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Medical adhesives that are strong, easy to apply and biocompatible are promising alternatives to sutures and staples in a large variety of surgical and clinical procedures. Despite progress in the development and regulatory approval of adhesives for use in the clinic, adhesion to wet tissue remains challenging. Marine organisms have evolved a diverse set of highly effective wet adhesive approaches that have inspired the design of new medical adhesives. Here we provide an overview of selected marine animals and their chemical and physical adhesion strategies, the state of clinical translation of adhesives inspired by these organisms, and target applications where marine-inspired adhesives can have a significant impact. We will focus on medical adhesive polymers inspired by mussels, sandcastle worms, and cephalopods, emphasize the history of bioinspired medical adhesives from the peer reviewed and patent literature, and explore future directions including overlooked sources of bioinspiration and materials that exploit multiple bioinspired strategies.For complex Wigner-type matrices, i.e. Hermitian random matrices with independent, not necessarily identically distributed entries above the diagonal, we show that at any cusp singularity of the limiting eigenvalue distribution the local eigenvalue statistics are universal and form a Pearcey process. Since the density of states typically exhibits only square root or cubic root cusp singularities, our work complements previous results on the bulk and edge universality and it thus completes the resolution of the Wigner-Dyson-Mehta universality conjecture for the last remaining universality type in the complex Hermitian class. Our analysis holds not only for exact cusps, but approximate cusps as well, where an extended Pearcey process emerges. LJC 11036 As a main technical ingredient we prove an optimal local law at the cusp for both symmetry classes. This result is also the key input in the companion paper (Cipolloni et al. in Pure Appl Anal, 2018. arXiv1811.04055) where the cusp universality for real symmetric Wigner-type matrices is proven. The novel cusp fluctuation mechanism is also essential for the recent results on the spectral radius of non-Hermitian random matrices (Alt et al. in Spectral radius of random matrices with independent entries, 2019. arXiv1907.13631), and the non-Hermitian edge universality (Cipolloni et al. in Edge universality for non-Hermitian random matrices, 2019. arXiv1908.00969).Given a closed orientable hyperbolic manifold of dimension ≠ 3 we prove that the multiplicity of the Pollicott-Ruelle resonance of the geodesic flow on perpendicular one-forms at zero agrees with the first Betti number of the manifold. Additionally, we prove that this equality is stable under small perturbations of the Riemannian metric and simultaneous small perturbations of the geodesic vector field within the class of contact vector fields. For more general perturbations we get bounds on the multiplicity of the resonance zero on all one-forms in terms of the first and zeroth Betti numbers. Furthermore, we identify for hyperbolic manifolds further resonance spaces whose multiplicities are given by higher Betti numbers.The dimension of the parameter space is typically unknown in a variety of models that rely on factorizations. For example, in factor analysis the number of latent factors is not known and has to be inferred from the data. Although classical shrinkage priors are useful in such contexts, increasing shrinkage priors can provide a more effective approach that progressively penalizes expansions with growing complexity. In this article we propose a novel increasing shrinkage prior, called the cumulative shrinkage process, for the parameters that control the dimension in overcomplete formulations. Our construction has broad applicability and is based on an interpretable sequence of spike-and-slab distributions which assign increasing mass to the spike as the model complexity grows. Using factor analysis as an illustrative example, we show that this formulation has theoretical and practical advantages relative to current competitors, including an improved ability to recover the model dimension. An adaptive Markov chain Monte Carlo algorithm is proposed, and the performance gains are outlined in simulations and in an application to personality data.We consider the problem of approximating smoothing spline estimators in a nonparametric regression model. When applied to a sample of size [Formula see text], the smoothing spline estimator can be expressed as a linear combination of [Formula see text] basis functions, requiring [Formula see text] computational time when the number [Formula see text] of predictors is two or more. Such a sizeable computational cost hinders the broad applicability of smoothing splines. In practice, the full-sample smoothing spline estimator can be approximated by an estimator based on [Formula see text] randomly selected basis functions, resulting in a computational cost of [Formula see text]. It is known that these two estimators converge at the same rate when [Formula see text] is of order [Formula see text], where [Formula see text] depends on the true function and [Formula see text] depends on the type of spline. Such a [Formula see text] is called the essential number of basis functions. In this article, we develop a more efficient basis selection method. By selecting basis functions corresponding to approximately equally spaced observations, the proposed method chooses a set of basis functions with great diversity. The asymptotic analysis shows that the proposed smoothing spline estimator can decrease [Formula see text] to around [Formula see text] when [Formula see text]. Applications to synthetic and real-world datasets show that the proposed method leads to a smaller prediction error than other basis selection methods.Mediation analysis is difficult when the number of potential mediators is larger than the sample size. In this paper we propose new inference procedures for the indirect effect in the presence of high-dimensional mediators for linear mediation models. We develop methods for both incomplete mediation, where a direct effect may exist, and complete mediation, where the direct effect is known to be absent. We prove consistency and asymptotic normality of our indirect effect estimators. Under complete mediation, where the indirect effect is equivalent to the total effect, we further prove that our approach gives a more powerful test compared to directly testing for the total effect. We confirm our theoretical results in simulations, as well as in an integrative analysis of gene expression and genotype data from a pharmacogenomic study of drug response. We present a novel analysis of gene sets to understand the molecular mechanisms of drug response, and also identify a genome-wide significant noncoding genetic variant that cannot be detected using standard analysis methods.