AMDconfigurations provides tools for analysing the geometry of configurations in high‑dimensional spaces through the lens of Average Minimum Distance (AMD) curves and synthetic configuration generation.
The package is part of a broader research program aimed at identifying recurrent geometric patterns across biological, ecological, geohistorical, and financial systems.
Rather than focusing on domain‑specific variables, AMDconfigurations treats each system as a set of points in a state space and studies the shape, dispersion, and internal structure of these point clouds.
The goal is to reveal universal geometric signatures that transcend the particularities of each domain.
Motivation
Many complex systems—cells, ecological communities, historical polities, financial markets—can be represented as configurations of points in a multidimensional space.
Despite their differences, these systems often exhibit:
- recurrent spatial arrangements
- characteristic scales of dispersion
- transitions between geometric regimes
- clustering patterns that reflect underlying energetic or organizational constraints
Traditional statistical tools tend to collapse these structures into aggregate descriptors.
AMDconfigurations instead focuses on the geometry of the configuration itself, using AMD curves and related quantities as a way to quantify:
- how points are distributed
- how “tight” or “spread” a configuration is
- how configurations compare to synthetic or null models
- how configurations cluster in configuration space
This geometric perspective is intended to support the search for cross‑domain regularities and universal organizational principles.
What the package provides
AMDconfigurations implements four core capabilities:
1. Compute AMD curves
compute_amd_curve() calculates the Average Minimum Distance curve of a configuration.
The AMD curve captures how the typical nearest‑neighbour distance changes as the configuration is progressively thinned, providing a compact geometric signature.
2. Generate synthetic configurations
create_synthetic_samples() produces synthetic point clouds under controlled geometric assumptions.
These synthetic configurations serve as reference models for comparison, calibration, and hypothesis testing.
3. Estimate equivalent dispersion parameters
estimate_sigma_equivalent() extracts a single parameter summarizing the effective dispersion of a configuration, based on its AMD curve or related metrics.
4. Assign configurations to clusters
assign_clusters_best() groups configurations according to their geometric similarity, enabling the detection of recurrent shapes or regimes.
Conceptual workflow
A typical analysis proceeds as follows:
- Represent each system or time slice as a configuration (a set of points in ℝⁿ).
- Compute its AMD curve, obtaining a geometric fingerprint.
- Generate synthetic configurations to establish baselines or null expectations.
- Estimate equivalent dispersion parameters to compare configurations across scales.
- Cluster configurations to identify recurrence, transitions, or regimes.
This workflow is intentionally domain‑agnostic: the same tools apply to transcriptomic states, ecological assemblages, historical polities, or financial portfolios.