The block numerical range of analytic operator functions

We introduce the block numerical range Wn(L) of an operator function L with respect to a decomposition H = H1⊕. . .⊕Hn of the underlying Hilbert space. Our main results include the spectral inclusion property and estimates of the norm of the resolvent for analytic L . They generalise, and improve, the corresponding results for the numerical range (which is the case n = 1) since the block numerical range is contained in, and may be much smaller than, the usual numerical range. We show that refinements of the decomposition entail inclusions between the corresponding block numerical ranges and that the block numerical range of the operator matrix function L contains those of its principal subminors. For the special case of operator polynomials, we investigate the boundedness of Wn(L) and we prove a Perron-Frobenius type result for the block numerical radius of monic operator polynomials with coefficients that are positive in Hilbert lattice sense.

Length of the Mitral Isthmus But Not Anatomical Location of Ablation Line Predicts Bidirectional Mitral Isthmus Block in Patients Undergoing Catheter Ablation of Persistent Atrial Fibrillation: A Randomized Controlled Trial

INTRODUCTION Mitral isthmus (MI) ablation is an effective option in patients undergoing ablation for persistent atrial fibrillation (AF). Achieving bidirectional conduction block across the MI is challenging, and predictors of MI ablation success remain incompletely understood. We sought to determine the impact of anatomical location of the ablation line on the efficacy of MI ablation. METHODS AND RESULTS A total of 40 consecutive patients (87% male; 54 ± 10 years) undergoing stepwise AF ablation were included. MI ablation was performed in sinus rhythm. MI ablation was performed from the left inferior PV to either the posterior (group 1) or the anterolateral (group 2) mitral annulus depending on randomization. The length of the MI line (measured with the 3D mapping system) and the amplitude of the EGMs at 3 positions on the MI were measured in each patient. MI block was achieved in 14/19 (74%) patients in group 1 and 15/21 (71%) patients in group 2 (P = NS). Total MI radiofrequency time (18 ± 7 min vs. 17 ± 8 min; P = NS) was similar between groups. Patients with incomplete MI block had a longer MI length (34 ± 6 mm vs. 24 ± 5 mm; P < 0.001), a higher bipolar voltage along the MI (1.75 ± 0.74 mV vs. 1.05 ± 0.69 mV; P < 0.01), and a longer history of continuous AF (19 ± 17 months vs. 10 ± 10 months; P < 0.05). In multivariate analysis, decreased length of the MI was an independent predictor of successful MI block (OR 1.5; 95% CI 1.1-2.1; P < 0.05). CONCLUSIONS Increased length but not anatomical location of the MI predicts failure to achieve bidirectional MI block during ablation of persistent AF.

Esophageal hiatal hernia in three exotic felines--Lynx lynx, Puma concolore, Panthera leo.

Hiatal hernia was diagnosed in three exotic felines-lynx (Lynx lynx), cougar (Puma concolore), and lion (Panthera leo). All cats had a history of anorexia. Thoracic and abdominal radiographs showed evidence of a soft tissue mass within the caudal mediastinum suggestive of a hiatal hernia in all animals. A barium esophagram was performed in one case. All animals underwent thoracic or abdominal surgery for hernia reduction. Surgical procedures included: intercostal thoracotomy with herniorrhaphy and esophagopexy (lynx and cougar), and incisional gastropexy (lion). Concurrent surgical procedures performed were gastrotomy for gastric foreign body removal and jejunostomy tube placement. Clinical signs related to the hiatal hernia disappeared after surgery and recurrence of signs was not reported for the time of follow-up.

Nonparametric location estimators in the randomized complete block design

Several tests for the comparison of different groups in the randomized complete block design exist. However, there is a lack of robust estimators for the location difference between one group and all the others on the original scale. The relative marginal effects are commonly used in this situation, but they are more difficult to interpret and use by less experienced people because of the different scale. In this paper two nonparametric estimators for the comparison of one group against the others in the randomized complete block design will be presented. Theoretical results such as asymptotic normality, consistency, translation invariance, scale preservation, unbiasedness, and median unbiasedness are derived. The finite sample behavior of these estimators is derived by simulations of different scenarios. In addition, possible confidence intervals with these estimators are discussed and their behavior derived also by simulations.