Contextual Geometric Structures (CGS): a hybrid modeling approach

Contextual Geometric Structures using parcels https://github.com/OceanParcels/parcels

Simulation Goals

The goals of this CGS-based project are the following:

1. To simulate how both words and their meanings evolve in a synthetic cultural context.

2. To discover factors that affect changing rates of word usage and meaning in a synthetic culture, using the concept of finite state machines, hydrodynamics, and genetic algorithms.

Key Concepts

Flow field:

This project utilizes particles and an environmental flow field to simulate the diversity of words and meanings in a population. Each particle is associated with a kernel, which contains a single word and a meaning of the word. Particles within the field flow freely, but also tend to collide in a flow-dependent manner.

Words:

In this model, a single word may have many meanings, but a particle represents a single word and meaning pair (word:meaning). There are different mechanisms for words and meanings, respectively.

For words, a finite state machine (FSM) is implemented to simulate the behavior of word-frequency alteration. The concept is described in Figure 1. Words may be in either 'active' or 'inactive' states. When a word is in an 'active' state, it may transition to an 'inactive' state at a probability of p. This active state may also be maintained after a triggering event with a probability of 1-p.

When a word is in an 'inactive' state, it always transforms to the 'active' state after a triggering event. While activation after a triggering event is deterministic, the triggering events themselves (a collision of particles) occur at a rate q (or a conditional probability of 1|q), and is dependent on the number of particles in the simulation.

As the simulation evolves, the active-to-inactive probability (p) tends to decrease with time. This is consistent with the idea that words are more likely to disappear when they are young and at low-frequencies in the population. As words persist with respect to time, their frequency is more likely to stabilize as well.

Figure 1. Probabilities of transitions between active and inactive states.

Meanings:

In CGS, every word:meaning combination (a single particle) is assigned a fitness value, which is used for the genetic algorithm component. Mutation occurs at a given rate (u) and changes the meaning of a word to another meaning of the same word with a probability proportional to the meaning's fitness value.

We can illustrate this by considering a group of meanings for a single word: if a given meaning has a higher fitness value, the other meanings have higher chances to transform into this meaning upon mutation.

Installation

This project can only be installed in windows currently.
To work with this project, users have to install python 2.7 first.

1. Please create a virtual environment first.

    $ virtualenv environment_name --python=2.7 --no-site-packages
    
    # For example, I create my virtual environment in C:\Users\User\Documents\parcels_package\venv_CGS, then the command is:  
    virtualenv C:\Users\User\Documents\parcels_package\venv_CGS --python=2.7 --no-site-packages
   

2. Activate virtual environment.

    $ cd path_to_environment/Scripts  
    $ activate
    
    # In my case, the command is:
    cd C:\Users\User\Documents\parcels_package\venv_CGS\Scripts
    activate
    # After giving the commands above, users will find the virtual environment has been activated.
   

3. Then install package with:

    $ pip install git+https://github.com/jimboH/CGS.git@master --process-dependency-links