Muscular and non-muscular contributions to maximum power cycling in children and adults: implications for developmental motor control

This article is available open access through the publisher’s website at the link below.During submaximal cycling, children demonstrate a different distribution between muscular and non-muscular (gravitational and motion-dependent) forces when compared with adults. This is partly due to anthropometric differences. In this study, we tested the hypothesis that during maximum power cycling, children would construct the task (in terms of the distribution between muscular and non-muscular pedal power) similarly to adults. Eleven children (aged 8–9 years) and 13 adults (aged 20–40 years) performed a maximal isokinetic cycling task over 3 s at 115 r.p.m. Multivariate analyses of variance revealed no significant differences in normalized maximum, minimum and average positive non-muscular pedal power between children and adults (Wilks' λ=0.755, F3,20=2.17, P=0.124). Thus, maximum cycling is a developmental `self-scaling' task and age-related differences in muscular power production are not confounded by differences in anthropometry. This information is useful to researchers who wish to differentiate between muscular and non-muscular power when studying developmental motor control. In addition to the similarities in the distribution between muscular and non-muscular pedal power, we found age-related differences in the relative joint power contributions to total pedal power. In children, a significantly smaller proportion of total pedal power was generated at the ankle joint (6.1±5.4% for children and 12.6±3.2% for adults), whilst relatively more power was generated at the knee and hip joints. These results suggest that intermuscular coordination may be contributing to children's limits in maximum power production during multi-joint tasks

The twisted XXZ chain at roots of unity revisited

The symmetries of the twisted XXZ spin-chain (alias the twisted six-vertex model) at roots of unity are investigated. It is shown that when the twist parameter is chosen to depend on the total spin an infinite-dimensional non-abelian symmetry algebra can be explicitly constructed for all spin sectors. This symmetry algebra is identified to be the upper or lower Borel subalgebra of the sl_2 loop algebra. The proof uses only the intertwining property of the six-vertex monodromy matrix and the familiar relations of the six-vertex Yang-Baxter algebra.Comment: 10 pages, 2 figures. One footnote and some comments in the conclusions adde

Auxiliary matrices on both sides of the equator

The spectra of previously constructed auxiliary matrices for the six-vertex model at roots of unity are investigated for spin-chains of even and odd length. The two cases show remarkable differences. In particular, it is shown that for even roots of unity and an odd number of sites the eigenvalues contain two linear independent solutions to Baxter's TQ-equation corresponding to the Bethe ansatz equations above and below the equator. In contrast, one finds for even spin-chains only one linear independent solution and complete strings. The other main result is the proof of a previous conjecture on the degeneracies of the six-vertex model at roots of unity. The proof rests on the derivation of a functional equation for the auxiliary matrices which is closely related to a functional equation for the eight-vertex model conjectured by Fabricius and McCoy.Comment: 22 pages; 2nd version: one paragraph added in the conclusion and some typos correcte

Children's Databases - Safety and Privacy

This report describes in detail the policy background, the systems that are being built, the problems with them, and the legal situation in the UK. An appendix looks at Europe, and examines in particular detail how France and Germany have dealt with these issues. Our report concludes with three suggested regulatory action strategies for the Commissioner: one minimal strategy in which he tackles only the clear breaches of the law, one moderate strategy in which he seeks to educate departments and agencies and guide them towards best practice, and finally a vigorous option in which he would seek to bring UK data protection practice in these areas more in line with normal practice in Europe, and indeed with our obligations under European law

XXZ Bethe states as highest weight vectors of the sl2sl_2 loop algebra at roots of unity

We show that every regular Bethe ansatz eigenvector of the XXZ spin chain at roots of unity is a highest weight vector of the $sl_2$ loop algebra, for some restricted sectors with respect to eigenvalues of the total spin operator $S^Z$, and evaluate explicitly the highest weight in terms of the Bethe roots. We also discuss whether a given regular Bethe state in the sectors generates an irreducible representation or not. In fact, we present such a regular Bethe state in the inhomogeneous case that generates a reducible Weyl module. Here, we call a solution of the Bethe ansatz equations which is given by a set of distinct and finite rapidities {\it regular Bethe roots}. We call a nonzero Bethe ansatz eigenvector with regular Bethe roots a {\it regular Bethe state}.Comment: 40pages; revised versio

