Tootfinder

Existence of Coupled Optical Vortex Solitons Propagating in a Quadratic Nonlinear Medium
Luciano Medina
https://arxiv.org/abs/2506.16452 https://

Existence of Coupled Optical Vortex Solitons Propagating in a Quadratic Nonlinear Medium
We consider the coupled propagation of an optical field and its second harmonic in a quadratic nonlinear medium governed by a coupled system of Schrodinger equations. We prove the existence of ring-profiled optical vortex solitons appearing as solutions to a constrained minimization problem and as solutions to a min-max problem. In the case of the constrained minimization problem solutions are shown to be positive with undetermined wave propagation constants, but in the min-max approach the wav…

Tighter Error Bounds for the qDRIFT Algorithm
I. J. David, I. Sinayskiy, F. Petruccione
https://arxiv.org/abs/2506.17199 https://arxi…

Tighter Error Bounds for the qDRIFT Algorithm
Randomized algorithms such as qDRIFT provide an efficient framework for quantum simulation by sampling terms from a decomposition of the system's generator. However, existing error bounds for qDRIFT scale quadratically with the norm of the generator, limiting their efficiency for large-scale closed or open quantum system simulation. In this work, we refine the qDRIFT error bound by incorporating Jensen's inequality and a careful treatment of the integral form of the error. This yields an improv…

„Streuobstwiese der Gemeinde xy“. Es sind ein paar hundert Quadratmeter Fläche, darauf eine gute Handvoll in exaktem Raster gepflanzte Apfelbäume auf kurz geschorenem, englischem Rasen. Mit Wiese hat das leider recht wenig zu tun. #vorpommern

Intersection numbers between horizontal foliations of quadratic differentials
Dragomir Saric, Taro Shima
https://arxiv.org/abs/2506.14943 https://

Intersection numbers between horizontal foliations of quadratic differentials
We establish that the intersection number between the horizontal foliations of any two finite-area holomorphic quadratic differentials on an arbitrary Riemann surface is finite. Our main result shows that the intersection number is jointly continuous in the $L^1$-norm on the quadratic differentials. A corollary is that the Jenkins-Strebel differentials are not dense in the space of all finite-area holomorphic quadratic differentials when the infinite Riemann surface is not parabolic.

On quadratic persistence and Pythagoras numbers of totally real projective varieties
Jong In Han, Jaewoo Jung, Euisung Park
https://arxiv.org/abs/2506.13247

On quadratic persistence and Pythagoras numbers of totally real projective varieties
In this paper, we study the relationship between quadratic persistence and the Pythagoras number of totally real projective varieties. Building upon the foundational work of Blekherman et al. in arXiv:1902.02754, we extend their characterizations of arithmetically Cohen-Macaulay varieties with next-to-maximal quadratic persistence to arbitrary case. Our main result classifies totally real non-aCM varieties of codimension $c$ and degree $d$ that exhibit next-to-maximal quadratic persistence in t…

Linearithmic Clean-up for Vector-Symbolic Key-Value Memory with Kroneker Rotation Products
Ruipeng Liu, Qinru Qiu, Simon Khan, Garrett E. Katz
https://arxiv.org/abs/2506.15793

Linearithmic Clean-up for Vector-Symbolic Key-Value Memory with Kroneker Rotation Products
A computational bottleneck in current Vector-Symbolic Architectures (VSAs) is the ``clean-up'' step, which decodes the noisy vectors retrieved from the architecture. Clean-up typically compares noisy vectors against a ``codebook'' of prototype vectors, incurring computational complexity that is quadratic or similar. We present a new codebook representation that supports efficient clean-up, based on Kroneker products of rotation-like matrices. The resulting clean-up time complexity is linearithm…

Quadrotor Morpho-Transition: Learning vs Model-Based Control Strategies
Ioannis Mandralis, Richard M. Murray, Morteza Gharib
https://arxiv.org/abs/2506.14039

Quadrotor Morpho-Transition: Learning vs Model-Based Control Strategies
Quadrotor Morpho-Transition, or the act of transitioning from air to ground through mid-air transformation, involves complex aerodynamic interactions and a need to operate near actuator saturation, complicating controller design. In recent work, morpho-transition has been studied from a model-based control perspective, but these approaches remain limited due to unmodeled dynamics and the requirement for planning through contacts. Here, we train an end-to-end Reinforcement Learning (RL) controll…

Probing quadratic gravity with black-hole ringdown gravitational waves measured by LIGO-Virgo-KAGRA detectors
Adrian Ka-Wai Chung, Nicol\'as Yunes
https://arxiv.org/abs/2506.14695

Probing quadratic gravity with black-hole ringdown gravitational waves measured by LIGO-Virgo-KAGRA detectors
Quadratic gravity theories emerge as the low-energy limit of many grand-unified and quantum-gravity theories. We report the first gravitational-wave ringdown constraints on such theories obtained purely from the quasinormal-mode spectra of rapidly-spinning black-hole remnants. We find no quadratic-gravity signatures from ringdown signals measured by the LIGO-Virgo-KAGRA detectors, thereby constraining the coupling length scale of axi-dilaton gravity below 34 km, dynamical Chern-Simons gravity b…

Sequence Modeling for Time-Optimal Quadrotor Trajectory Optimization with Sampling-based Robustness Analysis
Katherine Mao, Hongzhan Yu, Ruipeng Zhang, Igor Spasojevic, M Ani Hsieh, Sicun Gao, Vijay Kumar
https://arxiv.org/abs/2506.13915

Sequence Modeling for Time-Optimal Quadrotor Trajectory Optimization with Sampling-based Robustness Analysis
Time-optimal trajectories drive quadrotors to their dynamic limits, but computing such trajectories involves solving non-convex problems via iterative nonlinear optimization, making them prohibitively costly for real-time applications. In this work, we investigate learning-based models that imitate a model-based time-optimal trajectory planner to accelerate trajectory generation. Given a dataset of collision-free geometric paths, we show that modeling architectures can effectively learn the pat…

Spherically Symmetric Potentials in Quadratic $f(R)$ Gravity
Roger Anderson Hurtado
https://arxiv.org/abs/2506.15123 https://arxiv.or…

Spherically Symmetric Potentials in Quadratic $f(R)$ Gravity
We study the gravitational potential arising from static, spherically symmetric sources in a modified gravity theory described by a quadratic $f(R)$ model. The linearized field equations lead to a fourth-order differential equation, whose solution includes Newtonian and Yukawa-like terms. Imposing regularity at the origin and asymptotic flatness fixes all integration constants, making the potential fully determined by the mass distribution. We analyze classical profiles such as Plummer, Hernqui…