Tootfinder

Torsion in Persistent Homology and Neural Networks
Maria Walch
https://arxiv.org/abs/2506.03049 https://arxiv.org/pdf/2506.03049

Torsion in Persistent Homology and Neural Networks
We explore the role of torsion in hybrid deep learning models that incorporate topological data analysis, focusing on autoencoders. While most TDA tools use field coefficients, this conceals torsional features present in integer homology. We show that torsion can be lost during encoding, altered in the latent space, and in many cases, not reconstructed by standard decoders. Using both synthetic and high-dimensional data, we evaluate torsion sensitivity to perturbations and assess its recoverabi…

Many phases in a hairy box in three dimensions
Shoichiro Miyashita
https://arxiv.org/abs/2506.20528 https://arxiv.org/pdf/2506.20528

Many phases in a hairy box in three dimensions
In this paper, I investigate gravitational thermodynamics of the Einstein-Maxwell-scalar system in three dimensions without a cosmological constant. In the previous work by Krishnan,Shekhar, and Bala Subramanian (Nucl. Phys. B 958 (2020) 115115 [33]), it was argued that this system has no BH saddles, but has only empty (flat space) saddles and boson star saddles. It was then concluded that the structure of the thermodynamic phase space is much simpler than in the higher dimensional cases. I wil…

High-throughput Super-Resolution Imaging Chip based on Miniaturized Full-frequency Encoded-illumination
Xiaoyu Yang (State Key Laboratory of Extreme Photonics and Instrumentation, College of Optical Science and Engineering, Zhejiang University, Hangzhou, China, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Zhejiang University, Hangzhou, China, Department of Chemical Engineering and Biotechnology, University of Cambridge, Cambridge, UK), Haonan Zhang (State Key Lab…

High-throughput Super-Resolution Imaging Chip based on Miniaturized Full-frequency Encoded-illumination
A miniaturized full-frequency encoded illumination (mini-FEI) chip is presented for high-throughput super-resolution imaging using the spatial frequency shift (SFS) effect. A tunable full SFS scheme is achieved through propagating and evanescent wave. The multi-illumination modes are precisely and flexibly modulated by an encoded LED array. The light travels to the sample via a set of prisms, producing the super-resolution images with high signal-to-noise ratio (SNR). Mini-FEI super-resolution …