) were similar for two types of analyses. However, there were differences between estimated breeding values and rankings for the same trait from single versus multi-trait analyses. The range for rank correlation was 0.69-0.83 for all animals in the pedigree and 0.89-0.96 for sires with more than 25 daughters. As single-trait method is biased due to selection on milk yield, a multi-trait evaluation of fertility with milk yield is recommended. (C) 2002 Elsevier Science B.V. All rights reserved.

Near infrared reflectance spectroscopy (NIRS) to predict biological parameters of maize silage: effects of particle comminution, oven drying temperature and the presence of residual moisture

Maize silage nutritive quality is routinely determined by near infrared reflectance spectroscopy (NIRS). However, little is known about the impact of sample preparation on the accuracy of the calibration to predict biological traits. A sample population of 48 maize silages representing a wide range of physiological maturities was used in a study to determine the impact of different sample preparation procedures (i.e., drying regimes; the presence or absence of residual moisture; the degree of particle comminution) on resultant NIR prediction statistics. All silages were scanned using a total of 12 combinations of sample pre-treatments. Each sample preparation combination was subjected to three multivariate regression techniques to give a total of 36 predictions per biological trait. Increased sample preparations procedure, relative to scanning the unprocessed whole plant (WP) material, always resulted in a numerical minimisation of model statistics. However, the ability of each of the treatments to significantly minimise the model statistics differed. Particle comminution was the most important factor, oven-drying regime was intermediate, and residual moisture presence was the least important. Models to predict various biological parameters of maize silage will be improved if material is subjected to a high degree of particle comminution (i.e., having been passed through a 1 mm screen) and developed on plant material previously dried at 60 degrees C. The extra effort in terms of time and cost required to remove sample residual moisture cannot be justified. (c) 2005 Elsevier B.V. All rights reserved.

Effect of corn silage from an herbicide-tolerant genetically modified variety on milk production and absence of transgenic DNA in milk

Data from 60 multiparous Holstein cows were used in a 12-wk continuous design feeding trial. Cows were allocated to 1 of 4 experimental treatments (T1 to T4). In T1 and T2, the total mixed ration (TMR) contained either corn silage from the genetically modified (GM) variety Chardon Liberty Link, which is tolerant to the herbicide glufosinate ammonium, or its near isogenic nonGM counterpart, whereas the TMR used in T3 and T4 contained corn silage from the commercially available nonGM varieties Fabius and Antares, respectively. The objectives of the study were to determine if the inserted gene produced a marked effect on chemical composition, nutritive value, feed intake, and milk production, and to determine if transgenic DNA and the protein expressed by the inserted gene could be detected in bovine milk. The nutritive value, fermentation characteristics, mineral content, and amino acid composition of all 4 silages were similar. There were no significant treatment effects on milk yield, milk composition, and yield of milk constituents, and the dry matter (DM) intake of the GM variety was not significantly different from the 2 commercial varieties. However, although the DM intake noted for the nonGM near-isogenic variety was similar to the commercial varieties, it was significantly lower when compared with the GM variety. Polymerase chain reaction analyses of milk samples collected at wk 1, 6, and 12 of the study showed that none of the 90 milk samples tested positive, above a detection limit of 2.5 ng of total genomic DNA/mL of milk, for either tDNA (event T25) or the single-copy endogenous Zea mays gene, alcohol dehydrogenase. Using ELISA assays, the protein expressed by the T25 gene was not detected in milk.

Modeling of relationships between weather and Septoria tritici epidemics on winter wheat: A critical approach

Two models for predicting Septoria tritici on winter wheat (cv. Ri-band) were developed using a program based on an iterative search of correlations between disease severity and weather. Data from four consecutive cropping seasons (1993/94 until 1996/97) at nine sites throughout England were used. A qualitative model predicted the presence or absence of Septoria tritici (at a 5% severity threshold within the top three leaf layers) using winter temperature (January/February) and wind speed to about the first node detectable growth stage. For sites above the disease threshold, a quantitative model predicted severity of Septoria tritici using rainfall during stern elongation. A test statistic was derived to test the validity of the iterative search used to obtain both models. This statistic was used in combination with bootstrap analyses in which the search program was rerun using weather data from previous years, therefore uncorrelated with the disease data, to investigate how likely correlations such as the ones found in our models would have been in the absence of genuine relationships.

A practical comparison of group-sequential and adaptive designs

Sequential methods provide a formal framework by which clinical trial data can be monitored as they accumulate. The results from interim analyses can be used either to modify the design of the remainder of the trial or to stop the trial as soon as sufficient evidence of either the presence or absence of a treatment effect is available. The circumstances under which the trial will be stopped with a claim of superiority for the experimental treatment, must, however, be determined in advance so as to control the overall type I error rate. One approach to calculating the stopping rule is the group-sequential method. A relatively recent alternative to group-sequential approaches is the adaptive design method. This latter approach provides considerable flexibility in changes to the design of a clinical trial at an interim point. However, a criticism is that the method by which evidence from different parts of the trial is combined means that a final comparison of treatments is not based on a sufficient statistic for the treatment difference, suggesting that the method may lack power. The aim of this paper is to compare two adaptive design approaches with the group-sequential approach. We first compare the form of the stopping boundaries obtained using the different methods. We then focus on a comparison of the power of the different trials when they are designed so as to be as similar as possible. We conclude that all methods acceptably control type I error rate and power when the sample size is modified based on a variance estimate, provided no interim analysis is so small that the asymptotic properties of the test statistic no longer hold. In the latter case, the group-sequential approach is to be preferred. Provided that asymptotic assumptions hold, the adaptive design approaches control the type I error rate even if the sample size is adjusted on the basis of an estimate of the treatment effect, showing that the adaptive designs allow more modifications than the group-sequential method.

Application of one-list capture-recapture models to scrapie surveillance data in Great Britain

In this paper, we apply one-list capture-recapture models to estimate the number of scrapie-affected holdings in Great Britain. We applied this technique to the Compulsory Scrapie Flocks Scheme dataset where cases from all the surveillance sources monitoring the presence of scrapie in Great Britain, the abattoir survey, the fallen stock survey and the statutory reporting of clinical cases, are gathered. Consequently, the estimates of prevalence obtained from this scheme should be comprehensive and cover all the different presentations of the disease captured individually by the surveillance sources. Two estimators were applied under the one-list approach: the Zelterman estimator and Chao's lower bound estimator. Our results could only inform with confidence the scrapie-affected holding population with clinical disease; this moved around the figure of 350 holdings in Great Britain for the period under study, April 2005-April 2006. Our models allowed the stratification by surveillance source and the input of covariate information, holding size and country of origin. None of the covariates appear to inform the model significantly. Crown Copyright (C) 2008 Published by Elsevier B.V. All rights reserved.