Degrees of Freedom for Piecewise Lipschitz Estimators

A representation of the degrees of freedom akin to Stein's lemma is given for a class of estimators of a mean value parameter in $\mathbb{R}^n$. Contrary to previous results our representation holds for a range of discontinues estimators. It shows that even though the discontinuities form a Lebesgue null set, they cannot be ignored when computing degrees of freedom. Estimators with discontinuities arise naturally in regression if data driven variable selection is used. Two such examples, namely best subset selection and lasso-OLS, are considered in detail in this paper. For lasso-OLS the general representation leads to an estimate of the degrees of freedom based on the lasso solution path, which in turn can be used for estimating the risk of lasso-OLS. A similar estimate is proposed for best subset selection. The usefulness of the risk estimates for selecting the number of variables is demonstrated via simulations with a particular focus on lasso-OLS.Comment: 113 pages, 89 figure

Fixing Nonconvergence of Algebraic Iterative Reconstruction with an Unmatched Backprojector

We consider algebraic iterative reconstruction methods with applications in image reconstruction. In particular, we are concerned with methods based on an unmatched projector/backprojector pair; i.e., the backprojector is not the exact adjoint or transpose of the forward projector. Such situations are common in large-scale computed tomography, and we consider the common situation where the method does not converge due to the nonsymmetry of the iteration matrix. We propose a modified algorithm that incorporates a small shift parameter, and we give the conditions that guarantee convergence of this method to a fixed point of a slightly perturbed problem. We also give perturbation bounds for this fixed point. Moreover, we discuss how to use Krylov subspace methods to efficiently estimate the leftmost eigenvalue of a certain matrix to select a proper shift parameter. The modified algorithm is illustrated with test problems from computed tomography

EEG source imaging assists decoding in a face recognition task

EEG based brain state decoding has numerous applications. State of the art decoding is based on processing of the multivariate sensor space signal, however evidence is mounting that EEG source reconstruction can assist decoding. EEG source imaging leads to high-dimensional representations and rather strong a priori information must be invoked. Recent work by Edelman et al. (2016) has demonstrated that introduction of a spatially focal source space representation can improve decoding of motor imagery. In this work we explore the generality of Edelman et al. hypothesis by considering decoding of face recognition. This task concerns the differentiation of brain responses to images of faces and scrambled faces and poses a rather difficult decoding problem at the single trial level. We implement the pipeline using spatially focused features and show that this approach is challenged and source imaging does not lead to an improved decoding. We design a distributed pipeline in which the classifier has access to brain wide features which in turn does lead to a 15% reduction in the error rate using source space features. Hence, our work presents supporting evidence for the hypothesis that source imaging improves decoding

Recreational football for disease prevention and treatment in untrained men: a narrative review examining cardiovascular health, lipid profile, body composition, muscle strength and functional capacity

Over the past 10 years, researchers have studied the effects of recreational football training as a health-promoting activity for participants across the lifespan. This has important public health implications as over 400 million people play football annually. Results from the first randomised controlled trial, published in the BJSM in January 2009, showed that football increased maximal oxygen uptake and muscle and bone mass, and lowered fat percentage and blood pressure, in untrained men, and since then more than 70 articles about football for health have been published, including publications in two supplements of the Scandinavian Journal of Medicine and Science in Sports in 2010 and 2014, prior to the FIFA World Cup tournaments in South Africa and Brazil. While studies of football training effects have also been performed in women and children, this article reviews the current evidence linking recreational football training with favourable effects in the prevention and treatment of disease in adult men

Experimental investigation of cut-off phenomena in non-linear photonic crystal fibers

The modal cut-off is investigated experimentally in a series of high quality non-linear photonic crystal fibers. We demonstrate a suitable measurement technique to determine the cut-off wavelength and verify it by inspecting the near field of the modes that may be excited below and above the cut-off. We observe a double peak structure in the cut-off spectra, which is attributed to a splitting of the higher order modes. The cut-off is measured for seven different fiber geometries with different pitches and relative hole size, and a very good agreement with recent theoretical work is found.Comment: 3 pages including 1 table and 4 figures. Accepted for Optics Letter