Extremal optimization for sensor report pre-processing

We describe the recently introduced extremal optimization algorithm and apply it to target detection and association problems arising in pre-processing for multi-target tracking. Here we consider the problem of pre-processing for multiple target tracking when the number of sensor reports received is very large and arrives in large bursts. In this case, it is sometimes necessary to pre-process reports before sending them to tracking modules in the fusion system. The pre-processing step associates reports to known tracks (or initializes new tracks for reports on objects that have not been seen before). It could also be used as a pre-process step before clustering, e.g., in order to test how many clusters to use. The pre-processing is done by solving an approximate version of the original problem. In this approximation, not all pair-wise conflicts are calculated. The approximation relies on knowing how many such pair-wise conflicts that are necessary to compute. To determine this, results on phase-transitions occurring when coloring (or clustering) large random instances of a particular graph ensemble are used.Comment: 10 page

Freezing in random graph ferromagnets

Using T=0 Monte Carlo and simulated annealing simulation, we study the energy relaxation of ferromagnetic Ising and Potts models on random graphs. In addition to the expected exponential decay to a zero energy ground state, a range of connectivities for which there is power law relaxation and freezing to a metastable state is found. For some connectivities this freezing persists even using simulated annealing to find the ground state. The freezing is caused by dynamic frustration in the graphs, and is a feature of the local search-nature of the Monte Carlo dynamics used. The implications of the freezing on agent-based complex systems models are briefly considered.Comment: Published version: 1 reference deleted, 1 word added. 4 pages, 5 figure

A flock-based model for ad hoc communication networks

We introduce a model for simulating the movement of semi-autonomous mobile units that exhibit swarm-based behaviour and collectively form a mobile ad-hoc communication network. The mobility model is used to study how the topological properties of the resulting communication network change over time. The connectivity graphs are determined by allowing each unit to communicate with others inside a given radius. By varying the free parameters of the mobility model, qualitatively different regimes of movement can be emulated. A number of properties of the graphs (e.g., the size of largest connected component, overall network efficiency and the number of isolated units) are calculated and compared for the different regimes. Finally, we present several directions for future work, both in terms of further applications and extensions of the present model. 1

Contents

This thesis deals with some aspects of the physics of disordered systems. The thesis consists of two papers and an introductory part. The introduction briefly describes the theory of coarsening for regular lattice models and then gives an introduction to computational complexity theory. The definition of the Turing model of computation and of some important complexity classes are given, the Church-Turing hypothesis described, and the proofs of some important theorems reviewed. Paper I studies the relaxation behaviour using Monte Carlo simulation of some optimisation problems that, unless a very plausible conjecture in computer science is false, have worst case instances that require exponential time to solve. These problems can also be interpreted as spin glass models, and have previously been found to exhibit threshold phenomena akin to those of physical models undergoing phase transitions. In paper II, some preliminary results from Monte Carlo studies of a disordered ferromagnetic spin system are presented. Key-words: Spin glasses, relaxation, computational complexity, NP-completeness, boolean satisfiability, graph colouring. This licenciate thesis is based on the following papers, reprinted in the second part of the thesi