Tootfinder

Algorithmic methods of finite discrete structures. Topological graph drawing (part III)
Sergey Kurapov, Maxim Davidovsky
https://arxiv.org/abs/2506.10936 h…

Algorithmic methods of finite discrete structures. Topological graph drawing (part III)
The manuscript considers mathematical models for creating a topological drawing of a graph based on the methods of G. Ringel's vertex rotation theory. An algorithm is presented for generating a topological drawing of a flat part of a graph based on the selection of a basis for the cycle subspace C(G) using the Monte Carlo method. A steepest descent method for constructing a topological drawing of a flat subgraph is described in the manuscript. The topological drawing of a graph is constructed u…

Exploring Topological Effects in Thin-Film X-Ray Cavities
Hanns Zimmermann, Jonathan Sturm, Ion Cosma Fulga, Jeroen van den Brink, Adriana P\`alffy
https://arxiv.org/abs/2506.10588

Exploring Topological Effects in Thin-Film X-Ray Cavities
Quantum control of single x-ray photons can be achieved using thin-film nanostructure cavities with embedded layers of resonant nuclei. Here, we design and theoretically investigate tailored cavity structures that implement a non-Hermitian version of the Su-Schrieffer-Heeger one-dimensional topological model. By tuning the geometry of the structure, different topological phases can be realized. We show that the presence of topological edge states can be identified in the reflectivity spectra of…

Yupp, which rewards users in crypto for comparing answers from multiple AI models and giving feedback, emerges from stealth with a $33M seed led by a16z crypto (James Hunt/The Block)
https://www.theblock.co/post/358094/a16zcrypto-3…

Topological A-Model for $AdS_5\times S^5$ Superstring and the Maldacena Conjecture
Nathan Berkovits (ICTP-SAIFR/IFT-UNESP, Sao Paulo)
https://arxiv.org/abs/2506.10907

Topological A-Model for $AdS_5\times S^5$ Superstring and the Maldacena Conjecture
A topological A-model constructed from $CP^{3|4}$ supertwistor variables is proposed for the $AdS_5\times S^5$ superstring. At zero $AdS$ radius, free N=4 d=4 super-Yang-Mills amplitudes are reproduced by topological amplitudes of the corresponding gauged linear sigma model where the closed superstring vertex operator for a trace of $k$ super-Yang-Mills fields is described by a boundary state with U(1) worldsheet instanton number $k$. After turning on a Fayet-Iliopoulis term in the sigma m…

Topological defects as effective dynamical dark energy
Haipeng An, Chengcheng Han, Borui Zhang
https://arxiv.org/abs/2506.10075 https://

Topological defects as effective dynamical dark energy
In this work, we consider the possibility that the dynamical dark energy hinted at by recent DESI data may be mimicked by the effects of additional components in the universe, potentially arising from topological defects. We find that the data does not show a particular preference for the existence of cosmic strings. However, a domain wall contribution at the percent level can improve the fit, yielding a $Δχ^2= -1.72$ compared to the $Λ\rm{CDM}$ model. The improvement indicates that topologi…

This https://arxiv.org/abs/1804.05199 has been replaced.
link: https://scholar.google.com/scholar?q=a

A description of the topology of free topological vector spaces
We give a simple description of the topology of free topological vector space $\mathbb{V}(X)$ and the topology of the free locally convex space $L(X)$ over a Tychonoff space $X$. The case when $X$ is a pseudocompact space is also considered.

Exploring Topological and Localization Phenomena in SSH Chains under Generalized AAH Modulation: A Computational Approach
Souvik Ghosh, Sayak Roy
https://arxiv.org/abs/2506.10195 …

Exploring Topological and Localization Phenomena in SSH Chains under Generalized AAH Modulation: A Computational Approach
The Su-Schrieffer-Heeger (SSH) model serves as a canonical example of a one-dimensional topological insulator, yet its behavior under more complex, realistic conditions remains a fertile ground for research. This paper presents a comprehensive computational investigation into generalized SSH models, exploring the interplay between topology, quasi-periodic disorder, non-Hermiticity, and time-dependent driving. Using exact diagonalization and specialized numerical solvers, we map the system's pha…

TED-LaST: Towards Robust Backdoor Defense Against Adaptive Attacks
Xiaoxing Mo, Yuxuan Cheng, Nan Sun, Leo Yu Zhang, Wei Luo, Shang Gao
https://arxiv.org/abs/2506.10722

TED-LaST: Towards Robust Backdoor Defense Against Adaptive Attacks
Deep Neural Networks (DNNs) are vulnerable to backdoor attacks, where attackers implant hidden triggers during training to maliciously control model behavior. Topological Evolution Dynamics (TED) has recently emerged as a powerful tool for detecting backdoor attacks in DNNs. However, TED can be vulnerable to backdoor attacks that adaptively distort topological representation distributions across network layers. To address this limitation, we propose TED-LaST (Topological Evolution Dynamics agai…

Pump.fun raised $500M via a sale of PUMP tokens, which sold out in 12 minutes; it offered 12.5% of its total token supply at a fully diluted valuation of $4B (Zack Abrams/The Block)
https://www.theblock.co/post/362320/pump-fun-raise…

Engineering topological phase transitions via sliding ferroelectricity in MBi2Te4 (M = Ge, Sn, Pb) bilayers
Xinlong Dong, Dan Qiao, Zeyu Li, Zhenhua Qiao, Xiaohong Xu
https://arxiv.org/abs/2506.09317

Engineering topological phase transitions via sliding ferroelectricity in MBi2Te4 (M = Ge, Sn, Pb) bilayers
Materials combining electrically switchable ferroelectricity and tunable topological states hold significant promise for advancing both foundamental quantum phenomena and innovative device architectures. Here, we employ first-principles calculations to systematically investigate the sliding ferroelectricity-mediated topological transitions in bilayer MBi2Te4 (M = Ge, Sn, Pb). By strategically engineering interlayer sliding configurations with oppositely polarized states, we demonstrate reversib…