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{
    "pk": 64838,
    "title": "Sequence positivity through numeric analytic continuation: uniqueness of the Canham model for biomembranes",
    "subtitle": null,
    "abstract": "We prove solution uniqueness for the genus one Canham variational problem arising in the shape prediction of biomembranes. The proof builds on a result of Yu and Chen that reduces the variational problem to proving positivity of a sequence defined by a linear recurrence relation with polynomial coefficients. We combine rigorous numeric analytic continuation of D-finite functions with classic bounds from singularity analysis to derive an effective index where the asymptotic behaviour of the sequence, which is positive, dominates the sequence behaviour. Positivity of the finite number of remaining terms is then checked separately.\n \nMathematics Subject Classifications: 05A16, 68Q40, 30B40\nKeywords: Analytic combinatorics, D-finite, P-recursive, positivity, Canham model",
    "language": "en",
    "license": {
        "name": "Creative Commons Attribution 4.0",
        "short_name": "CC BY 4.0",
        "text": "Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.\n\nNo additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.",
        "url": "https://creativecommons.org/licenses/by/4.0"
    },
    "keywords": [
        {
            "word": "Analytic combinatorics"
        },
        {
            "word": "D-finite"
        },
        {
            "word": "P-recursive"
        },
        {
            "word": "positivity"
        },
        {
            "word": "Canham model"
        }
    ],
    "section": "Research Articles",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/3hx5h6ct",
    "frozenauthors": [
        {
            "first_name": "Stephen",
            "middle_name": "",
            "last_name": "Melczer",
            "name_suffix": "",
            "institution": "Department of Combinatorics & Optimization, University of Waterloo, Waterloo, Ontario, Canada",
            "department": ""
        },
        {
            "first_name": "Marc",
            "middle_name": "",
            "last_name": "Mezzarobba",
            "name_suffix": "",
            "institution": "CNRS, École polytechnique, Institut Polytechnique de Paris, Laboratoire d'informatique de l'École polytechnique (LIX, UMR 7161), 1, rue Honoré d'Estienne d'Orves, Bâtiment Alan Turing, CS35003, 91120 Palaiseau, France",
            "department": ""
        }
    ],
    "date_submitted": "2022-06-22T19:15:42Z",
    "date_accepted": "2022-06-22T19:15:42Z",
    "date_published": "2022-06-30T07:00:00Z",
    "render_galley": null,
    "galleys": [
        {
            "label": "",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/combinatorial_theory/article/64838/galley/49648/download/"
        }
    ]
}