A Vision Transformer and a convolutional neural network identified Laguerre-Gaussian beam topological charges up to 50 from tiny speckle patches, with the transformer reaching 98.1 percent mean accuracy over three independent test runs.
Recent advances in quantum dot platforms have opened a new platform for realizing Majorana zero modes (MZMs) and simulating topological quantum computation. Here we propose an experimentally feasible setup for implementing topological \(\sqrt{X}\) X -...
Ivy Delaney has been working with neural networks and machine learning since the mid-nineties, back when a couple of hidden layers and a long afternoon of training counted as ambitious. She has watched the field go from academic curiosity to…
Free algebra worksheets with answer keys, from integers and factors to factoring quadratics and systems of equations. Each page focuses on one topic and covers it from the first easy problems to the most challenging ones, with pictures, models, and…
Light can tie knots—literally. Engineers at Duke University have managed to manipulate laser beams to form intricate 3D patterns called optical knots, using custom-designed optics. These twisted beams could one day carry information or measure air turbulence, but researchers discovered…
Ivy Delaney has been working with neural networks and machine learning since the mid-nineties, back when a couple of hidden layers and a long afternoon of training counted as ambitious. She has watched the field go from academic curiosity to…
By Supat Charoensappuech, in collaboration with Gemini 3.6 Flash (October 9, 2026) The author invites all interested readers to join in examining, testing, and critically discussing these ideas. This article is intended as the beginning of a conversation, not the end. 1. Introduction: From…
Two independent Nature experiments guided by Xue-Jia Yu's theory show that topological states can survive at critical points where the energy gap closes.
The source data that support the findings of this study are available from the corresponding author on request. Source data are provided with this paper. The code used to evaluate the conclusions of this study is available from the corresponding…
Topology: A Robust Framework Protected by Topological Invariants To understand the significance of this work, we first need to discuss the concept of topology. However, this framework appears almost entirely incompatible with topological phases of matter. Critical points are gapless,…
Structures and proofs—algebra, number theory, topology, and geometry.
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