Tootfinder

Cooperative Circumnavigation for Multi-Quadrotor Systems via Onboard Sensing
Xueming Liu, Lin Li, Xiang Zhou, Qingrui Zhang, Tianjiang Hu
https://arxiv.org/abs/2506.20954

Cooperative Circumnavigation for Multi-Quadrotor Systems via Onboard Sensing
A cooperative circumnavigation framework is proposed for multi-quadrotor systems to enclose and track a moving target without reliance on external localization systems. The distinct relationships between quadrotor-quadrotor and quadrotor-target interactions are evaluated using a heterogeneous perception strategy and corresponding state estimation algorithms. A modified Kalman filter is developed to fuse visual-inertial odometry with range measurements to enhance the accuracy of inter-quadrotor …

Runge--Kutta generalized Convolution Quadrature for sectorial problems
Jing Guo, Maria Lopez-Fernandez
https://arxiv.org/abs/2506.21242 https://

Runge--Kutta generalized Convolution Quadrature for sectorial problems
We study the application of the generalized convolution quadrature (gCQ) based on Runge--Kutta methods to approximate the solution of an important class of sectorial problems. The gCQ generalizes Lubich's original convolution quadrature (CQ) to variable steps. High-order versions of the gCQ have been developed in the last decade, relying on certain Runge--Kutta methods. The Runge--Kutta based gCQ has been studied so far in a rather general setting, which includes applications to boundary integr…

Upper bounds on class numbers of real quadratic fields
Riccardo Bernardini
https://arxiv.org/abs/2506.21301 https://arxiv.org/pdf/250…

Upper bounds on class numbers of real quadratic fields
We prove that, for any $\varepsilon>0$, the number of real quadratic fields $\mathbb{Q}(\sqrt{d})$ of discriminant $d

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 …

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…

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 …

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…

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 …

More about solutions of quadratic equations
Wolf-Dieter Richter
https://arxiv.org/abs/2506.20429 https://arxiv.org/pdf/2506.20429

More about solutions of quadratic equations
For polynomials of degree two which have no zeros, the method of accompanying variables is developed and zeros of associated vector polynomials are determined. Our flexible method uses a wide variety of possible vector-valued vector squaring methods and can be adopted to a wide variety of application situations. Known solutions are made much more precise by replacing the imaginary component and supplemented by introducing a whole class of new vector solutions. Circular, generalized circular and…

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 …