Zonal polynomials via Stanley's coordinates and free cumulants

We study zonal characters which are defined as suitably normalized coefficients in the expansion of zonal polynomials in terms of power-sum symmetric functions. We show that the zonal characters, just like the characters of the symmetric groups, admit a nice combinatorial description in terms of Stanley's multirectangular coordinates of Young diagrams. We also study the analogue of Kerov polynomials, namely we express the zonal characters as polynomials in free cumulants and we give an explicit combinatorial interpretation of their coefficients. In this way, we prove two recent conjectures of Lassalle for Jack polynomials in the special case of zonal polynomials.Comment: 45 pages, second version, important change

Asymptotics of q-Plancherel measures

In this paper, we are interested in the asymptotic size of rows and columns of a random Young diagram under a natural deformation of the Plancherel measure coming from Hecke algebras. The first lines of such diagrams are typically of order $n$, so it does not fit in the context studied by P. Biane and P. \'Sniady. Using the theory of polynomial functions on Young diagrams of Kerov and Olshanski, we are able to compute explicitly the first- and second-order asymptotics of the length of the first rows. Our method works also for other measures, for instance those coming from Schur-Weyl representations.Comment: 27 pages, 5 figures. Version 2: a lot of corrections suggested by anonymous referees have been made. To appear in PTR

Religiosity and spatial demographic differences in the Netherlands

This paper investigates whether current differences in religiosity between the Dutch regions are also manifested in spatial demographic patterns. We use cluster analysis to distinguish relatively homogeneous clusters of regions, specified by religious affiliation and the frequency of churchgoing among their populations. Although the regional demographic differences are relatively modest in the Netherlands, between-clusters contrasts are consistent with the expected influence of religiosity. The cluster including the most conservative region, the so-called Bible Belt, also displays the most traditional demographic patterns. In order to differentiate the impact of religiosity from the social and economic factors, we perform stepwise regression of selected indicators of fertility, union formation and living arrangements. The frequency of churchgoing rather than the fact of belonging to a certain denomination manifested the strongest impact on the regional demographic contrasts. In case of fertility of parity four and higher, marriage rate and the proportion of young women cohabiting, churchgoing turned out to be the most important predictor of regional differentiation.

Gene Delivery by Hydroxyapatite and Calcium Phosphate Nanoparticles: A Review of Novel and Recent Applications

Gene therapy is a targeted therapy which can be used in the treatment of various acquired and inherited diseases. Inhabitation of a gene function, restoring or improving a gene, or gaining a new function can be achieved by gene therapy strategies. The most crucial step in this therapy is delivering the therapeutic material to the target. Nanosized calcium phosphates (CaPs) have been considered as promising carriers due to their excellent biocompatibility. In this chapter, the delivery of DNA, siRNA, and miRNA by using CaP nanocarriers were compiled in detail and the main parameters which can affect the carrier properties and thus the gene transfer efficiency were also discussed

Partial Jucys-Murphy elements and star factorizations

In this paper, we look at the number of factorizations of a given permutation into star transpositions. In particular, we give a natural explanation of a hidden symmetry, answering a question of I.P. Goulden and D.M. Jackson. We also have a new proof of their explicit formula. Another result is the normalized class expansion of some central elements of the symmetric group algebra introduced by P. Biane. To obtain this results, we use natural analogs of Jucys-Murphy elements in the algebra of partial permutations of V. Ivanov and S. Kerov. We investigate their properties and use a formula of A. Lascoux and J.Y. Thibon to give the expansion of their power sums on the natural basis of the invariant subalgebra.Comment: 12 pages; version 2: minor correction