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•TAVR is technically feasible and safe in patients with large and extra-large aortic annuli.•Balloon-expandable valves (BEVs) showed lower rates of moderate or greater paravalvular leak than self-expanding valves (SEVs).•Paravalvular leak was particularly frequent in patients with extra-large annuli (perimeter >96 mm and an area >730 mm²) treated with SEVs.•Careful imaging-based sizing and valve selection are key to optimizing outcomes in this challenging anatomy. Patients with large or extra-large aortic annuli pose a particular challenge for Transcatheter aortic valve replacement (TAVR), as clinical outcomes are less favorable than in patients with smaller annuli. This study aimed to evaluate periprocedural and clinical outcomes in patients with large and extra-large annuli undergoing TAVR and to compare results between balloon-expandable (BEVs) and self-expanding valves (SEVs). This study included patients with severe aortic stenosis (AS) and extra-large annuli who underwent TAVR with either BEVs or SEVs. The primary endpoints were periprocedural and clinical outcomes, including device success, rates of moderate or greater paravalvular leak (PVL), permanent pacemaker (PPM) implantation, new Left bundle branch block (LBBB), stroke, and in-hospital and 1-year mortality. Secondary endpoints included safety outcomes and subgroup analyses comparing outcomes between patients with large (annular perimeter >90 mm and an area >660 mm²) and extra-large annuli (perimeter >96 mm and an area >730 mm²). A total of 237 patients underwent TAVR, including 160 with BEVs and 77 with SEVs. The mean annular area and perimeter were 737 ± 76 mm² and 96.1 ± 4.1 mm, respectively, with no significant differences between groups. Overall device success was high, though slightly lower in the SEV group (84% vs. 93%, p = 0.034), a difference that was no longer statistically significant after multivariate analysis (p = 0.234). Moderate or greater PVL occurred more frequently with SEVs (13% vs. 4%, p = 0.016), particularly in patients with extra-large annuli (26% vs. 4%, p = 0.012). One-year mortality was similar between groups (SEV 13% vs. BEV 12%, p = 0.807), and no significant differences were observed in PPM implantation, new LBBB, stroke, or major vascular and bleeding complications. TAVR is feasible and safe in patients with large and extra-large annuli, with higher rates of moderate or greater paravalvular leak observed in SEV patients with extra-large annuli.

Creases are purposely introduced to thin structures for designing deployable origami, artistic geometries, and functional structures with tunable nonlinear mechanics. Modeling the mechanics of creased structures is challenging because creases introduce geometric discontinuity and often have complex mechanical responses due to local material damage. In this work, we propose a continuous description of the sharp geometry of creases and apply it to the study of creased annuli, made by introducing radial creases to annular strips with the creases annealed to behave elastically. We find that creased annuli have generic bistability and can be folded into various compact shapes, depending on the crease pattern and the overcurvature of the flat annulus. We use a regularized Dirac delta function (RDDF) to describe the geometry of a crease, with the finite spike of the RDDF capturing the localized curvature. Together with anisotropic rod theory, we solve the nonlinear mechanics of creased annuli, with its stability determined by the standard conjugate point test. We find excellent agreement between precision tabletop models, numerical predictions from our analytical framework, and modeling results from finite element simulations. We further show that by varying the rest curvature of the thin strip, dynamic switches between different states of creased annuli can be achieved, which could inspire the design of deployable and morphable structures. We believe that our smooth description of discontinuous geometries will benefit the mechanical modeling and design of a wide spectrum of engineering structures that embrace geometric and material discontinuities.

We establish a quantitative version of the isoperimetric inequality for the torsion of multiply connected domains, among sets with given area and with given joint area of the holes. Since the optimal shape is the annulus, we investigate how a given domain approaches an annular configuration when its torsion is close to the optimal value. Our result shows that when the torsional rigidity is nearly optimal, the domain \\(\\) must be close to an annulus.

In this paper, based on the charge simulation method, a conformal mapping computational method is proposed to map the unbounded multiply connected regions onto the annulus with spiral slit domains. In addition, for the system of pathological equations generated during the conformal mapping process, it is proposed to solve them by using the GMRES(m) method, which in turn constructs an approximate conformal mapping function with high accuracy. Finally, numerical examples validate the effectiveness of the algorithms in this paper.

For affine Coxeter groups of affine types \\( D\\) and \\( B\\), we model the interval \\([1,c]_T\\) in the absolute order by symmetric noncrossing partitions of an annulus with one or two double points. In type \\( B\\) (and almost in type \\( D\\)), the diagrams also model the larger lattice defined by McCammond and Sulway.

For affine Coxeter groups of affine types \\( D\\) and \\( B\\), we model the interval \\([1,c]_T\\) in the absolute order by symmetric noncrossing partitions of an annulus with one or two double points. In type \\( B\\) (and almost in type \\( D\\)), the diagrams also model the larger lattice defined by McCammond and Sulway.

We give an alternative proof to Agler's famous result on success of rational dilation on an annulus by an application of a result due to Dritschel and McCullough. We show interplay between operators associated with an annulus, \\(C_1,r\\) or quantum annulus and operator pairs living on a certain variety in \\( C^2\\) and its intersection with the biball. It is shown that the minimal spectral sets and von Neumann's inequality for these classes \\(C_1,r\\), quantum annulus can also be studied via appropriate operator pairs associated with the biball.

We use annular foam TQFTs introduced by the first two authors to define equivariant \\(SL(2)\\) and \\(SL(3)\\) web algebras in the annulus. To a diagram of a tangle in the thickened annulus we assign a complex of bimodules over these algebras whose chain homotopy type is an invariant of the tangle. Several properties of algebras and bimodules are established. An essential technical part of the paper provides a bijective correspondence between non-elliptic annular \\(SL(3)\\) webs and closed paths in the \\(SL(3)\\) weight lattice. This generalizes an analogous bijection in the planar setting.

We establish a quantitative version of the isoperimetric inequality for the torsion of multiply connected domains, among sets with given area and with given joint area of the holes. Since the optimal shape is the annulus, we investigate how a given domain approaches an annular configuration when its torsion is close to the optimal value. Our result shows that when the torsional rigidity is nearly optimal, the domain \\(\\) must be close to an annulus.

We consider a two-dimensional determinantal point process arising in the random normal matrix model and which is a two-parameter generalization of the complex Ginibre point process. In this paper, we prove that the probability that no points lie on any number of annuli centered at 0 satisfies large n asymptotics of the form exp ( C 1 n 2 + C 2 n log n + C 3 n + C 4 n + C 5 log n + C 6 + F n + O ( n - 1 12 ) ) , where n is the number of points of the process. We determine the constants C 1 , … , C 6 explicitly, as well as the oscillatory term F n which is of order 1. We also allow one annulus to be a disk, and one annulus to be unbounded. For the complex Ginibre point process, we improve on the best known results: (i) when the hole region is a disk, only C 1 , … , C 4 were previously known, (ii) when the hole region is an unbounded annulus, only C 1 , C 2 , C 3 were previously known, and (iii) when the hole region is a regular annulus in the bulk, only C 1 was previously known. For general values of our parameters, even C 1 is new. A main discovery of this work is that F n is given in terms of the Jacobi theta function. As far as we know this is the first time this function appears in a large gap problem of a two-dimensional point process.