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Uniform Transformation of Non-Separable Probability Distributions

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Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
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Eric Kee

Neural and Evolutionary Computing · Submitted 16 Aug 2016

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

The authors' main claim A potential function is shown to link probability density functions to their transformation, and to generalize the cumulative.

how it is stated · asserted 1.00 read the record →

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arXiv ID1609.01982 (version 1)
Pith IDKGK3OORX, Pith's permanent record of this paper and its review
CitationEric Kee. "Uniform Transformation of Non-Separable Probability Distributions." arXiv:1609.01982 (2016). https://pith.science/paper/KGK3OORX
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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-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,485 input tokens.

What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.38 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.04 · 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; .

A theoretical framework is developed to describe the transformation that distributes probability density functions uniformly over space. In one dimension, the cumulative distribution can be used, but does not generalize to higher dimensions, or non-separable distributions. A potential function is shown to link probability density functions to their transformation, and to generalize the cumulative. A numerical method is developed to compute the potential, and examples are shown in two dimensions.

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 A theoretical framework is developed to describe the transformation that distributes probability density functions uniformly over space. contribution 1.00 0.91 0.27 asserted 1.00
s1 In one dimension, the cumulative distribution can be used, but does not generalize to higher dimensions, or non-separable distributions. gap 0.88 0.22 0.07 asserted 1.00
s2 A potential function is shown to link probability density functions to their transformation, and to generalize the cumulative. contribution 0.93 0.91 0.43 asserted 1.00
s3 A numerical method is developed to compute the potential, and examples are shown in two dimensions. method 0.57 0.94 0.13 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.63 · evidence from proof or derivation 0.86.

What was examined, and what was not

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not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • 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

A theoretical framework is developed to describe the transformation that distributes probability density functions uniformly over space. In one dimension, the cumulative distribution can be used, but does not generalize to higher dimensions, or non-separable distributions. A potential function is shown to link probability density functions to their transformation, and to generalize the cumulative. A numerical method is developed to compute the potential, and examples are shown in two dimensions.

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