Digitisation, representation, and formalisation - Digital libraries of mathematics

One of the main tasks of the mathematical knowledge management community must surely be to enhance access to mathematics on digital systems. In this paper we present a spectrum of approaches to solving the various problems inherent in this task, arguing that a variety of approaches is both necessary and useful. The main ideas presented are about the differences between digitised mathematics, digitally represented mathematics and formalised mathematics. Each has its part to play in managing mathematical information in a connected world. Digitised material is that which is embodied in a computer file, accessible and displayable locally or globally. Represented material is digital material in which there is some structure (usually syntactic in nature) which maps to the mathematics contained in the digitised information. Formalised material is that in which both the syntax and semantics of the represented material, is automatically accessible. Given the range of mathematical information to which access is desired, and the limited resources available for managing that information, we must ensure that these resources are applied to digitise, form representations of or formalise, existing and new mathematical information in such a way as to extract the most benefit from the least expenditure of resources. We also analyse some of the various social and legal issues which surround the practical tasks.

ASYM20: a program for force constant and normal coordinate calculations, with a critical review of the theory involved

The theory of harmonic force constant refinement calculations is reviewed, and a general-purpose program for force constant and normal coordinate calculations is described. The program, called ASYM20. is available through Quantum Chemistry Program Exchange. It will work on molecules of any symmetry containing up to 20 atoms and will produce results on a series of isotopomers as desired. The vibrational secular equations are solved in either nonredundant valence internal coordinates or symmetry coordinates. As well as calculating the (harmonic) vibrational wavenumbers and normal coordinates, the program will calculate centrifugal distortion constants, Coriolis zeta constants, harmonic contributions to the α′s. root-mean-square amplitudes of vibration, and other quantities related to gas electron-diffraction studies and thermodynamic properties. The program will work in either a predict mode, in which it calculates results from an input force field, or in a refine mode, in which it refines an input force field by least squares to fit observed data on the quantities mentioned above. Predicate values of the force constants may be included in the data set for a least-squares refinement. The program is written in FORTRAN for use on a PC or a mainframe computer. Operation is mainly controlled by steering indices in the input data file, but some interactive control is also implemented.

Investigating age related changes in taste and affects on sensory perceptions of oral nutritional supplements

Background: sip feeds are oral nutritional supplements (ONSs) that are commonly prescribed to malnourished patients to improve their nutritional and clinical status. However, ONSs are poorly consumed and frequently wasted, with sweetness being identified as one of the factors leading to patients’ dislike of ONSs. Objectives: to investigate if age affects sweetness thresholds and if this impacts upon perceived sweetness intensity, hedonic (sweetness and overall) and ranked preference of ONS products. Design: prospective, observational. Subjects: thirty-six young adults (18–33 years) and 48 healthy older adults (63–85 years). Setting: Department of Food and Nutritional Sciences and the Clinical Health Sciences at the University of Reading. Methods: detection and recognition threshold levels, basic taste identification and ‘just about right’ level of sweetness were examined. Three ONSs (chocolate, vanilla, strawberry) and sucrose solutions were evaluated for hedonic sweetness, overall hedonic liking, sweetness intensity and rank preference. Results: significant differences were found in both sweetness detection and recognition thresholds (P = 0.0001) between young and older adults, with older adults more likely to incorrectly identify the taste (P = 0.0001). Despite the deterioration in sweetness sensitivity among the older adults, there were no significant differences found in sweetness intensity perceived for the ONS products presented (P > 0.05) when compared with the young adults. However, across both groups sweetness intensity was found to be correlated with overall product dislike across all flavour variants tested (R = 0.398, P = 0.0001). Conclusions: sweetness appears to be one of many factors contributing to the dislike of ONSs. Manufacturers are encouraged to reconsider the formulations of these products so that beneficial effects of ONSs can be delivered in a more palatable and acceptable form and wastage reduced.

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.

