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Mindone: Quadratisches KI-Smartphone mit Gratis-Internet für KI-Tools
Ikko bringt mit dem Mindone ein fast quadratisches Smartphone mit Fokus auf KI-Funktionen und kostenlosem Internet für KI-Anwendungen auf den Markt.

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…

On the density version of quadratic Waring's problem and the quadratic Waring--Goldbach problem
Zi Li Lim
https://arxiv.org/abs/2508.14939 https://arxi…

On the density version of quadratic Waring's problem and the quadratic Waring--Goldbach problem
We prove a sharp density theorem for quadratic Waring's problem over cyclic groups, when the number of variables is at least $5$. Also, we obtain some new improvements on the density version of the quadratic Waring--Goldbach problem over integers.

Quadratic Corrections to the Higher-Spin Equations by the Differential Homotopy Approach
P. T. Kirakosiants, D. A. Valerev, M. A. Vasiliev
https://arxiv.org/abs/2506.16634

Quadratic Corrections to the Higher-Spin Equations by the Differential Homotopy Approach
The recently proposed differential homotopy approach to the analysis of nonlinear higher spin theory is developed. The Ansatz is extended to the form applicable in the second order of the perturbation theory and general star-multiplication formulae are derived. The relation of the shifted homotopy and differential homotopy formalisms is worked out. Projectively-compact spin-local quadratic (anti)holomorphic vertices in the one-form sector of higher-spin equations are obtained within the differe…

Mean-Field Stochastic Linear-Quadratic Optimal Controls: Roles of Expectation and Conditional Expectation Operators
Hanxiao Wang, Jiongmin Yong
https://arxiv.org/abs/2507.16582

Mean-Field Stochastic Linear-Quadratic Optimal Controls: Roles of Expectation and Conditional Expectation Operators
This paper investigates a mean-field linear-quadratic optimal control problem where the state dynamics and cost functional incorporate both expectation and conditional expectation terms. We explicitly derive the pre-committed, na\"ıve, and equilibrium solutions and establish the well-posedness of the associated Riccati equations. This reveals how the expectation and conditional expectation operators influence time-consistency.

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…

Existence of Coupled Optical Vortex Solitons Propagating in a Quadratic Nonlinear Medium
Luciano Medina
https://arxiv.org/abs/2506.16452 https://

Existence of Coupled Optical Vortex Solitons Propagating in a Quadratic Nonlinear Medium
We consider the coupled propagation of an optical field and its second harmonic in a quadratic nonlinear medium governed by a coupled system of Schrodinger equations. We prove the existence of ring-profiled optical vortex solitons appearing as solutions to a constrained minimization problem and as solutions to a min-max problem. In the case of the constrained minimization problem solutions are shown to be positive with undetermined wave propagation constants, but in the min-max approach the wav…

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 …

General Linear-Quadratic Mean Field Stochastic Differential Game with Common Noise: a Direct Method
Yu Si, Jingtao Shi
https://arxiv.org/abs/2506.16779 htt…

General Linear-Quadratic Mean Field Stochastic Differential Game with Common Noise: a Direct Method
This paper investigates a class of general linear-quadratic mean field games with common noise, where the diffusion terms of the system contain the state variables, control variables, and the average state terms. We solve the problem using both the direct method and the fixed-point method in the paper. First, by using the variational method to solve a finite $N$-players game problem, we obtain the necessary and sufficient conditions for the centralized open-loop Nash equilibrium strategy. Subse…