Recently, V.Ginzburg introduced the notion of a principal nilpotent pair (= pn-pair) in a semisimple Lie algebra g [Gi99]. It is a double counterpart of the notion of a regular nilpotent element in g. A pair e = (e1, e2) ∈ g × g is called nilpotent, if [e1, e2] = 0 and there exists a pair h = (h1, h2) of semisimple elements such that [h1, h2] = 0, [hi, ej ] = δijej (i, j ∈ {1, 2}). A pn-pair e ...

In this section we describe a fundamental result, the Regularity Lemma, proved by Endre Szemerédi in the 70s. The original motivation for proving it has been an application in Combinatorial Number Theory, leading, together with several additional deep ideas, to a complete solution of the Erdős-Turán conjecture discussed in Appendix B.2: every set of integers of positive upper density contains a...

Chemically modified bases are frequently used to stabilize nucleic acids, to study the driving forces for nucleic acid structure formation and to tune DNA and RNA hybridization conditions. In particular, fluorobenzene and fluorobenzimidazole base analogues can act as universal bases able to pair with any natural base and to stabilize RNA duplex formation. Although these base analogues are compa...

We investigate property testing and related questions, where instead of the usual Hamming and edit distances between input strings, we consider the more relaxed edit distance with moves. Using a statistical embedding of words which has similarities with the Parikh mapping, we first construct a tolerant tester for the equality of two words, whose complexity is independent of the string size, and...

for all n large enough with respect to c and d. In a sense, this result is best possible: as shown by Bollobas and Erdos [1], our constant 1/500 cannot be increased beyond 5. Our argument hinges on a theorem asserting that every sufficiently large graph can be partitioned into a small number of classes in such a way that the partition exhibits strong regularity properties. To state the theorem ...

We investigated the effects of JTT-130 on glucose and lipid metabolism independent of the suppression of feeding by comparing with pair-fed animals. Male Zucker diabetic fatty (ZDF) rats were divided into control, JTT-130 treatment, and pair-fed groups. The rats were fed with a regular powdered diet with or without JTT-130 as a food admixture for 6 weeks. We compared the effects on glucose and ...