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 say that a first order sentence A defines a graph G if A is true on G but false on any graph non-isomorphic to G. Let L(G) (resp. D(G)) denote the minimum length (resp. quantifier rank) of a such sentence. We define the succinctness function s(n) (resp. its variant q(n)) to be the minimum L(G) (resp. D(G)) over all graphs on n vertices. We prove that s(n) and q(n) may be so small that for no...

OBJECTIVE To investigate the role of microRNA-145 (miR-145) in steroid-induced necrosis of the femoral head (SINFH) by evaluating its effects on the OPG/RANK/RANKL signaling pathway. METHODS A rat model of SINFH was constructed via injection of the lentiviral vector pLV-shRNA-miR-145. Pathological observation was performed via tartrate-resistant acid phosphatase (TRAP) staining, and serum OPG...

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...

Let the trunk of a graph G be the graph obtained by removing all leaves of G. We prove that, for every integer c ≥ 2, there are at most finitely many trunks of semiharmonic graphs with cyclomatic number c — in contrast to the fact established by the last two of the present authors in their paper Semiharmonic Bicyclic Graphs (this journal) that there are infinitely many connected semiharmonic gr...