A Purely Functional Computer Algebra System Embedded in Haskell

We demonstrate how methods in Functional Programming can be used to implement a computer algebra system. As a proof-of-concept, we present the computational-algebra package. It is a computer algebra system implemented as an embedded domain-specific language in Haskell, a purely functional programming language. Utilising methods in functional programming and prominent features of Haskell, this library achieves safety, composability, and correctness at the same time. To demonstrate the advantages of our approach, we have implemented advanced Gr\"{o}bner basis algorithms, such as Faug\`{e}re's $F_4$ and $F_5$, in a composable way.Comment: 16 pages, Accepted to CASC 201

Equianalytic and equisingular families of curves on surfaces

We consider flat families of reduced curves on a smooth surface S such that each member C has the same number of singularities of fixed singularity types and the corresponding (locally closed) subscheme H of the Hilbert scheme of S. We are mainly concerned with analytic resp. topological singularity types and give a sufficient condition for the smoothness of H (at C). Our results for S=P^2 seem to be quite sharp for families of cuves of small degree d.Comment: LaTeX v 2.0

Does the Powers™ strap influence the lower limb biomechanics during running?

Previous research has reported a prevalence of running related injuries in 25.9% to 72% of all runners. A greater hip internal rotation and adduction during the stance phase in running has been associated with many running related injuries, such as patellofemoral pain. Researchers in the USA designed a treatment device 'the PowersTM strap' to facilitate an external rotation of the femur and to thereby control abnormal hip and knee motion during leisure and sport activities. However, to date no literature exists to demonstrate whether the PowersTM strap is able to reduce hip internal rotation during running. 22 healthy participants, 11 males and 11 females (age: 27.45 ±4.43 years, height: 1.73 ± 0.06m, mass: 66.77 ±9.24kg) were asked to run on a 22m track under two conditions: without and with the PowersTM strap. Threedimensional motion analysis was conducted using ten Qualisys OQUS 7 cameras (Qualisys AB, Sweden) and force data was captured with three AMTI force plates (BP600900, Advanced Mechanical Technology, Inc.USA). Paired sample t-tests were performed at the 95% confidence interval on all lower limb kinematic and kinetic data. The PowersTM strap significantly reduced hip and knee internal rotation throughout the stance phase of running. These results showed that the PowersTM strap has the potential to influence hip motion during running related activities, in doing so this might be beneficial for patients with lower limb injuries. Future research should investigate the influence of the PowersTM strap in subjects who suffer from running related injuries, such as patellofemoral pain

How does acute pain influence biomechanics and quadriceps function in individuals with patellofemoral pain?

Objectives: Beside pathophysiological factors, pain is believed to play a crucial role in the progression of patellofemoral pain (PFP). However, the isolated effect of pain on biomechanics and quadriceps function has not been investigated in PFP. Thus, this study aimed to investigate the effect of pain on quadriceps function and lower limb biomechanics in individuals with PFP. Methods: Twenty-one individuals with PFP (11 males and 10 females, age: 29.76 ±6.36 years, height: 1.74 ± 0.09m, mass: 70.12 ±8.56kg) were measured at two different occasions: when not and when experiencing acute pain. Peak quadriceps torque (concentric, eccentric and isometric) and arthrogenic muscle inhibition (AMI) was assessed. Three-dimensional motion analysis and surface electromyography of the quadriceps and hamstrings muscles were collected during running, a single-leg-squat and step-down task. The normality was assessed using the Shapiro-Wilk test and a MANOVA was performed at the 95% confidence interval. Results: AMI increased significantly in acute pain. The net muscle activation of the knee extensors and flexors decreased during running in acute pain. The lower limb biomechanics and the quadriceps torque did not change in acute pain. Discussion: It appears that even if individuals with PFP experience pain they can still deliver maximal quadriceps contractions and maintain their moving patterns without biomechanical changes. However, the overall reduced activation of the quadriceps and the increased AMI indicate the presence of quadriceps inhibition in acute pain. Key words: patellofemoral pain, knee, PFP, AKP, inhibition, quadriceps, strength, pai

