Diagonalization and Jordan Normal Form – motivation through Maple

Following an introduction to the diagonalization of matrices, one of the more difficult topics for students to grasp in linear algebra is the concept of Jordan normal form. In this note, we show how the important notions of diagonalization and Jordan normal form can be introduced and developed through the use of the computer algebra package Maple®.

Comparison of methane produced by straw fed sheep in open-circuit respiration with methane predicted by fermentation characteristics measured by an in vitro gas procedure

Reducing carbon conversion of ruminally degraded feed into methane increases feed efficiency and reduces emission of this potent greenhouse gas into the environment. Accurate, yet simple, predictions of methane production of ruminants on any feeding regime are important in the nutrition of ruminants, and in modeling methane produced by them. The current work investigated feed intake, digestibility and methane production by open-circuit respiration measurements in sheep fed 15 untreated, sodium hydroxide (NaOH) treated and anhydrous ammonia (NH3) treated wheat, barley and oat straws. In vitro fermentation characteristics of straws were obtained from incubations using the Hohenheim gas production system that measured gas production, true substrate degradability, short-chain fatty acid production and efficiency of microbial production from the ratio of truly degraded substrate to gas volume. In the 15 straws, organic matter (OM) intake and in vivo OM digestibility ranged from 563 to 1201 g and from 0.464 to 0.643, respectively. Total daily methane production ranged from 13.0 to 34.4 l, whereas methane produced/kg OM matter apparently digested in vivo varied from 35.0 to 61.8 l. The OM intake was positively related to total methane production (R2 = 0.81, P<0.0001), and in vivo OM digestibility was also positively associated with methane production (R2 = 0.67, P<0.001), but negatively associated with methane production/kg digestible OM intake (R2 = 0.61, P<0.001). In the in vitro incubations of the 15 straws, the ratio of acetate to propionate ranged from 2.3 to 2.8 (P<0.05) and efficiencies of microbial production ranged from 0.21 to 0.37 (P<0.05) at half asymptotic gas production. Total daily methane production, calculated from in vitro fermentation characteristics (i.e., true degradability, SCFA ratio and efficiency of microbial production) and OM intake, compared well with methane measured in the open-circuit respiration chamber (y = 2.5 + 0.86x, R2 = 0.89, P<0.0001, Sy.x = 2.3). Methane production from forage fed ruminants can be predicted accurately by simple in vitro incubations combining true substrate degradability and gas volume measurements, if feed intake is known.

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.

Productivity change in Polish agriculture: an illustration of a bootstrapping procedure applied to Malmquist indices

This article illustrates the usefulness of applying bootstrap procedures to total factor productivity Malmquist indices, derived with data envelopment analysis (DEA), for a sample of 250 Polish farms during 1996-2000. The confidence intervals constructed as in Simar and Wilson suggest that the common portrayal of productivity decline in Polish agriculture may be misleading. However, a cluster analysis based on bootstrap confidence intervals reveals that important policy conclusions can be drawn regarding productivity enhancement.

In vitro microbial inoculum: A review of its function and properties

This review considers microbial inocula used in in vitro systems from the perspective of their ability to degrade or ferment a particular substrate, rather than the microbial species that it contains. By necessity, this required an examination of bacterial, protozoal and fungal populations of the rumen and hindgut with respect to factors influencing their activity. The potential to manipulate these populations through diet or sampling time are examined, as is inoculum preparation and level. The main alternatives to fresh rumen fluid (i.e., caecal digesta or faeces) are discussed with respect to end-point degradabilities and fermentation dynamics. Although the potential to use rumen contents obtained from donor animals at slaughter offers possibilities, the requirement to store it and its subsequent loss of activity are limitations. Statistical modelling of data, although still requiring a deal of developmental work, may offer an alternative approach. Finally, with respect to the range of in vitro methodologies and equipment employed, it is suggested that a degree of uniformity could be obtained through generation of a set of guidelines relating to the host animal, sampling technique and inoculum preparation. It was considered unlikely that any particular system would be accepted as the 'standard' procedure. However, before any protocol can be adopted, additional data are required (e.g., a method to assess inoculum 'quality' with respect to its fermentative and/or degradative activity), preparation/inoculation techniques need to be refined and a methodology to store inocula without loss of efficacy developed. (c) 2005 Elsevier B.V. All rights reserved.

Statistical evaluation of an acute dermal toxicity test using the dermal fixed dose procedure

The conventional method for the assessment of acute dermal toxicity (OECD Test Guideline 402, 1987) uses death of animals as an endpoint to identify the median lethal dose (LD50). A new OECD Testing Guideline called the dermal fixed dose procedure (dermal FDP) is being prepared to provide an alternative to Test Guideline 402. In contrast to Test Guideline 402, the dermal FDP does not provide a point estimate of the LD50, but aims to identify that dose of the substance under investigation that causes clear signs of nonlethal toxicity. This is then used to assign classification according to the new Globally Harmonised System of Classification and Labelling scheme (GHS). The dermal FDP has been validated using statistical modelling rather than by in vivo testing. The statistical modelling approach enables calculation of the probability of each GHS classification and the expected numbers of deaths and animals used in the test for imaginary substances with a range of LD50 values and dose-response curve slopes. This paper describes the dermal FDP and reports the results from the statistical evaluation. It is shown that the procedure will be completed with considerably less death and suffering than guideline 402, and will classify substances either in the same or a more stringent GHS class than that assigned on the basis of the LD50 value.

