Introduction to Multi-Agent Simulation

When designing systems that are complex, dynamic and stochastic in nature, simulation is generally recognised as one of the best design support technologies, and a valuable aid in the strategic and tactical decision making process. A simulation model consists of a set of rules that define how a system changes over time, given its current state. Unlike analytical models, a simulation model is not solved but is run and the changes of system states can be observed at any point in time. This provides an insight into system dynamics rather than just predicting the output of a system based on specific inputs. Simulation is not a decision making tool but a decision support tool, allowing better informed decisions to be made. Due to the complexity of the real world, a simulation model can only be an approximation of the target system. The essence of the art of simulation modelling is abstraction and simplification. Only those characteristics that are important for the study and analysis of the target system should be included in the simulation model. The purpose of simulation is either to better understand the operation of a target system, or to make predictions about a target system’s performance. It can be viewed as an artificial white-room which allows one to gain insight but also to test new theories and practices without disrupting the daily routine of the focal organisation. What you can expect to gain from a simulation study is very well summarised by FIRMA (2000). His idea is that if the theory that has been framed about the target system holds, and if this theory has been adequately translated into a computer model this would allow you to answer some of the following questions: · Which kind of behaviour can be expected under arbitrarily given parameter combinations and initial conditions? · Which kind of behaviour will a given target system display in the future? · Which state will the target system reach in the future? The required accuracy of the simulation model very much depends on the type of question one is trying to answer. In order to be able to respond to the first question the simulation model needs to be an explanatory model. This requires less data accuracy. In comparison, the simulation model required to answer the latter two questions has to be predictive in nature and therefore needs highly accurate input data to achieve credible outputs. These predictions involve showing trends, rather than giving precise and absolute predictions of the target system performance. The numerical results of a simulation experiment on their own are most often not very useful and need to be rigorously analysed with statistical methods. These results then need to be considered in the context of the real system and interpreted in a qualitative way to make meaningful recommendations or compile best practice guidelines. One needs a good working knowledge about the behaviour of the real system to be able to fully exploit the understanding gained from simulation experiments. The goal of this chapter is to brace the newcomer to the topic of what we think is a valuable asset to the toolset of analysts and decision makers. We will give you a summary of information we have gathered from the literature and of the experiences that we have made first hand during the last five years, whilst obtaining a better understanding of this exciting technology. We hope that this will help you to avoid some pitfalls that we have unwittingly encountered. Section 2 is an introduction to the different types of simulation used in Operational Research and Management Science with a clear focus on agent-based simulation. In Section 3 we outline the theoretical background of multi-agent systems and their elements to prepare you for Section 4 where we discuss how to develop a multi-agent simulation model. Section 5 outlines a simple example of a multi-agent system. Section 6 provides a collection of resources for further studies and finally in Section 7 we will conclude the chapter with a short summary.

Parcellation of fMRI datasets with ICA and PLS: a data driven approach

Inter-subject parcellation of functional Magnetic Resonance Imaging (fMRI) data based on a standard General Linear Model (GLM) and spectral clustering was recently proposed as a means to alleviate the issues associated with spatial normalization in fMRI. However, for all its appeal, a GLM-based parcellation approach introduces its own biases, in the form of a priori knowledge about the shape of Hemodynamic Response Function (HRF) and task-related signal changes, or about the subject behaviour during the task. In this paper, we introduce a data-driven version of the spectral clustering parcellation, based on Independent Component Analysis (ICA) and Partial Least Squares (PLS) instead of the GLM. First, a number of independent components are automatically selected. Seed voxels are then obtained from the associated ICA maps and we compute the PLS latent variables between the fMRI signal of the seed voxels (which covers regional variations of the HRF) and the principal components of the signal across all voxels. Finally, we parcellate all subjects data with a spectral clustering of the PLS latent variables. We present results of the application of the proposed method on both single-subject and multi-subject fMRI datasets. Preliminary experimental results, evaluated with intra-parcel variance of GLM t-values and PLS derived t-values, indicate that this data-driven approach offers improvement in terms of parcellation accuracy over GLM based techniques.