The Ernst equation and ergosurfaces

We show that analytic solutions \mcE of the Ernst equation with non-empty zero-level-set of \Re \mcE lead to smooth ergosurfaces in space-time. In fact, the space-time metric is smooth near a "Ernst ergosurface" $E_f$ if and only if \mcE is smooth near $E_f$ and does not have zeros of infinite order there.Comment: 23 pages, 4 figures; misprints correcte

The role of muscle dysfunction in patellofemoral pain : influence of different treatment approaches

Patellofemoral pain (PFP) is the most frequently diagnosed condition in patients with knee complaints and is particularly prevalent in young physically active individuals. Studies revealed that despite receiving treatment, the majority of individuals with PFP suffer from persistent complaints, indicating that current treatments fail to prevent the chronicity of symptoms. The failing long-term outcomes reflect the need to provide an update on the evidence of underlying muscular dysfunctional factors of PFP, as well as the investigation of different treatment approaches. As part of this PhD, a literature and a systematic review were conducted, which discussed the definition, risk factors, prognosis, pathophysiology and treatment of PFP. The meta-analysis showed that the majority of studies analysed muscle strength or muscular activity. Whereas, muscular dysfunctional factors such as atrophy, muscular inhibition, fatigue and flexibility remained understudied in individuals with PFP. To develop a robust and reliable test protocol for the investigation of muscular dysfunctional factors in individuals with PFP, a reliability study was performed, which enabled the development of a protocol that was applied in the following studies of the thesis. Knee braces are recommended in the acute phase of PFP. However, research on knee braces analysing the effect on stabilising the sagittal and coronal plane of the knee joint demonstrated conflicting results. Thus, the effect on lower limb biomechanics and pain of the PowersTM strap was investigated in 24 individuals with PFP and 22 healthy individuals and revealed that the PowersTM strap reduced pain and was able to modify lower limb biomechanics during functional tasks. Furthermore, a six week exercise programme for individuals with PFP was developed and investigated in 25 individuals with PFP. It could be shown that the treatment was effective to reduce pain, improve function and the functional performance of individuals with PFP. The final study of this PhD focused on the influence of acute pain on the functional performance, strength and quadriceps inhibition in 21 individuals with PFP. It was found that acute pain caused an increase of quadriceps inhibition in individuals with PFP, but did not affect functional performance or quadriceps strength. Thus, this thesis investigated the role of muscle dysfunction in PFP, explored the link to pain and showed how different treatment approaches were able to influence muscle dysfunction in individuals with PFP

Influence of the Powers™ strap on pain and lower limb biomechanics in individuals with patellofemoral pain

Background: Abnormal biomechanics, especially hip internal rotation and adduction are known to be associated with patellofemoral pain (PFP). The PowersTM strap was designed to decrease hip internal rotation and to thereby stabilise the patellofemoral joint. Objectives: This study aimed to investigate whether the PowersTM strap influenced pain and lower limb biomechanics during running and squatting in individuals with PFP. Methods: 24 individuals with PFP were recruited using advertisements that were placed at fitness centres. They were asked to perform a single leg squat task (SLS) and to run on an indoor track at their own selected speed during two conditions: with and without the PowersTM strap. Immediate pain was assessed with the numeric pain rating scale. Three-dimensional motion and ground reaction force data were collected with 10 Qualisys cameras and 3 AMTI force plates. Results: Immediate pain was significantly reduced with the PowersTM strap (without the PowersTM strap: 4.04±1.91; with the PowersTM strap: 1.93±2.13). The PowersTM strap condition significantly increased hip external rotation by 4.7° during the stance phase in running and by 2.5° during the single leg squat task. Furthermore, the external knee adduction moment during the SLS and running increased significantly. Conclusion: This study assessed the effect of the PowersTM strap on lower limbs kinematics and kinetics in individual with PFP. The results suggest that the PowersTM strap has the potential to improve abnormal hip motion. Furthermore, the PowersTM strap demonstrated an ability to significantly reduce pain during functional tasks in patients with PFP