We provide a uniform framework for proving the collapse of the hierarchy NC(C) for an exact arithmetic class C of polynomial degree. These hierarchies collapse all the way down to the third level of the AC-hierarchy, AC3(C). Our main collapsing exhibits are the classes C ∈ {C=NC,C=L,C=SAC,C=P}. NC(C=L) and NC(C=P) are already known to collapse [1,18,19]. We reiterate that our contribution is a ...

Let κ be a singular cardinal in V , and let W ⊇ V be a model such that κ+V = λ + W for some W -cardinal λ with W |= cf(κ) 6= cf(λ). We apply Shelah’s pcf theory to study this situation, and prove the following results. 1) W is not a κ+-c.c generic extension of V . 2) There is no “good scale for κ” in V , so in particular weak forms of square must fail at κ. 3) If V |= cf(κ) = א0 then V |= “κ is...

If M is a compact spin manifold, we give relationships between the vanishing of Â(M) and the possibility that M can collapse with curvature bounded below.

OBJECTIVES There is increasing evidence that rare variants play a role in some complex traits, but their analysis is not straightforward. Locus-based tests become necessary due to low power in rare variant single-point association analyses. In addition, variant quality scores are available for sequencing data, but are rarely taken into account. Here, we propose two locus-based methods that inco...

We will simplify the earlier proofs of Perelman’s collapsing theorem of 3-manifolds given by Shioya-Yamaguchi [SY00]-[SY05] and Morgan-Tian [MT08]. A version of Perelman’s collapsing theorem states that: “Let {M3 i } be a sequence of compact Riemannian 3-manifolds with curvature bounded from below by (−1) and diam(M3 i ) ≥ c0 > 0. Suppose that all unit metric balls in M3 i have very small volum...

While the wealth of projection matrices in plant demography permits comparative studies, variation in matrix dimensions complicates interspecific comparisons. Collapsing matrices to a common dimension may facilitate such comparisons but may also bias the inferred demographic parameters. Here we examine how matrix dimension affects inferred demographic elasticities and how different collapsing c...

INTRODUCTION High-intensity focused ultrasound (HIFU) produces collapsing cavitation bubbles. This study aims to investigate the efficacy of collapsing cavitation bubbles to deliver antibacterial nanoparticles into dentinal tubules to improve root canal disinfection. METHODS In stage 1, experiments were performed to characterize the efficacy of collapsing cavitation bubbles to deliver the min...

We present a flexible open-source framework that performs dependency parsing with collapsed dependencies. The parser framework features a rule-based annotator that directly works on the output of a dependency parser. Thus, it can introduce dependency collapsing and propagation (de Marneffe et al., 2006) to parsers that lack this functionality. Collapsing is a technique for dependency parses whe...

We prove a uniform Sobolev inequality for Ricci flow, which is independent of the number of surgeries. As an application, under less assumptions, a non-collapsing result stronger than Perelman’s κ non-collapsing with surgery is derived. The proof is shorter and seems more accessible. The result also improves some earlier ones where the Sobolev inequality depended on the number of surgeries.

The Greenfield-Chiclana Collapsing Defuzzifier comes in many variants, depending on the order of slice collapse. The accuracy of the fundamental variants of forward, backward, inward and outward, and the composite variants of forward-backward and outward right-left is compared experimentally for the discretised interval type-2 fuzzy set. Keywords— Centroid, Collapsing, Defuzzification, Interval...