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Tropical Geometry and Machine Learning [PDF]
Proceedings of the IEEE, 2021 Tropical geometry is a relatively recent field in mathematics and computer science, combining elements of algebraic geometry and polyhedral geometry. The scalar arithmetic of its analytic part preexisted in the form of max-plus and min-plus semiring arithmetic used in finite automata, nonlinear image processing, convex analysis, nonlinear control ...
Petros Maragos +2 more
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Geometry in the tropical limit [PDF]
Mathematische Semesterberichte, 2011 Complex algebraic varieties become easy piecewise-linear objects after passing to the so-called tropical limit. Geometry of these limiting objects is known as tropical geometry. In this short survey we take a look at motivation and intuition behind this limit and consider a few simple examples of correspondence principle between classical and tropical ...
Itenberg Ilia, Mikhalkin Grigory
exaly +3 more sources
Tropical geometry of statistical models. [PDF]
Proc Natl Acad Sci U S A, 2004 This article presents a unified mathematical framework for inference in graphical models, building on the observation that graphical models are algebraic varieties. From this geometric viewpoint, observations generated from a model are coordinates of a point in the variety, and the sum-product algorithm is an efficient tool for evaluating specific ...
Pachter L, Sturmfels B.
europepmc +7 more sources
Product-Mix Auctions and Tropical Geometry [PDF]
Mathematics of Operations Research, 2019 In a recent and ongoing work, Baldwin and Klemperer explore a connection between tropical geometry and economics. They give a sufficient condition for the existence of competitive equilibrium in product-mix auctions of indivisible goods. This result, which we call the unimodularity theorem, can also be traced back to the work of Danilov, Koshevoy, and
Ngoc Mai Tran, Josephine Yu
exaly +3 more sources
Tropical geometry of Rado matroids [PDF]
Discrete Mathematics LettersIn this note, we characterize the products of simplicial generators for the Chow ring of a loopless matroid, extending a result of Backman, Eur, and Simpson. We prove that the stable intersection of a collection of tropical hyperplanes centered at the origin with the Bergman fan of a matroid is the Bergman fan of the dual of a certain Rado matroid.
Calum Buchanan, Richard Danner
openaire +3 more sources
Hokkaido Mathematical Journal, 2009 The construction of a tropical hypersurface is given by modeling the classical construction of a complex hypersurface. A tropical meromorphic function of finite type is shown to be a tropical rational function. One also has tropical nullstellensatz.
Grigory Mikhalkin, Eugenii Shustin
exaly +6 more sources
Self-organized criticality and pattern emergence through the lens of tropical geometry [PDF]
Proceedings of the National Academy of Sciences of the United States of America, 2018 Nikita Kalinin +2 more
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Predicting need for heart failure advanced therapies using an interpretable tropical geometry-based fuzzy neural network. [PDF]
PLoS One, 2023 BackgroundTimely referral for advanced therapies (i.e., heart transplantation, left ventricular assist device) is critical for ensuring optimal outcomes for heart failure patients.
Zhang Y +6 more
europepmc +3 more sources
Imputing Phylogenetic Trees Using Tropical Polytopes over the Space of Phylogenetic Trees
Mathematics, 2023 When we apply comparative phylogenetic analyses to genome data, it poses a significant problem and challenge that some of the given species (or taxa) often have missing genes (i.e., data).
Ruriko Yoshida
doaj +1 more source
Clustering Methods over the Tropical Projective Torus
Mathematics, 2023 In this paper, we propose clustering methods for use on data described as tropically convex. Our approach is similar to clustering methods used in the Euclidean space, where we identify groupings of similar observations using tropical analogs of K-means ...
David Barnhill, Ruriko Yoshida
doaj +1 more source