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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeMay 8th 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexThis morning we received (J. Bergner and C. Rezk must have, too) an unlikely citation alert from a pure engineering publication ("[A Temporal-Spatial Spectrum Prediction Using the Concept of Homotopy Theory for UAV Communications](https://ieeexplore.ieee.org/document/9364740)"). I tried to look up what this is about and collected some references here. Can't vouch for this, not having dug into any details, but it seems to be a real thing. I found this one reference * Cheng-shi Liu, *The essence of the homotopy analysis method*, Applied Mathematics and Computation Volume 216, Issue 4, 15 April 2010, Pages 1299-1303 ([doi:10.1016/j.amc.2010.02.022](https://doi.org/10.1016/j.amc.2010.02.022)) which seems to say that the use of homotopies here ends up being equivalent to changing the origin for a Taylor expansion and then proceeding non-homotopically, though I can't quite see if the author means to imply that this makes the use of homotopies here redundant and inessential. Anyways, even if so, it might be good to have an entry about this to explain it. <a href="https://ncatlab.org/nlab/revision/homotopy+analysis+method/1">v1</a>, <a href="https://ncatlab.org/nlab/show/homotopy+analysis+method">current</a>

   This morning we received (J. Bergner and C. Rezk must have, too) an unlikely citation alert from a pure engineering publication (“A Temporal-Spatial Spectrum Prediction Using the Concept of Homotopy Theory for UAV Communications”).

   I tried to look up what this is about and collected some references here. Can’t vouch for this, not having dug into any details, but it seems to be a real thing.

   I found this one reference

   • Cheng-shi Liu, The essence of the homotopy analysis method, Applied Mathematics and Computation Volume 216, Issue 4, 15 April 2010, Pages 1299-1303 (doi:10.1016/j.amc.2010.02.022)

   which seems to say that the use of homotopies here ends up being equivalent to changing the origin for a Taylor expansion and then proceeding non-homotopically, though I can’t quite see if the author means to imply that this makes the use of homotopies here redundant and inessential.

   Anyways, even if so, it might be good to have an entry about this to explain it.

   v1, current