Tootfinder

RiNNAL : a Riemannian ALM Solver for SDP-RLT Relaxations of Mixed-Binary Quadratic Programs
Di Hou, Tianyun Tang, Kim-Chuan Toh
https://arxiv.org/abs/2507.13776

RiNNAL+: a Riemannian ALM Solver for SDP-RLT Relaxations of Mixed-Binary Quadratic Programs
Doubly nonnegative (DNN) relaxation usually provides a tight lower bound for a mixed-binary quadratic program (MBQP). However, solving DNN problems is challenging because: (1) the problem size is $Ω((n+l)^2)$ for an MBQP with $n$ variables and $l$ inequality constraints, and (2) the rank of optimal solutions cannot be estimated a priori due to the absence of theoretical bounds. In this work, we propose RiNNAL+, a Riemannian augmented Lagrangian method (ALM) for solving DNN problems. We prove t…

In #München startet in der alten #Paketposthalle das größte #Lastenrad-Zentrum Deutschlands.
Auf 2000 Quadratmetern werden Lieferungen für die „letzte Meile“ von

Lastenrad-Zentrum eröffnet in München im Keller der alten Paketposthalle
In der alten Paketposthalle in München entsteht auf 2000 Quadratmetern ein Logistikzentrum für Lastenfahrräder.

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.

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…

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…

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…

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.

A High-Order Quadrature Method for Implicitly Defined Hypersurfaces and Regions
Zibo Zhao
https://arxiv.org/abs/2506.13078 https://ar…

A High-Order Quadrature Method for Implicitly Defined Hypersurfaces and Regions
This paper presents a high-order accurate numerical quadrature algorithm for evaluating integrals over curved surfaces and regions defined implicitly via a level set of a given function restricted to a hyperrectangle. The domain is divided into small tetrahedrons, and by employing the change of variables formula, the approach yields an algorithm requiring only one-dimensional root finding and standard Gaussian quadrature. The resulting quadrature scheme guarantees strictly positive weights and …

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…

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…