ESTIMATION OF THE CENTRAL MOMENTS OF A RANDOM VECTOR BASED ON THE DEFINITION OF THE POWER OF A VECTOR

The moments of a random vector based on the definition of the power of a vector, proposed by J. Tatar, are scalar and vector characteristics of a multivariate distribution. Analogously to the univariate case, we distinguish the uncorrected and the central moments of a random vector. Other characteristics of a multivariate distribution, i.e. an index of skewness and kurtosis, have been introduced by using the central moments of a random vector. For the application of the mentioned quantities for the analysis of multivariate empirical data, it appears desirable to construct their respective estimators. This paper presents the consistent estimators of the central moments of a random vector, for which essential characteristics have been found, such as a mean vector and a mean squared error. In these formulas, the relevant orders of approximation have been taken into account

Estymacja momentów zwykłych wektora losowego opartych na definicji potęgi wektora

In this paper we propose the consistent and unbiased estimators of the raw (uncorrected) moments of a random vector, moments that are based on the definition of the power of a vector. For the distributions of the estimators we find essential characteristics, such as mean vector, variance or total variance. We also calculate the covariance and the covariance matrix between the relevant sample raw moments. Moreover, the asymptotic behaviour of their central moments of even orders are established.W artykule przedstawione zostały zgodne i nieobciążone estymatory momentów zwykłych wektora losowego opartych na definicji potęgi wektora. Wyznaczono podstawowe charakterystyki dla ich rozkładów takie jak wektor wartości oczekiwanych, wariancja lub wariancja całkowita. Obliczono także postaci kowariancji lub macierzy kowariancji miedzy odpowiednimi momentami w próbie wielowymiarowej. Ponadto ustalone zostało asymptotyczne tempo wzrostu ich momentów centralnych parzystych rzędów

Influence of glucocorticoids and glucocorticoid receptor gene polymorphisms on glucose metabolism

U ludzi glikokortykosteroidy (GS) regulują szeroki zakres funkcji fizjologicznych, w tym różnicowanie komórek, metabolizm i reakcje zapalne. Hormony te odgrywają ważną rolę w utrzymywaniu podstawowej homeostazy ustroju oraz odpowiedzi na stres. Ponadto GS stanowią jeden z najbardziej rozpowszechnionych związków terapeutycznych stosowanych w leczeniu chorób zapalnych, autoimmunologicznych i układu limfatycznego. Według klasycznego, genomowego modelu GS działają poprzez wewnątrzkomórkowy receptor glikokortykosteroidów (hGR) i bezpośrednio lub pośrednio regulują transkrypcję genów i syntezę białek odpowiedzialnych za proces zapalny. Zmiany w działaniu hGR mogą mieć istotne znaczenie dla wielu procesów biologicznych, takich jak behawioralne i fi­zjologiczne reakcje na stres, reakcje immunologiczne i zapalne, proces snu, a także podstawowe funkcje, takie jak wzrost i rozmnażanie czy odpowiedź na leczenie. Glikokortykosteroidy należą do hormonów antagonistycznych w stosunku do insuliny i odgrywa­ją istotną rolę w regulacji homeostazy metabolizmu glukozy. In humans glucocorticoids (GS) regulate a broad spectrum of physiologic functions, including cell differentiation, metabolism and inflammatory re­sponses. These hormones play an important role in the maintenance of basal and stress-related homeo­stasis. Furthermore, glucocorticoids represent one of the most widely used therapeutic compounds in the treatment of inflammatory, autoimmune and lymp­hoproliferative disorders. According to the classic genomic model GS bind to intracellular receptors (hGR) and directly or indirectly regulate gene transcription and synthesis of proteins responsible for inflammatory process. Alterations in hGR action may have important implications for many critical biological processes, such as the behavioral and physiologic responses to stress, the immune and inflammatory reaction, the process of sleep, as well as basic functions, such as growth and reproduction, or response to treatment. Glucocorti­coids belong to the antagonistic hormons compared to insulin and play an important role in maintaining the homeostasis of glucose metabolism

Massive burn > 90% of body surface – case report

Severe burns are life-threatening injuries very difficult to heal. Multidisciplinary treatment is necessary due to complicated pathophysiological cascades induced by massive tissue destruction. Children and elderly people are especially endangered in being burnt. We present case of 73 years old woman with massive burn injury of >90% body surface

Manipulacja: pedagogiczno-społeczne aspekty. Cz. 1, Interdyscyplinarne aspekty manipulacji

Praca recenzowana / peer-reviewed pape

Mutations in Radial Spoke Head Genes and Ultrastructural Cilia Defects in East-European Cohort of Primary Ciliary Dyskinesia Patients

Primary ciliary dyskinesia (PCD) is a rare (1/20,000), multisystem disease with a complex phenotype caused by the impaired motility of cilia/flagella, usually related to ultrastructural defects of these organelles. Mutations in genes encoding radial spoke head (RSPH) proteins, elements of the ciliary ultrastructure, have been recently described. However, the relative involvement of RSPH genes in PCD pathogenesis remained unknown, due to a small number of PCD families examined for mutations in these genes. The purpose of this study was to estimate the involvement of RSPH4A and RSPH9 in PCD pathogenesis among East Europeans (West Slavs), and to shed more light on ultrastructural ciliary defects caused by mutations in these genes. The coding sequences of RSPH4A and RSPH9 were screened in PCD patients from 184 families, using single strand conformational polymorphism analysis and sequencing. Two previously described (Q109X; R490X) and two new RSPH4A mutations (W356X; IVS3_2–5del), in/around exons 1 and 3, were identified; no mutations were found in RSPH9. We estimate that mutations in RSPH4A, but not in RSPH9, are responsible for 2–3% of cases in the East European PCD population (4% in PCD families without situs inversus; 11% in families preselected for microtubular defects). Analysis of the SNP-haplotype background provided insight into the ancestry of repetitively found mutations (Q109X; R490X; IVS3_2–5del), but further studies involving other PCD cohorts are required to elucidate whether these mutations are specific for Slavic people or spread among other European populations. Ultrastructural defects associated with the mutations were analyzed in the transmission electron microscope images; almost half of the ciliary cross-sections examined in patients with RSPH4A mutations had the microtubule transposition phenotype (9+0 and 8+1 pattern). While microtubule transposition was a prevalent ultrastructural defect in cilia from patients with RSPH4A mutations, similar defects were also observed in PCD patients with mutations in other genes

Excess Kurtosis of a Random Vector

Excess kurtosis of a univariate random variable is defined as its kurtosis minus 3, i.e. the kurtosis of a normal distribution. Excess kurtosis is a one of a dispersion measures. This parameter provides the information about peakedness and tail weight of a distribution compared to normal distribution. In the paper we propose a generalization of this characteristic for random vectors and analyze its basic properties. Moreover, we introduce the form of excess kurtosis for the selected multivariate distribution