The Radius of Metric Subregularity

There is a basic paradigm, called here the radius of well-posedness, which quantifies the "distance" from a given well-posed problem to the set of ill-posed problems of the same kind. In variational analysis, well-posedness is often understood as a regularity property, which is usually employed to measure the effect of perturbations and approximations of a problem on its solutions. In this paper we focus on evaluating the radius of the property of metric subregularity which, in contrast to its siblings, metric regularity, strong regularity and strong subregularity, exhibits a more complicated behavior under various perturbations. We consider three kinds of perturbations: by Lipschitz continuous functions, by semismooth functions, and by smooth functions, obtaining different expressions/bounds for the radius of subregularity, which involve generalized derivatives of set-valued mappings. We also obtain different expressions when using either Frobenius or Euclidean norm to measure the radius. As an application, we evaluate the radius of subregularity of a general constraint system. Examples illustrate the theoretical findings.Comment: 20 page

Variational Analysis Down Under Open Problem Session

© 2018, Springer Science+Business Media, LLC, part of Springer Nature. We state the problems discussed in the open problem session at Variational Analysis Down Under conference held in honour of Prof. Asen Dontchev on 19–21 February 2018 at Federation University Australia

The effect of a sports chiropractic manual therapy intervention on the prevention of back pain, hamstring and lower limb injuries in semi-elite Australian Rules footballers: a randomized controlled trial

<p>Abstract</p> <p>Background</p> <p>Hamstring injuries are the most common injury in Australian Rules football. It was the aims to investigate whether a sports chiropractic manual therapy intervention protocol provided in addition to the current best practice management could prevent the occurrence of and weeks missed due to hamstring and other lower-limb injuries at the semi-elite level of Australian football.</p> <p>Methods</p> <p>Sixty male subjects were assessed for eligibility with 59 meeting entry requirements and randomly allocated to an intervention (n = 29) or control group (n = 30), being matched for age and hamstring injury history. Twenty-eight intervention and 29 control group participants completed the trial. Both groups received the current best practice medical and sports science management, which acted as the control. Additionally, the intervention group received a sports chiropractic intervention. Treatment for the intervention group was individually determined and could involve manipulation/mobilization and/or soft tissue therapies to the spine and extremity. Minimum scheduling was: 1 treatment per week for 6 weeks, 1 treatment per fortnight for 3 months, 1 treatment per month for the remainder of the season (3 months). The main outcome measure was an injury surveillance with a missed match injury definition.</p> <p>Results</p> <p>After 24 matches there was no statistical significant difference between the groups for the incidence of hamstring injury (OR:0.116, 95% CI:0.013-1.019, p = 0.051) and primary non-contact knee injury (OR:0.116, 95% CI:0.013-1.019, p = 0.051). The difference for primary lower-limb muscle strains was significant (OR:0.097, 95%CI:0.011-0.839, p = 0.025). There was no significant difference for weeks missed due to hamstring injury (4 v14, χ2:1.12, p = 0.29) and lower-limb muscle strains (4 v 21, χ2:2.66, p = 0.10). A significant difference in weeks missed due to non-contact knee injury was noted (1 v 24, χ2:6.70, p = 0.01).</p> <p>Conclusions</p> <p>This study demonstrated a trend towards lower limb injury prevention with a significant reduction in primary lower limb muscle strains and weeks missed due to non-contact knee injuries through the addition of a sports chiropractic intervention to the current best practice management.</p> <p>Trial registration</p> <p>The study was registered with the Australian and New Zealand Clinical Trials Registry (ACTRN12608000533392).</p

A descriptive study of a manual therapy intervention within a randomised controlled trial for hamstring and lower limb injury prevention

The journal has been informed by its publisher BioMed Central that contrary to the statement in this article [Wayne Hoskins, Henry Pollard, Chiropractic & Osteopathy 2010, 18:23], they have been advised by the authors' institution Macquarie University, that its Human Research Ethics Committee did not approve this study. Because the study was conducted without institutional ethics committee approval it has been retracted

Patellofemoral pain syndrome (PFPS): a systematic review of anatomy and potential risk factors

Patellofemoral Pain Syndrome (PFPS), a common cause of anterior knee pain, is successfully treated in over 2/3 of patients through rehabilitation protocols designed to reduce pain and return function to the individual. Applying preventive medicine strategies, the majority of cases of PFPS may be avoided if a pre-diagnosis can be made by clinician or certified athletic trainer testing the current researched potential risk factors during a Preparticipation Screening Evaluation (PPSE). We provide a detailed and comprehensive review of the soft tissue, arterial system, and innervation to the patellofemoral joint in order to supply the clinician with the knowledge required to assess the anatomy and make recommendations to patients identified as potentially at risk. The purpose of this article is to review knee anatomy and the literature regarding potential risk factors associated with patellofemoral pain syndrome and prehabilitation strategies. A comprehensive review of knee anatomy will present the relationships of arterial collateralization, innervations, and soft tissue alignment to the possible multifactoral mechanism involved in PFPS, while attempting to advocate future use of different treatments aimed at non-soft tissue causes of PFPS