{
  "annotation_id": "53a9012d-0ca8-494f-bc59-871b8af4617f",
  "date_created": "2026-03-02T18:01:07.478000Z",
  "date_modified": "2026-03-02T18:01:07.478000Z",
  "file_hash": "cf18f4656b0a9218cd704aab03b5769ec582717b55057229a3cc8e66b782c0df",
  "private": false,
  "record": {
    "abstract": "A theory of symbolic dynamic systems with long-range correlations based on\nthe consideration of the binary N-step Markov chains developed earlier in Phys.\nRev. Lett. 90, 110601 (2003) is generalized to the biased case (non equal\nnumbers of zeros and unities in the chain). In the model, the conditional\nprobability that the i-th symbol in the chain equals zero (or unity) is a\nlinear function of the number of unities (zeros) among the preceding N symbols.\nThe correlation and distribution functions as well as the variance of number of\nsymbols in the words of arbitrary length L are obtained analytically and\nverified by numerical simulations. A self-similarity of the studied stochastic\nprocess is revealed and the similarity group transformation of the chain\nparameters is presented. The diffusion Fokker-Planck equation governing the\ndistribution function of the L-words is explored. If the persistent\ncorrelations are not extremely strong, the distribution function is shown to be\nthe Gaussian with the variance being nonlinearly dependent on L. An equation\nconnecting the memory and correlation function of the additive Markov chain is\npresented. This equation allows reconstructing a memory function using a\ncorrelation function of the system. Effectiveness and robustness of the\nproposed method is demonstrated by simple model examples. Memory functions of\nconcrete coarse-grained literary texts are found and their universal power-law\nbehavior at long distances is revealed.",
    "arxiv_id": "physics/0603170",
    "authors": [
      "Z. A. Mayzelis",
      "S. S. Apostolov",
      "S. S. Mel\u0027nyk",
      "O. V. Usatenko",
      "V. A. Yampol\u0027skii"
    ],
    "categories": [
      "physics.data-an",
      "physics.gen-ph"
    ],
    "doi": "10.1016/j.chaos.2007.01.054",
    "title": "Additive N-Step Markov Chains as Prototype Model of Symbolic Stochastic   Dynamical Systems with Long-Range Correlations",
    "url": "https://arxiv.org/abs/physics/0603170"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "e4baabbd-7505-44ab-936c-912efa5a0e3a",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}