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

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

The Structure of σ-Ideals of Compact Sets

Motivated by problems in certain areas of analysis, like measure theory and harmonic analysis, where σ-ideals of compact sets are encountered very often as notions of small or exceptional sets, we undertake in this paper a descriptive set theoretic study of σ-ideals of compact sets in compact metrizable spaces. In the first part we study the complexity of such ideals, showing that the structural condition of being a σ-ideal imposes severe definability restrictions. A typical instance is the dichotomy theorem, which states that σ-ideals which are analytic or coanalytic must be actually either complete coanalytic or else G_δ. In the second part we discuss (generators or as we call them here) bases for σ-ideals and in particular the problem of existence of Borel bases for coanalytic non-Borel σ-ideals. We derive here a criterion for the nonexistence of such bases which has several applications. Finally in the third part we develop the connections of the definability properties of σ-ideals with other structural properties, like the countable chain condition, etc

Descriptive Set Theory and Harmonic Analysis

During the 1989 European ASL Summer Meeting in Berlin, the authors gave a series of eight lectures (short course) on the topic of the title. This survey article consists basically of the lecture notes for that course distributed to the participants of that conference. We have purposely tried in this printed version to preserve the informal style of the original notes

Role of framework mutations and antibody flexibility in the evolution of broadly neutralizing antibodies

Eliciting antibodies that are cross reactive with surface proteins of diverse strains of highly mutable pathogens (e.g., HIV, influenza) could be key for developing effective universal vaccines. Mutations in the framework regions of such broadly neutralizing antibodies (bnAbs) have been reported to play a role in determining their properties. We used molecular dynamics simulations and models of affinity maturation to study specific bnAbs against HIV. Our results suggest that there are different classes of evolutionary lineages for the bnAbs. If germline B cells that initiate affinity maturation have high affinity for the conserved residues of the targeted epitope, framework mutations increase antibody rigidity as affinity maturation progresses to evolve bnAbs. If the germline B cells exhibit weak/moderate affinity for conserved residues, an initial increase in flexibility via framework mutations may be required for the evolution of bnAbs. Subsequent mutations that increase rigidity result in highly potent bnAbs. Implications of our results for immunogen design are discussed

Stimulation and Inhibition of Lymphangiogenesis Via Adeno-Associated Viral Gene Delivery

The lymphatic vessels can be selectively stimulated to grow in adult mice, rats and pigs by application of viral vectors expressing the lymphangiogenic factors VEGF-C or VEGF-D. Vice versa, lymphangiogenesis in various pathological settings can be inhibited by the blocking of the VEGF-C/VEGFR3 interaction using a ligand-binding soluble form of VEGFR3. Furthermore, the recently discovered plasticity of meningeal and lacteal lymphatic vessels provides novel opportunities for their manipulation in disease. Adenoviral and adeno-associated viral vectors (AAVs) provide suitable tools for establishing short- and long-term gene expression, respectively and adenoviral vectors have already been used in clinical trials. As an example, we describe here ways to manipulate the meningeal lymphatic vasculature in the adult mice via AAV-mediated gene delivery. The possibility of stimulation and inhibition of lymphangiogenesis in adult mice has enabled the analysis of the role and function of lymphatic vessels in mouse models of disease.Peer reviewe