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.

A note on atmospheric predictability

Using the method of Lorenz (1982), we have estimated the predictability of a recent version of the European Center for Medium-Range Weather Forecasting (ECMWF) model using two different estimates of the initial error corresponding to 6- and 24-hr forecast errors, respectively. For a 6-hr forecast error of the extratropical 500-hPa geopotential height field, a potential increase in forecast skill by more than 3 d is suggested, indicating a further increase in predictability by another 1.5 d compared to the use of a 24-hr forecast error. This is due to a smaller initial error and to an initial error reduction resulting in a smaller averaged growth rate for the whole 7-d forecast. A similar assessment for the tropics using the wind vector fields at 850 and 250 hPa suggests a huge potential improvement with a 7-d forecast providing the same skill as a 1-d forecast now. A contributing factor to the increase in the estimate of predictability is the apparent slow increase of error during the early part of the forecast.

On the impact of humidity observations in numerical weather prediction

The impact of humidity observations on forecast skill is explored by producing a series of global forecasts using initial data derived from the ERA-40 reanalyses system, in which all humidity data have been removed during the data assimilation. The new forecasts have been compared with the original ERA-40 analyses and forecasts made from them. Both sets of forecasts show virtually identical prediction skill in the extratropics and the tropics. Differences between the forecasts are small and undergo characteristic amplification rate. There are larger differences in temperature and geopotential in the tropics but the differences are small-scale and unstructured and have no noticeable effect on the skill of the wind forecasts. The results highlight the current very limited impact of the humidity observations, used to produce the initial state, on the forecasts.

Sensitivity of the ERA40 reanalysis to the observing system: determination of the global atmospheric circulation from reduced observations

The impact of selected observing systems on the European Centre for Medium-Range Weather Forecasts (ECMWF) 40-yr reanalysis (ERA40) is explored by mimicking observational networks of the past. This is accomplished by systematically removing observations from the present observational data base used by ERA40. The observing systems considered are a surface-based system typical of the period prior to 1945/50, obtained by only retaining the surface observations, a terrestrial-based system typical of the period 1950-1979, obtained by removing all space-based observations, and finally a space-based system, obtained by removing all terrestrial observations except those for surface pressure. Experiments using these different observing systems have been limited to seasonal periods selected from the last 10 yr of ERA40. The results show that the surface-based system has severe limitations in reconstructing the atmospheric state of the upper troposphere and stratosphere. The terrestrial system has major limitations in generating the circulation of the Southern Hemisphere with considerable errors in the position and intensity of individual weather systems. The space-based system is able to analyse the larger-scale aspects of the global atmosphere almost as well as the present observing system but performs less well in analysing the smaller-scale aspects as represented by the vorticity field. Here, terrestrial data such as radiosondes and aircraft observations are of paramount importance. The terrestrial system in the form of a limited number of radiosondes in the tropics is also required to analyse the quasi-biennial oscillation phenomenon in a proper way. The results also show the dominance of the satellite observing system in the Southern Hemisphere. These results all indicate that care is required in using current reanalyses in climate studies due to the large inhomogeneity of the available observations, in particular in time.

Improved simulation of water vapour and clear-sky radiation using 24 hour forecasts from ERA40

Monthly mean water vapour and clear-sky radiation extracted from the European Centre for Medium Range Weather Forecasts 40-year reanalysis (ERA40) forecasts are assessed using satellite observations and additional reanalysis data. There is a marked improvement in the interannual variability of column-integrated water vapour (CWV) over the oceans when using the 24-hour forecasts compared with the standard 6-hour forecasts products. The spatial distribution of CWV are well simulated by the 6-hour forecasts; using the 24-hour forecasts does not degrade this simulation substantially and in many cases improves on the quality. There is also an improved simulation of clear-sky radiation from the 24-hour forecasts compared with the 6-hour forecasts based on comparison with satellite observations and empirical estimates. Further work is required to assess the quality of water vapour simulation by reanalyses over land regions. Over the oceans, it is recommended that 24-hour forecasts of CWV and clear-sky radiation are used in preference to the standard 6-hour forecast products from ERA40

MEASUREMENT AND MODELING OF THE TOXICITY OF BINARY MIXTURES IN THE NEMATODE CAENORHABDITIS ELEGANS-A TEST OF INDEPENDENT ACTION

