On effective sigma-boundedness and sigma-compactness

We prove several theorems on sigma-bounded and sigma-compact pointsets. We start with a known theorem by Kechris, saying that any lightface \Sigma^1_1 set of the Baire space either is effectively sigma-bounded (that is, covered by a countable union of compact lightface \Delta^1_1 sets), or contains a superperfect subset (and then the set is not sigma-bounded, of course). We add different generalizations of this result, in particular, 1) such that the boundedness property involved includes covering by compact sets and equivalence classes of a given finite collection of lightface \Delta^1_1 equivalence relations, 2) generalizations to lightface \Sigma^1_2 sets, 3) generalizations true in the Solovay model. As for effective sigma-compactness, we start with a theorem by Louveau, saying that any lightface \Delta^1_1 set of the Baire space either is effectively sigma-compact (that is, is equal to a countable union of compact lightface \Delta^1_1 sets), or it contains a relatively closed superperfect subset. Then we prove a generalization of this result to lightface \Sigma^1_1 sets.Comment: arXiv admin note: substantial text overlap with arXiv:1103.106

The complexity of classifying separable Banach spaces up to isomorphism

It is proved that the relation of isomorphism between separable Banach spaces is a complete analytic equivalence relation, i.e., that any analytic equivalence relation Borel reduces to it. Thus, separable Banach spaces up to isomorphism provide complete invariants for a great number of mathematical structures up to their corresponding notion of isomorphism. The same is shown to hold for (1) complete separable metric spaces up to uniform homeomorphism, (2) separable Banach spaces up to Lipschitz isomorphism, and (3) up to (complemented) biembeddability, (4) Polish groups up to topological isomorphism, and (5) Schauder bases up to permutative equivalence. Some of the constructions rely on methods recently developed by S. Argyros and P. Dodos

Investigation of glycosyltransferases from oat

Plants produce a diversity of secondary metabolites crucial for their survival into specific ecological niches. Many of these compounds are glycosides generated by the action of family one UDP-dependant glycosyltransferases (UGTs). Glycosylated products of UGTs are known to be essential for reproductive fitness, defence against pathogens, and signalling; UGTs also have a role in the detoxification of xenobiotics. To date, little is known about monocot UGTs compare to their dicot counterparts, despite their potential role in defence and modification of health-promoting component of cereals essential to human diet. This thesis focuses on identification and functional investigation of UGTs expressed in in the diploid oat species Avena strigosa. Chapters 1 and 2 consist of the General Introduction and Material and Methods, respectively. In chapter 3, a systematic analysis of root-expressed UGTs was carried out using transcriptomic and proteomic approaches. A subset of UGTs was then selected for biochemical analysis. Of particular interest were candidates for glycosylation of avenacin, an antimicrobial triterpenoid glycoside that protects oat against fungi infection. In chapter 4, the sugar donor specificity of the recombinant UGTs and their activity towards different triterpenoid acceptors was investigated. In chapter 5, a transient expression system was established in Nicotiana benthamiana in order to investigate UGT activity. Heterologous co-expression of UGTs with early avenacin biosynthetic pathway enzymes leads to biosynthesis of new-to-nature triterpenoid glycosides, so providing a powerful system for functional analysis of terpene glycosylation in planta. In chapter 6, the catalytic properties of the UGT collection towards different plant natural products was investigated, leading to the production of glycosides of interest. The contribution of this study to the understanding of the evolution and function of monocot UGTs and to their potential commercial exploitation is discussed in the chapter 7

A Classification of Baire Class 1 Functions

We study in this paper various ordinal ranks of (bounded) Baire class 1 functions and we show their essential equivalence. This leads to a natural classification of the class of bounded Baire class 1 functions B_1 in a transfinite hierarchy B^ξ_1 ξ < ω_1) of "small" Baire classes, for which (for example) an analysis similar to the Hausdorff-Kuratowski analysis of Δ^0_2 sets via transfinite differences of closed sets can be carried out. The notions of pseudouniform convergence of a sequence of functions and optimal convergence of a sequence of continuous functions to a Baire class 1 function ƒ are introduced and used in this study

Pre- and postnatal development of adipose depots in meat animals with a specific focus on the pig

Pre- and postnatal development of adipose depots in meat animals with a specific focus on the pig. 65. International Congress of Meat Science and Technology (ICoMST

The Class Of Synthesizable Pseudomeasures

In this paper we study descriptive set theoretic questions related to concepts of harmonic synthesis on the unit circle T, and their relationship with the structure of uniqueness sets

Five Conferences on Undecidability

These five lectures on undecidability were given to students with a good level in mathematics but with no special knowledge on logic. The first conference presents the formalization of mathematics with a short historical survey, the language of first order predicates and the axioms of set theory. The second and third lectures explain the incompleteness phenomena from the Hilbert program until Gödel's theorems with a presentation of the sequent calculus of Gentzen.The fourth talk deepens model theory reasoning in the case of the continuum hypothesis, and the last conference gives examples of effective computability results