Multiplicative model

Block diagram representations of additive and multiplicative model uncertainly are shown in Figure 9.21. 

Chiu, M. H., Chung, S. L. (2007). Investigating correctness, consistency, and completeness of students mental models and paths of conceptual change in learning the nature ofgas particles via multiple modeling activities. Paper presented at the ESERA, Molmo, Sweden, August 21-25, 2007. 

Mathematical Models. As noted previously, a mathematical model must be fitted to the predicted results shown In each factorial table generated by each scientist. Ideally, each scientist selects and fits an appropriate model based upon theoretical constraints and physical principles. In some cases, however, appropriate models are unknown to the scientists. This Is likely to occur for experiments Involving multifactor, multidisciplinary systems. When this occurs, various standard models have been used to describe the predicted results shown In the factorial tables. For example, for effects associated with lognormal distributions a multiplicative model has been found useful. As a default model, the team statistician can fit a polynomial model using standard least square techniques. Although of limited use for Interpolation or extrapolation, a polynomial model can serve to Identify certain problems Involving the relationships among the factors as Implied by the values shown In the factorial tables. 

Cabrera et al. [50] modeled a set of 163 drugs using TOPS-MODE descriptors with a linear discriminant model to predict p-glycoprotein efflux. Model accuracy was 81% for the training set and 77.5% for a validation set of 40 molecules. A "combinatorial QSAR" approach was used by de Lima et al. [51] to test multiple model types (kNN, decision tree, binary QSAR, SVM) with multiple descriptor sets from various software packages (MolconnZ, Atom Pair, VoSurf, MOE) for the prediction of p-glycoprotein substrates for a dataset of 192 molecules. Best overall performance on a test set of 51 molecules was achieved with an SVM and AP or VolSurf descriptors (81% accuracy each). 

The association of host defense peptides with lipid bilayers has been observed to be directly related to the ratio of peptide to lipid. At low peptide/lipid ratios, peptides are oriented parallel to the membrane. As the ratio increases, the peptides reorient themselves perpendicular to the membrane, ultimately inserting into the bilayer. Following membrane insertion transmembrane pores are formed. The insertion of peptides into the lipid membrane and subsequent translocation of peptides into the cytoplasm or formation of transmembrane pores has been described by multiple models of host defense peptide insertion. 

RANDOM SCISSION KINETICS MULTIPLE DEAD-END INHIBITION MULTIPLE-TURNOVER CONDITIONS MULTIPLICATIVE MODEL MULTIPLICITY... 

The technique of seasonal decomposition uses the same additive and multiplicative models as in exponential smoothing, but without the smoothing procedure. 

The existence of non-HLA genes in many of the HLA associated diseases was established from theoretical considerations involving population prevalence, risks to relatives, and HLA IBD values in affected sib pairs (28-30). Type-1 diabetes shows an increased risk in siblings over population prevalence (Xs) of 15 in Caucasian populations (30), of which HLA contributes 3.4 approximately 45% of the type-1 diabetes genetic component under a multiplicative model (31). 

Conversely, the protein kinase Akt is deactivated in multiple model of cell death, including NMDA excitotoxicity (Corasaniti et al., 2007 Fukunawa and Kawano, 2003), free radical exposure (Konishi et al., 1999), and brain ischemia (Ouyang et al., 1999). 

Boyer, S., The Advantages of Multiple Modeling Methods for Metabolism and Toxicity Prediction, oral presentation, Royal Society of Chemistry - Drug Metabolism Group 2002 New Technologies in Drug Discovery, Heriott-Watt University, Edinburgh, December 12-13, 2002. 

Delay neuroprotective treatment-hypothermia by a minimum time interval (preferably 30 min or more) after ischemia onset Sustained neuroprotection at prolonged (weeks/months) time point Efficacy in multiple models of ischemia, particularly permanent ischemia models... 

The resulting semi-quantitative model was used in conjunction with structure-based docking and scoring, 3D-QS AR based affinity and selectivity predictions and in silico ADME models to estimate membrane permeability, solubility, and other key properties for the optimization process in this series. Hence, in this as well as in other series, multiple models can be collectively applied for ranking and prioritizing synthesis candidates and focused virtual libraries during advanced stages of multidimensional compound optimization. 

Albers EP, Dixon KR. 2002. A conceptual approach to multiple-model integration in whole site risk assessment. In Rizzoli AE, Jakeman AJ, editors, Integrated assessment and decision support. Proceedings of the First Biennial Meeting of the International Environmental Modelling and Software Society. Part 1. Manno (CH) iEMSs. p 293-298. 

Another consequence of this spatial isomorphism is that spatial indeterminacy due to multiple models can be dramatically reduced. For example, the solution to the following problem is indeterminate because there are two spatial models consistent with the text (from Johnson-Laird, 1996) ... 

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