Extracting reusable document components for variable data printing

Variable Data Printing (VDP) has brought new flexibility and dynamism to the printed page. Each printed instance of a specific class of document can now have different degrees of customized content within the document template. This flexibility comes at a cost. If every printed page is potentially different from all others it must be rasterized separately, which is a time-consuming process. Technologies such as PPML (Personalized Print Markup Language) attempt to address this problem by dividing the bitmapped page into components that can be cached at the raster level, thereby speeding up the generation of page instances. A large number of documents are stored in Page Description Languages at a higher level of abstraction than the bitmapped page. Much of this content could be reused within a VDP environment provided that separable document components can be identified and extracted. These components then need to be individually rasterisable so that each high-level component can be related to its low-level (bitmap) equivalent. Unfortunately, the unstructured nature of most Page Description Languages makes it difficult to extract content easily. This paper outlines the problems encountered in extracting component-based content from existing page description formats, such as PostScript, PDF and SVG, and how the differences between the formats affects the ease with which content can be extracted. The techniques are illustrated with reference to a tool called COG Extractor, which extracts content from PDF and SVG and prepares it for reuse.

Discrete breathers in a two-dimensional Fermi-Pasta-Ulam lattice

Using asymptotic methods, we investigate whether discrete breathers are supported by a two-dimensional Fermi-Pasta-Ulam lattice. A scalar (one-component) two-dimensional Fermi-Pasta-Ulam lattice is shown to model the charge stored within an electrical transmission lattice. A third-order multiple-scale analysis in the semi-discrete limit fails, since at this order, the lattice equations reduce to the (2+1)-dimensional cubic nonlinear Schrödinger (NLS) equation which does not support stable soliton solutions for the breather envelope. We therefore extend the analysis to higher order and find a generalised $(2+1)$-dimensional NLS equation which incorporates higher order dispersive and nonlinear terms as perturbations. We find an ellipticity criterion for the wave numbers of the carrier wave. Numerical simulations suggest that both stationary and moving breathers are supported by the system. Calculations of the energy show the expected threshold behaviour whereby the energy of breathers does {\em not} go to zero with the amplitude; we find that the energy threshold is maximised by stationary breathers, and becomes arbitrarily small as the boundary of the domain of ellipticity is approached.

Exact solutions for cluster-growth kinetics with evolving size and shape profiles

In this paper we construct a model for the simultaneous compaction by which clusters are restructured, and growth of clusters by pairwise coagulation. The model has the form of a multicomponent aggregation problem in which the components are cluster mass and cluster diameter. Following suitable approximations, exact explicit solutions are derived which may be useful for the verification of simulations of such systems. Numerical simulations are presented to illustrate typical behaviour and to show the accuracy of approximations made in deriving the model. The solutions are then simplified using asymptotic techniques to show the relevant timescales of the kinetic processes and elucidate the shape of the cluster distribution functions at large times.

An introduction to mathematical models of coagulation-fragmentation processes: a discrete deterministic mean-field approach

We summarise the properties and the fundamental mathematical results associated with basic models which describe coagulation and fragmentation processes in a deterministic manner and in which cluster size is a discrete quantity (an integer multiple of some basic unit size). In particular, we discuss Smoluchowski's equation for aggregation, the Becker-Döring model of simultaneous aggregation and fragmentation, and more general models involving coagulation and fragmentation.

DNA charge neutralisation by linear polymers I: irreversible binding

We develop a deterministic mathematical model to describe the way in which polymers bind to DNA by considering the dynamics of the gap distribution that forms when polymers bind to a DNA plasmid. In so doing, we generalise existing theory to account for overlaps and binding cooperativity whereby the polymer binding rate depends on the size of the overlap The proposed mean-field models are then solved using a combination of numerical and asymptotic methods. We find that overlaps lead to higher coverage and hence higher charge neutralisations, results which are more in line with recent experimental observations. Our work has applications to gene therapy where polymers are used to neutralise the negative charges of the DNA phosphate backbone, allowing condensation prior to delivery into the nucleus of an abnormal cell.

DNA charge neutralisation by linear polymers II: reversible binding

We model the way in which polymers bind to DNA and neutralise its charged backbone by analysing the dynamics of the distribution of gaps along the DNA. We generalise existing theory for irreversible binding to construct new deterministic models which include polymer removal, movement along the DNA and allow for binding with overlaps. We show that reversible binding alters the capacity of the DNA for polymers by allowing the rearrangement of polymer positions over a longer timescale than when binding is irreversible. When the polymers do not overlap, allowing reversible binding increases the number of polymers adhered and hence the charge that the DNA can accommodate; in contrast, when overlaps occur, reversible binding reduces the amount of charge neutralised by the polymers.