Predicting feed quality - chemical analysis and in vitro evaluation

As the ideal method of assessing the nutritive value of a feedstuff, namely offering it to the appropriate class of animal and recording the production response obtained, is neither practical nor cost effective a range of feed evaluation techniques have been developed. Each of these balances some degree of compromise with the practical situation against data generation. However, due to the impact of animal-feed interactions over and above that of feed composition, the target animal remains the ultimate arbitrator of nutritional value. In this review current in vitro feed evaluation techniques are examined according to the degree of animal-feed interaction. Chemical analysis provides absolute values and therefore differs from the majority of in vitro methods that simply rank feeds. However, with no host animal involvement, estimates of nutritional value are inferred by statistical association. In addition given the costs involved, the practical value of many analyses conducted should be reviewed. The in sacco technique has made a substantial contribution to both understanding rumen microbial degradative processes and the rapid evaluation of feeds, especially in developing countries. However, the numerous shortfalls of the technique, common to many in vitro methods, the desire to eliminate the use of surgically modified animals for routine feed evaluation, paralleled with improvements in in vitro techniques, will see this technique increasingly replaced. The majority of in vitro systems use substrate disappearance to assess degradation, however, this provides no information regarding the quantity of derived end-products available to the host animal. As measurement of volatile fatty acids or microbial biomass production greatly increases analytical costs, fermentation gas release, a simple and non-destructive measurement, has been used as an alternative. However, as gas release alone is of little use, gas-based systems, where both degradation and fermentation gas release are measured simultaneously, are attracting considerable interest. Alternative microbial inocula are being considered, as is the potential of using multi-enzyme systems to examine degradation dynamics. It is concluded that while chemical analysis will continue to form an indispensable part of feed evaluation, enhanced use will be made of increasingly complex in vitro systems. It is vital, however, the function and limitations of each methodology are fully understood and that the temptation to over-interpret the data is avoided so as to draw the appropriate conclusions. With careful selection and correct application in vitro systems offer powerful research tools with which to evaluate feedstuffs. (C) 2003 Elsevier B.V. All rights reserved.

Reproducibility of a short semi-quantitative food group questionnaire and its performance in estimating nutrient intake compared with a 7-day diet diary in the Million Women Study

Objectives: To assess the short- and long-term reproducibility of a short food group questionnaire, and to compare its performance for estimating nutrient intakes in comparison with a 7-day diet diary. Design: Participants for the reproducibility study completed the food group questionnaire at two time points, up to 2 years apart. Participants for the performance study completed both the food group questionnaire and a 7-day diet diary a few months apart. Reproducibility was assessed by kappa statistics and percentage change between the two questionnaires; performance was assessed by kappa statistics, rank correlations and percentages of participants classified into the same and opposite thirds of intake. Setting: A random sample of participants in the Million Women Study, a population-based prospective study in the UK. Subjects: In total, 12 221 women aged 50-64 years. Results: in the reproducibility study, 75% of the food group items showed at least moderate agreement for all four time-point comparisons. Items showing fair agreement or worse tended to be those where few respondents reported eating them more than once a week, those consumed in small amounts and those relating to types of fat consumed. Compared with the diet diary, the food group questionnaire showed consistently reasonable performance for the nutrients carbohydrate, saturated fat, cholesterol, total sugars, alcohol, fibre, calcium, riboflavin, folate and vitamin C. Conclusions: The short food group questionnaire used in this study has been shown to be reproducible over time and to perform reasonably well for the assessment of a number of dietary nutrients.

Multivariate relationships between groundwater chemistry and toxicity in an urban aquifer

Multivariate statistical methods were used to investigate file Causes of toxicity and controls on groundwater chemistry from 274 boreholes in an Urban area (London) of the United Kingdom. The groundwater was alkaline to neutral, and chemistry was dominated by calcium, sodium, and Sulfate. Contaminants included fuels, solvents, and organic compounds derived from landfill material. The presence of organic material in the aquifer caused decreases in dissolved oxygen, sulfate and nitrate concentrations. and increases in ferrous iron and ammoniacal nitrogen concentrations. Pearson correlations between toxicity results and the concentration of individual analytes indicated that concentrations of ammoinacal nitrogen, dissolved oxygen, ferrous iron, and hydrocarbons were important where present. However, principal component and regression analysis suggested no significant correlation between toxicity and chemistry over the whole area. Multidimensional Scaling was used to investigate differences in sites caused by historical use, landfill gas status, or position within the sample area. Significant differences were observed between sites with different historical land use and those with different gas status. Examination of the principal component matrix revealed that these differences are related to changes in the importance of reduced chemical species.

