Tootfinder

Quadratic Chabauty Experiments on Genus 2 Bielliptic Modular Curves in the LMFDB
Kate Finnerty
https://arxiv.org/abs/2507.03784 https://

Quadratic Chabauty Experiments on Genus 2 Bielliptic Modular Curves in the LMFDB
We present results of quadratic Chabauty experiments on genus 2 bielliptic modular curves of Jacobian rank 2 that have recently been added to the LMFDB. We apply quadratic Chabauty methods over both the rationals and quadratic imaginary fields. In a number of cases, the experiments yielded algebraic irrational points among the set of mock rational points. We highlight specific notable examples, including the non-split Cartan modular curve $X^+_{ns}(15)$. Lastly, we offer a conjecture relating t…

Class groups of imaginary quadratic points on $X_1(16)$
Maarten Derickx
https://arxiv.org/abs/2507.04604 https://arxiv.org/pdf/2507.0…

Class groups of imaginary quadratic points on $X_1(16)$
The main result is to show that if $K \ncong \mathbb Q(\sqrt{-15})$ is an imaginary quadratic field and $E$ is an elliptic curve over $K$ with a torsion point of order 16, then the class number of $K$ is divisible by 10. This gives an affirmative answer to a 12 year old question by David Krumm. This is done by setting up a more general framework for studying divisibility of class groups of imaginary quadratic points on hyper-elliptic curves and applying it to $X_1(16)$.

Benchmarking Spiking Neurons for Linear Quadratic Regulator Control of Multi-linked Pole on a Cart: from Single Neuron to Ensemble
Shreyan Banerjee, Luna Gava, Aasifa Rounak, Vikram Pakrashi
https://arxiv.org/abs/2507.03621

Benchmarking Spiking Neurons for Linear Quadratic Regulator Control of Multi-linked Pole on a Cart: from Single Neuron to Ensemble
The emerging field of neuromorphic computing for edge control applications poses the need to quantitatively estimate and limit the number of spiking neurons, to reduce network complexity and optimize the number of neurons per core and hence, the chip size, in an application-specific neuromorphic hardware. While rate-encoding for spiking neurons provides a robust way to encode signals with the same number of neurons as an ANN, it often lacks precision. To achieve the desired accuracy, a populati…

teaching a transformer net to approximate ray-tracing
input is a sequence of triangle data (limited to 4k triangles), and a sequence of 8x8 radiance pixels representing the camera (limited to 512x512 resolution)
output is a sequence of 8x8 pixels of the rendered scene. training was ~10 days. generation is ~100ms (NVIDIA A100)
the results are pretty good. scaling will be a challenge (since transformers are quadratic in sequence length)

This https://arxiv.org/abs/2504.15265 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

Realization of maximally-entangling two-qutrit gates using the Cross-Resonance scheme
In this letter, we present a comprehensive theoretical framework for realizing maximally entangling two-qutrit gates on fixed-frequency transmons that generalize the qubit-centric cross-resonance (CR) interaction beyond the 0-1 subspace, which we call as generalized cross-resonance (GCR) scheme. We use the GCR scheme to design parametric two-qutrit gates, namely, $U_{CR}^{01}$ and $U_{CR}^{12}$, that act on the $0{-}1$ and $1{-}2$ energy transitions of transmons, respectively. Our gates improve…

Higher differentiability for solutions to stationary $p$-Stokes systems under sub-quadratic growth conditions
Anna Cavagnoli
https://arxiv.org/abs/2507.03499

Higher differentiability for solutions to stationary $p$-Stokes systems under sub-quadratic growth conditions
We consider weak solutions $(u,π):\mathbb{R}^n\supsetΩ\to\ \mathbb{R}^n\times\ \mathbb{R}$ to stationary $p$-Stokes systems of the type \[ \begin{cases} -\mathrm{div} (a(\mathcal{E} u))+\nablaπ=f \\ \mathrm{div}(u)=0, \end{cases} \] in $Ω,$ where the function $a(ξ)$ satisfies $p$-growth conditions in $ξ$. By $\mathcal{E} u$ we denote the symmetric part of the gradient $Du$. In this setting, we establish results on the fractional higher differentiability of both the symmetric part of the…

On the construction of a gradient method of quadratic optimization, optimal from the point of view of minimizing the distance to the exact solution
N. V. Pletnev
https://arxiv.org/abs/2506.04866

On the construction of a gradient method of quadratic optimization, optimal from the point of view of minimizing the distance to the exact solution
Problems of quadratic optimization in Hilbert space often arise when solving ill-posed problems for differential equations. In this case, the target value of the functional is known. In addition, the structure of the functional allows calculating the gradient by solving well-posed problems, which allows applying first-order methods. This article is devoted to the construction of the $m$-moment minimum error method -- an effective method that minimizes the distance to the exact solution. The con…

Dass die Kantone und der Bund danach lechzen, unsere Daten zu ausländischen Cloudprovidern zu schicken, das ist ja schon länger ein Thema, nicht nur bei DNIP.
https://dnip.ch/2025/05/21/der-microso

Learned Controllers for Agile Quadrotors in Pursuit-Evasion Games
Alejandro Sanchez Roncero, Olov Andersson, Petter Ogren
https://arxiv.org/abs/2506.02849 …

Learned Controllers for Agile Quadrotors in Pursuit-Evasion Games
The increasing proliferation of small UAVs in civilian and military airspace has raised critical safety and security concerns, especially when unauthorized or malicious drones enter restricted zones. In this work, we present a reinforcement learning (RL) framework for agile 1v1 quadrotor pursuit-evasion. We train neural network policies to command body rates and collective thrust, enabling high-speed pursuit and evasive maneuvers that fully exploit the quadrotor's nonlinear dynamics. To mitigat…

Control Synthesis Along Uncertain Trajectories Using Integral Quadratic Constraints
Felix Biert\"umpfel, Peter Seiler, Harald Pfifer
https://arxiv.org/abs/2507.03101

Control Synthesis Along Uncertain Trajectories Using Integral Quadratic Constraints
The paper presents a novel approach to synthesize robust controllers for nonlinear systems along perturbed trajectories. The approach linearizes the system with respect to a reference trajectory. In contrast to existing methods rooted in robust linear time-varying synthesis, the approach accurately includes perturbations that drive the system away from the reference trajectory. Hence, the controller obtained in the linear framework provides a significantly more robust nonlinear performance. The…