A comparison of two methods for developing the linearization of a shallow-water model

We develop the linearization of a semi-implicit semi-Lagrangian model of the one-dimensional shallow-water equations using two different methods. The usual tangent linear model, formed by linearizing the discrete nonlinear model, is compared with a model formed by first linearizing the continuous nonlinear equations and then discretizing. Both models are shown to perform equally well for finite perturbations. However, the asymptotic behaviour of the two models differs as the perturbation size is reduced. This leads to difficulties in showing that the models are correctly coded using the standard tests. To overcome this difficulty we propose a new method for testing linear models, which we demonstrate both theoretically and numerically. © Crown copyright, 2003. Royal Meteorological Society

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.

Bayesian analysis of an inverse Gaussian correlated frailty model

In survival analysis frailty is often used to model heterogeneity between individuals or correlation within clusters. Typically frailty is taken to be a continuous random effect, yielding a continuous mixture distribution for survival times. A Bayesian analysis of a correlated frailty model is discussed in the context of inverse Gaussian frailty. An MCMC approach is adopted and the deviance information criterion is used to compare models. As an illustration of the approach a bivariate data set of corneal graft survival times is analysed. (C) 2006 Elsevier B.V. All rights reserved.

Bayesian decision procedures for binary and continuous bivariate dose-escalation studies

In this paper, Bayesian decision procedures are developed for dose-escalation studies based on binary measures of undesirable events and continuous measures of therapeutic benefit. The methods generalize earlier approaches where undesirable events and therapeutic benefit are both binary. A logistic regression model is used to model the binary responses, while a linear regression model is used to model the continuous responses. Prior distributions for the unknown model parameters are suggested. A gain function is discussed and an optional safety constraint is included. Copyright (C) 2006 John Wiley & Sons, Ltd.

In vitro three-stage continuous fermentation of gluco-oligosaccharides produced by Gluconobacter oxydans NCIMB 4943 by the human colonic microflora

Gluco-oligosaccharides produced by Gluconobacter oxydans NCIMB 4943 from maltodextrin as the source, were evaluated for their fermentability by the human colonic microflora. The selectivity of growth of desirable bacteria in the human colon was studied in a three-stage continuous model of the human large intestine. Populations of bacteria, and their fluctuations as a response to the fermentation, were enumerated using fluorescent in situ hybridization (FISH). The gluco-oligosaccharides resulted in increases in numbers of bifidobacteria and the Lactobacillus/Enterococcus group in all 3 vessels of the system, representing the proximal, transverse and distal colonic areas. The prebiotic indices of the glucooligosaccharides were 2.29, 4.23 and 2.74 in V1, V2 and V3 respectively.

Mathematical model for low density lipoprotein (LDL) endocytosis by hepatocytes

Individuals with elevated levels of plasma low density lipoprotein (LDL) cholesterol (LDL-C) are considered to be at risk of developing coronary heart disease. LDL particles are removed from the blood by a process known as receptor-mediated endocytosis, which occurs mainly in the liver. A series of classical experiments delineated the major steps in the endocytotic process; apolipoprotein B-100 present on LDL particles binds to a specific receptor (LDL receptor, LDL-R) in specialized areas of the cell surface called clathrin-coated pits. The pit comprising the LDL-LDL-R complex is internalized forming a cytoplasmic endosome. Fusion of the endosome with a lysosome leads to degradation of the LDL into its constituent parts (that is, cholesterol, fatty acids, and amino acids), which are released for reuse by the cell, or are excreted. In this paper, we formulate a mathematical model of LDL endocytosis, consisting of a system of ordinary differential equations. We validate our model against existing in vitro experimental data, and we use it to explore differences in system behavior when a single bolus of extracellular LDL is supplied to cells, compared to when a continuous supply of LDL particles is available. Whereas the former situation is common to in vitro experimental systems, the latter better reflects the in vivo situation. We use asymptotic analysis and numerical simulations to study the longtime behavior of model solutions. The implications of model-derived insights for experimental design are discussed.

