CPBM algorithm

(Capital-Pulse Behavioral Model) A conceptual model for tracking the pulse of local capital to predict purchasing behavior across demographics Central Idea Instead of categorizing individuals into fixed segments, we track the movement of capital as a dynamic phenomenon. Each individual is a unit of financial activity that pulsates to its own rhythm

Capital-Pulse Behavioral Model (CPBM)

A four-layer algorithmic framework for predicting purchase-trend diffusion across socioeconomic strata via individual capital-flow signatures.

ORCID: 0009-0000-5475-3970 OSF: osf.io/9ukxe Paper: see docs/cpbm_paper.pdf https://sciprofiles.com/profile/ahmed_elsayed

---

Installation

git clone https://github.com/ahmed-elsayed-99/CPBM-algorithm.git
cd CPBM-algorithm
pip install -e .

Quick Start

from cpbm.data.synthetic import SyntheticCommunity
from cpbm.core.signature import SignatureExtractor
from cpbm.core.diffusion import DiffusionLayer
from cpbm.core.stratum import StratumGradient
from cpbm.models.ensemble import CPBMEnsemble

community = SyntheticCommunity(n=500, seed=42).generate()
extractor = SignatureExtractor(window_days=90)
Phi = extractor.fit_transform(community["transactions"])

diffusion = DiffusionLayer()
diffusion.fit(community["adoption_history"])

stratum = StratumGradient()
tau = stratum.fit(community["stratum_adoption"])

model = CPBMEnsemble()
model.fit(Phi, community["labels"],
          tau=tau, diffusion_params=diffusion.params_)

probas = model.predict_proba(Phi)
print(f"AUC: {model.evaluate(Phi, community['labels'])['auc']:.4f}")

Architecture

Layer 1  →  Individual Pulse Signature  φᵢ ∈ ℝ⁷
Layer 2  →  Social Diffusion PDE        ∂P/∂t = D∇²P + αS - βP + γN
Layer 3  →  Stratum-Gradient Bass       τ = t*_lower - t†_upper
Layer 4  →  Hybrid Ensemble             XGBoost + LSTM + GAT

Citation

@misc{elsayed2026cpbm,
  author       = {Elsayed, Ahmed},
  title        = {Capital-Pulse Behavioral Model (CPBM)},
  year         = {2026},
  publisher    = {GitHub},
  journal      = {GitHub repository},
  howpublished = {\url{https://github.com/ahmed-elsayed-99/CPBM-algorithm}},
  note         = {OSF: https://osf.io/9ukxe/}
}