Tootfinder

Weak TransNet: A Petrov-Galerkin based neural network method for solving elliptic PDEs
Zhihang Xu, Min Wang, Zhu Wang
https://arxiv.org/abs/2506.14812 http…

Weak TransNet: A Petrov-Galerkin based neural network method for solving elliptic PDEs
While deep learning has achieved remarkable success in solving partial differential equations (PDEs), it still faces significant challenges, particularly when the PDE solutions have low regularity or singularities. To address these issues, we propose the Weak TransNet (WTN) method, based on a Petrov-Galerkin formulation, for solving elliptic PDEs in this work, though its framework may extend to other classes of equations. Specifically, the neural feature space defined by TransNet (Zhang et al.,…

Enkidu: Universal Frequential Perturbation for Real-Time Audio Privacy Protection against Voice Deepfakes
Zhou Feng, Jiahao Chen, Chunyi Zhou, Yuwen Pu, Qingming Li, Tianyu Du, Shouling Ji
https://arxiv.org/abs/2507.12932

Enkidu: Universal Frequential Perturbation for Real-Time Audio Privacy Protection against Voice Deepfakes
The rapid advancement of voice deepfake technologies has raised serious concerns about user audio privacy, as attackers increasingly exploit publicly available voice data to generate convincing fake audio for malicious purposes such as identity theft, financial fraud, and misinformation campaigns. While existing defense methods offer partial protection, they face critical limitations, including weak adaptability to unseen user data, poor scalability to long audio, rigid reliance on white-box kn…

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LP Relaxations for Routing and Wavelength Assignment with Partial Path Protection: Formulations and Computations
Xianyan Yang, Junyan Liu, Fan Zhang, Fabo Sun, Feng Li, Zhou Xu
https://arxiv.org/abs/2506.12838

LP Relaxations for Routing and Wavelength Assignment with Partial Path Protection: Formulations and Computations
As a variant of the routing and wavelength assignment problem (RWAP), the RWAP with partial path protection (RWAP-PPP) designs a reliable optical-fiber network for telecommunications. It assigns paths and wavelengths to meet communication requests, not only in normal working situations but also in potential failure cases where an optical link fails. The literature lacks efficient relaxations to produce tight lower bounds on the optimal objective value of the RWAP-PPP. Consequently, the solution…

Rieffel projections and 2-by-2 matrices
Olivier Isely, Alain Valette
https://arxiv.org/abs/2506.12640 https://arxiv.org/pdf/2506.1264…

Rieffel projections and 2-by-2 matrices
For a compact space $Y$, we view $C(Y\times S^1)$ as the crossed product $C(Y)\rtimes\mathbb{Z}$, with $\mathbb{Z}$ acting trivially. This allows us to study Rieffel projections in $M_2(C(Y\times S^1))$: we characterize them and compute their image under the projection $\partial_0:K_0(C(Y\times S^1))\rightarrow K_1(C(Y))$. We provide a new Rieffel projection in $M_2(C(\mathbb{T}^2))$, different from Loring's one, and involving only trigonometric polynomials plus the square root of $2-e^{2πiθ}…

Unser #Fachinformationsdienst

YSO Jets Driven by Magnetic Pressure Generated through Stellar Magnetosphere-Disk Interaction
Yisheng Tu, Zhi-Yun Li, Zhaohuan Zhu, Xiao Hu, Chun-Yen Hsu
https://arxiv.org/abs/2506.11333

YSO Jets Driven by Magnetic Pressure Generated through Stellar Magnetosphere-Disk Interaction
The origin of jets in young stellar objects (YSOs) remains a subject of active investigation. We present a 3D non-ideal magnetohydrodynamic simulation of jet launching in YSOs, focusing on the interaction between the stellar magnetosphere and the circumstellar disk. At the beginning of the simulation, the magnetosphere partially opens, forming two oppositely directed magnetic field regions: one threading the star and the other threading the inner disk. The latter dominates over the original dis…

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Deutschlands Freelancer schauen zunehmend über den Tellerrand – und das aus gutem Grund! 🌍
Zum Artikel: https://heise.de/-10474098

Partial independent transversals in multipartite graphs
Penny Haxell, Arpit Mittal, Yi Zhao
https://arxiv.org/abs/2506.09515 https://…

Partial independent transversals in multipartite graphs
Given integers $r>d\ge 0$ and an $r$-partite graph, an independent $(r-d)$-transversal or $(r-d)$-IT is an independent set of size $r-d$ that intersects each part in at most one vertex. We show that every $r$-partite graph with maximum degree $Δ$ and parts of size $n$ contains an $(r-d)$-IT if $n> 2Δ(1-\frac{1}{q})$, provided $q= \lfloor \frac{r}{d+1}\rfloor\ge \frac{4r}{4d+5}$. This is tight when $q$ is even and extends a classical result of Haxell in the $d=0$ case. When $q= \lfloor \frac{r…

Partial character tables for $\mathbb{Z}_\ell$-spetses
Radha Kessar, Gunter Malle, Jason Semeraro
https://arxiv.org/abs/2507.08502 https://

Partial character tables for $\mathbb{Z}_\ell$-spetses
Let ${\mathbb{G}}$ be a simply connected ${\mathbb{Z}}_\ell$-spets, let $q$ be a prime power, prime to $\ell$ and let $S$ be the underlying Sylow $\ell$-subgroup. Firstly, motivated by known formulae for values of Deligne-Lusztig characters of finite reductive groups, we propose a formula for the values of the unipotent characters of ${\mathbb{G}}(q)$ on the elements of $S$. Using this, we explicitly list the unipotent character values of the ${\mathbb{Z}}_2$-spets $G_{24}(q)$ related to the Be…