Low Complexity Regularization of Linear Inverse Problems

Inverse problems and regularization theory is a central theme in contemporary signal processing, where the goal is to reconstruct an unknown signal from partial indirect, and possibly noisy, measurements of it. A now standard method for recovering the unknown signal is to solve a convex optimization problem that enforces some prior knowledge about its structure. This has proved efficient in many problems routinely encountered in imaging sciences, statistics and machine learning. This chapter delivers a review of recent advances in the field where the regularization prior promotes solutions conforming to some notion of simplicity/low-complexity. These priors encompass as popular examples sparsity and group sparsity (to capture the compressibility of natural signals and images), total variation and analysis sparsity (to promote piecewise regularity), and low-rank (as natural extension of sparsity to matrix-valued data). Our aim is to provide a unified treatment of all these regularizations under a single umbrella, namely the theory of partial smoothness. This framework is very general and accommodates all low-complexity regularizers just mentioned, as well as many others. Partial smoothness turns out to be the canonical way to encode low-dimensional models that can be linear spaces or more general smooth manifolds. This review is intended to serve as a one stop shop toward the understanding of the theoretical properties of the so-regularized solutions. It covers a large spectrum including: (i) recovery guarantees and stability to noise, both in terms of $\ell^2$-stability and model (manifold) identification; (ii) sensitivity analysis to perturbations of the parameters involved (in particular the observations), with applications to unbiased risk estimation ; (iii) convergence properties of the forward-backward proximal splitting scheme, that is particularly well suited to solve the corresponding large-scale regularized optimization problem

Perfectionism and Grit in Competitive Sport

Perfectionism and grit have both been linked to the achievement-striving process in sport, yet very little is known about the relationships between the two constructs. The present study explored the degree to which perfectionistic strivings and perfectionistic concerns predicted two dimensions of grit—consistency of interest and perseverance of effort—in a sample of 251 intercollegiate varsity athletes (Mage = 20.34 years; SD = 2.0). Both perfectionism and grit were conceptualized and measured as multidimensional domain-specific constructs. Results of structural equation modeling analyses indicated that perfectionistic strivings was positively associated with consistency of interest (β = .49, p < .001) and perseverance of effort (β = .92, p < .001). In contrast, perfectionistic concerns was negatively associated with both consistency of interest (β = -.47, p < .001) and perseverance of effort (β = -.66, p < .001). Results indicate that higher-order dimensions of perfectionism (i.e., perfectionistic strivings and perfectionistic concerns) are associated with domain-specific aspects of grit in sport. Results highlight the importance of (a) differentiating between athletes’ perfectionistic strivings and perfectionistic concerns in sport, and (b) treating consistency of interest and perseverance of effort as separate components of grit. Future research that examines the combined effects of perfectionism and grit on the achievement-striving process in competitive sport is recommended

Search for gravitational waves from Scorpius X-1 in the second Advanced LIGO observing run with an improved hidden Markov model

We present results from a semicoherent search for continuous gravitational waves from the low-mass x-ray binary Scorpius X-1, using a hidden Markov model (HMM) to track spin wandering. This search improves on previous HMM-based searches of LIGO data by using an improved frequency domain matched filter, the J-statistic, and by analyzing data from Advanced LIGO's second observing run. In the frequency range searched, from 60 to 650 Hz, we find no evidence of gravitational radiation. At 194.6 Hz, the most sensitive search frequency, we report an upper limit on gravitational wave strain (at 95% confidence) of h095%=3.47×10-25 when marginalizing over source inclination angle. This is the most sensitive search for Scorpius X-1, to date, that is specifically designed to be robust in the presence of spin wandering. © 2019 American Physical Society

Recent Laboratory Studies of Dielectronic Recombinations

The breakthrough in 1978 by Brooks et al. and by Breton et al. provided the first plasma rate measurements on dielectronic recombination (DR), and their basic technique has been followed up on in a few other investigations. An important new plasma technique was introduced in 1982. Another breakthrough in 1982–1983 led to colliding beams cross section measurements for DR and to more direct comparisons with theory. Experiment/theory disagreements and agreements have led to follow-up experimental and theoretical efforts which are pointing to better understanding of DR and which emphasize issues that should be paid attention to by plasma modelers. An overview will be given with strong emphasis on the beams experiments and the implications.</jats:p

Toward the Combined Use of Nomothetic and Idiographic Methodologies in Sport Psychology: An Empirical Example

Traditionally, nomothetic and idiographic methodologies have been viewed as antithetical. This dichotomous perspective has caused many researchers to advocate the benefits associated with only one of the two approaches. Such a biased view hinders the acquisition of knowledge in the sport psychology field because the potential benefits that the nonfavored approach can offer are frequently overlooked. The present study demonstrates how research in sport psychology can be enhanced by combining nomothetic and idiographic procedures. This combined approach provides the researcher with the opportunity to validate nomothetic principles at the individual level, while simultaneously generating nomothetic hypotheses from idiographic analyses. To illustrate these points, a nomothetic profile of situational threat perceptions based upon the responses of 46 ice hockey players (reported by Dunn &amp; Nielsen, 1993) is compared with the perceptual profiles of three individual ice hockey players. The comparisons show many unique perceptual differences between the group and individual solutions.</jats:p