Fixed points of dynamic processes of set-valued F-contractions and application to functional equations

The article is a continuation of the investigations concerning F-contractions which have been recently introduced in [Wardowski in Fixed Point Theory Appl. 2012:94,2012]. The authors extend the concept of F-contractive mappings to the case of nonlinear F-contractions and prove a fixed point theorem via the dynamic processes. The paper includes a non-trivial example which shows the motivation for such investigations. The work is summarized by the application of the introduced nonlinear F-contractions to functional equations

Assessment of expression of selected Bcl-2 family proteins in lymphoid infiltration in patients with B-cell chronic lymphocytic leukaemia treated with nucleoside analogues.

B-cell chronic lymphocytic leukaemia (B-CLL) is characterized by clonal growth and accumulation of mature lymphoid cells due to disturbance in genetically regulated form of cell death called apoptosis. The intrinsic mechanism of apoptosis is controlled by Bcl-2 family proteins. Purine nucleoside analogues induce the apoptosis in cells in a state of quiescence. The aim of the study was to assess expression of selected Bcl-2 family proteins in neoplastic infiltration in bone marrow in patients with B-CLL treated with nucleoside analogues. The study comprised examination of bone marrow obtained routinely by trephine biopsy from 18 patients with B-CLL diagnosed before administration of purine nucleoside analogues treatment and after its completion. Expression of Bcl-2, Bcl-x and Bax proteins was examined. Lymphoid cells in bone marrow were present in all patients before administration of treatment. After treatment in two patients bone marrow was infiltrated in diffuse pattern, whereas other patients presented nodular pattern of infiltration. The difference between stage of infiltration before and after treatment was statistically significant (

The effect of levothyroxine on the proliferative activity of the thyroid follicular cells

Wstęp: Farmakologiczne leczenie nietoksycznego wola guzkowego lewotyroksyną wciąż pozostaje sprawą dyskusyjną. Celem pracy było określenie wpływu lewotyroksyny na aktywność proliferacyjną komórek pęcherzykowych tarczycy. Materiał i metody: Materiał cytologiczny uzyskano metodą biopsji aspiracyjnej cienkoigłowej (BAC) wykonanej pod kontrolą USG, przed i 6 miesięcy po leczeniu lewotyroksyną, od 32 kobiet w wieku 34-69 lat będących w stanie eutyreozy. Pacjentki podzielono na dwie grupy wiekowe: przed 45. rokiem życia (14 chorych) i po 45. roku życia (18 chorych). Aktywność proliferacyjną komórek pęcherzykowych oceniono poprzez określenie indeksu proliferacyjnego (PI, proliferative index), stanowiącego odsetek komórek pęcherzykowych z dodatnią reakcją z przeciwciałem Ki-67. Ocenę mikroskopową przeprowadzono, używając komputerowego programu morfometrycznego MicroImage InCD UDF (Olympus). Wyniki: Po 6 miesiącach leczenia wartość indeksu proliferacyjnego była znamiennie statystycznie niższa w obu badanych grupach (8,59 &plusmn; 3,07 vs. 6,51 &plusmn; 1,91; p < 0,001 u kobiet w wieku poniżej 45 lat i 7,72 &plusmn; 1,83 vs. 5,09 &plusmn; 1,51, p < 0,001 w starszej grupie wiekowej). Wnioski: Wyniki przeprowadzonej pracy wskazują, że lewotyroksyna wpływa na aktywność proliferacyjną komórek pęcherzykowych tarczycy, szczególnie u kobiet w wieku okołomenopauzalnym.Introduction: Pharmacological treatment of non-toxic nodular goitre with levothyroxine has caused a discussion about its effectiveness and safety. The aim of the study was to examine the influence of levothyroxine on the proliferative activity of the thyroid follicular cells. Material and methods: Cytological material was obtained from 32 euthyroid females, aged 34-69 years, by USG-guided Fine-Needle Aspiration Biopsy (FNAB), before and after 6 months treatment with levothyroxine. The patients were divided into 2 age groups: up to 45 years (14 patients) and above 45 years (18 females). Proliferative activity of the follicular cells was assessed by the proliferative index (PI), representing the percentage of follicular cells with positive reaction with the antibody Ki-67. Microscopic evaluation was carried out using morphometric computer system MicroImage InCD UDF (Olympus). Results: After 6-months of treatment IP values decreased significantly in both groups studied (8.59 &plusmn; 3.07 vs 6.51 &plusmn; &plusmn; 1.91; p < 0.001 in females aged < 45 years and 7.72 &plusmn; 1.83 vs 5.09 &plusmn; 1.51; p < 0.001 in the older group). Conclusion: Our results indicate that levothyroxine has an influence on the proliferative activity of the thyroid follicular cells, particularly in post-menopausal women

Fixed-point and coincidence theorems for set-valued maps with nonconvex or noncompact domains in topological vector spaces

A technique, based on the investigations of the images of maps, for obtaining fixed-point and coincidence results in a new class of maps and domains is described. In particular, we show that the problem concerning the existence of fixed points of expansive set-valued maps and inner set-valued maps on not necessarily convex or compact sets in Hausdorff topological vector spaces has a solution. As a consequence, we prove a new intersection theorem concerning not necessarily convex or compact sets and its applications. We also give new coincidence and section theorems for maps defined on not necessarily convex sets in Hausdorff topological vector spaces. Examples and counterexamples show a fundamental difference between our results and the well-known ones

Stratification of amyotrophic lateral sclerosis patients: a crowdsourcing approach

Amyotrophic lateral sclerosis (ALS) is a fatal neurodegenerative disease where substantial heterogeneity in clinical presentation urgently requires a better stratification of patients for the development of drug trials and clinical care. In this study we explored stratification through a crowdsourcing approach, the DREAM Prize4Life ALS Stratification Challenge. Using data from >10,000 patients from ALS clinical trials and 1479 patients from community-based patient registers, more than 30 teams developed new approaches for machine learning and clustering, outperforming the best current predictions of disease outcome. We propose a new method to integrate and analyze patient clusters across methods, showing a clear pattern of consistent and clinically relevant sub-groups of patients that also enabled the reliable classification of new patients. Our analyses reveal novel insights in ALS and describe for the first time the potential of a crowdsourcing to uncover hidden patient sub-populations, and to accelerate disease understanding and therapeutic development