Comparison of preferences for object properties in the rat using paired- and free-choice paradigms

A common method for testing preference for objects is to determine which of a pair of objects is approached first in a paired-choice paradigm. In comparison, many studies of preference for environmental enrichment (EE) devices have used paradigms in which total time spent with each of a pair of objects is used to determine preference. While each of these paradigms gives a specific measure of the preference for one object in comparison to another, neither method allows comparisons between multiple objects simultaneously. Since it is possible that several EE objects would be placed in a cage together to improve animal welfare, it is important to determine measures for rats' preferences in conditions that mimic this potential home cage environment. While it would be predicted that each type of measure would produce similar rankings of objects, this has never been tested empirically. In this study, we compared two paradigms: EE objects were either presented in pairs (paired-choice comparison) or four objects were presented simultaneously (simultaneous presentation comparison). We used frequency of first interaction and time spent with each object to rank the objects in the paired-choice experiment, and time spent with each object to rank the objects in the simultaneous presentation experiment. We also considered the behaviours elicited by the objects to determine if these might be contributing to object preference. We demonstrated that object ranking based on time spent with objects from the paired-choice experiment predicted object ranking in the simultaneous presentation experiment. Additionally, we confirmed that behaviours elicited were an important determinant of time spent with an object. This provides convergent evidence that both paired choice and simultaneous comparisons provide valid measures of preference for EE objects in rats. (C) 2007 Elsevier B.V. All rights reserved.

Soya phytoestrogens change cortical and hippocampal expression of BDNF mRNA in male rats

Adult male hooded Lister rats were either fed a diet containing 150 microg/g soya phytoestrogens or a soya-free diet for 18 days. This concentration of phytoestrogens should have been sufficient to occupy the oestrogen-beta, but not the oestrogen-alpha, receptors. Using in situ hybridisation, significant reductions were found in brain-derived neurotrophic factor (BDNF) mRNA expression in the CA3 and CA4 region of the hippocampus and in the cerebral cortex in the rats fed the diet containing phytoestrogens, compared with those on the soya-free diet. No changes in glutamic acid decarboxylase-67 or glial fibrillary acidic protein mRNA were found. This suggests a role for oestrogen-beta receptors in regulating BDNF mRNA expression.

Proceedings of the Rank Forum on Vitamin D

The Rank Forum on Vitamin D was held on 2nd and 3rd July 2009 at the University of Surrey, Guildford, UK. The workshop consisted of a series of scene-setting presentations to address the current issues and challenges concerning vitamin D and health, and included an open discussion focusing on the identification of the concentrations of serum 25-hydroxyvitamin D (25(OH)D) (a marker of vitamin D status) that may be regarded as optimal, and the implications this process may have in the setting of future dietary reference values for vitamin D in the UK. The Forum was in agreement with the fact that it is desirable for all of the population to have a serum 25(OH)D concentration above 25 nmol/l, but it discussed some uncertainty about the strength of evidence for the need to aim for substantially higher concentrations (25(OH)D concentrations . 75 nmol/l). Any discussion of ‘optimal’ concentration of serum 25(OH)D needs to define ‘optimal’ with care since it is important to consider the normal distribution of requirements and the vitamin D needs for a wide range of outcomes. Current UK reference values concentrate on the requirements of particular subgroups of the population; this differs from the approaches used in other European countries where a wider range of age groups tend to be covered. With the re-emergence of rickets and the public health burden of low vitamin D status being already apparent, there is a need for urgent action from policy makers and risk managers. The Forum highlighted concerns regarding the failure of implementation of existing strategies in the UK for achieving current vitamin D recommendations.

