Vorträge in der Woche 27.11.2023 bis 03.12.2023
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Mittwoch, 29.11.2023: Ferrers diagram rank-metric codes and a conjecture of Etzion and Silberstein
Mima Stanojkovski (Trento)
Ferrers diagram rank-metric codes were introduced by Etzion and Silberstein in 2009 as linear spaces of matrices defined over a finite field, whose nonzero elements are supported on a given Ferrers diagram and have rank lower bounded by a fixed positive integer d. In the same work, Etzion and Silberstein proposed a conjecture on the largest dimension of a Ferrers diagram rank-metric code in terms of the defining parameters. Since stated, the conjecture has been verified in a number of cases, often requiring additional constraints on the field size or on the minimum rank d in dependence of the corresponding Ferrers diagram. As of today, this conjecture still remains widely open. I will report on joint work with Alessandro Neri and on our proof of the Etzion-Silberstein conjecture for the classes of strictly monotone and MDS-constructible Ferrers diagrams, without any additional restrictions.
| Uhrzeit: | 10:15 |
| Ort: | C5H41 |
| Gruppe: | Oberseminar Kombinatorische Algebraische Geometrie |
| Einladender: | Daniele Agostini, Hannah Markwig |
Donnerstag, 30.11.2023: Robust and accurate dynamical low-rank approximation: From radiation therapy to neural networks
Jonas Kusch (Norwegian University of Life Sciences, Oslo)
While neural networks and radiation therapy appear very unrelated at first, they face the same shortcomings, namely demanding high computational costs and memory footprint. This stems from the fact that training weights in neural networks and evolving the radiation therapy dose in time require solving prohibitively large matrix ODEs. It has, however, been observed that both neural networks and radiation therapy exhibit low-rank structures. In this talk, we discuss the use of dynamical low-rank approximation (DLRA) which has been introduced in [1] to reduce costs and memory requirements in these two application fields. DLRA represents the solution as a low-rank matrix factorization and derives time evolution equations for the factors. Solving these evolution equations requires the construction of robust and efficient time integrators. Our discussion focuses on the parallel integrator [2], which is inherently only first order accurate. We will present a strategy to increase the accuracy of this integrator by an extension of the basis matrices. The talk concludes with a series of numerical experiments for radiation therapy and neural network training. References [1] Koch, O., & Lubich, C. (2007). Dynamical low-rank approximation. SIAM Journal on Matrix Analysis and Applications, 29(2), 434-454. [2] Ceruti, G., Kusch, J., & Lubich, C. (2023). A parallel rank-adaptive integrator for dynamical low-rank approximation. arXiv preprint arXiv:2304.05660.
| Uhrzeit: | 14:15 |
| Ort: | S6 (C5H05) |
| Gruppe: | Oberseminar Numerik |
| Einladender: | Lubich, Prohl |