Tootfinder

Boundary bilinear control of semilinear parabolic PDEs: quadratic convergence of the SQP method
Eduardo Casas, Mariano Mateos
https://arxiv.org/abs/2505.24237

Boundary bilinear control of semilinear parabolic PDEs: quadratic convergence of the SQP method
We analyze a bilinear control problem governed by a semilinear parabolic equation. The control variable is the Robin coefficient on the boundary. First-order necessary and second-order sufficient optimality conditions are derived. A sequential quadratic programming algorithm is then proposed to compute local solutions. Starting the iterations from an initial point in an $L^2$-neighborhood of the local solution we prove stability and quadratic convergence of the algorithm in $L^p$ ($p < \infty$)…

AFP: Russen nahmen im Mai viel Territorium ein
Die russischen Streitkräfte haben im Mai ihren Vormarsch in der Ukraine beschleunigen können. Dies geht aus Berechnungen der Nachrichtenagentur AFP mit Bezug auf Daten des in den USA ansässigen Instituts für Kriegsstudien (ISW) hervor. Demnach besetzte Russland im vergangenen Monat 507 Quadratkilometer. Alleine in der ostukrainischen Region Donezk sollen es fast 400 Quadratkilome…
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Ukraine-Liveblog: ++ Wadephul: Müssen Druck aufrechterhalten ++
Bundesaußenminister Wadephul hat nach einem Treffen mit US-Senator Graham eine gemeinsame harte Linie gegenüber Russlands Präsidenten Putin betont. Friedensforscher mahnen eine Verteidigungsstrategie für Europa an.

Quasi-affine and quasi-quadratic maps of groups with non-abelian targets
Primoz Moravec
https://arxiv.org/abs/2506.01577 https://arxi…

Quasi-affine and quasi-quadratic maps of groups with non-abelian targets
It is shown that the middle quasi-homomorphisms of Fujiwara and Kapovich are precisely constant perturbations of quasi-homomorphisms. Quasi-polynomial maps are defined and their constructibility is explored. In particular, it is shown that a large class of quasi-quadratic maps into torsion-free hyperbolic groups is rigid with respect to bounded perturbations.

Quadratic Segre indices
Felipe Espreafico, Stephen McKean, Sabrina Pauli
https://arxiv.org/abs/2506.01547 https://arxiv.org/pdf/2506.…

Quadratic Segre indices
We prove that the local Euler class of a line on a degree $2n-1$ hypersurface in projective $n+1$ space is given by a product of indices of Segre involutions. Segre involutions and their associated indices were first defined by Finashin and Kharlamov over the reals. Our result is valid over any field of characteristic not 2 and gives an infinite family of problems in enriched enumerative geometry with a shared geometric interpretation for the local type.

This https://arxiv.org/abs/2505.00493 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On the greatest prime factor and uniform equidistribution of quadratic polynomials
We show that the greatest prime factor of $n^2+h$ is at least $n^{1.312}$ infinitely often. This gives an unconditional proof for the range previously known under the Selberg eigenvalue conjecture. Furthermore, we get uniformity in $h \leq n^{1+o(1)}$ under a natural hypothesis on real characters. The same uniformity is obtained for the equidistribution of the roots of quadratic congruences modulo primes. We also prove a variant of the divisor problem for $ax^2+by^3$, which was used by the seco…

Der Hexe Flug zu blanker Nacht
Ihr sichtlich diebisch Freude macht.

This https://arxiv.org/abs/2303.17475 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLG_…

Learning distributed representations with efficient SoftMax normalization
Learning distributed representations, or embeddings, that encode the relational similarity patterns among objects is a relevant task in machine learning. A popular method to learn the embedding matrices $X, Y$ is optimizing a loss function of the term ${\rm SoftMax}(XY^T)$. The complexity required to calculate this term, however, runs quadratically with the problem size, making it a computationally heavy solution. In this article, we propose a linear-time heuristic approximation to compute the …

Reactive Aerobatic Flight via Reinforcement Learning
Zhichao Han, Xijie Huang, Zhuxiu Xu, Jiarui Zhang, Yuze Wu, Mingyang Wang, Tianyue Wu, Fei Gao
https://arxiv.org/abs/2505.24396

Reactive Aerobatic Flight via Reinforcement Learning
Quadrotors have demonstrated remarkable versatility, yet their full aerobatic potential remains largely untapped due to inherent underactuation and the complexity of aggressive maneuvers. Traditional approaches, separating trajectory optimization and tracking control, suffer from tracking inaccuracies, computational latency, and sensitivity to initial conditions, limiting their effectiveness in dynamic, high-agility scenarios. Inspired by recent breakthroughs in data-driven methods, we propose …

This https://arxiv.org/abs/2505.16529 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Modular forms of CM type mod $\ell$
We say that a normalized modular form without complex multiplication is of CM type modulo $\ell$ by an imaginary quadratic field $K$ if its Fourier coefficients $a_p$ are $0$ modulo a prime ideal dividing $\ell$ for every prime $p$ inert in $K$. In this paper, we address the following problem: Given a weight 2 cuspidal Hecke eigenform $f$ without CM which is of CM type modulo $\ell$ by an imaginary quadratic field $K$, does there exist a congruence modulo $\ell$ between $f$ and a genuine CM m…

This https://arxiv.org/abs/2401.06738 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

(Accelerated) Noise-adaptive Stochastic Heavy-Ball Momentum
Stochastic heavy ball momentum (SHB) is commonly used to train machine learning models, and often provides empirical improvements over stochastic gradient descent. By primarily focusing on strongly-convex quadratics, we aim to better understand the theoretical advantage of SHB and subsequently improve the method. For strongly-convex quadratics, Kidambi et al. (2018) show that SHB (with a mini-batch of size $1$) cannot attain accelerated convergence, and hence has no theoretical benefit over SGD…