From a discrete to a continuum model of cell dynamics in one dimension

Multiscale modeling is emerging as one of the key challenges in mathematical biology. However, the recent rapid increase in the number of modeling methodologies being used to describe cell populations has raised a number of interesting questions. For example, at the cellular scale, how can the appropriate discrete cell-level model be identified in a given context? Additionally, how can the many phenomenological assumptions used in the derivation of models at the continuum scale be related to individual cell behavior? In order to begin to address such questions, we consider a discrete one-dimensional cell-based model in which cells are assumed to interact via linear springs. From the discrete equations of motion, the continuous Rouse [P. E. Rouse, J. Chem. Phys. 21, 1272 (1953)] model is obtained. This formalism readily allows the definition of a cell number density for which a nonlinear "fast" diffusion equation is derived. Excellent agreement is demonstrated between the continuum and discrete models. Subsequently, via the incorporation of cell division, we demonstrate that the derived nonlinear diffusion model is robust to the inclusion of more realistic biological detail. In the limit of stiff springs, where cells can be considered to be incompressible, we show that cell velocity can be directly related to cell production. This assumption is frequently made in the literature but our derivation places limits on its validity. Finally, the model is compared with a model of a similar form recently derived for a different discrete cell-based model and it is shown how the different diffusion coefficients can be understood in terms of the underlying assumptions about cell behavior in the respective discrete models.

A model for the evolution of pathogen-induced leaf shedding

A size-structured plant population model is developed to study the evolution of pathogen-induced leaf shedding under various environmental conditions. The evolutionary stable strategy (ESS) of the leaf shedding rate is determined for two scenarios: i) a constant leaf shedding strategy and ii) an infection load driven leaf shedding strategy. The model predicts that ESS leaf shedding rates increase with nutrient availability. No effect of plant density on the ESS leaf shedding rate is found even though disease severity increases with plant density. When auto-infection, that is increased infection due to spores produced on the plant itself, plays a key role in further disease increase on the plant, shedding leaves removes disease that would otherwise contribute to disease increase on the plant itself. Consequently leaf shedding responses to infections may evolve. When external infection, that is infection due to immigrant spores, is the key determinant, shedding a leaf does not reduce the force of infection on the leaf shedding plant. In this case leaf shedding will not evolve. Under a low external disease pressure adopting an infection driven leaf shedding strategy is more efficient than adopting a constant leaf shedding strategy, since a plant adopting an infection driven leaf shedding strategy does not shed any leaves in the absence of infection, even when leaf shedding rates are high. A plant adopting a constant leaf shedding rate sheds the same amount of leaves regardless of the presence of infection. Based on the results we develop two hypotheses that can be tested if the appropriate plant material is available.

Low-molecular-weight gelators: Elucidating the principles of gelation based on gelator solubility and a cooperative self-assembly model

This paper highlights the key role played by solubility in influencing gelation and demonstrates that many facets of the gelation process depend on this vital parameter. In particular, we relate thermal stability (T-gel) and minimum gelation concentration (MGC) values of small-molecule gelation in terms of the solubility and cooperative self-assembly of gelator building blocks. By employing a van't Hoff analysis of solubility data, determined from simple NMR measurements, we are able to generate T-calc values that reflect the calculated temperature for complete solubilization of the networked gelator. The concentration dependence of T-calc allows the previously difficult to rationalize "plateau-region" thermal stability values to be elucidated in terms of gelator molecular design. This is demonstrated for a family of four gelators with lysine units attached to each end of an aliphatic diamine, with different peripheral groups (Z or Bee) in different locations on the periphery of the molecule. By tuning the peripheral protecting groups of the gelators, the solubility of the system is modified, which in turn controls the saturation point of the system and hence controls the concentration at which network formation takes place. We report that the critical concentration (C-crit) of gelator incorporated into the solid-phase sample-spanning network within the gel is invariant of gelator structural design. However, because some systems have higher solubilities, they are less effective gelators and require the application of higher total concentrations to achieve gelation, hence shedding light on the role of the MGC parameter in gelation. Furthermore, gelator structural design also modulates the level of cooperative self-assembly through solubility effects, as determined by applying a cooperative binding model to NMR data. Finally, the effect of gelator chemical design on the spatial organization of the networked gelator was probed by small-angle neutron and X-ray scattering (SANS/SAXS) on the native gel, and a tentative self-assembly model was proposed.