A Q-operator for the twisted XXX model

Taking the isotropic limit in a recent representation theoretic construction of Baxter's Q-operators for the XXZ model with quasi-periodic boundary conditions we obtain new results for the XXX model. We show that quasi-periodic boundary conditions are needed to ensure convergence of the Q-operator construction and derive a quantum Wronskian relation which implies two different sets of Bethe ansatz equations, one above the other below the "equator" of total spin zero. We discuss the limit to periodic boundary conditions at the end and explain how this construction might be useful in the context of correlation functions on the infinite lattice. We also identify a special subclass of solutions to the quantum Wronskian for chains up to a length of 10 sites and possibly higher.Comment: 19 page

Mechanical and material properties of the plantarflexor muscles and Achilles tendon in children with spastic cerebral palsy and typically developing children

© 2016 The Authors. Background: Children with spastic cerebral palsy (CP) experience secondary musculoskeletal adaptations, affecting the mechanical and material properties of muscles and tendons. CP-related changes in the spastic muscle are well documented whilst less is known about the tendon. From a clinical perspective, it is important to understand alterations in tendon properties in order to tailor interventions or interpret clinical tests more appropriately. The main purpose of this study was to compare the mechanical and material properties of the Achilles tendon in children with cerebral palsy to those of typically developing children. Methods: Using a combination of ultrasonography and motion analysis, we determined tendon mechanical properties in ten children with spastic cerebral palsy and ten aged-matched typically developing children. Specifically, we quantified muscle and tendon stiffness, tendon slack length, tendon strain, cross-sectional area, Young׳s Modulus and the strain rate dependence of tendon stiffness. Findings: Children with CP had a greater muscle to tendon stiffness ratio compared to typically developing children. Despite a smaller tendon cross-sectional area and greater tendon slack length, no group differences were observed in tendon stiffness or Young׳s Modulus. The slope describing the stiffness strain-rate response was steeper in children with cerebral palsy. Interpretation: These results provide us with a more differentiated understanding of the muscle and tendon mechanical properties, which would be relevant for future research and paediatric clinicians

Quantum cohomology via vicious and osculating walkers

We relate the counting of rational curves intersecting Schubert varieties of the Grassmannian to the counting of certain non-intersecting lattice paths on the cylinder, so-called vicious and osculating walkers. These lattice paths form exactly solvable statistical mechanics models and are obtained from solutions to the Yang–Baxter equation. The eigenvectors of the transfer matrices of these models yield the idempotents of the Verlinde algebra of the gauged u^(n)k -WZNW model. The latter is known to be closely related to the small quantum cohomology ring of the Grassmannian. We establish further that the partition functions of the vicious and osculating walker model are given in terms of Postnikov’s toric Schur functions and can be interpreted as generating functions for Gromov–Witten invariants. We reveal an underlying quantum group structure in terms of Yang–Baxter algebras and use it to give a generating formula for toric Schur functions in terms of divided difference operators which appear in known representations of the nil-Hecke algebra

Auxiliary matrices for the six-vertex model and the algebraic Bethe ansatz

We connect two alternative concepts of solving integrable models, Baxter's method of auxiliary matrices (or Q-operators) and the algebraic Bethe ansatz. The main steps of the calculation are performed in a general setting and a formula for the Bethe eigenvalues of the Q-operator is derived. A proof is given for states which contain up to three Bethe roots. Further evidence is provided by relating the findings to the six-vertex fusion hierarchy. For the XXZ spin-chain we analyze the cases when the deformation parameter of the underlying quantum group is evaluated both at and away from a root of unity.Comment: 32 page