AIOS Biology Calculus: Cognitive Modeling
SmartHaus Research • 2024 • In Review
Abstract
We present a mathematical framework for modeling biological intelligence in AI systems. Using differential equations inspired by neuroscience and systems biology, we demonstrate how emergent cognitive behaviors arise from simple mathematical rules.
Core Dynamics
∂C/∂t = D∇²C + R(C,N) - γC
Where C is cognition state, D is diffusion, R is reaction, N is network, γ is decay
Biological Principles
- Homeostasis: Self-regulating equilibrium maintenance
- Adaptation: Learning through environmental feedback
- Emergence: Complex behaviors from simple rules
- Resilience: Fault tolerance through redundancy
Applications
AIOS Subsystems
COE (brain), CNS (routing), ANS (autonomic), SNS (somatic)
Holographic Memory
Formal calculus for memory dynamics and retrieval