
Algorithms in Linear Algebraic Groups
This paper presents some algorithms in linear algebraic groups. These al...
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Linear Spaces of Symmetric Matrices with NonMaximal Maximum Likelihood Degree
We study the maximum likelihood degree of linear concentration models in...
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BSFskeleton: A Template for Parallelization of Iterative Numerical Algorithms on Cluster Computing Systems
This article describes a method for creating applications for cluster co...
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Computation of Maximal Determinants of Binary Circulant Matrices
We describe algorithms for computing maximal determinants of binary circ...
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Areas on the space of smooth probability density functions on S^2
We present symbolic and numerical methods for computing Poisson brackets...
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Computing Tropical Prevarieties in Parallel
The computation of the tropical prevariety is the first step in the appl...
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Lifts for Voronoi cells of lattices
Many polytopes arising in polyhedral combinatorics are linear projection...
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Parallel Computation of tropical varieties, their positive part, and tropical Grassmannians
In this article, we present a massively parallel framework for computing tropicalizations of algebraic varieties which can make use of finite symmetries. We compute the tropical Grassmannian TGr_0(3,8), and show that it refines the 15dimensional skeleton of the Dressian Dr(3,8) with the exception of 23 special cones for which we construct explicit obstructions to the realizability of their tropical linear spaces. Moreover, we propose algorithms for identifying maximaldimensional tropical cones which belong to the positive tropicalization. These algorithms exploit symmetries of the tropical variety even though the positive tropicalization need not be symmetric. We compute the maximaldimensional cones of the positive Grassmannian TGr^+(3,8) and compare them to the cluster complex of the classical Grassmannian Gr(3,8).
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