Ecological risk assessments must increasingly consider the effects of chemical mixtures on the environment as anthropogenic pollution continues to grow in complexity. Yet testing every possible mixture combination is impractical and unfeasible; thus, there is an urgent need for models that can accurately predict mixture toxicity from single-compound data. Currently, two models are frequently used to predict mixture toxicity from single-compound data: Concentration addition and independent action (IA). The accuracy of the predictions generated by these models is currently debated and needs to be resolved before their use in risk assessments can be fully justified. The present study addresses this issue by determining whether the IA model adequately described the toxicity of binary mixtures of five pesticides and other environmental contaminants (cadmium, chlorpyrifos, diuron, nickel, and prochloraz) each with dissimilar modes of action on the reproduction of the nematode Caenorhabditis elegans. In three out of 10 cases, the IA model failed to describe mixture toxicity adequately with significant or antagonism being observed. In a further three cases, there was an indication of synergy, antagonism, and effect-level-dependent deviations, respectively, but these were not statistically significant. The extent of the significant deviations that were found varied, but all were such that the predicted percentage effect seen on reproductive output would have been wrong by 18 to 35% (i.e., the effect concentration expected to cause a 50% effect led to an 85% effect). The presence of such a high number and variety of deviations has important implications for the use of existing mixture toxicity models for risk assessments, especially where all or part of the deviation is synergistic.

Farming systems methodology for efficient resource management at the farm level: a review from an Indian perspective

Farming systems research is a multi-disciplinary holistic approach to solve the problems of small farms. Small and marginal farmers are the core of the Indian rural economy Constituting 0.80 of the total farming community but possessing only 0.36 of the total operational land. The declining trend of per capita land availability poses a serious challenge to the sustainability and profitability of farming. Under such conditions, it is appropriate to integrate land-based enterprises such as dairy, fishery, poultry, duckery, apiary, field and horticultural cropping within the farm, with the objective of generating adequate income and employment for these small and marginal farmers Under a set of farm constraints and varying levels of resource availability and Opportunity. The integration of different farm enterprises can be achieved with the help of a linear programming model. For the current review, integrated farming systems models were developed, by Way Of illustration, for the marginal, small, medium and large farms of eastern India using linear programming. Risk analyses were carried out for different levels of income and enterprise combinations. The fishery enterprise was shown to be less risk-prone whereas the crop enterprise involved greater risk. In general, the degree of risk increased with the increasing level of income. With increase in farm income and risk level, the resource use efficiency increased. Medium and large farms proved to be more profitable than small and marginal farms with higher level of resource use efficiency and return per Indian rupee (Rs) invested. Among the different enterprises of integrated farming systems, a chain of interaction and resource flow was observed. In order to make fanning profitable and improve resource use efficiency at the farm level, the synergy among interacting components of farming systems should be exploited. In the process of technology generation, transfer and other developmental efforts at the farm level (contrary to the discipline and commodity-based approaches which have a tendency to be piecemeal and in isolation), it is desirable to place a whole-farm scenario before the farmers to enhance their farm income, thereby motivating them towards more efficient and sustainable fanning.

Understanding biodiversity effects on prey in multi-enemy systems

Biodiversity-ecosystem functioning theory would predict that increasing natural enemy richness should enhance prey consumption rate due to functional complementarity of enemy species. However, several studies show that ecological interactions among natural enemies may result in complex effects of enemy diversity on prey consumption. Therefore, the challenge in understanding natural enemy diversity effects is to predict consumption rates of multiple enemies taking into account effects arising from patterns of prey use together with species interactions. Here, we show how complementary and redundant prey use patterns result in additive and saturating effects, respectively, and how ecological interactions such as phenotypic niche shifts, synergy and intraguild predation enlarge the range of outcomes to include null, synergistic and antagonistic effects. This study provides a simple theoretical framework that can be applied to experimental studies to infer the biological mechanisms underlying natural enemy diversity effects on prey.

