Does forced or compensated turnout lead to musculoskeletal injuries in dancers? A systematic review on the complexity of causes

Injury prevalence in dancers is high, and misaligned turnout (TO) is claimed to bear injury risk. This systematic review aimed to investigate if compensating or forcing TO leads to musculoskeletal injuries.A systematic literature review was conducted according to the PRISMA Guidelines using the databases of PubMed, Embase, Emcare, Web of Science, Cochrane Library, Academic Search Premier, and ScienceDirect. Studies investigating the relationship between compensated or forced TO and injuries in all genders, all ages, and levels of dancers were included. Details on misaligned TO measurements and injuries had to be provided. Screening was performed by two researchers, data extraction and methodological quality assessment executed by one researcher and checked by another.7 studies with 1293 dancers were included. Methodological quality was low due to study designs and a general lack of standardised definition of pathology and methods of assessment of misaligned TO. The studies investigating the lower extremities showed a hip-focus only. Non-hip contributors as well as their natural anatomical variations were not accounted for, limiting the understanding of injury mechanisms underlying misaligned TO. As such no definite conclusions on the effect of compensating or forcing TO on musculoskeletal injuries could be made.Total TO is dependent on complex motion cycles rather than generalised (hip) joint dominance only. Objective dual assessment of maximum passive joint range of motion through 3D kinematic analysis in combination with physical examination is needed to account for anatomical variations, locate sites prone to (overuse)injury, and investigate underlying injury mechanisms. (C) 2020 Elsevier Ltd. All rights reserved.Clinical epidemiolog

Cantor and band spectra for periodic quantum graphs with magnetic fields

We provide an exhaustive spectral analysis of the two-dimensional periodic square graph lattice with a magnetic field. We show that the spectrum consists of the Dirichlet eigenvalues of the edges and of the preimage of the spectrum of a certain discrete operator under the discriminant (Lyapunov function) of a suitable Kronig-Penney Hamiltonian. In particular, between any two Dirichlet eigenvalues the spectrum is a Cantor set for an irrational flux, and is absolutely continuous and has a band structure for a rational flux. The Dirichlet eigenvalues can be isolated or embedded, subject to the choice of parameters. Conditions for both possibilities are given. We show that generically there are infinitely many gaps in the spectrum, and the Bethe-Sommerfeld conjecture fails in this case.Comment: Misprints correcte

Stability and symmetry-breaking bifurcation for the ground states of a NLS with a δ′\delta^\prime interaction

We determine and study the ground states of a focusing Schr\"odinger equation in dimension one with a power nonlinearity $|\psi|^{2\mu} \psi$ and a strong inhomogeneity represented by a singular point perturbation, the so-called (attractive) $\delta^\prime$ interaction, located at the origin. The time-dependent problem turns out to be globally well posed in the subcritical regime, and locally well posed in the supercritical and critical regime in the appropriate energy space. The set of the (nonlinear) ground states is completely determined. For any value of the nonlinearity power, it exhibits a symmetry breaking bifurcation structure as a function of the frequency (i.e., the nonlinear eigenvalue) $\omega$. More precisely, there exists a critical value \om^* of the nonlinear eigenvalue \om, such that: if \om_0 < \om < \om^*, then there is a single ground state and it is an odd function; if \om > \om^* then there exist two non-symmetric ground states. We prove that before bifurcation (i.e., for \om < \om^*) and for any subcritical power, every ground state is orbitally stable. After bifurcation (\om =\om^*+0), ground states are stable if $\mu$ does not exceed a value $\mu^\star$ that lies between 2 and 2.5, and become unstable for $\mu > \mu^*$. Finally, for $\mu > 2$ and \om \gg \om^*, all ground states are unstable. The branch of odd ground states for \om \om^*, obtaining a family of orbitally unstable stationary states. Existence of ground states is proved by variational techniques, and the stability properties of stationary states are investigated by means of the Grillakis-Shatah-Strauss framework, where some non standard techniques have to be used to establish the needed properties of linearization operators.Comment: 46 pages, 5 figure