Mathematical models rationale

The rationale for and development of mathematical models for single-cells are reviewed. The potential use of a computer model for Escherichia coll in ascertaining the plausibility of basic biological hypotheses is Illustrated with respect to the control of the Initiation of DNA synthesis and with respect to ammonium ion assimilation. 

D.G. Duguay, R.S. Labow, J.P. Santerre, D.D. McLean, Development of a mathematical model describing the enzymatic degradation of biomedical polyurethanes. 1. Background, rationale and model formulation. Polym. Degrad. Stab. 47, 229-249 (1995)... 

Program costs are determined by the tradeoffs between operational requirements and engineering design. Throughout the design and development phase, decisions must be made based on evaluation of alternatives and their effect on cost. One approach attempts to correlate the characteristics of alternative solutions to the requirements and constraints that make up the selection criteria for a particular element The rationale for alternative choices in the decision process are documented for review. Mathematical models or computer simulations maybe employed to aid in this evaluation decision making process. 

In this paper we have presented elements of our mathematical model relevant to the representation of epistemic uncertainty and show how the model can be used with the expert judgment elicited from the panel of engineers from the company. We have sought to explain the rationale for our elicitation protocol and provide insight into elements of the judgmental data collected and its analysis. 

Chapter 1 provides a general overview and introduction of the principles and techniques of physical and mathematical modeling discussed in the book. It provides the rationale for modeling two-phase flow in gas-agitated reactors of materials processes. Chapter 2 presents the turbulence structure of two-phase jets and the impact on the mixing and chemical reaction rates in materials reactors agitated by... 

Earlier sections presented chemical models for the extraction of acids and metals into organic solvents, and show that these models, expressed mathematically, agree with experimental data at trace metal concentrations and at constant activity coefficients. These models provide a rationale for understanding the chemical principles of solvent extraction. 

In case of a bilinear model the above reads (X — AB0W 2 = XW — AB W 2 = XW — AH 2. Thus, by fitting the bilinear model AH to the data scaled within the second mode, XW, in an ordinary least squares sense, the weighted loss function is automatically optimized. This is the basic mathematical rationale behind scaling. 

Interpret the data in Figures 13.9.1 and 13.9.2. How do the traces in Figure 13.9.2 relate to those in Figure 13.9.1 What implications can be derived from the flat region in the electrocapillary curves in the presence of n-heptyl alcohol Construct a chemical model to explain the very low differential capacitance from —0.4 to —1.4 V in the presence of n-heptyl alcohol. Can you provide a formal (i.e., mathematical) rationale for the sharp peaks in C Can you rationalize them chemically ... 

Over the past 15 years, the Huorescence Blob Model (FBM) in 1999 [36] and the Model Free Analysis (MFA) in 2005 [37] were introduced to, first, deal with the distribution of excimer rate constants that led to the multiexponential character of the fluorescence decays acquired with Py-WSPs and, second, provide a robust analytical framework to analyze the monomer and excimer fluorescence decays globally to yield reliable / gg values. The aim of this chapter is to describe the mathematic rationale underlying the application of the FBM and MFA to retrieve /agg firom the decay analysis and present experimental examples describing the implementation of these robust analytical tools. 

In this chapter, the methodological framework is provided for the developed model, which detects and ranks the complexity of ship-ship encounters. First, the available micro-level ship traffic data, as obtained from the Automatic Identification System (AIS), is outlined. Subsequently, the process and outcome of an expert elicitation related to the development of a quantitative Risk Indicator (I). The latter is a measure of risk in the sea area, based on detection of vessels encounters and their complexity. Then, the mathematical formulation of the indicator is presented, both in regards to the model structure and model parameters. Finally, the obtained results need to be clustered to arrive at qualitative Risk Indicator. Thus, the purpose and rationale of the applied clustering technique is outlined. 

Zhang and Wu (1987) administered an iv dose of 10 mg kg bodyweight to the pig. The rationale behind this dose is not revealed in the paper. The concentration-time profile of sulfur mustard in the blood could be mathematically described as a three compartment model, with a very fast initial distribution phase and a rapid elimination half-life. The AUC is about 3 times higher in the pig than in the rat for the same dose. The ealeulated toxicoki-netic parameters are listed in Table 7.1. 

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