Tootfinder

Linear Convergence of a Unified Primal--Dual Algorithm for Convex--Concave Saddle Point Problems with Quadratic Growth
Cody Melcher, Afrooz Jalilzadeh, Erfan Yazdandoost Hamedani
https://arxiv.org/abs/2510.11990

Linear Convergence of a Unified Primal--Dual Algorithm for Convex--Concave Saddle Point Problems with Quadratic Growth
In this paper, we study saddle point (SP) problems, focusing on convex-concave optimization involving functions that satisfy either two-sided quadratic functional growth (QFG) or two-sided quadratic gradient growth (QGG)--novel conditions tailored specifically for SP problems as extensions of quadratic growth conditions in minimization. These conditions relax the traditional requirement of strong convexity-strong concavity, thereby encompassing a broader class of problems. We propose a generali…

On the Walsh spectra of quadratic APN functions
Sophie Hannah B\'en\'eteau, Nicolas Goluboff, Lukas K\"olsch, Divyesh Vaghasiya
https://arxiv.org/abs/2510.12008 htt…

On the Walsh spectra of quadratic APN functions
APN functions play a central role as building blocks in the design of many block ciphers, serving as optimal functions to resist differential attacks. One of the most important properties of APN functions is their linearity, which is directly related to the Walsh spectrum of the function. In this paper, we establish two novel connections that allow us to derive strong conditions on the Walsh spectra of quadratic APN functions. We prove that the Walsh transform of a quadratic APN function $F$ op…

A Unidirectionally Connected FAS Approach for 6-DOF Quadrotor Control
Weijie Ren, Haowen Liu, Guang-Ren Duan
https://arxiv.org/abs/2510.12360 https://arxiv…

A Unidirectionally Connected FAS Approach for 6-DOF Quadrotor Control
This paper proposes a unidirectionally connected fully actuated system (UC-FAS) approach for the sub-stabilization and tracking control of 6-DOF quadrotors, tackling limitations both in state-space and FAS framework to some extent. The framework systematically converts underactuated quadrotor dynamics into a UC-FAS model, unifying the existing different FAS transformation ways. By eliminating estimation of the high-order derivatives of control inputs, a drawback of current methods, the UC-FAS m…

An elementary derivation of 3-cycles for a quadratic map
Arpad Benyi, Ioan Casu
https://arxiv.org/abs/2510.12558 https://arxiv.org/pdf/2510.12558

An elementary derivation of 3-cycles for a quadratic map
We present an elementary derivation of the period-three cycles for the real quadratic map $x\mapsto x^2+c$, a fundamental model in one-dimensional discrete dynamics. Using symmetric polynomials, we obtain a complete algebraic characterization of 3-cycles and determine explicit conditions for their existence and stability, without reliance on computer algebra. Through conjugacy with the logistic map, we recover the classical threshold values of the logistic parameter corresponding to the emergen…

On the quadratic complexity of subsets of $\mathbb{F}_p^n$ of bounded $\mathrm{VC_{2}}$-dimension
C. Terry, J. Wolf
https://arxiv.org/abs/2510.12767 https://

On the quadratic complexity of subsets of $\mathbb{F}_p^n$ of bounded $\mathrm{VC_{2}}$-dimension
In prior work, we showed that subsets of $\mathbb{F}_{p}^{n}$ of $\mathrm{VC_{2}}$-dimension at most $k$ are well approximated by a union of atoms of a quadratic factor of complexity $(\ell,q)$, where the complexity $\ell$ of the linear part and the complexity $q$ of the quadratic part are both bounded in terms of $k$, $p$, and the desired level of approximation $μ$. A key tool in the proof of this result was an arithmetic regularity lemma for the Gowers $U^3$-norm by Green and Tao, which resu…

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Implementing the Quantum Approximate Optimization Algorithms for QUBO problems Across Quantum Hardware Platforms: Performance Analysis, Challenges, and Strategies
Teemu Pihkakoski, Aravind Plathanam Babu, Pauli Taipale, Petri Liimatta, Matti Silveri
https://arxiv.org/abs/2510.12336

Implementing the Quantum Approximate Optimization Algorithms for QUBO problems Across Quantum Hardware Platforms: Performance Analysis, Challenges, and Strategies
Quantum computers are expected to offer significant advantages in solving complex optimization problems that are challenging for classical computers. Quadratic Unconstrained Binary Optimization (QUBO) problems represent an important class of problems with relevance in finance and logistics. The Quantum Approximate Optimization Algorithm (QAOA) is a prominent candidate for solving QUBO problems on near-term quantum devices. In this paper, we investigate the performance of both the standard QAOA …

Learning Robust Agile Flight Control with Stability Guarantees
Lukas Pries, Markus Ryll
https://arxiv.org/abs/2510.12611 https://arxiv.org/pdf/2510.12611…

Learning Robust Agile Flight Control with Stability Guarantees
In the evolving landscape of high-speed agile quadrotor flight, achieving precise trajectory tracking at the platform's operational limits is paramount. Controllers must handle actuator constraints, exhibit robustness to disturbances, and remain computationally efficient for safety-critical applications. In this work, we present a novel neural-augmented feedback controller for agile flight control. The controller addresses individual limitations of existing state-of-the-art control paradigms an…

Superradiance and Superabsorption Engine of $N$ Two-Level Systems: $N^{2}$-Power Scaling at Near-Unity Efficiency
L. F. Alves da Silva, H. Sanchez, M. A. Ponte, M. H. Y. Moussa, Norton G. de Almeida
https://arxiv.org/abs/2510.12017

Superradiance and Superabsorption Engine of $N$ Two-Level Systems: $N^{2}$-Power Scaling at Near-Unity Efficiency
We present a thermal engine that exploits the \emph{cooperative superradiance} and \emph{superabsorption} of a sample of \(N\) two-level atoms. This engine operates using a single cold reservoir via cycles of collective pumping followed by decay. Using an effective mean-field Hamiltonian to describe the many-body dynamics, we design optimized drive pulses that preserve adiabaticity and achieve an average power output scaling quadratically with the system size, \(P \propto N^2\). An experimental…