On Two Equivalent Dilation Theorems in VH-Spaces

We prove that a generalized version, essentially obtained by R. M. Loynes, of the B. Sz.-Nagy's Dilation Theorem for B*(H)-valued (here H is a VH-space in the sense of Loynes) positive semidefinite maps on *-semigroups is equivalent with a generalized version of the W. F. Stinespring's Dilation Theorem for B*(H)-valued completely positive linear maps on B*-algebras. This equivalence result is a generalization of a theorem of F. H. Szafraniec, originally proved for the case of operator valued maps (that is, when H is a Hilbert space). © 2011 Springer Basel AG

Spectra of self-similar laplacians on the sierpinski gasket with twists

We study the spectra of a two-parameter family of self-similar Laplacians on the Sierpinski gasket (SG) with twists. By this we mean that instead of the usual IFS that yields SG as its invariant set, we compose each mapping with a reflection to obtain a new IFS that still has SG as its invariant set, but changes the definition of self-similarity. Using recent results of Cucuringu and Strichartz, we are able to approximate the spectra of these Laplacians by two different methods. To each Laplacian we associate a self-similar embedding of SG into the plane, and we present experimental evidence that the method of outer approximation, recently introduced by Berry, Goff and Strichartz, when applied to this embedding, yields the spectrum of the Laplacian (up to a constant multiple). © 2008 World Scientific Publishing Company

International Nosocomial Infection Control Consortium report, data summary of 50 countries for 2010-2015: Device-associated module

•We report INICC device-associated module data of 50 countries from 2010-2015.•We collected prospective data from 861,284 patients in 703 ICUs for 3,506,562 days.•DA-HAI rates and bacterial resistance were higher in the INICC ICUs than in CDC-NHSN's.•Device utilization ratio in the INICC ICUs was similar to CDC-NHSN's. Background: We report the results of International Nosocomial Infection Control Consortium (INICC) surveillance study from January 2010-December 2015 in 703 intensive care units (ICUs) in Latin America, Europe, Eastern Mediterranean, Southeast Asia, and Western Pacific. Methods: During the 6-year study period, using Centers for Disease Control and Prevention National Healthcare Safety Network (CDC-NHSN) definitions for device-associated health care-associated infection (DA-HAI), we collected prospective data from 861,284 patients hospitalized in INICC hospital ICUs for an aggregate of 3,506,562 days. Results: Although device use in INICC ICUs was similar to that reported from CDC-NHSN ICUs, DA-HAI rates were higher in the INICC ICUs: in the INICC medical-surgical ICUs, the pooled rate of central line-associated bloodstream infection, 4.1 per 1,000 central line-days, was nearly 5-fold higher than the 0.8 per 1,000 central line-days reported from comparable US ICUs, the overall rate of ventilator-associated pneumonia was also higher, 13.1 versus 0.9 per 1,000 ventilator-days, as was the rate of catheter-associated urinary tract infection, 5.07 versus 1.7 per 1,000 catheter-days. From blood cultures samples, frequencies of resistance of Pseudomonas isolates to amikacin (29.87% vs 10%) and to imipenem (44.3% vs 26.1%), and of Klebsiella pneumoniae isolates to ceftazidime (73.2% vs 28.8%) and to imipenem (43.27% vs 12.8%) were also higher in the INICC ICUs compared with CDC-NHSN ICUs. Conclusions: Although DA-HAIs in INICC ICU patients continue to be higher than the rates reported in CDC-NSHN ICUs representing the developed world, we have observed a significant trend toward the reduction of DA-HAI rates in INICC ICUs as shown in each international report. It is INICC's main goal to continue facilitating education, training, and basic and cost-effective tools and resources, such as standardized forms and an online platform, to tackle this problem effectively and systematically