Modelling the formation of necrotic regions in avascular tumours

The mechanisms underlying the formation of necrotic regions within avascular tumours are not well understood. In this paper, we examine the relative roles of nutrient deprivation and of cell death, from both the proliferating phase of the cell cycle via apoptosis and from the quiescent phase via necrosis, in changing the structure within multicellular tumour spheroids and particularly the accumulation of dead cell material in the centre. A mathematical model is presented and studied that accounts for nutrient diffusion, changes in cell cycling rates, the two different routes to cell death as well as active motion of cells and passive motion of the dead cell material. In studying the accumulation of dead cell matter we do not distinguish between the route by which each was formed. The resulting mathematical model is examined for a number of scenarios. Results show that in many cases the size of the necrotic core is closely correlated with low levels in nutrient concentration. However, in certain cases, particularly where the rate of necrosis is large, the resulting necrotic core can lead to regions of non-negligible nutrient concentration-dependent upon the mode of cell death.

A practical approach to a multi-level analysis with a sparse binary outcome within a large surgical trial

Objectives: To assess the potential source of variation that surgeon may add to patient outcome in a clinical trial of surgical procedures. Methods: Two large (n = 1380) parallel multicentre randomized surgical trials were undertaken to compare laparoscopically assisted hysterectomy with conventional methods of abdominal and vaginal hysterectomy; involving 43 surgeons. The primary end point of the trial was the occurrence of at least one major complication. Patients were nested within surgeons giving the data set a hierarchical structure. A total of 10% of patients had at least one major complication, that is, a sparse binary outcome variable. A linear mixed logistic regression model (with logit link function) was used to model the probability of a major complication, with surgeon fitted as a random effect. Models were fitted using the method of maximum likelihood in SAS((R)). Results: There were many convergence problems. These were resolved using a variety of approaches including; treating all effects as fixed for the initial model building; modelling the variance of a parameter on a logarithmic scale and centring of continuous covariates. The initial model building process indicated no significant 'type of operation' across surgeon interaction effect in either trial, the 'type of operation' term was highly significant in the abdominal trial, and the 'surgeon' term was not significant in either trial. Conclusions: The analysis did not find a surgeon effect but it is difficult to conclude that there was not a difference between surgeons. The statistical test may have lacked sufficient power, the variance estimates were small with large standard errors, indicating that the precision of the variance estimates may be questionable.

An investigation of the germylene addition reaction, GeH2+C2H2: Time-resolved gas-phase kinetic studies and quantum chemical calculations of the reaction energy surface

Time resolved studies of germylene, GeH2, generated by laser flash photolysis of 3,4-dimethylgermacyclopentene-3, have been carried out to obtain rate constants for its bimolecular reaction with acetylene, C2H2. The reaction was studied in the gas-phase over the pressure range 1-100 Tort, with SF6 as bath gas, at 5 temperatures in the range 297-553 K. The reaction showed a very slight pressure dependence at higher temperatures. The high pressure rate constants (obtained by extrapolation at the three higher temperatures) gave the Arrhenius equation: log(k(infinity)/cm(3) molecule(-1) s(-1)) (-10.94 +/- 0.05) + (6.10 +/- 0.36 kJ mol(-1))/RTln10. These Arrhenius parameters are consistent with a fast reaction occurring at approximately 30% of the collision rate at 298 K. Quantum chemical calculations (both DFT and ab initio G2//B3LYP and G2//QCISD) of the GeC2H4 potential energy surface (PES), show that GeH2 + C2H2 react initially to form germirene which can isomerise to vinylgermylene with a relatively low barrier. RRKM modelling, based on a loose association transition state, but assuming vinylgermylene is the end product (used in combination with a weak collisional deactivation model) predicts a strong pressure dependence using the calculated energies, in conflict with the experimental evidence. The detailed GeC2H4 PES shows considerable complexity with ten other accessible stable minima (B3LYP level), the three most stable of which are all germylenes. Routes through this complex surface were examined in detail. The only product combination which appears capable of satisfying the (P-3) + C2H4.C2H4 was confirmed as a product by GC observed lack of a strong pressure dependence is Ge(P-3) + C2H4. C2H4 was confirmed as a product by GC analysis. Although the formation of these products are shown to be possible by singlet-triplet curve crossing during dissociation of 1-germiranylidene (1-germacyclopropylidene), it seems more likely (on thermochernical grounds) that the triplet biradical, (GeCH2CH2.)-Ge-., is the immediate product precursor. Comparisons are made with the reaction of SiH2 with C2H2.