Simple general method of generating non-oxo, non-amavadine model octacoordinated vanadium(IV) complexes of some tetradentate ONNO chelating ligands from various oxovanadium(IV/V) compounds and structural characterization of one of them

A simple general route of obtaining very stable octacoordinated non-oxovanadium( IV) complexes of the general formula VL2 (where H2L is a tetradentate ONNO donor) is presented. Six such complexes (1-6) are adequately characterized by elemental analysis, mass spectrometry, and various spectroscopic techniques. One of these compounds (1) has been structurally characterized. The molecule has crystallographic 4 symmetry and has a dodecahedral structure existing in a tetragonal space group P4n2. The non-oxo character and VL2 stoichiometry for all of the complexes are established from analytical and mass spectrometric data. In addition, the non-oxo character is clearly indicated by the complete absence of the strong nu(v=o) band in the 925-1025 cm(-1) region, which is a signature of all oxovanadium species. The complexes are quite stable in open air in the solid state and in solution, a phenomenon rarely observed in non-oxovanadium(IV) or bare vanadium(IV) complexes.

Key performance indicators (KPIs) and priority setting in using the multi-attribute approach for assessing sustainable intelligent buildings

The main objectives of this paper are to: firstly, identify key issues related to sustainable intelligent buildings (environmental, social, economic and technological factors); develop a conceptual model for the selection of the appropriate KPIs; secondly, test critically stakeholder's perceptions and values of selected KPIs intelligent buildings; and thirdly develop a new model for measuring the level of sustainability for sustainable intelligent buildings. This paper uses a consensus-based model (Sustainable Built Environment Tool- SuBETool), which is analysed using the analytical hierarchical process (AHP) for multi-criteria decision-making. The use of the multi-attribute model for priority setting in the sustainability assessment of intelligent buildings is introduced. The paper commences by reviewing the literature on sustainable intelligent buildings research and presents a pilot-study investigating the problems of complexity and subjectivity. This study is based upon a survey perceptions held by selected stakeholders and the value they attribute to selected KPIs. It is argued that the benefit of the new proposed model (SuBETool) is a ‘tool’ for ‘comparative’ rather than an absolute measurement. It has the potential to provide useful lessons from current sustainability assessment methods for strategic future of sustainable intelligent buildings in order to improve a building's performance and to deliver objective outcomes. Findings of this survey enrich the field of intelligent buildings in two ways. Firstly, it gives a detailed insight into the selection of sustainable building indicators, as well as their degree of importance. Secondly, it tesst critically stakeholder's perceptions and values of selected KPIs intelligent buildings. It is concluded that the priority levels for selected criteria is largely dependent on the integrated design team, which includes the client, architects, engineers and facilities managers.

Interaction of sulphur-containing aroma compounds with proteins in both model systems and real food systems

Irreversible binding of key flavour disulphides to ovalbumin has been shown previously to occur in model systems. The extent of binding is determined by the availability of the sulphydryl groups to participate in disulphide exchange, influenced either by pH, or the state of the protein (native or heat-denatured). In this study, two further proteins, one with sulphydryl groups available in the native state (beta-lactoglobulin) and one with no sulphydryl groups in the native state (lysozyme) were used to confirm this hypothesis. When the investigation was extended to real food systems, a similar effect was shown when a commercial meat flavouring containing disulphides was added to heat-denatured ovalbumin. Furthermore, comparison of the volatiles generated from onions, cooked either alone, or in the presence of meat, showed a significant reduction of key onion-derived disulphides when cooked in the presence of meat, and an even greater reduction of trisulphides. These findings may have implications for consumer acceptance of food products; where these compounds are used as flavourings or where they occur naturally.

