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Leaflet replacement in aortic valve repair (AVr) is associated with increased long-term repair failure. Hemodynamic performance and mechanical stress levels were investigated after porcine AVr with 5 types of clinically relevant replacement materials to ascertain which material(s) would be best suited for repair. Porcine aortic roots with intact aortic valves were placed in a left-heart simulator mounted with a high-speed camera for baseline valve assessment. Then, the non-coronary leaflet was excised and replaced with autologous porcine pericardium (APP), glutaraldehyde-fixed bovine pericardial patch (BPP; Synovis™), extracellular matrix scaffold (CorMatrix™), or collagen-impregnated Dacron (HEMASHIELD™). Hemodynamic parameters were measured over a range of cardiac outputs (2.5–6.5L/min) post-repair. Material properties of the above materials along with St. Jude Medical™ Pericardial Patch with EnCapTM Technology (SJM) were determined using pressurization experiments. Finite element models of the aortic valve and root complex were then constructed to verify the hemodynamic characteristics and determine leaflet stress levels. This study demonstrates that APP and SJM have the closest profiles to normal aortic valves; therefore, use of either replacement material may be best suited. Increased stresses found in BPP, HEMASHIELD™, and CorMatrix™ groups may be associated with late repair failure.

Leaflet replacement in aortic valve repair (AVr) is associated with increased long-term repair failure. Hemodynamic performance and mechanical stress levels were investigated after porcine AVr with 5 types of clinically relevant replacement materials to ascertain which material(s) would be best suited for repair. Porcine aortic roots with intact aortic valves were placed in a left-heart simulator mounted with a high-speed camera for baseline valve assessment. Then, the non-coronary leaflet was excised and replaced with autologous porcine pericardium (APP), glutaraldehyde-fixed bovine pericardial patch (BPP; Synovis™), extracellular matrix scaffold (CorMatrix™), or collagen-impregnated Dacron (HEMASHIELD™). Hemodynamic parameters were measured over a range of cardiac outputs (2.5–6.5L/min) post-repair. Material properties of the above materials along with St. Jude Medical™ Pericardial Patch with EnCapTM Technology (SJM) were determined using pressurization experiments. Finite element models of the aortic valve and root complex were then constructed to verify the hemodynamic characteristics and determine leaflet stress levels. This study demonstrates that APP and SJM have the closest profiles to normal aortic valves; therefore, use of either replacement material may be best suited. Increased stresses found in BPP, HEMASHIELD™, and CorMatrix™ groups may be associated with late repair failure.

<p dir="ltr">The generalization error of a classifier is related to the complexity of the set of functions among which the classifier is chosen. We study a family of low-complexity classifiers consisting of thresholding a random one-dimensional feature. The feature is obtained by projecting the data on a random line after embedding it into a higher-dimensional space parametrized by monomials of order up to k. More specifically, the extended data is projected n-times and the best classifier among those n, based on its performance on training data, is chosen. </p><p dir="ltr">We show that this type of classifier is extremely flexible, as it is likely to approximate, to an arbitrary precision, any continuous function on a compact set as well as any Boolean function on a compact set that splits the support into measurable subsets. In particular, given full knowledge of the class conditional densities, the error of these low-complexity classifiers would converge to the optimal (Bayes) error as k and n go to infinity. On the other hand, if only a training dataset is given, we show that the classifiers will perfectly classify all the training points as k and n go to infinity. </p><p dir="ltr">We also bound the generalization error of our random classifiers. In general, our bounds are better than those for any classifier with VC dimension greater than O(ln(n)). In particular, our bounds imply that, unless the number of projections n is extremely large, there is a significant advantageous gap between the generalization error of the random projection approach and that of a linear classifier in the extended space. Asymptotically, as the number of samples approaches infinity, the gap persists for any such n. Thus, there is a potentially large gain in generalization properties by selecting parameters at random, rather than optimization. </p><p dir="ltr">Given a classification problem and a family of classifiers, the Rashomon ratio measures the proportion of classifiers that yield less than a given loss. Previous work has explored the advantage of a large Rashomon ratio in the case of a finite family of classifiers. Here we consider the more general case of an infinite family. We show that a large Rashomon ratio guarantees that choosing the classifier with the best empirical accuracy among a random subset of the family, which is likely to improve generalizability, will not increase the empirical loss too much. </p><p dir="ltr">We quantify the Rashomon ratio in two examples involving infinite classifier families in order to illustrate situations in which it is large. In the first example, we estimate the Rashomon ratio of the classification of normally distributed classes using an affine classifier. In the second, we obtain a lower bound for the Rashomon ratio of a classification problem with a modified Gram matrix when the classifier family consists of two-layer ReLU neural networks. In general, we show that the Rashomon ratio can be estimated using a training dataset along with random samples from the classifier family and we provide guarantees that such an estimation is close to the true value of the Rashomon ratio.</p>