Polish 2010 growth references for school-aged children and adolescents

Growth references are useful in monitoring a child's growth, which is an essential part of child care. The aim of this paper was to provide updated growth references for Polish school-aged children and adolescents and show the prevalence of overweight and obesity among them. Growth references for height, weight, and body mass index (BMI) were constructed with the lambda, mu, sigma (LMS) method using data from a recent, large, population-representative sample of school-aged children and adolescents in Poland (n = 17,573). The prevalence of overweight and obesity according to the International Obesity Taskforce definition was determined with the use of LMSGrowth software. Updated growth references for Polish school-aged children and adolescents were compared with Polish growth references from the 1980s, the Warsaw 1996–1999 reference, German, and 2000 CDC references. A positive secular trend in height was observed in children and adolescents from 7 to 15 years of age. A significant shift of the upper tail of the BMI distribution occurred, especially in Polish boys at younger ages. The prevalence of overweight or obesity was 18.7% and 14.1% in school-aged boys and girls, respectively. The presented height, weight, and BMI references are based on a current, nationally representative sample of Polish children and adolescents without known disorders affecting growth. Changes in the body size of children and adolescents over the last three decades suggest an influence of the changing economical situation on anthropometric indices

Rationally almost periodic sequences, polynomial multiple recurrence and symbolic dynamics

A set $R\subset \mathbb{N}$ is called rational if it is well approximable by finite unions of arithmetic progressions, meaning that for every \unicode[STIX]{x1D716}>0 there exists a set $B=\bigcup _{i=1}^{r}a_{i}\mathbb{N}+b_{i}$, where $a_{1},\ldots ,a_{r},b_{1},\ldots ,b_{r}\in \mathbb{N}$, such that \begin{eqnarray}\overline{d}(R\triangle B):=\limsup _{N\rightarrow \infty }\frac{|(R\triangle B)\cap \{1,\ldots ,N\}|}{N}0$, then the following are equivalent:(a) $R$ is divisible, i.e. $\overline{d}(R\cap u\mathbb{N})>0$ for all $u\in \mathbb{N}$;(b) $R$ is an averaging set of polynomial single recurrence;(c) $R$ is an averaging set of polynomial multiple recurrence.As an application, we show that if $R\subset \mathbb{N}$ is rational and divisible, then for any set $E\subset \mathbb{N}$ with $\overline{d}(E)>0$ and any polynomials $p_{i}\in \mathbb{Q}[t]$, $i=1,\ldots ,\ell$, which satisfy $p_{i}(\mathbb{Z})\subset \mathbb{Z}$ and $p_{i}(0)=0$ for all $i\in \{1,\ldots ,\ell \}$, there exists $\unicode[STIX]{x1D6FD}>0$ such that the set \begin{eqnarray}\{n\in R:\overline{d}(E\cap (E-p_{1}(n))\cap \cdots \cap (E-p_{\ell }(n)))>\unicode[STIX]{x1D6FD}\}\end{eqnarray} has positive lower density.Ramsey-theoretical applications naturally lead to problems in symbolic dynamics, which involve rationally almost periodic sequences (sequences whose level-sets are rational). We prove that if ${\mathcal{A}}$ is a finite alphabet, $\unicode[STIX]{x1D702}\in {\mathcal{A}}^{\mathbb{N}}$ is rationally almost periodic, $S$ denotes the left-shift on ${\mathcal{A}}^{\mathbb{Z}}$ and \begin{eqnarray}X:=\{y\in {\mathcal{A}}^{\mathbb{Z}}:\text{each word appearing in}~y~\text{appears in}~\unicode[STIX]{x1D702}\},\end{eqnarray}$$ then \unicode[STIX]{x1D702} is a generic point for an $S$-invariant probability measure \unicode[STIX]{x1D708} on $X$ such that the measure-preserving system (X,\unicode[STIX]{x1D708},S) is ergodic and has rational discrete spectrum