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Movement Stability of D-Optimal Sensor Placement Under Projector Perturbations — arXiv:2610.08152

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.08152
License (as archived): CC0-1.0
Archived: 2026-10-07T11:49:20.736Z
SHA-256 of the archived text: 6854f459c4238de55ca06a0ee266a43fe24c6907f25cda7d3972900650b29f23
Stable URL of this page: https://metraipolis.com/documento/dc_cfceddfe8905

How to cite

Movement Stability of D-Optimal Sensor Placement Under Projector Perturbations — arXiv:2610.08152 — arXiv (en), https://arxiv.org/abs/2610.08152 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_cfceddfe8905 (Metraipolis archive dc_cfceddfe8905, sha256 6854f459c4238de55ca06a0ee266a43fe24c6907f25cda7d3972900650b29f23)

BibTeX

@misc{dccfceddfe8905,
  title = {Movement Stability of D-Optimal Sensor Placement Under Projector Perturbations — arXiv:2610.08152},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.08152},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_cfceddfe8905; sha256 6854f459c4238de55ca06a0ee266a43fe24c6907f25cda7d3972900650b29f23},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.08152. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

In time-varying D-optimal subset selection, the number of replaced coordinates does not measure physical displacement: when the optimal selection for a set of mobile sensors changes, a single sensor may have to cross the entire graph. We therefore measure movement by a bottleneck matching distance on a fixed mobility graph, and define the distance margin at radius P as the smallest old-objective loss among configurations farther than P from the current maximizer. Our main result shows that if the projector drift is small and the distance margin at a chosen radius exceeds an explicit threshold, then every maximizer of the new objective lies within that radius, without tie-breaking rules or uniform conditioning assumptions over subsets. Moreover, we show that separation information of this kind is genuinely needed: a weighted-path construction shows that, at a fixed baseline eigengap, an arbitrarily small perturbation can move an optimal sensor from one end of the graph to the other, so no bound depending only on perturbation size and eigengap can vanish with the perturbation. We also give a finite certificate, conditions under which local and Voronoi restrictions retain a global optimum, and oversampled and regularized extensions, and we identify the learned dictionary criteria to which the results apply.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.OC, nuovi lavori del giorno).
Categorie arXiv: Optimization and Control (math.OC) ; Signal Processing (eess.SP).
Pagina del lavoro: https://arxiv.org/abs/2610.08152 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-07T11:21:09.852Z dalla pagina https://arxiv.org/list/math.OC/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).