A few problems connected with invariantmeasures of Markov maps : verication of some claims and opinions that circulate inthe literature

We begin with the celebrated result of [3]. The authors were well aware that their result cannot be extended to expanding transformations with countably many one-to-one pieces in a simple way (see Th. 2, and the comment below on Cond. (17) there). The real task in that period of time was to find reasonable additional conditions which would guarantee the existence of density invariant under the action of expanding map with countably many one-to-one pieces. Several attempts was made to accomplish that task (for more details see e.g. a review article [4], and also [5], or [6], Sect. 6). One of the mentioned attempts was published in [7], as Adler’s Theorem. Since no proof was given there, the question arose whether it is true [8]. A solution was published in [1], and [2]. After the above two notes and a few other ones, related with them, were published, some further claims and opinions concerning the existence of invariant densities and their lower and upper bounds for Markov Maps appear in the literature. Those claims and opinions reveal that their authors were unacquainted with the essence of the problem. That problem is rather of delicate nature. It involves, among other things, the so-called measure-theoretic recurrence property. In this note we clear up, in a systematic way, the essence of the problems with the aid of examples, comments and some published results

Prognostic value of assessment of stool and serum IL-1Β, IL-1ra and IL-6 concentrations in children with active and inactive ulcerative colitis

Introduction: Interleukin-1b (IL-1b), interleukin-1 receptor antagonist (IL-1ra) and interleukin-6 (IL-6) contribute to the pathogenesis of ulcerative colitis (UC). The aim of our study was to evaluate the serum and stool IL-1b, IL-1ra and IL-6 concentrations as potential prognostic factors in children with UC. Material and methods: Thirty-eight children with UC (20 active, 18 inactive) and 14 healthy controls were prospectively included in the study. IL-1b, IL-1ra and IL-6 concentrations were measured in serum and stool supernatants at inclusion to the study using ELISA immunoassays. The children were followed up over 5 years, and at each follow-up clinical disease activity, quantity and severity of relapses, nutritional status, endoscopic and histopathologic activity, disease complications and the treatment regimen were evaluated. Results: In children with active and inactive UC who had relapsed during a 5-year follow-up period compared to the non-relapse groups we found significantly increased serum IL-1b (1.34 vs. 0.98 pg/ml, p < 0.05, and 1.02 vs. 0.68 pg/ml, p < 0.01, respectively,) and IL-1ra (718.0 vs. 453.2 pg/ml, p < 0.05, and 567.4 vs. 365.1 pg/ml, p < 0.01, respectively). Additionally, in children who had experienced complications during a 5-year follow-up period we observed significantly increased serum and stool IL-1b (p < 0.05) and serum IL-1ra (p < 0.01) compared to the group without complications. Conclusions: We concluded that serum IL-1b and IL-1ra and to a lesser extend stool IL-1b concentrations may be useful prognostic factors in children with active and inactive UC over a short-term follow-up period, which may help to identify children that require more aggressive therapy due to an increased risk of relapse or complications resulting from UC

Effect of selected factors on the serum 25(OH)D concentration in women treated for breast cancer

Maintaining an optimal vitamin D concentration reduces the risk of recurrence and extends survival time in patients after breast cancer treatment. Data on vitamin D deficiency among Polish women after breast cancer therapy are limited. Thus, the aim of the study was the analysis of vitamin D status in post-mastectomy patients, considering such factors as seasons, social habits, vitamin D supplementation and its measurements. The study involved 94 women after breast cancer treatment. Serum vitamin D concentration was measured, and a questionnaire, gathering demographic and clinical data regarding cancer, diet, exposure to sun radiation, and knowledge of recommendations on vitamin D supplementation, was delivered twice, in both winter and in summer. The control group consisted of 94 age-matched women with no oncological history. In women after breast cancer treatment, 25-hydroxyvitamin D (25(OH)D) deficiency was much more frequent than in the general population. Only about half of the patients supplemented vitamin D at the beginning of the study. After the first test and the issuing of recommendations on vitamin D supplementation, the percentage of vitamin D supplemented patients increased by about 30% in study groups. The average dose of supplement also increased. None of the women that were not supplementing vitamin D and were tested again in winter had optimal 25(OH)D concentration. It was concluded that vitamin deficiency is common in women treated for breast cancer. Medical advising about vitamin D supplementation and monitoring of 25(OH)D concentration should be improved

