Tootfinder

Algorithmic strategies for finding the best TSP 2-OPT move in average sub-quadratic time
Giuseppe Lancia, Paolo Vidoni
https://arxiv.org/abs/2403.19878 htt…

Algorithmic strategies for finding the best TSP 2-OPT move in average sub-quadratic time
We describe an exact algorithm for finding the best 2-OPT move which, experimentally, was observed to be much faster than the standard quadratic approach. To analyze its average-case complexity, we introduce a family of heuristic procedures and discuss their complexity when applied to a random tour in graphs whose edge costs are either uniform random numbers in [0, 1] or Euclidean distances between random points in the plane. We prove that, for any probability p: (i) there is a heuristic in the…

This https://arxiv.org/abs/2212.11869 has been replaced.
link: https://scholar.google.com/scholar?q=a

Beyond (and back to) Palatini quadratic gravity and inflation
We study single-field slow-roll inflation embedded in Palatini $F(R)$ gravity where $F(R)$ grows faster than $R^2$. Surprisingly, the consistency of the theory requires the Jordan frame inflaton potential to be unbounded from below. Even more surprisingly, this corresponds to an Einstein frame inflaton potential bounded from below and positive definite. We prove that for all such Palatini $F(R)$'s, there exists a universal strong coupling limit corresponding to a quadratic $F(R)$ with the wrong…

The Prime Geodesic Theorem for the Picard Manifold
Ikuya Kaneko
https://arxiv.org/abs/2403.06626 https://arxiv.org/pdf/2403.06626

The Prime Geodesic Theorem for the Picard Manifold
We prove the prime geodesic theorem for the Picard manifold whose error term shrinks as the hybrid subconvex exponent $θ$ for quadratic Dirichlet $L$-functions over Gaussian integers decreases. Our rate of decay is faster than that of Balkanova-Frolenkov (2022) and Kaneko (2022), and leads to the exponent $\frac{202}{139}+\varepsilon$ in the prime geodesic theorem under the generalised Lindelöf hypothesis $θ= 0$, improving upon the existing conditional results. This provides further solid ev…

The Prime Geodesic Theorem for the Picard Manifold
Ikuya Kaneko
https://arxiv.org/abs/2403.06626 https://arxiv.org/pdf/2403.06626

The Prime Geodesic Theorem for the Picard Manifold
We prove the prime geodesic theorem for the Picard manifold whose error term shrinks as the hybrid subconvex exponent $θ$ for quadratic Dirichlet $L$-functions over Gaussian integers decreases. Our rate of decay is faster than that of Balkanova-Frolenkov (2022) and Kaneko (2022), and leads to the exponent $\frac{202}{139}+\varepsilon$ in the prime geodesic theorem under the generalised Lindelöf hypothesis $θ= 0$, improving upon the existing conditional results. This provides further solid ev…