Similarity solutions of a Becker-Döring system with time-dependent monomer input

We formulate the Becker-Döring equations for cluster growth in the presence of a time-dependent source of monomer input. In the case of size-independent aggregation and ragmentation rate coefficients we find similarity solutions which are approached in the large time limit. The form of the solutions depends on the rate of monomer input and whether fragmentation is present in the model; four distinct types of solution are found.

Nonlinear breathing modes at a defect

Recent molecular dynamics (MD) simulations of Cubero et al (1999) of a DNA duplex containing the 'rogue' base difluorotoluene (F) in place of a thymine (T) base show that breathing events can occur on the nanosecond timescale, whereas breathing events in a normal DNA duplex take place on the microsecond timescale. The main aim of this paper is to analyse a nonlinear Klein-Gordon lattice model of the DNA duplex including both nonlinear interactions between opposing bases and a defect in the interaction at one lattice site; each of which can cause localisation of energy. Solutions for a breather mode either side of the defect are derived using multiple-scales asymptotics and are pieced together across the defect to form a solution which includes the effects of the nonlinearity and the defect. We consider defects in the inter-chain interactions and in the along chain interactions. In most cases we find in-phase breather modes and/or out-of-phase breather modes, with one case displaying a shifted mode.

The Becker-Döring equations with exponentially size-dependent rate coefficients

This paper is concerned with an analysis of the Becker-Döring equations which lie at the heart of a number of descriptions of non-equilibrium phase transitions and related complex dynamical processes. The Becker-Döring theory describes growth and fragmentation in terms of stepwise addition or removal of single particles to or from clusters of similar particles and has been applied to a wide range of problems of physicochemical and biological interest within recent years. Here we consider the case where the aggregation and fragmentation rates depend exponentially on cluster size. These choices of rate coefficients at least qualitatively correspond to physically realistic molecular clustering scenarios such as occur in, for example, simulations of simple fluids. New similarity solutions for the constant monomer Becker-Döring system are identified, and shown to be generic in the case of aggregation and fragmentation rates that depend exponentially on cluster size.

Coagulation equations with mass loss

We derive and solve models for coagulation with mass loss arising, for example, from industrial processes in which growing inclusions are lost from the melt by colliding with the wall of the vessel. We consider a variety of loss laws and a variety of coagulation kernels, deriving exact results where possible, and more generally reducing the equations to similarity solutions valid in the large-time limit. One notable result is the effect that mass removal has on gelation: for small loss rates, gelation is delayed, whilst above a critical threshold, gelation is completely prevented. Finally, by forming an exact explicit solution for a more general initial cluster size distribution function, we illustrate how numerical results from earlier work can be interpreted in the light of the theory presented herein.

The Becker-Döring equations with monomer input, competition and inhibition

We investigate the Becker-Döring model of nucleation with three generalisations; an input of monomer, an input of inhibitor and finally, we allow the monomers to form two morphologies of cluster. We assume size-independent aggregation and fragmentation rates. Initially we consider the problem of constant monomer input and determine the steady-state solution approached in the large-time limit, and the manner in which it is approached. Secondly, in addition to a constant input of monomer we allow a constant input of inhibitor, which prevents clusters growing any larger and this removes them from the kinetics of the process; the inhibitor is consumed in the action of poisoning a cluster. We determine a critical ratio of poison to monomer input below which the cluster concentrations tend to a non-zero steady-state solution and the poison concentration tends to a finite value. Above the critical input ratio, the concentrations of all cluster sizes tend to zero and the poison concentration grows without limit. In both cases the solution in the large-time limit is determined. Finally we consider a model where monomers form two morphologies, but the inhibitor only acts on one morphology. Four cases are identified, depending on the relative poison to monomer input rates and the relative thermodynamic stability. In each case we determine the final cluster distribution and poison concentration. We find that poisoning the less stable cluster type can have a significant impact on the structure of the more stable cluster distribution; a counter-intuitive result. All results are shown to agree with numerical simulation.

Effect of maternal cold exposure and nutrient restriction on insulin-like growth factor sensitivity in adipose tissue of newborn sheep

