Modelling solute transport in structured soils: Performance evaluation of the ADR and TRM models

The movement of chemicals through the soil to the groundwater or discharged to surface waters represents a degradation of these resources. In many cases, serious human and stock health implications are associated with this form of pollution. The chemicals of interest include nutrients, pesticides, salts, and industrial wastes. Recent studies have shown that current models and methods do not adequately describe the leaching of nutrients through soil, often underestimating the risk of groundwater contamination by surface-applied chemicals, and overestimating the concentration of resident solutes. This inaccuracy results primarily from ignoring soil structure and nonequilibrium between soil constituents, water, and solutes. A multiple sample percolation system (MSPS), consisting of 25 individual collection wells, was constructed to study the effects of localized soil heterogeneities on the transport of nutrients (NO3-, Cl-, PO43-) in the vadose zone of an agricultural soil predominantly dominated by clay. Very significant variations in drainage patterns across a small spatial scale were observed tone-way ANOVA, p < 0.001) indicating considerable heterogeneity in water flow patterns and nutrient leaching. Using data collected from the multiple sample percolation experiments, this paper compares the performance of two mathematical models for predicting solute transport, the advective-dispersion model with a reaction term (ADR), and a two-region preferential flow model (TRM) suitable for modelling nonequilibrium transport. These results have implications for modelling solute transport and predicting nutrient loading on a larger scale. (C) 2001 Elsevier Science Ltd. All rights reserved.

Computational immunology: The coming of age

The explosive growth in biotechnology combined with major advancesin information technology has the potential to radically transformimmunology in the postgenomics era. Not only do we now have readyaccess to vast quantities of existing data, but new data with relevanceto immunology are being accumulated at an exponential rate. Resourcesfor computational immunology include biological databases and methodsfor data extraction, comparison, analysis and interpretation. Publiclyaccessible biological databases of relevance to immunologists numberin the hundreds and are growing daily. The ability to efficientlyextract and analyse information from these databases is vital forefficient immunology research. Most importantly, a new generationof computational immunology tools enables modelling of peptide transportby the transporter associated with antigen processing (TAP), modellingof antibody binding sites, identification of allergenic motifs andmodelling of T-cell receptor serial triggering.

Analysis of dynamic process models for structural insight and model reduction .1. Structural identification measures

An important consideration in the development of mathematical models for dynamic simulation, is the identification of the appropriate mathematical structure. By building models with an efficient structure which is devoid of redundancy, it is possible to create simple, accurate and functional models. This leads not only to efficient simulation, but to a deeper understanding of the important dynamic relationships within the process. In this paper, a method is proposed for systematic model development for startup and shutdown simulation which is based on the identification of the essential process structure. The key tool in this analysis is the method of nonlinear perturbations for structural identification and model reduction. Starting from a detailed mathematical process description both singular and regular structural perturbations are detected. These techniques are then used to give insight into the system structure and where appropriate to eliminate superfluous model equations or reduce them to other forms. This process retains the ability to interpret the reduced order model in terms of the physico-chemical phenomena. Using this model reduction technique it is possible to attribute observable dynamics to particular unit operations within the process. This relationship then highlights the unit operations which must be accurately modelled in order to develop a robust plant model. The technique generates detailed insight into the dynamic structure of the models providing a basis for system re-design and dynamic analysis. The technique is illustrated on the modelling for an evaporator startup. Copyright (C) 1996 Elsevier Science Ltd

Riddling and invariance for discontinuous maps preserving Lebesgue measure

In this paper we use the mixture of topological and measure-theoretic dynamical approaches to consider riddling of invariant sets for some discontinuous maps of compact regions of the plane that preserve two-dimensional Lebesgue measure. We consider maps that are piecewise continuous and with invertible except on a closed zero measure set. We show that riddling is an invariant property that can be used to characterize invariant sets, and prove results that give a non-trivial decomposion of what we call partially riddled invariant sets into smaller invariant sets. For a particular example, a piecewise isometry that arises in signal processing (the overflow oscillation map), we present evidence that the closure of the set of trajectories that accumulate on the discontinuity is fully riddled. This supports a conjecture that there are typically an infinite number of periodic orbits for this system.

