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of 94
pro vyhledávání: '"Krone, Robert"'
Phylogenetic networks represent evolutionary histories of sets of taxa where horizontal evolution or hybridization has occurred. Placing a Markov model of evolution on a phylogenetic network gives a model that is particularly amenable to algebraic st
Externí odkaz:
http://arxiv.org/abs/2307.15166
Autor:
Krone, Robert Carlton
The thesis considers two distinct strategies for algebraic computation with polynomials in high dimension. The first concerns ideals and varieties with symmetry, which often arise in applications from areas such as algebraic statistics and optimizati
Externí odkaz:
http://hdl.handle.net/1853/53907
Publikováno v:
J. Softw. Alg. Geom. 12 (2022) 33-41
A primary ideal in a polynomial ring can be described by the variety it defines and a finite set of Noetherian operators, which are differential operators with polynomial coefficients. We implement both symbolic and numerical algorithms to produce su
Externí odkaz:
http://arxiv.org/abs/2101.01002
Autor:
Dressler, Mareike, Krone, Robert
Low-rank matrix completion addresses the problem of completing a matrix from a certain set of generic specified entries. Over the complex numbers a matrix with a given entry pattern can be uniquely completed to a specific rank, called the generic com
Externí odkaz:
http://arxiv.org/abs/2010.09777
Noetherian operators are differential operators that encode primary components of a polynomial ideal. We develop a framework, as well as algorithms, for computing Noetherian operators with local dual spaces, both symbolically and numerically. For a p
Externí odkaz:
http://arxiv.org/abs/2006.13881
Autor:
Krone, Robert, Kubjas, Kaie
Nonnegative matrix factorizations are often encountered in data mining applications where they are used to explain datasets by a small number of parts. For many of these applications it is desirable that there exists a unique nonnegative matrix facto
Externí odkaz:
http://arxiv.org/abs/1902.02868
Publikováno v:
SIAM J. Discrete Math. 33 (2019) no. 3 pp. 1725-1742
The Cayley-Menger variety is the Zariski closure of the set of vectors specifying the pairwise squared distances between $n$ points in $\mathbb{R}^d$. This variety is fundamental to algebraic approaches in rigidity theory. We study the tropicalizatio
Externí odkaz:
http://arxiv.org/abs/1812.09370
Akademický článek
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We describe the typical homological properties of monomial ideals defined by random generating sets. We show that, under mild assumptions, random monomial ideals (RMI's) will almost always have resolutions of maximal length; that is, the projective d
Externí odkaz:
http://arxiv.org/abs/1802.06537
Publikováno v:
In Journal of Symbolic Computation May-June 2022 110:1-23
