11 research outputs found
The critical window for the classical Ramsey-Tur\'an problem
The first application of Szemer\'edi's powerful regularity method was the
following celebrated Ramsey-Tur\'an result proved by Szemer\'edi in 1972: any
K_4-free graph on N vertices with independence number o(N) has at most (1/8 +
o(1)) N^2 edges. Four years later, Bollob\'as and Erd\H{o}s gave a surprising
geometric construction, utilizing the isoperimetric inequality for the high
dimensional sphere, of a K_4-free graph on N vertices with independence number
o(N) and (1/8 - o(1)) N^2 edges. Starting with Bollob\'as and Erd\H{o}s in
1976, several problems have been asked on estimating the minimum possible
independence number in the critical window, when the number of edges is about
N^2 / 8. These problems have received considerable attention and remained one
of the main open problems in this area. In this paper, we give nearly
best-possible bounds, solving the various open problems concerning this
critical window.Comment: 34 page
Thermal wavelength stabilization of Bragg gratings photowritten in hole-filled microstructured optical fibers
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Can We Use the Intrinsic Left Ventricular Delay (QLV) to Optimize the Pacing Configuration for Cardiac Resynchronization Therapy With a Quadripolar Left Ventricular Lead?
BACKGROUND: Previous studies indicated the importance of the intrinsic left ventricular (LV) electric delay (QLV) for optimal benefit to cardiac resynchronization therapy. We investigated the use of QLV for achieving optimal acute hemodynamic response to cardiac resynchronization therapy with a quadripolar LV lead. METHODS AND RESULTS: Forty-eight heart failure patients with a left bundle branch block were prospectively enrolled (31 men; age, 66±10 years; LV ejection fraction, 28±8%; QRS duration, 176±14 ms). Immediately after cardiac resynchronization therapy implantation, invasive LV pressure-volume loops were recorded during biventricular pacing with each separate electrode at 4 atrioventricular delays. Acute cardiac resynchronization therapy response, measured as change in stroke work (Δ%SW) compared with intrinsic conduction, was related to intrinsic interval between Q on the ECG and LV sensing delay (QLV), normalized for QRS duration (QLV/QRSd), and electrode position. QLV/QRSd was 84±9% and variation between the 4 electrodes 9±5%. Δ%SW was 89±64% and varied by 39±36% between the electrodes. In univariate analysis, an anterolateral or lateral electrode position and a high QLV/QRSd had a significant association with a large Δ%SW (all P <0.01). In a combined model, only QLV/QRSd remained significantly associated with Δ%SW (P<0.05). However, a direct relation between QLV/QRSd and Δ%SW was only seen in 24 patients, whereas 24 patients showed an inverse relation. CONCLUSIONS: The large variation in acute hemodynamic response indicates that the choice of the stimulated electrode on a quadripolar lead is important. Although QLV/QRSd was associated with acute hemodynamic response at group level, it cannot be used to select the optimal electrode in the individual patient