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Thermodynamic limit from small lattices of coupled maps

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R. Carretero-González, S. {O}rstavik, J. Huke, D. S. Broomhead, J. Stark

chao-dyn · Submitted 2 Apr 1999

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim This suggests that spatio-temporal embedding techniques using local observations cannot detect the presence of spatial extent in such systems and hence they may equally well be modelled by a local low dimensional stochastically driven system.

how it is stated · hedged possibility 1.00 read the record →

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arXiv IDchao-dyn/9904009 (version 1)
Pith ID2CLYYM27, Pith's permanent record of this paper and its review
CitationD. S. Broomhead, J. Huke, J. Stark, R. Carretero-Gonz\'alez, S. {\O}rstavik. "Thermodynamic limit from small lattices of coupled maps." arXiv:chao-dyn/9904009 (1999). https://pith.science/paper/2CLYYM27
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,967 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.02 · states limitation 0.48 · human participants 0.01 · controlled comparison 0.63 · randomized assignment 0.04 · states quantitative result 0.30 · compares with prior results 0.65 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We compare the behaviour of a small truncated coupled map lattice with random inputs at the boundaries with that of a large deterministic lattice essentially at the thermodynamic limit. We find exponential convergence for the probability density, predictability, power spectrum, and two-point correlation with increasing truncated lattice size. This suggests that spatio-temporal embedding techniques using local observations cannot detect the presence of spatial extent in such systems and hence they may equally well be modelled by a local low dimensional stochastically driven system.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We compare the behaviour of a small truncated coupled map lattice with random inputs at the boundaries with that of a large deterministic lattice essentially at the thermodynamic limit. contribution 0.72 0.89 0.06 asserted 0.75
s1 We find exponential convergence for the probability density, predictability, power spectrum, and two-point correlation with increasing truncated lattice size. result 1.00 0.95 0.30 asserted 1.00
s2 This suggests that spatio-temporal embedding techniques using local observations cannot detect the presence of spatial extent in such systems and hence they may equally well be modelled by a local low dimensional stochastically driven system. interpretation 1.00 0.43 0.74 hedged possibility 1.00

What kind of paper the classifier reports this is: simulation study 0.92 · evidence from simulation or computation 1.00.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We compare the behaviour of a small truncated coupled map lattice with random inputs at the boundaries with that of a large deterministic lattice essentially at the thermodynamic limit. We find exponential convergence for the probability density, predictability, power spectrum, and two-point correlation with increasing truncated lattice size. This suggests that spatio-temporal embedding techniques using local observations cannot detect the presence of spatial extent in such systems and hence they may equally well be modelled by a local low dimensional stochastically driven system.

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