Time-resolved gas-phase kinetic and quantum chemical studies of the reaction of silylene with oxygen

Time-resolved kinetic studies of the reaction of silylene, SiH2, generated by laser flash photolysis of phenylsilane, have been carried out to obtain rate constants for its bimolecular reaction with O-2. The reaction was studied in the gas phase over the pressure range 1-100 Torr in SF6 bath gas, at five temperatures in the range 297-600 K. The second order rate constants at 10 Torr were fitted to the Arrhenius equation: log(k/cm(3) molecule(-1) s(-1)) = (-11.08 +/- 0.04) + (1.57 +/- 0.32 kJ mol(-1))/RT ln10 The decrease in rate constant values with increasing temperature, although systematic is very small. The rate constants showed slight increases in value with pressure at each temperature, but this was scarcely beyond experimental uncertainty. From estimates of Lennard-Jones collision rates, this reaction is occurring at ca. 1 in 20 collisions, almost independent of pressure and temperature. Ab initio calculations at the G3 level backed further by multi-configurational (MC) SCF calculations, augmented by second order perturbation theory (MRMP2), support a mechanism in which the initial adduct, H2SiOO, formed in the triplet state (T), undergoes intersystem crossing to the more stable singlet state (S) prior to further low energy isomerisation processes leading, via a sequence of steps, ultimately to dissociation products of which the lowest energy pair are H2O + SiO. The decomposition of the intermediate cyclo-siladioxirane, via O-O bond fission, plays an important role in the overall process. The bottleneck for the overall process appears to be the T -> S process in H2SiOO. This process has a small spin orbit coupling matrix element, consistent with an estimate of its rate constant of 1 x 10(9) s(-1) obtained with the aid of RRKM theory. This interpretation preserves the idea that, as in its reactions in general, SiH2 initially reacts at the encounter rate with O-2. The low values for the secondary reaction barriers on the potential energy surface account for the lack of an observed pressure dependence. Some comparisons are drawn with the reactions of CH2 + O-2 and SiCl2 + O-2.

Modelling the cabling of rope systems

This paper presents a theoretical model of the torsional characteristics of parallel multi-part rope systems. In such systems, the ropes may cable, or wrap around each other, depending on the combination of applied torque, rope tension, length and spacing between the rope parts. Cabling constitutes a failure that might be retrievable but as such can seriously affect the performance of the rope system. The torsional characteristics of the system are very different before and after cabling, and theoretical models are given for both situations. Laboratory tests were performed on both two and four rope systems, with measurements being made of torque at rotations from 0 to 360 deg. Tests were run with different rope spacings, tensions and lengths and the results compared with predictions from the theoretical model. The conclusion from the test results was that the theoretical model predicts both the pre- and post-cabling torsional behaviour with an acceptable level of accuracy.

Crumpet structures: experimental and modelling studies

Crumpets are made by heating fermented batter on a hot plate at around 230°C. The characteristic structure dominated by vertical pores develops rapidly: structure has developed throughout around 75% of the product height within 30s, which is far faster than might be expected from transient heat conduction through the batter. Cooking is complete within around 3 min. Image analysis based on results from X-ray tomography shows that the voidage fraction is approximately constant and that there is continual coalescence between the larger pores throughout the product although there is also a steady level of small bubbles trapped within the solidified batter. We report here experimental studies which shed light on some of the mechanisms responsible for this structure, together with some models of key phenomena.Three aspects are discussed here: the role of gas (carbon dioxide and nitrogen) nuclei in initiating structure development; convective heat transfer inside the developing pores; and the kinetics of setting the batter into an elastic solid structure. It is shown conclusively that the small bubbles of carbon dioxide resulting from the fermentation stage play a crucial role as nuclei for pore development: without these nuclei, the result is not a porous structure, but rather a solid, elastic, inedible, gelatinized product. These nuclei are also responsible for the tiny bubbles which are set in the final product. The nuclei form the source of the dominant pore structure which is largely driven by the, initially explosive, release of water vapour from the batter together with the desorption of dissolved carbon dioxide. It is argued that the rapid evaporation, transport and condensation of steam within the growing pores provides an important mechanism, as in a heat pipe, for rapid heat transfer, and models for this process are developed and tested. The setting of the continuous batter phase is essential for final product quality: studies using differential scanning calorimetry and on the kinetics of change in the visco-elastic properties of the batter suggest that this process is driven by the kinetics of gelatinization. Unlike many thermally driven food processes the rates of heating are such that gelatinization kinetics cannot be neglected. The implications of these results for modelling and for the development of novel structures are discussed.

