{
  "abstract": "Time-domain boundary measurements of diffuse light are temporal point-spread functions whose peak position is used as a robust scalar datum in diffuse optical and fluorescence imaging. We consider the exact response generated by a single fluorescent point target in a homogeneous half-space with a Robin boundary condition. The response is a temporal convolution of two diffusion Green-function factors containing a complementary-error-function boundary correction. For every positive diffusion, absorption, depth, and source--target and detector--target distance parameter, and for every nonnegative Robin parameter, we prove that the normalized exact response is a generalized gamma convolution density. Its extension by zero to the negative half-line is bell-shaped. A differentiable small-time expansion, established by sectorial analyticity and Cauchy estimates, together with the sign-change structure of the first two derivatives, excludes tangential critical points and yields a unique peak with strict increase before it and strict decrease after it. The argument is exact and requires no large-distance, source--detector balance, symmetry, restricted-time, or small-parameter assumption. The same conclusion holds after convolution with an exponential fluorescence-lifetime density for every positive lifetime. The key ingredients are an explicit Stieltjes representation of the Robin factor, hyperbolic complete monotonicity, closure of the generalized gamma convolution class, and bell-shape theory. A derivation of the exact half-space model and the differentiated endpoint asymptotics are included in two appendices.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.21431",
  "author_total": 2,
  "authors": [
    {
      "name": "Junyong Eom"
    },
    {
      "name": "Jinwan Park"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8te0j8amab1v7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.21431",
  "fulltext_url": null,
  "id": "8te0j8amab1v7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.21431",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "2741|Optical Imaging and Spectroscopy Techniques"
    ]
  ],
  "openalex": "W7222557835",
  "pdf_url": "https://arxiv.org/pdf/2610.21431",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8te0j8amab1v7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:50Z",
      "native_id": "2610.21431",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.21431"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Strict unimodality of the exact time-domain diffuse-light response under a Robin boundary condition",
  "title_text": "Strict unimodality of the exact time-domain diffuse-light response under a Robin boundary condition",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/8te0j8amab1v7",
  "venue": "arXiv",
  "versions": []
}