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Mathematical Representation (mathematical + representation)
Selected AbstractsEvaluation of physiologically based pharmacokinetic models for use in risk assessment,JOURNAL OF APPLIED TOXICOLOGY, Issue 3 2007Weihsueh A. Chiu Abstract Physiologically based pharmacokinetic (PBPK) models are sophisticated dosimetry models that offer great flexibility in modeling exposure scenarios for which there are limited data. This is particularly of relevance to assessing human exposure to environmental toxicants, which often requires a number of extrapolations across species, route, or dose levels. The continued development of PBPK models ensures that regulatory agencies will increasingly experience the need to evaluate available models for their application in risk assessment. To date, there are few published criteria or well-defined standards for evaluating these models. Herein, important considerations for evaluating such models are described. The evaluation of PBPK models intended for risk assessment applications should include a consideration of: model purpose, model structure, mathematical representation, parameter estimation, computer implementation, predictive capacity and statistical analyses. Model purpose and structure require qualitative checks on the biological plausibility of a model. Mathematical representation, parameter estimation, computer implementation involve an assessment of the coding of the model, as well as the selection and justification of the physical, physicochemical and biochemical parameters chosen to represent a biological organism. Finally, the predictive capacity and sensitivity, variability and uncertainty of the model are analysed so that the applicability of a model for risk assessment can be determined. Published in 2007 by John Wiley & Sons, Ltd. [source] Near-fault ground motions, and the response of elastic and inelastic single-degree-of-freedom (SDOF) systemsEARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 9 2004G. P. Mavroeidis Abstract In order to investigate the response of structures to near-fault seismic excitations, the ground motion input should be properly characterized and parameterized in terms of simple, yet accurate and reliable, mathematical models whose input parameters have a clear physical interpretation and scale, to the extent possible, with earthquake magnitude. Such a mathematical model for the representation of the coherent (long-period) ground motion components has been proposed by the authors in a previous study and is being exploited in this article for the investigation of the elastic and inelastic response of the single-degree-of-freedom (SDOF) system to near-fault seismic excitations. A parametric analysis of the dynamic response of the SDOF system as a function of the input parameters of the mathematical model is performed to gain insight regarding the near-fault ground motion characteristics that significantly affect the elastic and inelastic structural performance. A parameter of the mathematical representation of near-fault motions, referred to as ,pulse duration' (TP), emerges as a key parameter of the problem under investigation. Specifically, TP is employed to normalize the elastic and inelastic response spectra of actual near-fault strong ground motion records. Such normalization makes feasible the specification of design spectra and reduction factors appropriate for near-fault ground motions. The ,pulse duration' (TP) is related to an important parameter of the rupture process referred to as ,rise time' (,) which is controlled by the dimension of the sub-events that compose the mainshock. Copyright © 2004 John Wiley & Sons, Ltd. [source] Spatial,temporal marked point processes: a spectrum of stochastic modelsENVIRONMETRICS, Issue 3-4 2010Eric Renshaw Abstract Many processes that develop through space and time do so in response not only to their own individual growth mechanisms but also in response to interactive pressures induced by their neighbours. The growth of trees in a forest which compete for light and nutrient resources, for example, provides a classic illustration of this general spatial,temporal growth-interaction process. Not only has its mathematical representation proved to be a powerful tool in the study and analysis of marked point patterns since it may easily be simulated, but it has also been shown to be highly flexible in terms of its application since it is robust with respect to incorrect choice of model selection. Moreover, it is highly amenable to maximum likelihood and least squares parameter estimation techniques. Currently the algorithm comprises deterministic growth and interaction coupled with a stochastic arrival and departure mechanism. So for systems with a fixed number of particles there is an inherent lack of randomness. A variety of different stochastic approaches are therefore presented, from the exact event,time model through to the