A Comparison between the Zero Forcing Number and the Strong Metric Dimension of Graphs

The \emph{zero forcing number}, $Z(G)$, of a graph $G$ is the minimum cardinality of a set $S$ of black vertices (whereas vertices in $V(G)-S$ are colored white) such that $V(G)$ is turned black after finitely many applications of "the color-change rule": a white vertex is converted black if it is the only white neighbor of a black vertex. The \emph{strong metric dimension}, $sdim(G)$, of a graph $G$ is the minimum among cardinalities of all strong resolving sets: $W \subseteq V(G)$ is a \emph{strong resolving set} of $G$ if for any $u, v \in V(G)$, there exists an $x \in W$ such that either $u$ lies on an $x-v$ geodesic or $v$ lies on an $x-u$ geodesic. In this paper, we prove that $Z(G) \le sdim(G)+3r(G)$ for a connected graph $G$, where $r(G)$ is the cycle rank of $G$. Further, we prove the sharp bound $Z(G) \leq sdim(G)$ when $G$ is a tree or a unicyclic graph, and we characterize trees $T$ attaining $Z(T)=sdim(T)$. It is easy to see that $sdim(T+e)-sdim(T)$ can be arbitrarily large for a tree $T$; we prove that $sdim(T+e) \ge sdim(T)-2$ and show that the bound is sharp.Comment: 8 pages, 5 figure

Transcatheter closure of complex iatrogenic ventricular septal defect: A case report

Background: Iatrogenic membranous ventricular septal defects (VSDs) are rare complications of cardiothoracic surgery, such as septal myectomy for hypertrophic obstructive cardiomyopathy (HOCM). Transcatheter closure is considered an appealing alternative to surgery, given the increased mortality associated with repeated surgical procedures, but reports are extremely limited. Case summary: We herein report the case of a 63-year-old woman with HOCM who underwent successful percutaneous closure of an iatrogenic VSD after septal myectomy. Two percutaneous techniques are discussed, namely the 'muscular anchoring' and the 'buddy wire delivery', aimed at increasing support and providing stability to the system during percutaneous intervention. Discussion: Transcatheter closure represents an attractive minimally invasive approach for the management of symptomatic iatrogenic VSDs. The new techniques described could help operators to cross tortuous and tunnelled defects and to deploy closure devices in case of complex VSD anatomy

On the Power Domination Number of de Bruijn and Kautz Digraphs

Let G=(V,A) be a directed graph, and let S⊆V be a set of vertices. Let the sequence S=S₀⊆S₁⊆S₂⊆⋯ be defined as follows: S₁ is obtained from S₀ by adding all out-neighbors of vertices in S₀. For k⩾2, Sₖ is obtained from Sₖ₋₁ by adding all vertices w such that for some vertex v∈Sₖ₋₁, w is the unique out-neighbor of v in V∖Sₖ₋₁. We set M(S)=S₀∪S₁∪⋯, and call S a power dominating set for G if M(S)=V(G). The minimum cardinality of such a set is called the power domination number of G. In this paper, we determine the power domination numbers of de Bruijn and Kautz digraphs

Transcatheter aortic valve replacement for bicuspid aortic valve stenosis with first- and new-generation bioprostheses: A systematic review and meta-analysis

Subjects with bicuspid aortic valve (BAV) have been excluded from transcatheter aortic valve replacement (TAVR) randomized trials

Impact of baseline hemorrhagic risk on the benefit of bivalirudin versus unfractionated heparin in patients treated with coronary angioplasty: A meta-regression analysis of randomized trials

BACKGROUND: Bivalirudin significantly reduces 30-day major and minor bleeding compared with unfractionated heparin (UFH), while resulting in similar or lower rates of ischemic events in both patients with stable and unstable coronary disease undergoing percutaneous coronary intervention. We performed a meta-analysis of randomized trials to evaluate the impact of bivalirudin compared with UFH, with or without glycoprotein IIb/IIIa receptor inhibitors (GPI), on the rates of mortality, myocardial infarction (MI), and major bleeding. METHODS: We searched electronic databases for randomized controlled trials with >100 patients comparing bivalirudin (+/-provisional GPI) with UFH with either routine or provisional GPI in patients undergoing percutaneous coronary intervention. The principal efficacy end points were mortality and MI within 30 day, whereas major bleeding was the principal safety end point. We assessed the benefit of bivalirudin for each efficacy end point relative to the baseline bleeding risk, using the control (UFH) major bleeding rate as proxy for that risk. RESULTS: A total of 12 randomized trials that enrolled 33,261 patients were included. Overall, there was no significant difference in mortality and MI between bivalirudin monotherapy and UFH (+/-GPI), whereas major bleeding was significantly lower with bivalirudin. Bivalirudin reduced major and minor bleeding across the entire bleeding risk spectrum. CONCLUSIONS: Bivalirudin significantly reduces major and minor bleeding regardless of the estimated baseline hemorrhagic risk

PRELIMINARY RESULTS OF CLINICAL EVALUATION OF THE FREE/TOTAL PROSTATE-SPECIFIC ANTIGEN RATIO IN A MULTICENTRIC STUDY

none13noneTERRONE C; G. AIMO; E. BOMBARDIERI; A. CIANETTI; M. CORREALE; P. BARIOLI; M. BARICHELLO; S. MASSARON; E. SEREGNI; D. MARZANO; I. ABBATE; A. PAGLIARULO; M. GIONTerrone, C; G., Aimo; E., Bombardieri; A., Cianetti; M., Correale; P., Barioli; M., Barichello; S., Massaron; E., Seregni; D., Marzano; I., Abbate; A., Pagliarulo; M., Gio