metastablex 0.1.3

Structural dynamics framework for complex systems

🧠 MetastableX

A Unified Computational Framework for Metastability and Critical Transitions in Complex Systems

Bridging statistical physics, machine learning and epidemiology to detect systemic instability in real-world dynamics.

⚙️ PyTorch • 📊 Time-Series • 🧠 Complex Systems • 🏥 Public Health • 🌍 Open Science • 🤖 LLM

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📌 Abstract

Complex systems—from biological organisms to healthcare infrastructures—operate near the edge of stability, where small perturbations can trigger large-scale transitions.

We introduce MetastableX, a computational framework for detecting:

• metastable regimes
• early warning signals
• critical transitions

using time-series analysis, statistical physics, and machine learning.

The framework integrates:

• statistical physics (energy, entropy, criticality)
• machine learning (HMM, clustering, prediction)
• epidemiology (DATASUS, COVID detection, SIR modeling)
• AI interpretation (local LLM)

and is validated on real-world epidemiological data from SIH/SUS (Brazil).

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🧠 1. Introduction

Most real-world systems are not static — they are dynamical, nonlinear, and unstable.

Healthcare systems, in particular, exhibit:

• regime shifts
• overload cascades
• systemic collapse under stress (e.g., COVID-19)

MetastableX treats epidemiology not as dashboards, but as:

a dynamical system evolving through regimes

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⚙️ 2. Theoretical Framework

2.1 Stochastic Dynamics

$$ \frac{dx}{dt} = f(x) + \sigma \eta(t) $$

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2.2 Energy Landscape

$$ U(x) = -\frac{\sigma^2}{2}\log P(x) $$

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2.3 Criticality

$$ \lambda \approx 0 $$

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2.4 Information Principle

$$ \max (H + F) $$

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⚠️ 3. Early Warning Signals

• Variance ↑ → instability
• Autocorrelation ↑ → critical slowing down
• Entropy ↑ → disorder

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🧬 4. Core Implementations

🧠 Hidden Markov Models (HMM)

• Detect latent epidemiological regimes
• Identify transitions (pre-critical → critical → collapse)
• Works at municipality level

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⚡ Phase Transition Detection

• Automatic rupture detection using ruptures

• Detects:

  • outbreaks
  • structural breaks
  • COVID onset

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🌪 Entropy Analysis

• Rolling entropy over time
• Measures system disorder
• Peaks indicate instability

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📉 Critical Slowing Down

• Variance + autocorrelation increase
• Early warning of collapse before events

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🔗 Temporal Clustering (MetastableX core)

• Groups time-series into regimes
• Identifies recurring epidemiological patterns

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🏥 5. Epidemiological Layer

📊 DATASUS Integration

• SIH/SUS real data ingestion
• Multi-state and multi-year analysis
• Municipality-level resolution

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🦠 COVID Detection

• CID-based filtering (U07, B34)

• Detects pandemic as:

  • phase transition
  • entropy spike
  • regime shift

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📍 CID Filtering

• Filter dashboard by disease

• Enables:

  • disease-specific analysis
  • risk stratification

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🏆 National Ranking

• Ranking by:

  • municipality
  • CID
  • normalized rates

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⚙️ SIR + ML Modeling

• Classical epidemiological modeling:

$$ S \rightarrow I \rightarrow R $$

• Combined with machine learning for:

  • prediction
  • anomaly detection

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🤖 6. LLM Interpretation Layer

Local AI (Llama3 via Ollama)

• Fully offline
• No API required

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Capabilities

• 🧠 Explain epidemiological dynamics

• 📊 Translate metrics into natural language

• 📋 Generate scientific reports

• 🔍 Interpret:

  • entropy
  • HMM states
  • outbreaks
  • transitions

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Pipeline

data → physics → ML → regimes → metrics → LLM → explanation