A moving mesh approach for modelling avascular tumour growth

A key step in many numerical schemes for time-dependent partial differential equations with moving boundaries is to rescale the problem to a fixed numerical mesh. An alternative approach is to use a moving mesh that can be adapted to focus on specific features of the model. In this paper we present and discuss two different velocity-based moving mesh methods applied to a two-phase model of avascular tumour growth formulated by Breward et al. (2002) J. Math. Biol. 45(2), 125-152. Each method has one moving node which tracks the moving boundary. The first moving mesh method uses a mesh velocity proportional to the boundary velocity. The second moving mesh method uses local conservation of volume fraction of cells (masses). Our results demonstrate that these moving mesh methods produce accurate results, offering higher resolution where desired whilst preserving the balance of fluxes and sources in the governing equations.

Global snow mass measurements and the effect of stratigraphic detail on inversion of microwave brightness temperatures

Snow provides large seasonal storage of freshwater, and information about the distribution of snow mass as Snow Water Equivalent (SWE) is important for hydrological planning and detecting climate change impacts. Large regional disagreements remain between estimates from reanalyses, remote sensing and modelling. Assimilating passive microwave information improves SWE estimates in many regions but the assimilation must account for how microwave scattering depends on snow stratigraphy. Physical snow models can estimate snow stratigraphy, but users must consider the computational expense of model complexity versus acceptable errors. Using data from the National Aeronautics and Space Administration Cold Land Processes Experiment (NASA CLPX) and the Helsinki University of Technology (HUT) microwave emission model of layered snowpacks, it is shown that simulations of the brightness temperature difference between 19 GHz and 37 GHz vertically polarised microwaves are consistent with Advanced Microwave Scanning Radiometer-Earth Observing System (AMSR-E) and Special Sensor Microwave Imager (SSM/I) retrievals once known stratigraphic information is used. Simulated brightness temperature differences for an individual snow profile depend on the provided stratigraphic detail. Relative to a profile defined at the 10 cm resolution of density and temperature measurements, the error introduced by simplification to a single layer of average properties increases approximately linearly with snow mass. If this brightness temperature error is converted into SWE using a traditional retrieval method then it is equivalent to ±13 mm SWE (7% of total) at a depth of 100 cm. This error is reduced to ±5.6 mm SWE (3 % of total) for a two-layer model.

A nonlinear oscillator describing storm track variability

We construct a two-variable model which describes the interaction between local baroclinicity and eddy heat flux in order to understand aspects of the variance in storm tracks. It is a heuristic model for diabatically forced baroclinic instability close to baroclinic neutrality. The two-variable model has the structure of a nonlinear oscillator. It exhibits some realistic properties of observed storm track variability, most notably the intermittent nature of eddy activity. This suggests that apparent threshold behaviour can be more accurately and succinctly described by a simple nonlinearity. An analogy is drawn with triggering of convective events.

Elastic net orthogonal forward regression

An efficient two-level model identification method aiming at maximising a model׳s generalisation capability is proposed for a large class of linear-in-the-parameters models from the observational data. A new elastic net orthogonal forward regression (ENOFR) algorithm is employed at the lower level to carry out simultaneous model selection and elastic net parameter estimation. The two regularisation parameters in the elastic net are optimised using a particle swarm optimisation (PSO) algorithm at the upper level by minimising the leave one out (LOO) mean square error (LOOMSE). There are two elements of original contributions. Firstly an elastic net cost function is defined and applied based on orthogonal decomposition, which facilitates the automatic model structure selection process with no need of using a predetermined error tolerance to terminate the forward selection process. Secondly it is shown that the LOOMSE based on the resultant ENOFR models can be analytically computed without actually splitting the data set, and the associate computation cost is small due to the ENOFR procedure. Consequently a fully automated procedure is achieved without resort to any other validation data set for iterative model evaluation. Illustrative examples are included to demonstrate the effectiveness of the new approaches.

