Tootfinder

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 …

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 …

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 …

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 …

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…

Precision Matrix Regularization in Sufficient Dimension Reduction for Improved Quadratic Discriminant Classification
Derik T. Boonstra, Rakheon Kim, Dean M. Young
https://arxiv.org/abs/2506.19192

Precision Matrix Regularization in Sufficient Dimension Reduction for Improved Quadratic Discriminant Classification
Sufficient dimension reduction (SDR) methods, which often rely on class precision matrices, are widely used in supervised statistical classification problems. However, when class-specific sample sizes are small relative to the original feature-space dimension, precision matrix estimation becomes unstable and, as a result, increases the variability of the linear dimension reduction (LDR) matrix. Ultimately, this fact causes suboptimal supervised classification. To address this problem, we develo…

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…

First moments of a polyhedron clipped by a quadratic cylinder
Valentin Wasquel, Fabien Evrard
https://arxiv.org/abs/2506.18811 https://

First moments of a polyhedron clipped by a quadratic cylinder
This manuscript extends previous work by Evrard et al. [arXiv:2210.07772] on calculating the geometric moments of the intersection between a polyhedron and the domain bounded by a quadratic surface. Specifically, we derive new closed-form expressions for the first geometric moments (i.e., the volume and volume-weighted centroid) of a polyhedron intersecting the interior of an infinite quadratic cylinder, following the same methodology of successive applications of the divergence theorem as in […

DiLQR: Differentiable Iterative Linear Quadratic Regulator via Implicit Differentiation
Shuyuan Wang, Philip D. Loewen, Michael Forbes, Bhushan Gopaluni, Wei Pan
https://arxiv.org/abs/2506.17473

DiLQR: Differentiable Iterative Linear Quadratic Regulator via Implicit Differentiation
While differentiable control has emerged as a powerful paradigm combining model-free flexibility with model-based efficiency, the iterative Linear Quadratic Regulator (iLQR) remains underexplored as a differentiable component. The scalability of differentiating through extended iterations and horizons poses significant challenges, hindering iLQR from being an effective differentiable controller. This paper introduces DiLQR, a framework that facilitates differentiation through iLQR, allowing it …