associated stochastic differential equation, taking in time-increment and Tau- and Langevin-Leaping approximations en route. The main algorithm is illustrated through application to forest management and high-intensity packing of hard particle systems, and comparisons are made with the established force biased approach. Copyright © 2009 John Wiley & Sons, Ltd. [source] Hierarchical model of the population dynamics of hippocampal dentate granule cellsHIPPOCAMPUS, Issue 5 2002G.A. Chauvet Abstract A hierarchical modeling approach is used as the basis for a mathematical representation of the population activity of hippocampal dentate granule cells. Using neural field equations, the variation in time and space of dentate granule cell activity is derived from the summed synaptic potential and summed action potential responses of a population of granule cells evoked by monosynaptic excitatory input from entorhinal cortical afferents. In this formulation of the problem, we have considered a two-level hierarchy: the synapses of entorhinal cortical axons define the first level of organization, and dentate granule cells, which include these synapses, define the second, higher level of organization. The model is specified by two state field variables, for membrane potential and for synaptic efficacy, respectively, with both evolving according to different time scales. The two state field variables introduce new parameters, physiological and anatomical, which characterize the dentate from the point of view of neuronal and synaptic populations: (1) a set of geometrical constraints corresponding to the morphological properties of granule cells and anatomical characteristics of entorhinal-dentate connections; and (2) a set of neuronal parameters corresponding to physiological mechanisms. Assuming no interaction between granule cells, i.e., neither ephaptic nor synaptic coupling, the model is shown to be mathematically tractable and allows solution of the field equations leading to the determination of activity. This treatment leads to the definition of two state variables, volume of stimulated synapses and firing time, which describe observed activity. Numerical simulations are used to investigate the populational characterization of the dentate by individual parameters: (1) the relationship between the conditions of stimulation of active perforant path fibers, e.g., stimulating intensity, and activity in the granule cell layer; and (2) the influence of geometry on the generation of activity, i.e., the influence of neuron density and synaptic density-connectivity. As an example application of the model, the granule cell population spike is reconstructed and compared with experimental data. Hippocampus 2002;12:698,712. © 2002 Wiley-Liss, Inc. [source] Accuracy analysis of super compact scheme in non-uniform grid with application to parabolized stability equationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 5 2004V. Esfahanian Abstract A brief derivation of the super compact finite difference method (SCFDM) in non-uniform grid points is presented. To investigate the accuracy of the SCFDM in non-uniform grid points the Fourier analysis is performed. The Fourier analysis shows that the grid aspect ratio plays a crucial role in the accuracy of the SCFDM in a non-uniform grid. It is also found that the accuracy of the higher order relations of the SCFDM is more sensitive to grid aspect ratio than the lower order relations. In addition, to obtain a mathematical representation of the accuracy and making clear the role of the aspect ratio in the accuracy of the SCFDM in non-uniform grids, the modified equation approach is used. For the sake of demonstrating the analytical results obtained from the Fourier analysis and the modified equation approach, the super compact finite difference method is applied to solve the Blasius boundary layer and the non-linear parabolized stability equations as numerical examples indicating the difficulty with non-uniform grid spacing using the super compact scheme. Copyright © 2004 John Wiley & Sons, Ltd. [source] Evaluation of physiologically based pharmacokinetic models for use in risk assessment,JOURNAL OF APPLIED TOXICOLOGY, Issue 3 2007Weihsueh A. Chiu Abstract Physiologically based pharmacokinetic (PBPK) models are sophisticated dosimetry models that offer great flexibility in modeling exposure scenarios for which there are limited data. This is particularly of relevance to assessing human exposure to environmental toxicants, which often requires a number of extrapolations across species, route, or dose levels. The continued development of PBPK models ensures that regulatory agencies will increasingly experience the need to evaluate available models for their application in risk assessment. To date, there are few published criteria or well-defined standards for evaluating these models. Herein, important considerations for evaluating such models are described. The