{
  "annotation_id": "39c5440b-47db-4f92-973b-e895411897cf",
  "date_created": "2026-02-17T05:53:12.605000Z",
  "date_modified": "2026-02-17T05:53:12.605000Z",
  "file_hash": "5eb20604986b83ca748d56c164635a176f53b8a82b09e6ba58b3d0e1e89ee7d2",
  "private": false,
  "record": {
    "abstract": "This work is concerned with the study of $w(mT)$ as $m$ goes to infinity, where $w(t)$ evolves according to $w(t)-w(t-1)=F(t)-A(t)w(t-1)$, and where $T$ is the period of the vector $F(t)$ and the matrix $A(t)$. Motivated by applications to associative learning, particularly to discrimination training, extra conditions are imposed on $F(t)$ and $A(t)$, one of them relating $A(t)$ to a symmetric non-negative definite matrix $K$ relevant to mathematical models of associative learning. Structural relationships between the matrices imply an identity satisfied by the Floquet multipliers driving the dynamics of $w(mT)$ from which follows that the unstable subspace is $\\ker K$. Then, the limit of $w(mT)$ is explicitly identified when $K$ is invertible, while the limit of $Kw(mT)$ is established otherwise. Given that divergence of $w(mT)$ can happen when $K$ is singular, while $Kw(mT)$ is the psychologically relevant quantity, the result can be considered optimal.",
    "arxiv_id": "2601.07113",
    "authors": [
      "Natham Aguirre"
    ],
    "categories": [
      "math.DS"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "Asymptotic values of solutions to a periodic linear difference equation modeling discrimination training",
    "url": "https://arxiv.org/abs/2601.07113",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "0edaf4e2-7a9f-499e-8f9d-3ce05eb42c30",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}