Tootfinder

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…

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 …

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…

Quantum sensing of displacements with stabilized GKP states
Lautaro Labarca, Sara Turcotte, Alexandre Blais, Baptiste Royer
https://arxiv.org/abs/2506.20627

Quantum sensing of displacements with stabilized GKP states
We demonstrate how recent protocols developed for the stabilization of Gottesman-Kitaev-Preskill (GKP) states can be used for the estimation of two-quadrature displacement sensing, with sensitivities approaching the multivariate quantum Cramer-Rao bound. Thanks to the stabilization, this sensor is backaction evading and can function continuously without reset, making it well suited for the detection of itinerant signals. Additionally, we provide numerical simulations showing that the protocol c…

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 …

Enhanced quantum sensing of gravitational acceleration constant
Giorgio Stucchi, Matteo G. A. Paris
https://arxiv.org/abs/2506.20352 https://

Enhanced quantum sensing of gravitational acceleration constant
We investigate the use of quantum probes to accurately determine the strength of the local gravitational field on Earth. Our findings show that delocalized probes generally outperform localized ones, with the precision enhancement scaling quadratically with the separation between the two wavefunction components. This advantage persists under realistic position measurements, which can achieve precision not too far from the ultimate bound. We also discuss the influence of Earth's surface, demonst…