Pre-conditioning the epigenetic response to high vapor pressure deficit increases the drought tolerance of Arabidopsis thaliana

Epigenetic modification of the genome via cytosine methylation is a dynamic process that responds to changes in the growing environment. This modification can also be heritable. The combination of both properties means that there is the potential for the life experiences of the parental generation to modify the methylation profiles of their offspring and so potentially to ‘pre-condition’ them to better accommodate abiotic conditions encountered by their parents. We recently identified high vapor pressure deficit (vpd)-induced DNA methylation at two gene loci in the stomatal development pathway and an associated reduction in leaf stomatal frequency.1 Here, we test whether this epigenetic modification pre-conditioned parents and their offspring to the more severe water stress of periodic drought. We found that three generations of high vpd-grown plants were better able to withstand periodic drought stress over two generations. This resistance was not directly associated with de novo methylation of the target stomata genes, but was associated with the cmt3 mutant’s inability to maintain asymmetric sequence context methylation. If our finding applies widely, it could have significant implications for evolutionary biology and breeding for stressful environments.

A risk-based framework for assessing the effectiveness of stratospheric aerosol geoengineering

Geoengineering by stratospheric aerosol injection has been proposed as a policy response to warming from human emissions of greenhouse gases, but it may produce unequal regional impacts. We present a simple, intuitive risk-based framework for classifying these impacts according to whether geoengineering increases or decreases the risk of substantial climate change, with further classification by the level of existing risk from climate change from increasing carbon dioxide concentrations. This framework is applied to two climate model simulations of geoengineering counterbalancing the surface warming produced by a quadrupling of carbon dioxide concentrations, with one using a layer of sulphate aerosol in the lower stratosphere, and the other a reduction in total solar irradiance. The solar dimming model simulation shows less regional inequality of impacts compared with the aerosol geoengineering simulation. In the solar dimming simulation, 10% of the Earth’s surface area, containing 10% of its population and 11% of its gross domestic product, experiences greater risk of substantial precipitation changes under geoengineering than under enhanced carbon dioxide concentrations. In the aerosol geoengineering simulation the increased risk of substantial precipitation change is experienced by 42% of Earth’s surface area, containing 36% of its population and 60% of its gross domestic product.

Transgenerational, dynamic methylation of stomata genes in response to low relative humidity

Transgenerational inheritance of abiotic stress-induced epigenetic modifications in plants has potential adaptive significance and might condition the offspring to improve the response to the same stress, but this is at least partly dependent on the potency, penetrance and persistence of the transmitted epigenetic marks. We examined transgenerational inheritance of low Relative Humidity-induced DNA methylation for two gene loci in the stomatal developmental pathway in Arabidopsis thaliana and the abundance of associated short-interfering RNAs (siRNAs). Heritability of low humidity-induced methylation was more predictable and penetrative at one locus (SPEECHLESS, entropy ≤ 0.02; χ2 < 0.001) than the other (FAMA, entropy ≤ 0.17; χ2 ns). Methylation at SPEECHLESS correlated positively with the continued presence of local siRNAs (r2 = 0.87; p = 0.013) which, however, could be disrupted globally in the progeny under repeated stress. Transgenerational methylation and a parental low humidity-induced stomatal phenotype were heritable, but this was reversed in the progeny under repeated treatment in a previously unsuspected manner.

Repulsion-induced surface-migration, by ballistics and bounce

The motion of adsorbate molecules across surfaces is fundamental to self-assembly, material growth, and heterogeneous catalysis. Recent Scanning Tunneling Microscopy studies have demonstrated the electron-induced long-range surface-migration of ethylene, benzene, and related molecules, moving tens of Angstroms across Si(100). We present a model of the previously unexplained long-range recoil of chemisorbed ethylene across the surface of silicon. The molecular dynamics reveal two key elements for directed long-range migration: first ‘ballistic’ motion that causes the molecule to leave the ab initio slab of the surface traveling 3–8 Å above it out of range of its roughness, and thereafter skipping-stone ‘bounces’ that transport it further to the observed long distances. Using a previously tested Impulsive Two-State model, we predict comparable long-range recoil of atomic chlorine following electron-induced dissociation of chlorophenyl chemisorbed at Cu(110)

Long-run restrictions and survey forecasts of output, consumption and investment

We consider the extent to which long-horizon survey forecasts of consumption, investment and output growth are consistent with theory-based steady-state values, and whether imposing these restrictions on long-horizon forecasts will enhance their accuracy. The restrictions we impose are consistent with a two-sector model in which the variables grow at different rates in steady state. The restrictions are imposed by exponential-tilting of simple auxiliary forecast densities. We show that imposing the consumption-output restriction yields modest improvements in the long-horizon output growth forecasts, and larger improvements in the forecasts of the cointegrating combination of consumption and output: the transformation of the data on which accuracy is assessed plays an important role.

