Let G be an arbitrary finite group and fix a prime number p. The McKay conjecture asserts that G and the normalizer in G of a Sylow p-subgroup have equal numbers of irreducible characters with degrees not divisible by p. The Alperin-McKay conjecture is version of this as applied to individual Brauer p-blocks of G. We offer evidence that perhaps much stronger forms of both of these conjectures a...

Calculation of the log-normalizer is a major computational obstacle in applications of log-linear models with large output spaces. The problem of fast normalizer computation has therefore attracted significant attention in the theoretical and applied machine learning literature. In this paper, we analyze a recently proposed technique known as “self-normalization”, which introduces a regularizat...

We present a non-deterministic finite-state transducer that acts as a tokenizer and normalizer for free text that is input to a broad-coverage LFG of German. We compare the basic tokenizer used in an earlier version of the grammar and the more sophisticated tokenizer that we now use. The revised tokenizer increases the coverage of the grammar in terms of full parses from 68.3% to 73.4% on sente...

Let A be the automorphism group of the unit interval with its usual order relation, and let B be the embedding of the multiplicative group of positive real numbers into A given by exponentiation. Strict t-norms are in one-to-one correspondence with the right cosets of B in A: Here, we identify the normalizer N of B in A and give explicit formulas for the corresponding set of t-norms.