evaluation of PBPK models intended for risk assessment applications should include a consideration of: model purpose, model structure, mathematical representation, parameter estimation, computer implementation, predictive capacity and statistical analyses. Model purpose and structure require qualitative checks on the biological plausibility of a model. Mathematical representation, parameter estimation, computer implementation involve an assessment of the coding of the model, as well as the selection and justification of the physical, physicochemical and biochemical parameters chosen to represent a biological organism. Finally, the predictive capacity and sensitivity, variability and uncertainty of the model are analysed so that the applicability of a model for risk assessment can be determined. Published in 2007 by John Wiley & Sons, Ltd. [source] On the Nitroxide Quasi-Equilibrium in the Alkoxyamine-Mediated Radical Polymerization of StyreneMACROMOLECULAR THEORY AND SIMULATIONS, Issue 2 2006Enrique Saldívar-Guerra Abstract Summary: The range of validity of two popular versions of the nitroxide quasi-equilibrium (NQE) approximation used in the theory of kinetics of alkoxyamine mediated styrene polymerization, are systematically tested by simulation comparing the approximate and exact solutions of the equations describing the system. The validity of the different versions of the NQE approximation is analyzed in terms of the relative magnitude of (dN/dt)/(dP/dt). The approximation with a rigorous NQE, kc[P][N],=,kd[PN], where P, N and PN are living, nitroxide radicals and dormant species respectively, with kinetic constants kc and kd, is found valid only for small values of the equilibrium constant K (10,11,10,12 mol,·,L,1) and its validity is found to depend strongly of the value of K. On the other hand, the relaxed NQE approximation of Fischer and Fukuda, kc[P][N],=,kd[PN]0 was found to be remarkably good up to values of K around 10,8 mol,·,L,1. This upper bound is numerically found to be 2,3 orders of magnitude smaller than the theoretical one given by Fischer. The relaxed NQE is a better one due to the fact that it never completely neglects dN/dt. It is found that the difference between these approximations lies essentially in the number of significant figures taken for the approximation; still this subtle difference results in dramatic changes in the predicted course of the reaction. Some results confirm previous findings, but a deeper understanding of the physico-chemical phenomena and their mathematical representation and another viewpoint of the theory is offered. Additionally, experiments and simulations indicate that polymerization rate data alone are not reliable to estimate the value of K, as recently suggested. Validity of the rigorous nitroxide quasi-equilibrium assumption as a function of the nitroxide equilibrium constant. [source] Mathematical skills in Williams syndrome: Insight into the importance of underlying representationsDEVELOPMENTAL DISABILITIES RESEARCH REVIEW, Issue 1 2009Kirsten O'Hearn Abstract Williams syndrome (WS) is a developmental disorder characterized by relatively spared verbal skills and severe visuospatial deficits. Serious impairments in mathematics have also been reported. This article reviews the evidence on mathematical ability in WS, focusing on the integrity and developmental path of two fundamental representations, namely those that support judgments of "how much" (i.e., magnitude) and "how many" (i.e., number of objects). Studies on magnitude or "number line" representation in WS suggest that this core aspect of mathematical ability, is atypical in WS throughout development, causing differences on some but not all aspects of math. Studies on the representation of small numbers of objects in WS are also reviewed, given the proposed links between this type of representation and early number skills such as counting. In WS, representation appears to be relatively typical in infancy but limitations become evident by maturity, suggesting a truncated developmental trajectory. The math deficits in WS are consistent with neurological data indicating decreased gray matter and hypoactivation in parietal areas in WS, as these areas are implicated in mathematical processing as well as visuospatial abilities and visual attention. In spite of their deficits in core mathematical representations, people with WS can learn many mathematical skills and show some strengths, such as reading numbers. Thus individuals with WS may be able to take advantage of their relatively strong verbal skills when learning some mathematical tasks. The uneven mathematical abilities found in persons with WS provide insight into not only appropriate remediation for this developmental disorder but also into the precursors of mathematical ability, their neural substrates, and their developmental importance. © 2009 Wiley-Liss, Inc. Dev Disabil Res Rev 2009;15:11,20. [source] | ||||||||||