Modelling the uptake and growth kinetics of Penicillium glabrum in a tannic acid-containing solid-state fermentation for tannase production

A mathematical growth model for the batch solid-state fermentation process for fungal tannase production was developed and tested experimentally. The unstructured model describes the uptake and growth kinetics of Penicillium glabrum in an impregnated polyurethane foam substrate system. In general, good agreement between the experimental data and model simulations was obtained. Biomass, tannase and spore production are described by logistic kinetics with a time delay between biomass production and tannase and spore formation. Possible induction mechanisms for the latter are proposed. Hydrolysis of tannic acid, the main carbon source in the substrate system, is reasonably well described with Michaelis-Menten kinetics with time-varying enzyme concentration but a more complex reaction mechanism is suspected. The metabolism of gallic acid, a tannase-hydrolysis product of tannic acid, was shown to be growth limiting during the main growth phase. (c) 2004 Elsevier Ltd. All rights reserved.

Bode's maximum available feedback and phase margin

'Maximum Available Feedback' is Bode's term for the highest possible loop gain over a given bandwidth, with specified stability margins, in a single loop feedback system. His work using asymptotic analysis allowed Bode to develop a methodology for achieving this. However, the actual system performance differs from that specified, due to the use of asymptotic approximations, and the author[2] has described how, for instance, the actual phase margin is often much lower than required when the bandwidth is high, and proposed novel modifications to the asymptotes to address the issue. This paper gives some new analysis of such systems, showing that the method also contravenes Bode's definition of phase margin, and shows how the author's modifications can be used for different amounts of bandwidth.

RBF equalizer design using directional evolutionary multi-objective optimization

Whilst radial basis function (RBF) equalizers have been employed to combat the linear and nonlinear distortions in modern communication systems, most of them do not take into account the equalizer's generalization capability. In this paper, it is firstly proposed that the. model's generalization capability can be improved by treating the modelling problem as a multi-objective optimization (MOO) problem, with each objective based on one of several training sets. Then, as a modelling application, a new RBF equalizer learning scheme is introduced based on the directional evolutionary MOO (EMOO). Directional EMOO improves the computational efficiency of conventional EMOO, which has been widely applied in solving MOO problems, by explicitly making use of the directional information. Computer simulation demonstrates that the new scheme can be used to derive RBF equalizers with good performance not only on explaining the training samples but on predicting the unseen samples.

A hybridised evolutionary algorithm for multi-criterion minimum spanning tree problems

A hybridised and Knowledge-based Evolutionary Algorithm (KEA) is applied to the multi-criterion minimum spanning tree problems. Hybridisation is used across its three phases. In the first phase a deterministic single objective optimization algorithm finds the extreme points of the Pareto front. In the second phase a K-best approach finds the first neighbours of the extreme points, which serve as an elitist parent population to an evolutionary algorithm in the third phase. A knowledge-based mutation operator is applied in each generation to reproduce individuals that are at least as good as the unique parent. The advantages of KEA over previous algorithms include its speed (making it applicable to large real-world problems), its scalability to more than two criteria, and its ability to find both the supported and unsupported optimal solutions.

