{
  "annotation_id": "47168bda-3399-427c-931c-4d0b3245ca71",
  "date_created": "2026-03-02T18:00:39.865000Z",
  "date_modified": "2026-03-02T18:00:39.865000Z",
  "file_hash": "76c6d5d3fe41958c3d047da219d2b0ae61870040d8ca5fce6310921cb59d301c",
  "private": false,
  "record": {
    "abstract": "The aim in this note is to define an algorithm to carry out minimal curvature\nspherical harmonics interpolation, which is then used to calculate the\nLaplacian for multi-electrode EEG data analysis. The approach taken is to\nrespect the data. That is, we implement a minimal curvature condition for the\ninterpolating surface subject to the constraints determined from the\nmulti-electrode data. We implement this approach using spherical harmonics\ninterpolation. In this elegant example we show that minimization requirement\nand constraints complement each other to fix all degrees of freedom\nautomatically, as occurs in gauge theories. That is, the constraints are\nrespected, while only the orthogonal subspace minimization constraints are\nenforced. As an example, we discuss the application to interpolate control data\nand calculate the temporal sequence of laplacians from an EEG Mismatch\nNegativity (MMN) experiment (using an implementation of the algorithm in IDL).",
    "arxiv_id": "physics/0206007",
    "authors": [
      "Giulio Ruffini",
      "Josep Marco",
      "Carles Grau"
    ],
    "categories": [
      "physics.med-ph",
      "physics.data-an",
      "q-bio.NC"
    ],
    "title": "Spherical Harmonics Interpolation, Computation of Laplacians and Gauge   Theory",
    "url": "https://arxiv.org/abs/physics/0206007"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "5bd6e71d-95c3-4090-8f86-82d559944509",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}