Decisiveness indices are semiindices: addendum

In the paper Decisiveness indices are semiindices (Freixas and Pons, 2016) it was shown that any decisiveness index obtained from an anonymous probability distribution is a semiindex, and that the converse is not true. In this note we characterize the semiindices which are indices of decisiveness.Peer ReviewedPostprint (author's final draft

Geometry of syzygies via Poncelet varieties

We consider the Grassmannian $\mathbb{G}r(k,n)$ of $(k+1)$-dimensional linear subspaces of V_n=H^0({\P^1},\O_{\P^1}(n)). We define $\frak{X}_{k,r,d}$ as the classifying space of the $k$-dimensional linear systems of degree $n$ on $\P^1$ whose basis realize a fixed number of polynomial relations of fixed degree, say a fixed number of syzygies of a certain degree. The first result of this paper is the computation of the dimension of $\frak{X}_{k,r,d}$. In the second part we make a link between $\frak{X}_{k,r,d}$ and the Poncelet varieties. In particular, we prove that the existence of linear syzygies implies the existence of singularities on the Poncelet varieties

Parallel dictionaries with local rules on AVL and brother trees

We present a set of local rules to deal with dictionaries, having as a main advantage their possible scheduling in a highly synchronized way to get parallel dictionaries on AVLs. Up to now trees used in massively parallel dictionaries needed to have all the leaves at the same depth, such as 2--3 trees. Therefore, it was possible (in insertions and deletions) to reconstruct the tree bottom-up in a very regular fashion, as a pipeline of plane waves moving up. On AVL trees the situation looks different because leaves can have different depth, therefore any wave in a pipeline is highly irregular. To solve this problem we define {\it virtual} plane waves allowing us to develop an EREW dictionary for $k$ keys with $k$ processors and time $O (\log n + \log k)$. Later on we generalize the sePostprint (published version

Hyperplane arrangements of Torelli type

We give a necessary and sufficient condition in order for a hyperplane arrangement to be of Torelli type, namely that it is recovered as the set of unstable hyperplanes of its Dolgachev sheaf of logarithmic differentials. Decompositions and semistability of non-Torelli arrangements are investigated.Comment: 2 Figue

Concurrent rebalancing on hyperred-black trees

The HyperRed-Black trees are a relaxed version of Red-Black trees accepting high degree of concurrency. In the Red-Black trees consecutive red nodes are forbidden. This restriction has been withdrawn in the Chromatic trees. They have been introduced by O.~Nurmi and E.~Soisalon-Soininen to work in a concurrent environment. A Chromatic tree can have big clusters of red nodes surrounded by black nodes. Nevertheless, concurrent rebalancing of Chromatic trees into Red-Black trees has a serious drawback: in big cluster of red nodes only the top node can be updated. Direct updating inside the cluster is forbidden. This approach gives us limited degree of concurrency. The HyperRed-Black trees has been designed to solve this problem. It is possible to update red nodes in the inside of a red cluster. In a HyperRed-Black tree nodes can have a multiplicity of colors; they can be red, black or hyper-red.Postprint (published version

Differential expression of conserved germ line markers and delayed segregation of male and female primordial germ cells in a hermaphrodite, the leech helobdella.

In sexually reproducing animals, primordial germ cells (PGCs) are often set aside early in embryogenesis, a strategy that minimizes the risk of genomic damage associated with replication and mitosis during the cell cycle. Here, we have used germ line markers (piwi, vasa, and nanos) and microinjected cell lineage tracers to show that PGC specification in the leech genus Helobdella follows a different scenario: in this hermaphrodite, the male and female PGCs segregate from somatic lineages only after more than 20 rounds of zygotic mitosis; the male and female PGCs share the same (mesodermal) cell lineage for 19 rounds of zygotic mitosis. Moreover, while all three markers are expressed in both male and female reproductive tissues of the adult, they are expressed differentially between the male and female PGCs of the developing embryo: piwi and vasa are expressed preferentially in female PGCs at a time when nanos is expressed preferentially in male PGCs. A priori, the delayed segregation of male and female PGCs from somatic tissues and from one another increases the probability of mutations affecting both male and female PGCs of a given individual. We speculate that this suite of features, combined with a capacity for self-fertilization, may contribute to the dramatically rearranged genome of Helobdella robusta relative to other animals