Downregulation of VAPB expression in motor neurons derived from induced pluripotent stem cells of ALS8 patients

Amyotrophic lateral sclerosis (ALS) is an incurable neuromuscular disease that leads to a profound loss of life quality and premature death. Around 10% of the cases are inherited and ALS8 is an autosomal dominant form of familial ALS caused by mutations in the vamp-associated protein B/C (VAPB) gene. The VAPB protein is involved in many cellular processes and it likely contributes to the pathogenesis of other forms of ALS besides ALS8. A number of successful drug tests in ALS animal models could not be translated to humans underscoring the need for novel approaches. The induced pluripotent stem cells (iPSC) technology brings new hope, since it can be used to model and investigate diseases in vitro. Here we present an additional tool to study ALS based on ALS8-iPSC. Fibroblasts from ALS8 patients and their non-carrier siblings were successfully reprogrammed to a pluripotent state and differentiated into motor neurons. We show for the first time that VAPB protein levels are reduced in ALS8-derived motor neurons but, in contrast to over-expression systems, cytoplasmic aggregates could not be identified. Our results suggest that optimal levels of VAPB may play a central role in the pathogenesis of ALS8, in agreement with the observed reduction of VAPB in sporadic ALS.

Lipid bilayer pre-transition as the beginning of the melting process

We investigate the bilayer pre-transition exhibited by some lipids at temperatures below their main phase transition, and which is generally associated to the formation of periodic ripples in the membrane. Experimentally we focus on the anionic lipid dipalmytoylphosphatidylglycerol (DPPG) at different ionic strengths, and on the neutral lipid dipalmytoylphosphatidylcholine (DPPC). From the analysis of differential scanning calorimetry traces of the two lipids we find that both pre- and main transitions are part of the same melting process. Electron spin resonance of spin labels and excitation generalized polarization of Laurdan reveal the coexistence of gel and fluid domains at temperatures between the pre- and main transitions of both lipids, reinforcing the first finding. Also, the melting process of DPPG at low ionic strength is found to be less cooperative than that of DPPC. From the theoretical side, we introduce a statistical model in which a next-nearest-neighbor competing interaction is added to the usual two-state model. For the first time, modulated phases (ordered and disordered lipids periodically aligned) emerge between the gel and fluid phases as a natural consequence of the competition between lipid-lipid interactions. (C) 2009 Elsevier B.V. All rights reserved.

Pedal : identification of models for duodenal administration of levodopa

Backgound and aims: The main purpose of the PEDAL study is to identify and estimate sample individual pharmacokinetic- pharmacodynamic (PK/PD) models for duodenal infusion of levodopa/carbidopa (Duodopa®) that can be used for in numero simulation of treatment strategies. Other objectives are to study the absorption of Duodopa® and to form a basis for power calculation for a future larger study. PK/PD based on oral levodopa is problematic because of irregular gastric emptying. Preliminary work with data from [Gundert-Remy U et al. Eur J Clin Pharmacol 1983;25:69-72] suggested that levodopa infusion pharmacokinetics can be described by a two-compartment model. Background research led to a hypothesis for an effect model incorporating concentration-unrelated fluctuations, more complex than standard E-max models. Methods: PEDAL involved a few patients already on Duodopa®. A bolus dose (normal morning dose plus 50%) was given after a washout during night. Data collection continued until the clinical effect was back at baseline. The procedure was repeated on two non-consecutive days per patient. The following data were collected in 5 to 15 minutes intervals: i) Accelerometer data. ii) Three e-diary questions about ability to walk, feelings of “off” and “dyskinesia”. iii) Clinical assessment of motor function by a physician. iv) Plasma concentrations of levodopa, carbidopa and the metabolite 3-O-methyldopa. The main effect variable will be the clinical assessment. Results: At date of abstract submission, lab analyses were currently being performed. Modelling results, simulation experiments and conclusions will be presented in our poster.