Statistical evaluation of the fixed concentration procedure for acute inhalation toxicity assessment

The conventional method for the assessment of acute inhalation toxicity (OECD Test Guideline 403, 1981) uses death of animals as an endpoint to identify the median lethal concentration (LC50). A new OECD Testing Guideline called the Fixed Concentration Procedure (FCP) is being prepared to provide an alternative to Test Guideline 403. Unlike Test Guideline 403, the FCP does not provide a point estimate of the LC50, but aims to identify an airborne exposure level that causes clear signs of nonlethal toxicity. This is then used to assign classification according to the new Globally Harmonized System of Classification and Labelling scheme (GHS). The FCP has been validated using statistical simulation rather than byin vivo testing. The statistical simulation approach predicts the GHS classification outcome and the numbers of deaths and animals used in the test for imaginary substances with a range of LC50 values and dose response curve slopes. This paper describes the FCP and reports the results from the statistical simulation study assessing its properties. It is shown that the procedure will be completed with considerably less death and suffering than Test Guideline 403, and will classify substances either in the same or a more stringent GHS class than that assigned on the basis of the LC50 value.

A statistical evaluation of the fixed dose procedure

The fixed-dose procedure (FDP) was introduced as OECD Test Guideline 420 in 1992, as an alternative to the conventional median lethal dose (LD50) test for the assessment of acute oral toxicity (OECD Test Guideline 401). The FDP uses fewer animals and causes less suffering than the conventional test, while providing information on the acute toxicity to allow substances to be ranked according to the EU hazard classification system. Recently the FDP has been revised, with the aim of providing further reductions and refinements, and classification according to the criteria of the Globally Harmonized Hazard Classification and Labelling scheme (GHS). This paper describes the revised FDP and analyses its properties, as determined by a statistical modelling approach. The analysis shows that the revised FDP classifies substances for acute oral toxicity generally in the same, or a more stringent, hazard class as that based on the LD50 value, according to either the GHS or the EU classification scheme. The likelihood of achieving the same classification is greatest for substances with a steep dose-response curve and median toxic dose (TD50) close to the LD50. The revised FDP usually requires five or six animals with two or fewer dying as a result of treatment in most cases.

Large vibrational variational calculations using 'multimode' and an iterative diagonalization technique

We have favoured the variational (secular equation) method for the determination of the (ro-) vibrational energy levels of polyatomic molecules. We use predominantly the Watson Hamiltonian in normal coordinates and an associated given potential in the variational code 'Multimode'. The dominant cost is the construction and diagonalization of matrices of ever-increasing size. Here we address this problem, using pertubation theory to select dominant expansion terms within the Davidson-Liu iterative diagonalization method. Our chosen example is the twelve-mode molecule methanol, for which we have an ab initio representation of the potential which includes the internal rotational motion of the OH group relative to CH3. Our new algorithm allows us to obtain converged energy levels for matrices of dimensions in excess of 100 000.

The competitive dialogue procedure: Advantages, disadvantages, and its implementation into English and Dutch law

Competitive Dialogue (CD) is a new contract award procedure of the European Community (EC). It is set out in Article 29 of the 'Public Sector Directive' 2004/18/EC. Over the last decades, projects were becoming more and more complex, and the existing EC procedures were no longer suitable to procure those projects. The call for a new procedure resulted in CD. This paper describes how the Directive has been implemented into the laws of two member states: the UK and the Netherlands. In order to implement the Directive, both lawmakers have set up a new and distinct piece of legislation. In each case, large parts of the Directive’s content have been repeated ‘word for word’; only minor parts have been reworded and/or restructured. In the next part of the paper, the CD procedure is examined in different respects. First, an overview is given on the different EC contract award procedures (open, restricted, negotiated, CD) and awarding methods (lowest price and Most Economically Advantageous Tender, MEAT). Second, the applicability of CD is described: Among other limitations, CD can only be applied to public contracts for works, supplies, and services, and this scope of application is further restricted by the exclusion of certain contract types. One such exclusion concerns services concessions. This means that PPP contracts which are set up as services concessions cannot be awarded by CD. The last two parts of the paper pertain to the main features of the CD procedure – from ‘contract notice’ to ‘contract award’ – and the advantages and disadvantages of the procedure. One advantage is that the dialogue allows the complexity of the project to be disentangled and clarified. Other advantages are the stimulation of innovation and creativity. These advantages are set against the procedure’s disadvantages, which include high transaction costs and a perceived hindrance of innovation (due to an ambiguity between transparency and fair competition). It is concluded that all advantages and disadvantages are related to one of three elements: communication, competition, and/or structure of the procedure. Further research is needed to find out how these elements are related.

Effects of enrichment of refined olive oil with phenolic compounds from olive leaves

The possibility of preparing olive oil, with the same nutritional value and stability characteristics found in virgin olive oil, by the enrichment of refined olive oil with olive leaf polyphenols was studied. To obtain antioxidant phenols similar to those found in virgin olive oil, these components were extracted from the leaves of several olive cultivars from the Northern region of Portugal, namely, Carrasca, Ripa, Negruche, Cordovil, Verdeal, Madural, and Bical cultivars, under several conditions. The concentration of a leaf extract required for addition to refined olive oil to obtain the same stability as virgin olive oil was determined. The extract from 1 kg of leaves was sufficient to fortify 50-320 L of refined olive oil to a similar stability as a virgin olive oil sample depending on the metal concentration of the oil, cultivar, and time of the year when the leaves were picked.

Case studies to demonstrate the range of applications of the Southampton Hand Assessment Procedure

The Southampton Hand Assessment Procedure (SHAP) was devised to assess quantitatively the functional range of injured and healthy adult hands. It was designed to be a practical tool for use in a busy clinical setting; thus, it was made simple to use and easy to interpret. This paper describes four examples of its use: before and after a surgical procedure, to observe the impact of an injury, use with prostheses, and during recovery following a fracture. The cases show that the SHAP is capable of monitoring progress and recovery, identifying functional abilities in prosthetic hands and comparing the capabilities of different groups of injuries.