Tootfinder

A Note on the Eilenberg-Mac Lane Isomorphism for Quadratic Forms
C\'esar Galindo
https://arxiv.org/abs/2507.15726 https://arxiv.o…

A Note on the Eilenberg-Mac Lane Isomorphism for Quadratic Forms
We give an elementary proof of the Eilenberg-Mac Lane trace isomorphism between the third 2-abelian cohomology group and quadratic forms. Our approach yields explicit constructions and we characterize when quadratic forms can be expressed as traces of bilinear forms for arbitrary coefficient groups.

Quadrature formulas from rational approximations
Andrew Horning, Lloyd N. Trefethen
https://arxiv.org/abs/2507.14971 https://arxiv.or…

Quadrature formulas from rational approximations
It is shown that quadrature formulas in many different applications can be derived from rational approximation of the Cauchy transform of a weight function. Since rational approximation is now a routine technology, this provides an easy new method to derive all kinds of quadrature formulas as well as fundamental insight into the mathematics of quadrature. Intervals or curves of quadrature nodes correspond to near-optimal branch cuts of the Cauchy transform.

Impact of quadrature measurement on quantum coherence
Luc\'ia \'Alvarez, Alfredo Luis
https://arxiv.org/abs/2507.13735 https://

Impact of quadrature measurement on quantum coherence
We examine the behavior of quadrature coherence under the measurement of the same field quadrature. This is carried out with the help of a beam splitter, that implies the contribution of the field state impinging at the other input port. We examine the case of Gaussian and number states.

Low-Latency Event-Based Velocimetry for Quadrotor Control in a Narrow Pipe
Leonard Bauersfeld, Davide Scaramuzza
https://arxiv.org/abs/2507.15444 https://

Low-Latency Event-Based Velocimetry for Quadrotor Control in a Narrow Pipe
Autonomous quadrotor flight in confined spaces such as pipes and tunnels presents significant challenges due to unsteady, self-induced aerodynamic disturbances. Very recent advances have enabled flight in such conditions, but they either rely on constant motion through the pipe to mitigate airflow recirculation effects or suffer from limited stability during hovering. In this work, we present the first closed-loop control system for quadrotors for hovering in narrow pipes that leverages real-ti…

Gravitational waveforms from inspiraling compact binaries in quadratic gravity and their parameterized post-Einstein characterization
Matheus F. S. Alves, L. G. Medeiros, Davi C. Rodrigues
https://arxiv.org/abs/2507.15571

Gravitational waveforms from inspiraling compact binaries in quadratic gravity and their parameterized post-Einstein characterization
We investigate gravitational waveforms from the inspiral phase of compact binary systems within the framework of quadratic gravity and map their deviations from general relativity into the parameterized post-Einstein (PPE) formalism to constrain the theory parameters. Quadratic gravity generically includes a massive spin-2 ghost, which leads to ill-defined energy and angular momentum fluxes. Following earlier proposals, we remove these unphysical features by imposing a constraint on the massive…

Dual-Channel Adaptive NMPC for Quadrotor under Instantaneous Impact and Payload Disturbances
Xinqi Chen, Xiuxian Li, Min Meng
https://arxiv.org/abs/2507.15261

Dual-Channel Adaptive NMPC for Quadrotor under Instantaneous Impact and Payload Disturbances
Capturing target objects using the quadrotor has gained increasing popularity in recent years, but most studies focus on capturing lightweight objects. The instantaneous contact force generated when capturing objects of a certain mass, along with the payload uncertainty after attachment, will pose significant challenges to the quadrotor control. This paper proposes a novel control architecture, namely Dual-Channel Adaptive Nonlinear Model Predictive Control (DCA-NMPC), which cascades a nonlinea…

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…

On an entropy inequality for quadratic forms and applications
Alex Iosevich, Thang Pham, Nguyen Dac Quan, Steven Senger, Boqing Xue
https://arxiv.org/abs/2507.15196

On an entropy inequality for quadratic forms and applications
Let $ϕ(x,y)$ be a non-degenerate rational quadratic form. Let $X$ and $Y$ be independent $(s, C)$-Frostman random variables whose ranges are contained in $[-c_1, c_1]$, with $0N$. The proof introduces a novel multi-step entropy framework, combining the submodularity formula, the discretized entrop…

RiNNAL : a Riemannian ALM Solver for SDP-RLT Relaxations of Mixed-Binary Quadratic Programs
Di Hou, Tianyun Tang, Kim-Chuan Toh
https://arxiv.org/abs/2507.13776

RiNNAL+: a Riemannian ALM Solver for SDP-RLT Relaxations of Mixed-Binary Quadratic Programs
Doubly nonnegative (DNN) relaxation usually provides a tight lower bound for a mixed-binary quadratic program (MBQP). However, solving DNN problems is challenging because: (1) the problem size is $Ω((n+l)^2)$ for an MBQP with $n$ variables and $l$ inequality constraints, and (2) the rank of optimal solutions cannot be estimated a priori due to the absence of theoretical bounds. In this work, we propose RiNNAL+, a Riemannian augmented Lagrangian method (ALM) for solving DNN problems. We prove t…

Entropy Stable Nodal Discontinuous Galerkin Methods via Quadratic Knapsack Limiting
Brian Christner, Jesse Chan
https://arxiv.org/abs/2507.14488 https://…

Entropy Stable Nodal Discontinuous Galerkin Methods via Quadratic Knapsack Limiting
Lin, Chan (High order entropy stable discontinuous Galerkin spectral element methods through subcell limiting, 2024) enforces a cell entropy inequality for nodal discontinuous Galerkin methods by combining flux corrected transport (FCT)-type limiting and a knapsack solver, which determines optimal limiting coefficients that result in a semi-discrete cell entropy inequality while preserving nodal bounds. In this work, we provide a slight modification of this approach, where we utilize a quadrati…