Effect of citric acid and glycine addition on acrylamide and flavor in a potato model system

Acrylamide levels in cooked/processed food can be reduced by treatment with citric acid or glycine. In a potato model system cooked at 180 degrees C for 10-60 min, these treatments affected the volatile profiles. Strecker aldehydes and alkylpyrazines, key flavor compounds of cooked potato, were monitored. Citric acid limited the generation of volatiles, particularly the alkylpyrazines. Glycine increased the total volatile yield by promoting the formation of certain alkylpyrazines, namely, 2,3-dimethylpyrazine, trimethylpyrazine, 2-ethyl-3,5-dimethylpyrazine, tetramethylpyrazine, and 2,5-diethyl-3- methylpyrazine. However, the formation of other pyrazines and Strecker aldehydes was suppressed. It was proposed that the opposing effects of these treatments on total volatile yield may be used to best advantage by employing a combined treatment at lower concentrations, especially as both treatments were found to have an additive effect in reducing acrylamide. This would minimize the impact on flavor but still achieve the desired reduction in acrylamide levels.

Acrylamide and pyrazine formation in model systems containing asparagine

The effect of different sugars and glyoxal on the formation of acrylamide in low-moisture starch-based model systems was studied, and kinetic data were obtained. Glucose was more effective than fructose, tagatose, or maltose in acrylamide formation, whereas the importance of glyoxal as a key sugar fragmentation intermediate was confirmed. Glyoxal formation was greater in model systems containing asparagine and glucose rather than fructose. A solid phase microextraction GC-MS method was employed to determine quantitatively the formation of pyrazines in model reaction systems. Substituted pyrazine formation was more evident in model systems containing fructose; however, the unsubstituted homologue, which was the only pyrazine identified in the headspace of glyoxal-asparagine systems, was formed at higher yields when aldoses were used as the reducing sugar. Highly significant correlations were obtained for the relationship between pyrazine and acrylamide formation. The importance of the tautomerization of the asparagine-carbonyl decarboxylated Schiff base in the relative yields of pyrazines and acrylamide is discussed.

Modelling oil absorption during post-frying cooling - I: model development

Several studies have highlighted the importance of the cooling period in oil absorption in deep-fat fried products. Specifically, it has been established that the largest proportion of oil which ends up into the food, is sucked into the porous crust region after the fried product is removed from the oil bath, stressing the importance of this time interval. The main objective of this paper was to develop a predictive mechanistic model that can be used to understand the principles behind post-frying cooling oil absorption kinetics, which can also help identifying the key parameters that affect the final oil intake by the fried product. The model was developed for two different geometries, an infinite slab and an infinite cylinder, and was divided into two main sub-models, one describing the immersion frying period itself and the other describing the post-frying cooling period. The immersion frying period was described by a transient moving-front model that considered the movement of the crust/core interface, whereas post-frying cooling oil absorption was considered to be a pressure driven flow mediated by capillary forces. A key element in the model was the hypothesis that oil suction would only begin once a positive pressure driving force had developed. The mechanistic model was based on measurable physical and thermal properties, and process parameters with no need of empirical data fitting, and can be used to study oil absorption in any deep-fat fried product that satisfies the assumptions made.

The Namib Sand Sea digital database of aeolian dunes and key forcing variables

A new digital atlas of the geomorphology of the Namib Sand Sea in southern Africa has been developed. This atlas incorporates a number of databases including a digital elevation model (ASTER and SRTM) and other remote sensing databases that cover climate (ERA-40) and vegetation (PAL and GIMMS). A map of dune types in the Namib Sand Sea has been derived from Landsat and CNES/SPOT imagery. The atlas also includes a collation of geochronometric dates, largely derived from luminescence techniques, and a bibliographic survey of the research literature on the geomorphology of the Namib dune system. Together these databases provide valuable information that can be used as a starting point for tackling important questions about the development of the Namib and other sand seas in the past, present and future.

Part load operation coefficient of air-conditioning system of public building

IPLV overall coefficient, presented by Air-Conditioning and Refrigeration Institute (ARI) of America, shows running/operation status of air-conditioning system host only. For overall operation coefficient, logical solution has not been developed, to reflect the whole air-conditioning system under part load. In this research undertaking, the running time proportions of air-conditioning systems under part load have been obtained through analysis on energy consumption data during practical operation in all public buildings in Chongqing. This was achieved by using analysis methods, based on the statistical energy consumption data distribution of public buildings month-by-month. Comparing with the weight number of IPLV, part load operation coefficient of air-conditioning system, based on this research, does not only show the status of system refrigerating host, but also reflects and calculate energy efficiency of the whole air-conditioning system. The coefficient results from the processing and analyzing of practical running data, shows the practical running status of area and building type (actual and objective) – not clear. The method is different from model analysis which gets IPLV weight number, in the sense that this method of coefficient results in both four equal proportions and also part load operation coefficient of air-conditioning system under any load rate as necessary.