Solid-state fermentation: a continuous process for fungal tannase production

Truly continuous solid-state fermentations with operating times of 2-3 weeks were conducted in a prototype bioreactor for the production of fungal (Penicillium glabrum) tannase from a tannin-containing model substrate. Substantial quantities of the enzyme were synthesized throughout the operating periods and (imperfect) steady-state conditions seemed to be achieved soon after start-up of the fermentations. This demonstrated for the first time the possibility of conducting solid-state fermentations in the continuous mode and with a constant noninoculated feed. The operating variables and fermentation conditions in the bioreactor were sufficiently well predicted for the basic reinoculation concept to succeed. However, an incomplete understanding of the microbial mechanisms, the experimental system, and their interaction indicated the need for more research in this novel area of solid-state fermentation. (C) 2004 Wiley Periodicals, Inc.

Polydextrose, lactitol, and fructo-oligosaccharide fermentation by colonic bacteria in a three-stage continuous culture system

In vitro fermentations were carried out by using a model of the human colon to simulate microbial activities of lower gut bacteria. Bacterial populations (and their metabolic products) were evaluated under the effects of various fermentable substrates. Carbohydrates tested were polydextrose, lactitol, and fructo-oligosaccharide (FOS). Bacterial groups of interest were evaluated by fluorescence in situ hybridization as well as by species-specific PCR to determine bifidobacterial species and percent-G+C profiling of the bacterial communities present. Short-chain fatty acids (SCFA) produced during the fermentations were also evaluated. Polydextrose had a stimulatory effect upon colonic bifidobacteria at concentrations of 1 and 2% (using a single and pooled human fecal inoculum, respectively). The bifidogenic effect was sustained throughout all three vessels of the in vitro system (P = 0.01 seen in vessel 3), as corroborated by the bacterial community profile revealed by %G+C analysis. This substrate supported a wide variety of bifidobacteria and was the only substrate where Bifidobacterium infantis was detected. The fermentation of lactitol had a deleterious effect on both bifidobacterial and bacteroides populations (P = 0.01) and decreased total cell numbers. SCFA production was stimulated, however, particularly butyrate (beneficial for host colonocytes). FOS also had a stimulatory effect upon bifidobacterial and lactobacilli populations that used a single inoculum (P = 0.01 for all vessels) as well as a bifidogenic effect in vessels 2 and 3 (P = 0.01) when a pooled inoculum was used. A decrease in bifidobacteria throughout the model was reflected in the percent-G+C profiles.

The Ca(v)2.3 calcium channel antagonist SNX-482 reduces dorsal horn neuronal responses in a rat model of chronic neuropathic pain

Neuropathic pain is a difficult state to treat, characterized by alterations in sensory processing that can include allodynia (touch-evoked pain). Evidence exists for nerve damage-induced plasticity in both transmission and modulatory systems, including changes in voltage-dependent calcium channel (VDCC) expression and function; however, the role of Ca(v)2.3 calcium channels has not clearly been defined. Here, the effects of SNX-482, a selective Ca(v)2.3 antagonist, on sensory transmission at the spinal cord level have been investigated in the rat. The spinal nerve ligation (SNL) model of chronic neuropathic pain [Kim & Chung, (1992) Pain, 50, 355-363] was used to induce mechanical allodynia, as tested on the ipsilateral hindpaw. In vivo electrophysiological measurements of dorsal horn neuronal responses to innocuous and noxious electrical and natural stimuli were made after SNL and compared to sham-operated animals. Spinal SNX-482 (0.5-4 mu g/50 mu L) exerted dose-related inhibitions of noxious C-fibre- and A delta-fibre-mediated neuronal responses in conditions of neuropathy, but not in sham-operated animals. Measures of spinal cord hyperexcitability and nociception were most susceptible to SNX-482. In contrast, non-noxious A beta-mediated responses were not affected by SNX-482. Moreover, responses to innocuous mechanical and also thermal stimuli were more sensitive to SNX-482 in SNL than control animals. This study is the first to demonstrate an antinociceptive role for SNX-482-sensitive channels in dorsal horn neurons during neuropathy. These data are consistent with plasticity in Ca(V)2.3 calcium channel expression and suggest a potential selective target to reduce nociceptive transmission during conditions of nerve damage.

An on-line algorithm of uncertain time delay estimation in a continuous system

In this paper, we present an on-line estimation algorithm for an uncertain time delay in a continuous system based on the observational input-output data, subject to observational noise. The first order Pade approximation is used to approximate the time delay. At each time step, the algorithm combines the well known Kalman filter algorithm and the recursive instrumental variable least squares (RIVLS) algorithm in cascade form. The instrumental variable least squares algorithm is used in order to achieve the consistency of the delay parameter estimate, since an error-in-the-variable model is involved. An illustrative example is utilized to demonstrate the efficacy of the proposed approach.