Adipose tissue mass in the newborn is determined in part by insulin-like growth factor (IGF)s, which are dependent on the maternal nutritional and metabolic environment during late gestation. The present study was designed to determine whether maternal cold exposure (CE) commencing in mid gestation could modulate some of the adaptive effects of nutrient restriction in late gestation on adipose tissue endocrine sensitivity in the resulting offspring. Twenty eight pregnant sheep were entered into the study and were either shorn, i.e. cold exposed, from 70 days gestation (term = 147 days), or remained unshorn, and were fed either their total calculated metabolisable energy (ME) requirements for body weight and pregnancy from 110 days gestation or 50% of this amount (n=7 per group). Adipose tissue was sampled from the offspring at one day of age and the mRNA abundance for IGF-I, II their receptors (R) and GH secretagogue receptor-1a (GHSR-1a) were determined. CE mothers produced larger offspring with more perirenal adipose tissue, an adaptation prevented by maternal nutrient restriction. Nutrient restriction in unshorn mothers increased IGF-I and IIR mRNA abundance. The mRNA abundances for IGF-I, II and IIR in adipose tissue were reduced by CE, adaptations independent of maternal food intake, whereas CE plus nutrient restriction increased GHSR-1a mRNA. In conclusion, maternal nutrient restriction with or without CE has very different effects on IGF sensitivity of adipose tissue and may act to ensure adequate fat stores are present in the newborn in the face of very different maternal endocrine and metabolic environments.

Ontogeny and nutritional programming of the hepatic growth hormone-insulin-like growth factor-prolactin axis in the sheep

The liver is an important metabolic and endocrine organ in the fetus but the extent to which its hormone receptor (R) sensitivity is developmentally regulated in early life is not fully established. We, therefore, examined developmental changes in mRNA abundance for the growth hormone (GH) and prolactin (PRL) receptors (R) plus insulin-like growth factor (IGF)-I and –II and their receptors. Fetal and postnatal sheep were sampled at either 80, or 140 days gestation, 1, 30 days or six months of age. The effect of maternal nutrient restriction between early to mid (i.e. 28 to 80 days gestation, the time of early liver growth) gestation on gene expression was also examined in the fetus and juvenile offspring. Gene expression for the GHR, PRLR and IGF-IR increased through gestation peaking at birth, whereas IGF-I was maximal near to term. In contrast, IGF-II mRNA decreased between mid and late gestation to increase after birth whereas IGF-IIR remained unchanged. A substantial decline in mRNA abundance for GHR, PRLR and IGF-IR then occurred up to six months. Maternal nutrient restriction reduced GHR and IGF-IIR mRNA abundance in the fetus, but caused a precocious increase in the PRLR. Gene expression for IGF-I and –II were increased in juvenile offspring born to nutrient restricted mothers. In conclusion, there are marked differences in the developmental ontogeny and nutritional programming of specific hormones and their receptors involved in hepatic growth and development in the fetus. These could contribute to changes in liver function during adult life.

Ontogeny and nutritional programming of mitochondrial proteins in the ovine kidney, liver and lung

This study investigated the developmental and nutritional programming of two important mitochondrial proteins, namely voltage dependent anion channel (VDAC) and cytochrome c in the sheep kidney, liver and lung. The effect of maternal nutrient restriction between early to mid gestation (i.e. 28 to 80 days gestation, the period of maximal placental growth) on the abundance of these proteins was also examined in fetal and juvenile offspring. Fetuses were sampled at 80 and 140 days gestation (term ~147 days), and postnatal animals at 1 and 30 days and 6 months of age. The abundance of VDAC peaked at 140 days gestation in the lung, compared with 1 day after birth in the kidney and liver, whereas cytochrome c abundance was greatest at 140 days gestation in the liver, 1 day after birth in the kidney and 6 months of age in lungs. This differential ontogeny in mitochondrial protein abundance between tissues was accompanied with very different tissue specific responses to changes in maternal food intake. In the liver, maternal nutrient restriction only increased mitochondrial protein abundance at 80 days gestation, compared with no effect in the kidney. In contrast, in the lung mitochondrial protein abundance was raised near to term, whereas VDAC abundance was decreased by 6 months of age. These findings demonstrate the tissue specific nature of mitochondrial protein development that reflects differences in functional adaptation after birth. The divergence in mitochondrial response between tissues to maternal nutrient restriction early in pregnancy further reflects these differential ontogeny’s.

Adaptive discontinuous Galerkin methods for eigenvalue problems arising in incompressible fluid flows

In this article we consider the a posteriori error estimation and adaptive mesh refinement of discontinuous Galerkin finite element approximations of the hydrodynamic stability problem associated with the incompressible Navier-Stokes equations. Particular attention is given to the reliable error estimation of the eigenvalue problem in channel and pipe geometries. Here, computable a posteriori error bounds are derived based on employing the generalization of the standard Dual-Weighted-Residual approach, originally developed for the estimation of target functionals of the solution, to eigenvalue/stability problems. The underlying analysis consists of constructing both a dual eigenvalue problem and a dual problem for the original base solution. In this way, errors stemming from both the numerical approximation of the original nonlinear flow problem, as well as the underlying linear eigenvalue problem are correctly controlled. Numerical experiments highlighting the practical performance of the proposed a posteriori error indicator on adaptively refined computational meshes are presented.