Sequence positivity through numeric analytic continuation: uniqueness of the Canham model for biomembranes

S Melczer, M Mezzarobba - arXiv preprint arXiv:2011.08155, 2020 - arxiv.org
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 …

Universal skolem sets

F Luca, J Ouaknine, J Worrell - 2021 36th Annual ACM/IEEE …, 2021 - ieeexplore.ieee.org
It is a longstanding open problem whether there is an algorithm to decide the Skolem
Problem for linear recurrence sequences, namely whether a given such sequence has a …

Deciding subspace reachability problems with application to Skolem's Problem

S Everett - arXiv preprint arXiv:2410.06528, 2024 - arxiv.org
The higher-dimensional version of Kannan and Lipton's Orbit Problem asks whether it is
decidable if a target vector space can be reached from a starting point under repeated …

On the Skolem Problem for Reversible Sequences

G Kenison - arXiv preprint arXiv:2203.07061, 2022 - arxiv.org
Given an integer linear recurrence sequence $\langle X_n\rangle_n $, the Skolem Problem
asks to determine whether there is a natural number $ n $ such that $ X_n= 0$. Recent work …

Fuchsian holonomic sequences

J van Der Hoeven - Applicable Algebra in Engineering, Communication …, 2023 - Springer
Many sequences that arise in combinatorics and the analysis of algorithms turn out to be
holonomic (note that some authors prefer the terminology D-finite). In this paper, we study …

Algorithms for linear recurrence sequences/Author Philipp Nuspl

P Nuspl - 2023 - epub.jku.at
In the past few decades, numerous tools for automatically discovering and proving identities
involving sequences and special functions were developed. These tools are often based on …

Towards complete methods for automatic complexity and termination analysis of (probabilistic) programs

MT Hark, L Kovács, J Giesl - 2021 - publications.rwth-aachen.de
Kurzfassung Die steigende Zahl von Computerprogrammen in unserem Alltag hat zu immer
umfangreicheren Softwaresystemen geführt. Die klassische Herangehensweise, um die …

[PDF][PDF] Sequence positivity through numeric analytic continuation: uniqueness of the Canham

S Melczer, M Mezzarobba - Combinatorial Theory, 2 (2), 2022 - scholar.archive.org
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 …

On termination and divergence of linear programs

M Hosseini - 2021 - ora.ox.ac.uk
The objective of this thesis is to shed some light on the boundaries of decidability by
answering some of the central problems in the study of linear programs, and to provide an …

Generating Functions and Analytic Combinatorics

I Newton - An Invitation to Analytic Combinatorics: From One to …, 2020 - books.google.com
Since there is a great conformity between the Operations in Species, and the same
Operations in common Numbers... I cannot but wonder that no body has thought of …