Semi-automatic knowledge extraction, representation and context-sensitive intelligent retrieval of video content using collateral context modelling with scalable ontological networks

Automatic indexing and retrieval of digital data poses major challenges. The main problem arises from the ever increasing mass of digital media and the lack of efficient methods for indexing and retrieval of such data based on the semantic content rather than keywords. To enable intelligent web interactions, or even web filtering, we need to be capable of interpreting the information base in an intelligent manner. For a number of years research has been ongoing in the field of ontological engineering with the aim of using ontologies to add such (meta) knowledge to information. In this paper, we describe the architecture of a system (Dynamic REtrieval Analysis and semantic metadata Management (DREAM)) designed to automatically and intelligently index huge repositories of special effects video clips, based on their semantic content, using a network of scalable ontologies to enable intelligent retrieval. The DREAM Demonstrator has been evaluated as deployed in the film post-production phase to support the process of storage, indexing and retrieval of large data sets of special effects video clips as an exemplar application domain. This paper provides its performance and usability results and highlights the scope for future enhancements of the DREAM architecture which has proven successful in its first and possibly most challenging proving ground, namely film production, where it is already in routine use within our test bed Partners' creative processes. (C) 2009 Published by Elsevier B.V.

A multi-agent architect for CSCW systems: from organisational semiotics perspective

This paper describes a multi-agent architecture to support CSCW systems modelling. Since CSCW involves different organizations, it can be seen as a social model. From this point of view, we investigate the possibility of modelling CSCW by agent technology, and then based on organizational semiotics method a multi-agent architecture is proposed via using EDA agent model. We explain the components of this multi-agent architecture and design process. It is argued that this approach provides a new perspective for modelling CSCW systems.

Mathematical modelling for the digital society

We argue the case for a new branch of mathematics and its applications: Mathematics for the Digital Society. There is a challenge for mathematics, a strong “pull” from new and emerging commercial and public activities; and a need to train and inspire a generation of quantitative scientists who will seek careers within the associated sectors. Although now going through an early phase of boiling up, prior to scholarly distillation, we discuss how data rich activities and applications may benefit from a wide range of continuous and discrete models, methods, analysis and inference. In ten years time such applications will be common place and associated courses may be embedded within the undergraduate curriculum.

Long-lived halocarbon trends and budgets from atmospheric chemistry modelling constrained with measurements in polar firn

The budgets of seven halogenated gases (CFC-11, CFC-12, CFC-113, CFC-114, CFC-115, CCl4 and SF6) are studied by comparing measurements in polar firn air from two Arctic and three Antarctic sites, and simulation results of two numerical models: a 2-D atmospheric chemistry model and a 1-D firn diffusion model. The first one is used to calculate atmospheric concentrations from emission trends based on industrial inventories; the calculated concentration trends are used by the second one to produce depth concentration profiles in the firn. The 2-D atmospheric model is validated in the boundary layer by comparison with atmospheric station measurements, and vertically for CFC-12 by comparison with balloon and FTIR measurements. Firn air measurements provide constraints on historical atmospheric concentrations over the last century. Age distributions in the firn are discussed using a Green function approach. Finally, our results are used as input to a radiative model in order to evaluate the radiative forcing of our target gases. Multi-species and multi-site firn air studies allow to better constrain atmospheric trends. The low concentrations of all studied gases at the bottom of the firn, and their consistency with our model results confirm that their natural sources are small. Our results indicate that the emissions, sinks and trends of CFC-11, CFC-12, CFC-113, CFC-115 and SF6 are well constrained, whereas it is not the case for CFC-114 and CCl4. Significant emission-dependent changes in the lifetimes of halocarbons destroyed in the stratosphere were obtained. Those result from the time needed for their transport from the surface where they are emitted to the stratosphere where they are destroyed. Efforts should be made to update and reduce the large uncertainties on CFC lifetimes.

A mixture of experts network structure construction algorithm for modelling and control

This paper introduces a new fast, effective and practical model structure construction algorithm for a mixture of experts network system utilising only process data. The algorithm is based on a novel forward constrained regression procedure. Given a full set of the experts as potential model bases, the structure construction algorithm, formed on the forward constrained regression procedure, selects the most significant model base one by one so as to minimise the overall system approximation error at each iteration, while the gate parameters in the mixture of experts network system are accordingly adjusted so as to satisfy the convex constraints required in the derivation of the forward constrained regression procedure. The procedure continues until a proper system model is constructed that utilises some or all of the experts. A pruning algorithm of the consequent mixture of experts network system is also derived to generate an overall parsimonious construction algorithm. Numerical examples are provided to demonstrate the effectiveness of the new algorithms. The mixture of experts network framework can be applied to a wide variety of applications ranging from multiple model controller synthesis to multi-sensor data fusion.