Psychometric properties of the Swedish version of the Fear of Complications Questionnaire

Objectives: To translate and evaluate the psychometric properties of the Swedish version of the Fear of Complications Questionnaire. Design: Cross-sectional study design and scale development. Settings: Totally, 469 adults (response rate 63.5%) with Type 1 diabetes completed the questionnaires. Participants were recruited from two university hospitals in Sweden. Participants: Eligible patients were those who met the following inclusion criteria: diagnosed with Type 1 diabetes, diabetes duration of at least 1 year and aged at least 18 years. Methods: The Fear of Complications Questionnaire was translated using the forward-backward translation method. Factor analyses of the questionnaire were performed in two steps using both exploratory and confirmatory factor analysis. Convergent validity was examined using the Hospital Anxiety and Depression Scale and the Fear of Hypoglycaemia Fear Survey. Internal consistency was estimated using Cronbach’s alpha.Results: Exploratory factor analysis supported a two-factor solution. One factor contained three items having to do with fear of kidney-related complications and one factor included the rest of items concerning fear of other diabetes-related complications, as well as fear of complications in general. Internal consistency was high Cronbach’s alpha 0.96. The findings also gave support for convergent validity, with significant positive correlations between measures (r = 0.51 to 0.54). Conclusion: The clinical relevance of the identified two-factor model with a structure of one dominant subdomain may be considered. We suggest, however a one-factor model covering all the items as a relevant basis to assess fear of complications among people with Type 1 diabetes.

Yet another reason to tax goods

The optimal taxation of goods, labor and capital income is considered in a two period model where: i) private information changes through time; ii) savings are not observed, and; iii) savings a§ect preferences conditional on the realization of types. The simultaneous appearance of these three elements cause optimal commodity taxes to depend on o§-equilibrium savings. As a consequence, separability no longer su¢ ces for the uniform taxation prescription of Atkinson and Stiglitz (AS) to obtain. If preferences are homothetic AS is partially restored: taxes are uniform within periods, however, future consumption is taxed at a higher rate than current consumption.

Brazilian indexing and inertial inflation: evidence from time-varying estimates of an inflation transfer function

This paper is a theoretica1 and empirica1 study of the re1ationship between indexing po1icy and feedback mechanisms in the inflationary adjustment process in Brazil. The focus of our study is on two policy issues: (1) did the Brazilian system of indexing of interest rates, the exchange rate, and wages make inflation so dependent on its own past values that it created a significant feedback process and inertia in the behaviour of inflation in and (2) was the feedback effect of past inf1ation upon itself so strong that dominated the effect of monetary/fiscal variables upon current inflation? This paper develops a simple model designed to capture several "stylized facts" of Brazi1ian indexing po1icy. Separate ru1es of "backward indexing" for interest rates, the exchange rate, and wages, reflecting the evolution of po1icy changes in Brazil, are incorporated in a two-sector model of industrial and agricultural prices. A transfer function derived irom this mode1 shows inflation depending on three factors: (1) past values of inflation, (2) monetary and fiscal variables, and (3) supply- .shock variables. The indexing rules for interest rates, the exchange rate, and wages place restrictions on the coefficients of the transfer function. Variations in the policy-determined parameters of the indexing rules imply changes in the coefficients of the transfer function for inflation. One implication of this model, in contrast to previous results derived in analytically simpler models of indexing, is that a higher degree of indexing does not make current inflation more responsive to current monetary shocks. The empirical section of this paper studies the central hypotheses of this model through estimation of the inflation transfer function with time-varying parameters. The results show a systematic non-random variation of the transfer function coefficients closely synchronized with changes in the observed values of the wage-indexing parameters. Non-parametric tests show the variation of the transfer function coefficients to be statistically significant at the time of the changes in wage indexing rules in Brazil. As the degree of indexing increased, the inflation feadback coefficients increased, while the effect of external price and agricultura shocs progressively increased and monetary effects progressively decreased.