Abstract:
In a previous study, we established reliability of a method for determining the angle of lumbopelvic sagittal alignment during active knee extension in sitting (AKEiS) using a flexible ruler and image analysis software (2-point-Method). In addition to this method, a flexible ruler can also be used to measure lumbopelvic sagittal alignment without image analysis software. This study primarily aimed to investigate the minimum number of repetitions, inter-session reliability and inter-examiner reliability of two alternative methods of measurement in a secondary analysis of our previous study. A flexible ruler was used to measure lumbopelvic curvature during AKEiS when the knee reached 10° flexion from 27 individuals with clinically tight hamstring muscles and subsequently analyzed. Lumbopelvic sagittal alignment was evaluated for the region between T12 and S2 using the maximum depth to the curvature (Max-Method) or depth to the curvature at the middle point between T12 and S2 vertebral levels (Mid-Method). It was determined that four repetitions for the Max-Method and 11 repetitions for the Mid-Method were required for the minimum number of repetitions, respectively. Inter-session reliability and inter-examiner reliability were assessed using Intraclass Correlation Coefficients and were 0.91 and 0.91 for the Max-Method and 0.90 and 0.91 for the Mid-Method, respectively. The current study suggests that the Mid-Method would not be recommended for use in the clinical setting as 11 repetitions of data sampling is required. The 2-point-Method or Max-Method may be promising but the ideal measurement method will be identified when the validity of these methods has been established.

Abstract:
A method is presented for constructing closed surfaces out of Euclidean polygons with infinitely many segment identifications along the boundary. The metric on the quotient is identified. A sufficient condition is presented which guarantees that the Euclidean structure on the polygons induces a unique conformal structure on the quotient surface, making it into a closed Riemann surface. In this case, a modulus of continuity for uniformizing coordinates is found which depends only on the geometry of the polygons and on the identifications. An application is presented in which a uniform modulus of continuity is obtained for a family of pseudo-Anosov homeomorphisms, making it possible to prove that they converge to a Teichm\"uller mapping on the Riemann sphere.

Abstract:
Let S be a surface obtained from a plane polygon by identifying infinitely many pairs of segments along its boundary. A condition is given under which the complex structure in the interior of the polygon extends uniquely across the quotient of its boundary to make S into a closed Riemann surface. When this condition holds, a modulus of continuity is obtained for a uniformizing map on S.

Abstract:
We present an efficient algorithm for calculating the number of components of an integral lamination on an $n$-punctured disk, given its Dynnikov coordinates. The algorithm requires $O(n^2M)$ arithmetic operations, where~$M$ is the sum of the absolute values of the Dynnikov coordinates.

Abstract:
Global results are proved about the way in which Boyland's forcing partial order organizes a set of braid types: those of periodic orbits of Smale's horseshoe map for which the associated train track is a star. This is a special case of a conjecture introduced in a previous paper, which claims that forcing organizes all horseshoe braid types into linearly ordered families which are, in turn, parameterized by homoclinic orbits to the fixed point of code 0.

Abstract:
An infinite family of generalized pseudo-Anosov homeomorphisms of the sphere S is constructed, and their invariant foliations and singular orbits are described explicitly by means of generalized train tracks. The complex strucure induced by the invariant foliations is described, and is shown to make S into a complex sphere. The generalized pseudo-Anosovs thus become quasiconformal automorphisms of the Riemann sphere, providing a complexification of the unimodal family which differs from that of the Fatou/Julia theory.

Abstract:
The Decoration Conjecture describes the structure of the set of braid types of Smale's horseshoe map ordered by forcing, providing information about the order in which periodic orbits can appear when a horseshoe is created. A proof of this conjecture is given for the class of so-called lone decorations, and it is explained how to calculate associated braid conjugacy invariants which provide additional information about forcing for horseshoe braids.

Abstract:
A method for computing the topological entropy of each braid in an infinite family, making use of Dynnikov's coordinates on the boundary of Teichm\"uller space, is described. The method is illustrated on two two-parameter families of braids.

Abstract:
Three groups of participants will be investigated: Groups 1 and 2 will be office workers with either NSAP or cervical radiculopathy and Group 3 will be a control group of non office workers without upper limb pain. Participants will undergo a clinical assessment, pain questionnaires (LANSS, Short Form McGill, DASH and TSK) and quantitative sensory testing comprising thermal detection and pain thresholds, vibration thresholds and pressure pain thresholds.The spectrum of clinically suspected neuropathic pain ranges from more obvious conditions such as trigeminal neuralgia to those with vague signs of nerve disorder such as NSAP. A thorough description of the somatosensory profiles of NSAP patients and a comparison with a more defined group of patients with evidence of neuropathic pain will help in the understanding of underlying neurophysiology in NSAP and may influence future classification and intervention studies relating to this condition.Work related upper limb disorders (WRULD) (often called repetitive strain injury) are a significant public health problem, estimated to constitute 45% of all occupational diseases [1]. Non specific arm pain (NSAP) constitutes a subgroup of WRULD [2-5] and has been defined as diffuse pain in the forearm (which can also involve the neck, arm, wrist and hand) in the absence of evidence of a specific upper limb disorder [2-6].NSAP is a vague clinical entity, the pathophysiological mechanisms of which remain unclear. While it is quite feasible that pain in NSAP is nociceptive in origin e.g. from muscle tissue, an underlying dysfunction of the nervous system has been proposed [7-9]. A mechanisms based approach to understanding pain has been advocated [10] but currently, there are no gold standards or valid or reliable methods to diagnose underlying neurophysiological pain mechanisms. It is proposed that the use of a pain mechanisms classification system would be valuable in identifying sub-groups of patients who are most likely to requ

Abstract:
Consider the space of sequences of k letters ordered lexicographically. We study the set M({\alpha}) of all maximal sequences for which the asymptotic proportions {\alpha} of the letters are prescribed, where a sequence is said to be maximal if it is at least as great as all of its tails. The infimum of M({\alpha}) is called the {\alpha}-infimax sequence, or the {\alpha}-minimax sequence if the infimum is a minimum. We give an algorithm which yields all infimax sequences, and show that the infimax is not a minimax if and only if it is the {\alpha}-infimax for every {\alpha} in a simplex of dimension 1 or greater. These results have applications to the theory of rotation sets of beta-shifts and torus homeomorphisms.