to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

Introduction. A Simple Model Problem. Abstract Nonlinear Equations. Finite Element Discretizations of Elliptic PDEs. Practical Implementation. Bibliography. Subject Index.

A Review of a Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques

Preface 1. Introduction: the problem of collective action 2. The prisoners' dilemma, chicken and other games in the provision of public goods 3. The two-person prisoners' dilemma supergame 4. The N-person prisoners' dilemma supergame 5. Altruism and superiority 6. The state 7. Epilogue: cooperation, the state and anarchy Annex Notes Bibliography Index.

The possibility of cooperation

A posteriori error estimation and adaptive mesh-refinement techniques

Parallel, adaptive finite element methods for conservation laws

We discuss mesh-moving, static mesh-regeneration, and local mesh-refinement algorithms that can be used with a finite difference or finite element scheme to solve initial-boundary value problems for vector systems of time-dependent partial differential equations in two space dimensions and time. A coarse base mesh of quadrilateral cells is moved by an algebraic mesh-movement function so as to follow and isolate spatially distinct phenomena. The local mesh-refinement method recursively divides the time step and spatial cells of the moving base mesh in regions where error indicators are high until a prescribed tolerance is satisfied. The static mesh-regeneration procedure is used to create a new base mesh when the existing one becomes too distorted. The adaptive methods have been combined with a MacCormack finite difference scheme for hyperbolic systems and an error indicator based upon estimates of the local discretization error obtained by Richardson extrapolation. Results are presented for several computational examples.

An adaptive mesh-moving and local refinement method for time-dependent partial differential equations

An adaptive local mesh refinement method for time-dependent partial differential equations

A two-dimensional mesh moving technique for time-dependent partial differential equations

The microcomputer and its graphics capabilities are used to investigate chaos in Newton's method for a complex-valued quartic polynomial. Convergence maps that show fractal geometry are presented.

Exhibiting chaos and fractals with a microcomputer

: The Army's myriad social networks connect not only humans and soldiers, but also machines, computers, and robots. And most of the social/biological/physical/informational connections in these networks are in the form of cooperation - entities working together to achieve a common goal. So how does this complex web of relationships, collaborations, and communities of diverse entities work? This paper introduces a new framework in which measures of cooperation can be precisely defined. We demonstrate how the framework can be applied to social networks, and examine the dynamic networks arising in the case of pursuit and evasion games. Finally, we relate the concepts of competitive and altruistic cooperation to trust and the nature of communication within a team.

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David C. Arney

Papers

An adaptive mesh-moving and local refinement method for time-dependent partial differential equations

An adaptive local mesh refinement method for time-dependent partial differential equations

A two-dimensional mesh moving technique for time-dependent partial differential equations

Exhibiting chaos and fractals with a microcomputer

Cooperation in Social Networks: Communication, Trust, and Selflessness