Results 11 to 20 of about 27,803 (231)
Journal of Symbolic Computation, 2023 We apply methods of machine-learning, such as neural networks, manifold learning and image processing, in order to study 2-dimensional amoebae in algebraic geometry and string theory. With the help of embedding manifold projection, we recover complicated conditions obtained from so-called lopsidedness.
Jiakang Bao, Yang-Hui He, Edward Hirst
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Incorporating Neural Networks into the AMOEBA Polarizable Force Field [PDF]
, 2023 Neural network potentials (NNPs) offer significant promise to bridge the gap be- tween the accuracy of quantum mechanics and the efficiency of molecular mechanics in molecular simulation. Most NNPs rely on the locality assumption that ensures the model’s
Yanxing, Wang +4 more
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Bacterial discrimination by dictyostelid amoebae reveals the complexity of ancient interspecies interactions [PDF]
, 2013 Background Amoebae and bacteria interact within predator-prey and host-pathogen relationships, but the general response of amoeba to bacteria is not well understood.
Juneja, Kavina +10 more
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Pacific Journal of Mathematics, 2022 An amoeba is the image of a subvariety of an algebraic torus under the logarithmic moment map. We consider some qualitative aspects of amoebas, establishing some results and posing problems for further study. These problems include determining the dimension of an amoeba, describing an amoeba as a semi-algebraic set, and identifying varieties whose ...
Nisse, Mounir, Sottile, Frank
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, 2021 Supporting data on amoeba force field parameters for ionic ...
Martin Klajmon (9530864)
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Annals of Mathematics, 2006 We study random surfaces which arise as height functions of random perfect matchings (a.k.a. dimer configurations) on an weighted, bipartite, doubly periodic graph G embedded in the plane. We derive explicit formulas for the surface tension and local Gibbs measure probabilities of these models. The answers involve a certain plane algebraic curve, which
Kenyon, Richard +2 more
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The dimension of an amoeba [PDF]
, 2020 \u3cp\u3eAnswering a question by Nisse and Sottile, we derive a formula for the dimension of the amoeba of an irreducible algebraic variety.\u3c/p ...
Rau, Johannes +3 more
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International Journal of Modern Physics A, 2007 We study a statistical model of random plane partitions. The statistical model has interpretations as five-dimensional [Formula: see text] supersymmetric SU (N) Yang–Mills on ℝ4× S1and as Kähler gravity on local SU (N) geometry. At the thermodynamic limit a typical plane partition called the limit shape dominates in the statistical model.
Maeda, Takashi, Nakatsu, Toshio
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Lopsided approximation of amoebas [PDF]
Mathematics of Computation, 2018 The amoeba of a Laurent polynomial is the image of the corresponding hypersurface under the coordinatewise log absolute value map. In this article, we demonstrate that a theoretical amoeba approximation method due to Purbhoo can be used efficiently in practice.
Jens Forsgård +3 more
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A Nullstellensatz for amoebas [PDF]
Duke Mathematical Journal, 2008 The amoeba of an affine algebraic variety V in (C^*)^r is the image of V under the map (z_1, ..., z_r) -> (log|z_1|, ..., log|z_r|). We give a characterisation of the amoeba based on the triangle inequality, which we call testing for lopsidedness.
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