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3869 results in Optimization

Page 48 of 194

A Course on Cooperative Game Theory
  • Satya R. Chakravarty, Manipushpak Mitra, Palash Sarkar
  • Published online:
    28 May 2018
    Print publication:
    17 October 2014
  • Cooperative game theory deals with situations where objectives of participants of the game are partially cooperative and partially conflicting. It is in the interest of participants to cooperate in the sense of making binding agreements to achieve the maximum possible benefit. When it comes to distribution of benefit/payoffs, participants have conflicting interests. Such situations are usually modelled as cooperative games. While the book mainly discusses transferable utility games, there is also a brief analysis of non-transferable utility games. Alternative solution concepts to cooperative game theoretic problems are presented in chapters 1-9 and the next four chapters present issues related to computations of solutions discussed in the earlier chapters. The proofs of all results presented in the book are quite explicit. Additionally the mathematical techniques employed in demonstrating the results will be helpful to those who wish to learn application of mathematics for solving problems in game theory.

  • A POROUS VISCOELASTIC MODEL FOR THE CELL CYTOSKELETON

  • Part of
  • CALINA A. COPOS, ROBERT D. GUY
  • Journal:
    The ANZIAM Journal / Volume 59 / Issue 4 / April 2018
    Published online by Cambridge University Press:
    25 May 2018, pp. 472-498
    • Article
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  • The immersed boundary method is a widely used mixed Eulerian/Lagrangian framework for simulating the motion of elastic structures immersed in viscous fluids. In this work, we consider a poroelastic immersed boundary method in which a fluid permeates a porous, elastic structure of negligible volume fraction, and extend this method to include stress relaxation of the material. The porous viscoelastic method presented here is validated for a prescribed oscillatory shear and for an expansion driven by the motion at the boundary of a circular material by comparing numerical solutions to an analytical solution of the Maxwell model for viscoelasticity. Finally, an application of the modelling framework to cell biology is provided: passage of a cell through a microfluidic channel. We demonstrate that the rheology of the cell cytoplasm is important for capturing the transit time through a narrow channel in the presence of a pressure drop in the extracellular fluid.

  • A MULTIPHASE MULTISCALE MODEL FOR NUTRIENT LIMITED TISSUE GROWTH

  • Part of
  • E. C. HOLDEN, J. COLLIS, B. S. BROOK, R. D. O’DEA
  • Journal:
    The ANZIAM Journal / Volume 59 / Issue 4 / April 2018
    Published online by Cambridge University Press:
    23 May 2018, pp. 499-532
    • Article
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  • We derive an effective macroscale description for the growth of tissue on a porous scaffold. A multiphase model is employed to describe the tissue dynamics; linearisation to facilitate a multiple-scale homogenisation provides an effective macroscale description, which incorporates dependence on the microscale structure and dynamics. In particular, the resulting description admits both interstitial growth and active cell motion. This model comprises Darcy flow, and differential equations for the volume fraction of cells within the scaffold and the concentration of nutrient, required for growth. These are coupled with Stokes-type cell problems on the microscale, incorporating dependence on active cell motion and pore scale structure. The cell problems provide the permeability tensors with which the macroscale flow is parameterised. A subset of solutions is illustrated by numerical simulations.

Chance, Strategy, and Choice
  • An Introduction to the Mathematics of Games and Elections
  • Samuel Bruce Smith
  • Published online:
    11 May 2018
    Print publication:
    29 June 2015
  • Games and elections are fundamental activities in society with applications in economics, political science, and sociology. These topics offer familiar, current, and lively subjects for a course in mathematics. This classroom-tested textbook, primarily intended for a general education course in game theory at the freshman or sophomore level, provides an elementary treatment of games and elections. Starting with basics such as gambling, zero-sum and combinatorial games, Nash equilibria, social dilemmas, and fairness and impossibility theorems for elections, the text then goes further into the theory with accessible proofs of advanced topics such as the Sprague–Grundy theorem and Arrow's impossibility theorem.Uses an integrative approach to probability, game, and social choice theoryProvides a gentle introduction to the logic of mathematical proof, thus equipping readers with the necessary tools for further mathematical studiesContains numerous exercises and examples of varying levels of difficultyRequires only a high school mathematical background.

Page 48 of 194