Persistence-Mayer-Homology-and-Laplacian

The code for persistence Mayer homology and laplacian for N-chain complexes

Data

The source data used in this work is provided.

https://github.com/WeilabMSU/PathHom/tree/main/data

Requirments

Python Dependencies

• python (>=3.7)
• numpy (1.23.5)
• biopandas (0.4.1)
• matplotlib (3.6.2)
• gudhi (3.8.0)

Tutorial

1. Basic examples, for calculating Mayer Bettis and Mayer Laplacians:

from Mayer_homology_Laplacian import betti_laplacian
##define your simplicial complex
X = [[0], [1], [2], [3],
[0, 1], [0, 2], [0, 3], [1, 2], [1, 3], [2, 3],
[0, 1, 2], [0, 1, 3], [0, 2, 3], [1, 2, 3]]
##define your N value and the maximal dimensions of homology and laplacian
N = 3
max_dim = 2 #default to be 1
#####
Betti,Gmin,_,_,_ = betti_laplacian(X,N,max_dim=max_dim)

str_betti = "The Mayer Betti {} at stage {} is:"
str_lap = "The smallest positive eigenvalue of Mayer Laplacian {} at stage {} is:"

for q in range(1,N):
    for i,(b,l) in enumerate(zip(Betti[q-1],Gmin[q-1])):
        print(str_betti.format(i,q),b)
        print(str_betti.format(i,q),l)

2. Persistent Mayer homology and Laplacian: the following example is the same as the 'main.py' file

import numpy as np
from persistence import calculate
from functions import read_file,process

##chose your example
file = 'X1.xy' # the 'xy' file, 'xyz' file or 'mol2' file you want to study,including 'X1.xy','X2.xyz','C20.xyz','C60.xyz','CB7.mol2'.
radius = np.linspace(0,2,201)# filtration radius.
n = 7 # N value for Mayer homology/Laplacian. Might be slow for big size molecules if N is too large.
##process your example and plot the results.
fig1,axes1,fig2,axes2 = process(file,radius,n)

Citing

To be added...

Contributors

The persistence Mayer homology and Laplacian code was created by Li Shen and is maintained by Li Shen, Jian Liu and Weilab at MSU Math.

License

All codes released in this study is under the MIT License.

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