Separation of lanthanides and actinides(III) using tridentate benzimidazole, benzoxazole and benzothiazole ligands

The ability of new hydrophobic tridentate ligands based on 2,6-bis(benziinidazol-2-yl)pyridine, 2,6-bis(benzoxazol-2-yl)pyridine and 2,6-bis(benzothiazol-2-yl)pyridine to selectively extract americium(III) from europium(III) was measured. The most promising ligand-2,6-bis(benzoxazol-2-yl)-4-(2-decyl-1-tetradecyloxy)pyridine L-9 was found to give separation factors (SFAm/Eu) of up to 70 when used to extract cations from 0.02-0.10 M HNO3 into TPH in synergy with 2-bromodecanoic acid. Six structures of lanthanide complexes with 2,6-bis(benzoxazol-2-yl)pyridine L-6 were then determined to evaluate the types of species that are likely to be involved in the separation process. Three structural types were observed, namely [LnL(6)(NO3)(3)(H2O)2], 11-coordinate only for La, [LnL(6) (NO3)(3) (CH3CN)], 10-coordinate for Pr, Nd and Eu and [LnL(6) (NO3)(3)(H2O)], L 10-coordinate for Eu and Gd. Quantum Mechanics calculations were carried out on the tridentate ligands to elucidate the conformational preferences of the ligands in the free state and protonated and diprotonated forms and to assess the electronic properties of the ligands for comparison with other terdentate ligands used in lanthanide/actinide separation processes.

Solvent extraction and lanthanide complexation studies with new terdentate ligands containing two 1,3,5-triazine moieties

The extracting agent 2,6-bis(4,6-di-pivaloylamino-1,3,5-triazin-2-yl)-pyridine (L-5) in n-octanol was found, in synergy with 2-bromodecanoic acid, to give D-Am/D-Eu separation factors (SFs) between 2.4 and 3.7 when used to extract the metal ions from 0.02-0.12 M HNO3. Slightly higher SFs (4-6) were obtained in the absence of the synergist when the ligand was used to extract Am(III) and Eu(III) from 0.98 M HNO3. In order to investigate the possible nature of the extracted species crystal structures of L-5 and the complex formed between Yb(III) with 2,6-bis(4,6-di-amino-1,3,5-triazin-2-yl)-pyridine (L-4) were also determined. The structure of L-5 shows 3 methanol solvent molecules all of which form 2 or 3 hydrogen bonds with triazine nitrogen atoms, amide nitrogen or oxygen atoms, or pyridine nitrogen atoms. However, L-5 is relatively unstable in metal complexation reactions and loses amide groups to form the parent tetramine L-4. The crystal structure of Yb(L-4)(NO3)(3) shows ytterbium in a 9-coordinate environment being bonded to three donor atoms of the ligand and three bidentate nitrate ions. The solvent extraction properties of L-4 and L-5 are far inferior to those found for the 2,6-bis-(1,2,4-triazin-3-yl)-pyridines (L-1) which have SF values of ca. 140 and theoretical calculations have been made to compare the electronic properties of the ligands. The electronic charge distribution in L-4 and L-5 is similar to that found in other terdentate ligands such as terpyridine which have equally poor extraction properties and suggests that the unique properties of L-1 evolve from the presence of two adjacent nitrogen atoms in the triazine rings.

Commercial management in project-based organisations

The term commercial management has been used for some time, similarly the job title commercial manager. However, as of yet, little emphasis has been placed on defining. This paper presents the findings from a two-year research initiative that has compared and contrasted the role of commercial managers from a range of organisations and across industry sectors, as a first step in developing a body of knowledge for commercial. It is argued that there are compelling arguments for considering commercial management, not solely as atask undertaken by commercial managers, but as a discipline in itself: a discipline that, arguably, bridges traditional project management and organisational theories. While the study has established differences in approach and application both between and within industry sectors, it has established sufficient similarity and synergy in practice to identify a specific role of commercial management in project-based organisations. These similarities encompass contract management and dispute resolution; the divergences include a greater involvement in financial and value management in construction and in bid management in defence/aerospace.

