Introduction Deterministic computer simulations of physical phenomena are becoming widely used in science and engineering. Computers are used to describe the flow of air over an airplane wing, combustion of gasses in a flame, behavior of a metal structure under stress, safety of a nuclear reactor, and so on. Some of the most widely used computer models, and the ones that lead us to work in this area, arise in the design of the semiconductors used in the computers themselves. A process simulator starts with a data structure representing an unprocessed piece of silicon and simulates the steps such as oxidation, etching and ion injection that produce a semiconductor device such as a transistor. A device simulator takes a description of such a device and simulates the flow of current through it under varying conditions to determine properties of the device such as its switching speed and the critical voltage at which it switches. A circuit simulator takes a list of devices and the

Abstract: Mathematical modeling is one of the key methodologies of metabolic engineering. Based on a given metabolic model different computational tools for the simulation, data evaluation, systems analysis, prediction, design and optimization of metabolic systems have been developed. The currently used metabolic modeling approaches can be subdivided into structural models, stoichiometric models, carbon flux models, stationary and nonstationary mechanistic models and models with gene regulation. However, the power of a model strongly depends on its basic modeling assumptions, the simplifications made and the data sources used. Model validation turns out to be particularly difficult for metabolic systems. The different modeling approaches are critically reviewed with respect to their potential and benefits for the metabolic engineering cycle. Several tools are discussed that have emerged from the different modeling approaches including structural pathway synthesis, stoichiometric pathway analysis, metabolic flux analysis, metabolic control analysis, optimization of regulatory architectures and the evaluation of rapid sampling experiments.

We show that combinatorial search, constrained by experimental evidence, domain knowledge, and simplicity, is sufficient to discover credible explanatory hypotheses in a scientific task of current importance.

To obtain a systems-level understanding of a biological system, the authors conducted quantitative dynamic experiments from which the system structure and the parameters have to be deduced. Since biological systems have to cope with different environmental conditions, certain properties are often robust with respect to variations in some of the parameters. Hence, it is important to use optimal experimental design considerations in advance of the experiments to improve the information content of the measurements. Using the MAP–Kinase pathway as an example, the authors present a simulation study investigating the application of different optimality criteria. It is demonstrated that experimental design significantly improves the parameter estimation accuracy and also reveals difficulties in parameter estimation due to robustness.

Abstract. It often occurs that a system can be described by several competing models. In order to distinguish among the alternative models, further information about the behavior of the system is required. One way to obtain such information is to perform suitably chosen perturbation experiments. We introduce a method for the selection of optimal perturbation experiments for discrimination among a set of dynamical models. The models are assumed to have the form of semi-quantitative differential equations. The method employs an optimization criterion based on the entropy measure of information. 1

This paper traces the strong relations between experimental design and control, such as the use of optimal inputs to obtain precise parameter estimation in dynamical systems and the introduction of suitably designed perturbations in adaptive control. The mathematical background of optimal experimental design is briefly presented, and the role of experimental design in the asymptotic properties of estimators is emphasized. Although most of the paper concerns parametric models, some results are also presented for statistical learning and prediction with nonparametric models.

It is well-known that different users navigate websites differently, being more or less inclined to browse or search and so forth. It is also very likely that the same user will exhibit different behaviors at different times- looking for a particular item one time, and browsing without a great deal of direction another. Knowing the type of behavior a user exhibits in a session would allow a website to tailor the information it displays to that behavior, and even to affect the behavior being displayed. We present a mathematical framework in which we directly try to learn a user’s mode of browsing during a given session. This framework is inspired by sequential analysis in the setting of educational testing. We demonstrate its feasibility and utility in the context of click-stream data and explore the range of models and variations that this framework makes available.

A simulation model is successful if it leads to policy action, i.e., if it is implemented. Studies show that for a model to be implemented, it must have good correspondence with the mental model of the system held by the user of the model. The user must feel confident that the simulation model corresponds to this mental model. An understanding of how the model works is required. Simulation models for implementation must be developed step by step, starting with a simple model, the simulation prototype. After this has been explained to the user, a more detailed model can be developed on the basis of feedback from the user. Software for simulation prototyping is discussed, e.g., with regard to the ease with which models and output can be explained and the speed with which small models can be written.

Towards a rational theory of human information acquisition

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