Three-dimensional space-borne synthetic aperture radar (SAR) imaging with multiple pass processing

Three-dimensional (3D) synthetic aperture radar (SAR) imaging via multiple-pass processing is an extension of interferometric SAR imaging. It exploits more than two flight passes to achieve a desired resolution in elevation. In this paper, a novel approach is developed to reconstruct a 3D space-borne SAR image with multiple-pass processing. It involves image registration, phase correction and elevational imaging. An image model matching is developed for multiple image registration, an eigenvector method is proposed for the phase correction and the elevational imaging is conducted using a Fourier transform or a super-resolution method for enhancement of elevational resolution. 3D SAR images are obtained by processing simulated data and real data from the first European Remote Sensing satellite (ERS-1) with the proposed approaches.

Visual-auditory integration during speech imitation in autism

Children with autistic spectrum disorder (ASD) may have poor audio-visual integration, possibly reflecting dysfunctional 'mirror neuron' systems which have been hypothesised to be at the core of the condition. In the present study, a computer program, utilizing speech synthesizer software and a 'virtual' head (Baldi), delivered speech stimuli for identification in auditory, visual or bimodal conditions. Children with ASD were poorer than controls at recognizing stimuli in the unimodal conditions, but once performance on this measure was controlled for, no group difference was found in the bimodal condition. A group of participants with ASD were also trained to develop their speech-reading ability. Training improved visual accuracy and this also improved the children's ability to utilize visual information in their processing of speech. Overall results were compared to predictions from mathematical models based on integration and non-integration, and were most consistent with the integration model. We conclude that, whilst they are less accurate in recognizing stimuli in the unimodal condition, children with ASD show normal integration of visual and auditory speech stimuli. Given that training in recognition of visual speech was effective, children with ASD may benefit from multi-modal approaches in imitative therapy and language training. (C) 2004 Elsevier Ltd. All rights reserved.

Using the canonical modelling approach to simplify the simulation of function in functional-structural plant models

Functional-structural plant models that include detailed mechanistic representation of underlying physiological processes can be expensive to construct and the resulting models can also be extremely complicated. On the other hand, purely empirical models are not able to simulate plant adaptability and response to different conditions. In this paper, we present an intermediate approach to modelling plant function that can simulate plant response without requiring detailed knowledge of underlying physiology. Plant function is modelled using a 'canonical' modelling approach, which uses compartment models with flux functions of a standard mathematical form, while plant structure is modelled using L-systems. Two modelling examples are used to demonstrate that canonical modelling can be used in conjunction with L-systems to create functional-structural plant models where function is represented either in an accurate and descriptive way, or in a more mechanistic and explanatory way. We conclude that canonical modelling provides a useful, flexible and relatively simple approach to modelling plant function at an intermediate level of abstraction.

A mathematical model of integrin-mediated haptotactic cell migration

Haptotactic cell migration, a directed response to gradients of cell—extracellular matrix adhesion, is an important process in a number of biological phenomena such as wound healing and tumour cell invasion. Previously, mathematical models of haptotaxis have been developed on the premise that cells migrate in response to gradients in the density of the extracellular matrix. In this paper, we develop a novel mathematical model of haptotaxis which includes the adhesion receptors known as integrins and a description of their functional activation, local recruitment and protrusion as part of lamellipodia. Through the inclusion of integrins, the modelled cell matter is able to respond to a true gradient of cell–matrix adhesion, represented by functionally active integrins. We also show that previous matrix-mediated models are in fact a subset of the novel integrin-mediated models, characterised by specific choices of diffusion and haptotaxis coefficients in their model equations. Numerical solutions suggest the existence of travelling waves of cell migration that are confirmed via a phase plane analysis of a simplified model.

Performance analysis using equivariant kernel density estimator in nonlinear mixture

This paper investigates the performance analysis of separation of mutually independent sources in nonlinear models. The nonlinear mapping constituted by an unsupervised linear mixture is followed by an unknown and invertible nonlinear distortion, are found in many signal processing cases. Generally, blind separation of sources from their nonlinear mixtures is rather difficult. We propose using a kernel density estimator incorporated with equivariant gradient analysis to separate the sources with nonlinear distortion. The kernel density estimator parameters of which are iteratively updated to minimize the output independence expressed as a mutual information criterion. The equivariant gradient algorithm has the form of nonlinear decorrelation to perform the convergence analysis. Experiments are proposed to illustrate these results.