Rule Based Artificial Intelligence: Agents

AB models are rule based models based on the collective behaviour of a set of

agents. By definition, “an agent is a computer system capable of exchanging in-

formation with other agents and its environment, taking decisions and performing autonomous actions” [130]. AB models have traditionally been used in fields like economics [124] or sociology [122, 131] to model the behaviour of complex systems such as stock markets and societies. For example, to model the stock market [124], agents can be identified with traders and, to model social phenomena, like the emergence of hierarchy in the society [131], agents can be identified as warriors. Agents share a set of characteristics: (i) they have a a set of properties, such as a position in space, a pot of money if they are traders, or an amount of “power” if they are warriors [131]; (ii) they evolve in time through a set of actions, for exam- ple buying and selling stocks or fighting; (iii) they are goal-oriented, for example traders want to maximise their income and warriors want to maximise their power. In order to reach their goal, agents will decide which action to perform basing their decision on a set of conditions. Conditions and actions form the rules of an AB

model. In general, the AB rules are: (i) nonlinear, as they can contain if-then

conditions or more complicated algorithmic decisions; (ii) local, because only the

local environment may be considered by the agent before undertaking an action;

and (iii) adaptive, allowing the rules to evolve in time, to best suit the goal of the

simulation. In particular, the adaptation is a characteristic of the AB rules not 26

2.4 Simulation Methods in Complexity Science

present in the CA ones. The adaptability of the rules can have a great effect on the performance of the algorithm, leading it to reach the expected goal with less computational effort, such as less memory storage and/or computing time.

AB models have been introduced in chemistry [132, 133, 134, 43, 135], under the assumption that chemical systems are complex systems and it is therefore possible to describe their complex dynamics with a set of rules. For example, Cartwright et al. [132, 133] modelled the enantiomeric crystallisation of molecules letting each agent correspond to a nucleation site of L or D handedness. Each agent is then put into a flux, to study the effect of the stirring on the growing crystals. The model is based on four simple rules: new agents can appear both as new nucleation sites (with random handedness), or derive from an already existing nucleus (therefore with its same handedness), they can then either grow or dissolve. This model shows that, in agreement with the experiments [136], crystals under stirring conditions are all D or L. Bradford and Dill studied the the self-organisation of proteins [134]. In their model, proteins acting as catalysts are identified as agents able to move in space, with moves biased such that each agent is driven towards a region of space rich in its reactant. The end simulation result is that proteins tend to self-assemble into multicomponent aggregates in order to catalyse all the reactions of a chain. Troisi, Wong, and Ratner [43] studied the packing of a set of molecules to find their lowest energy configuration. In their model, an agent is identified with a shape or a group of shapes on a square lattice. At the begginning of the simulation each agent coincides with a rigid shape and, as the simulation proceeds, the agent evolves to represent stable portions of the system. Each agent evolves due to three actions:

move to a new position of the lattice, merge with another agent, and split into

two agents. In Chap. 5 and 6 we will implement this model in order to describe off-lattice systems of idealised and of atomistic particles.

3 MONTE CARLO SIMULATION OF POLYDISPERSE SPHERES ON A SPHERICAL SURFACE

There is geometry in the humming of the strings, there is music in the spacing of the spheres. (Pythagoras, 6th.century BC)

I

tern of silica nanoparticles on the surface of spherical polystyrene la- tex droplets with MC simulations. The experimental system has been modelled as a set of interacting spheres on a spherical surface. The information supplied by this model has been complementary to the experimental data. We study the effect of the polydispersity of the spherical nanoparticles on the self- assembled structure. We show that broadening of the nanoparticle size distribution has pronounced effects on the self-assembled equilibrium packing structures, with the original 12-point dislocations or grain-boundary scars gradually fading out.

3.1 The Sphere Packing Problem

Packing patterns of identical and non-identical spherical and discotic objects on curved surfaces are often encountered in nature and science. Examples include C60 fullerenes [137, 138], 13-atom cuboctahedral metal clusters [139], S-layer pro- teins on outer cell membranes [140] which are all formed by the self-assembly of identical building blocks, and the lenses on insect eyes, biomineralized shells on coccolithophorids [141], solid-stabilised emulsion droplets [142] and bubbles [143], made of building blocks of different sizes.

It is well known that the maximum packing density of a single layer of spheres of identical size in an infinite 2D flat plane is achieved when they are arranged into a hexagonal lattice, with each of the spheres having six neighbours. It is also known from the literature [144] that a set of equally sized spheres, or calottes, on a spherical surface cannot form a regular hexagonal packing, due to the positive 28