HIOM example

Description

This example will be slightly more complex, as it involves different schemes and update functions to model the spread of opinion polarization within and across individuals.

The paper: The polarization within and across individuals: the hierarchical Ising opinion model (Han L J van der Maas, Jonas Dalege, Lourens Waldorp)

Code

import networkx as nx
import random
import numpy as np
import matplotlib.pyplot as plt

from ndlib.models.ContinuousModel import ContinuousModel
from ndlib.models.compartments.NodeStochastic import NodeStochastic

import ndlib.models.ModelConfig as mc

################### MODEL SPECIFICATIONS ###################

constants = {
    'dt': 0.01,
    'A_min': -0.5,
    'A_star': 1,
    's_O': 0.01,
    's_I': 0,
    'd_A': 0,
    'p': 1,
    'r_min': 0,
    't_O': np.inf,
}

def initial_I(node, graph, status, constants):
    return np.random.normal(0, 0.3)

def initial_O(node, graph, status, constants):
    return np.random.normal(0, 0.2)

initial_status = {
    'I': initial_I,
    'O': initial_O,
    'A': 1
}

def update_I(node, graph, status, attributes, constants):
    nb = np.random.choice(graph.neighbors(node))
    if abs(status[node]['O'] - status[nb]['O']) > constants['t_O']:
        return status[node]['I'] # Do nothing
    else:
        # Update information
        r = constants['r_min'] + (1 - constants['r_min']) / (1 + np.exp(-1 * constants['p'] * (status[node]['A'] - status[nb]['A'])))
        inf = r * status[node]['I'] + (1-r) * status[nb]['I'] + np.random.normal(0, constants['s_I'])

        # Update attention
        status[node]['A'] = status[node]['A'] + constants['d_A'] * (2 * constants['A_star'] - status[node]['A'])
        status[nb]['A'] = status[nb]['A'] + constants['d_A'] * (2 * constants['A_star'] - status[nb]['A'])

        return inf

    return

def update_A(node, graph, status, attributes, constants):
    return status[node]['A'] - 2 * constants['d_A'] * status[node]['A']/len(graph.nodes)

def update_O(node, graph, status, attributes, constants):
    noise = np.random.normal(0, constants['s_O'])
    x = status[node]['O'] - constants['dt'] * (status[node]['O']**3 - (status[node]['A'] + constants['A_min']) * status[node]['O'] - status[node]['I']) + noise
    return x

def shrink_I(node, graph, status, attributes, constants):
    return status[node]['I'] * 0.999

def shrink_A(node, graph, status, attributes, constants):
    return status[node]['A'] * 0.999

def sample_attention_weighted(graph, status):
    probs = []
    A = [stat['A'] for stat in list(status.values())]
    factor = 1.0/sum(A)
    for a in A:
        probs.append(a * factor)
    return np.random.choice(graph.nodes, size=1, replace=False, p=probs)

schemes = [
    {
        'name': 'random agent',
        'function': sample_attention_weighted,
    },
    {
        'name': 'all',
        'function': lambda graph, status: graph.nodes,
    },
    {
        'name': 'shrink I',
        'function': lambda graph, status: graph.nodes,
        'lower': 5000
    },
    {
        'name': 'shrink A',
        'function': lambda graph, status: graph.nodes,
        'lower': 10000
    },
]

################### MODEL CONFIGURATION ###################

# Network definition
g = nx.watts_strogatz_graph(400, 2, 0.02)

# Visualization config
visualization_config = {
    'layout': 'fr',
    'plot_interval': 100,
    'plot_variable': 'O',
    'variable_limits': {
        'A': [0, 1]
    },
    'cmin': -1,
    'cmax': 1,
    'color_scale': 'RdBu',
    'plot_output': './HIOM.gif',
    'plot_title': 'HIERARCHICAL ISING OPINION MODEL',
}

# Model definition
HIOM = ContinuousModel(g, constants=constants, iteration_schemes=schemes)
HIOM.add_status('I')
HIOM.add_status('A')
HIOM.add_status('O')

# Compartments
condition = NodeStochastic(1)

# Rules
HIOM.add_rule('I', update_I, condition, ['random agent'])
HIOM.add_rule('A', update_A, condition, ['all'])
HIOM.add_rule('O', update_O, condition, ['all'])
HIOM.add_rule('I', shrink_I, condition, ['shrink I'])
HIOM.add_rule('A', shrink_A, condition, ['shrink A'])

# Configuration
config = mc.Configuration()
HIOM.set_initial_status(initial_status, config)
HIOM.configure_visualization(visualization_config)

################### SIMULATION ###################

iterations = HIOM.iteration_bunch(15000, node_status=True)
trends = HIOM.build_trends(iterations)

################### VISUALIZATION ###################

HIOM.plot(trends, len(iterations), delta=True)
HIOM.visualize(iterations)

Output