Tootfinder

A quadratic Abramovich-Bertram formula
Erwan Brugall\'e, Kirsten Wickelgren
https://arxiv.org/abs/2506.17854 https://arxiv.org/pd…

A quadratic Abramovich-Bertram formula
Quadratic Gromov--Witten invariants allow one to obtain an arithmetically meaningful count of curves satisfying constraints over a field $k$ without assuming that $k$ is the field of complex or real numbers. This paper studies the behavior of quadratic genus $0$ Gromov--Witten invariants during an algebraic analogue of surgery on del Pezzo surfaces. For this, we define and study (twisted) binomial coefficients in the Grothendieck--Witt group, building on work of Serre. We obtain a formula expre…

Finite-Horizon Strategy in Infinite-Horizon Linear-Quadratic Discrete-Time Dynamic Games
Shengyuan Huang, Xiaoguang Yang, Yifen Mu, Wenjun Mei
https://arxiv.org/abs/2506.19565

Finite-Horizon Strategy in Infinite-Horizon Linear-Quadratic Discrete-Time Dynamic Games
This paper explores a finite-horizon strategy, ``watching $T$ steps into the future and moving one step now,'' in an $N$-person infinite-horizon discrete-time linear-quadratic dynamic game. The game involves linear input/output/state dynamics and quadratic cost functions with heterogeneous discount factors. For the finite-horizon version, which forms the basis of the infinite-horizon game, we analyze the structure of the coupled generalized discrete Riccati difference equations related to the f…

Instance Space Analysis for the Quadratic Assignment Problem
Jeffrey Christiansen (ARC Training Centre in Optimisation Technologies, Integrated Methodologies and Applications), Kate Smith-Miles (ARC Training Centre in Optimisation Technologies, Integrated Methodologies and Applications)
https://arxiv.org/abs/2506.20172

Instance Space Analysis for the Quadratic Assignment Problem
For any optimisation problem where diverse algorithmic approaches are available, the task of predicting algorithm performance and selecting the algorithm most likely to perform well on a given instance holds great practical interest. However, if our test instances do not adequately represent the potential problem space, we may be misled about the strengths and weaknesses of an algorithm. In this paper we consider algorithm prediction and selection for the Quadratic Assignment Problem (QAP). We …

Sturmian lattices and Aperiodic tile sets
Shigeki Akiyama, Tadahisa Hamada, Katsuki Ito
https://arxiv.org/abs/2506.19362 https://arxi…

Sturmian lattices and Aperiodic tile sets
We give aperiodic tile sets based on Sturmian words of quadratic slopes. The method works for any quadratic irrational slope and we can produce infinitely many aperiodic tile sets whose underlying scaling constant is a unit of any real quadratic field. There are two key ingredients in our construction. The first one is ``Sturmian lattices'', an interesting grid structure generated by Sturmian words that emerged in an aperiodic monotile called Smith Turtle.The second is the bounded displacement …

Explicit Constructions of Sum-Rank Metric Codes from Quadratic Kummer Extensions
Zhu Yunlong, Zhao Chang-An
https://arxiv.org/abs/2506.18653 https://

Explicit Constructions of Sum-Rank Metric Codes from Quadratic Kummer Extensions
This paper presents new constructions of sum-rank metric codes derived from algebraic function fields, while the existing results about such codes remain limited. A central challenge in this field involves the determination of parameters. We address this challenge through quadratic Kummer extensions, and propose two general constructions of $2\times2$ sum-rank codes. The novel sum-rank metric code constructions derived from algebraic function fields demonstrate superior code lengths compared to…

Tunable phase transitions from semimetals to Chern insulators in two-dimensional quadratic-band-crossing materials
Wen-Hao Bian, Jing Wang
https://arxiv.org/abs/2506.19378

Tunable phase transitions from semimetals to Chern insulators in two-dimensional quadratic-band-crossing materials
We systematically investigate how static symmetry-breaking perturbations and dynamic Floquet terms via a polarized light manipulate the topological phase transitions in the two-dimensional quadratic-band-crossing-point (QBCP) materials. The Berry curvature shows distinct behavior in such two situations. It is linearly and quadratically proportional to the product of microstructural parameters $t_{x,z}$ for the former and the latter, respectively. The static perturbation eliminates the QBCP and …

Safety Assurance for Quadrotor Kinodynamic Motion Planning
Theodoros Tavoulareas, Marzia Cescon
https://arxiv.org/abs/2507.17679 https://arxiv.org/pdf/2507…

Safety Assurance for Quadrotor Kinodynamic Motion Planning
Autonomous drones have gained considerable attention for applications in real-world scenarios, such as search and rescue, inspection, and delivery. As their use becomes ever more pervasive in civilian applications, failure to ensure safe operation can lead to physical damage to the system, environmental pollution, and even loss of human life. Recent work has demonstrated that motion planning techniques effectively generate a collision-free trajectory during navigation. However, these methods, w…

Weighted $L^2$ restriction and comparison of nondegeneracy conditions for quadratic manifolds of arbitrary codimensions
Zhenbin Cao, Jingyue Li, Changxing Miao, Yixuan Pang
https://arxiv.org/abs/2506.18657

Weighted $L^2$ restriction and comparison of nondegeneracy conditions for quadratic manifolds of arbitrary codimensions
We systematically study weighted $L^2$ restriction for quadratic manifolds of arbitrary codimensions by sharp uniform Fourier decay estimates and a refinement of the Du-Zhang method. Comparison with prior results is also discussed. In addition,we obtain an almost complete relation diagram for all existing nondegeneracy conditions for quadratic manifolds of arbitrary codimensions. These conditions come from various topics in harmonic analysis related to "curvature": Fourier restriction, decoupli…

Nonconvex Optimization Framework for Group-Sparse Feedback Linear-Quadratic Optimal Control I: Penalty Approach
Lechen Feng, Xun Li, Yuan-Hua Ni
https://arxiv.org/abs/2507.18114

Nonconvex Optimization Framework for Group-Sparse Feedback Linear-Quadratic Optimal Control I: Penalty Approach
This paper develops a unified nonconvex optimization framework for the design of group-sparse feedback controllers in infinite-horizon linear-quadratic (LQ) problems. We address two prominent extensions of the classical LQ problem: the distributed LQ problem with fixed communication topology (DFT-LQ) and the sparse feedback LQ problem (SF-LQ), both of which are motivated by the need for scalable and structure-aware control in large-scale systems. Unlike existing approaches that rely on convex r…

Online Adaptation for Flying Quadrotors in Tight Formations
Pei-An Hsieh, Kong Yao Chee, M. Ani Hsieh
https://arxiv.org/abs/2506.17488 https://

Online Adaptation for Flying Quadrotors in Tight Formations
The task of flying in tight formations is challenging for teams of quadrotors because the complex aerodynamic wake interactions can destabilize individual team members as well as the team. Furthermore, these aerodynamic effects are highly nonlinear and fast-paced, making them difficult to model and predict. To overcome these challenges, we present L1 KNODE-DW MPC, an adaptive, mixed expert learning based control framework that allows individual quadrotors to accurately track trajectories while …