A space X is called an α-Toronto space if X is scattered of Cantor– Bendixson rank α and is homeomorphic to each of its subspaces of the same rank. We answer a question of Steprāns by constructing a countable α-Toronto space for each α ≤ ω. We also construct consistent examples of countable α-Toronto spaces for each

For a graph G let μ(G) denote the cyclomatic number and let ν(G) denote the maximum number of edge-disjoint cycles of G. We prove that for every k ≥ 0 there is a finite set P(k) such that every 2-connected graph G for which μ(G)− ν(G) = k arises by applying a simple extension rule to a graph in P(k). Furthermore, we determine P(k) for k ≤ 2 exactly.

January 15, 2017 Version 3.0.0 Date 2016-09-16 Title Rank Product method for identifying differentially expressed genes with application in meta-analysis Author Francesco Del Carratore , Andris Janckevics Fangxin Hong , Ben Wittner , Rainer Breitling <r.breitling...

We combine the fundamental results of Breuillard, Green, and Tao (Publ Math Inst Hautes Études Sci 116:115–221, 2012) on structure approximate groups, together with “tame” arithmetic regularity methods based work authors Terry (J Eur Soc (JEMS) 24(2):583–621, 2022), to give a theorem for finite subsets A arbitrary groups G where has “small tripling” bounded VC-dimension: Roughly speaking, up sm...

Let $S$ be a dense subsemigroup of $(0,+infty)$. In this paper, we state   definition of thick near zero, and also  we will introduce a definition that is equivalent to the definition of piecewise syndetic near zero which presented by Hindman  and Leader in [6].  We define density near zero for subsets of $S$ by a collection of nonempty finite subsets of $S$ and we investigate the conditions un...

March 29, 2017 Version 3.0.0 Date 2016-09-16 Title Rank Product method for identifying differentially expressed genes with application in meta-analysis Author Francesco Del Carratore , Andris Janckevics Fangxin Hong , Ben Wittner , Rainer Breitling <r.breitling@b...

Celiac disease (CD) is a systemic immune-mediated disorder caused by the dietary gluten in individuals who are genetically susceptible to the disease. In fact, CD is a T cell-mediated immune disease in which gluten-derived peptides activate the lamina propria CD4+ Teff cells, and these T-cell subsets can cause the intestinal tissue damages. Also, there are additional subsets of CD4+ T cells wit...