Self-Organization and Templates in Swarm Computing Chapter 5 of Swarm Computing Presented by Qing Cao
Overview • The behavior of biological colonies • Self-organization Process • The function of templates • Two models in biological world • Applications and Inspirations to computer science
Biological Colonies • We will focus on the behavior of large colonies, such as termites, ants, etc. • In this presentation, we will model their building behavior. For example, we study how worker termites build chamber around the queen termite.
Self-Organization Process • Large clusters grow larger and they are more attractive. • The same rule applies to the building of the walls. The ants deposit more where there are more deposits already. • As a result, pillars are first formed and walls filled later.
The function of Templates • Template is a pattern that is used to construct another pattern. • Various kinds of templates available in the natural world. • Templates interplays with self-organization to determine the building pattern.
Different kinds of Templates • Template is a pre-pattern in the environment. • Templates may be the temperature and humidity gradients. • Templates are the body shape of the queen in the building of “royal chamber” of termites.
How the body shape template works? • The queen emits a pheromone that diffuses and creates decreasing gradient. • A worker deposits a soil pellet if the concentration of the pheromone is within the suitable window. • It is shown by experiments that wax dummy queen doesn’t stimulate construction.
Quantitative Evaluation of the first model • Goals: 1 The speed of building 2 The construction model
Goal 1: The speed of construction • The rate of the building process increases very rapidly, especially in large groups. • In the first 60 minutes, 0.2 depositions/per worker (20 workers) • The same interval. 2.2 depositions/per worker (80 workers)
The speed of construction • Comments? • Two factors, the time and group size. However, the author doesn’t specify clearly which one is more important.
Goal 2: The construction model • What the author wants to do is to build up a mathematical model for the building process. • First without templates: 1 The dynamics of pheromone. 2 The dynamics of loaded termites. 3 The dynamics of active material.
Step 1: The dynamics of pheromone. • H(r,t) is the concentration at location r and time t. • k2P is the pheromone emitted per unit of deposited material per unit time.
Step 1: The dynamics of pheromone. • k4H is the decay of pheromone. • is the pheromone diffusion. • What the equation states is that the current change of H is equal to the emit of pheromone minus the decay of pheromone, and then plus the diffused pheromone.
Step 2: The dynamics of loaded termites • denotes the attractiveness of the pheromone gradient. denotes the random component in individual motion. denotes a constant flow of loaded termites into the system. denotes the rate of unloading per termite per time unit.
Step 3: Dynamics of active material • This equation shows the dynamics of active material P. K1C denotes the drop of the loaded termites while k2P denotes the rate of disappearance of active material P.
Overall Behavior • When material is dropped, cement pheromone is emitted and diffuses, thus attracting more termites toward this area and thus more material is therefore dropped. • Positive feedback, leading to a pillars to exist.
Then… templates • The template is in the form of pheromonal template. • The amount of queen pheromone at location (x,y) is :
Template Model • Dynamics of loaded termites and the deposited active material.
Review of this model • It simulated the wall-generating process around the queen. • It explains the snowball effect and the formation of pillars. • However, it doesn’t take in account of many factors realistically. For example, it considers everything to be linear or constant. • Oversimplified? Comments and Questions?
The second Model • The second model studied is the wall building process by another kind of ants. The second model is different from the first model in several aspects. • The template for the second model remains unknown, but we know its function is to allow the size of the nest to be regulated by the colony size.
Overview of the model • The deposition behavior is influenced by the local density of grains and the distance from the cluster of ants and brood. • The model exhibits double mechanism, template and self organization.
Basic Model • According to the basic model of depositing grains, the possibility of depositing is pdpt. The possibility of picking up a grain is pd(1-pt). • Pd depends on the perceived number of grains. Pt accounts for the effect of the template.
The model result S is the density of the grain. In a stationary regime, we can get the two equations below.
Applications • Currently the idea of template and self-organizing mechanisms have been used in the context of data analysis and graph partition model. • The template method is an elegant way of restoring parametricity. However, no comparison with previous methods is provided.
Applications (cont.) • In the graph partitioning problem, the goal is to partition the graph into c clusters of equal size while minimizing the number of inter-cluster connections. • “Adding a template mechanism to the KLS algorithm solves this particular problem.” But the author didn’t show how he did this. • Questions?
Review • A template is a pattern used by insects to organize their activities. Building following a template is typical. • Two examples. Both have self-organized deposition following the template. • Template inspires new parametric solutions to some problems.