The bi-Poisson process: a quadratic harness

This paper is a continuation of our previous research on quadratic harnesses, that is, processes with linear regressions and quadratic conditional variances. Our main result is a construction of a Markov process from given orthogonal and martingale polynomials. The construction uses a two-parameter extension of the Al-Salam--Chihara polynomials and a relation between these polynomials for different values of parameters.Comment: Published in at http://dx.doi.org/10.1214/009117907000000268 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Recursive Neyman Algorithm for Optimum Sample Allocation under Box Constraints on Sample Sizes in Strata

The optimal sample allocation in stratified sampling is one of the basic issues of modern survey sampling methodology. It is a procedure of dividing the total sample among pairwise disjoint subsets of a finite population, called strata, such that for chosen survey sampling designs in strata, it produces the smallest variance for estimating a population total (or mean) of a given study variable. In this paper we are concerned with the optimal allocation of a sample, under lower and upper bounds imposed jointly on the sample strata-sizes. We will consider a family of sampling designs that give rise to variances of estimators of a natural generic form. In particular, this family includes simple random sampling without replacement (abbreviated as SI) in strata, which is perhaps, the most important example of stratified sampling design. First, we identify the allocation problem as a convex optimization problem. This methodology allows to establish a generic form of the optimal solution, so called optimality conditions. Second, based on these optimality conditions, we propose new and efficient recursive algorithm, named RNABOX, which solves the allocation problem considered. This new algorithm can be viewed as a generalization of the classical recursive Neyman allocation algorithm, a popular tool for optimal sample allocation in stratified sampling with SI design in all strata, when only upper bounds are imposed on sample strata-sizes. We implement the RNABOX in R as a part of our package stratallo, which is available from the Comprehensive R Archive Network (CRAN). Finally, in the context of the established optimality conditions, we briefly discuss two existing methodologies dedicated to the allocation problem being studied: the noptcond algorithm introduced in Gabler, Ganninger and M\"unnich (2012); and fixed iteration procedures from M\"unnich, Sachs and Wagner (2012)

Stem photosynthesis : a key element of grass pea (Lathyrus sativus L.) acclimatisation to salinity

Grass pea (Lathyrus sativus) is a leguminous plant of outstanding tolerance to abiotic stress. The aim of the presented study was to describe the mechanism of grass pea (Lathyrus sativus L.) photosynthetic apparatus acclimatisation strategies to salinity stress. The seedlings were cultivated in a hydroponic system in media containing various concentrations of NaCl (0, 50, and 100 mM), imitating none, moderate, and severe salinity, respectively, for three weeks. In order to characterise the function and structure of the photosynthetic apparatus, Chl a fluorescence, gas exchange measurements, proteome analysis, and Fourier-transform infrared spectroscopy (FT-IR) analysis were done inter alia. Significant differences in the response of the leaf and stem photosynthetic apparatus to severe salt stress were observed. Leaves became the place of harmful ion (Na+) accumulation, and the efficiency of their carboxylation decreased sharply. In turn, in stems, the reconstruction of the photosynthetic apparatus (antenna and photosystem complexes) activated alternative electron transport pathways, leading to effective ATP synthesis, which is required for the efficient translocation of Na+ to leaves. These changes enabled efficient stem carboxylation and made them the main source of assimilates. The observed changes indicate the high plasticity of grass pea photosynthetic apparatus, providing an effective mechanism of tolerance to salinity stress

Semigroups of distributions with linear Jacobi parameters

We show that a convolution semigroup of measures has Jacobi parameters polynomial in the convolution parameter $t$ if and only if the measures come from the Meixner class. Moreover, we prove the parallel result, in a more explicit way, for the free convolution and the free Meixner class. We then construct the class of measures satisfying the same property for the two-state free convolution. This class of two-state free convolution semigroups has not been considered explicitly before. We show that it also has Meixner-type properties. Specifically, it contains the analogs of the normal, Poisson, and binomial distributions, has a Laha-Lukacs-type characterization, and is related to the $q=0$ case of quadratic harnesses.Comment: v3: the article is merged back together with arXiv:1003.4025. A significant revision following suggestions by the referee. 2 pdf figure

Pro Libris: Lubuskie Pismo Literacko-Kulturalne, nr 4 (2008)

172 s. : il

Pro Libris: Lubuskie Pismo Literacko-Kulturalne, nr 2 (2009)

123 s. : il.

Pro Libris: Lubuskie Pismo Literacko-Kulturalne, nr 3 (2008)

152 s. : il.