Adding many Baumgartner clubs

I define a homogeneous ℵ2–c.c. proper product forcing for adding many clubs of ω1 with finite conditions. I use this forcing to build models of b(ω1)=ℵ2, together with d(ω1) and 2ℵ0 large and with very strong failures of club guessing at ω1

Some new directions in infinite-combinatorial topology

We give a light introduction to selection principles in topology, a young subfield of infinite-combinatorial topology. Emphasis is put on the modern approach to the problems it deals with. Recent results are described, and open problems are stated. Some results which do not appear elsewhere are also included, with proofs.Comment: Small update

The combinatorics of the Baer-Specker group

Denote the integers by Z and the positive integers by N. The groups Z^k (k a natural number) are discrete, and the classification up to isomorphism of their (topological) subgroups is trivial. But already for the countably infinite power Z^N of Z, the situation is different. Here the product topology is nontrivial, and the subgroups of Z^N make a rich source of examples of non-isomorphic topological groups. Z^N is the Baer-Specker group. We study subgroups of the Baer-Specker group which possess group theoretic properties analogous to properties introduced by Menger (1924), Hurewicz (1925), Rothberger (1938), and Scheepers (1996). The studied properties were introduced independently by Ko\v{c}inac and Okunev. We obtain purely combinatorial characterizations of these properties, and combine them with other techniques to solve several questions of Babinkostova, Ko\v{c}inac, and Scheepers.Comment: To appear in IJ

Combinatorics of Open Covers VI: Selectors for Sequences of Dense Sets

We consider the following two selection principles for topological spaces: [Principle 1:] { For each sequence of dense subsets, there is a sequence of points from the space, the n-th point coming from the n-th dense set, such that this set of points is dense in the space; [Principle 2:]{ For each sequence of dense subsets, there is a sequence of finite sets, the n-th a subset of the n-th dense set, such that the union of these finite sets is dense in the space. We show that for separable metric space X one of these principles holds for the space C_p(X) of realvalued continuous functions equipped with the pointwise convergence topology if, and only if, a corresponding principle holds for a special family of open covers of X. An example is given to show that these equivalences do not hold in general for Tychonoff spaces. It is further shown that these two principles give characterizations for two popular cardinal numbers, and that these two principles are intimately related to an infinite game that was studied by Berner and Juhasz

Identification of new participants in the rainbow trout (Oncorhynchus mykiss) oocyte maturation and ovulation processes using cDNA microarrays

BACKGROUND: The hormonal control of oocyte maturation and ovulation as well as the molecular mechanisms of nuclear maturation have been thoroughly studied in fish. In contrast, the other molecular events occurring in the ovary during post-vitellogenesis have received far less attention. METHODS: Nylon microarrays displaying 9152 rainbow trout cDNAs were hybridized using RNA samples originating from ovarian tissue collected during late vitellogenesis, post-vitellogenesis and oocyte maturation. Differentially expressed genes were identified using a statistical analysis. A supervised clustering analysis was performed using only differentially expressed genes in order to identify gene clusters exhibiting similar expression profiles. In addition, specific genes were selected and their preovulatory ovarian expression was analyzed using real-time PCR. RESULTS: From the statistical analysis, 310 differentially expressed genes were identified. Among those genes, 90 were up-regulated at the time of oocyte maturation while 220 exhibited an opposite pattern. After clustering analysis, 90 clones belonging to 3 gene clusters exhibiting the most remarkable expression patterns were kept for further analysis. Using real-time PCR analysis, we observed a strong up-regulation of ion and water transport genes such as aquaporin 4 (aqp4) and pendrin (slc26). In addition, a dramatic up-regulation of vasotocin (avt) gene was observed. Furthermore, angiotensin-converting-enzyme 2 (ace2), coagulation factor V (cf5), adam 22, and the chemokine cxcl14 genes exhibited a sharp up-regulation at the time of oocyte maturation. Finally, ovarian aromatase (cyp19a1) exhibited a dramatic down-regulation over the post-vitellogenic period while a down-regulation of Cytidine monophosphate-N-acetylneuraminic acid hydroxylase (cmah) was observed at the time of oocyte maturation. CONCLUSION: We showed the over or under expression of more that 300 genes, most of them being previously unstudied or unknown in the fish preovulatory ovary. Our data confirmed the down-regulation of estrogen synthesis genes during the preovulatory period. In addition, the strong up-regulation of aqp4 and slc26 genes prior to ovulation suggests their participation in the oocyte hydration process occurring at that time. Furthermore, among the most up-regulated clones, several genes such as cxcl14, ace2, adam22, cf5 have pro-inflammatory, vasodilatory, proteolytics and coagulatory functions. The identity and expression patterns of those genes support the theory comparing ovulation to an inflammatory-like reaction