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ChatGPT for computational topology [PDF]
Found Data SciChatGPT represents a significant milestone in the field of artificial intelligence (AI), finding widespread applications across diverse domains. However, its effectiveness in mathematical contexts has been somewhat constrained by its susceptibility to conceptual errors.
Guowei Wei
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Open-Source Computational Photonics with Auto Differentiable Topology Optimization
Mathematics, 2022 In recent years, technological advances in nanofabrication have opened up new applications in the field of nanophotonics. To engineer and develop novel functionalities, rigorous and efficient numerical methods are required.
Benjamin Vial, Yang Hao
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Computational topology for approximations of knots
Applied General Topology, 2014 The preservation of ambient isotopic equivalence under piecewise linear (PL) approximation for smooth knots are prominent in molecular modeling and simulation.
Ji Li, T. J. Peters, K. E. Jordan
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COMPUTER SYSTEMS SYNTHESIS INSPIRED FROM BIOLOGIC CELLS STRUCTURES [PDF]
Journal of Engineering Science (Chişinău), 2022 This paper deals with a synthesis method of membrane computer systems inspired from the biological cells structure. The functional concept of the computer system is based on the internal structure, chemical transformations and the way of interaction ...
MUNTEANU, Silvia +2 more
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The Journal of Symbolic Logic, 2023 AbstractWe investigate what it means for a (Hausdorff, second-countable) topological group to be computable. We compare several potential definitions based on classical notions in the literature. We relate these notions with the well-established definitions of effective presentability for discrete and profinite groups, and compare our results with ...
Heer Tern Koh +2 more
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A Survey of Topological Machine Learning Methods
Frontiers in Artificial Intelligence, 2021 The last decade saw an enormous boost in the field of computational topology: methods and concepts from algebraic and differential topology, formerly confined to the realm of pure mathematics, have demonstrated their utility in numerous areas such as ...
Felix Hensel +5 more
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Elementary Computable Topology [PDF]
J. Univers. Comput. Sci., 2009 JUCS - Journal of Universal Computer Science Volume Nr.
Weihrauch,Klaus, Grubba,Tanja
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Optimizing the Simplicial-Map Neural Network Architecture
Journal of Imaging, 2021 Simplicial-map neural networks are a recent neural network architecture induced by simplicial maps defined between simplicial complexes. It has been proved that simplicial-map neural networks are universal approximators and that they can be refined to be
Eduardo Paluzo-Hidalgo +3 more
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Topological quantum computation [PDF]
Bulletin of the American Mathematical Society, 2002 The theory of quantum computation can be constructed from the abstract study of anyonic systems. In mathematical terms, these are unitary topological modular functors. They underlie the Jones polynomial and arise in Witten-Chern-Simons theory.
Freedman, Michael H. +3 more
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Knowledge Discovery Using Topological Analysis for Building Sensor Data
Sensors, 2020 Distributed sensor networks are at the heart of smart buildings, providing greater detail and valuable insights into their energy consumption patterns.
Manik Gupta, Nigel Phillips
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