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Physical limits to concentration and gradient sensing by perfect monitors — arXiv:2608.08816

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.08816
License (as archived): CC0-1.0
Archived: 2026-10-19T09:06:21.491Z
SHA-256 of the archived text: 9abe5736e2d686a109fe9121cf9f55788d9038d94413b5e00d452a31ec1d4207
Stable URL of this page: https://metraipolis.com/documento/dc_3ff2c9bb27bc

How to cite

Physical limits to concentration and gradient sensing by perfect monitors — arXiv:2608.08816 — arXiv (en), https://arxiv.org/abs/2608.08816 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_3ff2c9bb27bc (Metraipolis archive dc_3ff2c9bb27bc, sha256 9abe5736e2d686a109fe9121cf9f55788d9038d94413b5e00d452a31ec1d4207)

BibTeX

@misc{dc3ff2c9bb27bc,
  title = {Physical limits to concentration and gradient sensing by perfect monitors — arXiv:2608.08816},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.08816},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_3ff2c9bb27bc; sha256 9abe5736e2d686a109fe9121cf9f55788d9038d94413b5e00d452a31ec1d4207},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.08816. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Cells often estimate chemical concentrations from only a few diffusing molecules, whose stochastic motion limits sensing precision. We consider a perfect monitoring instrument that records the instantaneous molecular density throughout a finite region without perturbing the concentration field or distinguishing molecular identities. The standard Berg-Purcell estimator weights all positions uniformly. Here we derive the optimal spatial weighting within a large class of unbiased estimators for both concentration and gradient sensing. Variance minimization maps to an electrostatic problem. Surprisingly, although the instrument monitors the entire volume, the optimal estimator assigns all weight to its boundary, reducing the uncertainty in both concentration and gradient sensing. We extend the results to arbitrary geometries and spatial dimensions.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-08-11 in math.ST).
Categorie arXiv: Biological Physics (physics.bio-ph) ; Mathematical Physics (math-ph); Probability (math.PR); Statistics Theory (math.ST); Classical Physics (physics.class-ph); Cell Behavior (q-bio.CB).
Pagina del lavoro: https://arxiv.org/abs/2608.08816 — 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 2026-10-19T09:04:01.373Z dalla pagina https://arxiv.org/catchup/math.ST/2026-08-11?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).