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pro vyhledávání: '"Brzezinski, A"'
It is shown that any Lie affgebra, that is an algebraic system consisting of an affine space together with a bi-affine bracket satisfying affine versions of the antisymmetry and Jacobi identity, is isomorphic to a Lie algebra together with an element
Externí odkaz:
http://arxiv.org/abs/2409.01996
Autor:
Chwilczyński, Sebastian, Trębacz, Kacper, Cyganik, Karol, Małecki, Mateusz, Brzezinski, Dariusz
Current interest in deep learning captures the attention of many programmers and researchers. Unfortunately, the lack of a unified schema for developing deep learning models results in methodological inconsistencies, unclear documentation, and proble
Externí odkaz:
http://arxiv.org/abs/2408.16285
Autor:
Brzeziński, Juliusz, Stevens, Jan
Kronecker observed that either all roots or only one root of a solvable irreducible equation of odd prime degree with integer coefficients are real. This gives a possibility to construct specific examples of equations not solvable by radicals. A rela
Externí odkaz:
http://arxiv.org/abs/2406.14221
Lie brackets or Lie affgebra structures on several classes of affine spaces of matrices are studied. These include general normalised affine matrices, special normalised affine matrices, anti-symmetric and anti-hermitian normalised affine matrices an
Externí odkaz:
http://arxiv.org/abs/2403.05142
Connections between heaps of modules and (affine) modules over rings are explored. This leads to explicit, often constructive, descriptions of some categorical constructions and properties that are implicit in universal algebra and algebraic theories
Externí odkaz:
http://arxiv.org/abs/2311.01979
Autor:
Brzeziński, Tomasz
The affine space of traceless complex matrices in which the sum of all elements in every row and every column is equal to one is presented as an example of an affine space with a Lie bracket or a Lie affgebra.
Comment: 8 pages; XL Workshop on Ge
Comment: 8 pages; XL Workshop on Ge
Externí odkaz:
http://arxiv.org/abs/2310.11930
Autor:
Brzeziński, Tomasz, Papworth, James
Lie algebras are extended to the affine case using the heap operation, giving them a definition that is not dependent on the unique element 0, such that they still adhere to antisymmetry and Jacobi properties. It is then looked at how Nijenhuis brack
Externí odkaz:
http://arxiv.org/abs/2310.08979
Autor:
Chevalley, Mathieu, Sackett-Sanders, Jacob, Roohani, Yusuf, Notin, Pascal, Bakulin, Artemy, Brzezinski, Dariusz, Deng, Kaiwen, Guan, Yuanfang, Hong, Justin, Ibrahim, Michael, Kotlowski, Wojciech, Kowiel, Marcin, Misiakos, Panagiotis, Nazaret, Achille, Püschel, Markus, Wendler, Chris, Mehrjou, Arash, Schwab, Patrick
In drug discovery, mapping interactions between genes within cellular systems is a crucial early step. This helps formulate hypotheses regarding molecular mechanisms that could potentially be targeted by future medicines. The CausalBench Challenge wa
Externí odkaz:
http://arxiv.org/abs/2308.15395
Towards Explainable TOPSIS: Visual Insights into the Effects of Weights and Aggregations on Rankings
Multi-Criteria Decision Analysis (MCDA) is extensively used across diverse industries to assess and rank alternatives. Among numerous MCDA methods developed to solve real-world ranking problems, TOPSIS remains one of the most popular choices in many
Externí odkaz:
http://arxiv.org/abs/2306.07706
To every Hopf heap or quantum cotorsor of Grunspan a Hopf algebra of translations is associated. This translation Hopf algebra acts on the Hopf heap making it a Hopf-Galois co-object. Conversely, any Hopf-Galois co-object has the natural structure of
Externí odkaz:
http://arxiv.org/abs/2303.13154