The role of Insulin-like Growth Factor 1, Receptor Activator for Nuclear Factor κB ligand — Osteoprotegerin system, Interleukin 6 and 1β in post-transplantation bone metabolic disease in childhood

Wstęp: Znanych jest kilka czynników mogących mieć wpływ na zaburzenia kostne obserwowane często po przeszczepieniu komórekkrwiotwórczych (PKK). Ich dokładna etiopatogeneza pozostaje jednak wciąż nie znana, szczególnie u pacjentów po PKK przebytym wdzieciństwie. Celem pracy była ocena surowiczych stężeń: IGF-1, RANKL, OPG, IL-6 i IL1β oraz ich korelacji z gęstością mineralną kości(BMD) u dzieci i młodzieży po PKK.Materiał i metody: Do badań włączono 35 pacjentów w średnim wieku 8,48 ± 5,18 lat po allogenicznych (N = 21) i autologicznych (N = 14)PKK. Próbki krwi pobierano przed PKK, w dniu transplantacji, 3 i 6 miesięcy po PKK, a następnie co rok przez 2–8 lat. Stężenia IGF-1,RANKL, OPG, IL-1β, IL-6 oznaczane były metodami immunochemicznymi. BMD całego ciała oceniane było metodą DEXA (dual-energyX-ray absorptiometry) 6 miesięcy po PKK, a następnie co rocznie.Wyniki: Stwierdzono ujemne wartości Z-core dla BMD u wszystkich pacjentów. Były one znacząco wyższe u pacjentów po autologicznychniż po allogenicznych PKK. Surowicze stężenia IGF-1 i IL-6 znamiennie zmieniały się w czasie po PKK. Stężenia IGF-1 wzrastały od 2.roku po PKK, zaś IL-6 narastały do 12. miesiąca po PKK. Obserwowano również dynamiczne, chociaż nieznamienne zmiany stężeń OPG iRANKL po PKK. Wykazano korelacje RANKL i IGF-1 z BMD. IL-6 korelowała pozytywnie z IL-1β, obie interleukiny nie korelowały z BMD.Wnioski: Stwierdzono istotne i dynamiczne zmiany czynników mogących mieć wpływ na metabolizm kostny po transplantacji.Sugeruje się, że surowicze stężenia RANKL i IGF-1 mogą być markerami metabolizmu kostnego po PKK u dzieci i młodzieży.Introduction: Bone disorders observed commonly after haematopoietic stem cells transplantation (HSCT) can be caused by several factors,but their detailed pathomechanism is still not well known, especially in childhood.The aim of this study was to evaluate: IGF-I, RANKL-OPG system, IL-6, and IL1β levels and their association with bone mineral density(BMD) in children and adolescents after HSCT.Material and methods: Thirty five patients after allogeneic (N = 21) and autologous (N = 14) HSCT, mean age 8.48 ± 5.18 years, wereincluded in the study. Blood samples were taken before HSCT, on the transplantation day, three and six months after HSCT, then eachyear after HSCT for 2–8 years. RANKL, OPG, and IL-1β, IGF-1, and IL-6 were measured by immunochemistry. Total BMD was evaluatedsix months after HSCT using dual energy X-ray absorptiometry, then annually.Results: All Z-core values for BMD were negative in all patients. It was significantly higher in patients after auto HSCT than after allo HSCT.Serum levels of IGF-1 and IL-6 significantly changed after HSCT. IGF-I levels started to increase in the second year after transplantation.IL-6 increased up to 12 months after transplantation. Dynamic although not significant changes of OPG and RANKL levels were observedafter HSCT. RANKL and IGF-1 values correlated with BMD. IL-6 correlated positively with IL-1β but both did not correlate with BMD.Conclusions: Our data indicates that factors influencing bone remodelling change dynamically in the post-transplantation period.It suggests that serum RANKL and IGF-1 levels could be markers of bone metabolism after HSCT in paediatric patients