A Tutorial on the Universality and Expressiveness of Fold

In functional programming, fold is a standard operator that encapsulates a simple pattern of recursion for processing lists. This article is a tutorial on two key aspects of the fold operator for lists. First of all, we emphasize the use of the universal property of fold both as a proof principle that avoids the need for inductive proofs, and as a definition principle that guides the transformation of recursive functions into definitions using fold. Secondly, we show that even though the pattern of recursion encapsulated by fold is simple, in a language with tuples and functions as first-class values the fold operator has greater expressive power than might first be expected.

'Artificial Immune Systems Tutorial'

The biological immune system is a robust, complex, adaptive system that defends the body from foreign pathogens. It is able to categorize all cells (or molecules) within the body as self-cells or non-self cells. It does this with the help of a distributed task force that has the intelligence to take action from a local and also a global perspective using its network of chemical messengers for communication. There are two major branches of the immune system. The innate immune system is an unchanging mechanism that detects and destroys certain invading organisms, whilst the adaptive immune system responds to previously unknown foreign cells and builds a response to them that can remain in the body over a long period of time. This remarkable information processing biological system has caught the attention of computer science in recent years. A novel computational intelligence technique, inspired by immunology, has emerged, called Artificial Immune Systems. Several concepts from the immune have been extracted and applied for solution to real world science and engineering problems. In this tutorial, we briefly describe the immune system metaphors that are relevant to existing Artificial Immune Systems methods. We will then show illustrative real-world problems suitable for Artificial Immune Systems and give a step-by-step algorithm walkthrough for one such problem. A comparison of the Artificial Immune Systems to other well-known algorithms, areas for future work, tips & tricks and a list of resources will round this tutorial off. It should be noted that as Artificial Immune Systems is still a young and evolving field, there is not yet a fixed algorithm template and hence actual implementations might differ somewhat from time to time and from those examples given here.

'Artificial Immune Systems Tutorial'

The biological immune system is a robust, complex, adaptive system that defends the body from foreign pathogens. It is able to categorize all cells (or molecules) within the body as self-cells or non-self cells. It does this with the help of a distributed task force that has the intelligence to take action from a local and also a global perspective using its network of chemical messengers for communication. There are two major branches of the immune system. The innate immune system is an unchanging mechanism that detects and destroys certain invading organisms, whilst the adaptive immune system responds to previously unknown foreign cells and builds a response to them that can remain in the body over a long period of time. This remarkable information processing biological system has caught the attention of computer science in recent years. A novel computational intelligence technique, inspired by immunology, has emerged, called Artificial Immune Systems. Several concepts from the immune have been extracted and applied for solution to real world science and engineering problems. In this tutorial, we briefly describe the immune system metaphors that are relevant to existing Artificial Immune Systems methods. We will then show illustrative real-world problems suitable for Artificial Immune Systems and give a step-by-step algorithm walkthrough for one such problem. A comparison of the Artificial Immune Systems to other well-known algorithms, areas for future work, tips & tricks and a list of resources will round this tutorial off. It should be noted that as Artificial Immune Systems is still a young and evolving field, there is not yet a fixed algorithm template and hence actual implementations might differ somewhat from time to time and from those examples given here.

A Pre-processing Moving Mesh Method for Discontinuous Galerkin Approximations of Advection-Diffusion-Reaction Problems

We propose a pre-processing mesh re-distribution algorithm based upon harmonic maps employed in conjunction with discontinuous Galerkin approximations of advection-diffusion-reaction problems. Extensive two-dimensional numerical experiments with different choices of monitor functions, including monitor functions derived from goal-oriented a posteriori error indicators are presented. The examples presented clearly demonstrate the capabilities and the benefits of combining our pre-processing mesh movement algorithm with both uniform, as well as, adaptive isotropic and anisotropic mesh refinement.

Error estimation and adaptive mesh refinement for aerodynamic flows

This lecture course covers the theory of so-called duality-based a posteriori error estimation of DG finite element methods. In particular, we formulate consistent and adjoint consistent DG methods for the numerical approximation of both the compressible Euler and Navier-Stokes equations; in the latter case, the viscous terms are discretized based on employing an interior penalty method. By exploiting a duality argument, adjoint-based a posteriori error indicators will be established. Moreover, application of these computable bounds within automatic adaptive finite element algorithms will be developed. Here, a variety of isotropic and anisotropic adaptive strategies, as well as $hp$-mesh refinement will be investigated.