Routhian reduction for quasi-invariant Lagrangians

In this paper we describe Routhian reduction as a special case of standard symplectic reduction, also called Marsden-Weinstein reduction. We use this correspondence to present a generalization of Routhian reduction for quasi-invariant Lagrangians, i.e. Lagrangians that are invariant up to a total time derivative. We show how functional Routhian reduction can be seen as a particular instance of reduction of a quasi-invariant Lagrangian, and we exhibit a Routhian reduction procedure for the special case of Lagrangians with quasi-cyclic coordinates. As an application we consider the dynamics of a charged particle in a magnetic field.Comment: 24 pages, 3 figure

Factors associated with limited exercise capacity and feasibility of high intensity interval training in people with mild to moderate Parkinson's disease

Background/Aims: Fitness and function can improve with exercise in people with Parkinson's disease. Animal models suggest that exercise may also have a neuroprotective effect, with higher intensity exercise being more beneficial than lower intensity exercise. However, in people with Parkinson's disease the factors limiting exercise capacity are not fully understood and it is unclear whether training at very high intensities would be safe, feasible and acceptable. Methods: Eighteen people with Parkinson's disease were recruited to explore respiratory and neuromuscular factors that may limit exercise capacity. In a purposive subgroup of 6 participants able to achieve &gt;75% of their predicted maximum heart rate the feasibility of undertaking six high intensity interval training sessions over 3 weeks was tested. Their experience was further explored in a focus group. Results: Lower exercise capacity was associated with lower limb flexor muscle strength (r2=0.51) but not with disease severity or respiratory function. There were no adverse events or drop-outs in those taking part in the exercise regimen. Improvements were seen in fitness, health related quality of life, activity levels, walking speed, muscle strength and cycle endurance. Participants reported that they enjoyed high intensity, supervised exercise. High intensity interval training may be feasible and safe. Conclusions: We concluded that high intensity interval training has the potential to be a safe and acceptable mode of exercise in this patient group. </jats:sec

Weak Poisson structures on infinite dimensional manifolds and hamiltonian actions

We introduce a notion of a weak Poisson structure on a manifold $M$ modeled on a locally convex space. This is done by specifying a Poisson bracket on a subalgebra \cA \subeq C^\infty(M) which has to satisfy a non-degeneracy condition (the differentials of elements of \cA separate tangent vectors) and we postulate the existence of smooth Hamiltonian vector fields. Motivated by applications to Hamiltonian actions, we focus on affine Poisson spaces which include in particular the linear and affine Poisson structures on duals of locally convex Lie algebras. As an interesting byproduct of our approach, we can associate to an invariant symmetric bilinear form $\kappa$ on a Lie algebra \g and a $\kappa$-skew-symmetric derivation $D$ a weak affine Poisson structure on \g itself. This leads naturally to a concept of a Hamiltonian $G$-action on a weak Poisson manifold with a \g-valued momentum map and hence to a generalization of quasi-hamiltonian group actions

Is treatment for alcohol use disorder associated with reductions in criminal offending? A national data linkage cohort study in England.

BACKGROUND: This is the first English national study of change in criminal offending following treatment for alcohol use disorder (AUD). METHODS: All adults treated for AUD by all publicly funded treatment services during April 2008-March 2009 (n=53,017), with data linked to the Police National Computer (April 2006-November 2011). Pre-treatment offender sub-populations were identified by Latent Profile Analysis. The outcome measure was the count of recordable criminal offences during two-year follow-up after admission. A mixed-effects, Poisson regression modelled outcome, adjusting for demographics and clinical information, the latent classes, and treatment exposure covariates. RESULTS: Twenty-two percent of the cohort committed one or more offences in the two years pre-treatment (n=11,742; crude rate, 221.5 offenders per 1000). During follow-up, the number of offenders and offences fell by 23.5% and 24.0%, respectively (crude rate, 69.4 offenders per 1000). During follow-up, a lower number of offences was associated with: completing treatment (adjusted incident rate ratio [IRR] 0.82; 95% confidence interval [CI] 0.79-0.85); receiving inpatient detoxification (IRR 0.84; CI 0.80-0.89); or community pharmacological therapy (IRR 0.89; CI 0.84-0.96). Reconviction was reduced in the sub-population characterised by driving offences (n=1,140; 11.7%), but was relatively high amongst acquisitive (n=768; 58.3% reconvicted) and violent offending sub-populations (n=602; 77.6% reconvicted). CONCLUSIONS: Reduced offending was associated with successful completion of AUD treatment and receiving inpatient and pharmacological therapy, but not enrolment in psychological and residential interventions. Treatment services (particularly those providing psychological therapy and residential care) should be alert to offending, especially violent and acquisitive crime, and enhance crime reduction interventions