A collaborative working environment for a large scale environmental model

Large scientific applications are usually developed, tested and used by a group of geographically dispersed scientists. The problems associated with the remote development and data sharing could be tackled by using collaborative working environments. There are various tools and software to create collaborative working environments. Some software frameworks, currently available, use these tools and software to enable remote job submission and file transfer on top of existing grid infrastructures. However, for many large scientific applications, further efforts need to be put to prepare a framework which offers application-centric facilities. Unified Air Pollution Model (UNI-DEM), developed by Danish Environmental Research Institute, is an example of a large scientific application which is in a continuous development and experimenting process by different institutes in Europe. This paper intends to design a collaborative distributed computing environment for UNI-DEM in particular but the framework proposed may also fit to many large scientific applications as well.

Using continuous ground-based radar and lidar measurements for evaluating the representation of clouds in four operational models

The ability of four operational weather forecast models [ECMWF, Action de Recherche Petite Echelle Grande Echelle model (ARPEGE), Regional Atmospheric Climate Model (RACMO), and Met Office] to generate a cloud at the right location and time (the cloud frequency of occurrence) is assessed in the present paper using a two-year time series of observations collected by profiling ground-based active remote sensors (cloud radar and lidar) located at three different sites in western Europe (Cabauw. Netherlands; Chilbolton, United Kingdom; and Palaiseau, France). Particular attention is given to potential biases that may arise from instrumentation differences (especially sensitivity) from one site to another and intermittent sampling. In a second step the statistical properties of the cloud variables involved in most advanced cloud schemes of numerical weather forecast models (ice water content and cloud fraction) are characterized and compared with their counterparts in the models. The two years of observations are first considered as a whole in order to evaluate the accuracy of the statistical representation of the cloud variables in each model. It is shown that all models tend to produce too many high-level clouds, with too-high cloud fraction and ice water content. The midlevel and low-level cloud occurrence is also generally overestimated, with too-low cloud fraction but a correct ice water content. The dataset is then divided into seasons to evaluate the potential of the models to generate different cloud situations in response to different large-scale forcings. Strong variations in cloud occurrence are found in the observations from one season to the same season the following year as well as in the seasonal cycle. Overall, the model biases observed using the whole dataset are still found at seasonal scale, but the models generally manage to well reproduce the observed seasonal variations in cloud occurrence. Overall, models do not generate the same cloud fraction distributions and these distributions do not agree with the observations. Another general conclusion is that the use of continuous ground-based radar and lidar observations is definitely a powerful tool for evaluating model cloud schemes and for a responsive assessment of the benefit achieved by changing or tuning a model cloud

Epicatechin and its methylated metabolite attenuate UVA-induced oxidative damage to human skin fibroblasts

The ultraviolet A component of sunlight causes both acute and chronic damage to human skin. In this study the potential of epicatechin, an abundant dietary flavanol, and 3'-O-methyl epicatechin, one of its major in vivo metabolites, to protect against UVA-induced damage was examined using cultured human skin fibroblasts as an in vitro model. The results obtained clearly show that both epicatechin and its metabolite protect these fibroblasts against UVA damage and cell death. The hydrogen-donating antioxidant properties of these compounds are probably not the mediators of this protective response. The protection is a consequence of induction of resistance to UVA mediated by the compounds and involves newly synthesized proteins. The study provides clear evidence that this dietary flavanol has the potential to protect human skin against the deleterious effects of sunlight.

Model predictive control using dynamic integrated system optimisation and parameter estimation (DISOPE)

DISOPE is a technique for solving optimal control problems where there are differences in structure and parameter values between reality and the model employed in the computations. The model reality differences can also allow for deliberate simplification of model characteristics and performance indices in order to facilitate the solution of the optimal control problem. The technique was developed originally in continuous time and later extended to discrete time. The main property of the procedure is that by iterating on appropriately modified model based problems the correct optimal solution is achieved in spite of the model-reality differences. Algorithms have been developed in both continuous and discrete time for a general nonlinear optimal control problem with terminal weighting, bounded controls and terminal constraints. The aim of this paper is to show how the DISOPE technique can aid receding horizon optimal control computation in nonlinear model predictive control.