Determination of the total antioxidant activity of fruits and vegetables by a liposome assay

The effects of mixtures of antioxidants on the oxidation of phospholipids have been investigated in large unilamellar liposomes following initiation by 2,2'-azobis(2-aminopropane) dihydrochloride. The lag phase increased linearly with antioxidant concentration. The lag phases of mixtures containing alpha-tocopherol with ascorbic acid showed synergy between the antioxidants, but mixtures of beta-carotene with cc-tocopherol or ascorbic acid were not synergistic. The liposome system was used to investigate the total antioxidant activity of lipid- and water-soluble extracts from 16 samples of fruits, vegetables, and related food products. The water-soluble extracts caused greater increases in lag phase than the lipid-soluble extracts. The lag phase of liposomes containing the water-soluble extracts from fruits and vegetables increased linearly with the total phenolic concentration, with the continental salad extract having the longest lag phase. The lipid-soluble extract from apples caused the largest increase in lag phase of the lipid-soluble extracts. The lag phases of the lipid-soluble and water-soluble extracts of all fruits and vegetables studied were additive, but no synergy was detected. The lag phase of the liposomes containing both the water-soluble and lipid-soluble extracts varied from 611.5 min for the continental salad extracts to 47.5 min for the cauliflower extracts.

Challenge testing the lactoperoxidase system against a range of bacteria using different activation agents

Lactoperoxidase (LP) exerts antimicrobial effects in combination with H2O2 and either thiocyanate (SCN-) or a halide (e. g., I-). Garlic extract in the presence of ethanol has also been used to activate the LP system. This study aimed to determine the effects of 3 LP activation systems (LP+SCN-+H2O2; LP+I-+H2O2; LP + garlic extract + ethanol) on the growth and activity of 3 test organisms (Staphylococcus aureus, Pseudomonas aeruginosa, and Bacillus cereus). Sterilized milk was used as the reaction medium, and the growth pattern of the organisms and a range of keeping quality (KQ) indicators (pH, titratable acidity, ethanol stability, clot on boiling) were monitored during storage at the respective optimum growth temperature for each organism. The LP+I-+H2O2 system reduced bacterial counts below the detection limit shortly after treatment for all 3 organisms, and no bacteria could be detected for the duration of the experiment (35 to 55 h). The KQ data confirmed that the milk remained unspoiled at the end of the experiments. The LP + garlic extract + ethanol system, on the other hand, had no effect on the growth or KQ with P. aeruginosa, but showed a small retardation of growth of the other 2 organisms, accompanied by small increases (5 to 10 h) in KQ. The effects of the LP+SCN-+H2O2 system were intermediate between those of the other 2 systems and differed between organisms. With P. aeruginosa, the system exerted total inhibition within 10 h of incubation, but the bacteria regained viability after a further 5 h, following a logarithmic growth curve. This was reflected in the KQ indicators, which implied an extension of 15 h. With the other 2 bacterial species, LP+SCN-+H2O2 exerted an obvious inhibitory effect, giving a lag phase in the growth curve of 5 to 10 h and KQ extension of 10 to 15 h. When used in combination, I- and SCN- displayed negative synergy.

Evaluation by volatile profile of the synergistic antioxidant effect between bovine serum albumin and virgin olive oil phenolic compounds in an oil-in-water emulsion

THE OXIDATIVE STABILITY OF OIL-IN-WATER EMULSIONS, CONTAINING BOVINE SERUM ALBUMIN (BSA) AND VIRGIN OLIVE OIL PHENOLIC COMPOUNDS, WAS STUDIED BY THE DETERMINATION OF THE FORMATION OF VOLATILE OXIDATION PRODUCTS. FOUR OIL-IN-WATER EMULSIONS WITH AND WITHOUT PHENOLS ISOLATED FROM VIRGIN OLIVE OIL AND BSA WERE PREPARED. THESE MODEL SYSTEMS WERE STORED AT 60 degrees C TO ACCELERATE LIPID OXIDATION. VOLATILE OXIDATION PRODUCTS WERE MONITORED EVERY THREE DAYS BY HEADSPACE SOLID-PHASE MICROEXTRACTION COUPLED WITH GAS CHROMATOGRAPHY. ALTHOUGH INDIVIDUALLY OLIVE OIL PHENOLIC COMPOUNDS AND BSA SHOWED A SIGNIFICANT ANTIOXIDANT ACTIVITY, THE COMBINATION OF THESE COMPONENTS SHOWED A VERY GOOD SYNERGY, QUANTIFIED AS 127%. IN FACT, THE EMULSION CONTAINING BOTH PHENOLIC COMPOUNDS AND BSA SHOWED A VERY LOW LEVEL OF OXIDATIVE DETERIORATION AFTER 45 DAYS STORAGE.