However, despite its claims, this book is an excellent introduction to mathematical modelling, with a wealth of interesting case studies and lovely mathematics that will appeal to many of its target audience final year undergraduates, Masters and PhD students working in 'practical' mathematical modelling. The source of most of the case studies comes from the Study Groups with Industry and Mathematics that originated in 1968 at Oxford, organized by Alan Taylor and Leslie Fox, but is now a global activity. The book describes the type of problem, how they are approached and funded (typically a surprisingly cheap £10 000 to £15 000). The first chapter covers the mathematical preliminaries for the case studies which are all based on continuous media, and so all that is needed is diffusion and flow and deformation of solids and fluids. The next four chapters are based on elliptic partial differential equations and relate to simulation of a type of compressor, determination of the viscosity of a carbon paste used in smelting, simulation of an instrument for determining density, and modelling a form of nondestructive testing of pressure vessels. There follow six chapters devoted to a range of applications of the diffusion equation and various non-linear effects. These cover the cooking of a single cereal grain, waves of epidemics in animal populations, catalytic converters, problems with blast furnaces, the cooling of hot glass, and crystal growth. Chapter 11 looks at the load responses of filled viscoelastic materials. The last two chapters, based on hyperbolic equations, model the noise produced by a bird scare gun and the paper tension variations in a printing press.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/FB9EBD3320909B8F7F968615CD8463B2/S0025557200173425a.pdf/div-class-title-span-class-italic-statistical-inference-span-2nd-edn-by-paul-h-garthwaite-ian-t-jolliffe-and-byron-jones-pp-328-40-hbk-2002-isbn-0-19-857226-3-oxford-university-press-div.pdf

Statistical inference (2nd edn), by Paul H. Garthwaite, Ian T. Jolliffe and Byron Jones. Pp.328. £40 (hbk). 2002. ISBN 0 19 857226 3 (Oxford University Press).

: In this project we have constructed a Markov Decision Process (MDP) model to demonstrate the value of not always expelling attackers found in a defender's information system. We have developed models to extract qualitative insights into the interaction of a defender trying to classify an attacker and an attacker trying to evade classification. In particular, we have developed a model in which the attacker chooses an attack rate and the defender chooses a detection threshold to apply after a fixed set of observations. In the model we show that often pure strategy equilibria do not exist. In a related model we allow the defender to dynamically adjust the observation window as he collects data, as in the well known sequential probability ratio test. We show numerically that equilibria appear to exist in the model. In a related model, we restructure the attacker's strategy to be a distribution across the number of hits to try in N steps (a mixed strategy). We show that the equilibrium can be computed efficiently, and we use that fact to extract qualitative insights. One insight is that the defender also ends up using a randomized detection threshold in Nash equilibrium, since with any fixed threshold the attacker will often just attack at a level just below the threshold. This finding suggests that defenders, and hence designers of security software, should consider using randomized detection and classification thresholds. Finally, our methodology allows us to efficiently analyze a broad class of games that are like zero-games except that one player has an extra additive term in their payoff function that only depends on their action. This finding makes a broader class of game models applicable to security settings analyzable.

Out-Learning Attackers: A Game Theoretic Approach to Cyber Defense

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Out-Learning Attackers: A Game Theoretic Approach to Cyber Defense