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pro vyhledávání: '"Draisma A"'
A $\mathbf{GL}$-variety is a (typically infinite dimensional) variety modeled on the polynomial representation theory of the general linear group. In previous work, we studied these varieties in characteristic 0. In this paper, we obtain results in p
Externí odkaz:
http://arxiv.org/abs/2406.07415
We prove that the infinite half-spin representations are topologically Noetherian with respect to the infinite spin group. As a consequence we obtain that half-spin varieties, which we introduce, are defined by the pullback of equations at a finite l
Externí odkaz:
http://arxiv.org/abs/2403.10274
We show that the border subrank of a sufficiently general tensor in $(\mathbb{C}^n)^{\otimes d}$ is $\mathcal{O}(n^{1/(d-1)})$ for $n \to \infty$. Since this matches the growth rate $\Theta(n^{1/(d-1)})$ for the generic (non-border) subrank recently
Externí odkaz:
http://arxiv.org/abs/2402.10674
Let $k$ be a Brauer field, that is, a field over which every diagonal form in sufficiently many variables has a nonzero solution; for instance, $k$ could be an imaginary quadratic number field. Brauer proved that if $f_1, \ldots, f_r$ are homogeneous
Externí odkaz:
http://arxiv.org/abs/2401.02067
There are many notions of rank in multilinear algebra: tensor rank, partition rank, slice rank, and strength (or Schmidt rank) are a few examples. Typically the rank $\le r$ locus is not Zariski closed, and understanding the closure (the locus with "
Externí odkaz:
http://arxiv.org/abs/2305.19866
Publikováno v:
BMC Genomics, Vol 25, Iss 1, Pp 1-15 (2024)
Abstract Background Organellar genomes have become increasingly essential for studying genetic diversity, phylogenetics, and evolutionary histories of seaweeds. The order Dictyotales (Dictyotophycidae), a highly diverse lineage within the Phaeophycea
Externí odkaz:
https://doaj.org/article/9b8f40dac387474fabecb96a61b8248c
Given a complex vector subspace $V$ of $\mathbb{C}^n$, the dimension of the amoeba of $V \cap (\mathbb{C}^*)^n$ depends only on the matroid that $V$ defines on the ground set $\{1,\ldots,n\}$. Here we prove that this dimension is given by the minimum
Externí odkaz:
http://arxiv.org/abs/2303.13143
Autor:
Draisma, Jan, Karam, Thomas
We prove that for every positive integer $d \ge 2$ there exist polynomial functions $F_d, G_d: \mathbb{N} \to \mathbb{N}$ such that for each positive integer $r$, every order-$d$ tensor $T$ over an arbitrary field and with partition rank at least $G_
Externí odkaz:
http://arxiv.org/abs/2303.03485
Publikováno v:
Bulletin of Mathematical Biology 86, 33 (2024)
The 3-dimensional (3D) structure of the genome is of significant importance for many cellular processes. In this paper, we study the problem of reconstructing the 3D structure of chromosomes from Hi-C data of diploid organisms, which poses additional
Externí odkaz:
http://arxiv.org/abs/2301.11764
Autor:
Blatter, Andreas1 (AUTHOR), Draisma, Jan2,3 (AUTHOR) jan.draisma@unibe.ch, Ventura, Emanuele4 (AUTHOR)
Publikováno v:
Foundations of Computational Mathematics. Oct2024, Vol. 24 Issue 5, p1567-1593. 27p.