Growth and public infrastructure

The paper analyzes a multicountry extension of the Barro model of productive public expenditure. In the presence of positive infrastructural externalities between countries, the provision of infrastructure will be inefficiently low if countries do not coordinate. This provides a role for a supranational body, such as the European Union, to coordinate the policies of the individual governments. It is shown how intervention by a supranational body can raise welfare by internalizing the infrastructural externality. Infrastructural externalities increase the importance of tax policy in the growth process and distribute the benefits of taxation across countries.

Using Doppler radar with a simple explicit microphysics model to diagnose problems with ice sublimation depth-scales in forecast models

Several previous studies have attempted to assess the sublimation depth-scales of ice particles from clouds into clear air. Upon examining the sublimation depth-scales in the Met Office Unified Model (MetUM), it was found that the MetUM has evaporation depth-scales 2–3 times larger than radar observations. Similar results can be seen in the European Centre for Medium-Range Weather Forecasts (ECMWF), Regional Atmospheric Climate Model (RACMO) and Météo-France models. In this study, we use radar simulation (converting model variables into radar observations) and one-dimensional explicit microphysics numerical modelling to test and diagnose the cause of the deep sublimation depth-scales in the forecast model. The MetUM data and parametrization scheme are used to predict terminal velocity, which can be compared with the observed Doppler velocity. This can then be used to test the hypothesis as to why the sublimation depth-scale is too large within the MetUM. Turbulence could lead to dry air entrainment and higher evaporation rates; particle density may be wrong, particle capacitance may be too high and lead to incorrect evaporation rates or the humidity within the sublimating layer may be incorrectly represented. We show that the most likely cause of deep sublimation zones is an incorrect representation of model humidity in the layer. This is tested further by using a one-dimensional explicit microphysics model, which tests the sensitivity of ice sublimation to key atmospheric variables and is capable of including sonde and radar measurements to simulate real cases. Results suggest that the MetUM grid resolution at ice cloud altitudes is not sufficient enough to maintain the sharp drop in humidity that is observed in the sublimation zone.

Selection of funding schemes by a borrowing decision model: a Hong Kong case study

In financial decision-making, a number of mathematical models have been developed for financial management in construction. However, optimizing both qualitative and quantitative factors and the semi-structured nature of construction finance optimization problems are key challenges in solving construction finance decisions. The selection of funding schemes by a modified construction loan acquisition model is solved by an adaptive genetic algorithm (AGA) approach. The basic objectives of the model are to optimize the loan and to minimize the interest payments for all projects. Multiple projects being undertaken by a medium-size construction firm in Hong Kong were used as a real case study to demonstrate the application of the model to the borrowing decision problems. A compromise monthly borrowing schedule was finally achieved. The results indicate that Small and Medium Enterprise (SME) Loan Guarantee Scheme (SGS) was first identified as the source of external financing. Selection of sources of funding can then be made to avoid the possibility of financial problems in the firm by classifying qualitative factors into external, interactive and internal types and taking additional qualitative factors including sovereignty, credit ability and networking into consideration. Thus a more accurate, objective and reliable borrowing decision can be provided for the decision-maker to analyse the financial options.

Sensitivity analysis of a cyanobacterial growth and movement model under two different flow regimes

Bloom-forming and toxin-producing cyanobacteria remain a persistent nuisance across the world. Modelling cyanobacterial behaviour in freshwaters is an important tool for understanding their population dynamics and predicting the location and timing of the bloom events in lakes, reservoirs and rivers. A new deterministic–mathematical model was developed, which simulates the growth and movement of cyanobacterial blooms in river systems. The model focuses on the mathematical description of the bloom formation, vertical migration and lateral transport of colonies within river environments by taking into account the major factors that affect the cyanobacterial bloom formation in rivers including light, nutrients and temperature. A parameter sensitivity analysis using a one-at-a-time approach was carried out. There were two objectives of the sensitivity analysis presented in this paper: to identify the key parameters controlling the growth and movement patterns of cyanobacteria and to provide a means for model validation. The result of the analysis suggested that maximum growth rate and day length period were the most significant parameters in determining the population growth and colony depth, respectively.