arXiv subjects

Taylor Garnowski

Publications and source records attributed to Taylor Garnowski.

4 recordsLinked to original sources

arXiv2025

Benchmarking of quantum and classical SDP relaxations for QUBO formulations of real-world logistics problems

Quadratic unconstrained binary optimization problems (QUBOs) are intensively discussed in the realm of quantum computing and polynomial optimization. We provide a vast experimental study of semidefinite programming (SDP) relaxations of QUBOs using sums of squares methods and on Hamiltonian Updates. We test on QUBO reformulations of industry-based instances of the (open) vehicle routing problem and the (affinity-based) slotting problem -- two common combinatorial optimization problems in logistics. Beyond comparing the performance of various methods and software, our results reaffirm that optimizing over non-generic, real-world instances provides additional challenges. In consequence, this study underscores recent developments towards structure exploitation and specialized solver development for the used methods and simultaneously shows that further research is necessary in this direction both on the classical and the quantum side.

math.OC↗

arXiv2022

Asymptotic distribution of odd-balanced unimodal sequences with rank congruent to a mod c

We compute an asymptotic estimate for odd balanced unimodal sequences for ranks congruent to $a \pmod{c}$ for $c\neq 1$ odd. We find the interesting result that the odd balanced unimodal sequences are asymptotically related to the overpartition function. This is in contrast to strongly unimodal sequences which, are asymptotically related to the partition function.

math.NT↗

arXiv2021

Asymptotics for the twisted eta-product and applications to sign changes in partitions

We prove asymptotic formulas for the complex coefficients of $(\zeta q;q)_\infty^{-1}$, where $\zeta$ is a root of unity, and apply our results to determine secondary terms in the asymptotics for $p(a,b,n)$, the number of integer partitions of $n$ with largest part congruent $a$ modulo $b$. Our results imply that, as $n \to \infty$, the difference $p(a_1,b,n)-p(a_2,b,n)$ for $a_1 \neq a_2$ oscillates like a cosine, when renormalized by elementary functions. Moreover, we give asymptotic formulas for arbitrary linear combinations of $\{p(a,b,n)\}_{1 \leq a \leq b}$.

math.NT↗

arXiv2021

Asymptotics of Bailey-type mock theta functions

We compute asymptotic estimates for the Fourier coefficients of two mixed mock modular forms, which come from Bailey pairs derived by Lovejoy and Osburn. To do so, we employ the circle method due to Wright and a modified Tauberian theorem. We encounter cancellation in our estimates for one of the mock theta functions due to the auxiliary function $\theta_{n,p}$ arising from the splitting of Hickerson and Mortenson. We deal with this by using higher order asymptotic expansions for the Jacobi theta functions.

math.NT↗