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  • Eran Nevo
  • Discrete & Computational Geometry
  • 2008
We prove that for d ≥ 3, the 1-skeleton of any (d− 1)-dimensional doubly Cohen-Macaulay (abbreviated 2-CM) complex is generically drigid. This implies that Barnette’s lower bound inequalities for boundary complexes of simplicial polytopes ([4],[3]) hold for every 2-CM complex of dimension ≥ 2 (see Kalai [8]). Moreover, the initial part (g0, g1, g2) of the(More)
OBJECTIVES The goal of this study was to develop and validate a method to estimate left ventricular end-systolic elastance (E(es)) in humans from noninvasive single-beat parameters. BACKGROUND Left ventricular end-systolic elastance is a major determinant of cardiac systolic function and ventricular-arterial interaction. However, its use in heart failure(More)
We try to understand the behavior of algebraic shifting with respect to some basic constructions on simplicial complexes, such as union, coning, and (more generally) join. In particular, for the disjoint union of simplicial complexes we prove ∆(K∪̇L) = ∆(∆(K)∪̇∆(L)) (conjectured by Kalai [2]), and for the join we give an example of simplicial complexes K(More)
In 1971, McMullen and Walkup posed the following conjecture, which is called the generalized lower bound conjecture: If P is a simplicial d-polytope then its h-vector (h0, h1, . . . , hd) satisfies h0 ≤ h1 ≤ · · · ≤ h⌊ d2 ⌋. Moreover, if hr−1 = hr for some r ≤ d2 then P can be triangulated without introducing simplices of dimension ≤ d− r. The first part of(More)
BACKGROUND Central aortic pressures and waveform convey important information about cardiovascular status, but direct measurements are invasive. Peripheral pressures can be measured noninvasively, and although they often differ substantially from central pressures, they may be mathematically transformed to approximate the latter. We tested this approach,(More)
BACKGROUND Ventricular pacing can improve hemodynamics in heart failure patients, but direct effects on left ventricular (LV) function from varying pacing site and atrioventricular (AV) delay remain unknown. We hypothesized that the magnitude and location of basal intraventricular conduction delay critically influences pacing responses and that single-site(More)
(MATH) A collection of simple closed Jordan curves in the plane is called a family of <i>pseudo-circles</i> if any two of its members intersect at most twice. A closed curve composed of two subarcs of distinct pseudo-circles is said to be an <i>empty lens</i> if it does not intersect any other member of the family. We establish a linear upper bound on the(More)
Aortic pressure can be estimated noninvasively by applying a transfer function (TF) to radial tonometry signals. This study compares the performance of prior approaches, based on Fourier transform and inverted aortic-to-radial model, with direct radial-to-aortic autoregressive exogenous (ARX) model. Simultaneous invasive aortic pressure and radial tonometry(More)
The notion of r-stackedness for simplicial polytopes was introduced by McMullen and Walkup in 1971 as a generalization of stacked polytopes. In this paper, we define the r-stackedness for triangulated homology manifolds and study their basic properties. In addition, we find a new necessary condition for face vectors of triangulated manifolds when all the(More)
Gluck [6] has proven that triangulated 2-spheres are generically 3-rigid. Equivalently, planar graphs are generically 3-stress free. We show that already the K5-minor freeness guarantees the stress freeness. More generally, we prove that every Kr+2-minor free graph is generically r-stress free for 1 ≤ r ≤ 4. (This assertion is false for r ≥ 6.) Some further(More)