Lie nilpotence in group algebras

Lie nilpotence in group algebra

A Generalization of Girod's Bidirectional Decoding Method to Codes with a Finite Deciphering Delay

Girod's encoding method has been introduced in order to efficiently decode from both directions messages encoded by using finite prefix codes. In the present paper, we generalize this method to finite codes with a finite deciphering delay. In particular, we show that our decoding algorithm can be realized by a deterministic finite transducer. We also investigate some properties of the underlying unlabeled graph

Building mutual trust: a framework project for implementing EU common standards in legal interpreting and translation

This edited volume addresses the establishment of core competencies for legal interpreters and translators(LITs) in the European common area, guides to core interpreter training curricula, the training of interpreter trainers, guidance for judicial professionals on working through legal interpreters and an extensive training materials resource bank

Growth, entropy and commutativity of algebras satisfying prescribed relations

In 1964, Golod and Shafarevich found that, provided that the number of relations of each degree satisfy some bounds, there exist infinitely dimensional algebras satisfying the relations. These algebras are called Golod-Shafarevich algebras. This paper provides bounds for the growth function on images of Golod-Shafarevich algebras based upon the number of defining relations. This extends results from [32], [33]. Lower bounds of growth for constructed algebras are also obtained, permitting the construction of algebras with various growth functions of various entropies. In particular, the paper answers a question by Drensky [7] by constructing algebras with subexponential growth satisfying given relations, under mild assumption on the number of generating relations of each degree. Examples of nil algebras with neither polynomial nor exponential growth over uncountable fields are also constructed, answering a question by Zelmanov [40]. Recently, several open questions concerning the commutativity of algebras satisfying a prescribed number of defining relations have arisen from the study of noncommutative singularities. Additionally, this paper solves one such question, posed by Donovan and Wemyss in [8].Comment: arXiv admin note: text overlap with arXiv:1207.650

MLL-fusion-driven leukemia requires SETD2 to safeguard genomic integrity

MLL-fusions represent a large group of leukemia drivers, whose diversity originates from the vast molecular heterogeneity of C-terminal fusion partners of MLL. While studies of selected MLL-fusions have revealed critical molecular pathways, unifying mechanisms across all MLL-fusions remain poorly understood. We present the first comprehensive survey of protein-protein interactions of seven distantly related MLL-fusion proteins. Functional investigation of 128 conserved MLL-fusion-interactors identifies a specific role for the lysine methyltransferase SETD2 in MLL-leukemia. SETD2 loss causes growth arrest and differentiation of AML cells, and leads to increased DNA damage. In addition to its role in H3K36 tri-methylation, SETD2 is required to maintain high H3K79 di-methylation and MLL-AF9-binding to critical target genes, such as Hoxa9. SETD2 loss synergizes with pharmacologic inhibition of the H3K79 methyltransferase DOT1L to induce DNA damage, growth arrest, differentiation, and apoptosis. These results uncover a dependency for SETD2 during MLL-leukemogenesis, revealing a novel actionable vulnerability in this disease