counterfusion 0.1.1

A light-weight package to solve large systems of interactions

CounterFusion

This repository implements algorithms for a paper in preparation. To dive deeper, please visit my personal website.

Prerequisites

To effectively engage with the notebook, the following Python packages are required:

• numpy: For handling numerical computations and array operations.
• matplotlib: Essential for creating and displaying graphs and visualizations.

Installation

Ensure you have the necessary packages installed by running:

pip install numpy matplotlib

Usage

For details, please refer to the jupyter notebook which provides many demo cases. Here you may find python snippets to showcase step-by-step the build-up from the bottom, a single interaction, to a system containing multiple sequences of interactions.

1. Define a single interaction

from counterfusion import interaction_builder
left_stochastic_matrix = interaction_builder(dim=2,id1=0,id2=1,value=[0.1,0.3])
right_stochastic_matrix = left_stochastsic_matrix.T
doubly_stochastic_matrix = interaction_builder(dim=2,id1=0,id2=1,value=0.5)

2. Define a sequence of interactions

from counterfusion import *
#===============================================================
# General information for the edge - Hyperparameters
totalNumMover = 4
numForwardMover = 2
initStates = [1,1,0.2,0.2]
#===============================================================
# Information of scattering events 
# Interaction parameters
v03 = 0.3
v01 = 0.5
v23 = 0.8
edgeDef = [[0,3,v03,10],[0,1,v01,10],[2,3,v23,10]]
edgeInfo = generate_bynumber(edgeDef)
edge = Edge(edgeInfo,totalNumMover,numForwardMover)

3. Define a system constituted by several Edge instances.

from counterfusion import *
# Define a six-terminal system
# C1--M1--C2--M2--C3--M3--C4--M4--C5--M5--C6--M6--C1
# Total number of edge states: 4
# Number of forward-moving edge states: 2 (#0,#1)
# Number of backward-moving edge states: 2 (#2,#3)
#===============================================================
# General information for the system - Hyperparameters
totalNumMover = 4
numForwardMover = 2
zeroVoltTerminal = 3
#===============================================================
# Information of scattering events 
# Interaction parameters
v02 = 0.9
v13 = 0.7
v12 = 0.3
# Define interaction between nodes (contacts)
# C1--M1--C2
edgeDef1 = [[0,2,v02,10],[1,3,v13,10]]
# C2--M2--C3
edgeDef2 = [[0,2,v02,10],[1,2,v12,10]]
# C3--M3--C4
edgeDef3 = [[0,2,v02,10],[1,3,v13,10]]
# C4--M4--C5
edgeDef4 = [[0,2,v02,10],[1,2,v12,10]]
# C5--M5--C6
edgeDef5 = [[0,2,v02,10],[1,3,v13,10]]
# C6--M6--C1
edgeDef6 = [[0,2,v02,10],[1,2,v12,10]]
#================================================================
edgesDef = [edgeDef1,edgeDef2,edgeDef3,edgeDef4,edgeDef5,edgeDef6]
edgesInfo = []
for edgeDef in edgesDef:
    edgesInfo.append(generate_bynumber(edgeDef))
graph = []
for edgeInfo in edgesInfo:
    graph.append(Edge(edgeInfo,totalNumMover,numForwardMover))
nodesCurrent = [1,0,0,-1,0,0]
sys = System(nodesCurrent,graph,numForwardMover,zeroVoltTerminal)

4. Define individual paths of flows

# The definition of blocking_state should strictly follow this rule: 
# [[index_of_terminal#1,[all blocked states in this terminal]],[[index_of_terminal#2,[all blocked states in this terminal],...]]]
blockStates = [[1,[0]],[0,[2]],[2,[3]],[3,[1]]]
sys = System(nodesCurrent,graph,numForwardMover,zeroVoltTerminal,blockStates)