A short and elementary proof of Hanner's theorem

Hanner's theorem is a classical theorem in the theory of retracts and extensors in topological spaces, which states that a local ANE is an ANE. While Hanner's original proof of the theorem is quite simple for separable spaces, it is rather involved for the general case. We provide a proof which is not only short, but also elementary, relying only on well-known classical point-set topology.Comment: 2 page

Topological stability through extremely tame retractions

AbstractSuppose that F:(Rn×Rd,0)→(Rp×Rd,0) is a smoothly stable, Rd-level preserving germ which unfolds f:(Rn,0)→(Rp,0); then f is smoothly stable if and only if we can find a pair of smooth retractions r:(Rn+d,0)→(Rn,0) and s:(Rp+d,0)→(Rp,0) such that f∘r=s∘F. Unfortunately, we do not know whether f will be topologically stable if we can find a pair of continuous retractions r and s.The class of extremely tame (E-tame) retractions, introduced by du Plessis and Wall, are defined by their nice geometric properties, which are sufficient to ensure that f is topologically stable.In this article, we present the E-tame retractions and their relation with topological stability, survey recent results by the author concerning their construction, and illustrate the use of our techniques by constructing E-tame retractions for certain germs belonging to the E- and Z-series of singularities

Learning from graphs with structural variation

We study the effect of structural variation in graph data on the predictive performance of graph kernels. To this end, we introduce a novel, noise-robust adaptation of the GraphHopper kernel and validate it on benchmark data, obtaining modestly improved predictive performance on a range of datasets. Next, we investigate the performance of the state-of-the-art Weisfeiler-Lehman graph kernel under increasing synthetic structural errors and find that the effect of introducing errors depends strongly on the dataset.Comment: Presented at the NIPS 2017 workshop "Learning on Distributions, Functions, Graphs and Groups

Psychological adjustment to craniofacial conditions (excluding oral clefts): A review of the literature

© 2016 Informa UK Limited, trading as Taylor & Francis Group. Objective: A congenital craniofacial anomaly (CFA) is expected to impact upon several domains of psychological, emotional and social functioning, yet no recent reviews have comprehensively summarised the available literature. Further, existing reviews tend to draw upon literature in the field of cleft lip and palate, and do not give substantive attention to other types of CFAs. Design: A review of 41 papers published between January 2000 and March 2016 pertaining to psychological adjustment to CFAs. Main outcome measures: Findings are presented according to key psychological domains: General Psychological Well-being, Quality of Life, Behaviour, Emotional Well-being, Social Experiences, Appearance, and Treatment-Related Experiences. Results: Current literature offers a contradictory picture of adjustment to CFAs. Psychological adjustment appeared to be comparable to norms and reference groups in approximately half of the papers related to non-syndromic CFAs, while more variation was found across domains among samples with syndromic CFAs. Associations were found between adjustment, physical health and cognitive function in several papers. The review identified a number of gaps in the literature, such as the inclusion of a wide range of diagnoses within research samples. Conclusions: This review demonstrates the complexity of findings, both within and across domains, and highlights a number of methodological challenges

Probabilistic Riemannian submanifold learning with wrapped Gaussian process latent variable models

Latent variable models (LVMs) learn probabilistic models of data manifolds lying in an \emph{ambient} Euclidean space. In a number of applications, a priori known spatial constraints can shrink the ambient space into a considerably smaller manifold. Additionally, in these applications the Euclidean geometry might induce a suboptimal similarity measure, which could be improved by choosing a different metric. Euclidean models ignore such information and assign probability mass to data points that can never appear as data, and vastly different likelihoods to points that are similar under the desired metric. We propose the wrapped Gaussian process latent variable model (WGPLVM), that extends Gaussian process latent variable models to take values strictly on a given ambient Riemannian manifold, making the model blind to impossible data points. This allows non-linear, probabilistic inference of low-dimensional Riemannian submanifolds from data. Our evaluation on diverse datasets show that we improve performance on several tasks, including encoding, visualization and uncertainty quantification

Psychological adjustment to cleft lip and/or palate: A narrative review of the literature

© 2016 Informa UK Limited, trading as Taylor & Francis Group. Objective: Adjustment to cleft lip and/or palate (CL/P) is multifaceted, involving several domains of psychological and social functioning. A substantial increase in research in this area has been evident in recent years, along with a preliminary shift in how adjustment to CL/P is conceptualised and measured. An updated and comprehensive review of the literature is needed in light of the rapidly expanding and changing field. Design: A narrative review of 148 quantitative and qualitative studies published between January 2004 and July 2015. Main outcome measures: Findings are presented according to five key domains of adjustment: Developmental Trajectory, Behaviour, Emotional Well-being, Social Experiences and Satisfaction with Appearance and Treatment. Data pertaining to General Psychological Well-being were also examined. Results: The overall impact of CL/P on psychological adjustment appears to be low. Nonetheless, the review demonstrates the complexity of findings both within and across domains, and highlights recurring methodological challenges. Conclusions: Research findings from the last decade are considered to be largely inconclusive, although some areas of emerging consensus and improvements in the approaches used were identified. Efforts to collect data from large, representative and longitudinal samples, which are comparable across studies and encompassing of the patient perspective, should be doubled