Generation, description and storage of dendritic morphology data

It is generally assumed that the variability of neuronal morphology has an important effect on both the connectivity and the activity of the nervous system, but this effect has not been thoroughly investigated. Neuroanatomical archives represent a crucial tool to explore structure–function relationships in the brain. We are developing computational tools to describe, generate, store and render large sets of three–dimensional neuronal structures in a format that is compact, quantitative, accurate and readily accessible to the neuroscientist. Single–cell neuroanatomy can be characterized quantitatively at several levels. In computer–aided neuronal tracing files, a dendritic tree is described as a series of cylinders, each represented by diameter, spatial coordinates and the connectivity to other cylinders in the tree. This ‘Cartesian’ description constitutes a completely accurate mapping of dendritic morphology but it bears little intuitive information for the neuroscientist. In contrast, a classical neuroanatomical analysis characterizes neuronal dendrites on the basis of the statistical distributions of morphological parameters, e.g. maximum branching order or bifurcation asymmetry. This description is intuitively more accessible, but it only yields information on the collective anatomy of a group of dendrites, i.e. it is not complete enough to provide a precise ‘blueprint’ of the original data. We are adopting a third, intermediate level of description, which consists of the algorithmic generation of neuronal structures within a certain morphological class based on a set of ‘fundamental’, measured parameters. This description is as intuitive as a classical neuroanatomical analysis (parameters have an intuitive interpretation), and as complete as a Cartesian file (the algorithms generate and display complete neurons). The advantages of the algorithmic description of neuronal structure are immense. If an algorithm can measure the values of a handful of parameters from an experimental database and generate virtual neurons whose anatomy is statistically indistinguishable from that of their real counterparts, a great deal of data compression and amplification can be achieved. Data compression results from the quantitative and complete description of thousands of neurons with a handful of statistical distributions of parameters. Data amplification is possible because, from a set of experimental neurons, many more virtual analogues can be generated. This approach could allow one, in principle, to create and store a neuroanatomical database containing data for an entire human brain in a personal computer. We are using two programs, L–NEURON and ARBORVITAE, to investigate systematically the potential of several different algorithms for the generation of virtual neurons. Using these programs, we have generated anatomically plausible virtual neurons for several morphological classes, including guinea pig cerebellar Purkinje cells and cat spinal cord motor neurons. These virtual neurons are stored in an online electronic archive of dendritic morphology. This process highlights the potential and the limitations of the ‘computational neuroanatomy’ strategy for neuroscience databases.

Ensemble prediction for nowcasting with a convection-permitting model—I: description of the system and the impact of radar-derived surface precipitation rates

A key strategy to improve the skill of quantitative predictions of precipitation, as well as hazardous weather such as severe thunderstorms and flash floods is to exploit the use of observations of convective activity (e.g. from radar). In this paper, a convection-permitting ensemble prediction system (EPS) aimed at addressing the problems of forecasting localized weather events with relatively short predictability time scale and based on a 1.5 km grid-length version of the Met Office Unified Model is presented. Particular attention is given to the impact of using predicted observations of radar-derived precipitation intensity in the ensemble transform Kalman filter (ETKF) used within the EPS. Our initial results based on the use of a 24-member ensemble of forecasts for two summer case studies show that the convective-scale EPS produces fairly reliable forecasts of temperature, horizontal winds and relative humidity at 1 h lead time, as evident from the inspection of rank histograms. On the other hand, the rank histograms seem also to show that the EPS generates too much spread for forecasts of (i) surface pressure and (ii) surface precipitation intensity. These may indicate that for (i) the value of surface pressure observation error standard deviation used to generate surface pressure rank histograms is too large and for (ii) may be the result of non-Gaussian precipitation observation errors. However, further investigations are needed to better understand these findings. Finally, the inclusion of predicted observations of precipitation from radar in the 24-member EPS considered in this paper does not seem to improve the 1-h lead time forecast skill.

An ECOOP web portal for visualising and comparing distributed coastal oceanography model and in situ data

As part of a large European coastal operational oceanography project (ECOOP), we have developed a web portal for the display and comparison of model and in situ marine data. The distributed model and in situ datasets are accessed via an Open Geospatial Consortium Web Map Service (WMS) and Web Feature Service (WFS) respectively. These services were developed independently and readily integrated for the purposes of the ECOOP project, illustrating the ease of interoperability resulting from adherence to international standards. The key feature of the portal is the ability to display co-plotted timeseries of the in situ and model data and the quantification of misfits between the two. By using standards-based web technology we allow the user to quickly and easily explore over twenty model data feeds and compare these with dozens of in situ data feeds without being concerned with the low level details of differing file formats or the physical location of the data. Scientific and operational benefits to this work include model validation, quality control of observations, data assimilation and decision support in near real time. In these areas it is essential to be able to bring different data streams together from often disparate locations.