Tootfinder

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…

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.

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…

Nonlinear Control of a Quadrotor UAV Using Backstepping-Based Sliding Mode Technique
Thien Nhan Vo
https://arxiv.org/abs/2506.14195 https://

Nonlinear Control of a Quadrotor UAV Using Backstepping-Based Sliding Mode Technique
This paper presents the development of a sliding mode controller using the backstepping approach. The controller is employed to synthesize tracking errors and Lyapunov functions. A novel state-space representation is formulated by incorporating the dynamics of the quadrotor and accounting for non-holonomic constraints. The proposed sliding mode controller effectively addresses system nonlinearities and improves tracking of predefined trajectories. Simulation results are presented graphically to…

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…

Stochastic Diagonal Estimation Based on Matrix Quadratic Form Oracles
Haishan Ye, Xiangyu Chang
https://arxiv.org/abs/2506.15360 https://

Stochastic Diagonal Estimation Based on Matrix Quadratic Form Oracles
We study the problem of estimating the diagonal of an implicitly given matrix $\Ab$. For such a matrix we have access to an oracle that allows us to evaluate the matrix quadratic form $ \ub^\top \Ab \ub$. Based on this query oracle, we propose a stochastic diagonal estimation method with random variable $\ub$ drawn from the standard Gaussian distribution. We provide the element-wise and norm-wise sample complexities of the proposed method. Our numerical experiments on different types and dimens…

Positive Sharing and Abstract Machines
Beniamino Accattoli, Claudio Sacerdoti Coen, Jui-Hsuan Wu
https://arxiv.org/abs/2506.14131 https://

Positive Sharing and Abstract Machines
Wu's positive $λ$-calculus is a recent call-by-value $λ$-calculus with sharing coming from Miller and Wu's study of the proof-theoretical concept of focalization. Accattoli and Wu showed that it simplifies a technical aspect of the study of sharing; namely it rules out the recurrent issue of renaming chains, that often causes a quadratic time slowdown. In this paper, we define the natural abstract machine for the positive $λ$-calculus and show that it suffers from an inefficiency: the quad…

On the solvability of some systems of quadratic integral equations in dimensions two and three
Vitali Vougalter
https://arxiv.org/abs/2506.15069 https://…

On the solvability of some systems of quadratic integral equations in dimensions two and three
The work deals with the existence of solutions of a certain system of quadratic integral equations in H^2(R^d,R^N), d = 2, 3. We demonstrate the existence of a perturbed solution by virtue of a fixed point technique.

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…