Tootfinder

Noise resilience of deterministic analog combinatorial optimization solvers
Clemens Gneiting, Farad Khoyratee, Enrico Rinaldi, Khyati Jain, Rishab Khincha, Franco Nori
https://arxiv.org/abs/2506.12914

Noise resilience of deterministic analog combinatorial optimization solvers
Several continuous dynamical systems have recently been proposed as special-purpose analog computers designed to solve combinatorial optimization problems such as $k$-SAT or the Ising problem. While combinatorial optimization problems are known to be NP-hard, and thus scale, in the worst case, exponentially with the problem size, these analog solvers promise substantial speed-up and scaling advantages in finding the solution. The underlying algorithms, which can be cast in the form of different…

Quasi-Homogeneous Integrable Systems: Free Parameters, Kovalevskaya Exponents, and the Painlev\'e Property
Changyu Zhou, Hayato Chiba
https://arxiv.org/abs/2505.24330

Quasi-Homogeneous Integrable Systems: Free Parameters, Kovalevskaya Exponents, and the Painlevé Property
This paper investigates quasi-homogeneous integrable systems by analyzing their Laurent series solutions near movable singularities, motivated by patterns observed in Kovalevskaya exponents of four-dimensional Painlevé-type equations. We introduce a parameter space encoding the free coefficients in these expansions and study its deformation under a commuting quasi-homogeneous vector field. Within this framework, we derive lower indicial loci from the principal one and establish an arithmetic…