Mapping of serotype-specific, immunodominant epitopes in the NS-4 region of hepatitis C virus (HCV):use of type-specific peptides to serologically differentiate infections with HCV types 1, 2, and 3

The effect of sequence variability between different types of hepatitis C virus (HCV) on the antigenicity of the NS-4 protein was investigated by epitope mapping and by enzyme-linked immunosorbent assay with branched oligopeptides. Epitope mapping of the region between amino acid residues 1679 and 1768 in the HCV polyprotein revealed two major antigenic regions (1961 to 1708 and 1710 to 1728) that were recognized by antibody elicited upon natural infection of HCV. The antigenic regions were highly variable between variants of HCV, with only 50 to 60% amino acid sequence similarity between types 1, 2, and 3. Although limited serological cross-reactivity between HCV types was detected between peptides, particularly in the first antigenic region of NS-4, type-specific reactivity formed the principal component of the natural humoral immune response to NS-4. Type-specific antibody to particular HCV types was detected in 89% of the samples from anti-HCV-positive blood donors and correlated almost exactly with genotypic analysis of HCV sequences amplified from the samples by polymerase chain reaction. Whereas almost all blood donors appeared to be infected with a single virus type (97%), a higher proportion of samples (40%) from hemophiliacs infected from transfusion of non-heat-inactivated clotting factor contained antibody to two or even all three HCV types, providing evidence that long-term exposure may lead to multiple infection with different variants of HCV

Integrable discretizations of some cases of the rigid body dynamics

A heavy top with a fixed point and a rigid body in an ideal fluid are important examples of Hamiltonian systems on a dual to the semidirect product Lie algebra $e(n)=so(n)\ltimes\mathbb R^n$. We give a Lagrangian derivation of the corresponding equations of motion, and introduce discrete time analogs of two integrable cases of these systems: the Lagrange top and the Clebsch case, respectively. The construction of discretizations is based on the discrete time Lagrangian mechanics on Lie groups, accompanied by the discrete time Lagrangian reduction. The resulting explicit maps on $e^*(n)$ are Poisson with respect to the Lie--Poisson bracket, and are also completely integrable. Lax representations of these maps are also found.Comment: arXiv version is already officia

Explicit Lie-Poisson integration and the Euler equations

We give a wide class of Lie-Poisson systems for which explicit, Lie-Poisson integrators, preserving all Casimirs, can be constructed. The integrators are extremely simple. Examples are the rigid body, a moment truncation, and a new, fast algorithm for the sine-bracket truncation of the 2D Euler equations.Comment: 7 pages, compile with AMSTEX; 2 figures available from autho

Lagrangian particle paths and ortho-normal quaternion frames

Experimentalists now measure intense rotations of Lagrangian particles in turbulent flows by tracking their trajectories and Lagrangian-average velocity gradients at high Reynolds numbers. This paper formulates the dynamics of an orthonormal frame attached to each Lagrangian fluid particle undergoing three-axis rotations, by using quaternions in combination with Ertel's theorem for frozen-in vorticity. The method is applicable to a wide range of Lagrangian flows including the three-dimensional Euler equations and its variants such as ideal MHD. The applicability of the quaterionic frame description to Lagrangian averaged velocity gradient dynamics is also demonstrated.Comment: 9 pages, one figure, revise